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To satisfy the unique needs of each node, we propose a new", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 246, + 470, + 258 + ], + "spans": [ + { + "bbox": [ + 141, + 246, + 470, + 258 + ], + "score": 1.0, + "content": "architecture – Graph Attention Multi-Layer Perceptron (GAMLP). This architecture", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 257, + 470, + 269 + ], + "spans": [ + { + "bbox": [ + 141, + 257, + 470, + 269 + ], + "score": 1.0, + "content": "combines multi-scale knowledge and learns to capture the underlying correlations", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 267, + 470, + 280 + ], + "spans": [ + { + "bbox": [ + 141, + 267, + 470, + 280 + ], + "score": 1.0, + "content": "between different scales of knowledge with two novel attention mechanisms:", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 279, + 470, + 292 + ], + "spans": [ + { + "bbox": [ + 141, + 279, + 470, + 292 + ], + "score": 1.0, + "content": "Recursive attention and Jumping Knowledge (JK) attention. Instead of using", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 290, + 469, + 302 + ], + "spans": [ + { + "bbox": [ + 141, + 290, + 469, + 302 + ], + "score": 1.0, + "content": "node feature only, the knowledge within node labels is also exploited to reinforce", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 301, + 469, + 313 + ], + "spans": [ + { + "bbox": [ + 141, + 301, + 469, + 313 + ], + "score": 1.0, + "content": "the performance of GAMLP. Extensive experiments on 12 real-world datasets", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 311, + 469, + 325 + ], + "spans": [ + { + "bbox": [ + 141, + 311, + 469, + 325 + ], + "score": 1.0, + "content": "demonstrate that GAMLP achieves state-of-the-art performance while enjoying", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 322, + 266, + 336 + ], + "spans": [ + { + "bbox": [ + 141, + 322, + 266, + 336 + ], + "score": 1.0, + "content": "high scalability and efficiency.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 10, + "bbox_fs": [ + 141, + 191, + 470, + 336 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 354, + 206, + 367 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 208, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 208, + 370 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 380, + 505, + 500 + ], + "lines": [ + { + "bbox": [ + 106, + 380, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 505, + 392 + ], + "score": 1.0, + "content": "Graph Neural Networks (GNNs) generalize convolutional neural networks to graph-structured data", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "and have achieved great success in a wide range of tasks, including node classification, link prediction,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 402, + 506, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 506, + 413 + ], + "score": 1.0, + "content": "and recommendation. (Kipf & Welling, 2016; Hamilton et al., 2017; Bo et al., 2020; Cui et al., 2020;", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 411, + 506, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 247, + 426 + ], + "score": 1.0, + "content": "Fan et al., 2019). 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The X-axis is the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "score": 1.0, + "content": "node id, and Y-axis is the propagation steps (layers). The color from white to blue represents the ratio", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "score": 1.0, + "content": "of being predicted correctly in 50 different runs. 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This imperfection", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 288, + 506, + 301 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 506, + 301 + ], + "score": 1.0, + "content": "either makes that long-range dependencies cannot be fully leveraged due to limited hops/layers or", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 299, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 505, + 311 + ], + "score": 1.0, + "content": "loses local information by introducing many irrelevant nodes into the receptive fields for many nodes", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 310, + 506, + 323 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 506, + 323 + ], + "score": 1.0, + "content": "when increasing the number of propagation depth (Chen et al., 2020a; Li et al., 2018; Xu et al., 2018).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 220, + 506, + 323 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 458 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 506, + 339 + ], + "score": 1.0, + "content": "The above observations motivate us to explicitly learn the importance and correlation of multi-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 338, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 505, + 350 + ], + "score": 1.0, + "content": "scale knowledge in a node-adaptive manner. 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These", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 382, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 506, + 394 + ], + "score": 1.0, + "content": "two attention mechanisms can capture the complex correlations between propagated features at", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "different propagation depths in a node-adaptive manner. Consequently, our architecture has the same", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 402, + 506, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 506, + 417 + ], + "score": 1.0, + "content": "benefits as the existing simplified and scalable GNN models while providing much better performance", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 415, + 505, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 505, + 427 + ], + "score": 1.0, + "content": "derived from its ability to utilizes a node-adaptive receptive field. 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Orthogonal to model simplification, sampling", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 202, + 506, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 506, + 214 + ], + "score": 1.0, + "content": "has already been widely used in many GNNs and GNN systems (Zheng et al., 2020; Zhu et al., 2019;", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 212, + 506, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 506, + 226 + ], + "score": 1.0, + "content": "Fey & Lenssen, 2019). 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Recently studies have observed that non-linear feature transformation", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 251, + 504, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 504, + 263 + ], + "score": 1.0, + "content": "contributes little to the performance of the GNNs as compared to feature propagation. 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By setting", + "type": "text" + }, + { + "bbox": [ + 487, + 322, + 506, + 332 + ], + "score": 0.81, + "content": "r =", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 330, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 104, + 330, + 158, + 348 + ], + "score": 1.0, + "content": "0.5, 1 and 0,", + "type": "text" + }, + { + "bbox": [ + 158, + 332, + 168, + 344 + ], + "score": 0.73, + "content": "\\hat { \\bf A }", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 330, + 399, + 348 + ], + "score": 1.0, + "content": "represents the symmetric normalization adjacency matrix", + "type": "text" + }, + { + "bbox": [ + 399, + 331, + 464, + 344 + ], + "score": 0.9, + "content": "\\widetilde { \\mathbf { D } } ^ { - 1 / 2 } \\widetilde { \\mathbf { A } } \\widetilde { \\mathbf { D } } ^ { - \\mathrm { i } / 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 330, + 506, + 348 + ], + "score": 1.0, + "content": "(Klicpera", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 344, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 294, + 360 + ], + "score": 1.0, + "content": "et al., 2019), the transition probability matrix", + "type": "text" + }, + { + "bbox": [ + 294, + 344, + 323, + 358 + ], + "score": 0.87, + "content": "\\widetilde { \\mathbf { A } } \\widetilde { \\mathbf { D } } ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 345, + 505, + 360 + ], + "score": 1.0, + "content": "(Zeng et al., 2020), or the reverse transition", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 357, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 104, + 358, + 182, + 373 + ], + "score": 1.0, + "content": "probability matrix", + "type": "text" + }, + { + "bbox": [ + 183, + 357, + 212, + 370 + ], + "score": 0.9, + "content": "\\widetilde { \\bf D } ^ { - 1 } \\widetilde { \\bf A }", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 358, + 217, + 373 + ], + "score": 1.0, + "content": "(", + "type": "text" + }, + { + "bbox": [ + 217, + 360, + 231, + 370 + ], + "score": 0.48, + "content": "\\mathrm { X u }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 358, + 451, + 373 + ], + "score": 1.0, + "content": "et al., 2018), respectively. As the propagated features", + "type": "text" + }, + { + "bbox": [ + 451, + 358, + 474, + 370 + ], + "score": 0.88, + "content": "\\mathbf { X } ^ { ( K ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 358, + 506, + 373 + ], + "score": 1.0, + "content": "can be", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 370, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 505, + 383 + ], + "score": 1.0, + "content": "precomputed, SGC is more scalable and efficient for the large graph. However, such graph-wise", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 381, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 104, + 381, + 505, + 394 + ], + "score": 1.0, + "content": "propagation restricts the same propagation steps and a fixed RF for each node. Therefore, some", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "score": 1.0, + "content": "nodes’ features may be over-smoothed or under-smoothed due to the inconsistent RF expansion", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 403, + 282, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 282, + 416 + ], + "score": 1.0, + "content": "speed, leading to non-optimal performance.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 106, + 420, + 506, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 420, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 506, + 433 + ], + "score": 1.0, + "content": "Layer-wise Propagation. Following SGC, some recent methods adopt layer-wise propagation to", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 431, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 506, + 444 + ], + "score": 1.0, + "content": "combine the features with different propagation layers. SIGN (Frasca et al., 2020) proposes to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 443, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 506, + 454 + ], + "score": 1.0, + "content": "concatenate the propagated features at different propagation depth after simple linear transformation:", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 452, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 453, + 248, + 466 + ], + "score": 0.91, + "content": "[ \\mathbf { X } ^ { ( 0 ) } \\mathbf { W } _ { 0 } , \\mathbf { X } ^ { ( 1 ) } \\mathbf { W } _ { 1 } , . . . , \\mathbf { X } ^ { ( K ) } \\mathbf { W } _ { K } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 452, + 255, + 468 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 255, + 453, + 282, + 465 + ], + "score": 0.83, + "content": "\\mathrm { { S ^ { 2 } G C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 452, + 506, + 468 + ], + "score": 1.0, + "content": "(Zhu & Koniusz, 2021) proposes the simple spectral", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 465, + 507, + 493 + ], + "spans": [ + { + "bbox": [ + 104, + 471, + 420, + 486 + ], + "score": 1.0, + "content": "graph convolution to average the propagated features in different iterations as", + "type": "text" + }, + { + "bbox": [ + 421, + 465, + 503, + 493 + ], + "score": 0.93, + "content": "\\mathbf { X } ^ { ( K ) } = \\sum _ { l = 0 } ^ { K } \\hat { \\mathbf { A } } ^ { l } \\mathbf { X } ^ { ( 0 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 504, + 471, + 507, + 486 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 489, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 104, + 489, + 506, + 505 + ], + "score": 1.0, + "content": "In addition, GBP (Chen et al., 2020b) further improves the combination process by weighted averaging", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 118, + 502, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 118, + 502, + 209, + 528 + ], + "score": 0.94, + "content": "\\mathbf { X } ^ { ( K ) } = \\sum _ { l = 0 } ^ { K } w _ { l } \\hat { \\mathbf { A } } ^ { l } \\mathbf { X } ^ { ( 0 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 507, + 296, + 522 + ], + "score": 1.0, + "content": "with the layer weight", + "type": "text" + }, + { + "bbox": [ + 296, + 507, + 361, + 521 + ], + "score": 0.94, + "content": "w _ { l } = \\beta { \\left( 1 - \\beta \\right) } ^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 507, + 506, + 522 + ], + "score": 1.0, + "content": ". 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However, there also exist some graph learning methods that directly exploit", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 615, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 628 + ], + "score": 1.0, + "content": "the labels of training nodes. Among them, the label propagation algorithm (Zhu & Ghahramani,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 625, + 504, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 625, + 454, + 640 + ], + "score": 1.0, + "content": "2002) is the most well-known one. It simply regards the partially observed label matrix", + "type": "text" + }, + { + "bbox": [ + 454, + 626, + 504, + 637 + ], + "score": 0.91, + "content": "\\mathbf { Y } \\in \\mathbb { R } ^ { N \\times C }", + "type": "inline_equation" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "as input features for nodes in the graph and propagates the input features through the graph structure,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 648, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 133, + 662 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 649, + 142, + 659 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 142, + 648, + 505, + 662 + ], + "score": 1.0, + "content": "is the number of candidate classes. 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Then,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 721, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 506, + 733 + ], + "score": 1.0, + "content": "it propagates the learning errors on the labeled nodes to connected nodes and smooths the output in a", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 208, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 210, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 210, + 96 + ], + "score": 1.0, + "content": "2.2 SCALABLE GNNS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 102, + 506, + 235 + ], + "lines": [ + { + "bbox": [ + 106, + 102, + 506, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 102, + 506, + 116 + ], + "score": 1.0, + "content": "Sampling. A commonly used method to tackle the scalability issue (i.e., the recursive neighborhood", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 114, + 507, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 507, + 128 + ], + "score": 1.0, + "content": "expansion) in GNN is sampling. As a node-wise sampling method, GraphSAGE (Hamilton et al.,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 125, + 506, + 137 + ], + "spans": [ + { + "bbox": [ + 106, + 125, + 506, + 137 + ], + "score": 1.0, + "content": "2017) randomly samples a fixed-size set of neighbors for computation in each mini-batch. VR-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 505, + 147 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 505, + 147 + ], + "score": 1.0, + "content": "GCN (Chen et al., 2018a) analyzes the variance reduction, and it reduces the size of samples with", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 146, + 506, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 146, + 506, + 160 + ], + "score": 1.0, + "content": "additional memory cost. For the layer-wise sampling, Fast-GCN (Chen et al., 2018b) samples a fixed", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 158, + 506, + 170 + ], + "spans": [ + { + "bbox": [ + 106, + 158, + 506, + 170 + ], + "score": 1.0, + "content": "number of nodes at each layer, and ASGCN (Huang et al., 2018) proposes the adaptive layer-wise", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 169, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 169, + 505, + 182 + ], + "score": 1.0, + "content": "sampling with better variance control. In the graph level, Cluster-GCN (Chiang et al., 2019) firstly", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 180, + 506, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 506, + 192 + ], + "score": 1.0, + "content": "clusters the nodes and then samples the nodes in the clusters, and GraphSAINT (Zeng et al., 2020)", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 189, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 104, + 189, + 506, + 205 + ], + "score": 1.0, + "content": "directly samples a subgraph for mini-batch training. Orthogonal to model simplification, sampling", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 202, + 506, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 506, + 214 + ], + "score": 1.0, + "content": "has already been widely used in many GNNs and GNN systems (Zheng et al., 2020; Zhu et al., 2019;", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 212, + 506, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 506, + 226 + ], + "score": 1.0, + "content": "Fey & Lenssen, 2019). However, these sampling-based GNNs are imperfect because they still face", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 224, + 485, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 485, + 236 + ], + "score": 1.0, + "content": "high communication costs, and the sampling quality highly influences the model performance.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 6.5, + "bbox_fs": [ + 104, + 102, + 507, + 236 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 240, + 505, + 296 + ], + "lines": [ + { + "bbox": [ + 106, + 241, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 505, + 253 + ], + "score": 1.0, + "content": "Graph-wise Propagation. Recently studies have observed that non-linear feature transformation", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 251, + 504, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 504, + 263 + ], + "score": 1.0, + "content": "contributes little to the performance of the GNNs as compared to feature propagation. Thus, a new", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 262, + 506, + 275 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 275 + ], + "score": 1.0, + "content": "direction recently emerging for scalable GNN is based on the simplified GCN (SGC) (Wu et al., 2019),", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 272, + 507, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 507, + 286 + ], + "score": 1.0, + "content": "which successively removes nonlinearities and collapsing weight matrices between consecutive layers.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 283, + 440, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 317, + 298 + ], + "score": 1.0, + "content": "This reduces GNNs into a linear model operating on", + "type": "text" + }, + { + "bbox": [ + 317, + 285, + 327, + 294 + ], + "score": 0.84, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 283, + 440, + 298 + ], + "score": 1.0, + "content": "-layers propagated features:", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 241, + 507, + 298 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 216, + 300, + 394, + 314 + ], + "lines": [ + { + "bbox": [ + 216, + 300, + 394, + 314 + ], + "spans": [ + { + "bbox": [ + 216, + 300, + 394, + 314 + ], + "score": 0.91, + "content": "\\mathbf { X } ^ { ( K ) } = \\hat { \\mathbf { A } } ^ { K } \\mathbf { X } ^ { ( 0 ) } , \\qquad \\mathbf { Y } = \\mathrm { s o f t m a x } ( \\Theta \\mathbf { X } ^ { ( K ) } ) ,", + "type": "interline_equation", + "image_path": "8923c86ac69becda0df81d0d105ddb8509003c69adbbb15ef20a2dd42f6120e4.jpg" + } + ] + } + ], + "index": 18, + "virtual_lines": [ + { + "bbox": [ + 216, + 300, + 394, + 314 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 318, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 317, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 136, + 335 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 136, + 320, + 178, + 331 + ], + "score": 0.86, + "content": "\\mathbf { X } ^ { ( 0 ) } = \\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 317, + 181, + 335 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 182, + 319, + 205, + 331 + ], + "score": 0.76, + "content": "\\mathbf { X } ^ { ( K ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 317, + 231, + 335 + ], + "score": 1.0, + "content": "is the", + "type": "text" + }, + { + "bbox": [ + 231, + 321, + 241, + 331 + ], + "score": 0.84, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 317, + 365, + 335 + ], + "score": 1.0, + "content": "-layers propagated feature, and", + "type": "text" + }, + { + "bbox": [ + 366, + 318, + 439, + 331 + ], + "score": 0.91, + "content": "\\hat { \\mathbf { A } } = \\widetilde { \\mathbf { D } } ^ { r - 1 } \\widetilde { \\mathbf { A } } \\widetilde { \\mathbf { D } } ^ { - r }", + "type": "inline_equation" + }, + { + "bbox": [ + 440, + 317, + 487, + 335 + ], + "score": 1.0, + "content": ". By setting", + "type": "text" + }, + { + "bbox": [ + 487, + 322, + 506, + 332 + ], + "score": 0.81, + "content": "r =", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 330, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 104, + 330, + 158, + 348 + ], + "score": 1.0, + "content": "0.5, 1 and 0,", + "type": "text" + }, + { + "bbox": [ + 158, + 332, + 168, + 344 + ], + "score": 0.73, + "content": "\\hat { \\bf A }", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 330, + 399, + 348 + ], + "score": 1.0, + "content": "represents the symmetric normalization adjacency matrix", + "type": "text" + }, + { + "bbox": [ + 399, + 331, + 464, + 344 + ], + "score": 0.9, + "content": "\\widetilde { \\mathbf { D } } ^ { - 1 / 2 } \\widetilde { \\mathbf { A } } \\widetilde { \\mathbf { D } } ^ { - \\mathrm { i } / 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 330, + 506, + 348 + ], + "score": 1.0, + "content": "(Klicpera", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 344, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 294, + 360 + ], + "score": 1.0, + "content": "et al., 2019), the transition probability matrix", + "type": "text" + }, + { + "bbox": [ + 294, + 344, + 323, + 358 + ], + "score": 0.87, + "content": "\\widetilde { \\mathbf { A } } \\widetilde { \\mathbf { D } } ^ { - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 345, + 505, + 360 + ], + "score": 1.0, + "content": "(Zeng et al., 2020), or the reverse transition", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 357, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 104, + 358, + 182, + 373 + ], + "score": 1.0, + "content": "probability matrix", + "type": "text" + }, + { + "bbox": [ + 183, + 357, + 212, + 370 + ], + "score": 0.9, + "content": "\\widetilde { \\bf D } ^ { - 1 } \\widetilde { \\bf A }", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 358, + 217, + 373 + ], + "score": 1.0, + "content": "(", + "type": "text" + }, + { + "bbox": [ + 217, + 360, + 231, + 370 + ], + "score": 0.48, + "content": "\\mathrm { X u }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 358, + 451, + 373 + ], + "score": 1.0, + "content": "et al., 2018), respectively. As the propagated features", + "type": "text" + }, + { + "bbox": [ + 451, + 358, + 474, + 370 + ], + "score": 0.88, + "content": "\\mathbf { X } ^ { ( K ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 358, + 506, + 373 + ], + "score": 1.0, + "content": "can be", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 370, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 505, + 383 + ], + "score": 1.0, + "content": "precomputed, SGC is more scalable and efficient for the large graph. However, such graph-wise", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 381, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 104, + 381, + 505, + 394 + ], + "score": 1.0, + "content": "propagation restricts the same propagation steps and a fixed RF for each node. 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Following SGC, some recent methods adopt layer-wise propagation to", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 431, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 506, + 444 + ], + "score": 1.0, + "content": "combine the features with different propagation layers. SIGN (Frasca et al., 2020) proposes to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 443, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 506, + 454 + ], + "score": 1.0, + "content": "concatenate the propagated features at different propagation depth after simple linear transformation:", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 452, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 107, + 453, + 248, + 466 + ], + "score": 0.91, + "content": "[ \\mathbf { X } ^ { ( 0 ) } \\mathbf { W } _ { 0 } , \\mathbf { X } ^ { ( 1 ) } \\mathbf { W } _ { 1 } , . . . , \\mathbf { X } ^ { ( K ) } \\mathbf { W } _ { K } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 452, + 255, + 468 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 255, + 453, + 282, + 465 + ], + "score": 0.83, + "content": "\\mathrm { { S ^ { 2 } G C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 452, + 506, + 468 + ], + "score": 1.0, + "content": "(Zhu & Koniusz, 2021) proposes the simple spectral", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 465, + 507, + 493 + ], + "spans": [ + { + "bbox": [ + 104, + 471, + 420, + 486 + ], + "score": 1.0, + "content": "graph convolution to average the propagated features in different iterations as", + "type": "text" + }, + { + "bbox": [ + 421, + 465, + 503, + 493 + ], + "score": 0.93, + "content": "\\mathbf { X } ^ { ( K ) } = \\sum _ { l = 0 } ^ { K } \\hat { \\mathbf { A } } ^ { l } \\mathbf { X } ^ { ( 0 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 504, + 471, + 507, + 486 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 489, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 104, + 489, + 506, + 505 + ], + "score": 1.0, + "content": "In addition, GBP (Chen et al., 2020b) further improves the combination process by weighted averaging", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 118, + 502, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 118, + 502, + 209, + 528 + ], + "score": 0.94, + "content": "\\mathbf { X } ^ { ( K ) } = \\sum _ { l = 0 } ^ { K } w _ { l } \\hat { \\mathbf { A } } ^ { l } \\mathbf { X } ^ { ( 0 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 507, + 296, + 522 + ], + "score": 1.0, + "content": "with the layer weight", + "type": "text" + }, + { + "bbox": [ + 296, + 507, + 361, + 521 + ], + "score": 0.94, + "content": "w _ { l } = \\beta { \\left( 1 - \\beta \\right) } ^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 507, + 506, + 522 + ], + "score": 1.0, + "content": ". 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However, there also exist some graph learning methods that directly exploit", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 615, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 628 + ], + "score": 1.0, + "content": "the labels of training nodes. Among them, the label propagation algorithm (Zhu & Ghahramani,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 625, + 504, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 625, + 454, + 640 + ], + "score": 1.0, + "content": "2002) is the most well-known one. It simply regards the partially observed label matrix", + "type": "text" + }, + { + "bbox": [ + 454, + 626, + 504, + 637 + ], + "score": 0.91, + "content": "\\mathbf { Y } \\in \\mathbb { R } ^ { N \\times C }", + "type": "inline_equation" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "as input features for nodes in the graph and propagates the input features through the graph structure,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 648, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 133, + 662 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 649, + 142, + 659 + ], + "score": 0.82, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 142, + 648, + 505, + 662 + ], + "score": 1.0, + "content": "is the number of candidate classes. UniMP (Shi et al., 2020) proposes to map the partially", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 195, + 672 + ], + "score": 1.0, + "content": "observed label matrix", + "type": "text" + }, + { + "bbox": [ + 196, + 660, + 206, + 670 + ], + "score": 0.36, + "content": "\\mathbf { Y }", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 660, + 383, + 672 + ], + "score": 1.0, + "content": "to the dimension of the node feature matrix", + "type": "text" + }, + { + "bbox": [ + 383, + 660, + 393, + 670 + ], + "score": 0.35, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "and add these two matrices", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "together as the new input feature. 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Note that both the feature", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 180, + 284, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 284, + 194 + ], + "score": 1.0, + "content": "and label propagation can be pre-processed.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 106, + 199, + 506, + 267 + ], + "lines": [ + { + "bbox": [ + 106, + 200, + 506, + 212 + ], + "spans": [ + { + "bbox": [ + 106, + 200, + 506, + 212 + ], + "score": 1.0, + "content": "Personalized PageRank manner like APPNP (Klicpera et al., 2019). Besides, SLE (Sun & Wu, 2021)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 211, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 211, + 505, + 223 + ], + "score": 1.0, + "content": "decouples the label utilization procedure in UniMP, and executes the propagation in advance. 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For example,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "some graphs have good features but low-quality labels (e.g., label noise or low label rate), and we", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 720, + 385, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 172, + 733 + ], + "score": 1.0, + "content": "should decrease", + "type": "text" + }, + { + "bbox": [ + 172, + 721, + 180, + 732 + ], + "score": 0.84, + "content": "\\beta", + "type": "inline_equation" + }, + { + "bbox": [ + 180, + 720, + 385, + 733 + ], + "score": 1.0, + "content": "so that more attention is paid to the graph features.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 44, + "bbox_fs": [ + 105, + 699, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 503, + 105 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 505, + 96 + ], + "score": 1.0, + "content": "We adopt the Cross-Entropy (CE) measurement between the predicted softmax outputs and the", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 369, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 369, + 106 + ], + "score": 1.0, + "content": "one-hot ground-truth label distributions as the objective function:", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "interline_equation", + "bbox": [ + 219, + 108, + 381, + 134 + ], + "lines": [ + { + "bbox": [ + 219, + 108, + 381, + 134 + ], + "spans": [ + { + "bbox": [ + 219, + 108, + 381, + 134 + ], + "score": 0.94, + "content": "\\mathcal { L } _ { C E } = - \\sum _ { i \\in \\mathcal { V } _ { l } } \\sum _ { j } \\mathbf { Y } _ { i j } \\log ( \\mathrm { s o f t m a x } ( \\widetilde { \\mathbf { H } } ) _ { i j } ) ,", + "type": "interline_equation", + "image_path": "03f4568e900cbd085b205d0b2dccea99e865158ae46b111d8595fbc079416892.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 219, + 108, + 381, + 134 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 137, + 292, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 137, + 293, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 133, + 150 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 138, + 146, + 149 + ], + "score": 0.89, + "content": "\\mathbf { Y } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 137, + 293, + 150 + ], + "score": 1.0, + "content": "is the one-hot label indicator vector.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 107, + 162, + 237, + 173 + ], + "lines": [ + { + "bbox": [ + 105, + 162, + 239, + 175 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 239, + 175 + ], + "score": 1.0, + "content": "3.5 PROPERTIES OF GAMLP", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 106, + 182, + 505, + 282 + ], + "lines": [ + { + "bbox": [ + 106, + 183, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 505, + 195 + ], + "score": 1.0, + "content": "High Efficiency and Scalability. 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Besides, it also cost less memory than the sampling-based GNNs, and thus can", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 237, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 506, + 250 + ], + "score": 1.0, + "content": "scale to a larger graph in a single machine. Notably, like other simplified GNNs (i.e., SGC and SIGN),", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "score": 1.0, + "content": "GAMLP can pre-compute the propagated features and labels only once. It doesn’t need to pull the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 259, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 272 + ], + "score": 1.0, + "content": "intermediate representation of other nodes during the MLP training. 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Unlike SAGN,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 602, + 506, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 506, + 616 + ], + "score": 1.0, + "content": "GAMLP adopts two attention mechanisms to learn the interactions between the propagated features", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 613, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 505, + 627 + ], + "score": 1.0, + "content": "over different sizes of receptive fields. 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We aim to answer the following four questions. Q1: Can", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 697, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 697, + 506, + 712 + ], + "score": 1.0, + "content": "GAMLP outperform the state-of-the-art GNN methods? Q2: If so, where does the performance gain", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "of GAMLP come from? Q3: How about the efficiency of GAMLP compared with current GNN", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 734 + ], + "score": 1.0, + "content": "methods? Q4: How does GAMLP perform when applied to highly sparse graphs (i.e., given few", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 26, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 503, + 105 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 505, + 96 + ], + "score": 1.0, + "content": "We adopt the Cross-Entropy (CE) measurement between the predicted softmax outputs and the", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 369, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 369, + 106 + ], + "score": 1.0, + "content": "one-hot ground-truth label distributions as the objective function:", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 105, + 81, + 505, + 106 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 219, + 108, + 381, + 134 + ], + "lines": [ + { + "bbox": [ + 219, + 108, + 381, + 134 + ], + "spans": [ + { + "bbox": [ + 219, + 108, + 381, + 134 + ], + "score": 0.94, + "content": "\\mathcal { L } _ { C E } = - \\sum _ { i \\in \\mathcal { V } _ { l } } \\sum _ { j } \\mathbf { Y } _ { i j } \\log ( \\mathrm { s o f t m a x } ( \\widetilde { \\mathbf { H } } ) _ { i j } ) ,", + "type": "interline_equation", + "image_path": "03f4568e900cbd085b205d0b2dccea99e865158ae46b111d8595fbc079416892.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 219, + 108, + 381, + 134 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 137, + 292, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 137, + 293, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 133, + 150 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 138, + 146, + 149 + ], + "score": 0.89, + "content": "\\mathbf { Y } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 137, + 293, + 150 + ], + "score": 1.0, + "content": "is the one-hot label indicator vector.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 106, + 137, + 293, + 150 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 162, + 237, + 173 + ], + "lines": [ + { + "bbox": [ + 105, + 162, + 239, + 175 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 239, + 175 + ], + "score": 1.0, + "content": "3.5 PROPERTIES OF GAMLP", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 106, + 182, + 505, + 282 + ], + "lines": [ + { + "bbox": [ + 106, + 183, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 505, + 195 + ], + "score": 1.0, + "content": "High Efficiency and Scalability. 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Besides, it also cost less memory than the sampling-based GNNs, and thus can", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 237, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 506, + 250 + ], + "score": 1.0, + "content": "scale to a larger graph in a single machine. Notably, like other simplified GNNs (i.e., SGC and SIGN),", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "score": 1.0, + "content": "GAMLP can pre-compute the propagated features and labels only once. It doesn’t need to pull the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 259, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 272 + ], + "score": 1.0, + "content": "intermediate representation of other nodes during the MLP training. Therefore, it can also be well", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 271, + 451, + 283 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 451, + 283 + ], + "score": 1.0, + "content": "adapted to the distributed environment. Further details can be found in Appendix A.3.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9, + "bbox_fs": [ + 104, + 183, + 506, + 283 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 287, + 505, + 365 + ], + "lines": [ + { + "bbox": [ + 105, + 287, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 301 + ], + "score": 1.0, + "content": "Deep propagation. 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However, the model prediction based on the concatenated", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "feature is just used as a reference vector for the attention-based combination branch in GAMLP", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "rather than the final results. Compared with JK-Net, GAMLP with JK attention is more effective in", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 564, + 448, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 448, + 577 + ], + "score": 1.0, + "content": "alleviating the over-smoothing and scalability issue that deep architecture introduces.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 520, + 505, + 577 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 581, + 505, + 636 + ], + "lines": [ + { + "bbox": [ + 106, + 581, + 506, + 593 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 506, + 593 + ], + "score": 1.0, + "content": "GAMLP vs. SAGN. SAGN also proposes to do node-specific propagation in GNN. 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Besides, node-wise label propagation is also employed in", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 625, + 286, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 625, + 286, + 637 + ], + "score": 1.0, + "content": "GAMLP for better utilization of node labels.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 581, + 506, + 637 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 652, + 200, + 664 + ], + "lines": [ + { + "bbox": [ + 105, + 651, + 201, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 201, + 667 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 678, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 505, + 688 + ], + "score": 1.0, + "content": "In this section, we verify the effectiveness of GAMLP on 12 real-world graph datasets under both", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "the transductive and inductive settings. We aim to answer the following four questions. Q1: Can", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 697, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 697, + 506, + 712 + ], + "score": 1.0, + "content": "GAMLP outperform the state-of-the-art GNN methods? Q2: If so, where does the performance gain", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "of GAMLP come from? Q3: How about the efficiency of GAMLP compared with current GNN", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 734 + ], + "score": 1.0, + "content": "methods? Q4: How does GAMLP perform when applied to highly sparse graphs (i.e., given few", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 258, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 505, + 272 + ], + "score": 1.0, + "content": "edges and low label rate)? More experimental results about the heterogeneous graph, propagation", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 270, + 327, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 327, + 282 + ], + "score": 1.0, + "content": "depth and interpretability can be found in Appendix B.", + "type": "text", + "cross_page": true + } + ], + "index": 5 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 678, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 129, + 95, + 485, + 247 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 173, + 81, + 435, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 174, + 80, + 436, + 93 + ], + "spans": [ + { + "bbox": [ + 174, + 80, + 436, + 93 + ], + "score": 1.0, + "content": "Table 1: Performance comparison on seven transductive datasets.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 129, + 95, + 485, + 247 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 129, + 95, + 485, + 247 + ], + "spans": [ + { + "bbox": [ + 129, + 95, + 485, + 247 + ], + "score": 0.985, + "html": "
MethodsCoraCiteseerPubMedAmazon ComputerAmazon PhotoCoauthor CSCoauthor Physics
GCN81.8±0.570.8±0.579.3±0.782.4±0.491.2±0.690.7±0.292.7±1.1
GAT83.0±0.772.5±0.779.0±0.380.1±0.690.8±1.087.4±0.290.2±1.4
JK-Net81.8±0.570.7±0.778.8±0.782.0±0.691.9±0.789.5±0.692.5±0.4
ResGCN82.2±0.670.8±0.778.3±0.681.1±0.791.3±0.987.9±0.692.2±1.5
APPNP83.3±0.571.8±0.580.1±0.281.7±0.391.4±0.392.1±0.492.8±0.9
AP-GCN83.4±0.371.3±0.579.7±0.383.7±0.692.1±0.391.6±0.793.1±0.9
SGC81.0±0.271.3±0.578.9±0.582.2±0.991.6±0.790.3±0.591.7±1.1
SIGN82.1±0.372.4±0.879.5±0.583.1±0.891.7±0.791.9±0.392.8±0.8
S²GC82.7±0.373.0±0.279.9±0.383.1±0.791.6±0.691.6±0.693.1±0.8
GBP83.9±0.772.9±0.580.6±0.483.5±0.892.1±0.892.3±0.493.3±0.7
UNIMP82.6±0.472.5±0.980.1±0.583.9±0.892.0±1.192.4±0.393.5±0.8
GAMLP(JK)84.3±0.874.6±0.480.7±0.484.5±0.792.8±0.792.6±0.593.6±1.0
GAMLP(R)83.9±0.673.9±0.680.8±0.584.2±0.592.6±0.892.8±0.793.2±1.0
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More experimental results about the heterogeneous graph, propagation", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 270, + 327, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 327, + 282 + ], + "score": 1.0, + "content": "depth and interpretability can be found in Appendix B.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5 + }, + { + "type": "title", + "bbox": [ + 107, + 304, + 230, + 315 + ], + "lines": [ + { + "bbox": [ + 106, + 303, + 231, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 231, + 316 + ], + "score": 1.0, + "content": "4.1 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 106, + 327, + 505, + 416 + ], + "lines": [ + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "score": 1.0, + "content": "Datasets. We evaluate the predictive accuracy of GAMLP under both transductive and inductive", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "score": 1.0, + "content": "settings. For transductive settings, we conduct experiments on nine transductive datasets: three", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 350, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 505, + 363 + ], + "score": 1.0, + "content": "citation network datasets (Cora, Citeseer, PubMed) (Sen et al., 2008), two user-item datasets (Amazon", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 360, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 506, + 374 + ], + "score": 1.0, + "content": "Computer, Amazon Photo), two co-author datasets (Coauthor CS, Coauthor Physics) (Shchur", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "score": 1.0, + "content": "et al., 2018), and two OGB datasets (ogbn-products, ogbn-papers100M) (Hu et al., 2021). For", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "score": 1.0, + "content": "inductive settings, we perform the comparison experiments on three inductive datasets: PPI, Flickr,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 394, + 506, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 406 + ], + "score": 1.0, + "content": "and Reddit (Zeng et al., 2019). The statistics about these datasets can be found in Table 10 in", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 405, + 167, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 167, + 418 + ], + "score": 1.0, + "content": "Appendix C.1.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 107, + 421, + 505, + 510 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "score": 1.0, + "content": "Baselines. Under the transductive setting, we compare GAMLP with the following representative", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 432, + 507, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 507, + 446 + ], + "score": 1.0, + "content": "baseline methods: GCN (Kipf & Welling, 2016), GAT (Velickovi ˇ c et al., 2017), JK-Net (Xu et al., ´", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "score": 1.0, + "content": "2018), ResGCN (Li et al., 2019), APPNP (Klicpera et al., 2018), AP-GCN (Spinelli et al., 2020),", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 454, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 312, + 468 + ], + "score": 1.0, + "content": "SGC (Wu et al., 2019), SIGN (Frasca et al., 2020),", + "type": "text" + }, + { + "bbox": [ + 313, + 454, + 339, + 466 + ], + "score": 0.84, + "content": "\\mathrm { { S ^ { 2 } G C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 454, + 506, + 468 + ], + "score": 1.0, + "content": "(Zhu & Koniusz, 2021), and GBP (Chen", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 466, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 506, + 479 + ], + "score": 1.0, + "content": "et al., 2020b). For the comparison in the OGB datasets, we choose the top-performing methods", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 476, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 505, + 490 + ], + "score": 1.0, + "content": "from the OGB leaderboard along with their accuracy results. Under the inductive setting, we choose", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 488, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 488, + 506, + 500 + ], + "score": 1.0, + "content": "following representative methods: SGC (Wu et al., 2019), GraphSAGE (Hamilton et al., 2017),", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 499, + 402, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 402, + 511 + ], + "score": 1.0, + "content": "Cluster-GCN (Chiang et al., 2019), and GraphSAINT (Zeng et al., 2019).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 107, + 515, + 506, + 549 + ], + "lines": [ + { + "bbox": [ + 105, + 515, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 506, + 527 + ], + "score": 1.0, + "content": "In addition, two variants of GAMLP are tested in the evaluation: GAMLP(JK) and GAMLP(R). “JK”", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "and “R” stand for adopting “JK attention” and “Recursive attention” for the node-adaptive attention", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 538, + 209, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 209, + 550 + ], + "score": 1.0, + "content": "mechanism, respectively.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24 + }, + { + "type": "table", + "bbox": [ + 109, + 584, + 308, + 734 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 108, + 554, + 297, + 576 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 553, + 297, + 566 + ], + "spans": [ + { + "bbox": [ + 108, + 553, + 297, + 566 + ], + "score": 1.0, + "content": "Table 2: Performance comparison on the ogbn-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 108, + 565, + 174, + 576 + ], + "spans": [ + { + "bbox": [ + 108, + 565, + 174, + 576 + ], + "score": 1.0, + "content": "products dataset.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5 + }, + { + "type": "table_body", + "bbox": [ + 109, + 584, + 308, + 734 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 109, + 584, + 308, + 734 + ], + "spans": [ + { + "bbox": [ + 109, + 584, + 308, + 734 + ], + "score": 0.979, + "html": "
MethodsVal AccuracyTest Accuracy
GCN92.00±0.0375.64±0.21
SGC92.13±0.0275.87±0.14
GraphSAGE92.24±0.0778.50±0.14
GraphSAINT92.52±0.1380.27±0.26
GBP92.82±0.1080.48±0.05
SIGN92.99±0.0480.52±0.16
DeeperGCN92.38±0.0980.98±0.20
UniMP93.08±0.1782.56±0.31
SAGN93.09±0.0481.20±0.07
SAGN+0-SLE93.27±0.0483.29±0.18
GAMLP(JK)93.19±0.0383.54±0.25
GAMLP(R)93.11±0.0583.59±0.09
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MethodsVal AccuracyTest Accuracy
SGC66.48±0.2063.29±0.19
SIGN69.32±0.0665.68±0.06
SIGN-XL69.84±0.0666.06±0.19
SAGN70.34±0.9966.75±0.84
SAGN+0-SLE71.06±0.0867.55±0.15
GAMLP(JK)71.92±0.0468.07±0.10
GAMLP(R)71.21±0.0367.46±0.02
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MethodsCoraCiteseerPubMedAmazon ComputerAmazon PhotoCoauthor CSCoauthor Physics
GCN81.8±0.570.8±0.579.3±0.782.4±0.491.2±0.690.7±0.292.7±1.1
GAT83.0±0.772.5±0.779.0±0.380.1±0.690.8±1.087.4±0.290.2±1.4
JK-Net81.8±0.570.7±0.778.8±0.782.0±0.691.9±0.789.5±0.692.5±0.4
ResGCN82.2±0.670.8±0.778.3±0.681.1±0.791.3±0.987.9±0.692.2±1.5
APPNP83.3±0.571.8±0.580.1±0.281.7±0.391.4±0.392.1±0.492.8±0.9
AP-GCN83.4±0.371.3±0.579.7±0.383.7±0.692.1±0.391.6±0.793.1±0.9
SGC81.0±0.271.3±0.578.9±0.582.2±0.991.6±0.790.3±0.591.7±1.1
SIGN82.1±0.372.4±0.879.5±0.583.1±0.891.7±0.791.9±0.392.8±0.8
S²GC82.7±0.373.0±0.279.9±0.383.1±0.791.6±0.691.6±0.693.1±0.8
GBP83.9±0.772.9±0.580.6±0.483.5±0.892.1±0.892.3±0.493.3±0.7
UNIMP82.6±0.472.5±0.980.1±0.583.9±0.892.0±1.192.4±0.393.5±0.8
GAMLP(JK)84.3±0.874.6±0.480.7±0.484.5±0.792.8±0.792.6±0.593.6±1.0
GAMLP(R)83.9±0.673.9±0.680.8±0.584.2±0.592.6±0.892.8±0.793.2±1.0
", + "type": "table", + "image_path": "4a5a59d4d0651ede12b6e4c74960b527874205dde34294e35476ab07cfb88049.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 129, + 95, + 485, + 145.66666666666666 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 129, + 145.66666666666666, + 485, + 196.33333333333331 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 129, + 196.33333333333331, + 485, + 246.99999999999997 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "text", + "bbox": [ + 108, + 259, + 504, + 281 + ], + "lines": [], + "index": 4.5, + "bbox_fs": [ + 106, + 258, + 505, + 282 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 304, + 230, + 315 + ], + "lines": [ + { + "bbox": [ + 106, + 303, + 231, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 231, + 316 + ], + "score": 1.0, + "content": "4.1 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 106, + 327, + 505, + 416 + ], + "lines": [ + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "score": 1.0, + "content": "Datasets. We evaluate the predictive accuracy of GAMLP under both transductive and inductive", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 506, + 352 + ], + "score": 1.0, + "content": "settings. For transductive settings, we conduct experiments on nine transductive datasets: three", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 350, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 505, + 363 + ], + "score": 1.0, + "content": "citation network datasets (Cora, Citeseer, PubMed) (Sen et al., 2008), two user-item datasets (Amazon", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 360, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 506, + 374 + ], + "score": 1.0, + "content": "Computer, Amazon Photo), two co-author datasets (Coauthor CS, Coauthor Physics) (Shchur", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "score": 1.0, + "content": "et al., 2018), and two OGB datasets (ogbn-products, ogbn-papers100M) (Hu et al., 2021). For", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "score": 1.0, + "content": "inductive settings, we perform the comparison experiments on three inductive datasets: PPI, Flickr,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 394, + 506, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 406 + ], + "score": 1.0, + "content": "and Reddit (Zeng et al., 2019). The statistics about these datasets can be found in Table 10 in", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 405, + 167, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 167, + 418 + ], + "score": 1.0, + "content": "Appendix C.1.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 329, + 506, + 418 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 421, + 505, + 510 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "score": 1.0, + "content": "Baselines. Under the transductive setting, we compare GAMLP with the following representative", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 432, + 507, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 507, + 446 + ], + "score": 1.0, + "content": "baseline methods: GCN (Kipf & Welling, 2016), GAT (Velickovi ˇ c et al., 2017), JK-Net (Xu et al., ´", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 457 + ], + "score": 1.0, + "content": "2018), ResGCN (Li et al., 2019), APPNP (Klicpera et al., 2018), AP-GCN (Spinelli et al., 2020),", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 454, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 312, + 468 + ], + "score": 1.0, + "content": "SGC (Wu et al., 2019), SIGN (Frasca et al., 2020),", + "type": "text" + }, + { + "bbox": [ + 313, + 454, + 339, + 466 + ], + "score": 0.84, + "content": "\\mathrm { { S ^ { 2 } G C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 454, + 506, + 468 + ], + "score": 1.0, + "content": "(Zhu & Koniusz, 2021), and GBP (Chen", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 466, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 506, + 479 + ], + "score": 1.0, + "content": "et al., 2020b). For the comparison in the OGB datasets, we choose the top-performing methods", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 476, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 505, + 490 + ], + "score": 1.0, + "content": "from the OGB leaderboard along with their accuracy results. Under the inductive setting, we choose", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 488, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 488, + 506, + 500 + ], + "score": 1.0, + "content": "following representative methods: SGC (Wu et al., 2019), GraphSAGE (Hamilton et al., 2017),", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 499, + 402, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 402, + 511 + ], + "score": 1.0, + "content": "Cluster-GCN (Chiang et al., 2019), and GraphSAINT (Zeng et al., 2019).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 421, + 507, + 511 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 515, + 506, + 549 + ], + "lines": [ + { + "bbox": [ + 105, + 515, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 506, + 527 + ], + "score": 1.0, + "content": "In addition, two variants of GAMLP are tested in the evaluation: GAMLP(JK) and GAMLP(R). “JK”", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "and “R” stand for adopting “JK attention” and “Recursive attention” for the node-adaptive attention", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 538, + 209, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 209, + 550 + ], + "score": 1.0, + "content": "mechanism, respectively.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 515, + 506, + 550 + ] + }, + { + "type": "table", + "bbox": [ + 109, + 584, + 308, + 734 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 108, + 554, + 297, + 576 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 553, + 297, + 566 + ], + "spans": [ + { + "bbox": [ + 108, + 553, + 297, + 566 + ], + "score": 1.0, + "content": "Table 2: Performance comparison on the ogbn-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 108, + 565, + 174, + 576 + ], + "spans": [ + { + "bbox": [ + 108, + 565, + 174, + 576 + ], + "score": 1.0, + "content": "products dataset.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5 + }, + { + "type": "table_body", + "bbox": [ + 109, + 584, + 308, + 734 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 109, + 584, + 308, + 734 + ], + "spans": [ + { + "bbox": [ + 109, + 584, + 308, + 734 + ], + "score": 0.979, + "html": "
MethodsVal AccuracyTest Accuracy
GCN92.00±0.0375.64±0.21
SGC92.13±0.0275.87±0.14
GraphSAGE92.24±0.0778.50±0.14
GraphSAINT92.52±0.1380.27±0.26
GBP92.82±0.1080.48±0.05
SIGN92.99±0.0480.52±0.16
DeeperGCN92.38±0.0980.98±0.20
UniMP93.08±0.1782.56±0.31
SAGN93.09±0.0481.20±0.07
SAGN+0-SLE93.27±0.0483.29±0.18
GAMLP(JK)93.19±0.0383.54±0.25
GAMLP(R)93.11±0.0583.59±0.09
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MethodsVal AccuracyTest Accuracy
SGC66.48±0.2063.29±0.19
SIGN69.32±0.0665.68±0.06
SIGN-XL69.84±0.0666.06±0.19
SAGN70.34±0.9966.75±0.84
SAGN+0-SLE71.06±0.0867.55±0.15
GAMLP(JK)71.92±0.0468.07±0.10
GAMLP(R)71.21±0.0367.46±0.02
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MethodsPPIFlickrReddit
SGC65.7±0.0150.2±0.1294.9±0.00
GraphSAGE61.2±0.0550.1±0.1395.4±0.01
Cluster-GCN99.2±0.0448.1±0.0595.7±0.00
GraphSAINT99.4±0.0351.1±0.1096.6±0.01
GAMLP(JK)99.82±0.0154.12±0.0197.04±0.01
GAMLP(R)99.66±0.0153.12±0.0096.62±0.01
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To answer Q1, we report the transductive performance of GAMLP in", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 228, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 241 + ], + "score": 1.0, + "content": "Tables 1, 2, and 3. We observe that both variants of GAMLP outperform all the baseline methods", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "score": 1.0, + "content": "on almost all the datasets. For example, on the small Citeseer dataset, GAMLP(JK) outperforms", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 250, + 506, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 250, + 216, + 264 + ], + "score": 1.0, + "content": "the state-of-the-art method", + "type": "text" + }, + { + "bbox": [ + 216, + 250, + 241, + 261 + ], + "score": 0.9, + "content": "\\mathrm { { S ^ { 2 } G C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 250, + 326, + 264 + ], + "score": 1.0, + "content": "by a large margin of", + "type": "text" + }, + { + "bbox": [ + 326, + 251, + 348, + 261 + ], + "score": 0.87, + "content": "1 . 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 250, + 506, + 264 + ], + "score": 1.0, + "content": "; on the medium-sized dataset Amazon", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 262, + 506, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 262, + 506, + 275 + ], + "score": 1.0, + "content": "Computers, the predictive accuracy of GAMLP (JK) exceeds the one of the state-of-the-art method", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 272, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 143, + 285 + ], + "score": 1.0, + "content": "GBP by", + "type": "text" + }, + { + "bbox": [ + 143, + 273, + 165, + 283 + ], + "score": 0.86, + "content": "1 . 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 272, + 415, + 285 + ], + "score": 1.0, + "content": "; on the two large OGB datasets, GAMLP takes the lead by", + "type": "text" + }, + { + "bbox": [ + 416, + 273, + 443, + 283 + ], + "score": 0.88, + "content": "1 . 0 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 272, + 463, + 285 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 463, + 273, + 491, + 283 + ], + "score": 0.88, + "content": "1 . 3 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 491, + 272, + 506, + 285 + ], + "score": 1.0, + "content": "on", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 284, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 506, + 297 + ], + "score": 1.0, + "content": "ogbn-products and ogbn-papers100M, respectively. Furthermore, the experimental results illustrate", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "that the contest between the two variants of GAMLP is not a one-horse race, which suggests that", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 304, + 471, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 471, + 319 + ], + "score": 1.0, + "content": "these two different attention mechanisms both have their irreplaceable sense in some ways.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 322, + 505, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "Inductive Performance. We also evaluate GAMLP under the inductive setting. The experiment", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "results in Table 4 show that GAMLP consistently outperforms all the baseline methods. The leading", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 453, + 356 + ], + "score": 1.0, + "content": "advantage of GAMLP(JK) over SOTA inductive method – GraphSAINT is more than", + "type": "text" + }, + { + "bbox": [ + 454, + 344, + 477, + 355 + ], + "score": 0.86, + "content": "3 . 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "on the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 354, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 505, + 369 + ], + "score": 1.0, + "content": "widely-used dataset – Filckr. The impressive performance of GAMLP under the inductive setting", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 365, + 437, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 437, + 379 + ], + "score": 1.0, + "content": "illustrates that GAMLP is alpowerful in predicting the properties of unseen nodes.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 108, + 402, + 299, + 466 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 120, + 383, + 284, + 394 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 119, + 382, + 285, + 395 + ], + "spans": [ + { + "bbox": [ + 119, + 382, + 285, + 395 + ], + "score": 1.0, + "content": "Table 5: Ablation study on label utilization.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "table_body", + "bbox": [ + 108, + 402, + 299, + 466 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 402, + 299, + 466 + ], + "spans": [ + { + "bbox": [ + 108, + 402, + 299, + 466 + ], + "score": 0.982, + "html": "
MethodsVal AccuracyTest Accuracy
GAMLP(R)93.11±0.0583.59±0.05
-no_label92.29±0.0681.43±0.18
-plain_label92.53±0.2181.12±0.45
-uniform92.72±0.1581.28±0.93
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MethodsVal AccuracyTest Accuracy
GAMLP(JK)82.5±0.580.7±0.4
-origin_feature82.2±0.480.5±0.4
-normal_noise81.8±0.479.8±0.5
-no_reference81.5±0.579.9±0.3
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The experimental results in Table 5 show that", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 357, + 606 + ], + "score": 1.0, + "content": "utilizing labels brings huge performance gain to GAMLP: from", + "type": "text" + }, + { + "bbox": [ + 357, + 594, + 389, + 605 + ], + "score": 0.87, + "content": "8 1 . 4 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 594, + 399, + 606 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 400, + 594, + 431, + 605 + ], + "score": 0.89, + "content": "8 3 . 5 9 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 594, + 505, + 606 + ], + "score": 1.0, + "content": ". 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It further demonstrates the effectiveness", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 649, + 275, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 275, + 661 + ], + "score": 1.0, + "content": "of our proposed last residual connections.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 106, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 664, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 506, + 678 + ], + "score": 1.0, + "content": "Reference Vector in Attention Mechanism. In this part, we study the role of the reference vector", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "(originally set as the concatenated features from different propagation steps) in our proposed JK", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 104, + 685, + 507, + 701 + ], + "spans": [ + { + "bbox": [ + 104, + 685, + 507, + 701 + ], + "score": 1.0, + "content": "attention. 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MethodsPPIFlickrReddit
SGC65.7±0.0150.2±0.1294.9±0.00
GraphSAGE61.2±0.0550.1±0.1395.4±0.01
Cluster-GCN99.2±0.0448.1±0.0595.7±0.00
GraphSAINT99.4±0.0351.1±0.1096.6±0.01
GAMLP(JK)99.82±0.0154.12±0.0197.04±0.01
GAMLP(R)99.66±0.0153.12±0.0096.62±0.01
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To answer Q1, we report the transductive performance of GAMLP in", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 228, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 241 + ], + "score": 1.0, + "content": "Tables 1, 2, and 3. We observe that both variants of GAMLP outperform all the baseline methods", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 504, + 252 + ], + "score": 1.0, + "content": "on almost all the datasets. 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Furthermore, the experimental results illustrate", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "that the contest between the two variants of GAMLP is not a one-horse race, which suggests that", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 304, + 471, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 471, + 319 + ], + "score": 1.0, + "content": "these two different attention mechanisms both have their irreplaceable sense in some ways.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 217, + 506, + 319 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 322, + 505, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "Inductive Performance. We also evaluate GAMLP under the inductive setting. The experiment", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "results in Table 4 show that GAMLP consistently outperforms all the baseline methods. The leading", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 453, + 356 + ], + "score": 1.0, + "content": "advantage of GAMLP(JK) over SOTA inductive method – GraphSAINT is more than", + "type": "text" + }, + { + "bbox": [ + 454, + 344, + 477, + 355 + ], + "score": 0.86, + "content": "3 . 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "on the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 354, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 505, + 369 + ], + "score": 1.0, + "content": "widely-used dataset – Filckr. The impressive performance of GAMLP under the inductive setting", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 365, + 437, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 437, + 379 + ], + "score": 1.0, + "content": "illustrates that GAMLP is alpowerful in predicting the properties of unseen nodes.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 322, + 505, + 379 + ] + }, + { + "type": "table", + "bbox": [ + 108, + 402, + 299, + 466 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 120, + 383, + 284, + 394 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 119, + 382, + 285, + 395 + ], + "spans": [ + { + "bbox": [ + 119, + 382, + 285, + 395 + ], + "score": 1.0, + "content": "Table 5: Ablation study on label utilization.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "table_body", + "bbox": [ + 108, + 402, + 299, + 466 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 402, + 299, + 466 + ], + "spans": [ + { + "bbox": [ + 108, + 402, + 299, + 466 + ], + "score": 0.982, + "html": "
MethodsVal AccuracyTest Accuracy
GAMLP(R)93.11±0.0583.59±0.05
-no_label92.29±0.0681.43±0.18
-plain_label92.53±0.2181.12±0.45
-uniform92.72±0.1581.28±0.93
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MethodsVal AccuracyTest Accuracy
GAMLP(JK)82.5±0.580.7±0.4
-origin_feature82.2±0.480.5±0.4
-normal_noise81.8±0.479.8±0.5
-no_reference81.5±0.579.9±0.3
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The performance", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "drop from removing the last residual connections (“-plain_label” in Table 5) is significant since", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 616, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 506, + 628 + ], + "score": 1.0, + "content": "directly adopting the raw training labels leads to the overfitting issue. 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MethodsSGCSIGNGAMLP(JK)GAMLP(R)GraphSAINTCluster-GCN
Training time1.04.08.09.3364503
Test accuracy75.8780.5283.5483.5979.0878.97
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We", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 377, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 389 + ], + "score": 1.0, + "content": "compare the efficiency of GAMLP with sampling-based GraphSAINT and Cluster-GCN, graph-wise-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 400 + ], + "score": 1.0, + "content": "propagation-based SGC, and layer-wise-propagation-based SIGN. Table 7 illustrates the relative", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "training time of each compared method along with its predictive accuracy. The training time of SGC", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 410, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 505, + 422 + ], + "score": 1.0, + "content": "is set to 1 as reference. We observe that (1) sampling-based methods (e.g., GraphSAINT) consume", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "much more time than graph/layer-wise-propagation based methods (e.g., SGC, SIGN) due to the high", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 432, + 506, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 506, + 445 + ], + "score": 1.0, + "content": "computation cost introduced by the sampling process; (2) the two variants of GAMLP achieve the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 443, + 416, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 416, + 455 + ], + "score": 1.0, + "content": "best predictive accuracy while requiring comparable training time with SGC.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20.5 + }, + { + "type": "title", + "bbox": [ + 109, + 469, + 281, + 480 + ], + "lines": [ + { + "bbox": [ + 106, + 468, + 283, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 283, + 482 + ], + "score": 1.0, + "content": "4.5 EXPERIMENTS ON SPARSE GRAPHS", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 490, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "score": 1.0, + "content": "To answer Q4, we conduct experiments to evaluate the predictive accuracy of GAMLP when faced", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 501, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 514 + ], + "score": 1.0, + "content": "with edge and label sparsity problems, where the number of edges and training labels are highly", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 511, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 525 + ], + "score": 1.0, + "content": "scarce. 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The experimental results in Figure 3 show that", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "GAMLP consistently outperforms all the baselines when faced with different levels of edge and", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 566, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 505, + 580 + ], + "score": 1.0, + "content": "label sparsity. This experiment further demonstrates the effectiveness of our proposed node-wise", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "score": 1.0, + "content": "propagation scheme. 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MethodsSGCSIGNGAMLP(JK)GAMLP(R)GraphSAINTCluster-GCN
Training time1.04.08.09.3364503
Test accuracy75.8780.5283.5483.5979.0878.97
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We", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 377, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 389 + ], + "score": 1.0, + "content": "compare the efficiency of GAMLP with sampling-based GraphSAINT and Cluster-GCN, graph-wise-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 400 + ], + "score": 1.0, + "content": "propagation-based SGC, and layer-wise-propagation-based SIGN. Table 7 illustrates the relative", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "training time of each compared method along with its predictive accuracy. The training time of SGC", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 410, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 505, + 422 + ], + "score": 1.0, + "content": "is set to 1 as reference. We observe that (1) sampling-based methods (e.g., GraphSAINT) consume", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "much more time than graph/layer-wise-propagation based methods (e.g., SGC, SIGN) due to the high", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 432, + 506, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 506, + 445 + ], + "score": 1.0, + "content": "computation cost introduced by the sampling process; (2) the two variants of GAMLP achieve the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 443, + 416, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 416, + 455 + ], + "score": 1.0, + "content": "best predictive accuracy while requiring comparable training time with SGC.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 366, + 506, + 455 + ] + }, + { + "type": "title", + "bbox": [ + 109, + 469, + 281, + 480 + ], + "lines": [ + { + "bbox": [ + 106, + 468, + 283, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 283, + 482 + ], + "score": 1.0, + "content": "4.5 EXPERIMENTS ON SPARSE GRAPHS", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 490, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "score": 1.0, + "content": "To answer Q4, we conduct experiments to evaluate the predictive accuracy of GAMLP when faced", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 501, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 514 + ], + "score": 1.0, + "content": "with edge and label sparsity problems, where the number of edges and training labels are highly", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 511, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 525 + ], + "score": 1.0, + "content": "scarce. We randomly remove a fixed percentage of edges from the original graph to simulate the edge", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 523, + 507, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 507, + 536 + ], + "score": 1.0, + "content": "sparsity problem. The removed edges are exactly the same for all the compared methods. Besides,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 534, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 506, + 546 + ], + "score": 1.0, + "content": "we enumerate the number of training nodes per class from 1 to 20 to evaluate the performance of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "score": 1.0, + "content": "GAMLP given different levels of label sparsity. The experimental results in Figure 3 show that", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "GAMLP consistently outperforms all the baselines when faced with different levels of edge and", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 566, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 505, + 580 + ], + "score": 1.0, + "content": "label sparsity. This experiment further demonstrates the effectiveness of our proposed node-wise", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 577, + 506, + 592 + ], + "score": 1.0, + "content": "propagation scheme. 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This initial attempt also motivates several interesting", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "future directions: (1) exploring other attention mechanisms and (2) studying the mechanisms on", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 720, + 198, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 198, + 734 + ], + "score": 1.0, + "content": "heterogeneous graphs.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 644, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 286, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 288, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 288, + 96 + ], + "score": 1.0, + "content": "6 REPRODUCIBILITY STATEMENT", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 506, + 162 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 507, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 507, + 118 + ], + "score": 1.0, + "content": "The source code of GAMLP can be found in Anonymous Github (https://anonymous.4open.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 117, + 506, + 130 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 506, + 130 + ], + "score": 1.0, + "content": "science/r/ICLR-GAMLP). 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Our experimental environment is presented in", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 150, + 477, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 477, + 163 + ], + "score": 1.0, + "content": "Appendix C.1, and please refer to “README.md” in the Github repository for more details.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 107, + 178, + 175, + 190 + ], + "lines": [ + { + "bbox": [ + 106, + 178, + 176, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 178, + 176, + 192 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 196, + 504, + 220 + ], + "lines": [ + { + "bbox": [ + 105, + 195, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 505, + 211 + ], + "score": 1.0, + "content": "Deyu Bo, Xiao Wang, Chuan Shi, Meiqi Zhu, Emiao Lu, and Peng Cui. 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TypeMethodPre-processingTrainingMemory
SamplingGraphSAGE=O(kKnf²)O(bkK f+Kf²)
FastGCNO(kKnf2)O(bkKf+Kf²)
Cluster-GCN0(m)O(Pmf+Pnf²)O(bKf+Kf²)
Graph-wise propagationSGCO(Kmf)O（nf²)O(bf+f²)
Layer-wise propagationSIGNO(Kmf)O(Pnf2)O(bLf+Pf²)
S²GCO(Kmf)O(nf2)O(bf+f²)
GBPO(Knf+KVmlgn)O(Pnf²)O(bf+Pf²)
Node-wise propagationGAMLPO(Kmf+Lmc)O(Pnf² +Qnc²)O(bf+Pf²+Qc²）
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MethodsValidation AccuracyTest Accuracy
R-GCN40.84±0.4139.77±0.46
SIGN40.68±0.1040.46±0.12
HGT49.84±0.4749.27±0.61
R-GSN51.82±0.4150.32±0.37
HGConv53.00±0.1850.45±0.17
R-HGNN53.61±0.2252.04±0.26
NARS53.72±0.0952.40±0.16
NARS-GAMLP55.52±0.0854.01±0.21
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TypeMethodPre-processingTrainingMemory
SamplingGraphSAGE=O(kKnf²)O(bkK f+Kf²)
FastGCNO(kKnf2)O(bkKf+Kf²)
Cluster-GCN0(m)O(Pmf+Pnf²)O(bKf+Kf²)
Graph-wise propagationSGCO(Kmf)O（nf²)O(bf+f²)
Layer-wise propagationSIGNO(Kmf)O(Pnf2)O(bLf+Pf²)
S²GCO(Kmf)O(nf2)O(bf+f²)
GBPO(Knf+KVmlgn)O(Pnf²)O(bf+Pf²)
Node-wise propagationGAMLPO(Kmf+Lmc)O(Pnf² +Qnc²)O(bf+Pf²+Qc²）
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MethodsValidation AccuracyTest Accuracy
R-GCN40.84±0.4139.77±0.46
SIGN40.68±0.1040.46±0.12
HGT49.84±0.4749.27±0.61
R-GSN51.82±0.4150.32±0.37
HGConv53.00±0.1850.45±0.17
R-HGNN53.61±0.2252.04±0.26
NARS53.72±0.0952.40±0.16
NARS-GAMLP55.52±0.0854.01±0.21
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The propagated", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 612, + 507, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 507, + 627 + ], + "score": 1.0, + "content": "features of the same propagation step across different subgraphs are aggregated using 1-d convolution.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 622, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 506, + 637 + ], + "score": 1.0, + "content": "After that, aggregated features of different steps are fed into our GAMLP to get the final results. This", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 634, + 438, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 438, + 647 + ], + "score": 1.0, + "content": "variant of our GAMLP is called NARS-GAMLP as it mimics the design of NARS.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24.5, + "bbox_fs": [ + 105, + 580, + 507, + 647 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 652, + 503, + 674 + ], + "lines": [ + { + "bbox": [ + 106, + 651, + 505, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 664 + ], + "score": 1.0, + "content": "As ogbn-mag dataset only contains node features for “paper” nodes, we here adopt the ComplEx", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 663, + 387, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 387, + 675 + ], + "score": 1.0, + "content": "algorithm (Trouillon et al., 2017) to generate features for other nodes.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 651, + 505, + 675 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "Experiment Results. We report the validation and test accuracy of our proposed GAMLP on the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "ogbn-mag dataset in Table 9. 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To", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "score": 1.0, + "content": "demonstrate this, Fig. 6 shows the average attention weights of propagated features of GAMLP(JK)", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "according to the number of steps and degrees of input nodes, where the maximum step is 6. 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The experimental", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "score": 1.0, + "content": "results in Fig. 5 show that even at propagation depth equals 100, the predictive accuracy of our", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 526, + 507, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 214, + 540 + ], + "score": 1.0, + "content": "GAMLP(JK) still exceeds", + "type": "text" + }, + { + "bbox": [ + 214, + 527, + 241, + 538 + ], + "score": 0.89, + "content": "8 0 . 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 526, + 507, + 540 + ], + "score": 1.0, + "content": ", higher than the predictive accuracy of most baselines in Table 1.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 537, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 104, + 537, + 506, + 551 + ], + "score": 1.0, + "content": "At the same time, the predictive accuracy of SGC and JK-Net both drops rapidly when propagation", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 549, + 235, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 235, + 561 + ], + "score": 1.0, + "content": "depth increases from 10 to 100.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24.5, + "bbox_fs": [ + 104, + 471, + 507, + 561 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 586, + 356, + 597 + ], + "lines": [ + { + "bbox": [ + 106, + 586, + 357, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 357, + 597 + ], + "score": 1.0, + "content": "B.3 INTERPRETABILITY OF THE ATTENTION MECHANISM", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 106, + 610, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "GAMLP can adaptively and effectively combine multi-scale propagated features for each node. To", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "score": 1.0, + "content": "demonstrate this, Fig. 6 shows the average attention weights of propagated features of GAMLP(JK)", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "according to the number of steps and degrees of input nodes, where the maximum step is 6. In this", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "score": 1.0, + "content": "experiment, we randomly select 20 nodes for each degree range (1-4, 5-8, 9-12) and plot the relative", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 655, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 668 + ], + "score": 1.0, + "content": "weight based on the maximum value. We get two observations from the heat map: 1) The 1-step and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 665, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 506, + 679 + ], + "score": 1.0, + "content": "2-step propagated features are always of great importance, which shows that GAMLP captures the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 104, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "local information as those widely 2-layer methods do; 2) The weights of propagated features with", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "larger steps drop faster as the degree grows, indicating that our attention mechanism could prevent", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "high-degree nodes from including excessive irrelevant nodes, leading to over-smoothing. From the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "score": 1.0, + "content": "two observations, we conclude that GAMLP can identify the different RF demands of nodes and", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 721, + 276, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 276, + 734 + ], + "score": 1.0, + "content": "explicitly weight each propagated feature.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 35, + "bbox_fs": [ + 104, + 610, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 108, + 100, + 505, + 224 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 234, + 81, + 376, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 233, + 80, + 377, + 92 + ], + "spans": [ + { + "bbox": [ + 233, + 80, + 377, + 92 + ], + "score": 1.0, + "content": "Table 10: Overview of the Datasets", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 108, + 100, + 505, + 224 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 100, + 505, + 224 + ], + "spans": [ + { + "bbox": [ + 108, + 100, + 505, + 224 + ], + "score": 0.981, + "html": "
Dataset#Nodes#Features#Edges#Classes#Train/Val/TestTask typeDescription
Cora2,7081,4335,4297140/500/1000Transductivecitation network
Citeseer3,3273,7034,7326120/500/1000Transductivecitation network
Pubmed19,71750044,338360/500/1000Transductivecitation network
Amazon Computer13,381767245,77810200/300/12881Transductiveco-purchase graph
Amazon Photo7,487745119,0438160/240/7,087Transductiveco-purchase graph
Coauthor CS18,3336,80581,89415300/450/17,583Transductiveco-authorship graph
Coauthor Physics34,4938,415247,9625100/150/34,243Transductiveco-authorship graph
ogbn-products2,449,02910061,859,14047196k/49k/2204kTransductiveco-purchase graph
ogbn-papers100M111,059,9561281,615,685,8721721207k/125k/214kTransductivecitation network
ogbn-mag1,939,74312821,111,007349626k/66k/37kTransductivecitation network
PPI56,94450818,71612145k/6k/6kInductiveprotein interactions network
Flickr89,250500899,756744k/22k/22kInductiveimage network
Reddit232.96560211,606,91941155k/23k/54kInductivesocial network
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ChoicesTest Accuracy
Fixed weight82.56±0.43
Linear-decreasing weight82.72±0.93
Cosine function83.59±0.05
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However, we find we instead choose", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 107, + 375, + 507, + 394 + ], + "spans": [ + { + "bbox": [ + 107, + 377, + 163, + 390 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\alpha _ { l } = \\cos ( \\frac { \\pi l } { 2 L } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 375, + 507, + 394 + ], + "score": 1.0, + "content": "to give more penalties to labels at large propagation steps. We provide the performance", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "comparison on the ogbn-products dataset in Table 11. Three weighting schemes for the last residual", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 397, + 507, + 415 + ], + "spans": [ + { + "bbox": [ + 104, + 397, + 356, + 415 + ], + "score": 1.0, + "content": "connection module are tested: \"Cosine function\" stands for", + "type": "text" + }, + { + "bbox": [ + 356, + 398, + 415, + 412 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\alpha _ { l } = \\cos ( \\frac { \\pi l } { 2 L } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 397, + 507, + 415 + ], + "score": 1.0, + "content": ", the one in GAMLP;", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 409, + 507, + 426 + ], + "spans": [ + { + "bbox": [ + 104, + 409, + 261, + 426 + ], + "score": 1.0, + "content": "\"Linear-decreasing weight\" stands for", + "type": "text" + }, + { + "bbox": [ + 261, + 411, + 301, + 426 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\alpha _ { l } = \\frac { L - l } { L } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 409, + 427, + 426 + ], + "score": 1.0, + "content": "; and \"Fixed weight\" stands for", + "type": "text" + }, + { + "bbox": [ + 428, + 412, + 465, + 424 + ], + "score": 0.88, + "content": "\\alpha _ { l } = 0 . 7", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 409, + 507, + 426 + ], + "score": 1.0, + "content": ". Table 11", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 424, + 508, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 307, + 440 + ], + "score": 1.0, + "content": "shows that the weighting scheme GAMLP adopts,", + "type": "text" + }, + { + "bbox": [ + 307, + 425, + 363, + 439 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\alpha _ { l } = \\cos ( \\frac { \\pi l } { 2 L } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 424, + 508, + 440 + ], + "score": 1.0, + "content": ", outperforms the other two options.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 108, + 453, + 285, + 466 + ], + "lines": [ + { + "bbox": [ + 106, + 453, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 287, + 468 + ], + "score": 1.0, + "content": "C DETAILED EXPERIMENT SETUP", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "title", + "bbox": [ + 108, + 478, + 257, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 478, + 259, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 259, + 491 + ], + "score": 1.0, + "content": "C.1 EXPERIMENT ENVIRONMENT", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 498, + 506, + 598 + ], + "lines": [ + { + "bbox": [ + 106, + 499, + 506, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 506, + 511 + ], + "score": 1.0, + "content": "We provide detailed information about the datasets we adopted during the experiment in Table 10.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 509, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 505, + 522 + ], + "score": 1.0, + "content": "To alleviate the influence of randomness, we repeat each method ten times and report the mean", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 521, + 506, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 534 + ], + "score": 1.0, + "content": "performance and the standard deviations. For the largest ogbn-papers100M dataset, we run each", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 532, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 506, + 544 + ], + "score": 1.0, + "content": "method five times instead. The experiments are conducted on a machine with Intel(R) Xeon(R)", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 181, + 555 + ], + "score": 1.0, + "content": "Platinum 8255C", + "type": "text" + }, + { + "bbox": [ + 182, + 543, + 244, + 554 + ], + "score": 0.36, + "content": "\\mathrm { P U } @ 2 . 5 0 \\mathrm { G H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 542, + 506, + 555 + ], + "score": 1.0, + "content": ", and a single Tesla V100 GPU with 32GB GPU memory. The", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 553, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 568 + ], + "score": 1.0, + "content": "operating system of the machine is Ubuntu 16.04. As for software versions, we use Python 3.6,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 564, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 578 + ], + "score": 1.0, + "content": "Pytorch 1.7.1, and CUDA 10.1. The hyper-parameters in each baseline are set according to the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 576, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 506, + 588 + ], + "score": 1.0, + "content": "original paper if available. Please refer to Appendix C.2 for the detailed hyperparameter settings for", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 586, + 161, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 161, + 598 + ], + "score": 1.0, + "content": "our GAMLP.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22 + }, + { + "type": "title", + "bbox": [ + 108, + 611, + 267, + 623 + ], + "lines": [ + { + "bbox": [ + 106, + 611, + 268, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 268, + 624 + ], + "score": 1.0, + "content": "C.2 DETAILED HYPERPARAMETERS", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "We provide the detailed hyperparameter setting on GAMLP in Table 12, 13 and 14 to help reproduce", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "the results. 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Dataset#Nodes#Features#Edges#Classes#Train/Val/TestTask typeDescription
Cora2,7081,4335,4297140/500/1000Transductivecitation network
Citeseer3,3273,7034,7326120/500/1000Transductivecitation network
Pubmed19,71750044,338360/500/1000Transductivecitation network
Amazon Computer13,381767245,77810200/300/12881Transductiveco-purchase graph
Amazon Photo7,487745119,0438160/240/7,087Transductiveco-purchase graph
Coauthor CS18,3336,80581,89415300/450/17,583Transductiveco-authorship graph
Coauthor Physics34,4938,415247,9625100/150/34,243Transductiveco-authorship graph
ogbn-products2,449,02910061,859,14047196k/49k/2204kTransductiveco-purchase graph
ogbn-papers100M111,059,9561281,615,685,8721721207k/125k/214kTransductivecitation network
ogbn-mag1,939,74312821,111,007349626k/66k/37kTransductivecitation network
PPI56,94450818,71612145k/6k/6kInductiveprotein interactions network
Flickr89,250500899,756744k/22k/22kInductiveimage network
Reddit232.96560211,606,91941155k/23k/54kInductivesocial network
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ChoicesTest Accuracy
Fixed weight82.56±0.43
Linear-decreasing weight82.72±0.93
Cosine function83.59±0.05
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However, we find we instead choose", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 107, + 375, + 507, + 394 + ], + "spans": [ + { + "bbox": [ + 107, + 377, + 163, + 390 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\alpha _ { l } = \\cos ( \\frac { \\pi l } { 2 L } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 375, + 507, + 394 + ], + "score": 1.0, + "content": "to give more penalties to labels at large propagation steps. We provide the performance", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "comparison on the ogbn-products dataset in Table 11. 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Table 11", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 424, + 508, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 307, + 440 + ], + "score": 1.0, + "content": "shows that the weighting scheme GAMLP adopts,", + "type": "text" + }, + { + "bbox": [ + 307, + 425, + 363, + 439 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\alpha _ { l } = \\cos ( \\frac { \\pi l } { 2 L } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 424, + 508, + 440 + ], + "score": 1.0, + "content": ", outperforms the other two options.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5, + "bbox_fs": [ + 104, + 351, + 508, + 440 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 453, + 285, + 466 + ], + "lines": [ + { + "bbox": [ + 106, + 453, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 287, + 468 + ], + "score": 1.0, + "content": "C DETAILED EXPERIMENT SETUP", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "title", + "bbox": [ + 108, + 478, + 257, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 478, + 259, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 259, + 491 + ], + "score": 1.0, + "content": "C.1 EXPERIMENT ENVIRONMENT", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 498, + 506, + 598 + ], + "lines": [ + { + "bbox": [ + 106, + 499, + 506, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 506, + 511 + ], + "score": 1.0, + "content": "We provide detailed information about the datasets we adopted during the experiment in Table 10.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 509, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 505, + 522 + ], + "score": 1.0, + "content": "To alleviate the influence of randomness, we repeat each method ten times and report the mean", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 521, + 506, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 534 + ], + "score": 1.0, + "content": "performance and the standard deviations. For the largest ogbn-papers100M dataset, we run each", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 532, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 506, + 544 + ], + "score": 1.0, + "content": "method five times instead. The experiments are conducted on a machine with Intel(R) Xeon(R)", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 181, + 555 + ], + "score": 1.0, + "content": "Platinum 8255C", + "type": "text" + }, + { + "bbox": [ + 182, + 543, + 244, + 554 + ], + "score": 0.36, + "content": "\\mathrm { P U } @ 2 . 5 0 \\mathrm { G H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 542, + 506, + 555 + ], + "score": 1.0, + "content": ", and a single Tesla V100 GPU with 32GB GPU memory. The", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 553, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 568 + ], + "score": 1.0, + "content": "operating system of the machine is Ubuntu 16.04. As for software versions, we use Python 3.6,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 564, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 578 + ], + "score": 1.0, + "content": "Pytorch 1.7.1, and CUDA 10.1. The hyper-parameters in each baseline are set according to the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 576, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 506, + 588 + ], + "score": 1.0, + "content": "original paper if available. Please refer to Appendix C.2 for the detailed hyperparameter settings for", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 586, + 161, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 161, + 598 + ], + "score": 1.0, + "content": "our GAMLP.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 499, + 506, + 598 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 611, + 267, + 623 + ], + "lines": [ + { + "bbox": [ + 106, + 611, + 268, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 268, + 624 + ], + "score": 1.0, + "content": "C.2 DETAILED HYPERPARAMETERS", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "We provide the detailed hyperparameter setting on GAMLP in Table 12, 13 and 14 to help reproduce", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 656 + ], + "score": 1.0, + "content": "the results. 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Datasetsattention typehidden sizenum layer in JKnum layeractivation
ogb-productsRecursive512/4leakyrelu,a=0.2
ogb-papers100MJK128046sigmoid
ogb-magJK51244leaky relu,a=0.2
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Datasetshopshops for labelinput dropout attention dropoutdropout
ogb-products5100.20.50.5
ogb-papers100M121000.50.5
ogb-mag530.100.5
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Datasetsbetapatiencelrbatch sizeepochs
ogb-products13000.00150000400
ogb-papers100M1600.00015000400
ogb-mag11000.00110000400
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Datasetsattention typehidden sizenum layer in JKnum layeractivation
ogb-productsRecursive512/4leakyrelu,a=0.2
ogb-papers100MJK128046sigmoid
ogb-magJK51244leaky relu,a=0.2
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Datasetshopshops for labelinput dropout attention dropoutdropout
ogb-products5100.20.50.5
ogb-papers100M121000.50.5
ogb-mag530.100.5
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Datasetsbetapatiencelrbatch sizeepochs
ogb-products13000.00150000400
ogb-papers100M1600.00015000400
ogb-mag11000.00110000400
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MethodsCoraCiteseerPubMedAmazon ComputerAmazon PhotoCoauthor CSCoauthor Physics
GCN81.8±0.570.8±0.579.3±0.782.4±0.491.2±0.690.7±0.292.7±1.1
GAT83.0±0.772.5±0.779.0±0.380.1±0.690.8±1.087.4±0.290.2±1.4
JK-Net81.8±0.570.7±0.778.8±0.782.0±0.691.9±0.789.5±0.692.5±0.4
ResGCN82.2±0.670.8±0.778.3±0.681.1±0.791.3±0.987.9±0.692.2±1.5
APPNP83.3±0.571.8±0.580.1±0.281.7±0.391.4±0.392.1±0.492.8±0.9
AP-GCN83.4±0.371.3±0.579.7±0.383.7±0.692.1±0.391.6±0.793.1±0.9
SGC81.0±0.271.3±0.578.9±0.582.2±0.991.6±0.790.3±0.591.7±1.1
SIGN82.1±0.372.4±0.879.5±0.583.1±0.891.7±0.791.9±0.392.8±0.8
S²GC82.7±0.373.0±0.279.9±0.383.1±0.791.6±0.691.6±0.693.1±0.8
GBP83.9±0.772.9±0.580.6±0.483.5±0.892.1±0.892.3±0.493.3±0.7
UNIMP82.6±0.472.5±0.980.1±0.583.9±0.892.0±1.192.4±0.393.5±0.8
GAMLP(JK)84.3±0.874.6±0.480.7±0.484.5±0.792.8±0.792.6±0.593.6±1.0
GAMLP(R)83.9±0.673.9±0.680.8±0.584.2±0.592.6±0.892.8±0.793.2±1.0
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MethodsVal AccuracyTest Accuracy
GCN92.00±0.0375.64±0.21
SGC92.13±0.0275.87±0.14
GraphSAGE92.24±0.0778.50±0.14
GraphSAINT92.52±0.1380.27±0.26
GBP92.82±0.1080.48±0.05
SIGN92.99±0.0480.52±0.16
DeeperGCN92.38±0.0980.98±0.20
UniMP93.08±0.1782.56±0.31
SAGN93.09±0.0481.20±0.07
SAGN+0-SLE93.27±0.0483.29±0.18
GAMLP(JK)93.19±0.0383.54±0.25
GAMLP(R)93.11±0.0583.59±0.09
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MethodsVal AccuracyTest Accuracy
SGC66.48±0.2063.29±0.19
SIGN69.32±0.0665.68±0.06
SIGN-XL69.84±0.0666.06±0.19
SAGN70.34±0.9966.75±0.84
SAGN+0-SLE71.06±0.0867.55±0.15
GAMLP(JK)71.92±0.0468.07±0.10
GAMLP(R)71.21±0.0367.46±0.02
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MethodsPPIFlickrReddit
SGC65.7±0.0150.2±0.1294.9±0.00
GraphSAGE61.2±0.0550.1±0.1395.4±0.01
Cluster-GCN99.2±0.0448.1±0.0595.7±0.00
GraphSAINT99.4±0.0351.1±0.1096.6±0.01
GAMLP(JK)99.82±0.0154.12±0.0197.04±0.01
GAMLP(R)99.66±0.0153.12±0.0096.62±0.01
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MethodsVal AccuracyTest Accuracy
GAMLP(R)93.11±0.0583.59±0.05
-no_label92.29±0.0681.43±0.18
-plain_label92.53±0.2181.12±0.45
-uniform92.72±0.1581.28±0.93
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MethodsVal AccuracyTest Accuracy
GAMLP(JK)82.5±0.580.7±0.4
-origin_feature82.2±0.480.5±0.4
-normal_noise81.8±0.479.8±0.5
-no_reference81.5±0.579.9±0.3
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MethodsSGCSIGNGAMLP(JK)GAMLP(R)GraphSAINTCluster-GCN
Training time1.04.08.09.3364503
Test accuracy75.8780.5283.5483.5979.0878.97
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MethodsValidation AccuracyTest Accuracy
R-GCN40.84±0.4139.77±0.46
SIGN40.68±0.1040.46±0.12
HGT49.84±0.4749.27±0.61
R-GSN51.82±0.4150.32±0.37
HGConv53.00±0.1850.45±0.17
R-HGNN53.61±0.2252.04±0.26
NARS53.72±0.0952.40±0.16
NARS-GAMLP55.52±0.0854.01±0.21
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TypeMethodPre-processingTrainingMemory
SamplingGraphSAGE=O(kKnf²)O(bkK f+Kf²)
FastGCNO(kKnf2)O(bkKf+Kf²)
Cluster-GCN0(m)O(Pmf+Pnf²)O(bKf+Kf²)
Graph-wise propagationSGCO(Kmf)O（nf²)O(bf+f²)
Layer-wise propagationSIGNO(Kmf)O(Pnf2)O(bLf+Pf²)
S²GCO(Kmf)O(nf2)O(bf+f²)
GBPO(Knf+KVmlgn)O(Pnf²)O(bf+Pf²)
Node-wise propagationGAMLPO(Kmf+Lmc)O(Pnf² +Qnc²)O(bf+Pf²+Qc²）
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Dataset#Nodes#Features#Edges#Classes#Train/Val/TestTask typeDescription
Cora2,7081,4335,4297140/500/1000Transductivecitation network
Citeseer3,3273,7034,7326120/500/1000Transductivecitation network
Pubmed19,71750044,338360/500/1000Transductivecitation network
Amazon Computer13,381767245,77810200/300/12881Transductiveco-purchase graph
Amazon Photo7,487745119,0438160/240/7,087Transductiveco-purchase graph
Coauthor CS18,3336,80581,89415300/450/17,583Transductiveco-authorship graph
Coauthor Physics34,4938,415247,9625100/150/34,243Transductiveco-authorship graph
ogbn-products2,449,02910061,859,14047196k/49k/2204kTransductiveco-purchase graph
ogbn-papers100M111,059,9561281,615,685,8721721207k/125k/214kTransductivecitation network
ogbn-mag1,939,74312821,111,007349626k/66k/37kTransductivecitation network
PPI56,94450818,71612145k/6k/6kInductiveprotein interactions network
Flickr89,250500899,756744k/22k/22kInductiveimage network
Reddit232.96560211,606,91941155k/23k/54kInductivesocial network
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ChoicesTest Accuracy
Fixed weight82.56±0.43
Linear-decreasing weight82.72±0.93
Cosine function83.59±0.05
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Even though the domain has +3 received a considerable amount of attention in the past years, most methods present +4 the common drawback of lacking theoretical guarantees. Our starting point is to +5 notice that the estimate of the risk that most discriminative SSL methods minimise +6 is biased, even asymptotically. This bias impedes the use of standard statistical +7 learning theory and can hurt empirical performance. We propose a simple way of +8 removing the bias. Our debiasing approach is straightforward to implement and +9 applicable to most deep SSL methods. We provide simple theoretical guarantees on +10 the trustworthiness of these modified methods, without having to rely on the strong +11 assumptions on the data distribution that SSL theory usually requires. In particular, +12 we provide generalisation error bounds for the proposed methods. We evaluate +13 debiased versions of different existing SSL methods, such as the Pseudo-label +14 method and Fixmatch, and show that debiasing can compete with classic deep SSL +15 techniques in various settings by providing better calibrated models. Additionally, +16 we provide a theoretical explanation of the intuition of the popular SSL methods. + +# 17 1 Introduction + +18 The promise of semi-supervised learning (SSL) is to be able to learn powerful predictive models +19 using partially labelled data. In turn, this would allow machine learning to be less dependent on +20 the often costly and sometimes dangerously biased task of labelling data. Early SSL approaches— +21 e.g. Scudder’s (1965) untaught pattern recognition machine—simply replaced unknown labels with +22 predictions made by some estimate of the predictive model and used the obtained pseudo-labels to +23 refine their initial estimate. Other more complex branches of SSL have been explored since, notably +24 using generative models (from McLachlan, 1977, to Kingma et al., 2014) or graphs (notably following +25 Zhu et al., 2003). Deep neural networks, which are state-of-the art supervised predictors, have been +26 trained successfully using SSL. Somewhat surprisingly, the main ingredient of their success is still the +27 notion of pseudo-labels (or one of its variants), combined with systematic use of data augmentation +28 (e.g. Xie et al., 2019; Sohn et al., 2020; Rizve et al., 2021). +29 An obvious SSL baseline is simply throwing away the unlabelled data. We will call such a baseline the +30 complete case, following the missing data literature (e.g. Tsiatis, 2006). As reported in van Engelen & +31 Hoos (2020), the main risk of SSL is the potential degradation caused by the introduction of unlabelled +32 data. Indeed, semi-supervised learning outperforms the complete case baseline only in specific cases +33 (Singh et al., 2008; Schölkopf et al., 2012; Li & Zhou, 2014). This degradation risk for generative +34 models has been analysed in Chapelle et al. (2006, Chapter 4). To overcome this issue, previous works +35 introduced the notion of safe semi-supervised learning for techniques which never reduce predictive +36 performance by introducing unlabelled data (Li & Zhou, 2014; Guo et al., 2020). Our loose definition +37 of safeness is as follows: an SSL algorithm is safe if it has theoretical guarantees that are similar +38 or stronger to the complete case baseline. The “theoretical” part of the definition is motivated by the +39 fact that any empirical assessment of generalisation performances of an SSL algorithm is jeopardised +40 by the scarcity of labels. Unfortunately, popular deep SSL techniques generally do not benefit from +41 theoretical guarantees without strong and essentially untestable assumptions on the data distribution +42 (Mey & Loog, 2019) such as the smoothness assumption (small perturbations on the features $x$ do not +43 cause large modification in the labels, $p ( y | p e r t ( x ) ) \tilde { } \approx p ( y | x ) )$ or the cluster assumption (data points +44 are distributed on discrete clusters and points in the same cluster are likely to share the same label). +45 Most semi-supervised methods rely on these dis +46 tributional assumptions to ensure performance +47 in entropy minimisation, pseudo-labelling and +48 consistency-based methods. However, no proof +49 is given that guarantees the effectiveness of state +50 of-the-art methods (Tarvainen & Valpola, 2017; +51 Miyato et al., 2018; Sohn et al., 2020; Pham +52 et al., 2021). To illustrate that SSL requires spe +53 cific assumptions, we show in a toy example that +54 pseudo-labelling fails at learning. To do so, we +55 draw samples from two uniform distributions +56 with a small overlap. Both supervised and semi +57 supervised neural networks are trained using the +58 same labelled dataset. While the supervised al +59 gorithm learns perfectly the true distribution of +60 ${ \bar { p } } ( 1 | x )$ , the semi-supervised learning methods +61 (both entropy minimisation and pseudo-label) +62 underestimate $p ( 1 | x )$ for $x \in [ 1 , { \bar { 3 } } ]$ (see Figure +63 1). We also test our proposed method (DeSSL) +64 on this dataset and show that the unbiased ver +65 sion of each SSL technique learns the true dis +66 tribution accurately. See Appendix A for the +67 results with Entropy Minimisation. + +![](images/9bbd5ee8f99a22bdb862dd26839a689557dd932dd84c25fec37515c7c8d5c0f4.jpg) +Figure 1: (Left) Data histogram. (Right) Posterior probabilities $p ( 1 | x )$ of the same model trained following either complete case (only labelled data), Pseudo-label or our DePseudo-label. + +# 68 1.1 Contributions + +69 Rather than relying on the strong geometric assumptions usually used in SSL theory, we simply use +70 the missing completely at random (MCAR) assumption, a standard assumption from the missing data +71 literature (see e.g. Little & Rubin, 2019). With this only assumption on the data distribution, we +72 propose a new safe SSL method derived from simply debiasing common SSL risk estimates. Our +73 main contributions are: + +• We introduce debiased SSL (DeSSL), a safe method that can be applied to most deep SSL algorithms without assumptions on the data distribution; +• We propose a theoretical explanation of the intuition of popular SSL methods. We provide theoretical guarantees on the safeness of using DeSSL both on consistency and calibration of the method. We also provide a generalisation error bound; +We show how simple it is to apply DeSSL to the most popular methods such as Pseudo-label and Fixmatch, and show empirically that DeSSL leads to models that are never worse than their classical counterparts, generally better calibrated and sometimes much more accurate. + +# 82 2 Semi-supervised learning + +# 2.1 Learning with labelled data + +84 The ultimate objective of most of the learning frameworks is to minimise a risk $\mathcal { R }$ , defined as +85 the expectation of a particular loss function $L$ over a data distribution $p ( x , y )$ , on a set of models +86 $f _ { \boldsymbol { \theta } } ( \boldsymbol { x } )$ , parametrised by $\theta ~ \in ~ \Theta$ . Thus, the learning task is finding $\theta ^ { * }$ that minimises the risk: +87 $\mathcal { R } ( \theta ) = \mathbb { E } _ { ( X , Y ) \sim p ( x , y ) } [ L ( \theta ; X , Y ) ]$ . The distribution $p ( x , y )$ being unknown, we generally minimise +88 an approximation of the risk, the empirical risk $\hat { \mathcal { R } } ( \theta )$ computed on a sample of $n$ i.i.d points drawn +89 from $p ( x , y )$ . $\hat { \mathcal { R } } ( \theta )$ is an unbiased and consistent estimate of ${ \mathcal { R } } ( \theta )$ under mild assumptions. Its +90 unbiased nature is one of the basic properties that is used for the development of traditional learning +91 theory and asymptotic statistics (van der Vaart, 2000; Shalev-Shwartz & Ben-David, 2014). + +# 2.2 Learning with both labelled and unlabelled data + +93 Semi-supervised learning leverages both labelled and unlabelled data to improve the model’s per +94 formance and generalisation. Further information on the distribution $p ( x )$ provides a better under +95 standing of the distributions $p ( x , y )$ and also $p ( y | x )$ . Indeed, $p ( x )$ may contain information on $p ( y | x )$ +96 (Schölkopf et al., 2012, Goodfellow et al., 2016, Chapter 7.6, van Engelen & Hoos, 2020). +97 In the following, we have access to $n$ samples drawn from the distribution $p ( x , y )$ where some of the +98 labels are missing. We introduce a new random variable $r \in \{ 0 , 1 \}$ that governs whether or not a +99 data point is labelled $\boldsymbol { r } = 0$ missing, $r = 1$ observed). We note $\cdot$ the number of labelled and $n _ { u }$ the +100 number of unlabelled datapoints.The MCAR assumption states that the missingness of a label $y$ is +101 independent of its features and the value of the label: $p ( x , y , r ) = p ( x , y ) p ( r )$ , then $\cdot$ . This +102 is the case when nor features nor label carry information about the potential missingness of the labels. +103 This description of semi-supervised learning as a missing data problem has already been done in +104 multiple works –e.g. Seeger, 2000; Ahfock & McLachlan, 2019. Moreover, the MCAR assumption +105 is implicitly made in most of the SSL works to design the experiments, indeed, missing labels are +106 drawn completely as random in datasets such as MNIST, CIFAR or SVHN (Tarvainen & Valpola, +107 2017; Miyato et al., 2018; Xie et al., 2019; Sohn et al., 2020). + +# 2.2.1 Complete case: throwing the unlabelled data away + +109 In missing data theory, the complete case is the learning scheme that only uses fully observed +110 instances, namely labelled data. The natural estimator of the risk is then simply the empirical risk +111 computed on the labelled data. Fortunately, in the MCAR setting, the complete case risk estimate +112 keeps the same good properties of the traditional supervised one: it is unbiased and converges +113 pointwisely to $\mathcal { R } \bar { ( \theta ) }$ . Therefore, traditional learning theory holds for the complete case under MCAR. +114 While these observations are hardly new (see e.g. Liu & Goldberg, 2020), they can be seen as +115 particular cases of the theory that we develop below. The risk to minimise is + +$$ +\hat { \mathcal { R } } _ { C C } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) . +$$ + +# 16 2.2.2 Incorporating unlabelled data + +117 A major drawback of the complete case framework is that a lot of data ends up not being exploited. A +118 class of SSL approaches, mainly inductive methods with respect to the taxonomy of van Engelen & +119 Hoos (2020), generally aim to minimise a modified estimator of the risk by including unlabelled data. +120 Therefore, the optimisation problem generally becomes finding $\hat { \theta }$ that minimises the SSL risk, + +$$ +\hat { \mathcal { R } } _ { S S L } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) . +$$ + +121 where $H$ is a term that does not depend on the labels and $\lambda$ is a scalar weight which balances the +122 labelled and unlabelled terms. In the literature, $H$ can generally be seen as a surrogate of $L$ . Indeed, +123 it looks like the intuitive choices of $H$ are equal or equivalent to a form of expectation of $L$ on a +124 distribution given by the model. + +# 2.2.3 Some examples of surrogates + +126 A recent overview of the recent SSL techniques has been proposed by van Engelen & Hoos (2020). +127 In this work, we focus on methods suited for a discriminative probabilistic model $p _ { \theta } ( y | x )$ that +128 approximates the conditional $p ( y | x )$ . We categorised methods into two distinct sections, entropy +129 and consistency-based. +130 Entropy-based methods Entropy-based methods aim to minimise a term of entropy of the predic +131 tions computed on unlabelled data. Thus, they encourage the model to be confident on unlabelled +132 data, implicitly using the cluster assumption. Entropy-based methods can all be described as an +133 expectation of $L$ under a distribution $\pi _ { x }$ computed at the datapoint $x$ : + +$$ +H ( \theta ; x ) = \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] . +$$ + +134 For instance, Grandvalet & Bengio (2004) simply use the Shannon entropy as $H ( \theta ; x )$ which can be +135 rewritten as equation (3) with $\pi _ { x } ( \tilde { x } , \tilde { y } ) = \delta _ { x } ( \tilde { x } ) p _ { \theta } ( \tilde { y } | \tilde { x } )$ , where $\cdot$ is the dirac distribution in $x$ . Also, +136 pseudo-label methods, which consist in picking the class with the maximum predicted probability +137 as a pseudo-label for the unlabelled data (Scudder, 1965), can also be described as Equation 3. See +138 Appendix B for complete description of the entropy-based literature (Berthelot et al., 2019; 2020; +139 Xie et al., 2019; Sohn et al., 2020; Rizve et al., 2021; Zhang et al., 2021a) and further details. +140 Consistency-based methods Another range of SSL methods minimise a consistency objective +141 that encourages invariant prediction for perturbations either on the data either on the model in order +142 to enforce stability on model predictions. These methods rely on the smoothness assumption. In +143 this category, we cite $\Pi$ -model from (Sajjadi et al., 2016), temporal ensembling from (Laine & Aila, +144 2017), Mean-teacher proposed by (Tarvainen & Valpola, 2017), virtual adversarial training (VAT) +145 from (Miyato et al., 2018) and interpolation consistent training (ICT) from (Verma et al., 2019). We +146 remark that these objectives $H$ are equivalent to an expectation of $L$ (see Appendix B). The general +147 form of the unsupervised objective can be written as + +$C _ { 1 } \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] \le H ( \theta ; x ) = \mathbf { D i v } ( f _ { \hat { \theta } } ( x , . ) , p e r t ( f _ { \theta } ( x , . ) ) \le C _ { 2 } \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] ,$ (4) 148 where $\cdot$ is the predictions of the model, the Div is a non-negative function that measures the 149 divergence between two distributions, $\hat { \theta }$ is a fixed copy of the current parameter $\theta$ (the gradient is not propagated through 150 $\hat { \theta }$ ), pert is a perturbation applied to the model or the data and $0 \leq C _ { 1 } \leq C _ { 2 }$ . + +Previous works also remarked that $H$ is an expectation of $L$ for entropy-minimisation and pseudolabel (Zhu et al., 2022; Aminian et al., 2022). We describe a more general framework covering further methods and provide with our theory an intuition on the choice of $H$ . + +# 2.3 Theoretical guarantees + +155 The main risk of SSL is the potential degradation caused by the introduction of unlabelled data when +156 distributional assumptions are not satisfied (Singh et al., 2008; Schölkopf et al., 2012; Li & Zhou, +157 2014), specifically in settings where the MCAR assumption does not hold anymore (Oliver et al., +158 2018; Guo et al., 2020). Additionally, in (Zhu et al., 2022), the authors show disparate impacts of +159 pseudo-labelling on the different sub-classes of the population. To mitigate these problems, previous +160 works introduced the notion safe semi-supervised learning for techniques which never reduce learning +161 performance by introducing unlabelled data (Li & Zhou, 2014; Kawakita & Takeuchi, 2014; Li et al., +162 2016; Gan et al., 2017; Trapp et al., 2017; Guo et al., 2020). As remark by Oliver et al. (2018), +163 SSL performances are enabled by leveraging large validation sets which is not suited for real-world +164 applications. Then, theoretical guarantees are required to use safely SSL algorithms. For this reason, +165 in our work, we consider as safe an SSL algorithm that has theoretical guarantees that are similar +166 or stronger than those of the complete case baseline. Even though the methods presented above +167 produce good performances in a variety of SSL benchmarks, they generally do not benefit from +168 theoretical guarantees, even elementary. More over,Schölkopf et al. (2012) identify settings on the +169 causal relation between the features $x$ and the target $y$ where SSL may systematically fail, even if +170 classic SSL assumptions hold. Our example of Figure 1 also shows that classic SSL may fail to +171 generalise in a very benign setting with a large number of labelled data. +172 Presented methods minimise a biased version of the risk under the MCAR assumption and therefore +173 classical learning theory cannot be applied anymore, as we argue more precisely in Appendix C. +174 Learning over a biased estimate of the risk is not necessarily unsafe but it is difficult to provide +175 theoretical guarantees on such methods even if some works try to do so with strong assumptions +176 on the data distribution (Mey & Loog 2019, Section 4 and 5). Additionally, we remark that the +177 choice of $H$ can be confusing as seen in the literature. For instance, Grandvalet & Bengio (2004) and +178 Corduneanu & Jaakkola (2003) perform respectively entropy and mutual information minimisation +179 whereas Pereyra et al. (2017) and Krause et al. (2010) perform maximisation of the same quantities. +181 Previous works already proposed safe SSL methods with theoretical guarantees. Unfortunately, +182 so far these methods come with either strong assumptions or important computational burdens. +183 Li & Zhou (2014) introduced a safe semi-supervised SVM and showed that the accuracy of their +184 method is never worse than SVMs trained with only labelled data with the assumption that the true +185 model is accessible. However, if the distributional assumptions are not satisfied, no improvement or +186 degeneration is expected. Sakai et al. (2017) proposed an unbiased estimate of the risk for binary +187 classification by including unlabelled data. The key idea is to use unlabelled data to better evaluate +188 on the one hand the risk of positive class samples and on the other the risk of negative samples. +189 They provided theoretical guarantees on its variance and a generalisation error bound. The method +190 is designed only for binary classification and has not been tested in a deep learning setting. It has +191 been extended to ordinal regression in follow-up work (Tsuchiya et al., 2021). In the context of +192 kernel machines, Liu & Goldberg (2020) used an unbiased estimate of risk, like ours, for a specific +193 choice of $H$ . Guo et al. (2020) proposed $D S ^ { 3 } L$ , a safe method that needs to approximately solve +194 a bi-level optimisation problem. In particular, the method is designed for a different setting, not +195 under the MCAR assumption, where there is a class mismatch between labelled and unlabelled data. +196 The resolution of the optimisation problem provides a solution not worse than the complete case but +197 comes with approximations. They provide a generalisation error bound. Also, the method does not +198 outperform classic SSL methods in the MCAR setting as it is designed for non-MCAR situations. +199 Sokolovska et al. (2008) proposed a safe method with strong assumptions such that the feature space +200 is finite and the marginal probability distribution of $x$ is fully known. Fox-Roberts & Rosten (2014) +201 proposed an unbiased estimator in the generative setting applicable to a large range of models and +202 they prove that this estimator has a lower variance than the one of the complete case. + +# 203 3 DeSSL: Unbiased semi-supervised learning + +204 To overcome the issues introduced by the second term in the approximation of the risk for the semi +205 supervised learning approach, we propose DeSSL, an unbiased version of the SSL estimator using +206 labelled data to annul the bias. The idea here is to retrieve the properties of classical learning theory. +207 Fortunately, we will see that the proposed method can eventually have better properties than the com +208 plete case, in particular with regard to the variance of the estimate. The proposed DeSSL objective is + +$$ +\hat { \mathcal { R } } _ { D e S S L } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) \qquad - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) . +$$ + +209 + +210 Under the MCAR assumption, this estimator is unbiased for any value of the parameter $\lambda$ . For proof +211 of this result see Appendix D. We prove the optimality of debiasing with the labelled data in Appendix +212 F. +213 Intuitively, for entropy-based methods, $H$ should be applied only on unlabelled data to enforce the +214 confidence of the model only on unlabelled datapoints. Whereas, for consistency-based methods, +215 $H$ can be applied to any subset of data points. Our theory and proposed method remain the same +216 whether $H$ is applied to all the available data or not (see Appendix K). + +# 217 3.1 Does the DeSSL risk estimator make sense? + +The most intuitive interpretation is that by debiasing the risk estimator, we get back to the basics of learning theory. This way of debiasing is closely related to the method of control variates (Owen, 2013, Chapter 8) which is a common variance reduction technique. The idea is to add an additional term to a Monte-Carlo estimator with a null expectation in order to reduce the variance of the estimator without modifying the expectation. Here, DeSSL can also be interpreted as a control variate on the risk’s gradient itself and should improve the optimisation scheme. This idea is close to the optimisation schemes introduced by Johnson & Zhang (2013) and Defazio et al. (2014) which reduce the variance of the gradients’ estimate to improve optimisation performance. + +226 Another interesting way to interpret $\scriptstyle { \mathrm { D e S S L } }$ is as a constrained optimisation problem. Indeed, minimising 227 $\hat { \mathcal { R } } _ { D e S S L }$ is equivalent to minimising the Lagrangian of the following optimisation problem: + +$$ +\begin{array} { c l } { \displaystyle \operatorname* { m i n } _ { \theta } } & { \displaystyle \hat { \mathcal { R } } _ { C C } ( \theta ) } \\ { \mathrm { s . t . } } & { \displaystyle \frac { 1 } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) . } \end{array} +$$ + +228 The idea of this optimisation problem is to minimise the complete case risk estimator by assessing +229 that some properties represented by $H$ are on average equal for the labelled data and the unlabelled +230 data. For example, if we consider entropy-minimisation, this program encourages the model to have +231 the same confidence on the unlabelled examples as on the labelled ones. +232 The debiasing term of our objective will penalise the confidence of the model on the labelled data. +233 Pereyra et al. (2017) show that penalising the entropy in a supervised context acts as a strong +234 regulator for supervised models and improves on the state-of-the-art on common benchmarks. This +235 comforts us in the idea of debiasing using labelled data in the case of entropy-minimisation. Similarly, +236 the debiasing term in pseudo-label turns the problem into plausibility inference as described by +237 Barndorff-Nielsen (1976). Our objective also resembles doubly-robust risk estimates used for SSL in +238 the context of kernel machines by Liu & Goldberg (2020) and for deep learning in a recent preprint +239 (Hu et al., 2022). In both cases, their focus is quite different, as they consider weaker conditions +240 than MCAR, but very specific choices of $H$ . + +# 3.2 Is $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ an accurate risk estimate? + +242 Because of the connections between our debiased estimate and variance reduction techniques, we +243 have a natural interest in the variance of the estimate. Having a lower-variance estimate of the risk +244 would mean estimating it more accurately, leading to better models. Similarly to traditional control +245 variates (Owen, 2013), the variance can be computed, and optimised in $\lambda$ : + +Theorem 3.1. The function 246 $\lambda \mapsto \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) )$ reaches its minimum for: + +$$ +\lambda _ { o p t } = \frac { n _ { u } } { n } \frac { \mathrm { C o v } ( L ( \theta ; x , y ) , H ( \theta ; x ) ) } { \mathbb { V } ( H ( \theta ; x ) ) } , +$$ + +247 and at $\lambda _ { o p t }$ + +$$ +\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ) | _ { \lambda _ { o p t } } = \left( 1 - \frac { n _ { u } } { n } \rho _ { L , H } ^ { 2 } \right) \mathbb { V } ( \hat { \mathcal { R } } _ { C C } ( \theta ) ) \leq \mathbb { V } ( \hat { \mathcal { R } } _ { C C } ( \theta ) ) , +$$ + +248 where $\rho _ { L , H } = \operatorname { C o r r } ( L ( \theta ; x , y ) , H ( \theta ; x ) ) .$ + +249 Additionally, $-$ for all $\cdot$ between 0 and $\cdot$ . A proof of this theorem +250 is available as Appendix E. This theorem provides a formal justification to the heuristic idea that +251 $H$ should be a surrogate of $L$ . Indeed, DeSSL is a more accurate risk estimate when $H$ is strongly +252 positively correlated with $L$ , which is likely to be the case when $H$ is equal or equivalent to an +253 expectation of $L$ . Then, choosing $\lambda$ positive is a coherent choice. We also demonstrate in Appendix E +254 that $L$ and $H$ are positively correlated when $L$ is the negative likelihood and $H$ is the entropy. Other +255 SSL methods have variance reduction guarantees and already has shown great promises in SSL, see +256 Fox-Roberts $\&$ Rosten (2014) and Sakai et al. (2017). In a purely supervised context, Chen et al. +257 (2020) show that the effectiveness of data augmentation techniques lays partially on the variance +258 reduction of the risk estimate. A natural application of this theorem would be to tune $\lambda$ automatically +259 by estimating $\lambda _ { o p t }$ . In our case however, the estimation of $\operatorname { C o v } ( L ( \theta ; x , y ) , H ( \theta ; x ) )$ with few labels +260 led to extremely unstable unsatisfactory results. However, we estimate it more accurately using the +261 test set (which is of course impossible in practice) on different datasets and methods to provide +262 intuition on the order of $\lambda _ { o p t }$ and the range of the variance reduction regime in Appendix M.2. + +# 3.3 Calibration + +264 The calibration of a model is its capacity of predicting probability estimates that are representative +265 of the true distribution. This property is determinant in real-world application when we need + +reliable predictions. A scoring rule $s$ is a function assigning a score to the predictive distribution $p _ { \theta } ( y | x )$ relative to the event $y \bar { | x \sim p ( y | x ) , S ( p _ { \theta } , ( x , y ) ) }$ , where $p ( x , y )$ is the true distribution (see e.g. Gneiting $\&$ Raftery, 2007). A scoring rule measures both the accuracy and the quality of predictive uncertainty, meaning that better calibration is rewarded. The expected scoring rule is defined as $\mathcal { S } ( p _ { \theta } , p ) \stackrel { \cdot } { = } \mathbb { E } _ { p } [ \mathcal { S } ( p \bar { \theta } , ( x , y ) ) ]$ . A proper scoring rule is defined as a scoring rule such that $S ( p _ { \theta } , p ) \leq S ( p , p )$ (Gneiting & Raftery, 2007). The motivation behind having proper scoring rules comes from the following: suppose that the true data distribution $p$ is accessible by our set of models. Then, the scoring rule encourages to predict $p _ { \theta } ~ = ~ p$ . The opposite of a proper scoring rule can then be used to train a model to encourage the calibration of predictive uncertainty: $L ( \theta ; \bar { x , y } ) = - \mathcal { S } ( p _ { \theta } , ( x , y ) )$ . Most common losses used to train models are proper scorings rule such as log-likelihood. + +$S ( p _ { \theta } , ( x , y ) ) = - L ( \theta ; x , y )$ is a proper scoring rule, then so a proper scoring rule. $S ^ { \prime } ( p _ { \theta } , ( x , y , r ) ) =$ $\begin{array} { r } { - \big ( \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda { n } \big ( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } \big ) H ( \theta ; x ) \big ) } \end{array}$ + +The proof is available in Appendix $\mathbf { G }$ , and follows directly from unbiasedness and the MCAR assumption. The main interpretation of this theorem is that we can expect DeSSL to be as wellcalibrated as the complete case. + +# 3.4 Consistency + +We say that $\hat { \theta }$ is consistent if $d ( { \hat { \theta } } , \theta ^ { * } ) \xrightarrow { p } 0$ when $n \to \infty$ , where $d$ is a distance on $\Theta$ . The asymptotic properties of $\hat { \theta }$ depend on the behaviours of the functions $L$ and $H$ . We will thus require the following standard assumptions. + +Assumption 3.3. The minimum $\theta ^ { * }$ of $\mathcal { R }$ is well-separated: $\begin{array} { r } { \operatorname* { i n f } _ { \theta : d ( \theta ^ { * } , \theta ) \geq \epsilon } \mathcal { R } ( \theta ) > \mathcal { R } ( \theta ^ { * } ) } \end{array}$ + +Assumption 3.4. The uniform weak law of large number holds for both $L$ and $H$ . + +Theorem 3.5. Under the MCAR assumption, Assumption 3.3 and Assumption 3.4, $\begin{array} { r l } { \hat { \theta } } & { { } = } \end{array}$ $\operatorname { a r g m i n } \hat { \mathcal { R } } _ { D e S S L }$ is consistent. + +For proof of this theorem see Appendix G. This theorem is a simple application of van der Vaart’s (2000) Theorem 5.7 proving the consistency of an M-estimator. Also, this result holds for the complete case, with $\lambda = 0$ which proves that the complete case is a solid baseline under the MCAR assumption. Going further, we prove the asymptotic normality of $\cdot$ and showed that the asymptotic variance can be optimised with respect to $\lambda$ . + +Coupling of $n _ { l }$ and $n _ { u }$ under the MCAR assumption Under the MCAR assumption, $n _ { l }$ and $n _ { u }$ are random variables. We have that $r \sim B ( \pi )$ (i.e. any $x$ has the probability $\pi$ of being labelled). Then, with $n$ growing to infinity, we have $\begin{array} { r } { \frac { n _ { l } } { n } = \frac { n _ { l } } { n _ { l } + n _ { u } } \to \pi } \end{array}$ . Therefore, both $n _ { l }$ and $n _ { u }$ grow to infinity and $\begin{array} { r } { \frac { n _ { l } } { n _ { u } } \to \frac { \pi - 1 } { \pi } } \end{array}$ . This implies $n _ { u } = \mathcal { O } ( n _ { l } )$ and then when $n$ goes to infinity, both $n _ { u }$ and $n _ { l }$ go to infinity too and even if $n _ { u } > > n _ { l }$ . + +# 3.5 Rademacher complexity and generalisation bounds + +In this section, we prove an upper bound for the generalisation error of DeSSL. The unbiasedness of $\hat { \mathcal { R } } _ { D e S S L }$ can directly be used to derive generalisation bounds based on the Rademacher complexity (Bartlett & Mendelson, 2002), defined in our case as + +$$ +R _ { n } = \mathbb { E } _ { ( \varepsilon _ { i } ) _ { i \leq n } } \left[ \operatorname* { s u p } _ { \theta \in \Theta } \left( \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \varepsilon _ { i } L ( \theta ; x _ { i } , y _ { i } ) - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \varepsilon _ { i } H ( \theta ; x _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } \varepsilon _ { i } H ( \theta ; x _ { i } ) \right) \right] , +$$ + +where $\varepsilon _ { i }$ are i.i.d. Rademacher variables independent of the data. In the particular case of $\lambda = 0$ , we recover the standard Rademacher complexity of the complete case. We can then now bound the generalisation error of a model trained using our new loss function. + +307 Theorem 3.6. We assume that labels are MCAR and that both $L$ and $H$ are bounded. Then, there +308 exists a constant $\kappa > 0$ , that depends on $\lambda$ , $L$ , $H$ , and the ratio of observed labels, such that, with +309 probability at least $1 - \delta$ , for all $\theta \in \Theta$ , + +$$ +\mathcal { R } ( \theta ) \leq \hat { \mathcal { R } } _ { D e S S L } ( \theta ) + 2 { R _ { n } } + \kappa \sqrt { \frac { \log ( 4 / \delta ) } { n } } . +$$ + +# 311 4 Experiments + +312 We evaluate the performance of DeSSL against different classic methods. The goal here is to compare +313 DeSSL methods and their original counterparts. In particular, we perform experiments with simple +314 SSL methods such as pseudo-label (PseudoLabel) and entropy minimisation (EntMIN) with varying +315 $\lambda$ on MNIST (LeCun & Cortes, 2010) and CIFAR-10 and CIFAR-100 (Krizhevsky, 2009) and +316 compare them to the debiased method, respectively DeEntMin and DePseudoLabel. We also compare +317 PseudoLabel and DePseudoLabel on five small datasets of MedMNIST (Yang et al., 2021a;b) with a +318 fixed $\lambda$ . The results of these experiments are reported below. In our figures, the error bars represent +319 the size of the $9 5 \%$ confidence interval (CI). Finally, we modified the implementation of Fixmatch +320 (Sohn et al., 2020) and compare it with its debiased version on CIFAR-10. +321 We also compare DeEntMin and DePseudoLabel to the biased version on a large range of tabular +322 datasets commonly used in SSL benchmarks (Chapelle et al., 2006; Guo et al., 2010). We do not +323 observe differences between the performance, see Appendix P. Finally, we show how simple it is to +324 debias an existing implementation, by demonstrating it on the consistency-based models benchmarked +325 by (Oliver et al., 2018), namely VAT, Π-model and MeanTeacher on CIFAR-10 and SVHN (Netzer +326 et al., 2011). We observe similar performances between the debiased and biased versions for the differ +327 ent methods, both in terms of cross-entropy and accuracy. Moreover, these results have been obtained +328 using the hyperparameters finetuned for the biased versions. Therefore, it is likely that optimising the +329 hyperparameters for DeSSL will yield even better with the right hyperparameters, see Appendix O. + +# 330 4.1 MNIST + +331 MNIST is an advantageous dataset for SSL since classes are +332 well-separated. We compare PseudoLabel and DePseudoLabel +333 for a LeNet-like architecture using $n _ { l } = 1 0 0 0$ labelled data on +334 10 different splits of the training dataset into a labelled and unla +335 belled set. Models are then evaluated using the standard 10, 000 +336 test samples. We used $10 \%$ of $n _ { l }$ as the validation set. We test +337 the influence of the hyperparameter $\lambda$ and report the accuracy, +338 the cross-entropy and the expected calibration error (ECE, Guo +339 et al., 2017) at the epoch of best validation accuracy, see Fig +340 ure 2 and Appendix L. In this example SSL and DeSSL have +341 almost the same accuracy for all $\lambda$ , however, DeSSL seems to +342 be always better calibrated. To break the cluster assumption, we +343 reproduced the same experiment on a modified MNIST. Indeed, +344 we had label noise by replacing the true label for $20 \%$ of the +345 dataset with a randomly sampled label, see Appendix L. In this +346 setting, DeSSL performs better for large $\lambda$ in terms of accuracy +347 and also provides a better calibration. + +![](images/83806ca371eb89b58a6591821085562db6bf9133ea57b7460a513e7af4591464.jpg) +Figure 2: The influence of $\lambda$ on Pseudo-label and DePseudo-label for a Lenet trained on MNIST with $n _ { l } =$ 1000: (Top) Mean test accuracy; (Bottom) Mean test cross-entropy, with $9 5 \%$ CI. + +# 348 4.2 MedMNIST + +349 We compare PseudoLabel and DePseudoLabel on different datasets of MedMNIST, a large-scale +350 MNIST-like collection of biomedical images. We selected the five smallest 2D datasets of the +351 collection, for these datasets it is likely that the cluster assumption no longer holds. We trained +352 a 5-layer CNN with a fixed $\lambda = 1$ and $n _ { l }$ at $10 \%$ of the training data. We report in Table 1 the +353 mean accuracy and cross-entropy on 5 different splits of the labelled and unlabelled data and the +354 number of labelled data used. We report the AUC in Appendix L. DePseudoLabel competes with +355 PseudoLabel in terms of accuracy and even success when PseudoLabel’s accuracy is less than the +356 complete case. Moreover, DePseudoLabel is always better in terms of cross-entropy, so calibration, +357 whereas PseudoLabel is always worse than the complete case. + +Table 1: Test accuracy and cross-entropy of Complete Case (CC), PseudoLabel (PL) and DePseudoLabel (DePL) on five datasets of MedMNIST. + +
DATASETNLCCPLDEPL
CROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACY
DERMA10001.95 ± 0.0968.99± 1.202.51±0.2068.88±1.031.88 ± 0.1269.30± 0.85
PNEUMONIA5851.47 ± 0.0483.94±2.402.04 ±0.0485.83±2.131.40 ± 0.0684.36±3.79
RETINA1601.68 ± 0.0348.30± 3.061.80 ±0.1847.75±2.501.67 ± 0.0649.40± 2.62
BREAST780.80±0.0476.15±0.751.00 ±0.2674.74±1.040.70±0.0376.67 ± 1.32
BLOOD17006.11 ± 0.1784.13±0.836.61 ±0.2284.09± 1.176.53 ±0.3083.68 ±0.59
+ +# 358 4.3 CIFAR + +We compare PseudoLabel and DePseudoLabel on CIFAR-10 and CIFAR-100. We trained a CNN-13 from Tarvainen & Valpola (2017) on 5 different splits. For this experiment, we use $n _ { l } = 4 0 0 0$ and use the rest of the dataset as unlabelled. Models are then evaluated using the standard 10, 000 test samples. For a more realistic validation set, we used $10 \%$ of $n _ { l }$ as the validation set. We test the influence of the hyperparameter $\lambda$ and report the accuracy and the cross-entropy at the epoch of best validation accuracy, see Figure 3. We report the ECE in Appendix M. The performance of both methods on CIFAR-100 with $n l = 1 0 0 0 0$ are reported in Appendix M. We observe DeSSL provides both a better cross-entropy and ECE with the same accuracy for small $\lambda$ . For larger $\lambda$ , DeSSL performs better in all the reported metrics. We performed a paired Student’s t-test to ensure that our results are significant and reported the p-values in Appendix M. The p-values indicate that for $\lambda$ close to 10, DeSSL is often significantly better in all the metrics. Moreover, DeSSL for large $\lambda$ provides a better cross-entropy and ECE than the complete case whereas SSL never does. + +![](images/27dc0293570e0a2e81bb247a2854fc5feb2e9993b5aa8bed75c5473ad4a03a1c.jpg) +Figure 3: Influence of $\lambda$ on Pseudolabel and DePseudo-label for a CNN trained on CIFAR with $n _ { l } ~ = ~ 4 0 0 0$ : (Left) Mean test accuracy; (Right) Mean test cross-entropy, with $9 5 \%$ CI. + +# 78 4.4 Fixmatch (Sohn et al., 2020) + +We debiased a version of Fixmatch, see Appendix N for further details. For this experiment, we use $n l = 4 0 0 0$ on 5 different folds.First, we report that a strong baseline using data augmentation reach $\bar { 8 } 7 . 2 7 \%$ accuracy. Then, we observe that on the debiasing method improve both accuracy and cross-entropy of this modified version of Fixmatch. Inspired by Zhu et al. (2022), we show that our method improved performance on “poor” classes more equally than the biased version. Indeed, DeFixmatch improves Fixmatch by $1 . 5 \hat { 7 } \%$ overall but by $4 . { \bar { 9 } } 1 \%$ on the worst class. We report in Appendix N the accuracy per class of the different methods and the benefit ratio as defined by Zhu et al. (2022). + +Table 2: 1st line: Accuracy, 2nd line: Worst class accuracy, 3rd line: Crossentropy. + +
COMPLETE CASEFIXMATCHDEFIXMATCH
87.27 ± 0.2593.87 ±0.1395.44 ± 0.10
70.08 ±0.9382.25 ±2.2787.16 ± 0.46
0.60 ± 0.010.27 ±0.010.20 ±0.01
+ +# 5 Conclusion + +Motivated by the remarks of van Engelen & Hoos (2020) and Oliver et al. (2018) on the missingness of theoretical guarantees in SSL, we proposed a simple modification of SSL frameworks. We consider frameworks based on the inclusion of unlabelled data in the computation of the risk estimator and debias them using labelled data. We show theoretically that this debiasing comes with several theoretical guarantees. We demonstrate these theoretical results experimentally on several common SSL datasets and some more challenging ones such as MNIST with label noise. DeSSL shows competitive performance in terms of accuracy compared to its biased version but improves significantly the calibration. There are several future directions open to us. We showed that $\lambda _ { o p t }$ exists (Theorem 3.1) and therefore our formula provides guidelines for the optimisation of $\lambda$ . 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[Yes] (b) Did you include complete proofs of all theoretical results? [Yes] See Appendices + +3. If you ran experiments... + +(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] code and instructions to run Fixmatch. +(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Appendices +(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] Confidence intervals on all figures. +(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] An estimation in Appendix + +4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... + +(a) If your work uses existing assets, did you cite the creators? [Yes] See Appendix +(b) Did you mention the license of the assets? [Yes] +(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] Code +(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A] +(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A] + +5. If you used crowdsourcing or conducted research with human subjects... + +(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] +(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] +(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] + +626 We trained a 4-layer neural network (1/20/100/20/1) with ReLU activation function using 25, 000 +627 labelled and 25, 000 unlabelled points drawn from two 1D uniform laws with an overlap. We used +628 $\lambda = 1$ and a confidence threshold for Pseudo-label $\tau = 0 . 7 0$ . We optimised the model’s weights +629 using a stochastic gradient descent (SGD) optimiser with a learning rate of 0.1. + +![](images/b9a035bbf60fd95fb8619a772b1164cc655b2546f65f90ec62a263d605b6538d.jpg) +Figure 4: Data histogram + +![](images/4b50857481bd2ff1d44d1fbdd6456286af15b9c26056dbccdc57cb1379de2e52.jpg) +Figure 5: 4-layer neural net trained using SSL methods on a 1D dataset drawn from two uniform laws. (Top-left) Posterior probabilities $p ( 1 | x )$ of the same model trained following either complete case (only labelled data), Pseudo-label or our DePseudo-label. (Top-right) Same for EntMin and DeEntMin (Bottom-left) Training crossentropy for Pseudo-label and DePseudo-label (Bottom-right) Training cross-entropy for EntMin and DeEntMin + +# 630 B Details on surrogates and more examples + +631 We provide in this appendix further details on our classification of SSL methods between entropy +632 based and consistency-based (see Section 2.2.3). We detail a general framework for both of these +633 methods’ classes. We also show how popular SSL methods are related to our framework. + +# B.1 Entropy-based + +635 We class as entropy-based, methods that aim to minimise a term of entropy such as Grandvalet & +636 Bengio (2004) which minimises Shannon’s entropy or pseudo-label which is a form of entropy, see +637 Remark E.5. These methods encourage the model to be confident on unlabelled data, implicitly using +638 the cluster assumption. We recall those entropy-based methods can all be described as an expectation +639 of $L$ under a distribution $\pi _ { x }$ computed at the datapoint $x$ : + +$$ +H ( \theta ; x ) = \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] . +$$ + +640 Pseudo-label: As presented in the core article, the unsupervised objective of pseudo-label can be +641 written as an expectation of $L$ on the distribution $\pi _ { x } ( \tilde { x } , \tilde { \tilde { y } } ) = \delta _ { x } ( \tilde { x } ) \bar { p _ { \theta } } ( \tilde { y } | \tilde { x } )$ . Recently, Lee (2013) +642 encouraged the pseudo-labels method for deep semi-supervised learning. Then, Rizve et al. (2021) +643 recently improved the pseudo-label selection by introducing an uncertainty-aware mechanism on +644 the confidence of the model concerning the predicted probabilities. Pham et al. (2021) reaches +645 state-of-the-art on the Imagenet challenge using pseudo-labels on a large dataset of additional images. + +# 646 B.2 Pseudo-label and data augmentation + +47 Recently, several methods based on data augmentation have been proposed and proven to perform well +648 on a large spectrum of SSL tasks. The idea is to have a model resilient to strong data-augmentation of +49 the input (Berthelot et al., 2019; 2020; Sohn et al., 2020; Xie et al., 2019; Zhang et al., 2021a). These +650 methods rely both on the cluster assumption and the smoothness assumption and are at the border +651 between entropy-based and consistency-based methods. The idea is to have the same prediction +652 for an input and an augmented version of it. For instance, in Sohn et al. (2020), we first compute +653 pseudo-labels predicted using a weakly-augmented version of $x$ (flip-and-shift data augmentation) +654 and then minimise the likelihood with the predictions of the model on a strongly augmented version +655 of $x$ . In Xie et al. (2019), the method is a little bit different as we minimise the cross entropy between +656 the prediction of the model on $x$ and the predictions of an augmented version. In both cases, the +657 unsupervised part of the risk estimator can be reformulated as Equation 11. + +658 Fixmatch: In Fixmatch, Sohn et al. (2020), the unsupervised objective can be written as: + +$$ +H ( \theta ; x ) = \mathbb { 1 } [ \operatorname* { m a x } _ { y } p _ { \hat { \theta } } ( y | x _ { 1 } ) > \tau ] L ( \theta ; x _ { 2 } , \operatorname* { a r g m a x } _ { y } p _ { \hat { \theta } } ( y | x _ { 1 } ) ) +$$ + +659 where $\hat { \theta }$ is a fixed copy of the current parameters $\theta$ indicating that the gradient is not prop +660 agated through it, $x _ { 1 }$ is a weakly-augmented version of $x$ and $x _ { 2 }$ a strongly-augmented +661 one. Therefore, we write $H$ as an expectation of $L$ on the distribution $\begin{array} { r l } { \overline { { \pi } } _ { x } ( \bar { \tilde { x } } , \tilde { y } ) } & { { } = } \end{array}$ +662 $\delta _ { x _ { 2 } } ( \tilde { x } ) \delta _ { \mathrm { a r g m a x } _ { y } p _ { \hat { \theta } } ( y | x _ { 1 } ) } ( \tilde { y } ) \mathbb { 1 } [ \operatorname* { m a x } _ { y } p _ { \hat { \theta } } ( y | x _ { 1 } ) > \tau ]$ . + +663 UDA: In UDA, Xie et al. (2019), the unsupervised objective can be written as: + +$$ +H ( \theta ; x ) = \sum _ { y } p _ { \hat { \theta } } ( y | x ) L ( \theta ; x _ { 1 } , y ) +$$ + +664 where $\hat { \theta }$ is a fixed copy of the current parameters $\theta$ indicating that the gradient is not propagated +665 through it and $x _ { 1 }$ is an augmented version of $x$ . Therefore, we write $H$ as an expectation of $L$ on the +666 distribution $\pi _ { x } ( \tilde { x } , \tilde { y } ) = \bar { \delta _ { x _ { 1 } } } ( \tilde { x } ) p _ { \hat { \theta } } ( \tilde { y } | \tilde { x } )$ . +667 Others: Recently, have been proposed in the literature Zhang et al. (2021a) and Rizve et al. (2021). +668 The former is an improved version of Fixmatch with a variable threshold $\tau$ with respect to the class +669 and the training stage. The latter introduces a measurement of uncertainty in the pseudo-labelling +670 step to improve the selection. They also introduce negative pseudo-labels to improve the single-label +671 classification. + +# B.3 Consistency-based + +673 Consistency-based methods aim to smooth the decision function of the models or have more stable +674 predictions. These objectives $H$ are not directly a form of expectation of $L$ but are equivalent to an +675 expectation of $L$ . For all the following methods we can write the unsupervised objective $H$ such that: +676 + +$$ +C _ { 1 } \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] \leq H ( \theta ; x ) \leq C _ { 2 } \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] , +$$ + +with $0 \leq C _ { 1 } \leq C _ { 2 }$ . + +678 Indeed, consistency-based methods minimise an unsupervised objective that is a divergence between +679 the model predictions and a modified version of the input (data augmentation) or a perturbation of the +680 model. Using the fact that all norms are equivalent in a finite-dimensional space such as the space of +681 the labels, we have the equivalence between a consistency-based $H$ and an expectation of $L$ . +82 VAT The virtual adversarial training method proposed by (Miyato et al., 2018) generates the most +83 impactful perturbation $r _ { a d \nu }$ to add to $x$ . The objective is to train a model robust to input perturbations. +84 This method is closely related to adversarial training introduced by Goodfellow et al. (2014). + +$$ +H ( \theta ; x ) = { \bf D i v } ( f _ { \hat { \theta } } ( x , . ) , f _ { \theta } ( x + r _ { a d \nu } , . ) ) +$$ + +685 where the Div is a non-negative function that measures the divergence between two distributions, the +686 cross-entropy or the KL divergence for instance. If the divergence function is the cross-entropy, it is +687 straightforward to write the unlabelled objective as Equation 3. If the objective function is the KL +688 divergence, we can write the objective as + +$$ +H ( \theta ; x ) = \mathbb { E } _ { \pi _ { x } ( \tilde { x } + r , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ] - \mathbb { E } _ { \pi _ { x } ( \tilde { x } , \tilde { y } ) } [ L ( \hat { \theta } ; \tilde { x } , \tilde { y } ) ] +$$ + +689 with $\pi _ { x } ( \tilde { x } , \tilde { y } ) = \delta _ { x } ( \tilde { x } ) p _ { \hat { \theta } } ( y | x )$ . Therefore, variation of $H$ with respect to $\theta$ are the same as +690 $\mathbb { E } _ { \pi _ { x } ( \tilde { x } + r , \tilde { y } ) } [ L ( \theta ; \tilde { x } , \tilde { y } ) ]$ . VAT is also a method between consistency-based and entropy-based methods +691 as long as we use the KL-divergence or the cross-entropy as the measure of divergence. +692 Mean-Teacher A different form of pseudo-labelling is the Mean-Teacher approach proposed by +693 (Tarvainen & Valpola, 2017) where pseudo-labels are generated by a teacher model for a student +694 model. The parameters of the student model are updated, while the teacher’s are a moving average +695 of the student’s parameters from the previous training steps. The idea is to have a more stable +696 pseudo-labelling using the teacher than in the classic Pseudo-label. Final predictions are made by the +697 student model. A generic form of the unsupervised part of the risk estimator is then + +$$ +H ( \theta ; x ) = \sum _ { y } ( p _ { \theta } ( y | x ) - p _ { \hat { \theta } } ( y | x ) ) ^ { 2 } , +$$ + +where 698 $\hat { \theta }$ are the fixed parameters of the teacher. + +699 Π-Model The Π-Models are intrinsically stochastic models (for example a model with dropout) +700 encouraged to make consistent predictions through several passes of the same $x$ in the model. The +701 SSL loss is using the stochastic behaviour of the model where the model $f _ { \theta }$ and penalises different +702 predictions for the same $x$ (Sajjadi et al., 2016). Let’s note $f _ { \boldsymbol { \theta } } ( x , . ) _ { 1 }$ and $f _ { \boldsymbol { \theta } } ( x , . ) _ { 2 }$ two passes of $x$ +703 through the model $f _ { \theta }$ . A generic form of the unsupervised part of the risk estimator is then + +$$ +H ( \theta ; x ) = { \bf D i v } ( f _ { \theta } ( x , . ) _ { 1 } , f _ { \hat { \theta } } ( x , . ) _ { 2 } ) , +$$ + +704 where Div is a measure of divergence between two distributions (often the Kullback-Leibler diver +705 gence). +706 Temporal ensembling Temporal ensembling (Laine & Aila, 2017) is a form of $\Pi$ -Model where +707 we compare the current prediction of the model on the input $x$ with an accumulation of the previous +708 passes through the model. Then, the training is faster as the network is evaluated only once per input +709 on each epoch and the perturbation is expected to be less noisy than for $\Pi$ -models. +710 ICT Interpolation consistency training (Verma et al., 2019) is an SSL method based on the mixup +711 operation (Zhang et al., 2017). The model trained is then consistent to predictions at interpolations. +712 The unsupervised term of the objective is then computed on two terms: + +$$ +H ( \theta ; x _ { 1 } , x _ { 2 } ) = { \bf D i v } \left( f _ { \theta } ( \alpha x _ { 1 } + ( 1 - \alpha ) x _ { 2 } , . ) , \alpha f _ { \hat { \theta } } ( x _ { 1 } , . ) + ( 1 - \alpha ) f _ { \hat { \theta } } ( x _ { 2 } , . ) \right) , +$$ + +713 with $\alpha$ drawn with from a distribution $B ( a , a )$ . With the exact same transformation, we will be able +714 to show that this objective is equivalent to a form of expectation of $L$ . + +# 715 C On the semi-supervised bias + +716 We provide in this appendix a further explanation of the risk induced by the SSL bias as introduced +717 in Section 2.3. +718 Presented methods minimise a biased version of the risk under the MCAR assumption and therefore +719 classical learning theory does not apply anymore, + +$$ +\mathbb { E } [ \hat { \mathcal { R } } _ { S S L } ( \theta ) ] = \mathbb { E } [ L ( \theta ; x , y ) ] + \lambda \mathbb { E } [ H ( \theta ; x , y ) ] \neq \mathcal { R } ( \theta ) . +$$ + +720 Learning over a biased estimate of the risk is not necessarily unsafe but it is difficult to provide +721 theoretical guarantees on such methods even if some works try to do so with strong assumptions on the +722 data distribution (Mey & Loog 2019, Section 4 and 5, Zhang et al. 2021b). Previous works proposed +723 generalisation error bounds of SSL methods under strong assumptions on the data distribution or the +724 true model. We refer to the survey by Mey & Loog (2019). More recently, Wei et al. (2021) proves an +725 upper bound for training deep models with the pseudo-label method under strong assumption. Under +726 soft assumptions, Aminian et al. (2022) provides an error bound showing that the choice of $H$ is +727 crucial to provide good performances. +728 Indeed, the unbiased nature of the risk estimate is crucial in the development of learning theory. This +729 bias on the risk estimate may look like the one of a regularisation, such as the ridge regularisation. +730 However, SSL and regularisation are intrinsically different for several reasons: + +• Regularisers have a vanishing impact in the limit of infinite data whereas SSL usually do not in the proposed methods, see Equation 18. A solution would be to choose $\lambda$ with respect of the number of data points and make it vanish when $n$ goes to infinity. However, in most works, the choice of $\lambda$ is independent of the number of $n$ or $n _ { l }$ (Oliver et al., 2018; Sohn et al., 2020). +• One of the main advantages of regularisation is to turn the learning problem into a “more convex” problem, see Shalev-Shwartz & Ben-David (2014, Chapter 13). Indeed, ridge regularisation will often turn a convex problem into a strongly-convex problem. However, SSL faces the danger to turn the learning problem as non-convex as previously noted by Sokolovska et al. (2008). +• The objective of a regulariser is to bias the risk towards optimum with smooth decision functions whereas entropy-based SSL will lead to sharp decision functions. +• Regularisation usually does not depend on the data whereas $H$ does in the SSL framework. + +744 A entropy bias has been actually used by Pereyra et al. (2017) as a regulariser but as entropy +745 maximisation which should has an effect that is the opposite of the SSL method introduced by +746 Grandvalet & Bengio (2004), the entropy minimisation. + +# D Proof that 747 $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ is unbiased under MCAR + +Theorem D.1. Under the MCAR assumption, $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ is an unbiased estimator of ${ \mathcal { R } } ( \theta )$ . + +As a consequence of the theorem, under the MCAR assumption, $\hat { \mathcal { R } } _ { C C } ( \theta )$ is also unbiased as a special case of $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ for $\lambda = 0$ + +Proof: We first recall that the DeSSL risk estimator 751 $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ is defined for any $\lambda$ by + +$$ +\begin{array} { l l l } { \displaystyle \hat { \mathcal { R } } _ { D e S S L } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) } \\ { \displaystyle \qquad = \sum _ { i = 1 } ^ { n } \left( \frac { r _ { i } } { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \lambda \left( \frac { 1 - r _ { i } } { n _ { u } } - \frac { r _ { i } } { n _ { l } } \right) H ( \theta ; x _ { i } ) \right) . } \end{array} +$$ + +752 By the law of total expectation: + +$$ +\mathbb { E } [ \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ] = \mathbb { E } _ { r } \left[ \mathbb { E } _ { x , y } [ \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ] \right] . +$$ + +753 As far as we are under the MCAR assumption, the data $( x , y )$ and the missingness variable $r$ are independent thus, 754 $\mathbb { E } _ { r } \left[ \mathbb { E } _ { \boldsymbol { x } , \boldsymbol { y } } [ \hat { \mathcal { R } } _ { D e S S L } ( \boldsymbol { \theta } ) | \boldsymbol { r } ] \right] = \mathbb { E } _ { r } \left[ \mathbb { E } _ { \boldsymbol { x } , \boldsymbol { y } } [ \hat { \mathcal { R } } _ { D e S S L } ( \boldsymbol { \theta } ) ] \right]$ . + +755 We focus on $\mathbb { E } _ { x , y } [ \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ]$ . First, we replace $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ by its definition and then use the +756 linearity of the expectation. Then, + +$$ +\begin{array} { r l r } { { _ { - x , y } [ \hat { R } _ { D e S S L } ( \theta ) ] = \mathbb { E } [ \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) ] } } & { \mathrm { b y ~ d e f i n i t i } } \\ & { } & { = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \mathbb { E } [ L ( \theta ; x _ { i } , y _ { i } ) ] + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } \mathbb { E } [ H ( \theta ; x _ { i } ) ] - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \mathbb { E } [ H ( \theta ; x _ { i } ) ] \quad \mathrm { b y ~ l i n e a r i t } . } \end{array} +$$ + +The couples 757 $( x _ { i } , y _ { i } )$ are i.i.d. samples following the same distribution. Then, we have + +$$ +\begin{array} { l } { _ { _ { - x , y } } [ \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ] = \displaystyle \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \mathbb { E } \left[ L ( \theta ; x , y ) \right] + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } \mathbb { E } \left[ H ( \theta ; x ) \right] - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \mathbb { E } \left[ H ( \theta ; x ) \right] \quad \mathrm { i . i . d ~ s a m p l e s } } \\ { = \mathbb { E } \left[ L ( \theta ; x , y ) \right] } \\ { = \mathcal { R } ( \theta ) . } \end{array} +$$ + +Finally, we have the results that , 758 $\hat { \mathcal { R } } _ { D e S S L } ( \theta )$ is unbiased as ${ \mathcal { R } } ( \theta )$ is a constant, + +$$ +\begin{array} { r } { \mathbb { E } [ \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ] = \mathbb { E } \left[ \mathbb { E } _ { x , y } [ \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ] | r \right] = \mathbb { E } _ { r } \left[ \mathcal { R } ( \theta ) \right] = \mathcal { R } ( \theta ) . } \end{array} +$$ + +# 759 E Proof and comments about Theorem 3.1 + +Theorem 3.1 The function 760 $\lambda \mapsto \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r )$ reaches its minimum for: + +$$ +\lambda _ { o p t } = \frac { n _ { u } } { n } \frac { \mathrm { C o v } ( L ( \theta ; x , y ) , H ( \theta ; x ) ) } { \mathbb { V } ( H ( \theta ; x ) ) } +$$ + +761 and + +$$ +\begin{array} { r l r } { { \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) | _ { \lambda _ { o p t } } = ( 1 - \frac { n _ { u } } { n } \rho _ { L , H } ^ { 2 } ) \mathbb { V } ( \hat { \mathcal { R } } _ { C C } ( \theta ) ) } } \\ & { } & { \leq \mathbb { V } ( \hat { \mathcal { R } } _ { C C } ( \theta ) ) , } \end{array} +$$ + +762 where $\rho _ { L , H } = \mathrm { C o r r } ( L ( \theta ; x , y ) , H ( \theta ; x ) )$ . + +763 Proof: For any $\lambda \in \mathbb R$ ,we want to compute the variance: + +$$ +\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) . +$$ + +764 Under the MCAR assumption, $x$ and $y$ are both jointly independent of $r$ . Also, the couples $( x _ { i } , y _ { i } , r _ { i } )$ +765 are independent. Therefore, we have + +$$ +{ \begin{array} { r l } { \langle ( { \hat { \mathcal { R } } } _ { D e S S L } ( \theta ) | r ) = \displaystyle \sum _ { i = 1 } ^ { n } \mathbb { V } _ { ( x _ { i } , y _ { i } ) \sim p ( x , y | r ) } \left( { \frac { r _ { i } } { n _ { l } } } L ( \theta , x _ { i } , y _ { i } ) + \lambda \left( { \frac { 1 - r _ { i } } { n _ { u } } } - { \frac { r _ { i } } { n _ { l } } } \right) H ( \theta , x _ { i } ) \right) } & { { \mathrm { i . i . d ~ s a m p } } } \\ { = \displaystyle \sum _ { i = 1 } ^ { n } \mathbb { V } _ { ( x _ { i } , y _ { i } ) \sim p ( x , y ) } \left( { \frac { r _ { i } } { n _ { l } } } L ( \theta , x _ { i } , y _ { i } ) + \lambda \left( { \frac { 1 - r _ { i } } { n _ { u } } } - { \frac { r _ { i } } { n _ { l } } } \right) H ( \theta , x _ { i } ) \right) } & { { \mathrm { ( } } x , y { \mathrm { ) ~ a n d ~ } } } \end{array} } +$$ + +Using the fact that the couples 766 $( x _ { i } , y _ { i } )$ are i.i.d. samples following the same distribution, we have + +$$ +\begin{array} { r l r } { { \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) = \displaystyle \sum _ { i = 1 } ^ { n } \mathbb { V } _ { ( x , y ) \sim p ( x , y ) } ( \frac { r _ { i } } { n _ { l } } L ( \theta , x , y ) + \lambda ( \frac { 1 - r _ { i } } { n _ { u } } - \frac { r _ { i } } { n _ { l } } ) H ( \theta , x ) ) } } \\ & { } & { = \displaystyle \sum _ { i = 1 } ^ { n } \frac { r _ { i } ^ { 2 } } { n _ { l } ^ { 2 } } \mathbb { V } ( L ( \theta , x , y ) ) + \lambda ^ { 2 } ( \frac { 1 - r _ { i } } { n _ { u } } - \frac { r _ { i } } { n _ { l } } ) ^ { 2 } \mathbb { V } ( H ( \theta , x ) ) } \\ & { } & { + 2 \lambda \frac { r _ { i } } { n _ { l } } ( \frac { 1 - r _ { i } } { n _ { u } } - \frac { r _ { i } } { n _ { l } } ) \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) } \end{array} +$$ + +767 Now, we remark that the variable $r$ is binary and therefore $r ^ { 2 } = r$ , $( 1 - r ) ^ { 2 } = 1 - r$ and $r ( 1 - r ) = 0$ . +768 Using that and simplifying, we have + +$$ +\begin{array} { r l r } { { \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) = \sum _ { i = 1 } ^ { n } \frac { r _ { i } } { n _ { l } ^ { 2 } } \mathbb { V } ( L ( \theta , x , y ) ) + \lambda ^ { 2 } \frac { ( 1 - r _ { i } ) n _ { l } ^ { 2 } + r _ { i } n _ { u } ^ { 2 } } { n _ { l } ^ { 2 } n _ { u } ^ { 2 } } \mathbb { V } ( H ( \theta , x ) ) } } \\ & { } & { \quad \quad - 2 \lambda \frac { r _ { i } } { n _ { l } ^ { 2 } } \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) } \end{array} +$$ + +769 Finally, by summing and simplifying the expression (note that $n _ { l } + n _ { u } = n _ { \cdot }$ ), we compute the +770 expression variance, + +$$ +\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) = \frac { 1 } { n _ { l } } \mathbb { V } ( L ( \theta , x , y ) ) + \lambda ^ { 2 } \frac { n } { n _ { l } n _ { u } } \mathbb { V } ( H ( \theta , x ) ) - \frac { 2 \lambda } { n _ { l } } \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) +$$ + +So 771 $\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r )$ is a quadratic function in $\lambda$ and reaches its minimum for $\lambda _ { o p t }$ such that: + +$$ +\lambda _ { o p t } = \frac { n _ { u } } { n } \frac { \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) } { \mathbb { V } ( H ( \theta , x ) ) } +$$ + +And, at 772 $\lambda _ { o p t }$ , the variance of $\hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r )$ becomes + +$$ +\begin{array} { r l } { { \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) = \frac { 1 } { n _ { l } } \mathbb { V } ( L ( \theta , x , y ) ) ( 1 - \frac { n _ { u } } { n } \frac { \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) ^ { 2 } } { \mathbb { V } ( H ( \theta , x ) ) \mathbb { V } ( L ( \theta ; x , y ) ) } ) } } \\ & { = \frac { 1 } { n _ { l } } \mathbb { V } ( L ( \theta , x , y ) ) ( 1 - \frac { n _ { u } } { n } \mathrm { C o r r } ( L ( \theta , x , y ) , H ( \theta , x ) ) ^ { 2 } ) } \\ & { = ( 1 - \frac { n _ { u } } { n } \rho _ { L , H } ^ { 2 } ) \frac { 1 } { n _ { l } } \mathbb { V } ( L ( \theta , x , y ) ) } \end{array} +$$ + +773 Remark E.1. If $H$ is perfectly correlated with $L$ $\begin{array} { r } { L \left( \rho _ { L , H } = 1 \right) } \end{array}$ , then the variance of the DeSSL estimator +774 is equal to the variance of the estimator with no missing labels. +775 Remark E.2. Is it possible to estimate $\lambda _ { o p t }$ in practice ? The data distribution $p ( x , y )$ being +776 unknown, the computation of $\lambda _ { o p t }$ is not possible directly. Therefore, we need to use an estimator of +777 the covariance $\mathrm { C o v } ( L ( \theta ; x , y ) , \hat { H } ( \theta ; x ) )$ and the variance $\mathbb { V } ( H ( \theta ; x ) )$ (See Equation 23). Also, we +778 have to be careful not to introduce a new bias with the computation of $\lambda _ { o p t }$ , indeed, if we compute +779 it using the training set, $\lambda _ { o p t }$ becomes dependent of $x$ and $y$ and therefore $\hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r )$ becomes +780 biased. A solution would be to use a validation dataset for its computation. Another approach is to +781 compute it using the splitting method (Avramidis $\&$ Wilson, 1993). Moreover, the computation of +782 $\lambda _ { o p t }$ is tiresome and time-consuming in practice as it has to be updated for every different value of $\theta$ , +783 so at each gradient step. + +$$ +\hat { \lambda } _ { o p t } = \frac { \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } ( L ( \theta ; x _ { i } , y _ { i } ) - \bar { L } ( \theta ) ) ( H ( \theta ; x _ { i } ) - \bar { H } ( \theta ) ) } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } ( H ( \theta ; x _ { i } ) - \bar { H } ( \theta ) ) ^ { 2 } } +$$ + +where 784 $\begin{array} { r } { \bar { H } ( \theta ) = \frac { 1 } { n } \sum _ { i = 1 } ^ { n } H ( \theta ; x _ { i } ) } \end{array}$ and $\begin{array} { r } { \bar { L } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) } \end{array}$ + +785 Remark E.3. About the sign of $\lambda$ As explained in the article, the theorem still has a quantitative +786 merit when it comes to choosing $\lambda$ , by telling that the sign of $\lambda$ is positive when $H$ and $L$ are +787 positively correlated which will generally be the case with the examples mentioned in the article. For +788 instance, concerning the entropy minimisation technique, the following proposition proves that the +789 log-likelihood is negatively correlated with its entropy and therefore it justifies the choice of $\lambda > 0$ in +790 the entropy minimisation. + +791 Proposition E.4. The log-likelihood of the true distribution $\log p ( y | x )$ is negatively correlated with its entropy 792 $\mathbb { H } _ { \tilde { y } } ( p ( \tilde { y } | x ) ) = - \mathbb { E } _ { \tilde { y } \sim p ( . | x ) } [ \log p ( \tilde { y } | x ) ]$ . + +$$ +\mathrm { C o v } ( \log p ( y | x ) , \mathbb { H } _ { \tilde { y } } ( p ( \tilde { y } | x ) ) ) < 0 +$$ + +Proof. + +$$ +\begin{array} { r l } & { \mathrm { \mathop { s o v } } ( \log p ( y | x ) , \mathbb { H } _ { \tilde { y } } ( p ( \tilde { y } | x ) ) ) = \mathbb { E } _ { x , y } [ \log p ( y | x ) \mathbb { H } _ { \tilde { y } } ( p ( \tilde { y } | x ) ) ] - \mathbb { E } _ { x , y } [ \log p ( y | x ) ] \mathbb { E } _ { x } [ \mathbb { H } _ { \tilde { y } } ( p ( \tilde { y } | x ) ) ] } \\ & { \mathrm { ~ } } \\ & { \mathrm { ~ } = - \mathbb { E } _ { x , y } [ \log p ( y | x ) \mathbb { E } _ { \tilde { y } | x } [ \log p ( \tilde { y } | x ) ] ] + \mathbb { E } _ { x , y } [ \log p ( y | x ) ] \mathbb { E } _ { x } [ \mathbb { E } _ { \tilde { y } | x } [ \log p ( \tilde { y } | x ) ] ] } \end{array} +$$ + +793 By the law of total expectation, we have that $\mathbb { E } _ { x } [ \mathbb { E } _ { \tilde { y } | x } [ \log p ( \tilde { y } | x ) ] ] = \mathbb { E } _ { x , \tilde { y } } [ \log p ( \tilde { y } | x ) ]$ , then + +$$ +\begin{array} { r l r } & { } & { \mathrm { C o v } ( \log p ( y | x ) , \mathbb H _ { \widetilde { y } } ( p ( \widetilde { y } | x ) ) = - \mathbb E _ { x , y } [ \log p ( y | x ) \mathbb E _ { \widetilde { y } | x } [ \log p ( \widetilde { y } | x ) ] ] + \mathbb E _ { x , y } [ \log p ( y | x ) ] ^ { 2 } } \\ & { } & { = \mathbb E _ { x , y } [ \log p ( y | x ) ] ^ { 2 } - \mathbb E _ { x , y } [ \log p ( y | x ) \mathbb E _ { \widetilde { y } | x } [ \log p ( \widetilde { y } | x ) ] ] } \end{array} +$$ + +794 On the other hand, also with the law of total expectation, $\mathbb { E } _ { \boldsymbol { x } , \boldsymbol { y } } [ \log p ( \boldsymbol { y } | \boldsymbol { x } ) \mathbb { E } _ { \boldsymbol { \tilde { y } } | \boldsymbol { x } } [ \log p ( \boldsymbol { \tilde { y } } | \boldsymbol { x } ) ] ] \ =$ +795 $\mathbb { E } _ { x } [ \mathbb { E } _ { y | x } [ \log p ( y | x ) ] \mathbb { E } _ { \tilde { y } | x } [ \log p ( \tilde { y } | x ) ] ]$ , so + +$$ +\begin{array} { r l r } & { } & { \mathbb { E } _ { x , y } [ \log p ( y | x ) \mathbb { E } _ { \tilde { y } | x } [ \log p ( \tilde { y } | x ) ] ] = \mathbb { E } _ { x } [ \mathbb { E } _ { y | x } [ \log p ( y | x ) ] ^ { 2 } ] } \\ & { } & { \geq \mathbb { E } _ { x } [ \mathbb { E } _ { y | x } [ \log p ( y | x ) ] ] ^ { 2 } } \\ & { } & { \geq \mathbb { E } _ { x , y } [ \log p ( y | x ) ] ^ { 2 } } \end{array} +$$ + +796 Finally, we have the results, + +$$ +\begin{array} { r l r } & { } & { \mathrm { C o v } ( \log p ( y | x ) , \mathbb H _ { \widetilde { y } } ( p ( \widetilde { y } | x ) ) ) \leq \mathbb E _ { x , y } [ \log p ( y | x ) ] ^ { 2 } - \mathbb E _ { x , y } [ \log p ( y | x ) ] ^ { 2 } } \\ & { } & { \quad \leq 0 } \end{array} +$$ + +798 Remark E.5. We can also see the Pseudo-label as a form of entropy. Indeed, modulo the confidence +799 selection on the predicted probability, the Pseudo-label objective is the inverse of the Rényi min +800 entropy: + +$$ +\mathbb { H } _ { \infty } ( x ) = - \operatorname* { m a x } _ { y } \log p ( y | x ) +$$ + +802 We remark that the debiasing can be performed with any subset of the training data, labelled and +803 unlabelled. The choice of debiasing only with the labelled data can be explained both intuitively and +804 computationally in regard to the Theorem 3.1. Intuitively, the debiasing term penalises the confidence +805 on the labelled datapoints and then prevents the overfitting on the train dataset. As remarked in section +806 3.1, Pereyra et al. (2017) showed that penalising low entropy models acts as a strong regulariser +807 in supervised settings. This comforts the idea of penalising low entropy on the labelled dataset, +808 i.e. debiaising the entropy minimisation with the labelled dataset. Considering Pseudo-Label-based +809 methods, the objective for the labelled data is to predict the correct labels with moderate confidence. +810 This is also similar to the concept of plausibility inference described by Barndorff-Nielsen (1976). +811 In regard to Theorem 3.1, we show that the optimum choice of subset for debiaising is either only the +812 labelled data or the whole dataset and both are equivalent. + +We consider a subset $\cdot$ of the training set. We defined $a$ as follow: + +$$ +\cdot +$$ + +813 The unbiased estimator is then: + +$$ +\hat { \mathcal { R } } _ { D e S S L , A } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) - \lambda \sum _ { i = 1 } ^ { n } a _ { i } H ( \theta ; x _ { i } ) . +$$ + +814 + +815 We compute the variance of this quantity as in the proof of Theorem 3.1 and show that: + +$$ +- +$$ + +816 Suppose that no labelled datapoints are in $\mathcal { A }$ . Then, the last term of the variance is null. Hence, +817 having no labelled datapoints in $\cdot$ leads to a variance increase. We also remark that debiasing with +818 the entire dataset is equivalent that debiasing with the labelled datapoints. Indeed + +$$ +\begin{array} { l l } { \displaystyle \hat { \mathcal { R } } _ { D e S S L } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) - \frac { 1 } { n } \sum _ { i = 1 } ^ { n } H ( \theta ; x _ { i } ) } \\ { \displaystyle \quad \quad = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) - \frac { \lambda } { n } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) - \frac { \lambda } { n } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) } \\ { \displaystyle \quad \quad = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \frac { \lambda n _ { l } } { n n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } H ( \theta ; x _ { i } ) - \frac { \lambda n _ { l } } { n n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) , } \end{array} +$$ + +which is equivalent to debiasing with only the labelled dataset by replacing 819 $\cdot$ by $\cdot$ . + +820 At this point we can still sample a random subset composed of $\it { l }$ labelled datapoints and $u$ unlabelled 821 datapoints. Therefore $a _ { i } = 1 / ( l + u ) \mathbf { 1 } \{ x _ { i } \in A \}$ , we show in the following that the optimum choice of the couple 822 $\cdot$ are $\cdot$ and $\cdot$ , so only the labelled or the whole dataset. + +We sample $\cdot$ labelled and $\cdot$ unlabelled datapoints to debiased the estimator, by simplifying the term in the sum of Equation 32 as follow: + +$$ +\cdot +$$ + +823 Then, by summing the term and simplifying, we get: + +$$ +\cdot +$$ + +We want to minimise $\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r )$ with respect to $( \lambda , l , u )$ . V $\cdot$ reaches is minimum in $\cdot$ at + +$$ +\lambda _ { o p t } = \frac { n _ { u } } { n _ { l } } \frac { l } { n _ { u } - u + l } \frac { \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) } { \mathbb { V } ( H ( \theta , x ) ) } . +$$ + +824 Then, + +$$ +\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) = \frac { 1 } { n _ { l } } \mathbb { V } ( L ( \theta , x , y ) ) - \frac { n _ { u } } { n _ { l } } \frac { l ^ { 2 } } { ( n _ { u } - u + l ) ( l + u ) } \frac { \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) ^ { 2 } } { \mathbb { V } ( H ( \theta , x ) ) } . +$$ + +825 We now want to minimise with respect to $0 \leq u \leq n _ { u }$ and $\cdot$ . We can easily show that the +826 $\_$ reaches its mininum for $\cdot$ or $\cdot$ and for both value: + +$$ +\mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) | r ) = \frac { 1 } { n _ { l } } \mathbb { V } ( L ( \theta , x , y ) ) - \frac { n _ { u } } { n _ { l } } \frac { l } { n _ { u } + l } \frac { \mathrm { C o v } ( L ( \theta , x , y ) , H ( \theta , x ) ) ^ { 2 } } { \mathbb { V } ( H ( \theta , x ) ) } . +$$ + +827 Then $l / ( n _ { u } + l )$ is a increasing function, then reaches its maximum a $l = n _ { l }$ . So finally, the optimal +828 choices for the couple $( n _ { l } , 0 )$ and $\cdot$ . We showed that these couples are equivalent. + +# 829 G Proof of Theorem 3.2 + +830 Theorem 3.2 If $\mathbf { \nabla } \cdot S ( p _ { \theta } , ( x , y ) ) = - L ( \theta ; x , y )$ is a proper scoring rule, then + +$$ +\mathcal { S } ^ { \prime } ( p _ { \theta } , ( x , y , r ) ) = - ( \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda n ( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } ) H ( \theta ; x ) ) +$$ + +831 is also a proper scoring rule. + +Proof. The scoring rule considered in our SSL framework is: + +$$ +\mathcal { S } ^ { \prime } ( p _ { \theta } , ( x , y , r ) ) = - \left( \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda n ( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } ) H ( \theta ; x ) \right) . +$$ + +The proper scoring rule of the fully supervised problem is + +$$ +S ( p _ { \theta } , ( x , y , r ) ) = - L ( \theta ; x , y ) . +$$ + +832 Let p be the true distribution of the data $( x , y , r )$ . Under MCAR, $r$ is independent of $x$ and $y$ , then +833 $p ( x , y , r ) = p ( r ) p ( x , y )$ . + +by independence + +$$ +\begin{array} { r l } { S ^ { \prime } ( y _ { 0 } , g ) = \int \psi ( x , y , \psi ) S ^ { \prime } ( y , ( x , y , y ) ) d x d y d x } \\ & { = \int \psi ( x , y ) \psi ( x ) \delta ( y , ( x , y , \psi ) ) d x d y d x } \\ & { = - \int p ( y , x , y ) g \psi ( \frac { \gamma \psi } { M } , L ( \beta , x , y ) + \lambda \ u ) \frac { 1 - \tau } { w _ { 0 } } - \frac { \tau } { w _ { 0 } } \mathcal { M } ( \beta , x ) d x d y d \mathcal { H } } \\ & { = - \int _ { x _ { 0 } } g ( x , y ) \underbrace { \left( \int p ( \gamma ) \frac { \partial \psi } { \partial x } \phi \right) } _ { = \mathcal { M } } \mathcal { L } ( \psi ( x , y , y ) ) d x d y d x d y } \\ & { \qquad - \lambda m \int _ { x _ { 0 } } g ( x , y ) \underbrace { \left( \int p ( \gamma ) \left( \frac { 1 - \tau } { \lambda w } - \frac { \tau } { \lambda w _ { 0 } } \right) d x \right) } _ { = 0 } H ( \theta , z ) d x d y } \\ & { = - \int _ { x _ { 0 } } g ( x , y ) g ( \theta , x , y ) d x d y } \\ & { = \delta ( y , 0 ) . } \end{array} +$$ + +834 Thereformathcal835 $S ( p _ { \theta } , ( x , y ) ) = - L ( \theta ; x , y )$ is also a proper scoring rule. $\begin{array} { r } { S ^ { \prime } ( p _ { \theta } , ( x , y , r ) ) = - ( \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda n ( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } ) H ( \theta ; x ) ) } \end{array}$ + +# 837 H Proof of Theorem 3.5 + +Assumption 3.3: the minimum 838 $\theta ^ { * }$ of $\mathcal { R }$ is well-separated. + +$$ +\operatorname* { i n f } _ { \theta : d ( \theta ^ { * } , \theta ) \geq \epsilon } \mathcal { R } ( \theta ) > \mathcal { R } ( \theta ^ { * } ) +$$ + +839 Assumption 3.4: uniform weak law of large numbers holds for a function $L$ if: + +$$ +\operatorname* { s u p } _ { \theta \in \Theta } \frac { 1 } { n } \sum _ { i = 1 } ^ { n } L ( \theta , x _ { i } , y _ { i } ) - \mathbb { E } [ L ( \theta , x , y ) ] \overset { p } { } 0 +$$ + +840 Theorem 3.5. Under assumption A and assumption $B$ for both $L$ and $H$ , $\hat { \theta } = \arg \operatorname* { m i n } \hat { \mathcal { R } } _ { D e S S L }$ is +841 asymptotically consistent with respect to $n$ . +842 This result is a direct application of Theorem 5.7 from van der Vaart (2000, Chapter 5) that states +843 that under assumption A and B for $L$ , $\hat { \theta } = \arg \operatorname* { m i n } \hat { \mathcal { R } }$ is asymptotically consistent with respect to $n$ +844 Assumption A remains unchanged as we have M-estimators of the same $\mathcal { R }$ . We now aim to prove that +845 under assumption B for both $L$ and $H$ , we have the assumption B on $\begin{array} { r l } { \theta \longrightarrow \frac { r n } { n _ { l } } L ( \theta ; x , y ) \overset { } { + } \lambda ( 1 - } & { { } } \end{array}$ +846 $\textstyle { \frac { r n } { n _ { l } } } ) H ( \theta ; x )$ . +47 Lemma H.1. If the uniform law of large number holds for both $L$ and $H$ , then it holds for $\theta \longrightarrow$ +8 $\begin{array} { r } { \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda ( 1 - \frac { r n } { n _ { l } } ) H ( \theta ; x ) } \end{array}$ . + +849 Proof. Suppose assumption $\mathbf { B }$ for $L$ , then the same result holds if we replace $n$ with $n _ { l }$ as $n$ and $n _ { l }$ are coupled by the law of 850 $r$ . Indeed, when $n$ grows to infinity, $n _ { l }$ too and inversely. Therefore, + +$$ +\operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) - \mathbb { E } [ L ( \theta ; x , y ) ] \right| \xrightarrow [ n ] { p } 0 +$$ + +851 Now, suppose we have assumption $\mathbf { B }$ for $H$ , then we can make the same remark than for $L$ . Now, we +852 have to show that: + +$$ +\operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda n \left( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } \right) H ( \theta ; x ) - \mathbb { E } [ L ( \theta ; x , y ) ] \right| \xrightarrow [ n ] { p } 0 +$$ + +853 We first split the absolute value and the sup operator as + +$$ +\begin{array} { r l } & { \underset { \theta \in \Theta } { \operatorname* { s u p } } \left| \frac { 1 } { n } \displaystyle \sum _ { i = 1 } ^ { n } \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda n \left( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } \right) H ( \theta ; x ) - \mathbb { E } [ L ( \theta ; x , y ) ] \right| } \\ & { \quad \le \underset { \theta \in \Theta } { \operatorname* { s u p } } \left| \frac { 1 } { n _ { l } } \displaystyle \sum _ { i = 1 } ^ { n } \frac { r n } { n _ { l } } L ( \theta ; x , y ) - \mathbb { E } [ L ( \theta ; x , y ) ] \right| + \left| \frac { 1 } { n } \displaystyle \sum _ { i = 1 } ^ { n } \lambda n \left( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } \right) H ( \theta ; x ) \right| } \\ & { \quad \le \underset { \theta \in \Theta } { \operatorname* { s u p } } \left| \frac { 1 } { n _ { l } } \displaystyle \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x , y ) - \mathbb { E } [ L ( \theta ; x , y ) ] \right| + \underset { \theta \in \Theta } { \operatorname* { s u p } } \left| \frac { 1 } { n } \displaystyle \sum _ { i = 1 } ^ { n } \lambda n \left( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } \right) H ( \theta ; x ) \right| . } \end{array} +$$ + +854 So we now have to prove that the second term is also converging to 0 in probability. Again by splitting +855 the absolute value and the sup, we have + +$$ +\operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \lambda n \left( \frac { 1 - r } { n _ { u } } - \frac { r } { n _ { l } } \right) H ( \theta ; x ) \right| = \operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { \lambda } { n } \sum _ { i = 1 } ^ { n } \frac { ( 1 - r ) n } { n _ { u } } H ( \theta ; x ) - \frac { \lambda } { n } \sum _ { i = 1 } ^ { n } \frac { r n } { n _ { l } } H ( \theta ; x ) \right| +$$ + +$$ +\begin{array} { r l } & { \displaystyle \operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n } ( 1 - r ) H ( \theta ; x ) - \frac { \lambda } { n _ { i } } \sum _ { i = 1 } ^ { n } r H ( \theta ; x ) \right| } \\ & { \displaystyle = \operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n } ( 1 - r ) H ( \theta ; x ) - \mathbb { E } [ H ( \theta ; x , y ) ] - \left( \frac { \lambda } { n _ { i } } \sum _ { i = 1 } ^ { n } r H ( \theta ; x ) - \mathbb { E } [ H ( \theta ; x , y ) ] \right) \right| } \\ & { \displaystyle = \operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { \lambda } { n _ { u } } \sum _ { i = n + 1 } ^ { n + { n } _ { s } } H ( \theta ; x ) - \mathbb { E } [ H ( \theta ; x , y ) ] - \left( \frac { \lambda } { n _ { i } } \sum _ { i = 1 } ^ { n } H ( \theta ; x ) - \mathbb { E } [ H ( \theta ; x , y ) ] \right) \right| } \\ & { \displaystyle \leq \operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { \lambda } { n _ { u } } \sum _ { i = n - l + 1 } ^ { { n + { n } _ { s } } } H ( \theta ; x ) - \mathbb { E } [ H ( \theta ; x , y ) ] \right| + \displaystyle \operatorname* { s u p } _ { \theta \in \Theta } \left| \left( \frac { \lambda } { n _ { t } } \sum _ { i = 1 } ^ { n } H ( \theta ; x ) - \mathbb { E } [ H ( \theta ; x , y ) ] \right) \right| . } \end{array} +$$ + +857 Thus, + +$$ +\operatorname* { s u p } _ { \theta \in \Theta } \left| \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda n \left( \frac { 1 - r } { n _ { u } } 1 - \frac { r } { n _ { l } } \right) H ( \theta ; x ) - \mathbb { E } [ L ( \theta ; x , y ) ] \right| \xrightarrow [ n ] { p } 0 +$$ + +858 And we now just have to apply the results of van der Vaart (2000, Theorem 5.7) to have the asymptotic consistent of 859 $\hat { \theta } = \arg \operatorname* { m i n } \hat { \mathcal { R } } _ { D e S S L }$ . + +860 + +861 Remark H.2. A sufficient condition on the function $H$ to verify assumption B, the uniform weak +862 law of large numbers, is to be bounded (Newey & McFadden, 1994, Lemma 2.4). For instance, +863 the entropy $\begin{array} { r } { H = - \sum _ { y } p _ { \theta } ( y | x ) \log ( p _ { \theta } ( y | x ) ) } \end{array}$ is bounded and therefore, the entropy minimisation is +864 asymptotically consistent. + +# 865 I Asymptotic normality of DeSSL + +866 In the following, we study a modified version of the objective to simplify the proof. Let us consider +867 the following DeSSL objective $-$ which has the +868 same properties than the original one (unbiasedness, variance reduction property, consistency and +869 benefit from generalisation error bounds). The idea is to replace $\cdot$ with $\pi m$ to simplify the expression. +870 The value $n _ { l }$ converges to $\pi m$ then the following Theorem should hold with the true DeSSL objective. +871 We define the cross-covariance matrice between random vectors $\nabla L ( \theta ; x , y )$ and $\nabla H ( \theta ; x )$ as +872 $-$ . +873 Theorem I.1. Suppose $\cdot$ and $\cdot$ are smooth functions in $\cdot$ . Assume ${ \mathcal { R } } ( \theta )$ admit a second +874 order Taylor expansion at $\theta ^ { * }$ with a non-singular second order derivative $V _ { \theta ^ { * } }$ . Under the MCAR +875 assumption, we have that $\cdot$ is asymptotically normal with covariance: + +$$ +\cdot +$$ + +876 As a consequence, we can minimise the trace of the covariance. Indeed, $\cdot$ reaches its +877 minimum at + +$$ +\lambda _ { o p t } = ( 1 - \pi ) \frac { \mathbf { T r } ( V _ { \theta ^ { * } } ^ { - 1 } K _ { \theta ^ { * } } V _ { \theta ^ { * } } ^ { - 1 } ) } { \mathbf { T r } ( V _ { \theta ^ { * } } ^ { - 1 } \mathbb { E } \left[ \nabla H ( \theta ^ { * } ; x ) \nabla H ( \theta ^ { * } ; x ) ^ { T } \right] V _ { \theta ^ { * } } ^ { - 1 } ) } , +$$ + +878 and at $\lambda _ { o p t }$ : + +$$ +- +$$ + +879 The complete case is the special case of DeSSL with $\cdot$ . Then, the Theorem holds for the +880 complete case. +881 Proof. We define $\begin{array} { r } { L ^ { \prime } ( \theta ; x , y , r ) = \frac { r } { \pi } L ( \theta ; x , y ) + \lambda \left( \frac { 1 - r } { 1 - \pi } - \frac { r } { \pi } \right) H ( \theta ; x ) } \end{array}$ The assumptions of the +882 theorem are sufficient assumptions to apply Theorem 5.23 of Van der Vaart 1998 to the couple +883 $( \hat { \theta } _ { D e S S L } , L ^ { \prime } )$ . Hence, we obtain the following representation for representation $\cdot$ : + +$$ +- +$$ + +884 + +$$ +- +$$ + +885 The asymptotic normality follows with variance: + +$$ +\begin{array} { r } { \Sigma _ { D e S S L } = V _ { \theta ^ { * } } ^ { - 1 } \mathbb { E } \left[ \nabla L ^ { \prime } ( \theta ^ { * } ; x , y ) \nabla L ^ { \prime } ( \theta ^ { * } ; x , y ) ^ { T } \right] V _ { \theta ^ { * } } ^ { - 1 } . } \end{array} +$$ + +886 Using the MCAR assumption, we simplify the expression of $\cdot$ : + +$$ +\cdot +$$ + +887 We remark that the complete case is the particular case of DeSSL with $\cdot$ . Then, + +$$ +\cdot +$$ + +888 The asymptotic relative efficiency of consequence, the asymptotic relative efficiency $\cdot$ com +889 pared to $\hat { \theta } _ { C C }$ is defined as the quotient $\frac { \mathbf { T r } ( \Sigma _ { D e S S L } ) } { \mathbf { T r } ( \Sigma _ { C C } ) }$ . This quotien can be minimised with respect to $\cdot$ : + +$$ +\lambda _ { o p t } = ( 1 - \pi ) \frac { \mathbf { T r } ( V _ { \theta ^ { * } } ^ { - 1 } K _ { \theta ^ { * } } V _ { \theta ^ { * } } ^ { - 1 } ) } { \mathbf { T r } ( V _ { \theta ^ { * } } ^ { - 1 } \mathbb { E } \left[ \nabla H ( \theta ^ { * } ; x ) \nabla H ( \theta ^ { * } ; x ) ^ { T } \right] V _ { \theta ^ { * } } ^ { - 1 } ) } , +$$ + +891 and at $\cdot$ : + +$$ +\frac { \mathbf { T r } \left( \Sigma _ { D e S S L } \right) } { \mathbf { T r } \left( \Sigma _ { C C } \right) } = 1 - \frac { 1 - \pi } { \pi } \frac { \mathbf { T r } ( V _ { \theta ^ { * } } ^ { - 1 } K _ { \theta ^ { * } } V _ { \theta ^ { * } } ^ { - 1 } ) ^ { 2 } } { \mathbf { T r } ( V _ { \theta ^ { * } } ^ { - 1 } \mathbb { E } \left[ \nabla H ( \theta ^ { * } ; x ) \nabla H ( \theta ^ { * } ; x ) ^ { T } \right] V _ { \theta ^ { * } } ^ { - 1 } ) \mathbf { T r } ( \Sigma _ { C C } ) } \le 1 . +$$ + +892 + +893 Remark I.2. On the sign of $\cdot$ It is easy to show that a sufficient condition to have $\lambda _ { o p t } > 0$ is to +894 have $K _ { \theta ^ { * } }$ positive semi-definite. Indeed, using that $V _ { \theta ^ { * } }$ is positive definite and Proposition 6.1 of +895 Serre (2010), we show that $\mathbf { T } \mathbf { r } ( V _ { \theta ^ { * } } ^ { - 1 } K _ { \theta ^ { * } } V _ { \theta ^ { * } } ^ { - 1 } ) > 0$ and then $\lambda _ { o p t } > 0$ . +896 Remark I.3. Why minimising the trace of $\cdot$ Minimising the trace of $\Sigma _ { D e S S L }$ leads to an +897 estimator with a smaller asymptotic MSE, see Chen et al. (2020). + +Remark I.4. Fully supervised setting. We also remark that our theorem matches the theorem for the supervised setting. Indeed, observing all the labelled corresponds to the case $\pi = 1$ and we obtain: + +$$ +\Sigma _ { D e S S L } = \Sigma _ { C C } = \Sigma _ { \mathrm { F u l l y s u p e r v i s e d } } . +$$ + +# 898 J Proof of Theorem 3.6 + +Our proof will be based on the following result from Shalev-Shwartz & Ben-David (2014, Theorem 26.5). + +01 Theorem J.1. Let $\mathcal { H }$ be a set of parameters, $z \sim \mathcal { D }$ a random variable living in a space $\mathcal { Z }$ , $c > 0$ , +02 and $\ell : \mathcal { H } \times \mathcal { Z } \longrightarrow [ - c , c ]$ . We denote + +$$ +L _ { \mathcal { D } } ( h ) = \mathbb { E } _ { z } [ \ell ( h , z ) ] , a n d L _ { \mathcal { S } } ( h ) = \frac { 1 } { m } \sum _ { i = 1 } ^ { m } \ell ( h , z _ { i } ) , +$$ + +903 where $z _ { 1 } , . . . , z _ { m }$ are i.i.d. samples from $\mathcal { D }$ . For any $\delta > 0$ , with probability at least $1 - \delta$ , we have + +$$ +L _ { \mathcal { D } } ( h ) \leq L _ { \mathcal { S } } ( h ) + 2 \mathbb { E } _ { ( \varepsilon _ { i } ) _ { i \leq m } } \left[ \operatorname* { s u p } _ { h \in \mathcal { H } } \left( \frac { 1 } { m } \sum _ { i = 1 } ^ { m } \varepsilon _ { i } \ell ( h , z _ { i } ) \right) \right] + 4 c \sqrt { \frac { 2 \log ( 4 / \delta ) } { m } } , +$$ + +904 where $\varepsilon _ { 1 } , . . . , \varepsilon _ { m }$ are i.i.d. Rademacher variables independent from $z _ { 1 } , . . . , z _ { m }$ + +905 We can now restate and prove our generalisation bound. + +906 Theorem 3.6. We assume that both $L$ and $H$ are bounded and that the labels are MCAR. Then, +907 there exists a constant $\kappa > 0$ , that depends on $\lambda , L , H$ , and the ratio of observed labels, such that, +908 with probability at least $1 - \delta$ , for all $\theta \in \Theta$ , + +$$ +\mathcal { R } ( \theta ) \leq \hat { \mathcal { R } } _ { D e S S L } ( \theta ) + 2 { R _ { n } } + \kappa \sqrt { \frac { \log ( 4 / \delta ) } { n } } , +$$ + +909 where $R _ { n }$ is the Rademacher complexity + +$$ +R _ { n } = \mathbb { E } _ { ( \varepsilon _ { i } ) _ { i \leq n } } \left[ \operatorname* { s u p } _ { \theta \in \Theta } \left( \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \varepsilon _ { i } L ( \theta ; x _ { i } , y _ { i } ) - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } \varepsilon _ { i } H ( \theta ; x _ { i } ) + \frac { \lambda } { n _ { u } } \sum _ { i = 1 } ^ { n _ { u } } \varepsilon _ { i } H ( \theta ; x _ { i } ) \right) \right] , +$$ + +910 with $\varepsilon _ { 1 } , . . . , \varepsilon _ { m }$ i.i.d. Rademacher variables independent from the data. + +911 Proof. We use Theorem J.1 with $z = ( x , y , r )$ , $\mathcal { H } = \Theta$ , $m = n$ , and + +$$ +\ell ( h , z ) = \frac { n r _ { i } } { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) + \lambda \left( \frac { n ( 1 - r _ { i } ) } { n _ { u } } - \frac { n r _ { i } } { n _ { l } } \right) H ( \theta ; x _ { i } ) . +$$ + +912 The unbiasedness of our estimate under the MCAR assumption, proven in Appendix D, ensures that +913 the condition of Equation (41) is satisfied with $L _ { \mathcal { D } } ( h ) = \mathcal { R } ( \theta )$ and $L _ { S } ( h ) = \hat { \mathcal { R } } _ { D e S S L } ( \theta )$ . Now, +914 since $L$ and $H$ are bounded, there exists $M > 0$ such that $| L | < M$ and $| H | < M$ . We can then +915 bound $\ell$ : + +$$ +| \ell ( h , z ) | \leq \frac { n } { n _ { l } } M + \lambda \operatorname* { m a x } \left\{ \frac { n } { n _ { u } } , \frac { n } { n _ { l } } \right\} M = c . +$$ + +916 Now that we have chosen a √ $c$ that bounds $\ell$ , we can use Theorem J.1 and finally get Equation (43) with917 $\kappa = 4 c \sqrt { 2 }$ . □ + +# 918 K DeSSL with $H$ applied on all available data + +919 For consistency-based SSL methods it is common to use all the available data for the consistency +920 term: + +$$ +\hat { \mathcal { R } } _ { S S L } ( \theta ) = \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) +$$ + +921 With the same idea, we debias the risk estimate with the labelled data: + +$$ +\begin{array} { r l r } { { \hat { \mathcal { R } } _ { D e S S L } ( \theta ) = \displaystyle \frac { 1 } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } L ( \theta ; x _ { i } , y _ { i } ) } } \\ & { } & { \ - \frac { \lambda } { n _ { l } } \sum _ { i = 1 } ^ { n _ { l } } H ( \theta ; x _ { i } ) . } \end{array} +$$ + +922 Under MCAR, this risk estimate is unbiased and the main theorem of the article hold with minor +923 modifications. In Theorem 3.1, $\lambda _ { o p t }$ is slightly different and the expression of the variance at $\lambda _ { o p t }$ +924 remains the same. The scoring rule in Theorem 3.2 is different but the theorem remains the same. +925 Both Theorem 3.5 and 3.6 remain the same with very similar proofs. + +Theorem K.1. The function 926 $\lambda \mapsto \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) )$ reaches its minimum for: + +$$ +\lambda _ { o p t } = \frac { \mathrm { C o v } ( L ( \theta ; x , y ) , H ( \theta ; x ) ) } { \mathbb { V } ( H ( \theta ; x ) ) } +$$ + +927 and + +$$ +\begin{array} { c } { { \mathbb { V } ( \hat { \mathcal { R } } _ { D e S S L } ( \theta ) ) | _ { \lambda _ { o p t } } = ( 1 - \frac { n _ { u } } { n } \rho _ { L , H } ^ { 2 } ) \mathbb { V } ( \hat { \mathcal { R } } _ { C C } ( \theta ) ) } } \\ { \leq \mathbb { V } ( \hat { \mathcal { R } } _ { C C } ( \theta ) ) } \end{array} +$$ + +928 where $\rho _ { L , H } = \operatorname { C o r r } ( L ( \theta ; x , y ) , H ( \theta ; x ) ) .$ . + +929 When $H$ is applied on all labelled and unlabelled data, the scoring rule used in the learning process +930 is then $\begin{array} { r } { S ^ { \prime } ( p _ { \theta } , ( x , y , r ) ) = - ( \frac { r n } { n _ { l } } L ( \theta ; x , y ) + \lambda ( 1 - \frac { r n } { n _ { l } } ) H ( \theta ; x ) ) } \end{array}$ and we have $S ^ { \prime }$ is a proper scoring +931 rule. + +![](images/6e6e13621fc7b516129cbc151bd9f558ded966d8ee4292e5e1819431875ba70f.jpg) +Figure 6: The influence of $\lambda$ on Pseudo-label and DePseudo-label for a Lenet trained on MNIST with $n _ { l } = 1 0 0 0$ : (Left) Test accuracy; (Middle) Mean test cross-entropy; (Right) Mean test ECE, with $9 5 \%$ CI + +![](images/678bc11f6d1173ade54db2966b63deb8ed001bbcf3442745a2575dda22607893.jpg) +Figure 7: The influence of $\lambda$ on Pseudo-label and DePseudo-label for a Lenet trained on MNIST with label noise with $n _ { l } = 1 0 0 0$ : (Left) Mean test accuracy; (Middle) Mean test cross-entropy; (Right) Test ECE, with $9 5 \%$ CI. + +Table 3: Test AUC of Complete Case , PseudoLabel and DePseudoLabel on five datasets of MedMNIST. + +
DATASETCOMPLETE CASEPSEUDOLABELDEPSEUDOLABEL
DERMA84.26 ± 0.5082.64 ±1.1983.82 ± 0.95
PNEUMONIA94.28 ±0.4694.34 ± 0.9194.15 ± 0.33
RETINA70.70 ± 0.7470.12 ±1.0169.97 ± 1.44
BREAST74.67 ± 3.6874.86 ±3.1875.33 ± 3.05
BLOOD97.83 ± 0.2397.83 ± 0.2397.72 ± 0.15
+ +![](images/59859faa8fb1cda3c64a7b0957d5af5273ad9afdb67d923641454835359366c4.jpg) +Figure 8: The influence of $\lambda$ on Pseudo-label and DePseudo-label on CIFAR-10 with $\mathrm { n l } { = } 4 0 0 0$ : (Left) Mean test accuracy; (Middle) Mean test cross-entropy; (Right) Test ECE, with $9 5 \%$ CI. + +![](images/6215616a8ca45ff0d81974c3e60dd6e14b3af1b28d8cf03277f38ed6066c622f.jpg) +Figure 9: p-values of a paired student test between PseudoLabel and DePseudoLabel (Right) DePseudoLabel is better than PseudoLabel; (Left) DePseudoLabel is worst than PseudoLabel. + +# 938 M.2 Computation of $\lambda _ { o p t }$ on the test set. + +939 As explained in the main text, the estimation of $\mathrm { C o v } ( L ( \theta ; x , y ) , H ( \theta ; x ) )$ with few labels led to +940 extremely unstable unsatisfactory results. However, we test the formula on CIFAR-10 and different +941 methods to provide intuition on the order of $\cdot$ and the range of the variance reduction regime +942 (between 0 and $\cdot$ ). To do so, we estimate $\cdot$ on the test set for CIFAR-10 by training a CNN13 +943 using only 4, 000 labelled data on 200 epochs. The value of $\lambda _ { o p t }$ is 1.67, 31.16 and 0.66 for entropy +944 minimisation, pseudo label and Fixmatch. Therefore, the reduced variance regime covers the intuitive +945 choices of $\cdot$ in the SSL literature. Unfortunately, computing $\lambda _ { o p t }$ on the test set is not applicable in +946 practice. + +![](images/a090c63876dfb6f81c69d6562549d015578a100859bd9bd7eb604c31c26c06d9.jpg) +Figure 10: The influence of $\lambda$ on Pseudo-label and DePseudo-label on CIFAR-100 with $\mathrm { n l } { = } 4 0 0 0$ : (Left) Mean test accuracy; (Middle) Mean test cross-entropy; (Right) Test ECE, with $9 5 \%$ CI. + +# 948 N Fixmatch (Sohn et al., 2020) + +# N.1 Per class accuracy + +In recent work, Zhu et al. (2022) exposed the disparate effect of SSL on different classes. Indeed, classes with a high complete case accuracy benefit more from SSL than classes with a low baseline accuracy. They introduced a metric called the benefit ratio $( B \mathcal { R } )$ that quantifies the impact of SSL on a class $C$ : + +$$ +B \mathcal { R } ( C ) = \frac { a c c _ { S S L } ( C ) - a c c _ { C C } ( C ) } { a c c _ { S } ( C ) - a c c _ { C C } ( C ) } , +$$ + +954 where $a c c _ { S S L } ( C )$ , $a c c _ { C C } ( C )$ and $a c c _ { S } ( C )$ are respectively the accuracy of the class with an SSL +955 trained model, a complete-case model and a fully supervised model (a model that has access to all +956 labels). Inspired by this work, we report the per class accuracy and the benefit ratio in Table N.1. We +957 see that the “poor” classes such as bird, cat and dog tend to benefit from DeFixmatch much more +958 than from Fixmatch. We compute $a c c _ { S } ( C )$ using a pre-trained model with the same architecture1. +959 Zhu et al. (2022) also promote the idea that a fair SSL algorithm should benefit different sub-classes +960 equally, then having $\bar { B ^ { \mathcal { R } } } ( C ) = B \mathcal { R } ( C ^ { \prime } )$ for all $C$ , $C ^ { \prime }$ . While perfect equality seems unachievable in +961 practice, we propose to look at the standard deviation of the $B \mathcal { R }$ through the different classes. While +962 the standard deviation of Fixmatch is 0.12, the one of DeFixmatch is 0.06. Therefore, DeFixmatch +963 improves the sub-populations’ accuracies more equally. + +Table 4: Mean accuracy per class and mean benefit ratio $( B \mathcal { R } )$ on 5 folds for Fixmatch, DeFixmatch and the Complete Case. Bold: “poor” complete case accuracy classes. + +
COMPLETE CASEFIXMATCHDEFIXMATCH
ACCURACYACCURACYBRACCURACYBR
AIRPLANE86.9495.940.8896.620.94
AUTOMOBILE95.2697.540.6898.220.89
BIRD80.4690.800.6892.640.80
CAT70.0882.500.5687.160.78
DEER88.8895.860.7897.260.94
DOG79.6687.160.5390.980.81
FROG93.1297.840.8098.620.94
HORSE90.9696.940.8397.640.92
SHIP94.1297.260.6798.060.84
TRUCK93.1896.820.8497.200.93
+ +# 964 N.2 Fixmatch details + +As first detailed in Appendix B, Fixmatch is a pseudo-label based method with data augmentation. Indeed, Fixmatch uses weak augmentations of $x$ (flip-and-shift) for the pseudo-labels selection and then minimises the likelihood with the prediction of the model on a strongly augmented version of $x$ . Weak augmentations are also used for the supervised part of the loss. In this context, + +$$ +L ( \theta ; x , y ) = \mathbb { E } _ { x _ { 1 } \sim w e a k ( x ) } [ - \log ( p _ { \theta } ( y | x _ { 1 } ) ) ] +$$ + +and + +$$ +H ( \theta ; x ) = \mathbb { E } _ { x _ { 1 } \sim w e a k ( x ) } \left[ \mathbb { 1 } [ \operatorname* { m a x } _ { y } p _ { \hat { \theta } } ( y | x _ { 1 } ) > \tau ] \mathbb { E } _ { x _ { 2 } \sim s t r o n g ( x ) } [ - \log ( p _ { \theta } ( \arg \operatorname* { m a x } _ { y } p _ { \hat { \theta } } ( y | x _ { 1 } ) | x _ { 2 } ) ) ] \right] +$$ + +965 where $x _ { 1 }$ is a weak augmentation of $x$ and $x _ { 2 }$ is a strong augmentation. We tried to debias an +966 implementation of Fixmatch 1 however training was very unstable and led to model that were much +967 worst than the complete case. We believed that this behaviour is because the supervised part of +968 the loss does not include strong augmentation. Indeed, our theoretical results encourage to have a +969 strong correlation between $L$ and $H$ , therefore including strong augmentations in the supervised term. +970 Moreover, a solid baseline for CIFAR-10 using only labelled data integrated strong augmentations +971 (Cubuk et al., 2020). We modify the implementation, see Code in supplementary materials. Therefore, +972 the supervised loss term can be written as: + +$$ +L ( \theta ; x , y ) = \frac { 1 } { 2 } \left( \mathbb { E } _ { x _ { 1 } \sim w e a k ( x ) } [ - \log ( p _ { \theta } ( y | x _ { 1 } ) ) ] + \mathbb { E } _ { x _ { 2 } \sim s t r o n g ( x ) } [ - \log ( p _ { \theta } ( y | x _ { 2 } ) ) ] \right) , +$$ + +973 where $x _ { 1 }$ is a weak augmentation of $x$ and $x _ { 2 }$ is a strong augmentation. This modification encourages +974 us to choose $\begin{array} { r } { \lambda = \frac { 1 } { 2 } } \end{array}$ as the original Fixmatch implementation used $\lambda = 1$ . We also remark that this +975 modification degrades the performance of Fixmatch (less than $2 \%$ ) reported in the work of Sohn +976 et al. (2020). However, including strong augmentations in the supervised part greatly improves the +977 performance of the Complete Case. + +# 978 O CIFAR and SVHN: Oliver et al. (2018) implementation of 979 consistency-based model. + +980 In this section, we present the results on CIFAR and SVHN by debiasing the implementation of +981 (Oliver et al., 2018) of Π-Model, Mean-Teacher and VAT 2. We mimic the experiments of Oliver et al. +982 (2018, figure-4) with the same configuration and the exact same hyperparameters (Oliver et al., 2018, +983 Appendix B and C). We perform an early stopping independently on both cross-entropy and accuracy. +984 As reported below, we reach almost the same results as the biased methods. + +# 985 O.1 CIFAR-10 + +![](images/710aa7324afc83f4bbe790382b4086a0f2d7cf63ab372c4ce27d99a9d92a5659.jpg) +Figure 11: Test accuracy for each SSL approaches on CIFAR-10 with various amounts of labelled data $n _ { l }$ .(Left) Π-model and DeΠ-model. (Right) VAT $^ +$ EntMin and $\mathrm { V A T + }$ DeEntMin. (Bottom) Mean-teacher and DeMeanteacher. Shadows represent $9 5 \%$ CI. + +![](images/39ad46ebc27a450f1a5114fafb3eb662c2b76e2673a2dce66613898a78f51c0b.jpg) +Figure 12: Test cross-entropy for each SSL approaches on CIFAR-10 with various amounts of labelled data $n _ { l }$ .(Left) $\Pi$ -model and DeΠ-model. (Right) VAT $^ +$ EntMin and VAT $+$ DeEntMin. (Bottom) Mean-teacher and DeMean-teacher. Shadows represent $9 5 \%$ CI. + +![](images/ad5b5fef0eefe2a28be1e9ca1247d3c6bc1cbe8f5989b655a03e20b8eb5f31de.jpg) +Figure 13: Test accuracy for each SSL approaches on CIFAR-10 with various amounts of labelled data $n _ { l }$ .(Left) Π-model and DeΠ-model. (Right) VAT $^ +$ EntMin and VAT $^ { + }$ DeEntMin. (Bottom) Mean-teacher and DeMeanteacher. Shadows represent $9 5 \%$ CI. + +![](images/a32722bff0d0a5c29a32e016ef4e69082d646cb8a94d3224304de4dcb9f4d3d2.jpg) +Figure 14: Test cross-entropy for each SSL approaches on CIFAR-10 with various amounts of labelled data $n _ { l }$ .(Left) Π-model and DeΠ-model. (Right) VAT $^ +$ EntMin and VAT $^ +$ DeEntMin. (Bottom) Mean-teacher and DeMean-teacher. Shadows represent $9 5 \%$ CI. + +# 987 P Tabular benchmarks + +988 In this section, we tested these methods against the benchmarks of Chapelle et al., 2006, Chapter +989 21 and UCI datasets already used in an SSL context in (Guo et al., 2010). We trained a logistic +990 regression for the case of 100 labelled datapoints and finetune $\lambda$ with a very small validation set, 20 +991 datapoints. We evaluated the performance in accuracy and cross-entropy of PseudoLabel, EntMin, +992 DePseudoLabel and DeEntMin + +![](images/e554521232c526337f20359b95431041644d7ec2fe2ef4ea8aca65105d0c4e34.jpg) +Figure 15: Mean accuracy and cross-entropy for each SSL datasets (Chapelle et al., 2006) on a logistic regression. (Top-Left) PseudoLabel and DePseudoLabel accuracy (Top-Right) PseudoLabel and DePseudoLabel cross-entropy (Bottom-Left) EntMin and DeEntMin accuracy (Bottom-Right) EntMin and DeEntMin crossentropy. + +![](images/8e36e4fd7d606f024339c7da0270892946ce8e1c0e3a2d6183225b7356a17e56.jpg) +Figure 16: Mean accuracy and cross-entropy for each UCI datasets (Guo et al., 2010) on a logistic regression. (Top-Left) PseudoLabel and DePseudoLabel accuracy (Top-Right) PseudoLabel and DePseudoLabel crossentropy (Bottom-Left) EntMin and DeEntMin accuracy (Bottom-Right) EntMin and DeEntMin cross-entropy. + +# Q Computation details + +# Q.1 Computation resources + +Deep Learning experiments of this work required approximately 9,200 hours of GPU computation. In particular, Fixmatch was trained using 4 GPUs. Here are the details: + +• MNIST : 300 hours +• medMNIST: 3 hours +• CIFAR-10: 525 hours +• CIFAR-100: 1500 hours +• Fixmatch : 960 hours +• Realistic SSL evaluation on both CIFAR and SVHN: 5880 hours + +# Q.2 Computation libraries and tools + +• Python (Van Rossum & Drake Jr, 1995) +• PyTorch (Paszke et al., 2019) +• TensorFlow (Abadi et al., 2015) +• Scikit-learn (Pedregosa et al., 2011) +• Seaborn (Waskom et al., 2017) +• Python imaging library (Lundh et al., 2012) +• Numpy (Harris et al., 2020) +• Pandas (McKinney et al., 2010) +• RandAugment (Cubuk et al., 2020) +• Fixmatch-Pytorch 3 +• Realistic-SSL-evaluation (Oliver et al., 2018) \ No newline at end of file diff --git a/parse/dev/D87gRf2-np/D87gRf2-np_middle.json b/parse/dev/D87gRf2-np/D87gRf2-np_middle.json new file mode 100644 index 0000000000000000000000000000000000000000..dc005278c313c1950a199010d51c572dbfacb5ef --- /dev/null +++ b/parse/dev/D87gRf2-np/D87gRf2-np_middle.json @@ -0,0 +1,111212 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 118, + 97, + 493, + 137 + ], + "lines": [ + { + "bbox": [ + 210, + 98, + 404, + 115 + ], + "spans": [ + { + "bbox": [ + 210, + 98, + 404, + 115 + ], + "score": 1.0, + "content": "Don’t fear the unlabelled:", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 117, + 115, + 494, + 140 + ], + "spans": [ + { + "bbox": [ + 117, + 115, + 494, + 140 + ], + "score": 1.0, + "content": "Safe semi-supervised learning via simple debiasing", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 259, + 179, + 355, + 223 + ], + "lines": [ + { + "bbox": [ + 258, + 179, + 355, + 191 + ], + "spans": [ + { + "bbox": [ + 258, + 179, + 355, + 191 + ], + "score": 1.0, + "content": "Anonymous Author(s)", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 283, + 189, + 328, + 202 + ], + "spans": [ + { + "bbox": [ + 283, + 189, + 328, + 202 + ], + "score": 1.0, + "content": "Affiliation", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 286, + 200, + 324, + 213 + ], + "spans": [ + { + "bbox": [ + 286, + 200, + 324, + 213 + ], + "score": 1.0, + "content": "Address", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 290, + 213, + 320, + 222 + ], + "spans": [ + { + "bbox": [ + 290, + 213, + 320, + 222 + ], + "score": 1.0, + "content": "email", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3.5 + }, + { + "type": "title", + "bbox": [ + 283, + 252, + 328, + 265 + ], + "lines": [ + { + "bbox": [ + 281, + 251, + 331, + 267 + ], + "spans": [ + { + "bbox": [ + 281, + 251, + 331, + 267 + ], + "score": 1.0, + "content": "Abstract", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 91, + 277, + 469, + 452 + ], + "lines": [ + { + "bbox": [ + 93, + 278, + 470, + 290 + ], + "spans": [ + { + "bbox": [ + 93, + 281, + 99, + 289 + ], + "score": 1.0, + "content": "1", + "type": "text" + }, + { + "bbox": [ + 142, + 278, + 470, + 290 + ], + "score": 1.0, + "content": "Semi-supervised learning (SSL) provides an effective means of leveraging un-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 289, + 470, + 301 + ], + "spans": [ + { + "bbox": [ + 93, + 291, + 99, + 300 + ], + "score": 1.0, + "content": "2", + "type": "text" + }, + { + "bbox": [ + 141, + 289, + 470, + 301 + ], + "score": 1.0, + "content": "labelled data to improve a model’s performance. 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Additionally,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 89, + 441, + 467, + 455 + ], + "spans": [ + { + "bbox": [ + 89, + 443, + 100, + 453 + ], + "score": 1.0, + "content": "16", + "type": "text" + }, + { + "bbox": [ + 142, + 441, + 467, + 455 + ], + "score": 1.0, + "content": "we provide a theoretical explanation of the intuition of the popular SSL methods.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 14.5 + }, + { + "type": "title", + "bbox": [ + 91, + 474, + 190, + 488 + ], + "lines": [ + { + "bbox": [ + 87, + 473, + 192, + 490 + ], + "spans": [ + { + "bbox": [ + 87, + 473, + 192, + 490 + ], + "score": 1.0, + "content": "17 1 Introduction", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 89, + 500, + 505, + 620 + ], + "lines": [ + { + "bbox": [ + 90, + 500, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 90, + 502, + 99, + 511 + ], + "score": 1.0, + "content": "18", + "type": "text" + }, + { + "bbox": [ + 106, + 500, + 505, + 512 + ], + "score": 1.0, + "content": "The promise of semi-supervised learning (SSL) is to be able to learn powerful predictive models", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 89, + 510, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 89, + 512, + 99, + 523 + ], + "score": 1.0, + "content": "19", + "type": "text" + }, + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "score": 1.0, + "content": "using partially labelled data. In turn, this would allow machine learning to be less dependent on", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 89, + 521, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 89, + 524, + 99, + 534 + ], + "score": 1.0, + "content": "20", + "type": "text" + }, + { + "bbox": [ + 105, + 521, + 506, + 535 + ], + "score": 1.0, + "content": "the often costly and sometimes dangerously biased task of labelling data. Early SSL approaches—", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 88, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 88, + 534, + 99, + 545 + ], + "score": 1.0, + "content": "21", + "type": "text" + }, + { + "bbox": [ + 104, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "e.g. Scudder’s (1965) untaught pattern recognition machine—simply replaced unknown labels with", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 88, + 543, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 88, + 545, + 100, + 556 + ], + "score": 1.0, + "content": "22", + "type": "text" + }, + { + "bbox": [ + 105, + 543, + 506, + 556 + ], + "score": 1.0, + "content": "predictions made by some estimate of the predictive model and used the obtained pseudo-labels to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 88, + 553, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 88, + 556, + 99, + 567 + ], + "score": 1.0, + "content": "23", + "type": "text" + }, + { + "bbox": [ + 104, + 553, + 506, + 568 + ], + "score": 1.0, + "content": "refine their initial estimate. Other more complex branches of SSL have been explored since, notably", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 88, + 564, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 88, + 567, + 100, + 578 + ], + "score": 1.0, + "content": "24", + "type": "text" + }, + { + "bbox": [ + 104, + 564, + 506, + 580 + ], + "score": 1.0, + "content": "using generative models (from McLachlan, 1977, to Kingma et al., 2014) or graphs (notably following", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 88, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 88, + 578, + 99, + 588 + ], + "score": 1.0, + "content": "25", + "type": "text" + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "Zhu et al., 2003). Deep neural networks, which are state-of-the art supervised predictors, have been", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 88, + 587, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 88, + 589, + 99, + 599 + ], + "score": 1.0, + "content": "26", + "type": "text" + }, + { + "bbox": [ + 106, + 587, + 505, + 599 + ], + "score": 1.0, + "content": "trained successfully using SSL. Somewhat surprisingly, the main ingredient of their success is still the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 89, + 598, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 89, + 600, + 100, + 610 + ], + "score": 1.0, + "content": "27", + "type": "text" + }, + { + "bbox": [ + 106, + 598, + 505, + 610 + ], + "score": 1.0, + "content": "notion of pseudo-labels (or one of its variants), combined with systematic use of data augmentation", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 89, + 609, + 343, + 621 + ], + "spans": [ + { + "bbox": [ + 89, + 611, + 100, + 620 + ], + "score": 1.0, + "content": "28", + "type": "text" + }, + { + "bbox": [ + 105, + 609, + 343, + 621 + ], + "score": 1.0, + "content": "(e.g. Xie et al., 2019; Sohn et al., 2020; Rizve et al., 2021).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 90, + 625, + 505, + 713 + ], + "lines": [ + { + "bbox": [ + 89, + 626, + 505, + 638 + ], + "spans": [ + { + "bbox": [ + 89, + 627, + 100, + 637 + ], + "score": 1.0, + "content": "29", + "type": "text" + }, + { + "bbox": [ + 105, + 626, + 505, + 638 + ], + "score": 1.0, + "content": "An obvious SSL baseline is simply throwing away the unlabelled data. We will call such a baseline the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 89, + 636, + 506, + 649 + ], + "spans": [ + { + "bbox": [ + 89, + 638, + 100, + 648 + ], + "score": 1.0, + "content": "30", + "type": "text" + }, + { + "bbox": [ + 104, + 636, + 506, + 649 + ], + "score": 1.0, + "content": "complete case, following the missing data literature (e.g. Tsiatis, 2006). 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Indeed, semi-supervised learning outperforms the complete case baseline only in specific cases", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 89, + 669, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 89, + 671, + 100, + 681 + ], + "score": 1.0, + "content": "33", + "type": "text" + }, + { + "bbox": [ + 105, + 669, + 506, + 682 + ], + "score": 1.0, + "content": "(Singh et al., 2008; Schölkopf et al., 2012; Li & Zhou, 2014). This degradation risk for generative", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 89, + 679, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 89, + 682, + 100, + 691 + ], + "score": 1.0, + "content": "34", + "type": "text" + }, + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "score": 1.0, + "content": "models has been analysed in Chapelle et al. (2006, Chapter 4). 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Do not distribute.", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 118, + 97, + 493, + 137 + ], + "lines": [ + { + "bbox": [ + 210, + 98, + 404, + 115 + ], + "spans": [ + { + "bbox": [ + 210, + 98, + 404, + 115 + ], + "score": 1.0, + "content": "Don’t fear the unlabelled:", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 117, + 115, + 494, + 140 + ], + "spans": [ + { + "bbox": [ + 117, + 115, + 494, + 140 + ], + "score": 1.0, + "content": "Safe semi-supervised learning via simple debiasing", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "list", + "bbox": [ + 259, + 179, + 355, + 223 + ], + "lines": [ + { + "bbox": [ + 258, + 179, + 355, + 191 + ], + "spans": [ + { + "bbox": [ + 258, + 179, + 355, + 191 + ], + "score": 1.0, + "content": "Anonymous Author(s)", + "type": "text" + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 283, + 189, + 328, + 202 + ], + "spans": [ + { + "bbox": [ + 283, + 189, + 328, + 202 + ], + "score": 1.0, + "content": "Affiliation", + "type": "text" + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 286, + 200, + 324, + 213 + ], + "spans": [ + { + "bbox": [ + 286, + 200, + 324, + 213 + ], + "score": 1.0, + "content": "Address", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 290, + 213, + 320, + 222 + ], + "spans": [ + { + "bbox": [ + 290, + 213, + 320, + 222 + ], + "score": 1.0, + "content": "email", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + } + ], + "index": 3.5, + "bbox_fs": [ + 258, + 179, + 355, + 222 + ] + }, + { + "type": "title", + "bbox": [ + 283, + 252, + 328, + 265 + ], + "lines": [ + { + "bbox": [ + 281, + 251, + 331, + 267 + ], + "spans": [ + { + "bbox": [ + 281, + 251, + 331, + 267 + ], + "score": 1.0, + "content": "Abstract", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "index", + "bbox": [ + 91, + 277, + 469, + 452 + ], + "lines": [ + { + "bbox": [ + 93, + 278, + 470, + 290 + ], + "spans": [ + { + "bbox": [ + 93, + 281, + 99, + 289 + ], + "score": 1.0, + "content": "1", + "type": "text" + }, + { + "bbox": [ + 142, + 278, + 470, + 290 + ], + "score": 1.0, + "content": "Semi-supervised learning (SSL) provides an effective means of leveraging un-", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 93, + 289, + 470, + 301 + ], + "spans": [ + { + "bbox": [ + 93, + 291, + 99, + 300 + ], + "score": 1.0, + "content": "2", + "type": "text" + }, + { + "bbox": [ + 141, + 289, + 470, + 301 + ], + "score": 1.0, + "content": "labelled data to improve a model’s performance. Even though the domain has", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 92, + 299, + 470, + 312 + ], + "spans": [ + { + "bbox": [ + 92, + 301, + 100, + 311 + ], + "score": 1.0, + "content": "3", + "type": "text" + }, + { + "bbox": [ + 141, + 299, + 470, + 312 + ], + "score": 1.0, + "content": "received a considerable amount of attention in the past years, most methods present", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 93, + 310, + 470, + 323 + ], + "spans": [ + { + "bbox": [ + 93, + 313, + 99, + 321 + ], + "score": 1.0, + "content": "4", + "type": "text" + }, + { + "bbox": [ + 141, + 310, + 470, + 323 + ], + "score": 1.0, + "content": "the common drawback of lacking theoretical guarantees. 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This bias impedes the use of standard statistical", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 92, + 343, + 470, + 356 + ], + "spans": [ + { + "bbox": [ + 92, + 345, + 100, + 355 + ], + "score": 1.0, + "content": "7", + "type": "text" + }, + { + "bbox": [ + 141, + 343, + 470, + 356 + ], + "score": 1.0, + "content": "learning theory and can hurt empirical performance. We propose a simple way of", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 92, + 353, + 470, + 367 + ], + "spans": [ + { + "bbox": [ + 92, + 356, + 100, + 366 + ], + "score": 1.0, + "content": "8", + "type": "text" + }, + { + "bbox": [ + 141, + 353, + 470, + 367 + ], + "score": 1.0, + "content": "removing the bias. Our debiasing approach is straightforward to implement and", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 92, + 365, + 470, + 378 + ], + "spans": [ + { + "bbox": [ + 92, + 367, + 99, + 376 + ], + "score": 1.0, + "content": "9", + "type": "text" + }, + { + "bbox": [ + 141, + 365, + 470, + 378 + ], + "score": 1.0, + "content": "applicable to most deep SSL methods. We provide simple theoretical guarantees on", + "type": "text" + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 90, + 374, + 470, + 390 + ], + "spans": [ + { + "bbox": [ + 90, + 379, + 99, + 388 + ], + "score": 1.0, + "content": "10", + "type": "text" + }, + { + "bbox": [ + 141, + 374, + 470, + 390 + ], + "score": 1.0, + "content": "the trustworthiness of these modified methods, without having to rely on the strong", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + }, + { + "bbox": [ + 90, + 387, + 471, + 400 + ], + "spans": [ + { + "bbox": [ + 90, + 389, + 99, + 398 + ], + "score": 1.0, + "content": "11", + "type": "text" + }, + { + "bbox": [ + 142, + 387, + 471, + 400 + ], + "score": 1.0, + "content": "assumptions on the data distribution that SSL theory usually requires. 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In turn, this would allow machine learning to be less dependent on", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 521, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 89, + 524, + 99, + 534 + ], + "score": 1.0, + "content": "20", + "type": "text" + }, + { + "bbox": [ + 105, + 521, + 506, + 535 + ], + "score": 1.0, + "content": "the often costly and sometimes dangerously biased task of labelling data. Early SSL approaches—", + "type": "text" + } + ], + "index": 26, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 88, + 534, + 99, + 545 + ], + "score": 1.0, + "content": "21", + "type": "text" + }, + { + "bbox": [ + 104, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "e.g. Scudder’s (1965) untaught pattern recognition machine—simply replaced unknown labels with", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 543, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 88, + 545, + 100, + 556 + ], + "score": 1.0, + "content": "22", + "type": "text" + }, + { + "bbox": [ + 105, + 543, + 506, + 556 + ], + "score": 1.0, + "content": "predictions made by some estimate of the predictive model and used the obtained pseudo-labels to", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 553, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 88, + 556, + 99, + 567 + ], + "score": 1.0, + "content": "23", + "type": "text" + }, + { + "bbox": [ + 104, + 553, + 506, + 568 + ], + "score": 1.0, + "content": "refine their initial estimate. Other more complex branches of SSL have been explored since, notably", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 564, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 88, + 567, + 100, + 578 + ], + "score": 1.0, + "content": "24", + "type": "text" + }, + { + "bbox": [ + 104, + 564, + 506, + 580 + ], + "score": 1.0, + "content": "using generative models (from McLachlan, 1977, to Kingma et al., 2014) or graphs (notably following", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 88, + 578, + 99, + 588 + ], + "score": 1.0, + "content": "25", + "type": "text" + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "Zhu et al., 2003). Deep neural networks, which are state-of-the art supervised predictors, have been", + "type": "text" + } + ], + "index": 31, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 587, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 88, + 589, + 99, + 599 + ], + "score": 1.0, + "content": "26", + "type": "text" + }, + { + "bbox": [ + 106, + 587, + 505, + 599 + ], + "score": 1.0, + "content": "trained successfully using SSL. Somewhat surprisingly, the main ingredient of their success is still the", + "type": "text" + } + ], + "index": 32, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 598, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 89, + 600, + 100, + 610 + ], + "score": 1.0, + "content": "27", + "type": "text" + }, + { + "bbox": [ + 106, + 598, + 505, + 610 + ], + "score": 1.0, + "content": "notion of pseudo-labels (or one of its variants), combined with systematic use of data augmentation", + "type": "text" + } + ], + "index": 33, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 609, + 343, + 621 + ], + "spans": [ + { + "bbox": [ + 89, + 611, + 100, + 620 + ], + "score": 1.0, + "content": "28", + "type": "text" + }, + { + "bbox": [ + 105, + 609, + 343, + 621 + ], + "score": 1.0, + "content": "(e.g. Xie et al., 2019; Sohn et al., 2020; Rizve et al., 2021).", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 626, + 505, + 638 + ], + "spans": [ + { + "bbox": [ + 89, + 627, + 100, + 637 + ], + "score": 1.0, + "content": "29", + "type": "text" + }, + { + "bbox": [ + 105, + 626, + 505, + 638 + ], + "score": 1.0, + "content": "An obvious SSL baseline is simply throwing away the unlabelled data. We will call such a baseline the", + "type": "text" + } + ], + "index": 35, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 636, + 506, + 649 + ], + "spans": [ + { + "bbox": [ + 89, + 638, + 100, + 648 + ], + "score": 1.0, + "content": "30", + "type": "text" + }, + { + "bbox": [ + 104, + 636, + 506, + 649 + ], + "score": 1.0, + "content": "complete case, following the missing data literature (e.g. Tsiatis, 2006). As reported in van Engelen &", + "type": "text" + } + ], + "index": 36, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 88, + 649, + 99, + 659 + ], + "score": 1.0, + "content": "31", + "type": "text" + }, + { + "bbox": [ + 104, + 646, + 506, + 659 + ], + "score": 1.0, + "content": "Hoos (2020), the main risk of SSL is the potential degradation caused by the introduction of unlabelled", + "type": "text" + } + ], + "index": 37, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 657, + 506, + 672 + ], + "spans": [ + { + "bbox": [ + 88, + 659, + 100, + 671 + ], + "score": 1.0, + "content": "32", + "type": "text" + }, + { + "bbox": [ + 104, + 657, + 506, + 672 + ], + "score": 1.0, + "content": "data. Indeed, semi-supervised learning outperforms the complete case baseline only in specific cases", + "type": "text" + } + ], + "index": 38, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 669, + 506, + 682 + ], + "spans": [ + { + "bbox": [ + 89, + 671, + 100, + 681 + ], + "score": 1.0, + "content": "33", + "type": "text" + }, + { + "bbox": [ + 105, + 669, + 506, + 682 + ], + "score": 1.0, + "content": "(Singh et al., 2008; Schölkopf et al., 2012; Li & Zhou, 2014). This degradation risk for generative", + "type": "text" + } + ], + "index": 39, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 679, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 89, + 682, + 100, + 691 + ], + "score": 1.0, + "content": "34", + "type": "text" + }, + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "score": 1.0, + "content": "models has been analysed in Chapelle et al. (2006, Chapter 4). To overcome this issue, previous works", + "type": "text" + } + ], + "index": 40, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 690, + 506, + 703 + ], + "spans": [ + { + "bbox": [ + 89, + 692, + 100, + 703 + ], + "score": 1.0, + "content": "35", + "type": "text" + }, + { + "bbox": [ + 105, + 690, + 506, + 703 + ], + "score": 1.0, + "content": "introduced the notion of safe semi-supervised learning for techniques which never reduce predictive", + "type": "text" + } + ], + "index": 41, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 702, + 505, + 714 + ], + "spans": [ + { + "bbox": [ + 89, + 704, + 100, + 713 + ], + "score": 1.0, + "content": "36", + "type": "text" + }, + { + "bbox": [ + 106, + 702, + 505, + 714 + ], + "score": 1.0, + "content": "performance by introducing unlabelled data (Li & Zhou, 2014; Guo et al., 2020). Our loose definition", + "type": "text" + } + ], + "index": 42, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 73, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 89, + 74, + 99, + 84 + ], + "score": 1.0, + "content": "37", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "of safeness is as follows: an SSL algorithm is safe if it has theoretical guarantees that are similar", + "type": "text", + "cross_page": true + } + ], + "index": 0, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 88, + 85, + 100, + 96 + ], + "score": 1.0, + "content": "38", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 104, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "or stronger to the complete case baseline. The “theoretical” part of the definition is motivated by the", + "type": "text", + "cross_page": true + } + ], + "index": 1, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 94, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 88, + 96, + 99, + 106 + ], + "score": 1.0, + "content": "39", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "score": 1.0, + "content": "fact that any empirical assessment of generalisation performances of an SSL algorithm is jeopardised", + "type": "text", + "cross_page": true + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 105, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 88, + 108, + 99, + 117 + ], + "score": 1.0, + "content": "40", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 105, + 506, + 119 + ], + "score": 1.0, + "content": "by the scarcity of labels. Unfortunately, popular deep SSL techniques generally do not benefit from", + "type": "text", + "cross_page": true + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 117, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 88, + 118, + 99, + 128 + ], + "score": 1.0, + "content": "41", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 117, + 505, + 129 + ], + "score": 1.0, + "content": "theoretical guarantees without strong and essentially untestable assumptions on the data distribution", + "type": "text", + "cross_page": true + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 127, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 88, + 129, + 99, + 139 + ], + "score": 1.0, + "content": "42", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 127, + 470, + 141 + ], + "score": 1.0, + "content": "(Mey & Loog, 2019) such as the smoothness assumption (small perturbations on the features", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 470, + 129, + 477, + 137 + ], + "score": 0.7, + "content": "x", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 477, + 127, + 506, + 141 + ], + "score": 1.0, + "content": "do not", + "type": "text", + "cross_page": true + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 137, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 88, + 140, + 99, + 150 + ], + "score": 1.0, + "content": "43", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 137, + 258, + 151 + ], + "score": 1.0, + "content": "cause large modification in the labels,", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 259, + 138, + 352, + 150 + ], + "score": 0.92, + "content": "p ( y | p e r t ( x ) ) \\tilde { } \\approx p ( y | x ) )", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 353, + 137, + 505, + 151 + ], + "score": 1.0, + "content": "or the cluster assumption (data points", + "type": "text", + "cross_page": true + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 149, + 504, + 161 + ], + "spans": [ + { + "bbox": [ + 89, + 151, + 100, + 160 + ], + "score": 1.0, + "content": "44", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 149, + 504, + 161 + ], + "score": 1.0, + "content": "are distributed on discrete clusters and points in the same cluster are likely to share the same label).", + "type": "text", + "cross_page": true + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 90, + 165, + 298, + 177 + ], + "spans": [ + { + "bbox": [ + 90, + 168, + 99, + 176 + ], + "score": 1.0, + "content": "45", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 165, + 298, + 177 + ], + "score": 1.0, + "content": "Most semi-supervised methods rely on these dis-", + "type": "text", + "cross_page": true + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 176, + 297, + 188 + ], + "spans": [ + { + "bbox": [ + 89, + 179, + 99, + 187 + ], + "score": 1.0, + "content": "46", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 176, + 297, + 188 + ], + "score": 1.0, + "content": "tributional assumptions to ensure performance", + "type": "text", + "cross_page": true + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 187, + 298, + 199 + ], + "spans": [ + { + "bbox": [ + 89, + 190, + 99, + 199 + ], + "score": 1.0, + "content": "47", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 187, + 298, + 199 + ], + "score": 1.0, + "content": "in entropy minimisation, pseudo-labelling and", + "type": "text", + "cross_page": true + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 198, + 298, + 210 + ], + "spans": [ + { + "bbox": [ + 89, + 201, + 99, + 209 + ], + "score": 1.0, + "content": "48", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 198, + 298, + 210 + ], + "score": 1.0, + "content": "consistency-based methods. However, no proof", + "type": "text", + "cross_page": true + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 209, + 299, + 221 + ], + "spans": [ + { + "bbox": [ + 89, + 211, + 100, + 221 + ], + "score": 1.0, + "content": "49", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 209, + 299, + 221 + ], + "score": 1.0, + "content": "is given that guarantees the effectiveness of state-", + "type": "text", + "cross_page": true + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 220, + 298, + 232 + ], + "spans": [ + { + "bbox": [ + 89, + 222, + 99, + 231 + ], + "score": 1.0, + "content": "50", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 220, + 298, + 232 + ], + "score": 1.0, + "content": "of-the-art methods (Tarvainen & Valpola, 2017;", + "type": "text", + "cross_page": true + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 230, + 298, + 243 + ], + "spans": [ + { + "bbox": [ + 89, + 233, + 99, + 242 + ], + "score": 1.0, + "content": "51", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 230, + 298, + 243 + ], + "score": 1.0, + "content": "Miyato et al., 2018; Sohn et al., 2020; Pham", + "type": "text", + "cross_page": true + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 241, + 298, + 254 + ], + "spans": [ + { + "bbox": [ + 88, + 244, + 100, + 254 + ], + "score": 1.0, + "content": "52", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 241, + 298, + 254 + ], + "score": 1.0, + "content": "et al., 2021). To illustrate that SSL requires spe-", + "type": "text", + "cross_page": true + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 253, + 298, + 264 + ], + "spans": [ + { + "bbox": [ + 89, + 255, + 99, + 264 + ], + "score": 1.0, + "content": "53", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 253, + 298, + 264 + ], + "score": 1.0, + "content": "cific assumptions, we show in a toy example that", + "type": "text", + "cross_page": true + } + ], + "index": 16, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 264, + 298, + 276 + ], + "spans": [ + { + "bbox": [ + 88, + 266, + 100, + 276 + ], + "score": 1.0, + "content": "54", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 264, + 298, + 276 + ], + "score": 1.0, + "content": "pseudo-labelling fails at learning. To do so, we", + "type": "text", + "cross_page": true + } + ], + "index": 17, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 275, + 298, + 286 + ], + "spans": [ + { + "bbox": [ + 88, + 276, + 100, + 286 + ], + "score": 1.0, + "content": "55", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 275, + 298, + 286 + ], + "score": 1.0, + "content": "draw samples from two uniform distributions", + "type": "text", + "cross_page": true + } + ], + "index": 18, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 286, + 298, + 297 + ], + "spans": [ + { + "bbox": [ + 88, + 288, + 100, + 297 + ], + "score": 1.0, + "content": "56", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 286, + 298, + 297 + ], + "score": 1.0, + "content": "with a small overlap. 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This", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 86, + 255, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 86, + 256, + 100, + 267 + ], + "score": 1.0, + "content": "102", + "type": "text" + }, + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "score": 1.0, + "content": "is the case when nor features nor label carry information about the potential missingness of the labels.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 86, + 264, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 86, + 267, + 100, + 278 + ], + "score": 1.0, + "content": "103", + "type": "text" + }, + { + "bbox": [ + 105, + 264, + 506, + 279 + ], + "score": 1.0, + "content": "This description of semi-supervised learning as a missing data problem has already been done in", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 86, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 86, + 279, + 99, + 288 + ], + "score": 1.0, + "content": "104", + "type": "text" + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "multiple works –e.g. Seeger, 2000; Ahfock & McLachlan, 2019. Moreover, the MCAR assumption", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 86, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 86, + 289, + 100, + 300 + ], + "score": 1.0, + "content": "105", + "type": "text" + }, + { + "bbox": [ + 105, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "is implicitly made in most of the SSL works to design the experiments, indeed, missing labels are", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 86, + 297, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 86, + 300, + 99, + 309 + ], + "score": 1.0, + "content": "106", + "type": "text" + }, + { + "bbox": [ + 105, + 297, + 506, + 312 + ], + "score": 1.0, + "content": "drawn completely as random in datasets such as MNIST, CIFAR or SVHN (Tarvainen & Valpola,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 86, + 309, + 354, + 322 + ], + "spans": [ + { + "bbox": [ + 86, + 312, + 99, + 321 + ], + "score": 1.0, + "content": "107", + "type": "text" + }, + { + "bbox": [ + 105, + 309, + 354, + 322 + ], + "score": 1.0, + "content": "2017; Miyato et al., 2018; Xie et al., 2019; Sohn et al., 2020).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 14 + }, + { + "type": "title", + "bbox": [ + 102, + 332, + 352, + 343 + ], + "lines": [ + { + "bbox": [ + 105, + 330, + 354, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 354, + 347 + ], + "score": 1.0, + "content": "2.2.1 Complete case: throwing the unlabelled data away", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 86, + 351, + 506, + 428 + ], + "lines": [ + { + "bbox": [ + 86, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 86, + 353, + 99, + 362 + ], + "score": 1.0, + "content": "109", + "type": "text" + }, + { + "bbox": [ + 105, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "In missing data theory, the complete case is the learning scheme that only uses fully observed", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 86, + 361, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 86, + 363, + 100, + 373 + ], + "score": 1.0, + "content": "110", + "type": "text" + }, + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "score": 1.0, + "content": "instances, namely labelled data. The natural estimator of the risk is then simply the empirical risk", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 86, + 372, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 86, + 375, + 99, + 384 + ], + "score": 1.0, + "content": "111", + "type": "text" + }, + { + "bbox": [ + 105, + 372, + 506, + 385 + ], + "score": 1.0, + "content": "computed on the labelled data. Fortunately, in the MCAR setting, the complete case risk estimate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 86, + 382, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 86, + 385, + 100, + 396 + ], + "score": 1.0, + "content": "112", + "type": "text" + }, + { + "bbox": [ + 105, + 382, + 506, + 397 + ], + "score": 1.0, + "content": "keeps the same good properties of the traditional supervised one: it is unbiased and converges", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 86, + 393, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 86, + 396, + 100, + 407 + ], + "score": 1.0, + "content": "113", + "type": "text" + }, + { + "bbox": [ + 105, + 393, + 164, + 407 + ], + "score": 1.0, + "content": "pointwisely to", + "type": "text" + }, + { + "bbox": [ + 165, + 394, + 187, + 406 + ], + "score": 0.92, + "content": "\\mathcal { R } \\bar { ( \\theta ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 393, + 506, + 407 + ], + "score": 1.0, + "content": ". Therefore, traditional learning theory holds for the complete case under MCAR.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 86, + 404, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 86, + 407, + 100, + 417 + ], + "score": 1.0, + "content": "114", + "type": "text" + }, + { + "bbox": [ + 105, + 404, + 506, + 419 + ], + "score": 1.0, + "content": "While these observations are hardly new (see e.g. Liu & Goldberg, 2020), they can be seen as", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 86, + 416, + 414, + 429 + ], + "spans": [ + { + "bbox": [ + 86, + 418, + 100, + 428 + ], + "score": 1.0, + "content": "115", + "type": "text" + }, + { + "bbox": [ + 105, + 416, + 414, + 429 + ], + "score": 1.0, + "content": "particular cases of the theory that we develop below. The risk to minimise is", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24 + }, + { + "type": "interline_equation", + "bbox": [ + 242, + 440, + 369, + 473 + ], + "lines": [ + { + "bbox": [ + 242, + 440, + 369, + 473 + ], + "spans": [ + { + "bbox": [ + 242, + 440, + 369, + 473 + ], + "score": 0.95, + "content": "\\hat { \\mathcal { R } } _ { C C } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) .", + "type": "interline_equation", + "image_path": "2e52c5584ec566d562b489563fab85e8bb1e8962e9213b8da9052b319e251df9.jpg" + } + ] + } + ], + "index": 28.5, + "virtual_lines": [ + { + "bbox": [ + 242, + 440, + 369, + 456.5 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 242, + 456.5, + 369, + 473.0 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "title", + "bbox": [ + 93, + 482, + 266, + 494 + ], + "lines": [ + { + "bbox": [ + 90, + 480, + 268, + 496 + ], + "spans": [ + { + "bbox": [ + 90, + 480, + 268, + 496 + ], + "score": 1.0, + "content": "16 2.2.2 Incorporating unlabelled data", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 87, + 501, + 506, + 547 + ], + "lines": [ + { + "bbox": [ + 86, + 501, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 86, + 502, + 100, + 514 + ], + "score": 1.0, + "content": "117", + "type": "text" + }, + { + "bbox": [ + 105, + 501, + 506, + 514 + ], + "score": 1.0, + "content": "A major drawback of the complete case framework is that a lot of data ends up not being exploited. A", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 86, + 511, + 506, + 525 + ], + "spans": [ + { + "bbox": [ + 86, + 513, + 100, + 524 + ], + "score": 1.0, + "content": "118", + "type": "text" + }, + { + "bbox": [ + 105, + 511, + 506, + 525 + ], + "score": 1.0, + "content": "class of SSL approaches, mainly inductive methods with respect to the taxonomy of van Engelen &", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 86, + 523, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 86, + 525, + 100, + 535 + ], + "score": 1.0, + "content": "119", + "type": "text" + }, + { + "bbox": [ + 106, + 523, + 506, + 536 + ], + "score": 1.0, + "content": "Hoos (2020), generally aim to minimise a modified estimator of the risk by including unlabelled data.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 86, + 535, + 484, + 549 + ], + "spans": [ + { + "bbox": [ + 86, + 538, + 100, + 547 + ], + "score": 1.0, + "content": "120", + "type": "text" + }, + { + "bbox": [ + 105, + 535, + 361, + 549 + ], + "score": 1.0, + "content": "Therefore, the optimisation problem generally becomes finding", + "type": "text" + }, + { + "bbox": [ + 361, + 535, + 367, + 546 + ], + "score": 0.82, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 535, + 484, + 549 + ], + "score": 1.0, + "content": "that minimises the SSL risk,", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32.5 + }, + { + "type": "interline_equation", + "bbox": [ + 203, + 564, + 408, + 596 + ], + "lines": [ + { + "bbox": [ + 203, + 564, + 408, + 596 + ], + "spans": [ + { + "bbox": [ + 203, + 564, + 408, + 596 + ], + "score": 0.94, + "content": "\\hat { \\mathcal { R } } _ { S S L } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) .", + "type": "interline_equation", + "image_path": "cc866efa71b7ff4f1ff699e30b854c8f17752f78772097962afc25123bbcce6e.jpg" + } + ] + } + ], + "index": 35.5, + "virtual_lines": [ + { + "bbox": [ + 203, + 564, + 408, + 580.0 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 203, + 580.0, + 408, + 596.0 + ], + "spans": [], + "index": 36 + } + ] + }, + { + "type": "text", + "bbox": [ + 87, + 604, + 505, + 648 + ], + "lines": [ + { + "bbox": [ + 86, + 603, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 86, + 606, + 99, + 615 + ], + "score": 1.0, + "content": "121", + "type": "text" + }, + { + "bbox": [ + 105, + 603, + 133, + 617 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 605, + 144, + 614 + ], + "score": 0.8, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 603, + 343, + 617 + ], + "score": 1.0, + "content": "is a term that does not depend on the labels and", + "type": "text" + }, + { + "bbox": [ + 343, + 605, + 350, + 614 + ], + "score": 0.81, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 603, + 505, + 617 + ], + "score": 1.0, + "content": "is a scalar weight which balances the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 86, + 614, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 86, + 617, + 100, + 626 + ], + "score": 1.0, + "content": "122", + "type": "text" + }, + { + "bbox": [ + 105, + 614, + 295, + 627 + ], + "score": 1.0, + "content": "labelled and unlabelled terms. 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Further information on the distribution", + "type": "text" + }, + { + "bbox": [ + 387, + 162, + 406, + 174 + ], + "score": 0.92, + "content": "p ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 162, + 506, + 174 + ], + "score": 1.0, + "content": "provides a better under-", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 173, + 505, + 187 + ], + "spans": [ + { + "bbox": [ + 89, + 175, + 100, + 185 + ], + "score": 1.0, + "content": "95", + "type": "text" + }, + { + "bbox": [ + 105, + 173, + 217, + 187 + ], + "score": 1.0, + "content": "standing of the distributions", + "type": "text" + }, + { + "bbox": [ + 218, + 173, + 246, + 185 + ], + "score": 0.92, + "content": "p ( x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 247, + 173, + 282, + 187 + ], + "score": 1.0, + "content": "and also", + "type": "text" + }, + { + "bbox": [ + 282, + 173, + 310, + 185 + ], + "score": 0.91, + "content": "p ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 173, + 345, + 187 + ], + "score": 1.0, + "content": ". 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We introduce a new random variable", + "type": "text" + }, + { + "bbox": [ + 339, + 211, + 381, + 223 + ], + "score": 0.92, + "content": "r \\in \\{ 0 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 211, + 506, + 223 + ], + "score": 1.0, + "content": "that governs whether or not a", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 88, + 221, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 88, + 224, + 99, + 234 + ], + "score": 1.0, + "content": "99", + "type": "text" + }, + { + "bbox": [ + 105, + 221, + 193, + 235 + ], + "score": 1.0, + "content": "data point is labelled", + "type": "text" + }, + { + "bbox": [ + 193, + 223, + 218, + 233 + ], + "score": 0.88, + "content": "\\boldsymbol { r } = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 221, + 254, + 235 + ], + "score": 1.0, + "content": "missing,", + "type": "text" + }, + { + "bbox": [ + 254, + 223, + 279, + 232 + ], + "score": 0.89, + "content": "r = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 221, + 358, + 235 + ], + "score": 1.0, + "content": "observed). We note", + "type": "text" + }, + { + "bbox": [ + 358, + 225, + 368, + 233 + ], + "score": 0.83, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 221, + 477, + 235 + ], + "score": 1.0, + "content": "the number of labelled and", + "type": "text" + }, + { + "bbox": [ + 477, + 224, + 489, + 233 + ], + "score": 0.75, + "content": "n _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 221, + 506, + 235 + ], + "score": 1.0, + "content": "the", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 233, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 86, + 235, + 99, + 245 + ], + "score": 1.0, + "content": "100", + "type": "text" + }, + { + "bbox": [ + 105, + 233, + 488, + 245 + ], + "score": 1.0, + "content": "number of unlabelled datapoints.The MCAR assumption states that the missingness of a label", + "type": "text" + }, + { + "bbox": [ + 488, + 236, + 495, + 245 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 233, + 505, + 245 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 244, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 86, + 245, + 100, + 256 + ], + "score": 1.0, + "content": "101", + "type": "text" + }, + { + "bbox": [ + 105, + 244, + 320, + 257 + ], + "score": 1.0, + "content": "independent of its features and the value of the label:", + "type": "text" + }, + { + "bbox": [ + 320, + 244, + 417, + 256 + ], + "score": 0.93, + "content": "p ( x , y , r ) = p ( x , y ) p ( r )", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 244, + 440, + 257 + ], + "score": 1.0, + "content": ", then", + "type": "text" + }, + { + "bbox": [ + 441, + 245, + 480, + 256 + ], + "score": 0.91, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 244, + 506, + 257 + ], + "score": 1.0, + "content": ". 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Fortunately, in the MCAR setting, the complete case risk estimate", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 382, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 86, + 385, + 100, + 396 + ], + "score": 1.0, + "content": "112", + "type": "text" + }, + { + "bbox": [ + 105, + 382, + 506, + 397 + ], + "score": 1.0, + "content": "keeps the same good properties of the traditional supervised one: it is unbiased and converges", + "type": "text" + } + ], + "index": 24, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 393, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 86, + 396, + 100, + 407 + ], + "score": 1.0, + "content": "113", + "type": "text" + }, + { + "bbox": [ + 105, + 393, + 164, + 407 + ], + "score": 1.0, + "content": "pointwisely to", + "type": "text" + }, + { + "bbox": [ + 165, + 394, + 187, + 406 + ], + "score": 0.92, + "content": "\\mathcal { R } \\bar { ( \\theta ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 393, + 506, + 407 + ], + "score": 1.0, + "content": ". Therefore, traditional learning theory holds for the complete case under MCAR.", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 404, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 86, + 407, + 100, + 417 + ], + "score": 1.0, + "content": "114", + "type": "text" + }, + { + "bbox": [ + 105, + 404, + 506, + 419 + ], + "score": 1.0, + "content": "While these observations are hardly new (see e.g. Liu & Goldberg, 2020), they can be seen as", + "type": "text" + } + ], + "index": 26, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 416, + 414, + 429 + ], + "spans": [ + { + "bbox": [ + 86, + 418, + 100, + 428 + ], + "score": 1.0, + "content": "115", + "type": "text" + }, + { + "bbox": [ + 105, + 416, + 414, + 429 + ], + "score": 1.0, + "content": "particular cases of the theory that we develop below. The risk to minimise is", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true + } + ], + "index": 24, + "bbox_fs": [ + 86, + 351, + 506, + 429 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 242, + 440, + 369, + 473 + ], + "lines": [ + { + "bbox": [ + 242, + 440, + 369, + 473 + ], + "spans": [ + { + "bbox": [ + 242, + 440, + 369, + 473 + ], + "score": 0.95, + "content": "\\hat { \\mathcal { R } } _ { C C } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) .", + "type": "interline_equation", + "image_path": "2e52c5584ec566d562b489563fab85e8bb1e8962e9213b8da9052b319e251df9.jpg" + } + ] + } + ], + "index": 28.5, + "virtual_lines": [ + { + "bbox": [ + 242, + 440, + 369, + 456.5 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 242, + 456.5, + 369, + 473.0 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "title", + "bbox": [ + 93, + 482, + 266, + 494 + ], + "lines": [ + { + "bbox": [ + 90, + 480, + 268, + 496 + ], + "spans": [ + { + "bbox": [ + 90, + 480, + 268, + 496 + ], + "score": 1.0, + "content": "16 2.2.2 Incorporating unlabelled data", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "index", + "bbox": [ + 87, + 501, + 506, + 547 + ], + "lines": [ + { + "bbox": [ + 86, + 501, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 86, + 502, + 100, + 514 + ], + "score": 1.0, + "content": "117", + "type": "text" + }, + { + "bbox": [ + 105, + 501, + 506, + 514 + ], + "score": 1.0, + "content": "A major drawback of the complete case framework is that a lot of data ends up not being exploited. A", + "type": "text" + } + ], + "index": 31, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 511, + 506, + 525 + ], + "spans": [ + { + "bbox": [ + 86, + 513, + 100, + 524 + ], + "score": 1.0, + "content": "118", + "type": "text" + }, + { + "bbox": [ + 105, + 511, + 506, + 525 + ], + "score": 1.0, + "content": "class of SSL approaches, mainly inductive methods with respect to the taxonomy of van Engelen &", + "type": "text" + } + ], + "index": 32, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 523, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 86, + 525, + 100, + 535 + ], + "score": 1.0, + "content": "119", + "type": "text" + }, + { + "bbox": [ + 106, + 523, + 506, + 536 + ], + "score": 1.0, + "content": "Hoos (2020), generally aim to minimise a modified estimator of the risk by including unlabelled data.", + "type": "text" + } + ], + "index": 33, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 535, + 484, + 549 + ], + "spans": [ + { + "bbox": [ + 86, + 538, + 100, + 547 + ], + "score": 1.0, + "content": "120", + "type": "text" + }, + { + "bbox": [ + 105, + 535, + 361, + 549 + ], + "score": 1.0, + "content": "Therefore, the optimisation problem generally becomes finding", + "type": "text" + }, + { + "bbox": [ + 361, + 535, + 367, + 546 + ], + "score": 0.82, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 535, + 484, + 549 + ], + "score": 1.0, + "content": "that minimises the SSL risk,", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true + } + ], + "index": 32.5, + "bbox_fs": [ + 86, + 501, + 506, + 549 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 203, + 564, + 408, + 596 + ], + "lines": [ + { + "bbox": [ + 203, + 564, + 408, + 596 + ], + "spans": [ + { + "bbox": [ + 203, + 564, + 408, + 596 + ], + "score": 0.94, + "content": "\\hat { \\mathcal { R } } _ { S S L } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) .", + "type": "interline_equation", + "image_path": "cc866efa71b7ff4f1ff699e30b854c8f17752f78772097962afc25123bbcce6e.jpg" + } + ] + } + ], + "index": 35.5, + "virtual_lines": [ + { + "bbox": [ + 203, + 564, + 408, + 580.0 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 203, + 580.0, + 408, + 596.0 + ], + "spans": [], + "index": 36 + } + ] + }, + { + "type": "index", + "bbox": [ + 87, + 604, + 505, + 648 + ], + "lines": [ + { + "bbox": [ + 86, + 603, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 86, + 606, + 99, + 615 + ], + "score": 1.0, + "content": "121", + "type": "text" + }, + { + "bbox": [ + 105, + 603, + 133, + 617 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 605, + 144, + 614 + ], + "score": 0.8, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 603, + 343, + 617 + ], + "score": 1.0, + "content": "is a term that does not depend on the labels and", + "type": "text" + }, + { + "bbox": [ + 343, + 605, + 350, + 614 + ], + "score": 0.81, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 603, + 505, + 617 + ], + "score": 1.0, + "content": "is a scalar weight which balances the", + "type": "text" + } + ], + "index": 37, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 614, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 86, + 617, + 100, + 626 + ], + "score": 1.0, + "content": "122", + "type": "text" + }, + { + "bbox": [ + 105, + 614, + 295, + 627 + ], + "score": 1.0, + "content": "labelled and unlabelled terms. 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Thus, they encourage the model to be confident on unlabelled", + "type": "text", + "cross_page": true + } + ], + "index": 1, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 86, + 96, + 100, + 107 + ], + "score": 1.0, + "content": "132", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 106, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "data, implicitly using the cluster assumption. 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See", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 85, + 179, + 506, + 191 + ], + "spans": [ + { + "bbox": [ + 85, + 181, + 100, + 191 + ], + "score": 1.0, + "content": "138", + "type": "text" + }, + { + "bbox": [ + 104, + 179, + 506, + 191 + ], + "score": 1.0, + "content": "Appendix B for complete description of the entropy-based literature (Berthelot et al., 2019; 2020;", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 86, + 191, + 479, + 202 + ], + "spans": [ + { + "bbox": [ + 86, + 192, + 100, + 202 + ], + "score": 1.0, + "content": "139", + "type": "text" + }, + { + "bbox": [ + 105, + 191, + 479, + 201 + ], + "score": 1.0, + "content": "Xie et al., 2019; Sohn et al., 2020; Rizve et al., 2021; Zhang et al., 2021a) and further details.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 86, + 212, + 505, + 301 + ], + "lines": [ + { + "bbox": [ + 86, + 213, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 86, + 215, + 99, + 225 + ], + "score": 1.0, + "content": "140", + "type": "text" + }, + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "score": 1.0, + "content": "Consistency-based methods Another range of SSL methods minimise a consistency objective", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 86, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 99, + 235 + ], + "score": 1.0, + "content": "141", + "type": "text" + }, + { + "bbox": [ + 105, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "that encourages invariant prediction for perturbations either on the data either on the model in order", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 86, + 235, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 86, + 237, + 100, + 246 + ], + "score": 1.0, + "content": "142", + "type": "text" + }, + { + "bbox": [ + 105, + 235, + 505, + 247 + ], + "score": 1.0, + "content": "to enforce stability on model predictions. 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We describe a more general framework covering further", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 399, + 385, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 371, + 411 + ], + "score": 1.0, + "content": "methods and provide with our theory an intuition on the choice of", + "type": "text" + }, + { + "bbox": [ + 371, + 400, + 381, + 410 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 399, + 385, + 411 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24 + }, + { + "type": "title", + "bbox": [ + 99, + 423, + 228, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 421, + 229, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 229, + 437 + ], + "score": 1.0, + "content": "2.3 Theoretical guarantees", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 87, + 443, + 505, + 630 + ], + "lines": [ + { + "bbox": [ + 86, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 86, + 445, + 100, + 456 + ], + "score": 1.0, + "content": "155", + "type": "text" + }, + { + "bbox": [ + 106, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "The main risk of SSL is the potential degradation caused by the introduction of unlabelled data when", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 86, + 453, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 86, + 456, + 100, + 466 + ], + "score": 1.0, + "content": "156", + "type": "text" + }, + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "score": 1.0, + "content": "distributional assumptions are not satisfied (Singh et al., 2008; Schölkopf et al., 2012; Li & Zhou,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 86, + 466, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 86, + 468, + 99, + 476 + ], + "score": 1.0, + "content": "157", + "type": "text" + }, + { + "bbox": [ + 106, + 466, + 506, + 477 + ], + "score": 1.0, + "content": "2014), specifically in settings where the MCAR assumption does not hold anymore (Oliver et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 86, + 475, + 506, + 488 + ], + "spans": [ + { + "bbox": [ + 86, + 478, + 100, + 488 + ], + "score": 1.0, + "content": "158", + "type": "text" + }, + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "score": 1.0, + "content": "2018; Guo et al., 2020). 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As remark by Oliver et al. (2018),", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 86, + 531, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 86, + 532, + 100, + 542 + ], + "score": 1.0, + "content": "163", + "type": "text" + }, + { + "bbox": [ + 105, + 531, + 506, + 543 + ], + "score": 1.0, + "content": "SSL performances are enabled by leveraging large validation sets which is not suited for real-world", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 86, + 540, + 507, + 555 + ], + "spans": [ + { + "bbox": [ + 86, + 543, + 100, + 554 + ], + "score": 1.0, + "content": "164", + "type": "text" + }, + { + "bbox": [ + 104, + 540, + 507, + 555 + ], + "score": 1.0, + "content": "applications. Then, theoretical guarantees are required to use safely SSL algorithms. 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Our example of Figure 1 also shows that classic SSL may fail to", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 86, + 618, + 394, + 630 + ], + "spans": [ + { + "bbox": [ + 86, + 620, + 99, + 630 + ], + "score": 1.0, + "content": "171", + "type": "text" + }, + { + "bbox": [ + 105, + 618, + 394, + 630 + ], + "score": 1.0, + "content": "generalise in a very benign setting with a large number of labelled data.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 86, + 634, + 505, + 723 + ], + "lines": [ + { + "bbox": [ + 86, + 635, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 86, + 636, + 100, + 646 + ], + "score": 1.0, + "content": "172", + "type": "text" + }, + { + "bbox": [ + 105, + 635, + 505, + 646 + ], + "score": 1.0, + "content": "Presented methods minimise a biased version of the risk under the MCAR assumption and therefore", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 85, + 645, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 85, + 646, + 100, + 657 + ], + "score": 1.0, + "content": "173", + "type": "text" + }, + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "score": 1.0, + "content": "classical learning theory cannot be applied anymore, as we argue more precisely in Appendix C.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 86, + 657, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 86, + 658, + 100, + 668 + ], + "score": 1.0, + "content": "174", + "type": "text" + }, + { + "bbox": [ + 105, + 657, + 505, + 668 + ], + "score": 1.0, + "content": "Learning over a biased estimate of the risk is not necessarily unsafe but it is difficult to provide", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 85, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 85, + 668, + 100, + 679 + ], + "score": 1.0, + "content": "175", + "type": "text" + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "theoretical guarantees on such methods even if some works try to do so with strong assumptions", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 85, + 678, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 85, + 679, + 100, + 690 + ], + "score": 1.0, + "content": "176", + "type": "text" + }, + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "score": 1.0, + "content": "on the data distribution (Mey & Loog 2019, Section 4 and 5). 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For instance, Grandvalet & Bengio (2004) and", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 85, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 85, + 701, + 100, + 712 + ], + "score": 1.0, + "content": "178", + "type": "text" + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "Corduneanu & Jaakkola (2003) perform respectively entropy and mutual information minimisation", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 86, + 710, + 507, + 724 + ], + "spans": [ + { + "bbox": [ + 86, + 712, + 100, + 723 + ], + "score": 1.0, + "content": "179", + "type": "text" + }, + { + "bbox": [ + 104, + 710, + 507, + 724 + ], + "score": 1.0, + "content": "whereas Pereyra et al. (2017) and Krause et al. 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See", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 179, + 506, + 191 + ], + "spans": [ + { + "bbox": [ + 85, + 181, + 100, + 191 + ], + "score": 1.0, + "content": "138", + "type": "text" + }, + { + "bbox": [ + 104, + 179, + 506, + 191 + ], + "score": 1.0, + "content": "Appendix B for complete description of the entropy-based literature (Berthelot et al., 2019; 2020;", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 191, + 479, + 202 + ], + "spans": [ + { + "bbox": [ + 86, + 192, + 100, + 202 + ], + "score": 1.0, + "content": "139", + "type": "text" + }, + { + "bbox": [ + 105, + 191, + 479, + 201 + ], + "score": 1.0, + "content": "Xie et al., 2019; Sohn et al., 2020; Rizve et al., 2021; Zhang et al., 2021a) and further details.", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 213, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 86, + 215, + 99, + 225 + ], + "score": 1.0, + "content": "140", + "type": "text" + }, + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "score": 1.0, + "content": "Consistency-based methods Another range of SSL methods minimise a consistency objective", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 223, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 99, + 235 + ], + "score": 1.0, + "content": "141", + "type": "text" + }, + { + "bbox": [ + 105, + 223, + 505, + 236 + ], + "score": 1.0, + "content": "that encourages invariant prediction for perturbations either on the data either on the model in order", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 235, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 86, + 237, + 100, + 246 + ], + "score": 1.0, + "content": "142", + "type": "text" + }, + { + "bbox": [ + 105, + 235, + 505, + 247 + ], + "score": 1.0, + "content": "to enforce stability on model predictions. 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The general", + "type": "text" + } + ], + "index": 17, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 290, + 318, + 302 + ], + "spans": [ + { + "bbox": [ + 86, + 291, + 100, + 301 + ], + "score": 1.0, + "content": "147", + "type": "text" + }, + { + "bbox": [ + 105, + 290, + 318, + 302 + ], + "score": 1.0, + "content": "form of the unsupervised objective can be written as", + "type": "text" + } + ], + "index": 18, + "is_list_start_line": true + } + ], + "index": 7.5, + "bbox_fs": [ + 85, + 135, + 507, + 202 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 212, + 505, + 301 + ], + "lines": [], + "index": 14.5, + "bbox_fs": [ + 86, + 213, + 507, + 302 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 87, + 318, + 505, + 374 + ], + "lines": [ + { + "bbox": [ + 118, + 318, + 507, + 334 + ], + "spans": [ + { + "bbox": [ + 118, + 319, + 480, + 333 + ], + "score": 0.89, + "content": "C _ { 1 } \\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } , \\tilde { y } ) } [ L ( \\theta ; \\tilde { x } , \\tilde { y } ) ] \\le H ( \\theta ; x ) = \\mathbf { D i v } ( f _ { \\hat { \\theta } } ( x , . ) , p e r t ( f _ { \\theta } ( x , . ) ) \\le C _ { 2 } \\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } , \\tilde { y } ) } [ L ( \\theta ; \\tilde { x } , \\tilde { y } ) ] ,", + "type": "inline_equation", + "image_path": "2f292a3457ffc73fd5544dd54c2c4af5b3bab392be63693fd664c4e70942b679.jpg" + }, + { + "bbox": [ + 480, + 318, + 507, + 334 + ], + "score": 1.0, + "content": "(4)", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 86, + 334, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 86, + 334, + 134, + 347 + ], + "score": 1.0, + "content": "148 where", + "type": "text" + }, + { + "bbox": [ + 135, + 335, + 145, + 348 + ], + "score": 0.89, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 334, + 506, + 347 + ], + "score": 1.0, + "content": "is the predictions of the model, the Div is a non-negative function that measures the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 86, + 347, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 86, + 350, + 100, + 359 + ], + "score": 1.0, + "content": "149", + "type": "text" + }, + { + "bbox": [ + 104, + 348, + 257, + 361 + ], + "score": 1.0, + "content": "divergence between two distributions,", + "type": "text" + }, + { + "bbox": [ + 257, + 347, + 264, + 359 + ], + "score": 0.83, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 348, + 421, + 361 + ], + "score": 1.0, + "content": "is a fixed copy of the current parameter", + "type": "text" + }, + { + "bbox": [ + 421, + 349, + 428, + 358 + ], + "score": 0.79, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 348, + 506, + 361 + ], + "score": 1.0, + "content": "(the gradient is not", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 84, + 360, + 491, + 374 + ], + "spans": [ + { + "bbox": [ + 84, + 361, + 186, + 374 + ], + "score": 1.0, + "content": "propagated through 150", + "type": "text" + }, + { + "bbox": [ + 187, + 360, + 193, + 371 + ], + "score": 0.65, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 361, + 432, + 374 + ], + "score": 1.0, + "content": "), pert is a perturbation applied to the model or the data and", + "type": "text" + }, + { + "bbox": [ + 432, + 361, + 487, + 373 + ], + "score": 0.91, + "content": "0 \\leq C _ { 1 } \\leq C _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 361, + 491, + 374 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5, + "bbox_fs": [ + 84, + 318, + 507, + 374 + ] + }, + { + "type": "text", + "bbox": [ + 100, + 377, + 503, + 411 + ], + "lines": [ + { + "bbox": [ + 106, + 378, + 504, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 248, + 390 + ], + "score": 1.0, + "content": "Previous works also remarked that", + "type": "text" + }, + { + "bbox": [ + 249, + 378, + 259, + 388 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 378, + 341, + 390 + ], + "score": 1.0, + "content": "is an expectation of", + "type": "text" + }, + { + "bbox": [ + 342, + 378, + 349, + 388 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 378, + 504, + 390 + ], + "score": 1.0, + "content": "for entropy-minimisation and pseudo-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 389, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 505, + 401 + ], + "score": 1.0, + "content": "label (Zhu et al., 2022; Aminian et al., 2022). We describe a more general framework covering further", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 399, + 385, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 371, + 411 + ], + "score": 1.0, + "content": "methods and provide with our theory an intuition on the choice of", + "type": "text" + }, + { + "bbox": [ + 371, + 400, + 381, + 410 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 399, + 385, + 411 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 378, + 505, + 411 + ] + }, + { + "type": "title", + "bbox": [ + 99, + 423, + 228, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 421, + 229, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 229, + 437 + ], + "score": 1.0, + "content": "2.3 Theoretical guarantees", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "index", + "bbox": [ + 87, + 443, + 505, + 630 + ], + "lines": [ + { + "bbox": [ + 86, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 86, + 445, + 100, + 456 + ], + "score": 1.0, + "content": "155", + "type": "text" + }, + { + "bbox": [ + 106, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "The main risk of SSL is the potential degradation caused by the introduction of unlabelled data when", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 453, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 86, + 456, + 100, + 466 + ], + "score": 1.0, + "content": "156", + "type": "text" + }, + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "score": 1.0, + "content": "distributional assumptions are not satisfied (Singh et al., 2008; Schölkopf et al., 2012; Li & Zhou,", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 466, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 86, + 468, + 99, + 476 + ], + "score": 1.0, + "content": "157", + "type": "text" + }, + { + "bbox": [ + 106, + 466, + 506, + 477 + ], + "score": 1.0, + "content": "2014), specifically in settings where the MCAR assumption does not hold anymore (Oliver et al.,", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 475, + 506, + 488 + ], + "spans": [ + { + "bbox": [ + 86, + 478, + 100, + 488 + ], + "score": 1.0, + "content": "158", + "type": "text" + }, + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "score": 1.0, + "content": "2018; Guo et al., 2020). Additionally, in (Zhu et al., 2022), the authors show disparate impacts of", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 487, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 86, + 489, + 100, + 499 + ], + "score": 1.0, + "content": "159", + "type": "text" + }, + { + "bbox": [ + 105, + 487, + 506, + 500 + ], + "score": 1.0, + "content": "pseudo-labelling on the different sub-classes of the population. To mitigate these problems, previous", + "type": "text" + } + ], + "index": 31, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 498, + 506, + 511 + ], + "spans": [ + { + "bbox": [ + 86, + 500, + 100, + 510 + ], + "score": 1.0, + "content": "160", + "type": "text" + }, + { + "bbox": [ + 104, + 498, + 506, + 511 + ], + "score": 1.0, + "content": "works introduced the notion safe semi-supervised learning for techniques which never reduce learning", + "type": "text" + } + ], + "index": 32, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 508, + 507, + 522 + ], + "spans": [ + { + "bbox": [ + 86, + 511, + 99, + 521 + ], + "score": 1.0, + "content": "161", + "type": "text" + }, + { + "bbox": [ + 104, + 508, + 507, + 522 + ], + "score": 1.0, + "content": "performance by introducing unlabelled data (Li & Zhou, 2014; Kawakita & Takeuchi, 2014; Li et al.,", + "type": "text" + } + ], + "index": 33, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 519, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 86, + 522, + 100, + 532 + ], + "score": 1.0, + "content": "162", + "type": "text" + }, + { + "bbox": [ + 105, + 519, + 506, + 532 + ], + "score": 1.0, + "content": "2016; Gan et al., 2017; Trapp et al., 2017; Guo et al., 2020). As remark by Oliver et al. (2018),", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 531, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 86, + 532, + 100, + 542 + ], + "score": 1.0, + "content": "163", + "type": "text" + }, + { + "bbox": [ + 105, + 531, + 506, + 543 + ], + "score": 1.0, + "content": "SSL performances are enabled by leveraging large validation sets which is not suited for real-world", + "type": "text" + } + ], + "index": 35, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 540, + 507, + 555 + ], + "spans": [ + { + "bbox": [ + 86, + 543, + 100, + 554 + ], + "score": 1.0, + "content": "164", + "type": "text" + }, + { + "bbox": [ + 104, + 540, + 507, + 555 + ], + "score": 1.0, + "content": "applications. Then, theoretical guarantees are required to use safely SSL algorithms. For this reason,", + "type": "text" + } + ], + "index": 36, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 86, + 555, + 99, + 564 + ], + "score": 1.0, + "content": "165", + "type": "text" + }, + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "in our work, we consider as safe an SSL algorithm that has theoretical guarantees that are similar", + "type": "text" + } + ], + "index": 37, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 563, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 86, + 566, + 100, + 575 + ], + "score": 1.0, + "content": "166", + "type": "text" + }, + { + "bbox": [ + 105, + 563, + 506, + 576 + ], + "score": 1.0, + "content": "or stronger than those of the complete case baseline. Even though the methods presented above", + "type": "text" + } + ], + "index": 38, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 574, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 86, + 576, + 100, + 586 + ], + "score": 1.0, + "content": "167", + "type": "text" + }, + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "score": 1.0, + "content": "produce good performances in a variety of SSL benchmarks, they generally do not benefit from", + "type": "text" + } + ], + "index": 39, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 86, + 587, + 100, + 597 + ], + "score": 1.0, + "content": "168", + "type": "text" + }, + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "score": 1.0, + "content": "theoretical guarantees, even elementary. More over,Schölkopf et al. (2012) identify settings on the", + "type": "text" + } + ], + "index": 40, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 596, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 86, + 598, + 100, + 608 + ], + "score": 1.0, + "content": "169", + "type": "text" + }, + { + "bbox": [ + 105, + 596, + 254, + 609 + ], + "score": 1.0, + "content": "causal relation between the features", + "type": "text" + }, + { + "bbox": [ + 254, + 598, + 261, + 606 + ], + "score": 0.69, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 596, + 320, + 609 + ], + "score": 1.0, + "content": "and the target", + "type": "text" + }, + { + "bbox": [ + 320, + 598, + 327, + 608 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 596, + 505, + 609 + ], + "score": 1.0, + "content": "where SSL may systematically fail, even if", + "type": "text" + } + ], + "index": 41, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 607, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 86, + 609, + 100, + 619 + ], + "score": 1.0, + "content": "170", + "type": "text" + }, + { + "bbox": [ + 105, + 607, + 506, + 620 + ], + "score": 1.0, + "content": "classic SSL assumptions hold. Our example of Figure 1 also shows that classic SSL may fail to", + "type": "text" + } + ], + "index": 42, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 618, + 394, + 630 + ], + "spans": [ + { + "bbox": [ + 86, + 620, + 99, + 630 + ], + "score": 1.0, + "content": "171", + "type": "text" + }, + { + "bbox": [ + 105, + 618, + 394, + 630 + ], + "score": 1.0, + "content": "generalise in a very benign setting with a large number of labelled data.", + "type": "text" + } + ], + "index": 43, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 635, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 86, + 636, + 100, + 646 + ], + "score": 1.0, + "content": "172", + "type": "text" + }, + { + "bbox": [ + 105, + 635, + 505, + 646 + ], + "score": 1.0, + "content": "Presented methods minimise a biased version of the risk under the MCAR assumption and therefore", + "type": "text" + } + ], + "index": 44, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 645, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 85, + 646, + 100, + 657 + ], + "score": 1.0, + "content": "173", + "type": "text" + }, + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "score": 1.0, + "content": "classical learning theory cannot be applied anymore, as we argue more precisely in Appendix C.", + "type": "text" + } + ], + "index": 45, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 657, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 86, + 658, + 100, + 668 + ], + "score": 1.0, + "content": "174", + "type": "text" + }, + { + "bbox": [ + 105, + 657, + 505, + 668 + ], + "score": 1.0, + "content": "Learning over a biased estimate of the risk is not necessarily unsafe but it is difficult to provide", + "type": "text" + } + ], + "index": 46, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 85, + 668, + 100, + 679 + ], + "score": 1.0, + "content": "175", + "type": "text" + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "theoretical guarantees on such methods even if some works try to do so with strong assumptions", + "type": "text" + } + ], + "index": 47, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 678, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 85, + 679, + 100, + 690 + ], + "score": 1.0, + "content": "176", + "type": "text" + }, + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "score": 1.0, + "content": "on the data distribution (Mey & Loog 2019, Section 4 and 5). Additionally, we remark that the", + "type": "text" + } + ], + "index": 48, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 86, + 691, + 100, + 700 + ], + "score": 1.0, + "content": "177", + "type": "text" + }, + { + "bbox": [ + 106, + 689, + 145, + 701 + ], + "score": 1.0, + "content": "choice of", + "type": "text" + }, + { + "bbox": [ + 145, + 689, + 155, + 699 + ], + "score": 0.76, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "can be confusing as seen in the literature. For instance, Grandvalet & Bengio (2004) and", + "type": "text" + } + ], + "index": 49, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 85, + 701, + 100, + 712 + ], + "score": 1.0, + "content": "178", + "type": "text" + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "Corduneanu & Jaakkola (2003) perform respectively entropy and mutual information minimisation", + "type": "text" + } + ], + "index": 50, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 710, + 507, + 724 + ], + "spans": [ + { + "bbox": [ + 86, + 712, + 100, + 723 + ], + "score": 1.0, + "content": "179", + "type": "text" + }, + { + "bbox": [ + 104, + 710, + 507, + 724 + ], + "score": 1.0, + "content": "whereas Pereyra et al. (2017) and Krause et al. (2010) perform maximisation of the same quantities.", + "type": "text" + } + ], + "index": 51, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 93, + 507, + 108 + ], + "spans": [ + { + "bbox": [ + 86, + 97, + 99, + 106 + ], + "score": 1.0, + "content": "181", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 105, + 93, + 507, + 108 + ], + "score": 1.0, + "content": "Previous works already proposed safe SSL methods with theoretical guarantees. 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This way of debiasing is closely related to the method of control variates (Owen,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 655, + 506, + 670 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 670 + ], + "score": 1.0, + "content": "2013, Chapter 8) which is a common variance reduction technique. The idea is to add an additional", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "term to a Monte-Carlo estimator with a null expectation in order to reduce the variance of the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 678, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 505, + 690 + ], + "score": 1.0, + "content": "estimator without modifying the expectation. Here, DeSSL can also be interpreted as a control variate", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 688, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 702 + ], + "score": 1.0, + "content": "on the risk’s gradient itself and should improve the optimisation scheme. This idea is close to the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "optimisation schemes introduced by Johnson & Zhang (2013) and Defazio et al. (2014) which reduce", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 711, + 414, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 414, + 724 + ], + "score": 1.0, + "content": "the variance of the gradients’ estimate to improve optimisation performance.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 43.5, + "bbox_fs": [ + 105, + 633, + 506, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 84, + 72, + 506, + 97 + ], + "lines": [ + { + "bbox": [ + 84, + 72, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 84, + 72, + 252, + 86 + ], + "score": 1.0, + "content": "226 Another interesting way to interpret", + "type": "text" + }, + { + "bbox": [ + 253, + 73, + 284, + 83 + ], + "score": 0.39, + "content": "\\scriptstyle { \\mathrm { D e S S L } }", + "type": "inline_equation" + }, + { + "bbox": [ + 284, + 72, + 506, + 86 + ], + "score": 1.0, + "content": "is as a constrained optimisation problem. Indeed, min-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 84, + 502, + 99 + ], + "spans": [ + { + "bbox": [ + 83, + 84, + 138, + 99 + ], + "score": 1.0, + "content": "imising 227", + "type": "text" + }, + { + "bbox": [ + 139, + 84, + 175, + 97 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 84, + 502, + 99 + ], + "score": 1.0, + "content": "is equivalent to minimising the Lagrangian of the following optimisation problem:", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "interline_equation", + "bbox": [ + 217, + 101, + 393, + 156 + ], + "lines": [ + { + "bbox": [ + 217, + 101, + 393, + 156 + ], + "spans": [ + { + "bbox": [ + 217, + 101, + 393, + 156 + ], + "score": 0.93, + "content": "\\begin{array} { c l } { \\displaystyle \\operatorname* { m i n } _ { \\theta } } & { \\displaystyle \\hat { \\mathcal { R } } _ { C C } ( \\theta ) } \\\\ { \\mathrm { s . t . } } & { \\displaystyle \\frac { 1 } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } H ( \\theta ; x _ { i } ) . } \\end{array}", + "type": "interline_equation", + "image_path": "59f763fc3820cd1c9fc9cb19e7caf0cf6317bb212de963cc2d6e9ba2dc64b284.jpg" + } + ] + } + ], + "index": 3.5, + "virtual_lines": [ + { + "bbox": [ + 217, + 101, + 393, + 114.75 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 217, + 114.75, + 393, + 128.5 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 217, + 128.5, + 393, + 142.25 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 217, + 142.25, + 393, + 156.0 + ], + "spans": [], + "index": 5 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 163, + 505, + 208 + ], + "lines": [ + { + "bbox": [ + 86, + 162, + 506, + 179 + ], + "spans": [ + { + "bbox": [ + 86, + 167, + 99, + 176 + ], + "score": 1.0, + "content": "228", + "type": "text" + }, + { + "bbox": [ + 104, + 162, + 506, + 179 + ], + "score": 1.0, + "content": "The idea of this optimisation problem is to minimise the complete case risk estimator by assessing", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 174, + 506, + 188 + ], + "spans": [ + { + "bbox": [ + 86, + 177, + 100, + 186 + ], + "score": 1.0, + "content": "229", + "type": "text" + }, + { + "bbox": [ + 104, + 174, + 251, + 188 + ], + "score": 1.0, + "content": "that some properties represented by", + "type": "text" + }, + { + "bbox": [ + 251, + 176, + 261, + 185 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 174, + 506, + 188 + ], + "score": 1.0, + "content": "are on average equal for the labelled data and the unlabelled", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 185, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 86, + 188, + 100, + 198 + ], + "score": 1.0, + "content": "230", + "type": "text" + }, + { + "bbox": [ + 105, + 185, + 505, + 199 + ], + "score": 1.0, + "content": "data. For example, if we consider entropy-minimisation, this program encourages the model to have", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 196, + 396, + 210 + ], + "spans": [ + { + "bbox": [ + 86, + 199, + 99, + 208 + ], + "score": 1.0, + "content": "231", + "type": "text" + }, + { + "bbox": [ + 105, + 196, + 396, + 210 + ], + "score": 1.0, + "content": "the same confidence on the unlabelled examples as on the labelled ones.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 86, + 213, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 86, + 214, + 507, + 226 + ], + "spans": [ + { + "bbox": [ + 86, + 216, + 99, + 225 + ], + "score": 1.0, + "content": "232", + "type": "text" + }, + { + "bbox": [ + 106, + 214, + 507, + 226 + ], + "score": 1.0, + "content": "The debiasing term of our objective will penalise the confidence of the model on the labelled data.", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 223, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 99, + 235 + ], + "score": 1.0, + "content": "233", + "type": "text" + }, + { + "bbox": [ + 105, + 223, + 506, + 238 + ], + "score": 1.0, + "content": "Pereyra et al. (2017) show that penalising the entropy in a supervised context acts as a strong", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 86, + 235, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 86, + 237, + 99, + 246 + ], + "score": 1.0, + "content": "234", + "type": "text" + }, + { + "bbox": [ + 105, + 235, + 506, + 248 + ], + "score": 1.0, + "content": "regulator for supervised models and improves on the state-of-the-art on common benchmarks. This", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 85, + 245, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 85, + 248, + 99, + 258 + ], + "score": 1.0, + "content": "235", + "type": "text" + }, + { + "bbox": [ + 105, + 245, + 506, + 259 + ], + "score": 1.0, + "content": "comforts us in the idea of debiasing using labelled data in the case of entropy-minimisation. Similarly,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 86, + 255, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 86, + 259, + 99, + 268 + ], + "score": 1.0, + "content": "236", + "type": "text" + }, + { + "bbox": [ + 104, + 255, + 506, + 271 + ], + "score": 1.0, + "content": "the debiasing term in pseudo-label turns the problem into plausibility inference as described by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 85, + 268, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 85, + 269, + 100, + 280 + ], + "score": 1.0, + "content": "237", + "type": "text" + }, + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "score": 1.0, + "content": "Barndorff-Nielsen (1976). Our objective also resembles doubly-robust risk estimates used for SSL in", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 86, + 277, + 506, + 292 + ], + "spans": [ + { + "bbox": [ + 86, + 281, + 99, + 290 + ], + "score": 1.0, + "content": "238", + "type": "text" + }, + { + "bbox": [ + 105, + 277, + 506, + 292 + ], + "score": 1.0, + "content": "the context of kernel machines by Liu & Goldberg (2020) and for deep learning in a recent preprint", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 85, + 289, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 85, + 291, + 100, + 302 + ], + "score": 1.0, + "content": "239", + "type": "text" + }, + { + "bbox": [ + 106, + 289, + 506, + 303 + ], + "score": 1.0, + "content": "(Hu et al., 2022). In both cases, their focus is quite different, as they consider weaker conditions", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 86, + 301, + 285, + 312 + ], + "spans": [ + { + "bbox": [ + 86, + 303, + 99, + 312 + ], + "score": 1.0, + "content": "240", + "type": "text" + }, + { + "bbox": [ + 106, + 301, + 271, + 312 + ], + "score": 1.0, + "content": "than MCAR, but very specific choices of", + "type": "text" + }, + { + "bbox": [ + 272, + 301, + 282, + 311 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 301, + 285, + 312 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14 + }, + { + "type": "title", + "bbox": [ + 106, + 326, + 303, + 338 + ], + "lines": [ + { + "bbox": [ + 105, + 323, + 305, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 139, + 341 + ], + "score": 1.0, + "content": "3.2 Is", + "type": "text" + }, + { + "bbox": [ + 140, + 325, + 188, + 339 + ], + "score": 0.92, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 323, + 305, + 341 + ], + "score": 1.0, + "content": "an accurate risk estimate?", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 90, + 346, + 505, + 391 + ], + "lines": [ + { + "bbox": [ + 88, + 346, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 88, + 349, + 100, + 358 + ], + "score": 1.0, + "content": "242", + "type": "text" + }, + { + "bbox": [ + 106, + 346, + 506, + 360 + ], + "score": 1.0, + "content": "Because of the connections between our debiased estimate and variance reduction techniques, we", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 88, + 357, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 88, + 360, + 100, + 369 + ], + "score": 1.0, + "content": "243", + "type": "text" + }, + { + "bbox": [ + 106, + 357, + 506, + 370 + ], + "score": 1.0, + "content": "have a natural interest in the variance of the estimate. Having a lower-variance estimate of the risk", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 88, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 88, + 370, + 100, + 380 + ], + "score": 1.0, + "content": "244", + "type": "text" + }, + { + "bbox": [ + 106, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "would mean estimating it more accurately, leading to better models. Similarly to traditional control", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 88, + 380, + 403, + 392 + ], + "spans": [ + { + "bbox": [ + 88, + 381, + 100, + 391 + ], + "score": 1.0, + "content": "245", + "type": "text" + }, + { + "bbox": [ + 105, + 380, + 392, + 392 + ], + "score": 1.0, + "content": "variates (Owen, 2013), the variance can be computed, and optimised in", + "type": "text" + }, + { + "bbox": [ + 392, + 380, + 399, + 389 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 380, + 403, + 392 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 87, + 394, + 406, + 408 + ], + "lines": [ + { + "bbox": [ + 86, + 393, + 408, + 410 + ], + "spans": [ + { + "bbox": [ + 86, + 394, + 220, + 410 + ], + "score": 1.0, + "content": "Theorem 3.1. The function 246", + "type": "text" + }, + { + "bbox": [ + 220, + 393, + 303, + 408 + ], + "score": 0.92, + "content": "\\lambda \\mapsto \\mathbb { V } ( \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 394, + 408, + 410 + ], + "score": 1.0, + "content": "reaches its minimum for:", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "interline_equation", + "bbox": [ + 228, + 411, + 381, + 439 + ], + "lines": [ + { + "bbox": [ + 228, + 411, + 381, + 439 + ], + "spans": [ + { + "bbox": [ + 228, + 411, + 381, + 439 + ], + "score": 0.95, + "content": "\\lambda _ { o p t } = \\frac { n _ { u } } { n } \\frac { \\mathrm { C o v } ( L ( \\theta ; x , y ) , H ( \\theta ; x ) ) } { \\mathbb { V } ( H ( \\theta ; x ) ) } ,", + "type": "interline_equation", + "image_path": "502a8a35bb7915323a83c0f1cd5eb49981cc20de5fb727af86fe877267b9f65e.jpg" + } + ] + } + ], + "index": 25.5, + "virtual_lines": [ + { + "bbox": [ + 228, + 411, + 381, + 425.0 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 228, + 425.0, + 381, + 439.0 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 87, + 443, + 156, + 455 + ], + "lines": [ + { + "bbox": [ + 84, + 441, + 153, + 457 + ], + "spans": [ + { + "bbox": [ + 84, + 441, + 134, + 457 + ], + "score": 1.0, + "content": "247 and at", + "type": "text" + }, + { + "bbox": [ + 135, + 443, + 153, + 455 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "interline_equation", + "bbox": [ + 168, + 459, + 442, + 481 + ], + "lines": [ + { + "bbox": [ + 168, + 459, + 442, + 481 + ], + "spans": [ + { + "bbox": [ + 168, + 459, + 442, + 481 + ], + "score": 0.83, + "content": "\\mathbb { V } ( \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ) | _ { \\lambda _ { o p t } } = \\left( 1 - \\frac { n _ { u } } { n } \\rho _ { L , H } ^ { 2 } \\right) \\mathbb { V } ( \\hat { \\mathcal { R } } _ { C C } ( \\theta ) ) \\leq \\mathbb { V } ( \\hat { \\mathcal { R } } _ { C C } ( \\theta ) ) ,", + "type": "interline_equation", + "image_path": "003bf3a85c148ed51e81f846451aea81d15cac70a457c033de943905f4d6e3cd.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 168, + 459, + 442, + 481 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 88, + 490, + 274, + 504 + ], + "lines": [ + { + "bbox": [ + 85, + 489, + 272, + 505 + ], + "spans": [ + { + "bbox": [ + 85, + 489, + 133, + 505 + ], + "score": 1.0, + "content": "248 where", + "type": "text" + }, + { + "bbox": [ + 133, + 491, + 272, + 504 + ], + "score": 0.88, + "content": "\\rho _ { L , H } = \\operatorname { C o r r } ( L ( \\theta ; x , y ) , H ( \\theta ; x ) ) .", + "type": "inline_equation" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 85, + 513, + 506, + 668 + ], + "lines": [ + { + "bbox": [ + 86, + 512, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 86, + 516, + 99, + 524 + ], + "score": 1.0, + "content": "249", + "type": "text" + }, + { + "bbox": [ + 105, + 513, + 161, + 527 + ], + "score": 1.0, + "content": "Additionally,", + "type": "text" + }, + { + "bbox": [ + 162, + 512, + 285, + 526 + ], + "score": 0.93, + "content": "-", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 513, + 312, + 527 + ], + "score": 1.0, + "content": "for all", + "type": "text" + }, + { + "bbox": [ + 313, + 514, + 320, + 524 + ], + "score": 0.81, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 513, + 381, + 527 + ], + "score": 1.0, + "content": "between 0 and", + "type": "text" + }, + { + "bbox": [ + 381, + 514, + 404, + 526 + ], + "score": 0.91, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 513, + 506, + 527 + ], + "score": 1.0, + "content": ". A proof of this theorem", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 85, + 524, + 506, + 537 + ], + "spans": [ + { + "bbox": [ + 85, + 526, + 100, + 536 + ], + "score": 1.0, + "content": "250", + "type": "text" + }, + { + "bbox": [ + 105, + 524, + 506, + 537 + ], + "score": 1.0, + "content": "is available as Appendix E. This theorem provides a formal justification to the heuristic idea that", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 85, + 534, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 85, + 537, + 100, + 547 + ], + "score": 1.0, + "content": "251", + "type": "text" + }, + { + "bbox": [ + 106, + 536, + 117, + 546 + ], + "score": 0.73, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 117, + 534, + 218, + 548 + ], + "score": 1.0, + "content": "should be a surrogate of", + "type": "text" + }, + { + "bbox": [ + 218, + 536, + 226, + 545 + ], + "score": 0.8, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 226, + 534, + 448, + 548 + ], + "score": 1.0, + "content": ". Indeed, DeSSL is a more accurate risk estimate when", + "type": "text" + }, + { + "bbox": [ + 449, + 536, + 459, + 545 + ], + "score": 0.79, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 534, + 505, + 548 + ], + "score": 1.0, + "content": "is strongly", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 86, + 546, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 86, + 549, + 99, + 558 + ], + "score": 1.0, + "content": "252", + "type": "text" + }, + { + "bbox": [ + 106, + 546, + 214, + 559 + ], + "score": 1.0, + "content": "positively correlated with", + "type": "text" + }, + { + "bbox": [ + 215, + 547, + 222, + 556 + ], + "score": 0.8, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 546, + 377, + 559 + ], + "score": 1.0, + "content": ", which is likely to be the case when", + "type": "text" + }, + { + "bbox": [ + 378, + 547, + 388, + 556 + ], + "score": 0.81, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 546, + 506, + 559 + ], + "score": 1.0, + "content": "is equal or equivalent to an", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 85, + 557, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 85, + 559, + 100, + 569 + ], + "score": 1.0, + "content": "253", + "type": "text" + }, + { + "bbox": [ + 105, + 557, + 164, + 569 + ], + "score": 1.0, + "content": "expectation of", + "type": "text" + }, + { + "bbox": [ + 164, + 558, + 172, + 567 + ], + "score": 0.78, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 557, + 239, + 569 + ], + "score": 1.0, + "content": ". Then, choosing", + "type": "text" + }, + { + "bbox": [ + 239, + 558, + 246, + 568 + ], + "score": 0.77, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 557, + 506, + 569 + ], + "score": 1.0, + "content": "positive is a coherent choice. We also demonstrate in Appendix E", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 86, + 567, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 86, + 570, + 100, + 579 + ], + "score": 1.0, + "content": "254", + "type": "text" + }, + { + "bbox": [ + 105, + 567, + 123, + 581 + ], + "score": 1.0, + "content": "that", + "type": "text" + }, + { + "bbox": [ + 124, + 569, + 132, + 578 + ], + "score": 0.83, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 567, + 150, + 581 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 150, + 569, + 160, + 578 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 567, + 282, + 581 + ], + "score": 1.0, + "content": "are positively correlated when", + "type": "text" + }, + { + "bbox": [ + 283, + 569, + 291, + 578 + ], + "score": 0.82, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 567, + 410, + 581 + ], + "score": 1.0, + "content": "is the negative likelihood and", + "type": "text" + }, + { + "bbox": [ + 410, + 568, + 420, + 578 + ], + "score": 0.78, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 567, + 506, + 581 + ], + "score": 1.0, + "content": "is the entropy. Other", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 85, + 578, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 85, + 581, + 100, + 591 + ], + "score": 1.0, + "content": "255", + "type": "text" + }, + { + "bbox": [ + 105, + 578, + 506, + 591 + ], + "score": 1.0, + "content": "SSL methods have variance reduction guarantees and already has shown great promises in SSL, see", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 86, + 590, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 86, + 592, + 99, + 601 + ], + "score": 1.0, + "content": "256", + "type": "text" + }, + { + "bbox": [ + 105, + 590, + 160, + 603 + ], + "score": 1.0, + "content": "Fox-Roberts", + "type": "text" + }, + { + "bbox": [ + 160, + 591, + 169, + 600 + ], + "score": 0.38, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 590, + 506, + 603 + ], + "score": 1.0, + "content": "Rosten (2014) and Sakai et al. (2017). In a purely supervised context, Chen et al.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 85, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 85, + 603, + 100, + 613 + ], + "score": 1.0, + "content": "257", + "type": "text" + }, + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "(2020) show that the effectiveness of data augmentation techniques lays partially on the variance", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 86, + 611, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 86, + 614, + 99, + 623 + ], + "score": 1.0, + "content": "258", + "type": "text" + }, + { + "bbox": [ + 105, + 611, + 441, + 624 + ], + "score": 1.0, + "content": "reduction of the risk estimate. A natural application of this theorem would be to tune", + "type": "text" + }, + { + "bbox": [ + 441, + 612, + 448, + 622 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 449, + 611, + 506, + 624 + ], + "score": 1.0, + "content": "automatically", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 86, + 623, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 86, + 625, + 99, + 634 + ], + "score": 1.0, + "content": "259", + "type": "text" + }, + { + "bbox": [ + 105, + 623, + 162, + 635 + ], + "score": 1.0, + "content": "by estimating", + "type": "text" + }, + { + "bbox": [ + 163, + 623, + 181, + 635 + ], + "score": 0.91, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 623, + 339, + 635 + ], + "score": 1.0, + "content": ". In our case however, the estimation of", + "type": "text" + }, + { + "bbox": [ + 339, + 623, + 441, + 635 + ], + "score": 0.91, + "content": "\\operatorname { C o v } ( L ( \\theta ; x , y ) , H ( \\theta ; x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 623, + 506, + 635 + ], + "score": 1.0, + "content": "with few labels", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 85, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 85, + 635, + 100, + 645 + ], + "score": 1.0, + "content": "260", + "type": "text" + }, + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "led to extremely unstable unsatisfactory results. However, we estimate it more accurately using the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 85, + 645, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 85, + 646, + 100, + 656 + ], + "score": 1.0, + "content": "261", + "type": "text" + }, + { + "bbox": [ + 106, + 645, + 505, + 656 + ], + "score": 1.0, + "content": "test set (which is of course impossible in practice) on different datasets and methods to provide", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 85, + 655, + 485, + 668 + ], + "spans": [ + { + "bbox": [ + 85, + 657, + 100, + 667 + ], + "score": 1.0, + "content": "262", + "type": "text" + }, + { + "bbox": [ + 105, + 655, + 204, + 667 + ], + "score": 1.0, + "content": "intuition on the order of", + "type": "text" + }, + { + "bbox": [ + 205, + 657, + 223, + 668 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 655, + 485, + 667 + ], + "score": 1.0, + "content": "and the range of the variance reduction regime in Appendix M.2.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 36.5 + }, + { + "type": "title", + "bbox": [ + 105, + 679, + 180, + 691 + ], + "lines": [ + { + "bbox": [ + 105, + 678, + 181, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 181, + 693 + ], + "score": 1.0, + "content": "3.3 Calibration", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 92, + 699, + 505, + 723 + ], + "lines": [ + { + "bbox": [ + 88, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 88, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "264 The calibration of a model is its capacity of predicting probability estimates that are representative", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 88, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 88, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "265 of the true distribution. This property is determinant in real-world application when we need", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 310, + 752 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 84, + 72, + 506, + 97 + ], + "lines": [ + { + "bbox": [ + 84, + 72, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 84, + 72, + 252, + 86 + ], + "score": 1.0, + "content": "226 Another interesting way to interpret", + "type": "text" + }, + { + "bbox": [ + 253, + 73, + 284, + 83 + ], + "score": 0.39, + "content": "\\scriptstyle { \\mathrm { D e S S L } }", + "type": "inline_equation" + }, + { + "bbox": [ + 284, + 72, + 506, + 86 + ], + "score": 1.0, + "content": "is as a constrained optimisation problem. Indeed, min-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 84, + 502, + 99 + ], + "spans": [ + { + "bbox": [ + 83, + 84, + 138, + 99 + ], + "score": 1.0, + "content": "imising 227", + "type": "text" + }, + { + "bbox": [ + 139, + 84, + 175, + 97 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 84, + 502, + 99 + ], + "score": 1.0, + "content": "is equivalent to minimising the Lagrangian of the following optimisation problem:", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 83, + 72, + 506, + 99 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 217, + 101, + 393, + 156 + ], + "lines": [ + { + "bbox": [ + 217, + 101, + 393, + 156 + ], + "spans": [ + { + "bbox": [ + 217, + 101, + 393, + 156 + ], + "score": 0.93, + "content": "\\begin{array} { c l } { \\displaystyle \\operatorname* { m i n } _ { \\theta } } & { \\displaystyle \\hat { \\mathcal { R } } _ { C C } ( \\theta ) } \\\\ { \\mathrm { s . t . } } & { \\displaystyle \\frac { 1 } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } H ( \\theta ; x _ { i } ) . } \\end{array}", + "type": "interline_equation", + "image_path": "59f763fc3820cd1c9fc9cb19e7caf0cf6317bb212de963cc2d6e9ba2dc64b284.jpg" + } + ] + } + ], + "index": 3.5, + "virtual_lines": [ + { + "bbox": [ + 217, + 101, + 393, + 114.75 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 217, + 114.75, + 393, + 128.5 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 217, + 128.5, + 393, + 142.25 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 217, + 142.25, + 393, + 156.0 + ], + "spans": [], + "index": 5 + } + ] + }, + { + "type": "index", + "bbox": [ + 86, + 163, + 505, + 208 + ], + "lines": [ + { + "bbox": [ + 86, + 162, + 506, + 179 + ], + "spans": [ + { + "bbox": [ + 86, + 167, + 99, + 176 + ], + "score": 1.0, + "content": "228", + "type": "text" + }, + { + "bbox": [ + 104, + 162, + 506, + 179 + ], + "score": 1.0, + "content": "The idea of this optimisation problem is to minimise the complete case risk estimator by assessing", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 174, + 506, + 188 + ], + "spans": [ + { + "bbox": [ + 86, + 177, + 100, + 186 + ], + "score": 1.0, + "content": "229", + "type": "text" + }, + { + "bbox": [ + 104, + 174, + 251, + 188 + ], + "score": 1.0, + "content": "that some properties represented by", + "type": "text" + }, + { + "bbox": [ + 251, + 176, + 261, + 185 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 174, + 506, + 188 + ], + "score": 1.0, + "content": "are on average equal for the labelled data and the unlabelled", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 185, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 86, + 188, + 100, + 198 + ], + "score": 1.0, + "content": "230", + "type": "text" + }, + { + "bbox": [ + 105, + 185, + 505, + 199 + ], + "score": 1.0, + "content": "data. For example, if we consider entropy-minimisation, this program encourages the model to have", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 196, + 396, + 210 + ], + "spans": [ + { + "bbox": [ + 86, + 199, + 99, + 208 + ], + "score": 1.0, + "content": "231", + "type": "text" + }, + { + "bbox": [ + 105, + 196, + 396, + 210 + ], + "score": 1.0, + "content": "the same confidence on the unlabelled examples as on the labelled ones.", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 214, + 507, + 226 + ], + "spans": [ + { + "bbox": [ + 86, + 216, + 99, + 225 + ], + "score": 1.0, + "content": "232", + "type": "text" + }, + { + "bbox": [ + 106, + 214, + 507, + 226 + ], + "score": 1.0, + "content": "The debiasing term of our objective will penalise the confidence of the model on the labelled data.", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 223, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 99, + 235 + ], + "score": 1.0, + "content": "233", + "type": "text" + }, + { + "bbox": [ + 105, + 223, + 506, + 238 + ], + "score": 1.0, + "content": "Pereyra et al. (2017) show that penalising the entropy in a supervised context acts as a strong", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 235, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 86, + 237, + 99, + 246 + ], + "score": 1.0, + "content": "234", + "type": "text" + }, + { + "bbox": [ + 105, + 235, + 506, + 248 + ], + "score": 1.0, + "content": "regulator for supervised models and improves on the state-of-the-art on common benchmarks. This", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 245, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 85, + 248, + 99, + 258 + ], + "score": 1.0, + "content": "235", + "type": "text" + }, + { + "bbox": [ + 105, + 245, + 506, + 259 + ], + "score": 1.0, + "content": "comforts us in the idea of debiasing using labelled data in the case of entropy-minimisation. Similarly,", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 255, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 86, + 259, + 99, + 268 + ], + "score": 1.0, + "content": "236", + "type": "text" + }, + { + "bbox": [ + 104, + 255, + 506, + 271 + ], + "score": 1.0, + "content": "the debiasing term in pseudo-label turns the problem into plausibility inference as described by", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 268, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 85, + 269, + 100, + 280 + ], + "score": 1.0, + "content": "237", + "type": "text" + }, + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "score": 1.0, + "content": "Barndorff-Nielsen (1976). Our objective also resembles doubly-robust risk estimates used for SSL in", + "type": "text" + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 277, + 506, + 292 + ], + "spans": [ + { + "bbox": [ + 86, + 281, + 99, + 290 + ], + "score": 1.0, + "content": "238", + "type": "text" + }, + { + "bbox": [ + 105, + 277, + 506, + 292 + ], + "score": 1.0, + "content": "the context of kernel machines by Liu & Goldberg (2020) and for deep learning in a recent preprint", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 289, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 85, + 291, + 100, + 302 + ], + "score": 1.0, + "content": "239", + "type": "text" + }, + { + "bbox": [ + 106, + 289, + 506, + 303 + ], + "score": 1.0, + "content": "(Hu et al., 2022). 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The function 246", + "type": "text" + }, + { + "bbox": [ + 220, + 393, + 303, + 408 + ], + "score": 0.92, + "content": "\\lambda \\mapsto \\mathbb { V } ( \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 394, + 408, + 410 + ], + "score": 1.0, + "content": "reaches its minimum for:", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24, + "bbox_fs": [ + 86, + 393, + 408, + 410 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 228, + 411, + 381, + 439 + ], + "lines": [ + { + "bbox": [ + 228, + 411, + 381, + 439 + ], + "spans": [ + { + "bbox": [ + 228, + 411, + 381, + 439 + ], + "score": 0.95, + "content": "\\lambda _ { o p t } = \\frac { n _ { u } } { n } \\frac { \\mathrm { C o v } ( L ( \\theta ; x , y ) , H ( \\theta ; x ) ) } { \\mathbb { V } ( H ( \\theta ; x ) ) } ,", + "type": "interline_equation", + "image_path": "502a8a35bb7915323a83c0f1cd5eb49981cc20de5fb727af86fe877267b9f65e.jpg" + } + ] + } + ], + "index": 25.5, + "virtual_lines": [ + { + "bbox": [ + 228, + 411, + 381, + 425.0 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 228, + 425.0, + 381, + 439.0 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 87, + 443, + 156, + 455 + ], + "lines": [ + { + "bbox": [ + 84, + 441, + 153, + 457 + ], + "spans": [ + { + "bbox": [ + 84, + 441, + 134, + 457 + ], + "score": 1.0, + "content": "247 and at", + "type": "text" + }, + { + "bbox": [ + 135, + 443, + 153, + 455 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + } + ], + "index": 27 + } + ], + "index": 27, + "bbox_fs": [ + 84, + 441, + 153, + 457 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 168, + 459, + 442, + 481 + ], + "lines": [ + { + "bbox": [ + 168, + 459, + 442, + 481 + ], + "spans": [ + { + "bbox": [ + 168, + 459, + 442, + 481 + ], + "score": 0.83, + "content": "\\mathbb { V } ( \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ) | _ { \\lambda _ { o p t } } = \\left( 1 - \\frac { n _ { u } } { n } \\rho _ { L , H } ^ { 2 } \\right) \\mathbb { V } ( \\hat { \\mathcal { R } } _ { C C } ( \\theta ) ) \\leq \\mathbb { V } ( \\hat { \\mathcal { R } } _ { C C } ( \\theta ) ) ,", + "type": "interline_equation", + "image_path": "003bf3a85c148ed51e81f846451aea81d15cac70a457c033de943905f4d6e3cd.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 168, + 459, + 442, + 481 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 88, + 490, + 274, + 504 + ], + "lines": [ + { + "bbox": [ + 85, + 489, + 272, + 505 + ], + "spans": [ + { + "bbox": [ + 85, + 489, + 133, + 505 + ], + "score": 1.0, + "content": "248 where", + "type": "text" + }, + { + "bbox": [ + 133, + 491, + 272, + 504 + ], + "score": 0.88, + "content": "\\rho _ { L , H } = \\operatorname { C o r r } ( L ( \\theta ; x , y ) , H ( \\theta ; x ) ) .", + "type": "inline_equation" + } + ], + "index": 29 + } + ], + "index": 29, + "bbox_fs": [ + 85, + 489, + 272, + 505 + ] + }, + { + "type": "index", + "bbox": [ + 85, + 513, + 506, + 668 + ], + "lines": [ + { + "bbox": [ + 86, + 512, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 86, + 516, + 99, + 524 + ], + "score": 1.0, + "content": "249", + "type": "text" + }, + { + "bbox": [ + 105, + 513, + 161, + 527 + ], + "score": 1.0, + "content": "Additionally,", + "type": "text" + }, + { + "bbox": [ + 162, + 512, + 285, + 526 + ], + "score": 0.93, + "content": "-", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 513, + 312, + 527 + ], + "score": 1.0, + "content": "for all", + "type": "text" + }, + { + "bbox": [ + 313, + 514, + 320, + 524 + ], + "score": 0.81, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 513, + 381, + 527 + ], + "score": 1.0, + "content": "between 0 and", + "type": "text" + }, + { + "bbox": [ + 381, + 514, + 404, + 526 + ], + "score": 0.91, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 513, + 506, + 527 + ], + "score": 1.0, + "content": ". A proof of this theorem", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 524, + 506, + 537 + ], + "spans": [ + { + "bbox": [ + 85, + 526, + 100, + 536 + ], + "score": 1.0, + "content": "250", + "type": "text" + }, + { + "bbox": [ + 105, + 524, + 506, + 537 + ], + "score": 1.0, + "content": "is available as Appendix E. 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Other", + "type": "text" + } + ], + "index": 35, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 578, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 85, + 581, + 100, + 591 + ], + "score": 1.0, + "content": "255", + "type": "text" + }, + { + "bbox": [ + 105, + 578, + 506, + 591 + ], + "score": 1.0, + "content": "SSL methods have variance reduction guarantees and already has shown great promises in SSL, see", + "type": "text" + } + ], + "index": 36, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 590, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 86, + 592, + 99, + 601 + ], + "score": 1.0, + "content": "256", + "type": "text" + }, + { + "bbox": [ + 105, + 590, + 160, + 603 + ], + "score": 1.0, + "content": "Fox-Roberts", + "type": "text" + }, + { + "bbox": [ + 160, + 591, + 169, + 600 + ], + "score": 0.38, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 590, + 506, + 603 + ], + "score": 1.0, + "content": "Rosten (2014) and Sakai et al. 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This property is determinant in real-world application when we need", + "type": "text" + } + ], + "index": 46, + "is_list_start_line": true + } + ], + "index": 45.5, + "bbox_fs": [ + 88, + 699, + 505, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 103, + 72, + 505, + 193 + ], + "lines": [ + { + "bbox": [ + 105, + 73, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 73, + 252, + 85 + ], + "score": 1.0, + "content": "reliable predictions. A scoring rule", + "type": "text" + }, + { + "bbox": [ + 252, + 73, + 260, + 83 + ], + "score": 0.81, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "is a function assigning a score to the predictive distribution", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 138, + 96 + ], + "score": 0.91, + "content": "p _ { \\theta } ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 83, + 222, + 96 + ], + "score": 1.0, + "content": "relative to the event", + "type": "text" + }, + { + "bbox": [ + 222, + 83, + 333, + 96 + ], + "score": 0.73, + "content": "y \\bar { | x \\sim p ( y | x ) , S ( p _ { \\theta } , ( x , y ) ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 83, + 364, + 96 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 364, + 83, + 393, + 96 + ], + "score": 0.93, + "content": "p ( x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "is the true distribution (see", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 94, + 507, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 94, + 166, + 108 + ], + "score": 1.0, + "content": "e.g. Gneiting", + "type": "text" + }, + { + "bbox": [ + 166, + 95, + 176, + 105 + ], + "score": 0.37, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 94, + 507, + 108 + ], + "score": 1.0, + "content": "Raftery, 2007). A scoring rule measures both the accuracy and the quality of", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "predictive uncertainty, meaning that better calibration is rewarded. The expected scoring rule is", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 115, + 506, + 130 + ], + "spans": [ + { + "bbox": [ + 104, + 115, + 151, + 130 + ], + "score": 1.0, + "content": "defined as", + "type": "text" + }, + { + "bbox": [ + 151, + 116, + 270, + 128 + ], + "score": 0.92, + "content": "\\mathcal { S } ( p _ { \\theta } , p ) \\stackrel { \\cdot } { = } \\mathbb { E } _ { p } [ \\mathcal { S } ( p \\bar { \\theta } , ( x , y ) ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 115, + 506, + 130 + ], + "score": 1.0, + "content": ". A proper scoring rule is defined as a scoring rule such", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 126, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 104, + 126, + 124, + 141 + ], + "score": 1.0, + "content": "that", + "type": "text" + }, + { + "bbox": [ + 124, + 128, + 201, + 139 + ], + "score": 0.91, + "content": "S ( p _ { \\theta } , p ) \\leq S ( p , p )", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 126, + 506, + 141 + ], + "score": 1.0, + "content": "(Gneiting & Raftery, 2007). The motivation behind having proper scoring", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 137, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 410, + 151 + ], + "score": 1.0, + "content": "rules comes from the following: suppose that the true data distribution", + "type": "text" + }, + { + "bbox": [ + 410, + 140, + 417, + 149 + ], + "score": 0.78, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 137, + 506, + 151 + ], + "score": 1.0, + "content": "is accessible by our", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 358, + 162 + ], + "score": 1.0, + "content": "set of models. Then, the scoring rule encourages to predict", + "type": "text" + }, + { + "bbox": [ + 359, + 150, + 392, + 160 + ], + "score": 0.9, + "content": "p _ { \\theta } ~ = ~ p", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 149, + 506, + 162 + ], + "score": 1.0, + "content": ". The opposite of a proper", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "score": 1.0, + "content": "scoring rule can then be used to train a model to encourage the calibration of predictive uncertainty:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 170, + 506, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 219, + 183 + ], + "score": 0.92, + "content": "L ( \\theta ; \\bar { x , y } ) = - \\mathcal { S } ( p _ { \\theta } , ( x , y ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 170, + 506, + 184 + ], + "score": 1.0, + "content": ". Most common losses used to train models are proper scorings rule such", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 182, + 179, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 179, + 195 + ], + "score": 1.0, + "content": "as log-likelihood.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 102, + 195, + 503, + 221 + ], + "lines": [ + { + "bbox": [ + 180, + 193, + 504, + 227 + ], + "spans": [ + { + "bbox": [ + 180, + 195, + 297, + 207 + ], + "score": 0.87, + "content": "S ( p _ { \\theta } , ( x , y ) ) = - L ( \\theta ; x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 193, + 426, + 227 + ], + "score": 1.0, + "content": "is a proper scoring rule, then so a proper scoring rule.", + "type": "text" + }, + { + "bbox": [ + 426, + 195, + 504, + 208 + ], + "score": 0.89, + "content": "S ^ { \\prime } ( p _ { \\theta } , ( x , y , r ) ) =", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 207, + 275, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 207, + 275, + 221 + ], + "score": 0.88, + "content": "\\begin{array} { r } { - \\big ( \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda { n } \\big ( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\big ) H ( \\theta ; x ) \\big ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 11 + } + ], + "index": 11.5 + }, + { + "type": "text", + "bbox": [ + 106, + 226, + 505, + 261 + ], + "lines": [ + { + "bbox": [ + 106, + 227, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 256, + 239 + ], + "score": 1.0, + "content": "The proof is available in Appendix", + "type": "text" + }, + { + "bbox": [ + 257, + 227, + 266, + 237 + ], + "score": 0.31, + "content": "\\mathbf { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 266, + 227, + 505, + 239 + ], + "score": 1.0, + "content": ", and follows directly from unbiasedness and the MCAR", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 238, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 506, + 250 + ], + "score": 1.0, + "content": "assumption. The main interpretation of this theorem is that we can expect DeSSL to be as well-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 248, + 235, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 235, + 262 + ], + "score": 1.0, + "content": "calibrated as the complete case.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + }, + { + "type": "title", + "bbox": [ + 107, + 272, + 181, + 284 + ], + "lines": [ + { + "bbox": [ + 104, + 270, + 182, + 288 + ], + "spans": [ + { + "bbox": [ + 104, + 270, + 182, + 288 + ], + "score": 1.0, + "content": "3.4 Consistency", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 293, + 505, + 330 + ], + "lines": [ + { + "bbox": [ + 105, + 293, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 153, + 308 + ], + "score": 1.0, + "content": "We say that", + "type": "text" + }, + { + "bbox": [ + 153, + 293, + 160, + 305 + ], + "score": 0.84, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 293, + 219, + 308 + ], + "score": 1.0, + "content": "is consistent if", + "type": "text" + }, + { + "bbox": [ + 219, + 293, + 273, + 307 + ], + "score": 0.93, + "content": "d ( { \\hat { \\theta } } , \\theta ^ { * } ) \\xrightarrow { p } 0", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 293, + 297, + 308 + ], + "score": 1.0, + "content": "when", + "type": "text" + }, + { + "bbox": [ + 298, + 297, + 330, + 305 + ], + "score": 0.87, + "content": "n \\to \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 293, + 360, + 308 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 360, + 295, + 366, + 305 + ], + "score": 0.83, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 293, + 429, + 308 + ], + "score": 1.0, + "content": "is a distance on", + "type": "text" + }, + { + "bbox": [ + 429, + 295, + 438, + 305 + ], + "score": 0.72, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 293, + 505, + 308 + ], + "score": 1.0, + "content": ". The asymptotic", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 306, + 506, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 158, + 323 + ], + "score": 1.0, + "content": "properties of", + "type": "text" + }, + { + "bbox": [ + 158, + 306, + 165, + 318 + ], + "score": 0.82, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 306, + 330, + 323 + ], + "score": 1.0, + "content": "depend on the behaviours of the functions", + "type": "text" + }, + { + "bbox": [ + 330, + 309, + 338, + 318 + ], + "score": 0.82, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 306, + 355, + 323 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 356, + 308, + 366, + 318 + ], + "score": 0.81, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 306, + 506, + 323 + ], + "score": 1.0, + "content": ". We will thus require the following", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 319, + 197, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 197, + 332 + ], + "score": 1.0, + "content": "standard assumptions.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 103, + 332, + 459, + 345 + ], + "lines": [ + { + "bbox": [ + 104, + 330, + 462, + 348 + ], + "spans": [ + { + "bbox": [ + 104, + 330, + 239, + 348 + ], + "score": 1.0, + "content": "Assumption 3.3. The minimum", + "type": "text" + }, + { + "bbox": [ + 239, + 333, + 249, + 343 + ], + "score": 0.86, + "content": "\\theta ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 330, + 261, + 348 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 262, + 333, + 271, + 343 + ], + "score": 0.84, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 330, + 345, + 348 + ], + "score": 1.0, + "content": "is well-separated:", + "type": "text" + }, + { + "bbox": [ + 346, + 333, + 462, + 346 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\operatorname* { i n f } _ { \\theta : d ( \\theta ^ { * } , \\theta ) \\geq \\epsilon } \\mathcal { R } ( \\theta ) > \\mathcal { R } ( \\theta ^ { * } ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 105, + 347, + 437, + 358 + ], + "lines": [ + { + "bbox": [ + 105, + 346, + 437, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 396, + 359 + ], + "score": 1.0, + "content": "Assumption 3.4. The uniform weak law of large number holds for both", + "type": "text" + }, + { + "bbox": [ + 397, + 347, + 405, + 357 + ], + "score": 0.83, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 346, + 423, + 359 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 423, + 347, + 433, + 357 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 346, + 437, + 359 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 105, + 362, + 502, + 387 + ], + "lines": [ + { + "bbox": [ + 105, + 360, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 480, + 375 + ], + "score": 1.0, + "content": "Theorem 3.5. Under the MCAR assumption, Assumption 3.3 and Assumption 3.4,", + "type": "text" + }, + { + "bbox": [ + 480, + 360, + 505, + 374 + ], + "score": 0.85, + "content": "\\begin{array} { r l } { \\hat { \\theta } } & { { } = } \\end{array}", + "type": "inline_equation" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 373, + 232, + 387 + ], + "spans": [ + { + "bbox": [ + 107, + 373, + 177, + 387 + ], + "score": 0.85, + "content": "\\operatorname { a r g m i n } \\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 177, + 374, + 232, + 387 + ], + "score": 1.0, + "content": "is consistent.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 106, + 393, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 505, + 406 + ], + "score": 1.0, + "content": "For proof of this theorem see Appendix G. This theorem is a simple application of van der Vaart’s", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 404, + 505, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 505, + 416 + ], + "score": 1.0, + "content": "(2000) Theorem 5.7 proving the consistency of an M-estimator. Also, this result holds for the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 416, + 505, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 187, + 427 + ], + "score": 1.0, + "content": "complete case, with", + "type": "text" + }, + { + "bbox": [ + 188, + 416, + 213, + 426 + ], + "score": 0.9, + "content": "\\lambda = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 416, + 505, + 427 + ], + "score": 1.0, + "content": "which proves that the complete case is a solid baseline under the MCAR", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 427, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 384, + 441 + ], + "score": 1.0, + "content": "assumption. Going further, we prove the asymptotic normality of", + "type": "text" + }, + { + "bbox": [ + 384, + 427, + 416, + 440 + ], + "score": 0.92, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 428, + 505, + 441 + ], + "score": 1.0, + "content": "and showed that the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 439, + 330, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 320, + 451 + ], + "score": 1.0, + "content": "asymptotic variance can be optimised with respect to", + "type": "text" + }, + { + "bbox": [ + 320, + 440, + 327, + 449 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 439, + 330, + 451 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 504, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 159, + 475 + ], + "score": 1.0, + "content": "Coupling of", + "type": "text" + }, + { + "bbox": [ + 159, + 463, + 169, + 473 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 460, + 189, + 475 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 189, + 463, + 201, + 473 + ], + "score": 0.87, + "content": "n _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 460, + 463, + 475 + ], + "score": 1.0, + "content": "under the MCAR assumption Under the MCAR assumption,", + "type": "text" + }, + { + "bbox": [ + 463, + 464, + 473, + 473 + ], + "score": 0.81, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 460, + 491, + 475 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 491, + 464, + 504, + 473 + ], + "score": 0.85, + "content": "n _ { u }", + "type": "inline_equation" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 472, + 507, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 254, + 486 + ], + "score": 1.0, + "content": "are random variables. We have that", + "type": "text" + }, + { + "bbox": [ + 254, + 473, + 295, + 484 + ], + "score": 0.92, + "content": "r \\sim B ( \\pi )", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 472, + 334, + 486 + ], + "score": 1.0, + "content": "(i.e. any", + "type": "text" + }, + { + "bbox": [ + 334, + 475, + 340, + 483 + ], + "score": 0.72, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 341, + 472, + 421, + 486 + ], + "score": 1.0, + "content": "has the probability", + "type": "text" + }, + { + "bbox": [ + 421, + 476, + 428, + 483 + ], + "score": 0.71, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 472, + 507, + 486 + ], + "score": 1.0, + "content": "of being labelled).", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 483, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 153, + 497 + ], + "score": 1.0, + "content": "Then, with", + "type": "text" + }, + { + "bbox": [ + 154, + 486, + 161, + 494 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 161, + 483, + 281, + 497 + ], + "score": 1.0, + "content": "growing to infinity, we have", + "type": "text" + }, + { + "bbox": [ + 281, + 484, + 355, + 498 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\frac { n _ { l } } { n } = \\frac { n _ { l } } { n _ { l } + n _ { u } } \\to \\pi } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 483, + 428, + 500 + ], + "score": 1.0, + "content": ". 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This implies", + "type": "text" + }, + { + "bbox": [ + 258, + 498, + 308, + 510 + ], + "score": 0.93, + "content": "n _ { u } = \\mathcal { O } ( n _ { l } )", + "type": "inline_equation" + }, + { + "bbox": [ + 308, + 495, + 370, + 511 + ], + "score": 1.0, + "content": "and then when", + "type": "text" + }, + { + "bbox": [ + 370, + 500, + 377, + 507 + ], + "score": 0.71, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 495, + 462, + 511 + ], + "score": 1.0, + "content": "goes to infinity, both", + "type": "text" + }, + { + "bbox": [ + 463, + 499, + 475, + 509 + ], + "score": 0.86, + "content": "n _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 495, + 493, + 511 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 493, + 499, + 504, + 509 + ], + "score": 0.81, + "content": "n _ { l }", + "type": "inline_equation" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 510, + 269, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 222, + 523 + ], + "score": 1.0, + "content": "go to infinity too and even if", + "type": "text" + }, + { + "bbox": [ + 222, + 511, + 264, + 521 + ], + "score": 0.9, + "content": "n _ { u } > > n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 510, + 269, + 523 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31 + }, + { + "type": "title", + "bbox": [ + 105, + 533, + 349, + 546 + ], + "lines": [ + { + "bbox": [ + 106, + 534, + 348, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 348, + 547 + ], + "score": 1.0, + "content": "3.5 Rademacher complexity and generalisation bounds", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 88, + 553, + 506, + 589 + ], + "lines": [ + { + "bbox": [ + 103, + 553, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 103, + 553, + 506, + 566 + ], + "score": 1.0, + "content": "In this section, we prove an upper bound for the generalisation error of DeSSL. The unbiasedness of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 143, + 578 + ], + "score": 0.91, + "content": "\\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "can directly be used to derive generalisation bounds based on the Rademacher complexity", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 577, + 319, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 319, + 590 + ], + "score": 1.0, + "content": "(Bartlett & Mendelson, 2002), defined in our case as", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36 + }, + { + "type": "interline_equation", + "bbox": [ + 117, + 591, + 482, + 624 + ], + "lines": [ + { + "bbox": [ + 117, + 591, + 482, + 624 + ], + "spans": [ + { + "bbox": [ + 117, + 591, + 482, + 624 + ], + "score": 0.93, + "content": "R _ { n } = \\mathbb { E } _ { ( \\varepsilon _ { i } ) _ { i \\leq n } } \\left[ \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left( \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\varepsilon _ { i } L ( \\theta ; x _ { i } , y _ { i } ) - \\frac { \\lambda } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\varepsilon _ { i } H ( \\theta ; x _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } \\varepsilon _ { i } H ( \\theta ; x _ { i } ) \\right) \\right] ,", + "type": "interline_equation", + "image_path": "22bb146a8ce5616f710d450da252122d3ccb81ccaf18e954e000b350f14f7b55.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 117, + 591, + 482, + 602.0 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 117, + 602.0, + 482, + 613.0 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 117, + 613.0, + 482, + 624.0 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 84, + 627, + 508, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 133, + 640 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 629, + 143, + 638 + ], + "score": 0.86, + "content": "\\varepsilon _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 626, + 476, + 640 + ], + "score": 1.0, + "content": "are i.i.d. Rademacher variables independent of the data. In the particular case of", + "type": "text" + }, + { + "bbox": [ + 477, + 627, + 502, + 637 + ], + "score": 0.88, + "content": "\\lambda = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 626, + 506, + 640 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "we recover the standard Rademacher complexity of the complete case. We can then now bound the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 649, + 377, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 377, + 661 + ], + "score": 1.0, + "content": "generalisation error of a model trained using our new loss function.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 86, + 662, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 86, + 662, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 86, + 665, + 100, + 673 + ], + "score": 1.0, + "content": "307", + "type": "text" + }, + { + "bbox": [ + 104, + 662, + 362, + 674 + ], + "score": 1.0, + "content": "Theorem 3.6. We assume that labels are MCAR and that both", + "type": "text" + }, + { + "bbox": [ + 362, + 664, + 370, + 672 + ], + "score": 0.68, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 370, + 662, + 389, + 674 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 389, + 664, + 399, + 672 + ], + "score": 0.58, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 400, + 662, + 505, + 674 + ], + "score": 1.0, + "content": "are bounded. 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A scoring rule", + "type": "text" + }, + { + "bbox": [ + 252, + 73, + 260, + 83 + ], + "score": 0.81, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "is a function assigning a score to the predictive distribution", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 138, + 96 + ], + "score": 0.91, + "content": "p _ { \\theta } ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 83, + 222, + 96 + ], + "score": 1.0, + "content": "relative to the event", + "type": "text" + }, + { + "bbox": [ + 222, + 83, + 333, + 96 + ], + "score": 0.73, + "content": "y \\bar { | x \\sim p ( y | x ) , S ( p _ { \\theta } , ( x , y ) ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 83, + 364, + 96 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 364, + 83, + 393, + 96 + ], + "score": 0.93, + "content": "p ( x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "is the true distribution (see", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 94, + 507, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 94, + 166, + 108 + ], + "score": 1.0, + "content": "e.g. Gneiting", + "type": "text" + }, + { + "bbox": [ + 166, + 95, + 176, + 105 + ], + "score": 0.37, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 94, + 507, + 108 + ], + "score": 1.0, + "content": "Raftery, 2007). A scoring rule measures both the accuracy and the quality of", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "predictive uncertainty, meaning that better calibration is rewarded. The expected scoring rule is", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 115, + 506, + 130 + ], + "spans": [ + { + "bbox": [ + 104, + 115, + 151, + 130 + ], + "score": 1.0, + "content": "defined as", + "type": "text" + }, + { + "bbox": [ + 151, + 116, + 270, + 128 + ], + "score": 0.92, + "content": "\\mathcal { S } ( p _ { \\theta } , p ) \\stackrel { \\cdot } { = } \\mathbb { E } _ { p } [ \\mathcal { S } ( p \\bar { \\theta } , ( x , y ) ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 115, + 506, + 130 + ], + "score": 1.0, + "content": ". A proper scoring rule is defined as a scoring rule such", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 126, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 104, + 126, + 124, + 141 + ], + "score": 1.0, + "content": "that", + "type": "text" + }, + { + "bbox": [ + 124, + 128, + 201, + 139 + ], + "score": 0.91, + "content": "S ( p _ { \\theta } , p ) \\leq S ( p , p )", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 126, + 506, + 141 + ], + "score": 1.0, + "content": "(Gneiting & Raftery, 2007). The motivation behind having proper scoring", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 137, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 410, + 151 + ], + "score": 1.0, + "content": "rules comes from the following: suppose that the true data distribution", + "type": "text" + }, + { + "bbox": [ + 410, + 140, + 417, + 149 + ], + "score": 0.78, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 137, + 506, + 151 + ], + "score": 1.0, + "content": "is accessible by our", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 358, + 162 + ], + "score": 1.0, + "content": "set of models. Then, the scoring rule encourages to predict", + "type": "text" + }, + { + "bbox": [ + 359, + 150, + 392, + 160 + ], + "score": 0.9, + "content": "p _ { \\theta } ~ = ~ p", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 149, + 506, + 162 + ], + "score": 1.0, + "content": ". The opposite of a proper", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "score": 1.0, + "content": "scoring rule can then be used to train a model to encourage the calibration of predictive uncertainty:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 170, + 506, + 184 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 219, + 183 + ], + "score": 0.92, + "content": "L ( \\theta ; \\bar { x , y } ) = - \\mathcal { S } ( p _ { \\theta } , ( x , y ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 170, + 506, + 184 + ], + "score": 1.0, + "content": ". Most common losses used to train models are proper scorings rule such", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 182, + 179, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 179, + 195 + ], + "score": 1.0, + "content": "as log-likelihood.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5, + "bbox_fs": [ + 104, + 73, + 507, + 195 + ] + }, + { + "type": "text", + "bbox": [ + 102, + 195, + 503, + 221 + ], + "lines": [ + { + "bbox": [ + 180, + 193, + 504, + 227 + ], + "spans": [ + { + "bbox": [ + 180, + 195, + 297, + 207 + ], + "score": 0.87, + "content": "S ( p _ { \\theta } , ( x , y ) ) = - L ( \\theta ; x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 193, + 426, + 227 + ], + "score": 1.0, + "content": "is a proper scoring rule, then so a proper scoring rule.", + "type": "text" + }, + { + "bbox": [ + 426, + 195, + 504, + 208 + ], + "score": 0.89, + "content": "S ^ { \\prime } ( p _ { \\theta } , ( x , y , r ) ) =", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 207, + 275, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 207, + 275, + 221 + ], + "score": 0.88, + "content": "\\begin{array} { r } { - \\big ( \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda { n } \\big ( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\big ) H ( \\theta ; x ) \\big ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 11 + } + ], + "index": 11.5, + "bbox_fs": [ + 106, + 193, + 504, + 227 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 226, + 505, + 261 + ], + "lines": [ + { + "bbox": [ + 106, + 227, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 256, + 239 + ], + "score": 1.0, + "content": "The proof is available in Appendix", + "type": "text" + }, + { + "bbox": [ + 257, + 227, + 266, + 237 + ], + "score": 0.31, + "content": "\\mathbf { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 266, + 227, + 505, + 239 + ], + "score": 1.0, + "content": ", and follows directly from unbiasedness and the MCAR", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 238, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 506, + 250 + ], + "score": 1.0, + "content": "assumption. The main interpretation of this theorem is that we can expect DeSSL to be as well-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 248, + 235, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 235, + 262 + ], + "score": 1.0, + "content": "calibrated as the complete case.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 227, + 506, + 262 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 272, + 181, + 284 + ], + "lines": [ + { + "bbox": [ + 104, + 270, + 182, + 288 + ], + "spans": [ + { + "bbox": [ + 104, + 270, + 182, + 288 + ], + "score": 1.0, + "content": "3.4 Consistency", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 293, + 505, + 330 + ], + "lines": [ + { + "bbox": [ + 105, + 293, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 153, + 308 + ], + "score": 1.0, + "content": "We say that", + "type": "text" + }, + { + "bbox": [ + 153, + 293, + 160, + 305 + ], + "score": 0.84, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 293, + 219, + 308 + ], + "score": 1.0, + "content": "is consistent if", + "type": "text" + }, + { + "bbox": [ + 219, + 293, + 273, + 307 + ], + "score": 0.93, + "content": "d ( { \\hat { \\theta } } , \\theta ^ { * } ) \\xrightarrow { p } 0", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 293, + 297, + 308 + ], + "score": 1.0, + "content": "when", + "type": "text" + }, + { + "bbox": [ + 298, + 297, + 330, + 305 + ], + "score": 0.87, + "content": "n \\to \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 293, + 360, + 308 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 360, + 295, + 366, + 305 + ], + "score": 0.83, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 293, + 429, + 308 + ], + "score": 1.0, + "content": "is a distance on", + "type": "text" + }, + { + "bbox": [ + 429, + 295, + 438, + 305 + ], + "score": 0.72, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 293, + 505, + 308 + ], + "score": 1.0, + "content": ". The asymptotic", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 306, + 506, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 158, + 323 + ], + "score": 1.0, + "content": "properties of", + "type": "text" + }, + { + "bbox": [ + 158, + 306, + 165, + 318 + ], + "score": 0.82, + "content": "\\hat { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 306, + 330, + 323 + ], + "score": 1.0, + "content": "depend on the behaviours of the functions", + "type": "text" + }, + { + "bbox": [ + 330, + 309, + 338, + 318 + ], + "score": 0.82, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 306, + 355, + 323 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 356, + 308, + 366, + 318 + ], + "score": 0.81, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 306, + 506, + 323 + ], + "score": 1.0, + "content": ". We will thus require the following", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 319, + 197, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 197, + 332 + ], + "score": 1.0, + "content": "standard assumptions.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 293, + 506, + 332 + ] + }, + { + "type": "text", + "bbox": [ + 103, + 332, + 459, + 345 + ], + "lines": [ + { + "bbox": [ + 104, + 330, + 462, + 348 + ], + "spans": [ + { + "bbox": [ + 104, + 330, + 239, + 348 + ], + "score": 1.0, + "content": "Assumption 3.3. The minimum", + "type": "text" + }, + { + "bbox": [ + 239, + 333, + 249, + 343 + ], + "score": 0.86, + "content": "\\theta ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 330, + 261, + 348 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 262, + 333, + 271, + 343 + ], + "score": 0.84, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 330, + 345, + 348 + ], + "score": 1.0, + "content": "is well-separated:", + "type": "text" + }, + { + "bbox": [ + 346, + 333, + 462, + 346 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\operatorname* { i n f } _ { \\theta : d ( \\theta ^ { * } , \\theta ) \\geq \\epsilon } \\mathcal { R } ( \\theta ) > \\mathcal { R } ( \\theta ^ { * } ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 20 + } + ], + "index": 20, + "bbox_fs": [ + 104, + 330, + 462, + 348 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 347, + 437, + 358 + ], + "lines": [ + { + "bbox": [ + 105, + 346, + 437, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 396, + 359 + ], + "score": 1.0, + "content": "Assumption 3.4. The uniform weak law of large number holds for both", + "type": "text" + }, + { + "bbox": [ + 397, + 347, + 405, + 357 + ], + "score": 0.83, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 346, + 423, + 359 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 423, + 347, + 433, + 357 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 346, + 437, + 359 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 346, + 437, + 359 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 362, + 502, + 387 + ], + "lines": [ + { + "bbox": [ + 105, + 360, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 480, + 375 + ], + "score": 1.0, + "content": "Theorem 3.5. Under the MCAR assumption, Assumption 3.3 and Assumption 3.4,", + "type": "text" + }, + { + "bbox": [ + 480, + 360, + 505, + 374 + ], + "score": 0.85, + "content": "\\begin{array} { r l } { \\hat { \\theta } } & { { } = } \\end{array}", + "type": "inline_equation" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 373, + 232, + 387 + ], + "spans": [ + { + "bbox": [ + 107, + 373, + 177, + 387 + ], + "score": 0.85, + "content": "\\operatorname { a r g m i n } \\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 177, + 374, + 232, + 387 + ], + "score": 1.0, + "content": "is consistent.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 360, + 505, + 387 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 393, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 505, + 406 + ], + "score": 1.0, + "content": "For proof of this theorem see Appendix G. This theorem is a simple application of van der Vaart’s", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 404, + 505, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 505, + 416 + ], + "score": 1.0, + "content": "(2000) Theorem 5.7 proving the consistency of an M-estimator. Also, this result holds for the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 416, + 505, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 187, + 427 + ], + "score": 1.0, + "content": "complete case, with", + "type": "text" + }, + { + "bbox": [ + 188, + 416, + 213, + 426 + ], + "score": 0.9, + "content": "\\lambda = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 416, + 505, + 427 + ], + "score": 1.0, + "content": "which proves that the complete case is a solid baseline under the MCAR", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 427, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 384, + 441 + ], + "score": 1.0, + "content": "assumption. Going further, we prove the asymptotic normality of", + "type": "text" + }, + { + "bbox": [ + 384, + 427, + 416, + 440 + ], + "score": 0.92, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 428, + 505, + 441 + ], + "score": 1.0, + "content": "and showed that the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 439, + 330, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 320, + 451 + ], + "score": 1.0, + "content": "asymptotic variance can be optimised with respect to", + "type": "text" + }, + { + "bbox": [ + 320, + 440, + 327, + 449 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 439, + 330, + 451 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 393, + 505, + 451 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 504, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 159, + 475 + ], + "score": 1.0, + "content": "Coupling of", + "type": "text" + }, + { + "bbox": [ + 159, + 463, + 169, + 473 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 460, + 189, + 475 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 189, + 463, + 201, + 473 + ], + "score": 0.87, + "content": "n _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 460, + 463, + 475 + ], + "score": 1.0, + "content": "under the MCAR assumption Under the MCAR assumption,", + "type": "text" + }, + { + "bbox": [ + 463, + 464, + 473, + 473 + ], + "score": 0.81, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 473, + 460, + 491, + 475 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 491, + 464, + 504, + 473 + ], + "score": 0.85, + "content": "n _ { u }", + "type": "inline_equation" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 472, + 507, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 254, + 486 + ], + "score": 1.0, + "content": "are random variables. We have that", + "type": "text" + }, + { + "bbox": [ + 254, + 473, + 295, + 484 + ], + "score": 0.92, + "content": "r \\sim B ( \\pi )", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 472, + 334, + 486 + ], + "score": 1.0, + "content": "(i.e. any", + "type": "text" + }, + { + "bbox": [ + 334, + 475, + 340, + 483 + ], + "score": 0.72, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 341, + 472, + 421, + 486 + ], + "score": 1.0, + "content": "has the probability", + "type": "text" + }, + { + "bbox": [ + 421, + 476, + 428, + 483 + ], + "score": 0.71, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 472, + 507, + 486 + ], + "score": 1.0, + "content": "of being labelled).", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 483, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 153, + 497 + ], + "score": 1.0, + "content": "Then, with", + "type": "text" + }, + { + "bbox": [ + 154, + 486, + 161, + 494 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 161, + 483, + 281, + 497 + ], + "score": 1.0, + "content": "growing to infinity, we have", + "type": "text" + }, + { + "bbox": [ + 281, + 484, + 355, + 498 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\frac { n _ { l } } { n } = \\frac { n _ { l } } { n _ { l } + n _ { u } } \\to \\pi } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 483, + 428, + 500 + ], + "score": 1.0, + "content": ". Therefore, both", + "type": "text" + }, + { + "bbox": [ + 428, + 486, + 438, + 495 + ], + "score": 0.81, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 483, + 457, + 500 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 457, + 485, + 469, + 495 + ], + "score": 0.85, + "content": "n _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 483, + 505, + 500 + ], + "score": 1.0, + "content": "grow to", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 495, + 504, + 511 + ], + "spans": [ + { + "bbox": [ + 104, + 495, + 155, + 511 + ], + "score": 1.0, + "content": "infinity and", + "type": "text" + }, + { + "bbox": [ + 155, + 496, + 201, + 511 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\frac { n _ { l } } { n _ { u } } \\to \\frac { \\pi - 1 } { \\pi } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 495, + 257, + 511 + ], + "score": 1.0, + "content": ". This implies", + "type": "text" + }, + { + "bbox": [ + 258, + 498, + 308, + 510 + ], + "score": 0.93, + "content": "n _ { u } = \\mathcal { O } ( n _ { l } )", + "type": "inline_equation" + }, + { + "bbox": [ + 308, + 495, + 370, + 511 + ], + "score": 1.0, + "content": "and then when", + "type": "text" + }, + { + "bbox": [ + 370, + 500, + 377, + 507 + ], + "score": 0.71, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 495, + 462, + 511 + ], + "score": 1.0, + "content": "goes to infinity, both", + "type": "text" + }, + { + "bbox": [ + 463, + 499, + 475, + 509 + ], + "score": 0.86, + "content": "n _ { u }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 495, + 493, + 511 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 493, + 499, + 504, + 509 + ], + "score": 0.81, + "content": "n _ { l }", + "type": "inline_equation" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 510, + 269, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 222, + 523 + ], + "score": 1.0, + "content": "go to infinity too and even if", + "type": "text" + }, + { + "bbox": [ + 222, + 511, + 264, + 521 + ], + "score": 0.9, + "content": "n _ { u } > > n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 510, + 269, + 523 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 104, + 460, + 507, + 523 + ] + }, + { + "type": "title", + "bbox": [ + 105, + 533, + 349, + 546 + ], + "lines": [ + { + "bbox": [ + 106, + 534, + 348, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 348, + 547 + ], + "score": 1.0, + "content": "3.5 Rademacher complexity and generalisation bounds", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 88, + 553, + 506, + 589 + ], + "lines": [ + { + "bbox": [ + 103, + 553, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 103, + 553, + 506, + 566 + ], + "score": 1.0, + "content": "In this section, we prove an upper bound for the generalisation error of DeSSL. The unbiasedness of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 143, + 578 + ], + "score": 0.91, + "content": "\\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "can directly be used to derive generalisation bounds based on the Rademacher complexity", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 577, + 319, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 319, + 590 + ], + "score": 1.0, + "content": "(Bartlett & Mendelson, 2002), defined in our case as", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36, + "bbox_fs": [ + 103, + 553, + 506, + 590 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 117, + 591, + 482, + 624 + ], + "lines": [ + { + "bbox": [ + 117, + 591, + 482, + 624 + ], + "spans": [ + { + "bbox": [ + 117, + 591, + 482, + 624 + ], + "score": 0.93, + "content": "R _ { n } = \\mathbb { E } _ { ( \\varepsilon _ { i } ) _ { i \\leq n } } \\left[ \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left( \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\varepsilon _ { i } L ( \\theta ; x _ { i } , y _ { i } ) - \\frac { \\lambda } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\varepsilon _ { i } H ( \\theta ; x _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } \\varepsilon _ { i } H ( \\theta ; x _ { i } ) \\right) \\right] ,", + "type": "interline_equation", + "image_path": "22bb146a8ce5616f710d450da252122d3ccb81ccaf18e954e000b350f14f7b55.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 117, + 591, + 482, + 602.0 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 117, + 602.0, + 482, + 613.0 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 117, + 613.0, + 482, + 624.0 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 84, + 627, + 508, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 133, + 640 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 629, + 143, + 638 + ], + "score": 0.86, + "content": "\\varepsilon _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 626, + 476, + 640 + ], + "score": 1.0, + "content": "are i.i.d. Rademacher variables independent of the data. In the particular case of", + "type": "text" + }, + { + "bbox": [ + 477, + 627, + 502, + 637 + ], + "score": 0.88, + "content": "\\lambda = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 626, + 506, + 640 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "we recover the standard Rademacher complexity of the complete case. We can then now bound the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 649, + 377, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 377, + 661 + ], + "score": 1.0, + "content": "generalisation error of a model trained using our new loss function.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 626, + 506, + 661 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 662, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 86, + 662, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 86, + 665, + 100, + 673 + ], + "score": 1.0, + "content": "307", + "type": "text" + }, + { + "bbox": [ + 104, + 662, + 362, + 674 + ], + "score": 1.0, + "content": "Theorem 3.6. We assume that labels are MCAR and that both", + "type": "text" + }, + { + "bbox": [ + 362, + 664, + 370, + 672 + ], + "score": 0.68, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 370, + 662, + 389, + 674 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 389, + 664, + 399, + 672 + ], + "score": 0.58, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 400, + 662, + 505, + 674 + ], + "score": 1.0, + "content": "are bounded. Then, there", + "type": "text" + } + ], + "index": 44, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 674, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 86, + 676, + 100, + 684 + ], + "score": 1.0, + "content": "308", + "type": "text" + }, + { + "bbox": [ + 105, + 674, + 176, + 685 + ], + "score": 1.0, + "content": "exists a constant", + "type": "text" + }, + { + "bbox": [ + 176, + 674, + 201, + 684 + ], + "score": 0.88, + "content": "\\kappa > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 674, + 272, + 685 + ], + "score": 1.0, + "content": ", that depends on", + "type": "text" + }, + { + "bbox": [ + 273, + 675, + 279, + 683 + ], + "score": 0.45, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 674, + 283, + 685 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 284, + 674, + 290, + 683 + ], + "score": 0.38, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 674, + 295, + 685 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 295, + 674, + 305, + 683 + ], + "score": 0.58, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 674, + 505, + 685 + ], + "score": 1.0, + "content": ", and the ratio of observed labels, such that, with", + "type": "text" + } + ], + "index": 45, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 684, + 268, + 696 + ], + "spans": [ + { + "bbox": [ + 86, + 686, + 100, + 696 + ], + "score": 1.0, + "content": "309", + "type": "text" + }, + { + "bbox": [ + 104, + 684, + 184, + 696 + ], + "score": 1.0, + "content": "probability at least", + "type": "text" + }, + { + "bbox": [ + 185, + 685, + 208, + 695 + ], + "score": 0.76, + "content": "1 - \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 208, + 684, + 239, + 696 + ], + "score": 1.0, + "content": ", for all", + "type": "text" + }, + { + "bbox": [ + 239, + 685, + 264, + 694 + ], + "score": 0.87, + "content": "\\theta \\in \\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 684, + 268, + 696 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 46, + "is_list_start_line": true + } + ], + "index": 45, + "bbox_fs": [ + 86, + 662, + 505, + 696 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 213, + 698, + 398, + 726 + ], + "lines": [ + { + "bbox": [ + 213, + 698, + 398, + 726 + ], + "spans": [ + { + "bbox": [ + 213, + 698, + 398, + 726 + ], + "score": 0.93, + "content": "\\mathcal { R } ( \\theta ) \\leq \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) + 2 { R _ { n } } + \\kappa \\sqrt { \\frac { \\log ( 4 / \\delta ) } { n } } .", + "type": "interline_equation", + "image_path": "6812e392c68ce207447e3a5b552c862c076f662e0d94a185d4f38bb8dbc46691.jpg" + } + ] + } + ], + "index": 47.5, + "virtual_lines": [ + { + "bbox": [ + 213, + 698, + 398, + 712.0 + ], + "spans": [], + "index": 47 + }, + { + "bbox": [ + 213, + 712.0, + 398, + 726.0 + ], + "spans": [], + "index": 48 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 87, + 109, + 191, + 123 + ], + "lines": [ + { + "bbox": [ + 84, + 108, + 192, + 126 + ], + "spans": [ + { + "bbox": [ + 84, + 108, + 192, + 126 + ], + "score": 1.0, + "content": "311 4 Experiments", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 86, + 140, + 505, + 239 + ], + "lines": [ + { + "bbox": [ + 85, + 140, + 505, + 152 + ], + "spans": [ + { + "bbox": [ + 85, + 142, + 100, + 152 + ], + "score": 1.0, + "content": "312", + "type": "text" + }, + { + "bbox": [ + 105, + 140, + 505, + 152 + ], + "score": 1.0, + "content": "We evaluate the performance of DeSSL against different classic methods. 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We also compare", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 195, + 505, + 207 + ], + "spans": [ + { + "bbox": [ + 85, + 197, + 100, + 207 + ], + "score": 1.0, + "content": "317", + "type": "text" + }, + { + "bbox": [ + 106, + 195, + 505, + 207 + ], + "score": 1.0, + "content": "PseudoLabel and DePseudoLabel on five small datasets of MedMNIST (Yang et al., 2021a;b) with a", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 85, + 205, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 85, + 208, + 100, + 218 + ], + "score": 1.0, + "content": "318", + "type": "text" + }, + { + "bbox": [ + 105, + 205, + 128, + 219 + ], + "score": 1.0, + "content": "fixed", + "type": "text" + }, + { + "bbox": [ + 129, + 207, + 136, + 216 + ], + "score": 0.64, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 205, + 505, + 219 + ], + "score": 1.0, + "content": ". The results of these experiments are reported below. In our figures, the error bars represent", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 217, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 85, + 218, + 100, + 228 + ], + "score": 1.0, + "content": "319", + "type": "text" + }, + { + "bbox": [ + 106, + 217, + 165, + 228 + ], + "score": 1.0, + "content": "the size of the", + "type": "text" + }, + { + "bbox": [ + 165, + 217, + 185, + 227 + ], + "score": 0.87, + "content": "9 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 217, + 505, + 228 + ], + "score": 1.0, + "content": "confidence interval (CI). Finally, we modified the implementation of Fixmatch", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 227, + 405, + 240 + ], + "spans": [ + { + "bbox": [ + 86, + 230, + 100, + 240 + ], + "score": 1.0, + "content": "320", + "type": "text" + }, + { + "bbox": [ + 104, + 227, + 405, + 240 + ], + "score": 1.0, + "content": "(Sohn et al., 2020) and compare it with its debiased version on CIFAR-10.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 86, + 244, + 505, + 343 + ], + "lines": [ + { + "bbox": [ + 85, + 244, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 85, + 246, + 99, + 256 + ], + "score": 1.0, + "content": "321", + "type": "text" + }, + { + "bbox": [ + 106, + 244, + 506, + 256 + ], + "score": 1.0, + "content": "We also compare DeEntMin and DePseudoLabel to the biased version on a large range of tabular", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 254, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 86, + 257, + 99, + 266 + ], + "score": 1.0, + "content": "322", + "type": "text" + }, + { + "bbox": [ + 105, + 254, + 506, + 267 + ], + "score": 1.0, + "content": "datasets commonly used in SSL benchmarks (Chapelle et al., 2006; Guo et al., 2010). We do not", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 86, + 265, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 86, + 268, + 99, + 277 + ], + "score": 1.0, + "content": "323", + "type": "text" + }, + { + "bbox": [ + 105, + 265, + 506, + 279 + ], + "score": 1.0, + "content": "observe differences between the performance, see Appendix P. Finally, we show how simple it is to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 85, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 85, + 278, + 100, + 289 + ], + "score": 1.0, + "content": "324", + "type": "text" + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "debias an existing implementation, by demonstrating it on the consistency-based models benchmarked", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 85, + 287, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 85, + 289, + 100, + 299 + ], + "score": 1.0, + "content": "325", + "type": "text" + }, + { + "bbox": [ + 105, + 287, + 506, + 300 + ], + "score": 1.0, + "content": "by (Oliver et al., 2018), namely VAT, Π-model and MeanTeacher on CIFAR-10 and SVHN (Netzer", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 85, + 299, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 85, + 300, + 100, + 311 + ], + "score": 1.0, + "content": "326", + "type": "text" + }, + { + "bbox": [ + 106, + 299, + 506, + 311 + ], + "score": 1.0, + "content": "et al., 2011). We observe similar performances between the debiased and biased versions for the differ-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 85, + 310, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 85, + 311, + 100, + 321 + ], + "score": 1.0, + "content": "327", + "type": "text" + }, + { + "bbox": [ + 105, + 310, + 506, + 321 + ], + "score": 1.0, + "content": "ent methods, both in terms of cross-entropy and accuracy. Moreover, these results have been obtained", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 85, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 85, + 322, + 100, + 333 + ], + "score": 1.0, + "content": "328", + "type": "text" + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "using the hyperparameters finetuned for the biased versions. Therefore, it is likely that optimising the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 86, + 331, + 504, + 344 + ], + "spans": [ + { + "bbox": [ + 86, + 334, + 99, + 343 + ], + "score": 1.0, + "content": "329", + "type": "text" + }, + { + "bbox": [ + 105, + 331, + 504, + 344 + ], + "score": 1.0, + "content": "hyperparameters for DeSSL will yield even better with the right hyperparameters, see Appendix O.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14 + }, + { + "type": "title", + "bbox": [ + 87, + 366, + 162, + 377 + ], + "lines": [ + { + "bbox": [ + 83, + 365, + 164, + 379 + ], + "spans": [ + { + "bbox": [ + 83, + 365, + 164, + 379 + ], + "score": 1.0, + "content": "330 4.1 MNIST", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 85, + 390, + 360, + 576 + ], + "lines": [ + { + "bbox": [ + 86, + 390, + 361, + 402 + ], + "spans": [ + { + "bbox": [ + 86, + 392, + 99, + 402 + ], + "score": 1.0, + "content": "331", + "type": "text" + }, + { + "bbox": [ + 106, + 390, + 361, + 402 + ], + "score": 1.0, + "content": "MNIST is an advantageous dataset for SSL since classes are", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 86, + 401, + 360, + 412 + ], + "spans": [ + { + "bbox": [ + 86, + 403, + 99, + 412 + ], + "score": 1.0, + "content": "332", + "type": "text" + }, + { + "bbox": [ + 106, + 401, + 360, + 412 + ], + "score": 1.0, + "content": "well-separated. We compare PseudoLabel and DePseudoLabel", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 86, + 412, + 361, + 424 + ], + "spans": [ + { + "bbox": [ + 86, + 414, + 99, + 423 + ], + "score": 1.0, + "content": "333", + "type": "text" + }, + { + "bbox": [ + 106, + 412, + 249, + 424 + ], + "score": 1.0, + "content": "for a LeNet-like architecture using", + "type": "text" + }, + { + "bbox": [ + 249, + 412, + 293, + 423 + ], + "score": 0.91, + "content": "n _ { l } = 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 412, + 361, + 424 + ], + "score": 1.0, + "content": "labelled data on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 86, + 422, + 361, + 435 + ], + "spans": [ + { + "bbox": [ + 86, + 425, + 99, + 434 + ], + "score": 1.0, + "content": "334", + "type": "text" + }, + { + "bbox": [ + 106, + 422, + 361, + 435 + ], + "score": 1.0, + "content": "10 different splits of the training dataset into a labelled and unla-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 86, + 434, + 361, + 446 + ], + "spans": [ + { + "bbox": [ + 86, + 436, + 99, + 445 + ], + "score": 1.0, + "content": "335", + "type": "text" + }, + { + "bbox": [ + 106, + 434, + 361, + 446 + ], + "score": 1.0, + "content": "belled set. Models are then evaluated using the standard 10, 000", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 86, + 445, + 361, + 456 + ], + "spans": [ + { + "bbox": [ + 86, + 447, + 99, + 456 + ], + "score": 1.0, + "content": "336", + "type": "text" + }, + { + "bbox": [ + 106, + 445, + 199, + 456 + ], + "score": 1.0, + "content": "test samples. We used", + "type": "text" + }, + { + "bbox": [ + 199, + 445, + 218, + 455 + ], + "score": 0.87, + "content": "10 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 445, + 230, + 456 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 231, + 446, + 241, + 456 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 445, + 361, + 456 + ], + "score": 1.0, + "content": "as the validation set. We test", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 86, + 455, + 362, + 469 + ], + "spans": [ + { + "bbox": [ + 86, + 457, + 99, + 467 + ], + "score": 1.0, + "content": "337", + "type": "text" + }, + { + "bbox": [ + 105, + 455, + 253, + 469 + ], + "score": 1.0, + "content": "the influence of the hyperparameter", + "type": "text" + }, + { + "bbox": [ + 254, + 456, + 261, + 466 + ], + "score": 0.69, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 455, + 362, + 469 + ], + "score": 1.0, + "content": "and report the accuracy,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 85, + 467, + 361, + 479 + ], + "spans": [ + { + "bbox": [ + 85, + 468, + 100, + 479 + ], + "score": 1.0, + "content": "338", + "type": "text" + }, + { + "bbox": [ + 106, + 467, + 361, + 478 + ], + "score": 1.0, + "content": "the cross-entropy and the expected calibration error (ECE, Guo", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 86, + 477, + 362, + 490 + ], + "spans": [ + { + "bbox": [ + 86, + 479, + 99, + 489 + ], + "score": 1.0, + "content": "339", + "type": "text" + }, + { + "bbox": [ + 105, + 477, + 362, + 490 + ], + "score": 1.0, + "content": "et al., 2017) at the epoch of best validation accuracy, see Fig-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 86, + 488, + 361, + 500 + ], + "spans": [ + { + "bbox": [ + 86, + 491, + 99, + 500 + ], + "score": 1.0, + "content": "340", + "type": "text" + }, + { + "bbox": [ + 106, + 488, + 361, + 500 + ], + "score": 1.0, + "content": "ure 2 and Appendix L. In this example SSL and DeSSL have", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 86, + 499, + 361, + 512 + ], + "spans": [ + { + "bbox": [ + 86, + 501, + 99, + 511 + ], + "score": 1.0, + "content": "341", + "type": "text" + }, + { + "bbox": [ + 106, + 499, + 240, + 512 + ], + "score": 1.0, + "content": "almost the same accuracy for all", + "type": "text" + }, + { + "bbox": [ + 240, + 500, + 248, + 510 + ], + "score": 0.72, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 499, + 361, + 512 + ], + "score": 1.0, + "content": ", however, DeSSL seems to", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 86, + 510, + 361, + 522 + ], + "spans": [ + { + "bbox": [ + 86, + 512, + 99, + 522 + ], + "score": 1.0, + "content": "342", + "type": "text" + }, + { + "bbox": [ + 106, + 510, + 361, + 522 + ], + "score": 1.0, + "content": "be always better calibrated. 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We report in Table 1 the", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 86, + 667, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 86, + 669, + 99, + 678 + ], + "score": 1.0, + "content": "353", + "type": "text" + }, + { + "bbox": [ + 105, + 667, + 506, + 679 + ], + "score": 1.0, + "content": "mean accuracy and cross-entropy on 5 different splits of the labelled and unlabelled data and the", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 84, + 677, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 84, + 680, + 100, + 690 + ], + "score": 1.0, + "content": "354", + "type": "text" + }, + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "score": 1.0, + "content": "number of labelled data used. We report the AUC in Appendix L. DePseudoLabel competes with", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 86, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 86, + 691, + 99, + 700 + ], + "score": 1.0, + "content": "355", + "type": "text" + }, + { + "bbox": [ + 105, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "PseudoLabel in terms of accuracy and even success when PseudoLabel’s accuracy is less than the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 85, + 699, + 507, + 713 + ], + "spans": [ + { + "bbox": [ + 85, + 702, + 100, + 712 + ], + "score": 1.0, + "content": "356", + "type": "text" + }, + { + "bbox": [ + 105, + 699, + 507, + 713 + ], + "score": 1.0, + "content": "complete case. Moreover, DePseudoLabel is always better in terms of cross-entropy, so calibration,", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 86, + 710, + 356, + 723 + ], + "spans": [ + { + "bbox": [ + 86, + 713, + 99, + 722 + ], + "score": 1.0, + "content": "357", + "type": "text" + }, + { + "bbox": [ + 105, + 710, + 356, + 723 + ], + "score": 1.0, + "content": "whereas PseudoLabel is always worse than the complete case.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 49 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 9 + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 86, + 73, + 505, + 84 + ], + "lines": [ + { + "bbox": [ + 85, + 72, + 507, + 86 + ], + "spans": [ + { + "bbox": [ + 85, + 72, + 507, + 86 + ], + "score": 1.0, + "content": "310 The proof follows Shalev-Shwartz & Ben-David (2014, Chapter 26), and is available in Appendix J.", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 87, + 109, + 191, + 123 + ], + "lines": [ + { + "bbox": [ + 84, + 108, + 192, + 126 + ], + "spans": [ + { + "bbox": [ + 84, + 108, + 192, + 126 + ], + "score": 1.0, + "content": "311 4 Experiments", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "index", + "bbox": [ + 86, + 140, + 505, + 239 + ], + "lines": [ + { + "bbox": [ + 85, + 140, + 505, + 152 + ], + "spans": [ + { + "bbox": [ + 85, + 142, + 100, + 152 + ], + "score": 1.0, + "content": "312", + "type": "text" + }, + { + "bbox": [ + 105, + 140, + 505, + 152 + ], + "score": 1.0, + "content": "We evaluate the performance of DeSSL against different classic methods. The goal here is to compare", + "type": "text" + } + ], + "index": 1, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 150, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 85, + 153, + 100, + 163 + ], + "score": 1.0, + "content": "313", + "type": "text" + }, + { + "bbox": [ + 105, + 150, + 505, + 164 + ], + "score": 1.0, + "content": "DeSSL methods and their original counterparts. In particular, we perform experiments with simple", + "type": "text" + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 160, + 506, + 177 + ], + "spans": [ + { + "bbox": [ + 85, + 164, + 100, + 174 + ], + "score": 1.0, + "content": "314", + "type": "text" + }, + { + "bbox": [ + 105, + 160, + 506, + 177 + ], + "score": 1.0, + "content": "SSL methods such as pseudo-label (PseudoLabel) and entropy minimisation (EntMIN) with varying", + "type": "text" + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 172, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 86, + 176, + 99, + 185 + ], + "score": 1.0, + "content": "315", + "type": "text" + }, + { + "bbox": [ + 106, + 174, + 114, + 183 + ], + "score": 0.63, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 172, + 505, + 186 + ], + "score": 1.0, + "content": "on MNIST (LeCun & Cortes, 2010) and CIFAR-10 and CIFAR-100 (Krizhevsky, 2009) and", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 185, + 505, + 196 + ], + "spans": [ + { + "bbox": [ + 85, + 186, + 100, + 196 + ], + "score": 1.0, + "content": "316", + "type": "text" + }, + { + "bbox": [ + 105, + 185, + 505, + 196 + ], + "score": 1.0, + "content": "compare them to the debiased method, respectively DeEntMin and DePseudoLabel. We also compare", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 195, + 505, + 207 + ], + "spans": [ + { + "bbox": [ + 85, + 197, + 100, + 207 + ], + "score": 1.0, + "content": "317", + "type": "text" + }, + { + "bbox": [ + 106, + 195, + 505, + 207 + ], + "score": 1.0, + "content": "PseudoLabel and DePseudoLabel on five small datasets of MedMNIST (Yang et al., 2021a;b) with a", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 205, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 85, + 208, + 100, + 218 + ], + "score": 1.0, + "content": "318", + "type": "text" + }, + { + "bbox": [ + 105, + 205, + 128, + 219 + ], + "score": 1.0, + "content": "fixed", + "type": "text" + }, + { + "bbox": [ + 129, + 207, + 136, + 216 + ], + "score": 0.64, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 205, + 505, + 219 + ], + "score": 1.0, + "content": ". The results of these experiments are reported below. In our figures, the error bars represent", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 217, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 85, + 218, + 100, + 228 + ], + "score": 1.0, + "content": "319", + "type": "text" + }, + { + "bbox": [ + 106, + 217, + 165, + 228 + ], + "score": 1.0, + "content": "the size of the", + "type": "text" + }, + { + "bbox": [ + 165, + 217, + 185, + 227 + ], + "score": 0.87, + "content": "9 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 217, + 505, + 228 + ], + "score": 1.0, + "content": "confidence interval (CI). Finally, we modified the implementation of Fixmatch", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 227, + 405, + 240 + ], + "spans": [ + { + "bbox": [ + 86, + 230, + 100, + 240 + ], + "score": 1.0, + "content": "320", + "type": "text" + }, + { + "bbox": [ + 104, + 227, + 405, + 240 + ], + "score": 1.0, + "content": "(Sohn et al., 2020) and compare it with its debiased version on CIFAR-10.", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 244, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 85, + 246, + 99, + 256 + ], + "score": 1.0, + "content": "321", + "type": "text" + }, + { + "bbox": [ + 106, + 244, + 506, + 256 + ], + "score": 1.0, + "content": "We also compare DeEntMin and DePseudoLabel to the biased version on a large range of tabular", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 254, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 86, + 257, + 99, + 266 + ], + "score": 1.0, + "content": "322", + "type": "text" + }, + { + "bbox": [ + 105, + 254, + 506, + 267 + ], + "score": 1.0, + "content": "datasets commonly used in SSL benchmarks (Chapelle et al., 2006; Guo et al., 2010). We do not", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 265, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 86, + 268, + 99, + 277 + ], + "score": 1.0, + "content": "323", + "type": "text" + }, + { + "bbox": [ + 105, + 265, + 506, + 279 + ], + "score": 1.0, + "content": "observe differences between the performance, see Appendix P. Finally, we show how simple it is to", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 85, + 278, + 100, + 289 + ], + "score": 1.0, + "content": "324", + "type": "text" + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "debias an existing implementation, by demonstrating it on the consistency-based models benchmarked", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 287, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 85, + 289, + 100, + 299 + ], + "score": 1.0, + "content": "325", + "type": "text" + }, + { + "bbox": [ + 105, + 287, + 506, + 300 + ], + "score": 1.0, + "content": "by (Oliver et al., 2018), namely VAT, Π-model and MeanTeacher on CIFAR-10 and SVHN (Netzer", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 299, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 85, + 300, + 100, + 311 + ], + "score": 1.0, + "content": "326", + "type": "text" + }, + { + "bbox": [ + 106, + 299, + 506, + 311 + ], + "score": 1.0, + "content": "et al., 2011). We observe similar performances between the debiased and biased versions for the differ-", + "type": "text" + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 310, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 85, + 311, + 100, + 321 + ], + "score": 1.0, + "content": "327", + "type": "text" + }, + { + "bbox": [ + 105, + 310, + 506, + 321 + ], + "score": 1.0, + "content": "ent methods, both in terms of cross-entropy and accuracy. Moreover, these results have been obtained", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 85, + 322, + 100, + 333 + ], + "score": 1.0, + "content": "328", + "type": "text" + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "using the hyperparameters finetuned for the biased versions. Therefore, it is likely that optimising the", + "type": "text" + } + ], + "index": 17, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 331, + 504, + 344 + ], + "spans": [ + { + "bbox": [ + 86, + 334, + 99, + 343 + ], + "score": 1.0, + "content": "329", + "type": "text" + }, + { + "bbox": [ + 105, + 331, + 504, + 344 + ], + "score": 1.0, + "content": "hyperparameters for DeSSL will yield even better with the right hyperparameters, see Appendix O.", + "type": "text" + } + ], + "index": 18, + "is_list_start_line": true + } + ], + "index": 5, + "bbox_fs": [ + 85, + 140, + 506, + 240 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 244, + 505, + 343 + ], + "lines": [], + "index": 14, + "bbox_fs": [ + 85, + 244, + 506, + 344 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 87, + 366, + 162, + 377 + ], + "lines": [ + { + "bbox": [ + 83, + 365, + 164, + 379 + ], + "spans": [ + { + "bbox": [ + 83, + 365, + 164, + 379 + ], + "score": 1.0, + "content": "330 4.1 MNIST", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "index", + "bbox": [ + 85, + 390, + 360, + 576 + ], + "lines": [ + { + "bbox": [ + 86, + 390, + 361, + 402 + ], + "spans": [ + { + "bbox": [ + 86, + 392, + 99, + 402 + ], + "score": 1.0, + "content": "331", + "type": "text" + }, + { + "bbox": [ + 106, + 390, + 361, + 402 + ], + "score": 1.0, + "content": "MNIST is an advantageous dataset for SSL since classes are", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 401, + 360, + 412 + ], + "spans": [ + { + "bbox": [ + 86, + 403, + 99, + 412 + ], + "score": 1.0, + "content": "332", + "type": "text" + }, + { + "bbox": [ + 106, + 401, + 360, + 412 + ], + "score": 1.0, + "content": "well-separated. We compare PseudoLabel and DePseudoLabel", + "type": "text" + } + ], + "index": 21, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 412, + 361, + 424 + ], + "spans": [ + { + "bbox": [ + 86, + 414, + 99, + 423 + ], + "score": 1.0, + "content": "333", + "type": "text" + }, + { + "bbox": [ + 106, + 412, + 249, + 424 + ], + "score": 1.0, + "content": "for a LeNet-like architecture using", + "type": "text" + }, + { + "bbox": [ + 249, + 412, + 293, + 423 + ], + "score": 0.91, + "content": "n _ { l } = 1 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 412, + 361, + 424 + ], + "score": 1.0, + "content": "labelled data on", + "type": "text" + } + ], + "index": 22, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 422, + 361, + 435 + ], + "spans": [ + { + "bbox": [ + 86, + 425, + 99, + 434 + ], + "score": 1.0, + "content": "334", + "type": "text" + }, + { + "bbox": [ + 106, + 422, + 361, + 435 + ], + "score": 1.0, + "content": "10 different splits of the training dataset into a labelled and unla-", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 434, + 361, + 446 + ], + "spans": [ + { + "bbox": [ + 86, + 436, + 99, + 445 + ], + "score": 1.0, + "content": "335", + "type": "text" + }, + { + "bbox": [ + 106, + 434, + 361, + 446 + ], + "score": 1.0, + "content": "belled set. Models are then evaluated using the standard 10, 000", + "type": "text" + } + ], + "index": 24, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 445, + 361, + 456 + ], + "spans": [ + { + "bbox": [ + 86, + 447, + 99, + 456 + ], + "score": 1.0, + "content": "336", + "type": "text" + }, + { + "bbox": [ + 106, + 445, + 199, + 456 + ], + "score": 1.0, + "content": "test samples. We used", + "type": "text" + }, + { + "bbox": [ + 199, + 445, + 218, + 455 + ], + "score": 0.87, + "content": "10 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 445, + 230, + 456 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 231, + 446, + 241, + 456 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 445, + 361, + 456 + ], + "score": 1.0, + "content": "as the validation set. We test", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 455, + 362, + 469 + ], + "spans": [ + { + "bbox": [ + 86, + 457, + 99, + 467 + ], + "score": 1.0, + "content": "337", + "type": "text" + }, + { + "bbox": [ + 105, + 455, + 253, + 469 + ], + "score": 1.0, + "content": "the influence of the hyperparameter", + "type": "text" + }, + { + "bbox": [ + 254, + 456, + 261, + 466 + ], + "score": 0.69, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 455, + 362, + 469 + ], + "score": 1.0, + "content": "and report the accuracy,", + "type": "text" + } + ], + "index": 26, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 467, + 361, + 479 + ], + "spans": [ + { + "bbox": [ + 85, + 468, + 100, + 479 + ], + "score": 1.0, + "content": "338", + "type": "text" + }, + { + "bbox": [ + 106, + 467, + 361, + 478 + ], + "score": 1.0, + "content": "the cross-entropy and the expected calibration error (ECE, Guo", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 477, + 362, + 490 + ], + "spans": [ + { + "bbox": [ + 86, + 479, + 99, + 489 + ], + "score": 1.0, + "content": "339", + "type": "text" + }, + { + "bbox": [ + 105, + 477, + 362, + 490 + ], + "score": 1.0, + "content": "et al., 2017) at the epoch of best validation accuracy, see Fig-", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 488, + 361, + 500 + ], + "spans": [ + { + "bbox": [ + 86, + 491, + 99, + 500 + ], + "score": 1.0, + "content": "340", + "type": "text" + }, + { + "bbox": [ + 106, + 488, + 361, + 500 + ], + "score": 1.0, + "content": "ure 2 and Appendix L. In this example SSL and DeSSL have", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 499, + 361, + 512 + ], + "spans": [ + { + "bbox": [ + 86, + 501, + 99, + 511 + ], + "score": 1.0, + "content": "341", + "type": "text" + }, + { + "bbox": [ + 106, + 499, + 240, + 512 + ], + "score": 1.0, + "content": "almost the same accuracy for all", + "type": "text" + }, + { + "bbox": [ + 240, + 500, + 248, + 510 + ], + "score": 0.72, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 499, + 361, + 512 + ], + "score": 1.0, + "content": ", however, DeSSL seems to", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 510, + 361, + 522 + ], + "spans": [ + { + "bbox": [ + 86, + 512, + 99, + 522 + ], + "score": 1.0, + "content": "342", + "type": "text" + }, + { + "bbox": [ + 106, + 510, + 361, + 522 + ], + "score": 1.0, + "content": "be always better calibrated. To break the cluster assumption, we", + "type": "text" + } + ], + "index": 32, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 522, + 361, + 533 + ], + "spans": [ + { + "bbox": [ + 86, + 523, + 99, + 533 + ], + "score": 1.0, + "content": "343", + "type": "text" + }, + { + "bbox": [ + 106, + 522, + 361, + 532 + ], + "score": 1.0, + "content": "reproduced the same experiment on a modified MNIST. 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DATASETNLCCPLDEPL
CROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACY
DERMA10001.95 ± 0.0968.99± 1.202.51±0.2068.88±1.031.88 ± 0.1269.30± 0.85
PNEUMONIA5851.47 ± 0.0483.94±2.402.04 ±0.0485.83±2.131.40 ± 0.0684.36±3.79
RETINA1601.68 ± 0.0348.30± 3.061.80 ±0.1847.75±2.501.67 ± 0.0649.40± 2.62
BREAST780.80±0.0476.15±0.751.00 ±0.2674.74±1.040.70±0.0376.67 ± 1.32
BLOOD17006.11 ± 0.1784.13±0.836.61 ±0.2284.09± 1.176.53 ±0.3083.68 ±0.59
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The", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 306, + 360, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 311, + 318 + ], + "score": 1.0, + "content": "performance of both methods on CIFAR-100 with", + "type": "text" + }, + { + "bbox": [ + 311, + 306, + 360, + 317 + ], + "score": 0.89, + "content": "n l = 1 0 0 0 0", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 317, + 361, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 361, + 329 + ], + "score": 1.0, + "content": "are reported in Appendix M. We observe DeSSL provides both", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 328, + 361, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 361, + 340 + ], + "score": 1.0, + "content": "a better cross-entropy and ECE with the same accuracy for", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 339, + 361, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 130, + 352 + ], + "score": 1.0, + "content": "small", + "type": "text" + }, + { + "bbox": [ + 130, + 339, + 137, + 349 + ], + "score": 0.62, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 339, + 183, + 352 + ], + "score": 1.0, + "content": ". For larger", + "type": "text" + }, + { + "bbox": [ + 183, + 339, + 190, + 349 + ], + "score": 0.6, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 339, + 361, + 352 + ], + "score": 1.0, + "content": ", DeSSL performs better in all the reported", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 350, + 361, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 361, + 362 + ], + "score": 1.0, + "content": "metrics. We performed a paired Student’s t-test to ensure that", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 361, + 360, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 360, + 372 + ], + "score": 1.0, + "content": "our results are significant and reported the p-values in Appendix", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 371, + 361, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 240, + 384 + ], + "score": 1.0, + "content": "M. The p-values indicate that for", + "type": "text" + }, + { + "bbox": [ + 240, + 372, + 248, + 381 + ], + "score": 0.63, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 371, + 361, + 384 + ], + "score": 1.0, + "content": "close to 10, DeSSL is often", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 382, + 360, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 360, + 395 + ], + "score": 1.0, + "content": "significantly better in all the metrics. 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For this experiment, we use", + "type": "text" + }, + { + "bbox": [ + 275, + 461, + 319, + 471 + ], + "score": 0.9, + "content": "n l = 4 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 461, + 339, + 473 + ], + "score": 1.0, + "content": "on 5", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 471, + 339, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 471, + 339, + 484 + ], + "score": 1.0, + "content": "different folds.First, we report that a strong baseline using", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 482, + 340, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 208, + 494 + ], + "score": 1.0, + "content": "data augmentation reach", + "type": "text" + }, + { + "bbox": [ + 209, + 483, + 241, + 493 + ], + "score": 0.89, + "content": "\\bar { 8 } 7 . 2 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 482, + 340, + 494 + ], + "score": 1.0, + "content": "accuracy. Then, we ob-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 493, + 340, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 340, + 506 + ], + "score": 1.0, + "content": "serve that on the debiasing method improve both accuracy", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 505, + 341, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 341, + 516 + ], + "score": 1.0, + "content": "and cross-entropy of this modified version of Fixmatch.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 515, + 340, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 515, + 340, + 527 + ], + "score": 1.0, + "content": "Inspired by Zhu et al. (2022), we show that our method", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35 + }, + { + "type": "table", + "bbox": [ + 347, + 482, + 515, + 525 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 346, + 444, + 506, + 478 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 346, + 443, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 346, + 443, + 506, + 457 + ], + "score": 1.0, + "content": "Table 2: 1st line: Accuracy, 2nd line:", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 346, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 346, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "Worst class accuracy, 3rd line: Cross-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 345, + 466, + 382, + 480 + ], + "spans": [ + { + "bbox": [ + 345, + 466, + 382, + 480 + ], + "score": 1.0, + "content": "entropy.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40 + }, + { + "type": "table_body", + "bbox": [ + 347, + 482, + 515, + 525 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 347, + 482, + 515, + 525 + ], + "spans": [ + { + "bbox": [ + 347, + 482, + 515, + 525 + ], + "score": 0.969, + "html": "
COMPLETE CASEFIXMATCHDEFIXMATCH
87.27 ± 0.2593.87 ±0.1395.44 ± 0.10
70.08 ±0.9382.25 ±2.2787.16 ± 0.46
0.60 ± 0.010.27 ±0.010.20 ±0.01
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Indeed, DeFixmatch", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 537, + 506, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 201, + 550 + ], + "score": 1.0, + "content": "improves Fixmatch by", + "type": "text" + }, + { + "bbox": [ + 201, + 537, + 228, + 548 + ], + "score": 0.88, + "content": "1 . 5 \\hat { 7 } \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 537, + 289, + 550 + ], + "score": 1.0, + "content": "overall but by", + "type": "text" + }, + { + "bbox": [ + 289, + 537, + 317, + 548 + ], + "score": 0.89, + "content": "4 . { \\bar { 9 } } 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 317, + 537, + 506, + 550 + ], + "score": 1.0, + "content": "on the worst class. We report in Appendix N", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 549, + 504, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 504, + 560 + ], + "score": 1.0, + "content": "the accuracy per class of the different methods and the benefit ratio as defined by Zhu et al. (2022).", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46 + }, + { + "type": "title", + "bbox": [ + 97, + 576, + 182, + 589 + ], + "lines": [ + { + "bbox": [ + 104, + 574, + 185, + 592 + ], + "spans": [ + { + "bbox": [ + 104, + 574, + 185, + 592 + ], + "score": 1.0, + "content": "5 Conclusion", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 48 + }, + { + "type": "text", + "bbox": [ + 105, + 601, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 601, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 614 + ], + "score": 1.0, + "content": "Motivated by the remarks of van Engelen & Hoos (2020) and Oliver et al. (2018) on the missingness", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "of theoretical guarantees in SSL, we proposed a simple modification of SSL frameworks. We consider", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 624, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 635 + ], + "score": 1.0, + "content": "frameworks based on the inclusion of unlabelled data in the computation of the risk estimator and", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 635, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 647 + ], + "score": 1.0, + "content": "debias them using labelled data. We show theoretically that this debiasing comes with several the-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 645, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 505, + 657 + ], + "score": 1.0, + "content": "oretical guarantees. We demonstrate these theoretical results experimentally on several common SSL", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "datasets and some more challenging ones such as MNIST with label noise. DeSSL shows competitive", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 106, + 668, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 505, + 679 + ], + "score": 1.0, + "content": "performance in terms of accuracy compared to its biased version but improves significantly the", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 402, + 691 + ], + "score": 1.0, + "content": "calibration. There are several future directions open to us. We showed that", + "type": "text" + }, + { + "bbox": [ + 402, + 678, + 420, + 690 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 678, + 506, + 691 + ], + "score": 1.0, + "content": "exists (Theorem 3.1)", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 106, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 388, + 701 + ], + "score": 1.0, + "content": "and therefore our formula provides guidelines for the optimisation of", + "type": "text" + }, + { + "bbox": [ + 388, + 690, + 395, + 699 + ], + "score": 0.73, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 689, + 506, + 701 + ], + "score": 1.0, + "content": ". 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DATASETNLCCPLDEPL
CROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACY
DERMA10001.95 ± 0.0968.99± 1.202.51±0.2068.88±1.031.88 ± 0.1269.30± 0.85
PNEUMONIA5851.47 ± 0.0483.94±2.402.04 ±0.0485.83±2.131.40 ± 0.0684.36±3.79
RETINA1601.68 ± 0.0348.30± 3.061.80 ±0.1847.75±2.501.67 ± 0.0649.40± 2.62
BREAST780.80±0.0476.15±0.751.00 ±0.2674.74±1.040.70±0.0376.67 ± 1.32
BLOOD17006.11 ± 0.1784.13±0.836.61 ±0.2284.09± 1.176.53 ±0.3083.68 ±0.59
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We trained a CNN-13 from Tarvainen &", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 229, + 361, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 229, + 361, + 243 + ], + "score": 1.0, + "content": "Valpola (2017) on 5 different splits. For this experiment, we use", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 241, + 361, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 150, + 252 + ], + "score": 0.91, + "content": "n _ { l } = 4 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 241, + 361, + 253 + ], + "score": 1.0, + "content": "and use the rest of the dataset as unlabelled. Models", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 252, + 361, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 361, + 264 + ], + "score": 1.0, + "content": "are then evaluated using the standard 10, 000 test samples. 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The", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 306, + 360, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 311, + 318 + ], + "score": 1.0, + "content": "performance of both methods on CIFAR-100 with", + "type": "text" + }, + { + "bbox": [ + 311, + 306, + 360, + 317 + ], + "score": 0.89, + "content": "n l = 1 0 0 0 0", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 317, + 361, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 361, + 329 + ], + "score": 1.0, + "content": "are reported in Appendix M. We observe DeSSL provides both", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 328, + 361, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 361, + 340 + ], + "score": 1.0, + "content": "a better cross-entropy and ECE with the same accuracy for", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 339, + 361, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 130, + 352 + ], + "score": 1.0, + "content": "small", + "type": "text" + }, + { + "bbox": [ + 130, + 339, + 137, + 349 + ], + "score": 0.62, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 339, + 183, + 352 + ], + "score": 1.0, + "content": ". For larger", + "type": "text" + }, + { + "bbox": [ + 183, + 339, + 190, + 349 + ], + "score": 0.6, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 339, + 361, + 352 + ], + "score": 1.0, + "content": ", DeSSL performs better in all the reported", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 350, + 361, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 361, + 362 + ], + "score": 1.0, + "content": "metrics. We performed a paired Student’s t-test to ensure that", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 361, + 360, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 360, + 372 + ], + "score": 1.0, + "content": "our results are significant and reported the p-values in Appendix", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 371, + 361, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 240, + 384 + ], + "score": 1.0, + "content": "M. The p-values indicate that for", + "type": "text" + }, + { + "bbox": [ + 240, + 372, + 248, + 381 + ], + "score": 0.63, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 371, + 361, + 384 + ], + "score": 1.0, + "content": "close to 10, DeSSL is often", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 382, + 360, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 360, + 395 + ], + "score": 1.0, + "content": "significantly better in all the metrics. 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Then, we ob-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 493, + 340, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 340, + 506 + ], + "score": 1.0, + "content": "serve that on the debiasing method improve both accuracy", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 505, + 341, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 341, + 516 + ], + "score": 1.0, + "content": "and cross-entropy of this modified version of Fixmatch.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 515, + 340, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 515, + 340, + 527 + ], + "score": 1.0, + "content": "Inspired by Zhu et al. (2022), we show that our method", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 527, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 506, + 540 + ], + "score": 1.0, + "content": "improved performance on “poor” classes more equally than the biased version. Indeed, DeFixmatch", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 537, + 506, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 201, + 550 + ], + "score": 1.0, + "content": "improves Fixmatch by", + "type": "text" + }, + { + "bbox": [ + 201, + 537, + 228, + 548 + ], + "score": 0.88, + "content": "1 . 5 \\hat { 7 } \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 537, + 289, + 550 + ], + "score": 1.0, + "content": "overall but by", + "type": "text" + }, + { + "bbox": [ + 289, + 537, + 317, + 548 + ], + "score": 0.89, + "content": "4 . { \\bar { 9 } } 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 317, + 537, + 506, + 550 + ], + "score": 1.0, + "content": "on the worst class. We report in Appendix N", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 549, + 504, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 504, + 560 + ], + "score": 1.0, + "content": "the accuracy per class of the different methods and the benefit ratio as defined by Zhu et al. 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COMPLETE CASEFIXMATCHDEFIXMATCH
87.27 ± 0.2593.87 ±0.1395.44 ± 0.10
70.08 ±0.9382.25 ±2.2787.16 ± 0.46
0.60 ± 0.010.27 ±0.010.20 ±0.01
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(2018) on the missingness", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "of theoretical guarantees in SSL, we proposed a simple modification of SSL frameworks. We consider", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 624, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 635 + ], + "score": 1.0, + "content": "frameworks based on the inclusion of unlabelled data in the computation of the risk estimator and", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 635, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 647 + ], + "score": 1.0, + "content": "debias them using labelled data. We show theoretically that this debiasing comes with several the-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 645, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 505, + 657 + ], + "score": 1.0, + "content": "oretical guarantees. We demonstrate these theoretical results experimentally on several common SSL", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "datasets and some more challenging ones such as MNIST with label noise. DeSSL shows competitive", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 106, + 668, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 505, + 679 + ], + "score": 1.0, + "content": "performance in terms of accuracy compared to its biased version but improves significantly the", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 402, + 691 + ], + "score": 1.0, + "content": "calibration. There are several future directions open to us. 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Recently, Lee (2013)", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 85, + 277, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 85, + 279, + 100, + 289 + ], + "score": 1.0, + "content": "642", + "type": "text" + }, + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "score": 1.0, + "content": "encouraged the pseudo-labels method for deep semi-supervised learning. Then, Rizve et al. (2021)", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 85, + 289, + 506, + 302 + ], + "spans": [ + { + "bbox": [ + 85, + 291, + 100, + 300 + ], + "score": 1.0, + "content": "643", + "type": "text" + }, + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "score": 1.0, + "content": "recently improved the pseudo-label selection by introducing an uncertainty-aware mechanism on", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 85, + 299, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 85, + 301, + 101, + 311 + ], + "score": 1.0, + "content": "644", + "type": "text" + }, + { + "bbox": [ + 105, + 299, + 506, + 312 + ], + "score": 1.0, + "content": "the confidence of the model concerning the predicted probabilities. Pham et al. (2021) reaches", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 85, + 311, + 506, + 324 + ], + "spans": [ + { + "bbox": [ + 85, + 312, + 101, + 322 + ], + "score": 1.0, + "content": "645", + "type": "text" + }, + { + "bbox": [ + 104, + 311, + 506, + 324 + ], + "score": 1.0, + "content": "state-of-the-art on the Imagenet challenge using pseudo-labels on a large dataset of additional images.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "title", + "bbox": [ + 87, + 337, + 288, + 349 + ], + "lines": [ + { + "bbox": [ + 84, + 336, + 288, + 351 + ], + "spans": [ + { + "bbox": [ + 84, + 336, + 288, + 351 + ], + "score": 1.0, + "content": "646 B.2 Pseudo-label and data augmentation", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 92, + 357, + 505, + 479 + ], + "lines": [ + { + "bbox": [ + 90, + 358, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 90, + 360, + 100, + 370 + ], + "score": 1.0, + "content": "47", + "type": "text" + }, + { + "bbox": [ + 105, + 358, + 506, + 372 + ], + "score": 1.0, + "content": "Recently, several methods based on data augmentation have been proposed and proven to perform well", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 89, + 369, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 89, + 371, + 100, + 381 + ], + "score": 1.0, + "content": "648", + "type": "text" + }, + { + "bbox": [ + 105, + 369, + 506, + 382 + ], + "score": 1.0, + "content": "on a large spectrum of SSL tasks. The idea is to have a model resilient to strong data-augmentation of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 90, + 380, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 90, + 382, + 100, + 392 + ], + "score": 1.0, + "content": "49", + "type": "text" + }, + { + "bbox": [ + 106, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "the input (Berthelot et al., 2019; 2020; Sohn et al., 2020; Xie et al., 2019; Zhang et al., 2021a). 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(2021)", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 289, + 506, + 302 + ], + "spans": [ + { + "bbox": [ + 85, + 291, + 100, + 300 + ], + "score": 1.0, + "content": "643", + "type": "text" + }, + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "score": 1.0, + "content": "recently improved the pseudo-label selection by introducing an uncertainty-aware mechanism on", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 299, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 85, + 301, + 101, + 311 + ], + "score": 1.0, + "content": "644", + "type": "text" + }, + { + "bbox": [ + 105, + 299, + 506, + 312 + ], + "score": 1.0, + "content": "the confidence of the model concerning the predicted probabilities. Pham et al. (2021) reaches", + "type": "text" + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 311, + 506, + 324 + ], + "spans": [ + { + "bbox": [ + 85, + 312, + 101, + 322 + ], + "score": 1.0, + "content": "645", + "type": "text" + }, + { + "bbox": [ + 104, + 311, + 506, + 324 + ], + "score": 1.0, + "content": "state-of-the-art on the Imagenet challenge using pseudo-labels on a large dataset of additional images.", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + } + ], + "index": 13.5, + "bbox_fs": [ + 85, + 256, + 506, + 324 + ] + }, + { + "type": "title", + "bbox": [ + 87, + 337, + 288, + 349 + ], + "lines": [ + { + "bbox": [ + 84, + 336, + 288, + 351 + ], + "spans": [ + { + "bbox": [ + 84, + 336, + 288, + 351 + ], + "score": 1.0, + "content": "646 B.2 Pseudo-label and data augmentation", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "index", + "bbox": [ + 92, + 357, + 505, + 479 + ], + "lines": [ + { + "bbox": [ + 90, + 358, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 90, + 360, + 100, + 370 + ], + "score": 1.0, + "content": "47", + "type": "text" + }, + { + "bbox": [ + 105, + 358, + 506, + 372 + ], + "score": 1.0, + "content": "Recently, several methods based on data augmentation have been proposed and proven to perform well", + "type": "text" + } + ], + "index": 18, + "is_list_start_line": true + }, + { + "bbox": [ + 89, + 369, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 89, + 371, + 100, + 381 + ], + "score": 1.0, + "content": "648", + "type": "text" + }, + { + "bbox": [ + 105, + 369, + 506, + 382 + ], + "score": 1.0, + "content": "on a large spectrum of SSL tasks. 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These objectives", + "type": "text" + }, + { + "bbox": [ + 226, + 173, + 236, + 182 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 236, + 171, + 400, + 186 + ], + "score": 1.0, + "content": "are not directly a form of expectation of", + "type": "text" + }, + { + "bbox": [ + 400, + 173, + 408, + 182 + ], + "score": 0.84, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 171, + 506, + 186 + ], + "score": 1.0, + "content": "but are equivalent to an", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 183, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 85, + 184, + 100, + 195 + ], + "score": 1.0, + "content": "675", + "type": "text" + }, + { + "bbox": [ + 106, + 183, + 164, + 196 + ], + "score": 1.0, + "content": "expectation of", + "type": "text" + }, + { + "bbox": [ + 165, + 183, + 172, + 193 + ], + "score": 0.78, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 183, + 454, + 196 + ], + "score": 1.0, + "content": ". For all the following methods we can write the unsupervised objective", + "type": "text" + }, + { + "bbox": [ + 455, + 184, + 465, + 193 + ], + "score": 0.84, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 183, + 506, + 196 + ], + "score": 1.0, + "content": "such that:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 85, + 195, + 100, + 206 + ], + "spans": [ + { + "bbox": [ + 85, + 195, + 100, + 206 + ], + "score": 1.0, + "content": "676", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5 + }, + { + "type": "interline_equation", + "bbox": [ + 184, + 204, + 426, + 219 + ], + "lines": [ + { + "bbox": [ + 184, + 204, + 426, + 219 + ], + "spans": [ + { + "bbox": [ + 184, + 204, + 426, + 219 + ], + "score": 0.88, + "content": "C _ { 1 } \\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } , \\tilde { y } ) } [ L ( \\theta ; \\tilde { x } , \\tilde { y } ) ] \\leq H ( \\theta ; x ) \\leq C _ { 2 } \\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } , \\tilde { y } ) } [ L ( \\theta ; \\tilde { x } , \\tilde { y } ) ] ,", + "type": "interline_equation", + "image_path": "87e5abe77358df98f5516ab7033c0b15bb5173481e228f3c5a948e9d643c7bc7.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 184, + 204, + 426, + 219 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 98, + 220, + 185, + 232 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 186, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 126, + 234 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 127, + 220, + 182, + 232 + ], + "score": 0.89, + "content": "0 \\leq C _ { 1 } \\leq C _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 218, + 186, + 234 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 86, + 237, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 86, + 235, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 86, + 239, + 100, + 249 + ], + "score": 1.0, + "content": "678", + "type": "text" + }, + { + "bbox": [ + 105, + 235, + 506, + 250 + ], + "score": 1.0, + "content": "Indeed, consistency-based methods minimise an unsupervised objective that is a divergence between", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 86, + 248, + 505, + 260 + ], + "spans": [ + { + "bbox": [ + 86, + 249, + 100, + 259 + ], + "score": 1.0, + "content": "679", + "type": "text" + }, + { + "bbox": [ + 106, + 248, + 505, + 260 + ], + "score": 1.0, + "content": "the model predictions and a modified version of the input (data augmentation) or a perturbation of the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 86, + 259, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 86, + 261, + 100, + 270 + ], + "score": 1.0, + "content": "680", + "type": "text" + }, + { + "bbox": [ + 106, + 259, + 505, + 271 + ], + "score": 1.0, + "content": "model. Using the fact that all norms are equivalent in a finite-dimensional space such as the space of", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 85, + 270, + 477, + 282 + ], + "spans": [ + { + "bbox": [ + 85, + 272, + 99, + 281 + ], + "score": 1.0, + "content": "681", + "type": "text" + }, + { + "bbox": [ + 106, + 270, + 366, + 282 + ], + "score": 1.0, + "content": "the labels, we have the equivalence between a consistency-based", + "type": "text" + }, + { + "bbox": [ + 366, + 270, + 376, + 280 + ], + "score": 0.8, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 270, + 466, + 282 + ], + "score": 1.0, + "content": "and an expectation of", + "type": "text" + }, + { + "bbox": [ + 466, + 271, + 473, + 279 + ], + "score": 0.83, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 270, + 477, + 282 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 92, + 293, + 506, + 326 + ], + "lines": [ + { + "bbox": [ + 91, + 293, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 91, + 296, + 99, + 303 + ], + "score": 1.0, + "content": "82", + "type": "text" + }, + { + "bbox": [ + 104, + 293, + 506, + 306 + ], + "score": 1.0, + "content": "VAT The virtual adversarial training method proposed by (Miyato et al., 2018) generates the most", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 91, + 304, + 507, + 316 + ], + "spans": [ + { + "bbox": [ + 91, + 307, + 99, + 314 + ], + "score": 1.0, + "content": "83", + "type": "text" + }, + { + "bbox": [ + 105, + 304, + 196, + 316 + ], + "score": 1.0, + "content": "impactful perturbation", + "type": "text" + }, + { + "bbox": [ + 197, + 306, + 213, + 315 + ], + "score": 0.87, + "content": "r _ { a d \\nu }", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 304, + 251, + 316 + ], + "score": 1.0, + "content": "to add to", + "type": "text" + }, + { + "bbox": [ + 251, + 306, + 258, + 314 + ], + "score": 0.76, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 304, + 507, + 316 + ], + "score": 1.0, + "content": ". The objective is to train a model robust to input perturbations.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 91, + 315, + 478, + 327 + ], + "spans": [ + { + "bbox": [ + 91, + 318, + 99, + 325 + ], + "score": 1.0, + "content": "84", + "type": "text" + }, + { + "bbox": [ + 105, + 315, + 478, + 327 + ], + "score": 1.0, + "content": "This method is closely related to adversarial training introduced by Goodfellow et al. (2014).", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17 + }, + { + "type": "interline_equation", + "bbox": [ + 224, + 348, + 386, + 362 + ], + "lines": [ + { + "bbox": [ + 224, + 348, + 386, + 362 + ], + "spans": [ + { + "bbox": [ + 224, + 348, + 386, + 362 + ], + "score": 0.91, + "content": "H ( \\theta ; x ) = { \\bf D i v } ( f _ { \\hat { \\theta } } ( x , . ) , f _ { \\theta } ( x + r _ { a d \\nu } , . ) )", + "type": "interline_equation", + "image_path": "5ee298f3f093816c37c63e9ad03f97eaa6546e3088120f6da1e273c11fff8fe6.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 224, + 348, + 386, + 362 + ], + "spans": [], + "index": 19 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 367, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 85, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 85, + 369, + 100, + 379 + ], + "score": 1.0, + "content": "685", + "type": "text" + }, + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "score": 1.0, + "content": "where the Div is a non-negative function that measures the divergence between two distributions, the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 85, + 377, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 85, + 380, + 100, + 390 + ], + "score": 1.0, + "content": "686", + "type": "text" + }, + { + "bbox": [ + 104, + 377, + 506, + 392 + ], + "score": 1.0, + "content": "cross-entropy or the KL divergence for instance. If the divergence function is the cross-entropy, it is", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 86, + 389, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 86, + 391, + 99, + 401 + ], + "score": 1.0, + "content": "687", + "type": "text" + }, + { + "bbox": [ + 105, + 389, + 505, + 402 + ], + "score": 1.0, + "content": "straightforward to write the unlabelled objective as Equation 3. If the objective function is the KL", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 85, + 400, + 273, + 412 + ], + "spans": [ + { + "bbox": [ + 85, + 402, + 100, + 412 + ], + "score": 1.0, + "content": "688", + "type": "text" + }, + { + "bbox": [ + 106, + 400, + 273, + 412 + ], + "score": 1.0, + "content": "divergence, we can write the objective as", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "interline_equation", + "bbox": [ + 192, + 425, + 418, + 441 + ], + "lines": [ + { + "bbox": [ + 192, + 425, + 418, + 441 + ], + "spans": [ + { + "bbox": [ + 192, + 425, + 418, + 441 + ], + "score": 0.89, + "content": "H ( \\theta ; x ) = \\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } + r , \\tilde { y } ) } [ L ( \\theta ; \\tilde { x } , \\tilde { y } ) ] - \\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } , \\tilde { y } ) } [ L ( \\hat { \\theta } ; \\tilde { x } , \\tilde { y } ) ]", + "type": "interline_equation", + "image_path": "073139ad1e7072d293022714fdc49036c7260d738162b81e7e5fa682b0700bb9.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 192, + 425, + 418, + 441 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 444, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 86, + 443, + 506, + 458 + ], + "spans": [ + { + "bbox": [ + 86, + 446, + 100, + 456 + ], + "score": 1.0, + "content": "689", + "type": "text" + }, + { + "bbox": [ + 102, + 443, + 129, + 458 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 129, + 444, + 236, + 457 + ], + "score": 0.91, + "content": "\\pi _ { x } ( \\tilde { x } , \\tilde { y } ) = \\delta _ { x } ( \\tilde { x } ) p _ { \\hat { \\theta } } ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 443, + 346, + 458 + ], + "score": 1.0, + "content": ". Therefore, variation of", + "type": "text" + }, + { + "bbox": [ + 346, + 444, + 357, + 454 + ], + "score": 0.81, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 357, + 443, + 426, + 458 + ], + "score": 1.0, + "content": "with respect to", + "type": "text" + }, + { + "bbox": [ + 426, + 445, + 433, + 454 + ], + "score": 0.81, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 443, + 506, + 458 + ], + "score": 1.0, + "content": "are the same as", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 85, + 454, + 507, + 470 + ], + "spans": [ + { + "bbox": [ + 85, + 457, + 100, + 466 + ], + "score": 1.0, + "content": "690", + "type": "text" + }, + { + "bbox": [ + 107, + 456, + 195, + 468 + ], + "score": 0.91, + "content": "\\mathbb { E } _ { \\pi _ { x } ( \\tilde { x } + r , \\tilde { y } ) } [ L ( \\theta ; \\tilde { x } , \\tilde { y } ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 454, + 507, + 470 + ], + "score": 1.0, + "content": ". 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(2021) proves an", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 246, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 86, + 248, + 100, + 257 + ], + "score": 1.0, + "content": "725", + "type": "text" + }, + { + "bbox": [ + 105, + 246, + 506, + 259 + ], + "score": 1.0, + "content": "upper bound for training deep models with the pseudo-label method under strong assumption. Under", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 86, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 86, + 259, + 100, + 268 + ], + "score": 1.0, + "content": "726", + "type": "text" + }, + { + "bbox": [ + 106, + 257, + 484, + 269 + ], + "score": 1.0, + "content": "soft assumptions, Aminian et al. (2022) provides an error bound showing that the choice of", + "type": "text" + }, + { + "bbox": [ + 484, + 257, + 494, + 267 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 257, + 505, + 269 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 86, + 268, + 261, + 280 + ], + "spans": [ + { + "bbox": [ + 86, + 270, + 99, + 279 + ], + "score": 1.0, + "content": "727", + "type": "text" + }, + { + "bbox": [ + 105, + 268, + 261, + 280 + ], + "score": 1.0, + "content": "crucial to provide good performances.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 87, + 284, + 506, + 317 + ], + "lines": [ + { + "bbox": [ + 86, + 283, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 86, + 286, + 99, + 295 + ], + "score": 1.0, + "content": "728", + "type": "text" + }, + { + "bbox": [ + 104, + 283, + 505, + 297 + ], + "score": 1.0, + "content": "Indeed, the unbiased nature of the risk estimate is crucial in the development of learning theory. This", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 86, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 86, + 297, + 100, + 306 + ], + "score": 1.0, + "content": "729", + "type": "text" + }, + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "bias on the risk estimate may look like the one of a regularisation, such as the ridge regularisation.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 86, + 306, + 421, + 318 + ], + "spans": [ + { + "bbox": [ + 86, + 307, + 100, + 317 + ], + "score": 1.0, + "content": "730", + "type": "text" + }, + { + "bbox": [ + 105, + 306, + 421, + 318 + ], + "score": 1.0, + "content": "However, SSL and regularisation are intrinsically different for several reasons:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 129, + 326, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 133, + 326, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 133, + 326, + 506, + 339 + ], + "score": 1.0, + "content": "• Regularisers have a vanishing impact in the limit of infinite data whereas SSL usually do", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 337, + 506, + 349 + ], + "spans": [ + { + "bbox": [ + 141, + 337, + 447, + 349 + ], + "score": 1.0, + "content": "not in the proposed methods, see Equation 18. A solution would be to choose", + "type": "text" + }, + { + "bbox": [ + 447, + 338, + 454, + 347 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 337, + 506, + 349 + ], + "score": 1.0, + "content": "with respect", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 142, + 348, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 142, + 348, + 359, + 360 + ], + "score": 1.0, + "content": "of the number of data points and make it vanish when", + "type": "text" + }, + { + "bbox": [ + 359, + 351, + 366, + 358 + ], + "score": 0.62, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 348, + 505, + 360 + ], + "score": 1.0, + "content": "goes to infinity. However, in most", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 359, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 141, + 359, + 227, + 371 + ], + "score": 1.0, + "content": "works, the choice of", + "type": "text" + }, + { + "bbox": [ + 227, + 360, + 234, + 369 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 359, + 368, + 371 + ], + "score": 1.0, + "content": "is independent of the number of", + "type": "text" + }, + { + "bbox": [ + 368, + 361, + 375, + 369 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 359, + 387, + 371 + ], + "score": 1.0, + "content": "or", + "type": "text" + }, + { + "bbox": [ + 388, + 361, + 398, + 370 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 359, + 505, + 371 + ], + "score": 1.0, + "content": "(Oliver et al., 2018; Sohn", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 370, + 194, + 381 + ], + "spans": [ + { + "bbox": [ + 141, + 370, + 194, + 381 + ], + "score": 1.0, + "content": "et al., 2020).", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 134, + 384, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 134, + 384, + 505, + 397 + ], + "score": 1.0, + "content": "• One of the main advantages of regularisation is to turn the learning problem into a “more", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 141, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "convex” problem, see Shalev-Shwartz & Ben-David (2014, Chapter 13). Indeed, ridge", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 141, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "regularisation will often turn a convex problem into a strongly-convex problem. However,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 141, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "SSL faces the danger to turn the learning problem as non-convex as previously noted by", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 142, + 429, + 244, + 440 + ], + "spans": [ + { + "bbox": [ + 142, + 429, + 244, + 440 + ], + "score": 1.0, + "content": "Sokolovska et al. (2008).", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "• The objective of a regulariser is to bias the risk towards optimum with smooth decision", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 454, + 444, + 466 + ], + "spans": [ + { + "bbox": [ + 141, + 454, + 444, + 466 + ], + "score": 1.0, + "content": "functions whereas entropy-based SSL will lead to sharp decision functions.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 133, + 469, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 133, + 469, + 381, + 482 + ], + "score": 1.0, + "content": "• Regularisation usually does not depend on the data whereas", + "type": "text" + }, + { + "bbox": [ + 382, + 469, + 392, + 479 + ], + "score": 0.73, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 469, + 506, + 482 + ], + "score": 1.0, + "content": "does in the SSL framework.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 88, + 489, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 84, + 488, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 84, + 488, + 506, + 504 + ], + "score": 1.0, + "content": "744 A entropy bias has been actually used by Pereyra et al. (2017) as a regulariser but as entropy", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 86, + 501, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 86, + 502, + 102, + 512 + ], + "score": 1.0, + "content": "745", + "type": "text" + }, + { + "bbox": [ + 104, + 501, + 505, + 513 + ], + "score": 1.0, + "content": "maximisation which should has an effect that is the opposite of the SSL method introduced by", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 86, + 511, + 331, + 524 + ], + "spans": [ + { + "bbox": [ + 86, + 513, + 100, + 523 + ], + "score": 1.0, + "content": "746", + "type": "text" + }, + { + "bbox": [ + 105, + 511, + 331, + 524 + ], + "score": 1.0, + "content": "Grandvalet & Bengio (2004), the entropy minimisation.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31 + } + ], + "page_idx": 18, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "spans": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "score": 1.0, + "content": "19", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 87, + 71, + 271, + 85 + ], + "lines": [ + { + "bbox": [ + 84, + 69, + 274, + 88 + ], + "spans": [ + { + "bbox": [ + 84, + 69, + 274, + 88 + ], + "score": 1.0, + "content": "715 C On the semi-supervised bias", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "index", + "bbox": [ + 90, + 95, + 507, + 118 + ], + "lines": [ + { + "bbox": [ + 86, + 95, + 506, + 109 + ], + "spans": [ + { + "bbox": [ + 86, + 95, + 506, + 109 + ], + "score": 1.0, + "content": "716 We provide in this appendix a further explanation of the risk induced by the SSL bias as introduced", + "type": "text" + } + ], + "index": 1, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 106, + 167, + 118 + ], + "spans": [ + { + "bbox": [ + 86, + 106, + 167, + 118 + ], + "score": 1.0, + "content": "717 in Section 2.3.", + "type": "text" + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 86, + 139, + 102, + 149 + ], + "score": 1.0, + "content": "718", + "type": "text" + }, + { + "bbox": [ + 102, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "Presented methods minimise a biased version of the risk under the MCAR assumption and therefore", + "type": "text" + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 84, + 148, + 307, + 162 + ], + "spans": [ + { + "bbox": [ + 84, + 148, + 307, + 162 + ], + "score": 1.0, + "content": "719 classical learning theory does not apply anymore,", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + } + ], + "index": 1.5, + "bbox_fs": [ + 86, + 95, + 506, + 118 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 137, + 506, + 160 + ], + "lines": [], + "index": 3.5, + "bbox_fs": [ + 84, + 137, + 505, + 162 + ], + "lines_deleted": true + }, + { + "type": "interline_equation", + "bbox": [ + 195, + 165, + 416, + 181 + ], + "lines": [ + { + "bbox": [ + 195, + 165, + 416, + 181 + ], + "spans": [ + { + "bbox": [ + 195, + 165, + 416, + 181 + ], + "score": 0.91, + "content": "\\mathbb { E } [ \\hat { \\mathcal { R } } _ { S S L } ( \\theta ) ] = \\mathbb { E } [ L ( \\theta ; x , y ) ] + \\lambda \\mathbb { E } [ H ( \\theta ; x , y ) ] \\neq \\mathcal { R } ( \\theta ) .", + "type": "interline_equation", + "image_path": "39a71df1e806e44c3dab6bb255bec7bbae94e5f32198ca02ec5bbbe6d0b4d549.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 195, + 165, + 416, + 181 + ], + "spans": [], + "index": 5 + } + ] + }, + { + "type": "index", + "bbox": [ + 86, + 191, + 505, + 279 + ], + "lines": [ + { + "bbox": [ + 86, + 191, + 505, + 203 + ], + "spans": [ + { + "bbox": [ + 86, + 193, + 99, + 202 + ], + "score": 1.0, + "content": "720", + "type": "text" + }, + { + "bbox": [ + 105, + 191, + 505, + 203 + ], + "score": 1.0, + "content": "Learning over a biased estimate of the risk is not necessarily unsafe but it is difficult to provide", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 203, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 85, + 204, + 99, + 214 + ], + "score": 1.0, + "content": "721", + "type": "text" + }, + { + "bbox": [ + 106, + 203, + 505, + 215 + ], + "score": 1.0, + "content": "theoretical guarantees on such methods even if some works try to do so with strong assumptions on the", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 214, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 86, + 215, + 100, + 224 + ], + "score": 1.0, + "content": "722", + "type": "text" + }, + { + "bbox": [ + 105, + 214, + 505, + 226 + ], + "score": 1.0, + "content": "data distribution (Mey & Loog 2019, Section 4 and 5, Zhang et al. 2021b). Previous works proposed", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 223, + 506, + 236 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 100, + 235 + ], + "score": 1.0, + "content": "723", + "type": "text" + }, + { + "bbox": [ + 104, + 223, + 506, + 236 + ], + "score": 1.0, + "content": "generalisation error bounds of SSL methods under strong assumptions on the data distribution or the", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 234, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 86, + 237, + 100, + 246 + ], + "score": 1.0, + "content": "724", + "type": "text" + }, + { + "bbox": [ + 104, + 234, + 506, + 248 + ], + "score": 1.0, + "content": "true model. We refer to the survey by Mey & Loog (2019). More recently, Wei et al. (2021) proves an", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 246, + 506, + 259 + ], + "spans": [ + { + "bbox": [ + 86, + 248, + 100, + 257 + ], + "score": 1.0, + "content": "725", + "type": "text" + }, + { + "bbox": [ + 105, + 246, + 506, + 259 + ], + "score": 1.0, + "content": "upper bound for training deep models with the pseudo-label method under strong assumption. Under", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 86, + 259, + 100, + 268 + ], + "score": 1.0, + "content": "726", + "type": "text" + }, + { + "bbox": [ + 106, + 257, + 484, + 269 + ], + "score": 1.0, + "content": "soft assumptions, Aminian et al. 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This", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 86, + 297, + 100, + 306 + ], + "score": 1.0, + "content": "729", + "type": "text" + }, + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "bias on the risk estimate may look like the one of a regularisation, such as the ridge regularisation.", + "type": "text" + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 306, + 421, + 318 + ], + "spans": [ + { + "bbox": [ + 86, + 307, + 100, + 317 + ], + "score": 1.0, + "content": "730", + "type": "text" + }, + { + "bbox": [ + 105, + 306, + 421, + 318 + ], + "score": 1.0, + "content": "However, SSL and regularisation are intrinsically different for several reasons:", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + } + ], + "index": 9.5, + "bbox_fs": [ + 85, + 191, + 506, + 280 + ] + }, + { + "type": "index", + "bbox": [ + 87, + 284, + 506, + 317 + ], + "lines": [], + "index": 15, + "bbox_fs": [ + 86, + 283, + 506, + 318 + ], + "lines_deleted": true + }, + { + "type": "list", + "bbox": [ + 129, + 326, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 133, + 326, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 133, + 326, + 506, + 339 + ], + "score": 1.0, + "content": "• Regularisers have a vanishing impact in the limit of infinite data whereas SSL usually do", + "type": "text" + } + ], + "index": 17, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 337, + 506, + 349 + ], + "spans": [ + { + "bbox": [ + 141, + 337, + 447, + 349 + ], + "score": 1.0, + "content": "not in the proposed methods, see Equation 18. 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Indeed, ridge", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 141, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "regularisation will often turn a convex problem into a strongly-convex problem. However,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 141, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "SSL faces the danger to turn the learning problem as non-convex as previously noted by", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 142, + 429, + 244, + 440 + ], + "spans": [ + { + "bbox": [ + 142, + 429, + 244, + 440 + ], + "score": 1.0, + "content": "Sokolovska et al. (2008).", + "type": "text" + } + ], + "index": 26, + "is_list_end_line": true + }, + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "• The objective of a regulariser is to bias the risk towards optimum with smooth decision", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 454, + 444, + 466 + ], + "spans": [ + { + "bbox": [ + 141, + 454, + 444, + 466 + ], + "score": 1.0, + "content": "functions whereas entropy-based SSL will lead to sharp decision functions.", + "type": "text" + } + ], + "index": 28, + "is_list_end_line": true + }, + { + "bbox": [ + 133, + 469, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 133, + 469, + 381, + 482 + ], + "score": 1.0, + "content": "• Regularisation usually does not depend on the data whereas", + "type": "text" + }, + { + "bbox": [ + 382, + 469, + 392, + 479 + ], + "score": 0.73, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 469, + 506, + 482 + ], + "score": 1.0, + "content": "does in the SSL framework.", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true + } + ], + "index": 23, + "bbox_fs": [ + 133, + 326, + 506, + 482 + ] + }, + { + "type": "index", + "bbox": [ + 88, + 489, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 84, + 488, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 84, + 488, + 506, + 504 + ], + "score": 1.0, + "content": "744 A entropy bias has been actually used by Pereyra et al. (2017) as a regulariser but as entropy", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 501, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 86, + 502, + 102, + 512 + ], + "score": 1.0, + "content": "745", + "type": "text" + }, + { + "bbox": [ + 104, + 501, + 505, + 513 + ], + "score": 1.0, + "content": "maximisation which should has an effect that is the opposite of the SSL method introduced by", + "type": "text" + } + ], + "index": 31, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 511, + 331, + 524 + ], + "spans": [ + { + "bbox": [ + 86, + 513, + 100, + 523 + ], + "score": 1.0, + "content": "746", + "type": "text" + }, + { + "bbox": [ + 105, + 511, + 331, + 524 + ], + "score": 1.0, + "content": "Grandvalet & Bengio (2004), the entropy minimisation.", + "type": "text" + } + ], + "index": 32, + "is_list_start_line": true + } + ], + "index": 31, + "bbox_fs": [ + 84, + 488, + 506, + 524 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 86, + 70, + 372, + 87 + ], + "lines": [ + { + "bbox": [ + 82, + 69, + 373, + 87 + ], + "spans": [ + { + "bbox": [ + 82, + 69, + 182, + 87 + ], + "score": 1.0, + "content": "D Proof that 747", + "type": "text" + }, + { + "bbox": [ + 182, + 70, + 236, + 86 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 69, + 373, + 87 + ], + "score": 1.0, + "content": "is unbiased under MCAR", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 97, + 98, + 478, + 113 + ], + "lines": [ + { + "bbox": [ + 104, + 97, + 479, + 114 + ], + "spans": [ + { + "bbox": [ + 104, + 97, + 291, + 114 + ], + "score": 1.0, + "content": "Theorem D.1. Under the MCAR assumption,", + "type": "text" + }, + { + "bbox": [ + 292, + 98, + 341, + 112 + ], + "score": 0.92, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 341, + 97, + 453, + 114 + ], + "score": 1.0, + "content": "is an unbiased estimator of", + "type": "text" + }, + { + "bbox": [ + 453, + 100, + 475, + 112 + ], + "score": 0.91, + "content": "{ \\mathcal { R } } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 97, + 479, + 114 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 104, + 120, + 506, + 148 + ], + "lines": [ + { + "bbox": [ + 106, + 120, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 106, + 121, + 358, + 135 + ], + "score": 1.0, + "content": "As a consequence of the theorem, under the MCAR assumption,", + "type": "text" + }, + { + "bbox": [ + 358, + 120, + 393, + 134 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { C C } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 121, + 505, + 135 + ], + "score": 1.0, + "content": "is also unbiased as a special", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 133, + 227, + 148 + ], + "spans": [ + { + "bbox": [ + 106, + 134, + 137, + 148 + ], + "score": 1.0, + "content": "case of", + "type": "text" + }, + { + "bbox": [ + 137, + 133, + 186, + 147 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 134, + 201, + 148 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 202, + 135, + 227, + 145 + ], + "score": 0.87, + "content": "\\lambda = 0", + "type": "inline_equation" + } + ], + "index": 3 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 87, + 158, + 465, + 173 + ], + "lines": [ + { + "bbox": [ + 83, + 157, + 466, + 175 + ], + "spans": [ + { + "bbox": [ + 83, + 157, + 322, + 175 + ], + "score": 1.0, + "content": "Proof: We first recall that the DeSSL risk estimator 751", + "type": "text" + }, + { + "bbox": [ + 322, + 159, + 371, + 172 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 157, + 444, + 175 + ], + "score": 1.0, + "content": "is defined for any", + "type": "text" + }, + { + "bbox": [ + 445, + 161, + 451, + 170 + ], + "score": 0.81, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 157, + 466, + 175 + ], + "score": 1.0, + "content": "by", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "interline_equation", + "bbox": [ + 158, + 177, + 453, + 245 + ], + "lines": [ + { + "bbox": [ + 158, + 177, + 453, + 245 + ], + "spans": [ + { + "bbox": [ + 158, + 177, + 453, + 245 + ], + "score": 0.94, + "content": "\\begin{array} { l l l } { \\displaystyle \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) - \\frac { \\lambda } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } H ( \\theta ; x _ { i } ) } \\\\ { \\displaystyle \\qquad = \\sum _ { i = 1 } ^ { n } \\left( \\frac { r _ { i } } { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\lambda \\left( \\frac { 1 - r _ { i } } { n _ { u } } - \\frac { r _ { i } } { n _ { l } } \\right) H ( \\theta ; x _ { i } ) \\right) . } \\end{array}", + "type": "interline_equation", + "image_path": "a9a5230c88eecf2df68584735a133b60173271274dd61550ea674ade8b0d256a.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 158, + 177, + 453, + 199.66666666666666 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 158, + 199.66666666666666, + 453, + 222.33333333333331 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 158, + 222.33333333333331, + 453, + 244.99999999999997 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "text", + "bbox": [ + 87, + 247, + 233, + 259 + ], + "lines": [ + { + "bbox": [ + 84, + 247, + 234, + 261 + ], + "spans": [ + { + "bbox": [ + 84, + 247, + 234, + 261 + ], + "score": 1.0, + "content": "752 By the law of total expectation:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "interline_equation", + "bbox": [ + 215, + 264, + 396, + 286 + ], + "lines": [ + { + "bbox": [ + 215, + 264, + 396, + 286 + ], + "spans": [ + { + "bbox": [ + 215, + 264, + 396, + 286 + ], + "score": 0.93, + "content": "\\mathbb { E } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ] = \\mathbb { E } _ { r } \\left[ \\mathbb { E } _ { x , y } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) | r ] \\right] .", + "type": "interline_equation", + "image_path": "7f4cd214fe584e9672519e2dca97bf2aa146a7036bbb11f53be8d29d10e454fa.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 215, + 264, + 396, + 286 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 295, + 505, + 329 + ], + "lines": [ + { + "bbox": [ + 84, + 294, + 507, + 311 + ], + "spans": [ + { + "bbox": [ + 84, + 294, + 337, + 311 + ], + "score": 1.0, + "content": "753 As far as we are under the MCAR assumption, the data", + "type": "text" + }, + { + "bbox": [ + 337, + 297, + 360, + 309 + ], + "score": 0.91, + "content": "( x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 294, + 482, + 311 + ], + "score": 1.0, + "content": "and the missingness variable", + "type": "text" + }, + { + "bbox": [ + 483, + 299, + 488, + 307 + ], + "score": 0.77, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 294, + 507, + 311 + ], + "score": 1.0, + "content": "are", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 82, + 307, + 392, + 330 + ], + "spans": [ + { + "bbox": [ + 82, + 307, + 180, + 330 + ], + "score": 1.0, + "content": "independent thus, 754", + "type": "text" + }, + { + "bbox": [ + 180, + 308, + 388, + 328 + ], + "score": 0.86, + "content": "\\mathbb { E } _ { r } \\left[ \\mathbb { E } _ { \\boldsymbol { x } , \\boldsymbol { y } } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\boldsymbol { \\theta } ) | \\boldsymbol { r } ] \\right] = \\mathbb { E } _ { r } \\left[ \\mathbb { E } _ { \\boldsymbol { x } , \\boldsymbol { y } } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\boldsymbol { \\theta } ) ] \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 307, + 392, + 330 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 85, + 332, + 507, + 357 + ], + "lines": [ + { + "bbox": [ + 86, + 332, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 86, + 336, + 100, + 345 + ], + "score": 1.0, + "content": "755", + "type": "text" + }, + { + "bbox": [ + 102, + 333, + 162, + 347 + ], + "score": 1.0, + "content": "We focus on", + "type": "text" + }, + { + "bbox": [ + 162, + 332, + 234, + 346 + ], + "score": 0.92, + "content": "\\mathbb { E } _ { x , y } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 333, + 313, + 347 + ], + "score": 1.0, + "content": ". First, we replace", + "type": "text" + }, + { + "bbox": [ + 314, + 332, + 363, + 346 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 333, + 506, + 347 + ], + "score": 1.0, + "content": "by its definition and then use the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 83, + 344, + 245, + 358 + ], + "spans": [ + { + "bbox": [ + 83, + 344, + 245, + 358 + ], + "score": 1.0, + "content": "756 linearity of the expectation. 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Therefore, we have", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + }, + { + "type": "interline_equation", + "bbox": [ + 111, + 298, + 514, + 365 + ], + "lines": [ + { + "bbox": [ + 111, + 298, + 514, + 365 + ], + "spans": [ + { + "bbox": [ + 111, + 298, + 514, + 365 + ], + "score": 0.92, + "content": "{ \\begin{array} { r l } { \\langle ( { \\hat { \\mathcal { R } } } _ { D e S S L } ( \\theta ) | r ) = \\displaystyle \\sum _ { i = 1 } ^ { n } \\mathbb { V } _ { ( x _ { i } , y _ { i } ) \\sim p ( x , y | r ) } \\left( { \\frac { r _ { i } } { n _ { l } } } L ( \\theta , x _ { i } , y _ { i } ) + \\lambda \\left( { \\frac { 1 - r _ { i } } { n _ { u } } } - { \\frac { r _ { i } } { n _ { l } } } \\right) H ( \\theta , x _ { i } ) \\right) } & { { \\mathrm { i . i . d ~ s a m p } } } \\\\ { = \\displaystyle \\sum _ { i = 1 } ^ { n } \\mathbb { V } _ { ( x _ { i } , y _ { i } ) \\sim p ( x , y ) } \\left( { \\frac { r _ { i } } { n _ { l } } } L ( \\theta , x _ { i } , y _ { i } ) + \\lambda \\left( { \\frac { 1 - r _ { i } } { n _ { u } } } - { \\frac { r _ { i } } { n _ { l } } } \\right) H ( \\theta , x _ { i } ) \\right) } & { { \\mathrm { ( } } x , y { \\mathrm { ) ~ a n d ~ } } } \\end{array} }", + "type": "interline_equation", + "image_path": "88a4abb72800827d1729ac693da17b6d95b3e258f0be32251a7c468249440fa5.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 111, + 298, + 514, + 320.3333333333333 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 111, + 320.3333333333333, + 514, + 342.66666666666663 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 111, + 342.66666666666663, + 514, + 364.99999999999994 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 381, + 496, + 395 + ], + "lines": [ + { + "bbox": [ + 85, + 381, + 496, + 396 + ], + "spans": [ + { + "bbox": [ + 85, + 381, + 230, + 396 + ], + "score": 1.0, + "content": "Using the fact that the couples 766", + "type": "text" + }, + { + "bbox": [ + 230, + 383, + 260, + 394 + ], + "score": 0.92, + "content": "( x _ { i } , y _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 381, + 496, + 396 + ], + "score": 1.0, + "content": "are i.i.d. samples following the same distribution, we have", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "interline_equation", + "bbox": [ + 106, + 398, + 448, + 493 + ], + "lines": [ + { + "bbox": [ + 106, + 398, + 448, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 448, + 493 + ], + "score": 0.95, + "content": "\\begin{array} { r l r } { { \\mathbb { V } ( \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) | r ) = \\displaystyle \\sum _ { i = 1 } ^ { n } \\mathbb { V } _ { ( x , y ) \\sim p ( x , y ) } ( \\frac { r _ { i } } { n _ { l } } L ( \\theta , x , y ) + \\lambda ( \\frac { 1 - r _ { i } } { n _ { u } } - \\frac { r _ { i } } { n _ { l } } ) H ( \\theta , x ) ) } } \\\\ & { } & { = \\displaystyle \\sum _ { i = 1 } ^ { n } \\frac { r _ { i } ^ { 2 } } { n _ { l } ^ { 2 } } \\mathbb { V } ( L ( \\theta , x , y ) ) + \\lambda ^ { 2 } ( \\frac { 1 - r _ { i } } { n _ { u } } - \\frac { r _ { i } } { n _ { l } } ) ^ { 2 } \\mathbb { V } ( H ( \\theta , x ) ) } \\\\ & { } & { + 2 \\lambda \\frac { r _ { i } } { n _ { l } } ( \\frac { 1 - r _ { i } } { n _ { u } } - \\frac { r _ { i } } { n _ { l } } ) \\mathrm { C o v } ( L ( \\theta , x , y ) , H ( \\theta , x ) ) } \\end{array}", + "type": "interline_equation", + "image_path": "5fe60ec83ee7cde3bc75b10e8ddc5f784245540e364a7ba97c185fbe820944ba.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 106, + 398, + 448, + 429.6666666666667 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 106, + 429.6666666666667, + 448, + 461.33333333333337 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 106, + 461.33333333333337, + 448, + 493.00000000000006 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 509, + 506, + 533 + ], + "lines": [ + { + "bbox": [ + 86, + 509, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 86, + 512, + 100, + 522 + ], + "score": 1.0, + "content": "767", + "type": "text" + }, + { + "bbox": [ + 103, + 509, + 237, + 523 + ], + "score": 1.0, + "content": "Now, we remark that the variable", + "type": "text" + }, + { + "bbox": [ + 237, + 513, + 243, + 520 + ], + "score": 0.79, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 509, + 334, + 523 + ], + "score": 1.0, + "content": "is binary and therefore", + "type": "text" + }, + { + "bbox": [ + 335, + 510, + 363, + 521 + ], + "score": 0.83, + "content": "r ^ { 2 } = r", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 509, + 367, + 523 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 367, + 510, + 433, + 523 + ], + "score": 0.86, + "content": "( 1 - 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\\frac { n _ { u } } { n } \\frac { \\mathrm { C o v } ( L ( \\theta , x , y ) , H ( \\theta , x ) ) ^ { 2 } } { \\mathbb { V } ( H ( \\theta , x ) ) \\mathbb { V } ( L ( \\theta ; x , y ) ) } ) } } \\\\ & { = \\frac { 1 } { n _ { l } } \\mathbb { V } ( L ( \\theta , x , y ) ) ( 1 - \\frac { n _ { u } } { n } \\mathrm { C o r r } ( L ( \\theta , x , y ) , H ( \\theta , x ) ) ^ { 2 } ) } \\\\ & { = ( 1 - \\frac { n _ { u } } { n } \\rho _ { L , H } ^ { 2 } ) \\frac { 1 } { n _ { l } } \\mathbb { V } ( L ( \\theta , x , y ) ) } \\end{array}", + "type": "interline_equation", + "image_path": "535ff5ce4a612491322b0d0830833dbcdac999d05bb444ef662fc5315581d700.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 153, + 88, + 457, + 114.33333333333333 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 153, + 114.33333333333333, + 457, + 140.66666666666666 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 153, + 140.66666666666666, + 457, + 167.0 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "text", + "bbox": [ + 84, + 167, + 506, + 190 + ], + "lines": [ + { + "bbox": [ + 86, + 167, + 506, + 180 + ], + "spans": [ + { + "bbox": [ + 86, + 167, + 167, + 180 + ], + "score": 1.0, + "content": "773 Remark E.1. If", + "type": "text" + }, + { + "bbox": [ + 168, + 168, + 178, + 178 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 167, + 285, + 180 + ], + "score": 1.0, + "content": "is perfectly correlated with", + "type": "text" + }, + { + "bbox": [ + 285, + 168, + 293, + 178 + ], + "score": 0.58, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 168, + 338, + 180 + ], + "score": 0.85, + "content": "\\begin{array} { r } { L \\left( \\rho _ { L , H } = 1 \\right) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 167, + 506, + 180 + ], + "score": 1.0, + "content": ", then the variance of the DeSSL estimator", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 84, + 178, + 360, + 191 + ], + "spans": [ + { + "bbox": [ + 84, + 178, + 360, + 191 + ], + "score": 1.0, + "content": "774 is equal to the variance of the estimator with no missing labels.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 85, + 191, + 506, + 293 + ], + "lines": [ + { + "bbox": [ + 86, + 190, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 86, + 193, + 100, + 203 + ], + "score": 1.0, + "content": "775", + "type": "text" + }, + { + "bbox": [ + 105, + 190, + 275, + 204 + ], + "score": 1.0, + "content": "Remark E.2. Is it possible to estimate", + "type": "text" + }, + { + "bbox": [ + 275, + 191, + 293, + 203 + ], + "score": 0.91, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 190, + 448, + 204 + ], + "score": 1.0, + "content": "in practice ? 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Therefore, we need to use an estimator of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 212, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 86, + 215, + 99, + 224 + ], + "score": 1.0, + "content": "777", + "type": "text" + }, + { + "bbox": [ + 105, + 212, + 167, + 225 + ], + "score": 1.0, + "content": "the covariance", + "type": "text" + }, + { + "bbox": [ + 168, + 213, + 269, + 225 + ], + "score": 0.91, + "content": "\\mathrm { C o v } ( L ( \\theta ; x , y ) , \\hat { H } ( \\theta ; x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 212, + 339, + 225 + ], + "score": 1.0, + "content": "and the variance", + "type": "text" + }, + { + "bbox": [ + 340, + 213, + 386, + 225 + ], + "score": 0.9, + "content": "\\mathbb { V } ( H ( \\theta ; x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 212, + 506, + 225 + ], + "score": 1.0, + "content": "(See Equation 23). Also, we", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 224, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 100, + 236 + ], + "score": 1.0, + "content": "778", + "type": "text" + }, + { + "bbox": [ + 105, + 224, + 390, + 237 + ], + "score": 1.0, + "content": "have to be careful not to introduce a new bias with the computation of", + "type": "text" + }, + { + "bbox": [ + 391, + 225, + 409, + 236 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 224, + 505, + 237 + ], + "score": 1.0, + "content": ", indeed, if we compute", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 86, + 236, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 86, + 240, + 99, + 249 + ], + "score": 1.0, + "content": "779", + "type": "text" + }, + { + "bbox": [ + 105, + 237, + 204, + 250 + ], + "score": 1.0, + "content": "it using the training set,", + "type": "text" + }, + { + "bbox": [ + 204, + 237, + 222, + 249 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 237, + 316, + 250 + ], + "score": 1.0, + "content": "becomes dependent of", + "type": "text" + }, + { + "bbox": [ + 316, + 239, + 324, + 247 + ], + "score": 0.77, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 237, + 341, + 250 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 342, + 239, + 348, + 249 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 237, + 405, + 250 + ], + "score": 1.0, + "content": "and therefore", + "type": "text" + }, + { + "bbox": [ + 406, + 236, + 466, + 249 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) | r )", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 237, + 506, + 250 + ], + "score": 1.0, + "content": "becomes", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 85, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 85, + 250, + 100, + 260 + ], + "score": 1.0, + "content": "780", + "type": "text" + }, + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "biased. A solution would be to use a validation dataset for its computation. Another approach is to", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 85, + 259, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 85, + 261, + 100, + 271 + ], + "score": 1.0, + "content": "781", + "type": "text" + }, + { + "bbox": [ + 104, + 259, + 308, + 271 + ], + "score": 1.0, + "content": "compute it using the splitting method (Avramidis", + "type": "text" + }, + { + "bbox": [ + 308, + 259, + 317, + 269 + ], + "score": 0.42, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 259, + 506, + 271 + ], + "score": 1.0, + "content": "Wilson, 1993). Moreover, the computation of", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 85, + 269, + 507, + 283 + ], + "spans": [ + { + "bbox": [ + 85, + 272, + 100, + 283 + ], + "score": 1.0, + "content": "782", + "type": "text" + }, + { + "bbox": [ + 106, + 271, + 125, + 282 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 269, + 496, + 283 + ], + "score": 1.0, + "content": "is tiresome and time-consuming in practice as it has to be updated for every different value of", + "type": "text" + }, + { + "bbox": [ + 497, + 271, + 502, + 280 + ], + "score": 0.79, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 269, + 507, + 283 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 86, + 279, + 205, + 295 + ], + "spans": [ + { + "bbox": [ + 86, + 283, + 100, + 292 + ], + "score": 1.0, + "content": "783", + "type": "text" + }, + { + "bbox": [ + 104, + 279, + 205, + 295 + ], + "score": 1.0, + "content": "so at each gradient step.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10 + }, + { + "type": "interline_equation", + "bbox": [ + 188, + 304, + 423, + 335 + ], + "lines": [ + { + "bbox": [ + 188, + 304, + 423, + 335 + ], + "spans": [ + { + "bbox": [ + 188, + 304, + 423, + 335 + ], + "score": 0.93, + "content": "\\hat { \\lambda } _ { o p t } = \\frac { \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } ( L ( \\theta ; x _ { i } , y _ { i } ) - \\bar { L } ( \\theta ) ) ( H ( \\theta ; x _ { i } ) - \\bar { H } ( \\theta ) ) } { \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } ( H ( \\theta ; x _ { i } ) - \\bar { H } ( \\theta ) ) ^ { 2 } }", + "type": "interline_equation", + "image_path": "7a5ccc35d7e406e9786a1ae8f690d704e45b0b9f255b41dd953a8e124ca996d6.jpg" + } + ] + } + ], + "index": 15.5, + "virtual_lines": [ + { + "bbox": [ + 188, + 304, + 423, + 319.5 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 188, + 319.5, + 423, + 335.0 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 90, + 336, + 374, + 351 + ], + "lines": [ + { + "bbox": [ + 85, + 332, + 375, + 354 + ], + "spans": [ + { + "bbox": [ + 85, + 332, + 133, + 354 + ], + "score": 1.0, + "content": "where 784", + "type": "text" + }, + { + "bbox": [ + 133, + 336, + 239, + 351 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\bar { H } ( \\theta ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x _ { i } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 332, + 257, + 354 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 258, + 336, + 375, + 352 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\bar { L } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 86, + 352, + 506, + 417 + ], + "lines": [ + { + "bbox": [ + 86, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 86, + 353, + 99, + 362 + ], + "score": 1.0, + "content": "785", + "type": "text" + }, + { + "bbox": [ + 105, + 351, + 240, + 363 + ], + "score": 1.0, + "content": "Remark E.3. About the sign of", + "type": "text" + }, + { + "bbox": [ + 240, + 352, + 247, + 361 + ], + "score": 0.79, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "As explained in the article, the theorem still has a quantitative", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 86, + 363, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 86, + 365, + 99, + 373 + ], + "score": 1.0, + "content": "786", + "type": "text" + }, + { + "bbox": [ + 105, + 363, + 246, + 374 + ], + "score": 1.0, + "content": "merit when it comes to choosing", + "type": "text" + }, + { + "bbox": [ + 247, + 363, + 254, + 372 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 363, + 369, + 374 + ], + "score": 1.0, + "content": ", by telling that the sign of", + "type": "text" + }, + { + "bbox": [ + 369, + 363, + 376, + 372 + ], + "score": 0.82, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 363, + 449, + 374 + ], + "score": 1.0, + "content": "is positive when", + "type": "text" + }, + { + "bbox": [ + 449, + 363, + 460, + 372 + ], + "score": 0.81, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 363, + 479, + 374 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 480, + 363, + 488, + 372 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 363, + 505, + 374 + ], + "score": 1.0, + "content": "are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 86, + 374, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 86, + 375, + 99, + 384 + ], + "score": 1.0, + "content": "787", + "type": "text" + }, + { + "bbox": [ + 105, + 374, + 505, + 385 + ], + "score": 1.0, + "content": "positively correlated which will generally be the case with the examples mentioned in the article. For", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 86, + 385, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 86, + 386, + 100, + 396 + ], + "score": 1.0, + "content": "788", + "type": "text" + }, + { + "bbox": [ + 105, + 385, + 505, + 396 + ], + "score": 1.0, + "content": "instance, concerning the entropy minimisation technique, the following proposition proves that the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 86, + 395, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 86, + 397, + 100, + 407 + ], + "score": 1.0, + "content": "789", + "type": "text" + }, + { + "bbox": [ + 105, + 395, + 468, + 407 + ], + "score": 1.0, + "content": "log-likelihood is negatively correlated with its entropy and therefore it justifies the choice of", + "type": "text" + }, + { + "bbox": [ + 469, + 395, + 494, + 405 + ], + "score": 0.9, + "content": "\\lambda > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 395, + 505, + 407 + ], + "score": 1.0, + "content": "in", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 86, + 407, + 212, + 418 + ], + "spans": [ + { + "bbox": [ + 86, + 407, + 100, + 417 + ], + "score": 1.0, + "content": "790", + "type": "text" + }, + { + "bbox": [ + 105, + 407, + 212, + 418 + ], + "score": 1.0, + "content": "the entropy minimisation.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5 + }, + { + "type": "text", + "bbox": [ + 92, + 419, + 504, + 443 + ], + "lines": [ + { + "bbox": [ + 87, + 417, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 87, + 417, + 346, + 433 + ], + "score": 1.0, + "content": "791 Proposition E.4. 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\\mathbb { E } _ { x , y } [ \\log p ( y | x ) ] \\mathbb { E } _ { x } [ \\mathbb { H } _ { \\tilde { y } } ( p ( \\tilde { y } | x ) ) ] } \\\\ & { \\mathrm { ~ } } \\\\ & { \\mathrm { ~ } = - \\mathbb { E } _ { x , y } [ \\log p ( y | x ) \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] + \\mathbb { E } _ { x , y } [ \\log p ( y | x ) ] \\mathbb { E } _ { x } [ \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] } \\end{array}", + "type": "interline_equation", + "image_path": "dd26ea9d86b2b6aad0d8f9a221db4762c6d1b7e007db6c40dbdd28c8f7ae2ab1.jpg" + } + ] + } + ], + "index": 29, + "virtual_lines": [ + { + "bbox": [ + 111, + 482, + 514, + 497.0 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 111, + 497.0, + 514, + 512.0 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 111, + 512.0, + 514, + 527.0 + ], + "spans": [], + "index": 30 + } + ] + }, + { + "type": "text", + "bbox": [ + 83, + 553, + 470, + 567 + ], + "lines": [ + { + "bbox": [ + 84, + 553, + 470, + 568 + ], + "spans": [ + { + "bbox": [ + 84, + 553, + 286, + 568 + ], + "score": 1.0, + "content": "793 By the law of total expectation, we have that", + "type": "text" + }, + { + "bbox": [ + 286, + 554, + 446, + 567 + ], + "score": 0.91, + "content": "\\mathbb { E } _ { x } [ \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] = \\mathbb { E } _ { x , \\tilde { y } } [ \\log p ( \\tilde { y } | x ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 553, + 470, + 568 + ], + "score": 1.0, + "content": ", then", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "interline_equation", + "bbox": [ + 124, + 570, + 468, + 602 + ], + "lines": [ + { + "bbox": [ + 124, + 570, + 468, + 602 + ], + "spans": [ + { + "bbox": [ + 124, + 570, + 468, + 602 + ], + "score": 0.92, + "content": "\\begin{array} { r l r } & { } & { \\mathrm { C o v } ( \\log p ( y | x ) , \\mathbb H _ { \\widetilde { y } } ( p ( \\widetilde { y } | x ) ) = - 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\\frac { n _ { u } } { n } \\frac { \\mathrm { C o v } ( L ( \\theta , x , y ) , H ( \\theta , x ) ) ^ { 2 } } { \\mathbb { V } ( H ( \\theta , x ) ) \\mathbb { V } ( L ( \\theta ; x , y ) ) } ) } } \\\\ & { = \\frac { 1 } { n _ { l } } \\mathbb { V } ( L ( \\theta , x , y ) ) ( 1 - \\frac { n _ { u } } { n } \\mathrm { C o r r } ( L ( \\theta , x , y ) , H ( \\theta , x ) ) ^ { 2 } ) } \\\\ & { = ( 1 - \\frac { n _ { u } } { n } \\rho _ { L , H } ^ { 2 } ) \\frac { 1 } { n _ { l } } \\mathbb { V } ( L ( \\theta , x , y ) ) } \\end{array}", + "type": "interline_equation", + "image_path": "535ff5ce4a612491322b0d0830833dbcdac999d05bb444ef662fc5315581d700.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 153, + 88, + 457, + 114.33333333333333 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 153, + 114.33333333333333, + 457, + 140.66666666666666 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 153, + 140.66666666666666, + 457, + 167.0 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "index", + "bbox": [ + 84, + 167, + 506, + 190 + ], + "lines": [ + { + "bbox": [ + 86, + 167, + 506, + 180 + ], + "spans": [ + { + "bbox": [ + 86, + 167, + 167, + 180 + ], + "score": 1.0, + "content": "773 Remark E.1. If", + "type": "text" + }, + { + "bbox": [ + 168, + 168, + 178, + 178 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 167, + 285, + 180 + ], + "score": 1.0, + "content": "is perfectly correlated with", + "type": "text" + }, + { + "bbox": [ + 285, + 168, + 293, + 178 + ], + "score": 0.58, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 168, + 338, + 180 + ], + "score": 0.85, + "content": "\\begin{array} { r } { L \\left( \\rho _ { L , H } = 1 \\right) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 167, + 506, + 180 + ], + "score": 1.0, + "content": ", then the variance of the DeSSL estimator", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 84, + 178, + 360, + 191 + ], + "spans": [ + { + "bbox": [ + 84, + 178, + 360, + 191 + ], + "score": 1.0, + "content": "774 is equal to the variance of the estimator with no missing labels.", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 190, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 86, + 193, + 100, + 203 + ], + "score": 1.0, + "content": "775", + "type": "text" + }, + { + "bbox": [ + 105, + 190, + 275, + 204 + ], + "score": 1.0, + "content": "Remark E.2. Is it possible to estimate", + "type": "text" + }, + { + "bbox": [ + 275, + 191, + 293, + 203 + ], + "score": 0.91, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 190, + 448, + 204 + ], + "score": 1.0, + "content": "in practice ? 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Therefore, we need to use an estimator of", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 212, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 86, + 215, + 99, + 224 + ], + "score": 1.0, + "content": "777", + "type": "text" + }, + { + "bbox": [ + 105, + 212, + 167, + 225 + ], + "score": 1.0, + "content": "the covariance", + "type": "text" + }, + { + "bbox": [ + 168, + 213, + 269, + 225 + ], + "score": 0.91, + "content": "\\mathrm { C o v } ( L ( \\theta ; x , y ) , \\hat { H } ( \\theta ; x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 212, + 339, + 225 + ], + "score": 1.0, + "content": "and the variance", + "type": "text" + }, + { + "bbox": [ + 340, + 213, + 386, + 225 + ], + "score": 0.9, + "content": "\\mathbb { V } ( H ( \\theta ; x ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 212, + 506, + 225 + ], + "score": 1.0, + "content": "(See Equation 23). Also, we", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 224, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 86, + 226, + 100, + 236 + ], + "score": 1.0, + "content": "778", + "type": "text" + }, + { + "bbox": [ + 105, + 224, + 390, + 237 + ], + "score": 1.0, + "content": "have to be careful not to introduce a new bias with the computation of", + "type": "text" + }, + { + "bbox": [ + 391, + 225, + 409, + 236 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 224, + 505, + 237 + ], + "score": 1.0, + "content": ", indeed, if we compute", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 236, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 86, + 240, + 99, + 249 + ], + "score": 1.0, + "content": "779", + "type": "text" + }, + { + "bbox": [ + 105, + 237, + 204, + 250 + ], + "score": 1.0, + "content": "it using the training set,", + "type": "text" + }, + { + "bbox": [ + 204, + 237, + 222, + 249 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 237, + 316, + 250 + ], + "score": 1.0, + "content": "becomes dependent of", + "type": "text" + }, + { + "bbox": [ + 316, + 239, + 324, + 247 + ], + "score": 0.77, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 237, + 341, + 250 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 342, + 239, + 348, + 249 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 237, + 405, + 250 + ], + "score": 1.0, + "content": "and therefore", + "type": "text" + }, + { + "bbox": [ + 406, + 236, + 466, + 249 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) | r )", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 237, + 506, + 250 + ], + "score": 1.0, + "content": "becomes", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 85, + 250, + 100, + 260 + ], + "score": 1.0, + "content": "780", + "type": "text" + }, + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "biased. A solution would be to use a validation dataset for its computation. Another approach is to", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 259, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 85, + 261, + 100, + 271 + ], + "score": 1.0, + "content": "781", + "type": "text" + }, + { + "bbox": [ + 104, + 259, + 308, + 271 + ], + "score": 1.0, + "content": "compute it using the splitting method (Avramidis", + "type": "text" + }, + { + "bbox": [ + 308, + 259, + 317, + 269 + ], + "score": 0.42, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 259, + 506, + 271 + ], + "score": 1.0, + "content": "Wilson, 1993). Moreover, the computation of", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 269, + 507, + 283 + ], + "spans": [ + { + "bbox": [ + 85, + 272, + 100, + 283 + ], + "score": 1.0, + "content": "782", + "type": "text" + }, + { + "bbox": [ + 106, + 271, + 125, + 282 + ], + "score": 0.9, + "content": "\\lambda _ { o p t }", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 269, + 496, + 283 + ], + "score": 1.0, + "content": "is tiresome and time-consuming in practice as it has to be updated for every different value of", + "type": "text" + }, + { + "bbox": [ + 497, + 271, + 502, + 280 + ], + "score": 0.79, + "content": "\\theta", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 269, + 507, + 283 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 279, + 205, + 295 + ], + "spans": [ + { + "bbox": [ + 86, + 283, + 100, + 292 + ], + "score": 1.0, + "content": "783", + "type": "text" + }, + { + "bbox": [ + 104, + 279, + 205, + 295 + ], + "score": 1.0, + "content": "so at each gradient step.", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + } + ], + "index": 4.5, + "bbox_fs": [ + 84, + 167, + 506, + 191 + ] + }, + { + "type": "index", + "bbox": [ + 85, + 191, + 506, + 293 + ], + "lines": [], + "index": 10, + "bbox_fs": [ + 85, + 190, + 507, + 295 + ], + "lines_deleted": true + }, + { + "type": "interline_equation", + "bbox": [ + 188, + 304, + 423, + 335 + ], + "lines": [ + { + "bbox": [ + 188, + 304, + 423, + 335 + ], + "spans": [ + { + "bbox": [ + 188, + 304, + 423, + 335 + ], + "score": 0.93, + "content": "\\hat { \\lambda } _ { o p t } = \\frac { \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } ( L ( \\theta ; x _ { i } , y _ { i } ) - \\bar { L } ( \\theta ) ) ( H ( \\theta ; x _ { i } ) - \\bar { H } ( \\theta ) ) } { \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } ( H ( \\theta ; x _ { i } ) - \\bar { H } ( \\theta ) ) ^ { 2 } }", + "type": "interline_equation", + "image_path": "7a5ccc35d7e406e9786a1ae8f690d704e45b0b9f255b41dd953a8e124ca996d6.jpg" + } + ] + } + ], + "index": 15.5, + "virtual_lines": [ + { + "bbox": [ + 188, + 304, + 423, + 319.5 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 188, + 319.5, + 423, + 335.0 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 90, + 336, + 374, + 351 + ], + "lines": [ + { + "bbox": [ + 85, + 332, + 375, + 354 + ], + "spans": [ + { + "bbox": [ + 85, + 332, + 133, + 354 + ], + "score": 1.0, + "content": "where 784", + "type": "text" + }, + { + "bbox": [ + 133, + 336, + 239, + 351 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\bar { H } ( \\theta ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x _ { i } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 332, + 257, + 354 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 258, + 336, + 375, + 352 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\bar { L } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 17 + } + ], + "index": 17, + "bbox_fs": [ + 85, + 332, + 375, + 354 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 352, + 506, + 417 + ], + "lines": [ + { + "bbox": [ + 86, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 86, + 353, + 99, + 362 + ], + "score": 1.0, + "content": "785", + "type": "text" + }, + { + "bbox": [ + 105, + 351, + 240, + 363 + ], + "score": 1.0, + "content": "Remark E.3. About the sign of", + "type": "text" + }, + { + "bbox": [ + 240, + 352, + 247, + 361 + ], + "score": 0.79, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "As explained in the article, the theorem still has a quantitative", + "type": "text" + } + ], + "index": 18, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 363, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 86, + 365, + 99, + 373 + ], + "score": 1.0, + "content": "786", + "type": "text" + }, + { + "bbox": [ + 105, + 363, + 246, + 374 + ], + "score": 1.0, + "content": "merit when it comes to choosing", + "type": "text" + }, + { + "bbox": [ + 247, + 363, + 254, + 372 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 363, + 369, + 374 + ], + "score": 1.0, + "content": ", by telling that the sign of", + "type": "text" + }, + { + "bbox": [ + 369, + 363, + 376, + 372 + ], + "score": 0.82, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 363, + 449, + 374 + ], + "score": 1.0, + "content": "is positive when", + "type": "text" + }, + { + "bbox": [ + 449, + 363, + 460, + 372 + ], + "score": 0.81, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 363, + 479, + 374 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 480, + 363, + 488, + 372 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 363, + 505, + 374 + ], + "score": 1.0, + "content": "are", + "type": "text" + } + ], + "index": 19, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 374, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 86, + 375, + 99, + 384 + ], + "score": 1.0, + "content": "787", + "type": "text" + }, + { + "bbox": [ + 105, + 374, + 505, + 385 + ], + "score": 1.0, + "content": "positively correlated which will generally be the case with the examples mentioned in the article. For", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 385, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 86, + 386, + 100, + 396 + ], + "score": 1.0, + "content": "788", + "type": "text" + }, + { + "bbox": [ + 105, + 385, + 505, + 396 + ], + "score": 1.0, + "content": "instance, concerning the entropy minimisation technique, the following proposition proves that the", + "type": "text" + } + ], + "index": 21, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 395, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 86, + 397, + 100, + 407 + ], + "score": 1.0, + "content": "789", + "type": "text" + }, + { + "bbox": [ + 105, + 395, + 468, + 407 + ], + "score": 1.0, + "content": "log-likelihood is negatively correlated with its entropy and therefore it justifies the choice of", + "type": "text" + }, + { + "bbox": [ + 469, + 395, + 494, + 405 + ], + "score": 0.9, + "content": "\\lambda > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 395, + 505, + 407 + ], + "score": 1.0, + "content": "in", + "type": "text" + } + ], + "index": 22, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 407, + 212, + 418 + ], + "spans": [ + { + "bbox": [ + 86, + 407, + 100, + 417 + ], + "score": 1.0, + "content": "790", + "type": "text" + }, + { + "bbox": [ + 105, + 407, + 212, + 418 + ], + "score": 1.0, + "content": "the entropy minimisation.", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true + } + ], + "index": 20.5, + "bbox_fs": [ + 86, + 351, + 505, + 418 + ] + }, + { + "type": "text", + "bbox": [ + 92, + 419, + 504, + 443 + ], + "lines": [ + { + "bbox": [ + 87, + 417, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 87, + 417, + 346, + 433 + ], + "score": 1.0, + "content": "791 Proposition E.4. The log-likelihood of the true distribution", + "type": "text" + }, + { + "bbox": [ + 347, + 419, + 389, + 432 + ], + "score": 0.93, + "content": "\\log p ( y | x )", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 417, + 505, + 433 + ], + "score": 1.0, + "content": "is negatively correlated with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 88, + 430, + 308, + 444 + ], + "spans": [ + { + "bbox": [ + 88, + 430, + 151, + 444 + ], + "score": 1.0, + "content": "its entropy 792", + "type": "text" + }, + { + "bbox": [ + 151, + 430, + 305, + 444 + ], + "score": 0.89, + "content": "\\mathbb { H } _ { \\tilde { y } } ( p ( \\tilde { y } | x ) ) = - \\mathbb { E } _ { \\tilde { y } \\sim p ( . | x ) } [ \\log p ( \\tilde { y } | x ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 305, + 430, + 308, + 444 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24.5, + "bbox_fs": [ + 87, + 417, + 505, + 444 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 237, + 446, + 375, + 460 + ], + "lines": [ + { + "bbox": [ + 237, + 446, + 375, + 460 + ], + "spans": [ + { + "bbox": [ + 237, + 446, + 375, + 460 + ], + "score": 0.89, + "content": "\\mathrm { C o v } ( \\log p ( y | x ) , \\mathbb { H } _ { \\tilde { y } } ( p ( \\tilde { y } | x ) ) ) < 0", + "type": "interline_equation", + "image_path": "b23376caea45aea948dd1e51c556af1cf7051b06fa936f0d40df0524dcc4301f.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 237, + 446, + 375, + 460 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 133, + 481 + ], + "lines": [ + { + "bbox": [ + 104, + 468, + 135, + 484 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 135, + 484 + ], + "score": 1.0, + "content": "Proof.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27, + "bbox_fs": [ + 104, + 468, + 135, + 484 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 111, + 482, + 514, + 527 + ], + "lines": [ + { + "bbox": [ + 111, + 482, + 514, + 527 + ], + "spans": [ + { + "bbox": [ + 111, + 482, + 514, + 527 + ], + "score": 0.84, + "content": "\\begin{array} { r l } & { \\mathrm { \\mathop { s o v } } ( \\log p ( y | x ) , \\mathbb { H } _ { \\tilde { y } } ( p ( \\tilde { y } | x ) ) ) = \\mathbb { E } _ { x , y } [ \\log p ( y | x ) \\mathbb { H } _ { \\tilde { y } } ( p ( \\tilde { y } | x ) ) ] - \\mathbb { E } _ { x , y } [ \\log p ( y | x ) ] \\mathbb { E } _ { x } [ \\mathbb { H } _ { \\tilde { y } } ( p ( \\tilde { y } | x ) ) ] } \\\\ & { \\mathrm { ~ } } \\\\ & { \\mathrm { ~ } = - \\mathbb { E } _ { x , y } [ \\log p ( y | x ) \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] + \\mathbb { E } _ { x , y } [ \\log p ( y | x ) ] \\mathbb { E } _ { x } [ \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] } \\end{array}", + "type": "interline_equation", + "image_path": "dd26ea9d86b2b6aad0d8f9a221db4762c6d1b7e007db6c40dbdd28c8f7ae2ab1.jpg" + } + ] + } + ], + "index": 29, + "virtual_lines": [ + { + "bbox": [ + 111, + 482, + 514, + 497.0 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 111, + 497.0, + 514, + 512.0 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 111, + 512.0, + 514, + 527.0 + ], + "spans": [], + "index": 30 + } + ] + }, + { + "type": "text", + "bbox": [ + 83, + 553, + 470, + 567 + ], + "lines": [ + { + "bbox": [ + 84, + 553, + 470, + 568 + ], + "spans": [ + { + "bbox": [ + 84, + 553, + 286, + 568 + ], + "score": 1.0, + "content": "793 By the law of total expectation, we have that", + "type": "text" + }, + { + "bbox": [ + 286, + 554, + 446, + 567 + ], + "score": 0.91, + "content": "\\mathbb { E } _ { x } [ \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] = \\mathbb { E } _ { x , \\tilde { y } } [ \\log p ( \\tilde { y } | x ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 553, + 470, + 568 + ], + "score": 1.0, + "content": ", then", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31, + "bbox_fs": [ + 84, + 553, + 470, + 568 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 124, + 570, + 468, + 602 + ], + "lines": [ + { + "bbox": [ + 124, + 570, + 468, + 602 + ], + "spans": [ + { + "bbox": [ + 124, + 570, + 468, + 602 + ], + "score": 0.92, + "content": "\\begin{array} { r l r } & { } & { \\mathrm { C o v } ( \\log p ( y | x ) , \\mathbb H _ { \\widetilde { y } } ( p ( \\widetilde { y } | x ) ) = - \\mathbb E _ { x , y } [ \\log p ( y | x ) \\mathbb E _ { \\widetilde { y } | x } [ \\log p ( \\widetilde { y } | x ) ] ] + \\mathbb E _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } } \\\\ & { } & { = \\mathbb E _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } - \\mathbb E _ { x , y } [ \\log p ( y | x ) \\mathbb E _ { \\widetilde { y } | x } [ \\log p ( \\widetilde { y } | x ) ] ] } \\end{array}", + "type": "interline_equation", + "image_path": "aabf2577c46832d089f330d87628ad72e320525e4bb31d815f0744a5135babc5.jpg" + } + ] + } + ], + "index": 33, + "virtual_lines": [ + { + "bbox": [ + 124, + 570, + 468, + 580.6666666666666 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 124, + 580.6666666666666, + 468, + 591.3333333333333 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 124, + 591.3333333333333, + 468, + 601.9999999999999 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "index", + "bbox": [ + 84, + 617, + 508, + 643 + ], + "lines": [ + { + "bbox": [ + 83, + 616, + 504, + 632 + ], + "spans": [ + { + "bbox": [ + 83, + 616, + 360, + 632 + ], + "score": 1.0, + "content": "794 On the other hand, also with the law of total expectation,", + "type": "text" + }, + { + "bbox": [ + 360, + 617, + 504, + 631 + ], + "score": 0.89, + "content": "\\mathbb { E } _ { \\boldsymbol { x } , \\boldsymbol { y } } [ \\log p ( \\boldsymbol { y } | \\boldsymbol { x } ) \\mathbb { E } _ { \\boldsymbol { \\tilde { y } } | \\boldsymbol { x } } [ \\log p ( \\boldsymbol { \\tilde { y } } | \\boldsymbol { x } ) ] ] \\ =", + "type": "inline_equation" + } + ], + "index": 35, + "is_list_start_line": true + }, + { + "bbox": [ + 84, + 628, + 268, + 643 + ], + "spans": [ + { + "bbox": [ + 84, + 628, + 106, + 643 + ], + "score": 1.0, + "content": "795", + "type": "text" + }, + { + "bbox": [ + 106, + 629, + 253, + 643 + ], + "score": 0.9, + "content": "\\mathbb { E } _ { x } [ \\mathbb { E } _ { y | x } [ \\log p ( y | x ) ] \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ]", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 628, + 268, + 643 + ], + "score": 1.0, + "content": ", so", + "type": "text" + } + ], + "index": 36, + "is_list_start_line": true + } + ], + "index": 35.5, + "bbox_fs": [ + 83, + 616, + 504, + 643 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 134, + 658, + 366, + 708 + ], + "lines": [ + { + "bbox": [ + 134, + 658, + 366, + 708 + ], + "spans": [ + { + "bbox": [ + 134, + 658, + 366, + 708 + ], + "score": 0.89, + "content": "\\begin{array} { r l r } & { } & { \\mathbb { E } _ { x , y } [ \\log p ( y | x ) \\mathbb { E } _ { \\tilde { y } | x } [ \\log p ( \\tilde { y } | x ) ] ] = \\mathbb { E } _ { x } [ \\mathbb { E } _ { y | x } [ \\log p ( y | x ) ] ^ { 2 } ] } \\\\ & { } & { \\geq \\mathbb { E } _ { x } [ \\mathbb { E } _ { y | x } [ \\log p ( y | x ) ] ] ^ { 2 } } \\\\ & { } & { \\geq \\mathbb { E } _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } } \\end{array}", + "type": "interline_equation", + "image_path": "46f85c4baff1ec1fda26654fd5e721832a25d50ce987890b012532193d21dc6f.jpg" + } + ] + } + ], + "index": 38, + "virtual_lines": [ + { + "bbox": [ + 134, + 658, + 366, + 674.6666666666666 + ], + "spans": [], + "index": 37 + }, + { + "bbox": [ + 134, + 674.6666666666666, + 366, + 691.3333333333333 + ], + "spans": [], + "index": 38 + }, + { + "bbox": [ + 134, + 691.3333333333333, + 366, + 707.9999999999999 + ], + "spans": [], + "index": 39 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 87, + 73, + 220, + 84 + ], + "lines": [ + { + "bbox": [ + 84, + 71, + 220, + 87 + ], + "spans": [ + { + "bbox": [ + 84, + 71, + 220, + 87 + ], + "score": 1.0, + "content": "796 Finally, we have the results,", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "interline_equation", + "bbox": [ + 164, + 89, + 446, + 118 + ], + "lines": [ + { + "bbox": [ + 164, + 89, + 446, + 118 + ], + "spans": [ + { + "bbox": [ + 164, + 89, + 446, + 118 + ], + "score": 0.92, + "content": "\\begin{array} { r l r } & { } & { \\mathrm { C o v } ( \\log p ( y | x ) , \\mathbb H _ { \\widetilde { y } } ( p ( \\widetilde { y } | x ) ) ) \\leq \\mathbb E _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } - \\mathbb E _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } } \\\\ & { } & { \\quad \\leq 0 } \\end{array}", + "type": "interline_equation", + "image_path": "9bab9bd773caf12958ec9fa13b59e4be95ab0e2541d1f6ca6eb46abda2b53c6f.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 164, + 89, + 446, + 98.66666666666667 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 164, + 98.66666666666667, + 446, + 108.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 164, + 108.33333333333334, + 446, + 118.00000000000001 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 141, + 507, + 173 + ], + "lines": [ + { + "bbox": [ + 86, + 140, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 86, + 143, + 100, + 153 + ], + "score": 1.0, + "content": "798", + "type": "text" + }, + { + "bbox": [ + 105, + 140, + 505, + 154 + ], + "score": 1.0, + "content": "Remark E.5. We can also see the Pseudo-label as a form of entropy. Indeed, modulo the confidence", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 152, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 86, + 154, + 100, + 163 + ], + "score": 1.0, + "content": "799", + "type": "text" + }, + { + "bbox": [ + 105, + 152, + 505, + 164 + ], + "score": 1.0, + "content": "selection on the predicted probability, the Pseudo-label objective is the inverse of the Rényi min-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 86, + 163, + 143, + 177 + ], + "spans": [ + { + "bbox": [ + 86, + 165, + 100, + 175 + ], + "score": 1.0, + "content": "800", + "type": "text" + }, + { + "bbox": [ + 105, + 163, + 143, + 177 + ], + "score": 1.0, + "content": "entropy:", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + }, + { + "type": "interline_equation", + "bbox": [ + 247, + 172, + 363, + 191 + ], + "lines": [ + { + "bbox": [ + 247, + 172, + 363, + 191 + ], + "spans": [ + { + "bbox": [ + 247, + 172, + 363, + 191 + ], + "score": 0.93, + "content": "\\mathbb { H } _ { \\infty } ( x ) = - \\operatorname* { m a x } _ { y } \\log p ( y | x )", + "type": "interline_equation", + "image_path": "8519497248f9c9ad086a80aa3bd5f0aee18f14fcf80a357190e6490352abcec9.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 247, + 172, + 363, + 191 + ], + "spans": [], + "index": 7 + } + ] + } + ], + "page_idx": 22, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 312, + 754 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 312, + 754 + ], + "score": 1.0, + "content": "23", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 494, + 123, + 505, + 134 + ], + "lines": [ + { + "bbox": [ + 495, + 125, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 495, + 125, + 505, + 133 + ], + "score": 0.998, + "content": "□", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 87, + 125, + 98, + 133 + ], + "lines": [ + { + "bbox": [ + 86, + 126, + 100, + 135 + ], + "spans": [ + { + "bbox": [ + 86, + 126, + 100, + 135 + ], + "score": 1.0, + "content": "797", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 87, + 73, + 220, + 84 + ], + "lines": [ + { + "bbox": [ + 84, + 71, + 220, + 87 + ], + "spans": [ + { + "bbox": [ + 84, + 71, + 220, + 87 + ], + "score": 1.0, + "content": "796 Finally, we have the results,", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0, + "bbox_fs": [ + 84, + 71, + 220, + 87 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 164, + 89, + 446, + 118 + ], + "lines": [ + { + "bbox": [ + 164, + 89, + 446, + 118 + ], + "spans": [ + { + "bbox": [ + 164, + 89, + 446, + 118 + ], + "score": 0.92, + "content": "\\begin{array} { r l r } & { } & { \\mathrm { C o v } ( \\log p ( y | x ) , \\mathbb H _ { \\widetilde { y } } ( p ( \\widetilde { y } | x ) ) ) \\leq \\mathbb E _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } - \\mathbb E _ { x , y } [ \\log p ( y | x ) ] ^ { 2 } } \\\\ & { } & { \\quad \\leq 0 } \\end{array}", + "type": "interline_equation", + "image_path": "9bab9bd773caf12958ec9fa13b59e4be95ab0e2541d1f6ca6eb46abda2b53c6f.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 164, + 89, + 446, + 98.66666666666667 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 164, + 98.66666666666667, + 446, + 108.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 164, + 108.33333333333334, + 446, + 118.00000000000001 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "index", + "bbox": [ + 86, + 141, + 507, + 173 + ], + "lines": [ + { + "bbox": [ + 86, + 140, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 86, + 143, + 100, + 153 + ], + "score": 1.0, + "content": "798", + "type": "text" + }, + { + "bbox": [ + 105, + 140, + 505, + 154 + ], + "score": 1.0, + "content": "Remark E.5. We can also see the Pseudo-label as a form of entropy. Indeed, modulo the confidence", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 152, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 86, + 154, + 100, + 163 + ], + "score": 1.0, + "content": "799", + "type": "text" + }, + { + "bbox": [ + 105, + 152, + 505, + 164 + ], + "score": 1.0, + "content": "selection on the predicted probability, the Pseudo-label objective is the inverse of the Rényi min-", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 163, + 143, + 177 + ], + "spans": [ + { + "bbox": [ + 86, + 165, + 100, + 175 + ], + "score": 1.0, + "content": "800", + "type": "text" + }, + { + "bbox": [ + 105, + 163, + 143, + 177 + ], + "score": 1.0, + "content": "entropy:", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + } + ], + "index": 5, + "bbox_fs": [ + 86, + 140, + 505, + 177 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 247, + 172, + 363, + 191 + ], + "lines": [ + { + "bbox": [ + 247, + 172, + 363, + 191 + ], + "spans": [ + { + "bbox": [ + 247, + 172, + 363, + 191 + ], + "score": 0.93, + "content": "\\mathbb { H } _ { \\infty } ( x ) = - \\operatorname* { m a x } _ { y } \\log p ( y | x )", + "type": "interline_equation", + "image_path": "8519497248f9c9ad086a80aa3bd5f0aee18f14fcf80a357190e6490352abcec9.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 247, + 172, + 363, + 191 + ], + "spans": [], + "index": 7 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 85, + 97, + 506, + 196 + ], + "lines": [ + { + "bbox": [ + 86, + 97, + 505, + 109 + ], + "spans": [ + { + "bbox": [ + 86, + 100, + 100, + 108 + ], + "score": 1.0, + "content": "802", + "type": "text" + }, + { + "bbox": [ + 106, + 97, + 505, + 109 + ], + "score": 1.0, + "content": "We remark that the debiasing can be performed with any subset of the training data, labelled and", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 86, + 108, + 505, + 120 + ], + "spans": [ + { + "bbox": [ + 86, + 110, + 99, + 119 + ], + "score": 1.0, + "content": "803", + "type": "text" + }, + { + "bbox": [ + 106, + 108, + 505, + 120 + ], + "score": 1.0, + "content": "unlabelled. The choice of debiasing only with the labelled data can be explained both intuitively and", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 86, + 118, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 86, + 121, + 99, + 129 + ], + "score": 1.0, + "content": "804", + "type": "text" + }, + { + "bbox": [ + 104, + 118, + 506, + 131 + ], + "score": 1.0, + "content": "computationally in regard to the Theorem 3.1. Intuitively, the debiasing term penalises the confidence", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 130, + 505, + 142 + ], + "spans": [ + { + "bbox": [ + 86, + 132, + 99, + 141 + ], + "score": 1.0, + "content": "805", + "type": "text" + }, + { + "bbox": [ + 106, + 130, + 505, + 142 + ], + "score": 1.0, + "content": "on the labelled datapoints and then prevents the overfitting on the train dataset. As remarked in section", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 141, + 505, + 153 + ], + "spans": [ + { + "bbox": [ + 86, + 143, + 99, + 152 + ], + "score": 1.0, + "content": "806", + "type": "text" + }, + { + "bbox": [ + 106, + 141, + 505, + 153 + ], + "score": 1.0, + "content": "3.1, Pereyra et al. (2017) showed that penalising low entropy models acts as a strong regulariser", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 152, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 86, + 154, + 99, + 163 + ], + "score": 1.0, + "content": "807", + "type": "text" + }, + { + "bbox": [ + 106, + 152, + 505, + 164 + ], + "score": 1.0, + "content": "in supervised settings. This comforts the idea of penalising low entropy on the labelled dataset,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 162, + 505, + 175 + ], + "spans": [ + { + "bbox": [ + 85, + 165, + 100, + 174 + ], + "score": 1.0, + "content": "808", + "type": "text" + }, + { + "bbox": [ + 105, + 162, + 505, + 175 + ], + "score": 1.0, + "content": "i.e. debiaising the entropy minimisation with the labelled dataset. Considering Pseudo-Label-based", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 174, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 86, + 176, + 99, + 185 + ], + "score": 1.0, + "content": "809", + "type": "text" + }, + { + "bbox": [ + 106, + 174, + 505, + 185 + ], + "score": 1.0, + "content": "methods, the objective for the labelled data is to predict the correct labels with moderate confidence.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 184, + 500, + 196 + ], + "spans": [ + { + "bbox": [ + 85, + 186, + 100, + 196 + ], + "score": 1.0, + "content": "810", + "type": "text" + }, + { + "bbox": [ + 106, + 184, + 500, + 196 + ], + "score": 1.0, + "content": "This is also similar to the concept of plausibility inference described by Barndorff-Nielsen (1976).", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 87, + 201, + 506, + 223 + ], + "lines": [ + { + "bbox": [ + 85, + 200, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 85, + 203, + 100, + 213 + ], + "score": 1.0, + "content": "811", + "type": "text" + }, + { + "bbox": [ + 105, + 200, + 505, + 213 + ], + "score": 1.0, + "content": "In regard to Theorem 3.1, we show that the optimum choice of subset for debiaising is either only the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 85, + 212, + 339, + 223 + ], + "spans": [ + { + "bbox": [ + 85, + 213, + 100, + 223 + ], + "score": 1.0, + "content": "812", + "type": "text" + }, + { + "bbox": [ + 106, + 212, + 339, + 223 + ], + "score": 1.0, + "content": "labelled data or the whole dataset and both are equivalent.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 105, + 228, + 375, + 240 + ], + "lines": [ + { + "bbox": [ + 106, + 227, + 375, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 192, + 241 + ], + "score": 1.0, + "content": "We consider a subset", + "type": "text" + }, + { + "bbox": [ + 192, + 230, + 201, + 238 + ], + "score": 0.81, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 227, + 326, + 241 + ], + "score": 1.0, + "content": "of the training set. We defined", + "type": "text" + }, + { + "bbox": [ + 326, + 233, + 332, + 238 + ], + "score": 0.72, + "content": "a", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 227, + 375, + 241 + ], + "score": 1.0, + "content": "as follow:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "interline_equation", + "bbox": [ + 246, + 246, + 365, + 275 + ], + "lines": [ + { + "bbox": [ + 246, + 246, + 365, + 275 + ], + "spans": [ + { + "bbox": [ + 246, + 246, + 365, + 275 + ], + "score": 0.94, + "content": "\\cdot", + "type": "interline_equation", + "image_path": "bc5ef7c68f79e22d7049387d1c982d7ee1be2a18af7e0c76e3fe95f83234993c.jpg" + } + ] + } + ], + "index": 12.5, + "virtual_lines": [ + { + "bbox": [ + 246, + 246, + 365, + 260.5 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 246, + 260.5, + 365, + 275.0 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 286, + 233, + 298 + ], + "lines": [ + { + "bbox": [ + 86, + 286, + 233, + 298 + ], + "spans": [ + { + "bbox": [ + 86, + 286, + 233, + 298 + ], + "score": 1.0, + "content": "813 The unbiased estimator is then:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "interline_equation", + "bbox": [ + 156, + 303, + 455, + 336 + ], + "lines": [ + { + "bbox": [ + 156, + 303, + 455, + 336 + ], + "spans": [ + { + "bbox": [ + 156, + 303, + 455, + 336 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L , A } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) - \\lambda \\sum _ { i = 1 } ^ { n } a _ { i } H ( \\theta ; x _ { i } ) .", + "type": "interline_equation", + "image_path": "0e065e3c91f8b28bf4fe2ccf8cad75ebb2ac0b46e69c9bcab70b74b425390228.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 156, + 303, + 455, + 314.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 156, + 314.0, + 455, + 325.0 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 156, + 325.0, + 455, + 336.0 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 339, + 98, + 347 + ], + "lines": [ + { + "bbox": [ + 86, + 339, + 100, + 347 + ], + "spans": [ + { + "bbox": [ + 86, + 339, + 100, + 347 + ], + "score": 1.0, + "content": "814", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 81, + 352, + 456, + 365 + ], + "lines": [ + { + "bbox": [ + 85, + 352, + 456, + 364 + ], + "spans": [ + { + "bbox": [ + 85, + 352, + 456, + 364 + ], + "score": 1.0, + "content": "815 We compute the variance of this quantity as in the proof of Theorem 3.1 and show that:", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "interline_equation", + "bbox": [ + 111, + 385, + 514, + 418 + ], + "lines": [ + { + "bbox": [ + 111, + 385, + 514, + 418 + ], + "spans": [ + { + "bbox": [ + 111, + 385, + 514, + 418 + ], + "score": 0.91, + "content": "-", + "type": "interline_equation", + "image_path": "11c4c6a4a7a6aa721fba53269e053962ccbf3efc9abd28023eace955475e130a.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 111, + 385, + 514, + 396.0 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 111, + 396.0, + 514, + 407.0 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 111, + 407.0, + 514, + 418.0 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 432, + 507, + 466 + ], + "lines": [ + { + "bbox": [ + 85, + 431, + 506, + 445 + ], + "spans": [ + { + "bbox": [ + 85, + 434, + 101, + 444 + ], + "score": 1.0, + "content": "816", + "type": "text" + }, + { + "bbox": [ + 104, + 431, + 282, + 445 + ], + "score": 1.0, + "content": "Suppose that no labelled datapoints are in", + "type": "text" + }, + { + "bbox": [ + 282, + 435, + 291, + 442 + ], + "score": 0.88, + "content": "\\mathcal { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 431, + 506, + 445 + ], + "score": 1.0, + "content": ". Then, the last term of the variance is null. Hence,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 85, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 85, + 445, + 100, + 455 + ], + "score": 1.0, + "content": "817", + "type": "text" + }, + { + "bbox": [ + 104, + 443, + 236, + 455 + ], + "score": 1.0, + "content": "having no labelled datapoints in", + "type": "text" + }, + { + "bbox": [ + 237, + 446, + 245, + 453 + ], + "score": 0.88, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "leads to a variance increase. We also remark that debiasing with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 85, + 453, + 433, + 466 + ], + "spans": [ + { + "bbox": [ + 85, + 456, + 100, + 465 + ], + "score": 1.0, + "content": "818", + "type": "text" + }, + { + "bbox": [ + 105, + 453, + 433, + 466 + ], + "score": 1.0, + "content": "the entire dataset is equivalent that debiasing with the labelled datapoints. Indeed", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24 + }, + { + "type": "interline_equation", + "bbox": [ + 123, + 473, + 488, + 575 + ], + "lines": [ + { + "bbox": [ + 123, + 473, + 488, + 575 + ], + "spans": [ + { + "bbox": [ + 123, + 473, + 488, + 575 + ], + "score": 0.95, + "content": "\\begin{array} { l l } { \\displaystyle \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) - \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x _ { i } ) } \\\\ { \\displaystyle \\quad \\quad = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) - \\frac { \\lambda } { n } \\sum _ { i = 1 } ^ { n _ { l } } H ( \\theta ; x _ { i } ) - \\frac { \\lambda } { n } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) } \\\\ { \\displaystyle \\quad \\quad = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda n _ { l } } { n n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) - \\frac { \\lambda n _ { l } } { n n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } H ( \\theta ; x _ { i } ) , } \\end{array}", + "type": "interline_equation", + "image_path": "1ff6c41c73f42c0b7b97af74e47ea7e6e38d822d20c95ab6275450f2b36e7928.jpg" + } + ] + } + ], + "index": 27, + "virtual_lines": [ + { + "bbox": [ + 123, + 473, + 488, + 507.0 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 123, + 507.0, + 488, + 541.0 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 123, + 541.0, + 488, + 575.0 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 84, + 579, + 449, + 592 + ], + "lines": [ + { + "bbox": [ + 82, + 576, + 450, + 595 + ], + "spans": [ + { + "bbox": [ + 82, + 576, + 408, + 595 + ], + "score": 1.0, + "content": "which is equivalent to debiasing with only the labelled dataset by replacing 819", + "type": "text" + }, + { + "bbox": [ + 408, + 582, + 415, + 590 + ], + "score": 0.87, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 576, + 429, + 595 + ], + "score": 1.0, + "content": "by", + "type": "text" + }, + { + "bbox": [ + 429, + 582, + 446, + 593 + ], + "score": 0.92, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 576, + 450, + 595 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 83, + 596, + 505, + 630 + ], + "lines": [ + { + "bbox": [ + 84, + 596, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 84, + 596, + 355, + 608 + ], + "score": 1.0, + "content": "820 At this point we can still sample a random subset composed of", + "type": "text" + }, + { + "bbox": [ + 355, + 599, + 359, + 606 + ], + "score": 0.84, + "content": "\\it { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 596, + 454, + 608 + ], + "score": 1.0, + "content": "labelled datapoints and", + "type": "text" + }, + { + "bbox": [ + 454, + 601, + 460, + 606 + ], + "score": 0.83, + "content": "u", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 596, + 506, + 608 + ], + "score": 1.0, + "content": "unlabelled", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 84, + 607, + 506, + 619 + ], + "spans": [ + { + "bbox": [ + 84, + 607, + 194, + 619 + ], + "score": 1.0, + "content": "821 datapoints. Therefore", + "type": "text" + }, + { + "bbox": [ + 195, + 609, + 300, + 619 + ], + "score": 0.91, + "content": "a _ { i } = 1 / ( l + u ) \\mathbf { 1 } \\{ x _ { i } \\in A \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 607, + 506, + 619 + ], + "score": 1.0, + "content": ", we show in the following that the optimum choice", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 84, + 617, + 449, + 631 + ], + "spans": [ + { + "bbox": [ + 84, + 617, + 161, + 631 + ], + "score": 1.0, + "content": "of the couple 822", + "type": "text" + }, + { + "bbox": [ + 162, + 620, + 183, + 630 + ], + "score": 0.93, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 617, + 200, + 631 + ], + "score": 1.0, + "content": "are", + "type": "text" + }, + { + "bbox": [ + 200, + 620, + 226, + 630 + ], + "score": 0.92, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 617, + 245, + 631 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 245, + 619, + 279, + 630 + ], + "score": 0.9, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 617, + 449, + 631 + ], + "score": 1.0, + "content": ", so only the labelled or the whole dataset.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 104, + 634, + 503, + 657 + ], + "lines": [ + { + "bbox": [ + 105, + 632, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 153, + 648 + ], + "score": 1.0, + "content": "We sample", + "type": "text" + }, + { + "bbox": [ + 153, + 637, + 156, + 644 + ], + "score": 0.38, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 632, + 209, + 648 + ], + "score": 1.0, + "content": "labelled and", + "type": "text" + }, + { + "bbox": [ + 209, + 639, + 216, + 644 + ], + "score": 0.87, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 632, + 505, + 648 + ], + "score": 1.0, + "content": "unlabelled datapoints to debiased the estimator, by simplifying the term", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 644, + 254, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 254, + 657 + ], + "score": 1.0, + "content": "in the sum of Equation 32 as follow:", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33.5 + }, + { + "type": "interline_equation", + "bbox": [ + 177, + 664, + 434, + 725 + ], + "lines": [ + { + "bbox": [ + 177, + 664, + 434, + 725 + ], + "spans": [ + { + "bbox": [ + 177, + 664, + 434, + 725 + ], + "score": 0.94, + "content": "\\cdot", + "type": "interline_equation", + "image_path": "8bae53e5a92ddca232c55443b0ad0c17dabdf1373bec3ff0a343c2f673b05b22.jpg" + } + ] + } + ], + "index": 36, + "virtual_lines": [ + { + "bbox": [ + 177, + 664, + 434, + 684.3333333333334 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 177, + 684.3333333333334, + 434, + 704.6666666666667 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 177, + 704.6666666666667, + 434, + 725.0000000000001 + ], + "spans": [], + "index": 37 + } + ] + } + ], + "page_idx": 23, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 313, + 755 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 313, + 755 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 15 + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 85, + 71, + 336, + 84 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 336, + 84 + ], + "spans": [ + { + "bbox": [ + 86, + 74, + 100, + 84 + ], + "score": 1.0, + "content": "801", + "type": "text" + }, + { + "bbox": [ + 104, + 72, + 120, + 84 + ], + "score": 1.0, + "content": "F", + "type": "text" + }, + { + "bbox": [ + 124, + 70, + 336, + 84 + ], + "score": 1.0, + "content": "Why debiasing with the labelled dataset?", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "index", + "bbox": [ + 85, + 97, + 506, + 196 + ], + "lines": [ + { + "bbox": [ + 86, + 97, + 505, + 109 + ], + "spans": [ + { + "bbox": [ + 86, + 100, + 100, + 108 + ], + "score": 1.0, + "content": "802", + "type": "text" + }, + { + "bbox": [ + 106, + 97, + 505, + 109 + ], + "score": 1.0, + "content": "We remark that the debiasing can be performed with any subset of the training data, labelled and", + "type": "text" + } + ], + "index": 0, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 108, + 505, + 120 + ], + "spans": [ + { + "bbox": [ + 86, + 110, + 99, + 119 + ], + "score": 1.0, + "content": "803", + "type": "text" + }, + { + "bbox": [ + 106, + 108, + 505, + 120 + ], + "score": 1.0, + "content": "unlabelled. The choice of debiasing only with the labelled data can be explained both intuitively and", + "type": "text" + } + ], + "index": 1, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 118, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 86, + 121, + 99, + 129 + ], + "score": 1.0, + "content": "804", + "type": "text" + }, + { + "bbox": [ + 104, + 118, + 506, + 131 + ], + "score": 1.0, + "content": "computationally in regard to the Theorem 3.1. Intuitively, the debiasing term penalises the confidence", + "type": "text" + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 130, + 505, + 142 + ], + "spans": [ + { + "bbox": [ + 86, + 132, + 99, + 141 + ], + "score": 1.0, + "content": "805", + "type": "text" + }, + { + "bbox": [ + 106, + 130, + 505, + 142 + ], + "score": 1.0, + "content": "on the labelled datapoints and then prevents the overfitting on the train dataset. As remarked in section", + "type": "text" + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 141, + 505, + 153 + ], + "spans": [ + { + "bbox": [ + 86, + 143, + 99, + 152 + ], + "score": 1.0, + "content": "806", + "type": "text" + }, + { + "bbox": [ + 106, + 141, + 505, + 153 + ], + "score": 1.0, + "content": "3.1, Pereyra et al. (2017) showed that penalising low entropy models acts as a strong regulariser", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 152, + 505, + 164 + ], + "spans": [ + { + "bbox": [ + 86, + 154, + 99, + 163 + ], + "score": 1.0, + "content": "807", + "type": "text" + }, + { + "bbox": [ + 106, + 152, + 505, + 164 + ], + "score": 1.0, + "content": "in supervised settings. This comforts the idea of penalising low entropy on the labelled dataset,", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 162, + 505, + 175 + ], + "spans": [ + { + "bbox": [ + 85, + 165, + 100, + 174 + ], + "score": 1.0, + "content": "808", + "type": "text" + }, + { + "bbox": [ + 105, + 162, + 505, + 175 + ], + "score": 1.0, + "content": "i.e. debiaising the entropy minimisation with the labelled dataset. Considering Pseudo-Label-based", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 174, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 86, + 176, + 99, + 185 + ], + "score": 1.0, + "content": "809", + "type": "text" + }, + { + "bbox": [ + 106, + 174, + 505, + 185 + ], + "score": 1.0, + "content": "methods, the objective for the labelled data is to predict the correct labels with moderate confidence.", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 184, + 500, + 196 + ], + "spans": [ + { + "bbox": [ + 85, + 186, + 100, + 196 + ], + "score": 1.0, + "content": "810", + "type": "text" + }, + { + "bbox": [ + 106, + 184, + 500, + 196 + ], + "score": 1.0, + "content": "This is also similar to the concept of plausibility inference described by Barndorff-Nielsen (1976).", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 200, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 85, + 203, + 100, + 213 + ], + "score": 1.0, + "content": "811", + "type": "text" + }, + { + "bbox": [ + 105, + 200, + 505, + 213 + ], + "score": 1.0, + "content": "In regard to Theorem 3.1, we show that the optimum choice of subset for debiaising is either only the", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 212, + 339, + 223 + ], + "spans": [ + { + "bbox": [ + 85, + 213, + 100, + 223 + ], + "score": 1.0, + "content": "812", + "type": "text" + }, + { + "bbox": [ + 106, + 212, + 339, + 223 + ], + "score": 1.0, + "content": "labelled data or the whole dataset and both are equivalent.", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + } + ], + "index": 4, + "bbox_fs": [ + 85, + 97, + 506, + 196 + ] + }, + { + "type": "index", + "bbox": [ + 87, + 201, + 506, + 223 + ], + "lines": [], + "index": 9.5, + "bbox_fs": [ + 85, + 200, + 505, + 223 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 105, + 228, + 375, + 240 + ], + "lines": [ + { + "bbox": [ + 106, + 227, + 375, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 192, + 241 + ], + "score": 1.0, + "content": "We consider a subset", + "type": "text" + }, + { + "bbox": [ + 192, + 230, + 201, + 238 + ], + "score": 0.81, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 227, + 326, + 241 + ], + "score": 1.0, + "content": "of the training set. We defined", + "type": "text" + }, + { + "bbox": [ + 326, + 233, + 332, + 238 + ], + "score": 0.72, + "content": "a", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 227, + 375, + 241 + ], + "score": 1.0, + "content": "as follow:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11, + "bbox_fs": [ + 106, + 227, + 375, + 241 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 246, + 246, + 365, + 275 + ], + "lines": [ + { + "bbox": [ + 246, + 246, + 365, + 275 + ], + "spans": [ + { + "bbox": [ + 246, + 246, + 365, + 275 + ], + "score": 0.94, + "content": "\\cdot", + "type": "interline_equation", + "image_path": "bc5ef7c68f79e22d7049387d1c982d7ee1be2a18af7e0c76e3fe95f83234993c.jpg" + } + ] + } + ], + "index": 12.5, + "virtual_lines": [ + { + "bbox": [ + 246, + 246, + 365, + 260.5 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 246, + 260.5, + 365, + 275.0 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 286, + 233, + 298 + ], + "lines": [ + { + "bbox": [ + 86, + 286, + 233, + 298 + ], + "spans": [ + { + "bbox": [ + 86, + 286, + 233, + 298 + ], + "score": 1.0, + "content": "813 The unbiased estimator is then:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14, + "bbox_fs": [ + 86, + 286, + 233, + 298 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 156, + 303, + 455, + 336 + ], + "lines": [ + { + "bbox": [ + 156, + 303, + 455, + 336 + ], + "spans": [ + { + "bbox": [ + 156, + 303, + 455, + 336 + ], + "score": 0.93, + "content": "\\hat { \\mathcal { R } } _ { D e S S L , A } ( \\theta ) = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } H ( \\theta ; x _ { i } ) - \\lambda \\sum _ { i = 1 } ^ { n } a _ { i } H ( \\theta ; x _ { i } ) .", + "type": "interline_equation", + "image_path": "0e065e3c91f8b28bf4fe2ccf8cad75ebb2ac0b46e69c9bcab70b74b425390228.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 156, + 303, + 455, + 314.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 156, + 314.0, + 455, + 325.0 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 156, + 325.0, + 455, + 336.0 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 339, + 98, + 347 + ], + "lines": [ + { + "bbox": [ + 86, + 339, + 100, + 347 + ], + "spans": [ + { + "bbox": [ + 86, + 339, + 100, + 347 + ], + "score": 1.0, + "content": "814", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18, + "bbox_fs": [ + 86, + 339, + 100, + 347 + ] + }, + { + "type": "text", + "bbox": [ + 81, + 352, + 456, + 365 + ], + "lines": [ + { + "bbox": [ + 85, + 352, + 456, + 364 + ], + "spans": [ + { + "bbox": [ + 85, + 352, + 456, + 364 + ], + "score": 1.0, + "content": "815 We compute the variance of this quantity as in the proof of Theorem 3.1 and show that:", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19, + "bbox_fs": [ + 85, + 352, + 456, + 364 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 111, + 385, + 514, + 418 + ], + "lines": [ + { + "bbox": [ + 111, + 385, + 514, + 418 + ], + "spans": [ + { + "bbox": [ + 111, + 385, + 514, + 418 + ], + "score": 0.91, + "content": "-", + "type": "interline_equation", + "image_path": "11c4c6a4a7a6aa721fba53269e053962ccbf3efc9abd28023eace955475e130a.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 111, + 385, + 514, + 396.0 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 111, + 396.0, + 514, + 407.0 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 111, + 407.0, + 514, + 418.0 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "index", + "bbox": [ + 86, + 432, + 507, + 466 + ], + "lines": [ + { + "bbox": [ + 85, + 431, + 506, + 445 + ], + "spans": [ + { + "bbox": [ + 85, + 434, + 101, + 444 + ], + "score": 1.0, + "content": "816", + "type": "text" + }, + { + "bbox": [ + 104, + 431, + 282, + 445 + ], + "score": 1.0, + "content": "Suppose that no labelled datapoints are in", + "type": "text" + }, + { + "bbox": [ + 282, + 435, + 291, + 442 + ], + "score": 0.88, + "content": "\\mathcal { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 431, + 506, + 445 + ], + "score": 1.0, + "content": ". Then, the last term of the variance is null. Hence,", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 85, + 445, + 100, + 455 + ], + "score": 1.0, + "content": "817", + "type": "text" + }, + { + "bbox": [ + 104, + 443, + 236, + 455 + ], + "score": 1.0, + "content": "having no labelled datapoints in", + "type": "text" + }, + { + "bbox": [ + 237, + 446, + 245, + 453 + ], + "score": 0.88, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "leads to a variance increase. We also remark that debiasing with", + "type": "text" + } + ], + "index": 24, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 453, + 433, + 466 + ], + "spans": [ + { + "bbox": [ + 85, + 456, + 100, + 465 + ], + "score": 1.0, + "content": "818", + "type": "text" + }, + { + "bbox": [ + 105, + 453, + 433, + 466 + ], + "score": 1.0, + "content": "the entire dataset is equivalent that debiasing with the labelled datapoints. 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x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 93, + 415, + 110 + ], + "score": 1.0, + "content": "is a proper scoring rule, then", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1, + "bbox_fs": [ + 86, + 93, + 415, + 110 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 175, + 113, + 435, + 138 + ], + "lines": [ + { + "bbox": [ + 175, + 113, + 435, + 138 + ], + "spans": [ + { + "bbox": [ + 175, + 113, + 435, + 138 + ], + "score": 0.93, + "content": "\\mathcal { S } ^ { \\prime } ( p _ { \\theta } , ( x , y , r ) ) = - ( \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda n ( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } ) H ( \\theta ; x ) )", + "type": "interline_equation", + "image_path": "da0f21b616109ebc3d9badd5a9e032a226d1e56d6d3b8140ab90842447cd7dae.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 175, + 113, + 435, + 138 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 142, + 224, + 155 + ], + "lines": [ + { + "bbox": [ + 85, + 142, + 224, + 156 + ], + "spans": [ + { + "bbox": [ + 85, + 142, + 224, + 156 + ], + "score": 1.0, + "content": "831 is also a proper scoring rule.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 85, + 142, + 224, + 156 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 165, + 353, + 178 + ], + "lines": [ + { + "bbox": [ + 106, + 164, + 353, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 164, + 353, + 178 + ], + "score": 1.0, + "content": "Proof. 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x , y )", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 498, + 509, + 533 + ], + "score": 1.0, + "content": "is also a proper scoring rule.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 144, + 511, + 388, + 525 + ], + "spans": [ + { + "bbox": [ + 144, + 511, + 388, + 525 + ], + "score": 0.79, + "content": "\\begin{array} { r } { S ^ { \\prime } ( p _ { \\theta } , ( x , y , r ) ) = - ( \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda n ( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } ) H ( \\theta ; x ) ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 15 + } + ], + "index": 14.5, + "bbox_fs": [ + 79, + 498, + 509, + 533 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 87, + 70, + 238, + 85 + ], + "lines": [ + { + "bbox": [ + 83, + 69, + 239, + 86 + ], + "spans": [ + { + "bbox": [ + 83, + 69, + 239, + 86 + ], + "score": 1.0, + "content": "837 H Proof of Theorem 3.5", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 86, + 96, + 336, + 108 + ], + "lines": [ + { + "bbox": [ + 84, + 94, + 337, + 111 + ], + "spans": [ + { + "bbox": [ + 84, + 94, + 231, + 111 + ], + "score": 1.0, + "content": "Assumption 3.3: the minimum 838", + "type": "text" + }, + { + "bbox": [ + 231, + 97, + 241, + 106 + ], + "score": 0.86, + "content": "\\theta ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 94, + 254, + 111 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 254, + 97, + 263, + 106 + ], + "score": 0.84, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 94, + 337, + 111 + ], + "score": 1.0, + "content": "is well-separated.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "interline_equation", + "bbox": [ + 253, + 114, + 358, + 135 + ], + "lines": [ + { + "bbox": [ + 253, + 114, + 358, + 135 + ], + "spans": [ + { + "bbox": [ + 253, + 114, + 358, + 135 + ], + "score": 0.93, + "content": "\\operatorname* { i n f } _ { \\theta : d ( \\theta ^ { * } , \\theta ) \\geq \\epsilon } \\mathcal { R } ( \\theta ) > \\mathcal { R } ( \\theta ^ { * } )", + "type": "interline_equation", + "image_path": "18a6465d65f27a50c3723daa5138135cca799256f6f1ac5f5301cccebec594f3.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 253, + 114, + 358, + 135 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 85, + 146, + 421, + 159 + ], + "lines": [ + { + "bbox": [ + 84, + 146, + 422, + 159 + ], + "spans": [ + { + "bbox": [ + 84, + 146, + 401, + 159 + ], + "score": 1.0, + "content": "839 Assumption 3.4: uniform weak law of large numbers holds for a function", + "type": "text" + }, + { + "bbox": [ + 401, + 147, + 408, + 157 + ], + "score": 0.84, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 146, + 422, + 159 + ], + "score": 1.0, + "content": "if:", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "interline_equation", + "bbox": [ + 213, + 164, + 397, + 199 + ], + "lines": [ + { + "bbox": [ + 213, + 164, + 397, + 199 + ], + "spans": [ + { + "bbox": [ + 213, + 164, + 397, + 199 + ], + "score": 0.93, + "content": "\\operatorname* { s u p } _ { \\theta \\in \\Theta } \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } L ( \\theta , x _ { i } , y _ { i } ) - \\mathbb { E } [ L ( \\theta , x , y ) ] \\overset { p } { } 0", + "type": "interline_equation", + "image_path": "19e4fc2f3cbb32035372765d7df95c3c99eef288946caed43dd8127fb13994f5.jpg" + } + ] + } + ], + "index": 4.5, + "virtual_lines": [ + { + "bbox": [ + 213, + 164, + 397, + 181.5 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 213, + 181.5, + 397, + 199.0 + ], + "spans": [], + "index": 5 + } + ] + }, + { + "type": "text", + "bbox": [ + 90, + 211, + 505, + 235 + ], + "lines": [ + { + "bbox": [ + 88, + 210, + 506, + 226 + ], + "spans": [ + { + "bbox": [ + 88, + 214, + 100, + 223 + ], + "score": 1.0, + "content": "840", + "type": "text" + }, + { + "bbox": [ + 103, + 210, + 322, + 226 + ], + "score": 1.0, + "content": "Theorem 3.5. Under assumption A and assumption", + "type": "text" + }, + { + "bbox": [ + 322, + 213, + 330, + 223 + ], + "score": 0.53, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 210, + 365, + 226 + ], + "score": 1.0, + "content": "for both", + "type": "text" + }, + { + "bbox": [ + 365, + 213, + 373, + 222 + ], + "score": 0.76, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 210, + 392, + 226 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 392, + 212, + 402, + 222 + ], + "score": 0.59, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 210, + 406, + 226 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 406, + 210, + 494, + 224 + ], + "score": 0.81, + "content": "\\hat { \\theta } = \\arg \\operatorname* { m i n } \\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 210, + 506, + 226 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 87, + 224, + 281, + 236 + ], + "spans": [ + { + "bbox": [ + 87, + 224, + 270, + 236 + ], + "score": 1.0, + "content": "841 asymptotically consistent with respect to", + "type": "text" + }, + { + "bbox": [ + 271, + 226, + 277, + 233 + ], + "score": 0.56, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 224, + 281, + 236 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5 + }, + { + "type": "text", + "bbox": [ + 85, + 239, + 505, + 300 + ], + "lines": [ + { + "bbox": [ + 86, + 239, + 506, + 253 + ], + "spans": [ + { + "bbox": [ + 86, + 242, + 100, + 252 + ], + "score": 1.0, + "content": "842", + "type": "text" + }, + { + "bbox": [ + 105, + 239, + 506, + 253 + ], + "score": 1.0, + "content": "This result is a direct application of Theorem 5.7 from van der Vaart (2000, Chapter 5) that states", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 251, + 503, + 266 + ], + "spans": [ + { + "bbox": [ + 86, + 254, + 100, + 264 + ], + "score": 1.0, + "content": "843", + "type": "text" + }, + { + "bbox": [ + 106, + 251, + 247, + 266 + ], + "score": 1.0, + "content": "that under assumption A and B for", + "type": "text" + }, + { + "bbox": [ + 247, + 252, + 255, + 262 + ], + "score": 0.57, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 251, + 258, + 266 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 259, + 251, + 321, + 263 + ], + "score": 0.89, + "content": "\\hat { \\theta } = \\arg \\operatorname* { m i n } \\hat { \\mathcal { R } }", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 251, + 496, + 266 + ], + "score": 1.0, + "content": "is asymptotically consistent with respect to", + "type": "text" + }, + { + "bbox": [ + 496, + 255, + 503, + 262 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + } + ], + "index": 9 + }, + { + "bbox": [ + 85, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 85, + 265, + 100, + 276 + ], + "score": 1.0, + "content": "844", + "type": "text" + }, + { + "bbox": [ + 106, + 264, + 389, + 275 + ], + "score": 1.0, + "content": "Assumption A remains unchanged as we have M-estimators of the same", + "type": "text" + }, + { + "bbox": [ + 389, + 264, + 398, + 273 + ], + "score": 0.76, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 264, + 505, + 275 + ], + "score": 1.0, + "content": ". We now aim to prove that", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 271, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 86, + 276, + 100, + 286 + ], + "score": 1.0, + "content": "845", + "type": "text" + }, + { + "bbox": [ + 103, + 271, + 225, + 291 + ], + "score": 1.0, + "content": "under assumption B for both", + "type": "text" + }, + { + "bbox": [ + 226, + 275, + 234, + 284 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 271, + 252, + 291 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 252, + 275, + 262, + 284 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 271, + 388, + 291 + ], + "score": 1.0, + "content": ", we have the assumption B on", + "type": "text" + }, + { + "bbox": [ + 388, + 274, + 505, + 288 + ], + "score": 0.89, + "content": "\\begin{array} { r l } { \\theta \\longrightarrow \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) \\overset { } { + } \\lambda ( 1 - } & { { } } \\end{array}", + "type": "inline_equation" + } + ], + "index": 11 + }, + { + "bbox": [ + 85, + 282, + 161, + 306 + ], + "spans": [ + { + "bbox": [ + 85, + 289, + 100, + 300 + ], + "score": 1.0, + "content": "846", + "type": "text" + }, + { + "bbox": [ + 107, + 286, + 154, + 302 + ], + "score": 0.88, + "content": "\\textstyle { \\frac { r n } { n _ { l } } } ) H ( \\theta ; x )", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 282, + 161, + 306 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 96, + 303, + 504, + 329 + ], + "lines": [ + { + "bbox": [ + 93, + 303, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 93, + 303, + 369, + 317 + ], + "score": 1.0, + "content": "47 Lemma H.1. If the uniform law of large number holds for both", + "type": "text" + }, + { + "bbox": [ + 369, + 305, + 378, + 314 + ], + "score": 0.75, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 303, + 397, + 317 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 397, + 305, + 407, + 314 + ], + "score": 0.75, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 303, + 478, + 317 + ], + "score": 1.0, + "content": ", then it holds for", + "type": "text" + }, + { + "bbox": [ + 478, + 304, + 505, + 315 + ], + "score": 0.84, + "content": "\\theta \\longrightarrow", + "type": "inline_equation" + } + ], + "index": 13 + }, + { + "bbox": [ + 94, + 310, + 250, + 332 + ], + "spans": [ + { + "bbox": [ + 94, + 318, + 99, + 325 + ], + "score": 1.0, + "content": "8", + "type": "text" + }, + { + "bbox": [ + 107, + 315, + 244, + 329 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda ( 1 - \\frac { r n } { n _ { l } } ) H ( \\theta ; x ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 310, + 250, + 332 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 85, + 343, + 506, + 367 + ], + "lines": [ + { + "bbox": [ + 85, + 343, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 85, + 345, + 101, + 355 + ], + "score": 1.0, + "content": "849", + "type": "text" + }, + { + "bbox": [ + 104, + 343, + 221, + 357 + ], + "score": 1.0, + "content": "Proof. Suppose assumption", + "type": "text" + }, + { + "bbox": [ + 221, + 344, + 229, + 354 + ], + "score": 0.41, + "content": "\\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 343, + 244, + 357 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 244, + 345, + 252, + 354 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 343, + 416, + 357 + ], + "score": 1.0, + "content": ", then the same result holds if we replace", + "type": "text" + }, + { + "bbox": [ + 417, + 346, + 424, + 354 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 343, + 445, + 357 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 446, + 346, + 456, + 355 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 343, + 468, + 357 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 468, + 347, + 475, + 354 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 343, + 493, + 357 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 493, + 346, + 504, + 355 + ], + "score": 0.8, + "content": "n _ { l }", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 83, + 354, + 484, + 368 + ], + "spans": [ + { + "bbox": [ + 83, + 354, + 210, + 368 + ], + "score": 1.0, + "content": "are coupled by the law of 850", + "type": "text" + }, + { + "bbox": [ + 210, + 357, + 216, + 365 + ], + "score": 0.73, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 354, + 276, + 368 + ], + "score": 1.0, + "content": ". Indeed, when", + "type": "text" + }, + { + "bbox": [ + 276, + 357, + 284, + 365 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 284, + 354, + 354, + 368 + ], + "score": 1.0, + "content": "grows to infinity,", + "type": "text" + }, + { + "bbox": [ + 355, + 356, + 365, + 366 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 354, + 484, + 368 + ], + "score": 1.0, + "content": "too and inversely. 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Under assumption A and assumption", + "type": "text" + }, + { + "bbox": [ + 322, + 213, + 330, + 223 + ], + "score": 0.53, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 210, + 365, + 226 + ], + "score": 1.0, + "content": "for both", + "type": "text" + }, + { + "bbox": [ + 365, + 213, + 373, + 222 + ], + "score": 0.76, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 210, + 392, + 226 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 392, + 212, + 402, + 222 + ], + "score": 0.59, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 210, + 406, + 226 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 406, + 210, + 494, + 224 + ], + "score": 0.81, + "content": "\\hat { \\theta } = \\arg \\operatorname* { m i n } \\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 210, + 506, + 226 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 87, + 224, + 281, + 236 + ], + "spans": [ + { + "bbox": [ + 87, + 224, + 270, + 236 + ], + "score": 1.0, + "content": "841 asymptotically consistent with respect to", + "type": "text" + }, + { + "bbox": [ + 271, + 226, + 277, + 233 + ], + "score": 0.56, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 224, + 281, + 236 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 239, + 506, + 253 + ], + "spans": [ + { + "bbox": [ + 86, + 242, + 100, + 252 + ], + "score": 1.0, + "content": "842", + "type": "text" + }, + { + "bbox": [ + 105, + 239, + 506, + 253 + ], + "score": 1.0, + "content": "This result is a direct application of Theorem 5.7 from van der Vaart (2000, Chapter 5) that states", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 251, + 503, + 266 + ], + "spans": [ + { + "bbox": [ + 86, + 254, + 100, + 264 + ], + "score": 1.0, + "content": "843", + "type": "text" + }, + { + "bbox": [ + 106, + 251, + 247, + 266 + ], + "score": 1.0, + "content": "that under assumption A and B for", + "type": "text" + }, + { + "bbox": [ + 247, + 252, + 255, + 262 + ], + "score": 0.57, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 251, + 258, + 266 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 259, + 251, + 321, + 263 + ], + "score": 0.89, + "content": "\\hat { \\theta } = \\arg \\operatorname* { m i n } \\hat { \\mathcal { R } }", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 251, + 496, + 266 + ], + "score": 1.0, + "content": "is asymptotically consistent with respect to", + "type": "text" + }, + { + "bbox": [ + 496, + 255, + 503, + 262 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 85, + 265, + 100, + 276 + ], + "score": 1.0, + "content": "844", + "type": "text" + }, + { + "bbox": [ + 106, + 264, + 389, + 275 + ], + "score": 1.0, + "content": "Assumption A remains unchanged as we have M-estimators of the same", + "type": "text" + }, + { + "bbox": [ + 389, + 264, + 398, + 273 + ], + "score": 0.76, + "content": "\\mathcal { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 264, + 505, + 275 + ], + "score": 1.0, + "content": ". We now aim to prove that", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 271, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 86, + 276, + 100, + 286 + ], + "score": 1.0, + "content": "845", + "type": "text" + }, + { + "bbox": [ + 103, + 271, + 225, + 291 + ], + "score": 1.0, + "content": "under assumption B for both", + "type": "text" + }, + { + "bbox": [ + 226, + 275, + 234, + 284 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 271, + 252, + 291 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 252, + 275, + 262, + 284 + ], + "score": 0.82, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 271, + 388, + 291 + ], + "score": 1.0, + "content": ", we have the assumption B on", + "type": "text" + }, + { + "bbox": [ + 388, + 274, + 505, + 288 + ], + "score": 0.89, + "content": "\\begin{array} { r l } { \\theta \\longrightarrow \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) \\overset { } { + } \\lambda ( 1 - } & { { } } \\end{array}", + "type": "inline_equation" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 282, + 161, + 306 + ], + "spans": [ + { + "bbox": [ + 85, + 289, + 100, + 300 + ], + "score": 1.0, + "content": "846", + "type": "text" + }, + { + "bbox": [ + 107, + 286, + 154, + 302 + ], + "score": 0.88, + "content": "\\textstyle { \\frac { r n } { n _ { l } } } ) H ( \\theta ; x )", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 282, + 161, + 306 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 93, + 303, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 93, + 303, + 369, + 317 + ], + "score": 1.0, + "content": "47 Lemma H.1. If the uniform law of large number holds for both", + "type": "text" + }, + { + "bbox": [ + 369, + 305, + 378, + 314 + ], + "score": 0.75, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 303, + 397, + 317 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 397, + 305, + 407, + 314 + ], + "score": 0.75, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 303, + 478, + 317 + ], + "score": 1.0, + "content": ", then it holds for", + "type": "text" + }, + { + "bbox": [ + 478, + 304, + 505, + 315 + ], + "score": 0.84, + "content": "\\theta \\longrightarrow", + "type": "inline_equation" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 94, + 310, + 250, + 332 + ], + "spans": [ + { + "bbox": [ + 94, + 318, + 99, + 325 + ], + "score": 1.0, + "content": "8", + "type": "text" + }, + { + "bbox": [ + 107, + 315, + 244, + 329 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda ( 1 - \\frac { r n } { n _ { l } } ) H ( \\theta ; x ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 310, + 250, + 332 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + } + ], + "index": 6.5, + "bbox_fs": [ + 87, + 210, + 506, + 236 + ] + }, + { + "type": "index", + "bbox": [ + 85, + 239, + 505, + 300 + ], + "lines": [], + "index": 10, + "bbox_fs": [ + 85, + 239, + 506, + 306 + ], + "lines_deleted": true + }, + { + "type": "index", + "bbox": [ + 96, + 303, + 504, + 329 + ], + "lines": [], + "index": 13.5, + "bbox_fs": [ + 93, + 303, + 505, + 332 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 85, + 343, + 506, + 367 + ], + "lines": [ + { + "bbox": [ + 85, + 343, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 85, + 345, + 101, + 355 + ], + "score": 1.0, + "content": "849", + "type": "text" + }, + { + "bbox": [ + 104, + 343, + 221, + 357 + ], + "score": 1.0, + "content": "Proof. Suppose assumption", + "type": "text" + }, + { + "bbox": [ + 221, + 344, + 229, + 354 + ], + "score": 0.41, + "content": "\\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 229, + 343, + 244, + 357 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 244, + 345, + 252, + 354 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 343, + 416, + 357 + ], + "score": 1.0, + "content": ", then the same result holds if we replace", + "type": "text" + }, + { + "bbox": [ + 417, + 346, + 424, + 354 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 343, + 445, + 357 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 446, + 346, + 456, + 355 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 343, + 468, + 357 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 468, + 347, + 475, + 354 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 343, + 493, + 357 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 493, + 346, + 504, + 355 + ], + "score": 0.8, + "content": "n _ { l }", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 83, + 354, + 484, + 368 + ], + "spans": [ + { + "bbox": [ + 83, + 354, + 210, + 368 + ], + "score": 1.0, + "content": "are coupled by the law of 850", + "type": "text" + }, + { + "bbox": [ + 210, + 357, + 216, + 365 + ], + "score": 0.73, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 354, + 276, + 368 + ], + "score": 1.0, + "content": ". Indeed, when", + "type": "text" + }, + { + "bbox": [ + 276, + 357, + 284, + 365 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 284, + 354, + 354, + 368 + ], + "score": 1.0, + "content": "grows to infinity,", + "type": "text" + }, + { + "bbox": [ + 355, + 356, + 365, + 366 + ], + "score": 0.84, + "content": "n _ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 354, + 484, + 368 + ], + "score": 1.0, + "content": "too and inversely. Therefore,", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 83, + 343, + 504, + 368 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 211, + 372, + 399, + 407 + ], + "lines": [ + { + "bbox": [ + 211, + 372, + 399, + 407 + ], + "spans": [ + { + "bbox": [ + 211, + 372, + 399, + 407 + ], + "score": 0.93, + "content": "\\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x _ { i } , y _ { i } ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| \\xrightarrow [ n ] { p } 0", + "type": "interline_equation", + "image_path": "07d511c59fe77f8ac39964e6a4c588b2831255f57a389efda08c5580e8f0bf82.jpg" + } + ] + } + ], + "index": 17.5, + "virtual_lines": [ + { + "bbox": [ + 211, + 372, + 399, + 389.5 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 211, + 389.5, + 399, + 407.0 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": "index", + "bbox": [ + 83, + 417, + 507, + 441 + ], + "lines": [ + { + "bbox": [ + 85, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 85, + 419, + 101, + 429 + ], + "score": 1.0, + "content": "851", + "type": "text" + }, + { + "bbox": [ + 104, + 417, + 245, + 430 + ], + "score": 1.0, + "content": "Now, suppose we have assumption", + "type": "text" + }, + { + "bbox": [ + 245, + 418, + 253, + 428 + ], + "score": 0.63, + "content": "\\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 417, + 268, + 430 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 268, + 418, + 279, + 428 + ], + "score": 0.84, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 417, + 456, + 430 + ], + "score": 1.0, + "content": ", then we can make the same remark than for", + "type": "text" + }, + { + "bbox": [ + 456, + 419, + 464, + 428 + ], + "score": 0.81, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 417, + 505, + 430 + ], + "score": 1.0, + "content": ". Now, we", + "type": "text" + } + ], + "index": 19, + "is_list_start_line": true + }, + { + "bbox": [ + 84, + 429, + 181, + 440 + ], + "spans": [ + { + "bbox": [ + 84, + 429, + 181, + 440 + ], + "score": 1.0, + "content": "852 have to show that:", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true + } + ], + "index": 19.5, + "bbox_fs": [ + 84, + 417, + 505, + 440 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 149, + 460, + 462, + 495 + ], + "lines": [ + { + "bbox": [ + 149, + 460, + 462, + 495 + ], + "spans": [ + { + "bbox": [ + 149, + 460, + 462, + 495 + ], + "score": 0.92, + "content": "\\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda n \\left( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| \\xrightarrow [ n ] { p } 0", + "type": "interline_equation", + "image_path": "82feb407a2a8a58384d15d87e9a54dfc80585e9cb8373b4b42ae27b5593a46d2.jpg" + } + ] + } + ], + "index": 22, + "virtual_lines": [ + { + "bbox": [ + 149, + 460, + 462, + 471.6666666666667 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 149, + 471.6666666666667, + 462, + 483.33333333333337 + ], + "spans": [], + "index": 22 + }, + { + "bbox": [ + 149, + 483.33333333333337, + 462, + 495.00000000000006 + ], + "spans": [], + "index": 23 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 500, + 327, + 513 + ], + "lines": [ + { + "bbox": [ + 84, + 499, + 329, + 515 + ], + "spans": [ + { + "bbox": [ + 84, + 499, + 329, + 515 + ], + "score": 1.0, + "content": "853 We first split the absolute value and the sup operator as", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24, + "bbox_fs": [ + 84, + 499, + 329, + 515 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 123, + 532, + 487, + 657 + ], + "lines": [ + { + "bbox": [ + 123, + 532, + 487, + 657 + ], + "spans": [ + { + "bbox": [ + 123, + 532, + 487, + 657 + ], + "score": 0.94, + "content": "\\begin{array} { r l } & { \\underset { \\theta \\in \\Theta } { \\operatorname* { s u p } } \\left| \\frac { 1 } { n } \\displaystyle \\sum _ { i = 1 } ^ { n } \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda n \\left( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| } \\\\ & { \\quad \\le \\underset { \\theta \\in \\Theta } { \\operatorname* { s u p } } \\left| \\frac { 1 } { n _ { l } } \\displaystyle \\sum _ { i = 1 } ^ { n } \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| + \\left| \\frac { 1 } { n } \\displaystyle \\sum _ { i = 1 } ^ { n } \\lambda n \\left( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) \\right| } \\\\ & { \\quad \\le \\underset { \\theta \\in \\Theta } { \\operatorname* { s u p } } \\left| \\frac { 1 } { n _ { l } } \\displaystyle \\sum _ { i = 1 } ^ { n _ { l } } L ( \\theta ; x , y ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| + \\underset { \\theta \\in \\Theta } { \\operatorname* { s u p } } \\left| \\frac { 1 } { n } \\displaystyle \\sum _ { i = 1 } ^ { n } \\lambda n \\left( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) \\right| . } \\end{array}", + "type": "interline_equation", + "image_path": "ebee6d6d0b10804e3a881748f5ec28603d781e43f1d1c07816dcfd4881cbcb0d.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 123, + 532, + 487, + 573.6666666666666 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 123, + 573.6666666666666, + 487, + 615.3333333333333 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 123, + 615.3333333333333, + 487, + 656.9999999999999 + ], + "spans": [], + "index": 27 + } + ] + }, + { + "type": "index", + "bbox": [ + 83, + 663, + 504, + 686 + ], + "lines": [ + { + "bbox": [ + 86, + 661, + 506, + 677 + ], + "spans": [ + { + "bbox": [ + 86, + 664, + 101, + 674 + ], + "score": 1.0, + "content": "854", + "type": "text" + }, + { + "bbox": [ + 104, + 661, + 506, + 677 + ], + "score": 1.0, + "content": "So we now have to prove that the second term is also converging to 0 in probability. Again by splitting", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 673, + 266, + 686 + ], + "spans": [ + { + "bbox": [ + 86, + 673, + 266, + 686 + ], + "score": 1.0, + "content": "855 the absolute value and the sup, we have", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true + } + ], + "index": 28.5, + "bbox_fs": [ + 86, + 661, + 506, + 686 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 115, + 691, + 494, + 726 + ], + "lines": [ + { + "bbox": [ + 115, + 691, + 494, + 726 + ], + "spans": [ + { + "bbox": [ + 115, + 691, + 494, + 726 + ], + "score": 0.94, + "content": "\\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\lambda n \\left( \\frac { 1 - r } { n _ { u } } - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) \\right| = \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n } \\sum _ { i = 1 } ^ { n } \\frac { ( 1 - r ) n } { n _ { u } } H ( \\theta ; x ) - \\frac { \\lambda } { n } \\sum _ { i = 1 } ^ { n } \\frac { r n } { n _ { l } } H ( \\theta ; x ) \\right|", + "type": "interline_equation", + "image_path": "816f9a3ba296b2f70dc10d7358d299bd2adf547696bfef37105e880a20f9b6d2.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 115, + 691, + 494, + 702.6666666666666 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 115, + 702.6666666666666, + 494, + 714.3333333333333 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 115, + 714.3333333333333, + 494, + 725.9999999999999 + ], + "spans": [], + "index": 32 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "interline_equation", + "bbox": [ + 112, + 89, + 498, + 251 + ], + "lines": [ + { + "bbox": [ + 112, + 89, + 498, + 251 + ], + "spans": [ + { + "bbox": [ + 112, + 89, + 498, + 251 + ], + "score": 0.93, + "content": "\\begin{array} { r l } & { \\displaystyle \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n } ( 1 - r ) H ( \\theta ; x ) - \\frac { \\lambda } { n _ { i } } \\sum _ { i = 1 } ^ { n } r H ( \\theta ; x ) \\right| } \\\\ & { \\displaystyle = \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n } ( 1 - r ) H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] - \\left( \\frac { \\lambda } { n _ { i } } \\sum _ { i = 1 } ^ { n } r H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right) \\right| } \\\\ & { \\displaystyle = \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = n + 1 } ^ { n + { n } _ { s } } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] - \\left( \\frac { \\lambda } { n _ { i } } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right) \\right| } \\\\ & { \\displaystyle \\leq \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = n - l + 1 } ^ { { n + { n } _ { s } } } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right| + \\displaystyle \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\left( \\frac { \\lambda } { n _ { t } } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right) \\right| . } \\end{array}", + "type": "interline_equation", + "image_path": "403524e5f898bb91036fb4de487b8ac4e831fb18ee4fbbdb009a52a1d2ac98d6.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 112, + 89, + 498, + 143.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 112, + 143.0, + 498, + 197.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 112, + 197.0, + 498, + 251.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 270, + 130, + 281 + ], + "lines": [ + { + "bbox": [ + 84, + 268, + 132, + 284 + ], + "spans": [ + { + "bbox": [ + 84, + 268, + 132, + 284 + ], + "score": 1.0, + "content": "857 Thus,", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "interline_equation", + "bbox": [ + 145, + 286, + 464, + 320 + ], + "lines": [ + { + "bbox": [ + 145, + 286, + 464, + 320 + ], + "spans": [ + { + "bbox": [ + 145, + 286, + 464, + 320 + ], + "score": 0.92, + "content": "\\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda n \\left( \\frac { 1 - r } { n _ { u } } 1 - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| \\xrightarrow [ n ] { p } 0", + "type": "interline_equation", + "image_path": "1f881cc1a586143a3ef0ba7e126a5eb31a3ccdd90788fb7c4d401e3b08017bd7.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 145, + 286, + 464, + 297.3333333333333 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 145, + 297.3333333333333, + 464, + 308.66666666666663 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 145, + 308.66666666666663, + 464, + 319.99999999999994 + ], + "spans": [], + "index": 6 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 324, + 507, + 350 + ], + "lines": [ + { + "bbox": [ + 84, + 324, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 84, + 324, + 505, + 337 + ], + "score": 1.0, + "content": "858 And we now just have to apply the results of van der Vaart (2000, Theorem 5.7) to have the asymptotic", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 335, + 253, + 352 + ], + "spans": [ + { + "bbox": [ + 83, + 335, + 160, + 352 + ], + "score": 1.0, + "content": "consistent of 859", + "type": "text" + }, + { + "bbox": [ + 160, + 335, + 248, + 349 + ], + "score": 0.91, + "content": "\\hat { \\theta } = \\arg \\operatorname* { m i n } \\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 335, + 253, + 352 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 86, + 356, + 99, + 364 + ], + "lines": [ + { + "bbox": [ + 86, + 356, + 100, + 365 + ], + "spans": [ + { + "bbox": [ + 86, + 356, + 100, + 365 + ], + "score": 1.0, + "content": "860", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 86, + 371, + 506, + 417 + ], + "lines": [ + { + "bbox": [ + 86, + 371, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 86, + 373, + 99, + 383 + ], + "score": 1.0, + "content": "861", + "type": "text" + }, + { + "bbox": [ + 105, + 371, + 320, + 384 + ], + "score": 1.0, + "content": "Remark H.2. A sufficient condition on the function", + "type": "text" + }, + { + "bbox": [ + 320, + 372, + 330, + 381 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 371, + 506, + 384 + ], + "score": 1.0, + "content": "to verify assumption B, the uniform weak", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 85, + 380, + 507, + 396 + ], + "spans": [ + { + "bbox": [ + 85, + 383, + 100, + 394 + ], + "score": 1.0, + "content": "862", + "type": "text" + }, + { + "bbox": [ + 105, + 380, + 507, + 396 + ], + "score": 1.0, + "content": "law of large numbers, is to be bounded (Newey & McFadden, 1994, Lemma 2.4). For instance,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 85, + 392, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 85, + 394, + 100, + 405 + ], + "score": 1.0, + "content": "863", + "type": "text" + }, + { + "bbox": [ + 105, + 392, + 154, + 407 + ], + "score": 1.0, + "content": "the entropy", + "type": "text" + }, + { + "bbox": [ + 154, + 393, + 288, + 407 + ], + "score": 0.92, + "content": "\\begin{array} { r } { H = - \\sum _ { y } p _ { \\theta } ( y | x ) \\log ( p _ { \\theta } ( y | x ) ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 392, + 506, + 407 + ], + "score": 1.0, + "content": "is bounded and therefore, the entropy minimisation is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 86, + 406, + 213, + 419 + ], + "spans": [ + { + "bbox": [ + 86, + 408, + 100, + 417 + ], + "score": 1.0, + "content": "864", + "type": "text" + }, + { + "bbox": [ + 105, + 406, + 213, + 419 + ], + "score": 1.0, + "content": "asymptotically consistent.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + } + ], + "page_idx": 27, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 495, + 354, + 504, + 364 + ], + "lines": [ + { + "bbox": [ + 496, + 356, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 496, + 356, + 504, + 364 + ], + "score": 0.999, + "content": "□", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 87, + 73, + 183, + 84 + ], + "lines": [ + { + "bbox": [ + 84, + 72, + 185, + 86 + ], + "spans": [ + { + "bbox": [ + 84, + 72, + 185, + 86 + ], + "score": 1.0, + "content": "856 Then we have that,", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 313, + 753 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 313, + 753 + ], + "score": 1.0, + "content": "28", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "interline_equation", + "bbox": [ + 112, + 89, + 498, + 251 + ], + "lines": [ + { + "bbox": [ + 112, + 89, + 498, + 251 + ], + "spans": [ + { + "bbox": [ + 112, + 89, + 498, + 251 + ], + "score": 0.93, + "content": "\\begin{array} { r l } & { \\displaystyle \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n } ( 1 - r ) H ( \\theta ; x ) - \\frac { \\lambda } { n _ { i } } \\sum _ { i = 1 } ^ { n } r H ( \\theta ; x ) \\right| } \\\\ & { \\displaystyle = \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n } ( 1 - r ) H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] - \\left( \\frac { \\lambda } { n _ { i } } \\sum _ { i = 1 } ^ { n } r H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right) \\right| } \\\\ & { \\displaystyle = \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = n + 1 } ^ { n + { n } _ { s } } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] - \\left( \\frac { \\lambda } { n _ { i } } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right) \\right| } \\\\ & { \\displaystyle \\leq \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { \\lambda } { n _ { u } } \\sum _ { i = n - l + 1 } ^ { { n + { n } _ { s } } } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right| + \\displaystyle \\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\left( \\frac { \\lambda } { n _ { t } } \\sum _ { i = 1 } ^ { n } H ( \\theta ; x ) - \\mathbb { E } [ H ( \\theta ; x , y ) ] \\right) \\right| . } \\end{array}", + "type": "interline_equation", + "image_path": "403524e5f898bb91036fb4de487b8ac4e831fb18ee4fbbdb009a52a1d2ac98d6.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 112, + 89, + 498, + 143.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 112, + 143.0, + 498, + 197.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 112, + 197.0, + 498, + 251.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 270, + 130, + 281 + ], + "lines": [ + { + "bbox": [ + 84, + 268, + 132, + 284 + ], + "spans": [ + { + "bbox": [ + 84, + 268, + 132, + 284 + ], + "score": 1.0, + "content": "857 Thus,", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 84, + 268, + 132, + 284 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 145, + 286, + 464, + 320 + ], + "lines": [ + { + "bbox": [ + 145, + 286, + 464, + 320 + ], + "spans": [ + { + "bbox": [ + 145, + 286, + 464, + 320 + ], + "score": 0.92, + "content": "\\operatorname* { s u p } _ { \\theta \\in \\Theta } \\left| \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\frac { r n } { n _ { l } } L ( \\theta ; x , y ) + \\lambda n \\left( \\frac { 1 - r } { n _ { u } } 1 - \\frac { r } { n _ { l } } \\right) H ( \\theta ; x ) - \\mathbb { E } [ L ( \\theta ; x , y ) ] \\right| \\xrightarrow [ n ] { p } 0", + "type": "interline_equation", + "image_path": "1f881cc1a586143a3ef0ba7e126a5eb31a3ccdd90788fb7c4d401e3b08017bd7.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 145, + 286, + 464, + 297.3333333333333 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 145, + 297.3333333333333, + 464, + 308.66666666666663 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 145, + 308.66666666666663, + 464, + 319.99999999999994 + ], + "spans": [], + "index": 6 + } + ] + }, + { + "type": "text", + "bbox": [ + 86, + 324, + 507, + 350 + ], + "lines": [ + { + "bbox": [ + 84, + 324, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 84, + 324, + 505, + 337 + ], + "score": 1.0, + "content": "858 And we now just have to apply the results of van der Vaart (2000, Theorem 5.7) to have the asymptotic", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 83, + 335, + 253, + 352 + ], + "spans": [ + { + "bbox": [ + 83, + 335, + 160, + 352 + ], + "score": 1.0, + "content": "consistent of 859", + "type": "text" + }, + { + "bbox": [ + 160, + 335, + 248, + 349 + ], + "score": 0.91, + "content": "\\hat { \\theta } = \\arg \\operatorname* { m i n } \\hat { \\mathcal { R } } _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 335, + 253, + 352 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5, + "bbox_fs": [ + 83, + 324, + 505, + 352 + ] + }, + { + "type": "text", + "bbox": [ + 86, + 356, + 99, + 364 + ], + "lines": [ + { + "bbox": [ + 86, + 356, + 100, + 365 + ], + "spans": [ + { + "bbox": [ + 86, + 356, + 100, + 365 + ], + "score": 1.0, + "content": "860", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9, + "bbox_fs": [ + 86, + 356, + 100, + 365 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 371, + 506, + 417 + ], + "lines": [ + { + "bbox": [ + 86, + 371, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 86, + 373, + 99, + 383 + ], + "score": 1.0, + "content": "861", + "type": "text" + }, + { + "bbox": [ + 105, + 371, + 320, + 384 + ], + "score": 1.0, + "content": "Remark H.2. A sufficient condition on the function", + "type": "text" + }, + { + "bbox": [ + 320, + 372, + 330, + 381 + ], + "score": 0.83, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 371, + 506, + 384 + ], + "score": 1.0, + "content": "to verify assumption B, the uniform weak", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 380, + 507, + 396 + ], + "spans": [ + { + "bbox": [ + 85, + 383, + 100, + 394 + ], + "score": 1.0, + "content": "862", + "type": "text" + }, + { + "bbox": [ + 105, + 380, + 507, + 396 + ], + "score": 1.0, + "content": "law of large numbers, is to be bounded (Newey & McFadden, 1994, Lemma 2.4). For instance,", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 392, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 85, + 394, + 100, + 405 + ], + "score": 1.0, + "content": "863", + "type": "text" + }, + { + "bbox": [ + 105, + 392, + 154, + 407 + ], + "score": 1.0, + "content": "the entropy", + "type": "text" + }, + { + "bbox": [ + 154, + 393, + 288, + 407 + ], + "score": 0.92, + "content": "\\begin{array} { r } { H = - \\sum _ { y } p _ { \\theta } ( y | x ) \\log ( p _ { \\theta } ( y | x ) ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 392, + 506, + 407 + ], + "score": 1.0, + "content": "is bounded and therefore, the entropy minimisation is", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 406, + 213, + 419 + ], + "spans": [ + { + "bbox": [ + 86, + 408, + 100, + 417 + ], + "score": 1.0, + "content": "864", + "type": "text" + }, + { + "bbox": [ + 105, + 406, + 213, + 419 + ], + "score": 1.0, + "content": "asymptotically consistent.", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + } + ], + "index": 11.5, + "bbox_fs": [ + 85, + 371, + 507, + 419 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 86, + 71, + 288, + 85 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 289, + 85 + ], + "spans": [ + { + "bbox": [ + 85, + 75, + 100, + 84 + ], + "score": 1.0, + "content": "865", + "type": "text" + }, + { + "bbox": [ + 103, + 70, + 289, + 85 + ], + "score": 1.0, + "content": "I Asymptotic normality of DeSSL", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 85, + 98, + 506, + 161 + ], + "lines": [ + { + "bbox": [ + 86, + 98, + 505, + 111 + ], + "spans": [ + { + "bbox": [ + 86, + 100, + 99, + 110 + ], + "score": 1.0, + "content": "866", + "type": "text" + }, + { + "bbox": [ + 105, + 98, + 505, + 111 + ], + "score": 1.0, + "content": "In the following, we study a modified version of the objective to simplify the proof. Let us consider", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 86, + 111, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 86, + 115, + 99, + 124 + ], + "score": 1.0, + "content": "867", + "type": "text" + }, + { + "bbox": [ + 105, + 111, + 232, + 126 + ], + "score": 1.0, + "content": "the following DeSSL objective", + "type": "text" + }, + { + "bbox": [ + 233, + 111, + 446, + 129 + ], + "score": 0.93, + "content": "-", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 111, + 505, + 126 + ], + "score": 1.0, + "content": "which has the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 126, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 86, + 129, + 99, + 139 + ], + "score": 1.0, + "content": "868", + "type": "text" + }, + { + "bbox": [ + 104, + 126, + 506, + 141 + ], + "score": 1.0, + "content": "same properties than the original one (unbiasedness, variance reduction property, consistency and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 138, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 86, + 140, + 99, + 150 + ], + "score": 1.0, + "content": "869", + "type": "text" + }, + { + "bbox": [ + 106, + 138, + 357, + 151 + ], + "score": 1.0, + "content": "benefit from generalisation error bounds). 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Suppose", + "type": "text" + }, + { + "bbox": [ + 204, + 197, + 211, + 204 + ], + "score": 0.84, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 193, + 231, + 207 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 231, + 197, + 240, + 204 + ], + "score": 0.87, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 193, + 340, + 207 + ], + "score": 1.0, + "content": "are smooth functions in", + "type": "text" + }, + { + "bbox": [ + 340, + 196, + 377, + 207 + ], + "score": 0.93, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 378, + 193, + 416, + 207 + ], + "score": 1.0, + "content": ". 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We define", + "type": "text" + }, + { + "bbox": [ + 182, + 530, + 402, + 549 + ], + "score": 0.92, + "content": "\\begin{array} { r } { L ^ { \\prime } ( \\theta ; x , y , r ) = \\frac { r } { \\pi } L ( \\theta ; x , y ) + \\lambda \\left( \\frac { 1 - r } { 1 - \\pi } - \\frac { r } { \\pi } \\right) H ( \\theta ; x ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 530, + 506, + 546 + ], + "score": 1.0, + "content": "The assumptions of the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 86, + 546, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 86, + 549, + 100, + 558 + ], + "score": 1.0, + "content": "882", + "type": "text" + }, + { + "bbox": [ + 105, + 546, + 506, + 560 + ], + "score": 1.0, + "content": "theorem are sufficient assumptions to apply Theorem 5.23 of Van der Vaart 1998 to the couple", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 85, + 558, + 462, + 574 + ], + "spans": [ + { + "bbox": [ + 85, + 561, + 100, + 571 + ], + "score": 1.0, + "content": "883", + "type": "text" + }, + { + "bbox": [ + 107, + 559, + 160, + 572 + ], + "score": 0.91, + "content": "( \\hat { \\theta } _ { D e S S L } , L ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 558, + 424, + 574 + ], + "score": 1.0, + "content": ". 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On the sign of", + "type": "text" + }, + { + "bbox": [ + 223, + 480, + 232, + 487 + ], + "score": 0.86, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 476, + 447, + 490 + ], + "score": 1.0, + "content": "It is easy to show that a sufficient condition to have", + "type": "text" + }, + { + "bbox": [ + 447, + 480, + 483, + 490 + ], + "score": 0.91, + "content": "\\lambda _ { o p t } > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 476, + 506, + 490 + ], + "score": 1.0, + "content": "is to", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + }, + { + "bbox": [ + 85, + 487, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 85, + 490, + 101, + 500 + ], + "score": 1.0, + "content": "894", + "type": "text" + }, + { + "bbox": [ + 104, + 487, + 128, + 500 + ], + "score": 1.0, + "content": "have", + "type": "text" + }, + { + "bbox": [ + 128, + 490, + 146, + 500 + ], + "score": 0.88, + "content": "K _ { \\theta ^ { * } }", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 487, + 317, + 500 + ], + "score": 1.0, + "content": "positive semi-definite. 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Why minimising the trace of", + "type": "text" + }, + { + "bbox": [ + 284, + 515, + 322, + 525 + ], + "score": 0.85, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 511, + 423, + 526 + ], + "score": 1.0, + "content": "Minimising the trace of", + "type": "text" + }, + { + "bbox": [ + 424, + 515, + 458, + 525 + ], + "score": 0.89, + "content": "\\Sigma _ { D e S S L }", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 511, + 506, + 526 + ], + "score": 1.0, + "content": "leads to an", + "type": "text" + } + ], + "index": 19, + "is_list_start_line": true + }, + { + "bbox": [ + 86, + 523, + 368, + 536 + ], + "spans": [ + { + "bbox": [ + 86, + 526, + 99, + 535 + ], + "score": 1.0, + "content": "897", + "type": "text" + }, + { + "bbox": [ + 105, + 523, + 368, + 536 + ], + "score": 1.0, + "content": "estimator with a smaller asymptotic MSE, see Chen et al. (2020).", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true + } + ], + "index": 17, + "bbox_fs": [ + 85, + 476, + 506, + 514 + ] + }, + { + "type": "index", + "bbox": [ + 88, + 513, + 505, + 536 + ], + "lines": [], + "index": 19.5, + "bbox_fs": [ + 86, + 511, + 506, + 536 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 94, + 537, + 504, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 536, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 505, + 548 + ], + "score": 1.0, + "content": "Remark I.4. Fully supervised setting. We also remark that our theorem matches the theorem for the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 547, + 502, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 414, + 560 + ], + "score": 1.0, + "content": "supervised setting. Indeed, observing all the labelled corresponds to the case", + "type": "text" + }, + { + "bbox": [ + 414, + 549, + 439, + 558 + ], + "score": 0.88, + "content": "\\pi = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 440, + 547, + 502, + 560 + ], + "score": 1.0, + "content": "and we obtain:", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5, + "bbox_fs": [ + 106, + 536, + 505, + 560 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 236, + 565, + 375, + 578 + ], + "lines": [ + { + "bbox": [ + 236, + 565, + 375, + 578 + ], + "spans": [ + { + "bbox": [ + 236, + 565, + 375, + 578 + ], + "score": 0.9, + "content": "\\Sigma _ { D e S S L } = \\Sigma _ { C C } = \\Sigma _ { \\mathrm { F u l l y s u p e r v i s e d } } .", + "type": "interline_equation", + "image_path": "863b338804d183b2724e617e59666241e6f4a28c040f59a1210a43d6710b8f48.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 236, + 565, + 375, + 578 + ], + "spans": [], + "index": 23 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 87, + 70, + 235, + 85 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 236, + 86 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 236, + 86 + ], + "score": 1.0, + "content": "898 J Proof of Theorem 3.6", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 102, + 95, + 504, + 118 + ], + "lines": [ + { + "bbox": [ + 105, + 94, + 505, + 109 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 109 + ], + "score": 1.0, + "content": "Our proof will be based on the following result from Shalev-Shwartz & Ben-David (2014, Theorem", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 134, + 120 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 134, + 120 + ], + "score": 1.0, + "content": "26.5).", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 94, + 122, + 505, + 145 + ], + "lines": [ + { + "bbox": [ + 91, + 120, + 506, + 135 + ], + "spans": [ + { + "bbox": [ + 91, + 120, + 183, + 135 + ], + "score": 1.0, + "content": "01 Theorem J.1. Let", + "type": "text" + }, + { + "bbox": [ + 184, + 122, + 193, + 132 + ], + "score": 0.63, + "content": "\\mathcal { H }", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 120, + 289, + 135 + ], + "score": 1.0, + "content": "be a set of parameters,", + "type": "text" + }, + { + "bbox": [ + 290, + 122, + 317, + 132 + ], + "score": 0.88, + "content": "z \\sim \\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 120, + 466, + 135 + ], + "score": 1.0, + "content": "a random variable living in a space", + "type": "text" + }, + { + "bbox": [ + 466, + 124, + 474, + 131 + ], + "score": 0.81, + "content": "\\mathcal { Z }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 120, + 479, + 135 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 479, + 124, + 502, + 132 + ], + "score": 0.78, + "content": "c > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 120, + 506, + 135 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 131, + 262, + 145 + ], + "spans": [ + { + "bbox": [ + 91, + 131, + 124, + 145 + ], + "score": 1.0, + "content": "02 and", + "type": "text" + }, + { + "bbox": [ + 124, + 133, + 214, + 145 + ], + "score": 0.91, + "content": "\\ell : \\mathcal { H } \\times \\mathcal { Z } \\longrightarrow [ - c , c ]", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 131, + 262, + 145 + ], + "score": 1.0, + "content": ". We denote", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + }, + { + "type": "interline_equation", + "bbox": [ + 198, + 149, + 412, + 182 + ], + "lines": [ + { + "bbox": [ + 198, + 149, + 412, + 182 + ], + "spans": [ + { + "bbox": [ + 198, + 149, + 412, + 182 + ], + "score": 0.93, + "content": "L _ { \\mathcal { D } } ( h ) = \\mathbb { E } _ { z } [ \\ell ( h , z ) ] , a n d L _ { \\mathcal { S } } ( h ) = \\frac { 1 } { m } \\sum _ { i = 1 } ^ { m } \\ell ( h , z _ { i } ) ,", + "type": "interline_equation", + "image_path": "94c85f61dccd272772e0525c60c05b3921fa899aadb91ace19520cffc6d37d07.jpg" + } + ] + } + ], + "index": 5.5, + "virtual_lines": [ + { + "bbox": [ + 198, + 149, + 412, + 165.5 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 198, + 165.5, + 412, + 182.0 + ], + "spans": [], + "index": 6 + } + ] + }, + { + "type": "text", + "bbox": [ + 87, + 186, + 498, + 199 + ], + "lines": [ + { + "bbox": [ + 84, + 186, + 501, + 200 + ], + "spans": [ + { + "bbox": [ + 84, + 186, + 133, + 200 + ], + "score": 1.0, + "content": "903 where", + "type": "text" + }, + { + "bbox": [ + 133, + 189, + 172, + 199 + ], + "score": 0.9, + "content": "z _ { 1 } , . . . , z _ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 186, + 266, + 200 + ], + "score": 1.0, + "content": "are i.i.d. samples from", + "type": "text" + }, + { + "bbox": [ + 266, + 187, + 275, + 197 + ], + "score": 0.75, + "content": "\\mathcal { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 186, + 312, + 200 + ], + "score": 1.0, + "content": ". 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Rademacher variables independent from", + "type": "text" + }, + { + "bbox": [ + 375, + 244, + 414, + 253 + ], + "score": 0.88, + "content": "z _ { 1 } , . . . , z _ { m }", + "type": "inline_equation" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 86, + 262, + 331, + 275 + ], + "lines": [ + { + "bbox": [ + 85, + 262, + 331, + 275 + ], + "spans": [ + { + "bbox": [ + 85, + 262, + 331, + 275 + ], + "score": 1.0, + "content": "905 We can now restate and prove our generalisation bound.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 86, + 284, + 506, + 319 + ], + "lines": [ + { + "bbox": [ + 86, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 86, + 287, + 100, + 297 + ], + "score": 1.0, + "content": "906", + "type": "text" + }, + { + "bbox": [ + 105, + 284, + 261, + 298 + ], + "score": 1.0, + "content": "Theorem 3.6. We assume that both", + "type": "text" + }, + { + "bbox": [ + 261, + 286, + 269, + 295 + ], + "score": 0.77, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 284, + 288, + 298 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 289, + 286, + 299, + 295 + ], + "score": 0.79, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "are bounded and that the labels are MCAR. 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Rademacher variables independent from", + "type": "text" + }, + { + "bbox": [ + 375, + 244, + 414, + 253 + ], + "score": 0.88, + "content": "z _ { 1 } , . . . , z _ { m }", + "type": "inline_equation" + } + ], + "index": 11 + } + ], + "index": 11, + "bbox_fs": [ + 84, + 239, + 414, + 258 + ] + }, + { + "type": "text", + "bbox": [ + 86, + 262, + 331, + 275 + ], + "lines": [ + { + "bbox": [ + 85, + 262, + 331, + 275 + ], + "spans": [ + { + "bbox": [ + 85, + 262, + 331, + 275 + ], + "score": 1.0, + "content": "905 We can now restate and prove our generalisation bound.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12, + "bbox_fs": [ + 85, + 262, + 331, + 275 + ] + }, + { + "type": "index", + "bbox": [ + 86, + 284, + 506, + 319 + ], + "lines": [ + { + "bbox": [ + 86, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 86, + 287, + 100, + 297 + ], + "score": 1.0, + "content": "906", + "type": "text" + }, + { + "bbox": [ + 105, + 284, + 261, + 298 + ], + "score": 1.0, + "content": "Theorem 3.6. We assume that both", + "type": "text" + }, + { + "bbox": [ + 261, + 286, + 269, + 295 + ], + "score": 0.77, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 284, + 288, + 298 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 289, + 286, + 299, + 295 + ], + "score": 0.79, + "content": "H", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "are bounded and that the labels are MCAR. 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DATASETCOMPLETE CASEPSEUDOLABELDEPSEUDOLABEL
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DATASETNLCCPLDEPL
CROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACYCROSS-ENTROPYACCURACY
DERMA10001.95 ± 0.0968.99± 1.202.51±0.2068.88±1.031.88 ± 0.1269.30± 0.85
PNEUMONIA5851.47 ± 0.0483.94±2.402.04 ±0.0485.83±2.131.40 ± 0.0684.36±3.79
RETINA1601.68 ± 0.0348.30± 3.061.80 ±0.1847.75±2.501.67 ± 0.0649.40± 2.62
BREAST780.80±0.0476.15±0.751.00 ±0.2674.74±1.040.70±0.0376.67 ± 1.32
BLOOD17006.11 ± 0.1784.13±0.836.61 ±0.2284.09± 1.176.53 ±0.3083.68 ±0.59
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COMPLETE CASEFIXMATCHDEFIXMATCH
87.27 ± 0.2593.87 ±0.1395.44 ± 0.10
70.08 ±0.9382.25 ±2.2787.16 ± 0.46
0.60 ± 0.010.27 ±0.010.20 ±0.01
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( \\theta ; x _ { i } ) ] } } & { \\mathrm { b y ~ d e f i n i t i } } \\\\ & { } & { = \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\mathbb { E } [ L ( \\theta ; x _ { i } , y _ { i } ) ] + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } \\mathbb { E } [ H ( \\theta ; x _ { i } ) ] - \\frac { \\lambda } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\mathbb { E } [ H ( \\theta ; x _ { i } ) ] \\quad \\mathrm { b y ~ l i n e a r i t } . } \\end{array}" + }, + { + "category_id": 13, + "poly": [ + 451, + 924, + 651, + 924, + 651, + 963, + 451, + 963 + ], + "score": 0.92, + "latex": "\\mathbb { E } _ { x , y } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ]" + }, + { + "category_id": 14, + "poly": [ + 486, + 1547, + 1213, + 1547, + 1213, + 1607, + 486, + 1607 + ], + "score": 0.92, + "latex": "\\begin{array} { r } { \\mathbb { E } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ] = \\mathbb { E } \\left[ \\mathbb { E } _ { x , y } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ] | r \\right] = \\mathbb { E } _ { r } \\left[ \\mathcal { R } ( \\theta ) \\right] = \\mathcal { R } ( \\theta ) . } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 310, + 1292, + 1422, + 1292, + 1422, + 1467, + 310, + 1467 + ], + "score": 0.91, + "latex": "\\begin{array} { l } { _ { _ { - x , y } } [ \\hat { \\mathcal { R } } _ { D e S S L } ( \\theta ) ] = \\displaystyle \\frac { 1 } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\mathbb { E } \\left[ L ( \\theta ; x , y ) \\right] + \\frac { \\lambda } { n _ { u } } \\sum _ { i = 1 } ^ { n _ { u } } \\mathbb { E } \\left[ H ( \\theta ; x ) \\right] - \\frac { \\lambda } { n _ { l } } \\sum _ { i = 1 } ^ { n _ { l } } \\mathbb { E } \\left[ H ( \\theta ; x ) \\right] \\quad \\mathrm { i . i . d ~ s a m p l e s } } \\\\ { = \\mathbb { E } \\left[ L ( \\theta ; x , y ) \\right] } \\\\ { = \\mathcal { R } ( \\theta ) . } \\end{array}" + }, + { + "category_id": 13, + 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DATASETCOMPLETE CASEPSEUDOLABELDEPSEUDOLABEL
DERMA84.26 ± 0.5082.64 ±1.1983.82 ± 0.95
PNEUMONIA94.28 ±0.4694.34 ± 0.9194.15 ± 0.33
RETINA70.70 ± 0.7470.12 ±1.0169.97 ± 1.44
BREAST74.67 ± 3.6874.86 ±3.1875.33 ± 3.05
BLOOD97.83 ± 0.2397.83 ± 0.2397.72 ± 0.15
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Code is available at https://github.com/Atten4Vis/", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 141, + 478, + 248, + 490 + ], + "spans": [ + { + "bbox": [ + 141, + 478, + 248, + 490 + ], + "score": 1.0, + "content": "DemystifyLocalViT.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25, + "bbox_fs": [ + 141, + 390, + 471, + 490 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 510, + 206, + 523 + ], + "lines": [ + { + "bbox": [ + 105, + 509, + 208, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 208, + 526 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 530, + 506, + 619 + ], + "lines": [ + { + "bbox": [ + 106, + 530, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 506, + 542 + ], + "score": 1.0, + "content": "Vision Transformer (Chu et al., 2021b; d’Ascoli et al., 2021; Dosovitskiy et al., 2021; Guo et al.,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 541, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 506, + 554 + ], + "score": 1.0, + "content": "2021; Han et al., 2020; Khan et al., 2021; Touvron et al., 2020; Wang et al., 2021b; Wu et al., 2021;", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "Xu et al., 2021; Yuan et al., 2021b) has shown promising performance in ImageNet classification.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 564, + 506, + 575 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 506, + 575 + ], + "score": 1.0, + "content": "The improved variants, Local Vision Transformer (Chu et al., 2021a; Liu et al., 2021b; Vaswani et al.,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "score": 1.0, + "content": "2021), adopt the local attention mechanism, which partitions the image space into a set of small", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 586, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 506, + 598 + ], + "score": 1.0, + "content": "windows, and conducts the attention over the windows simultaneously. Local attention leads to great", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 596, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 608 + ], + "score": 1.0, + "content": "improvement in memory and computation efficiency and makes the extension to downstream tasks", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 608, + 419, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 608, + 419, + 619 + ], + "score": 1.0, + "content": "easier and more efficient, such as object detection and semantic segmentation.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 530, + 506, + 619 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 624, + 505, + 702 + ], + "lines": [ + { + "bbox": [ + 106, + 624, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 637 + ], + "score": 1.0, + "content": "We exploit the network regularization schemes (Goodfellow et al., 2016), sparse connectivity that", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 635, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 505, + 648 + ], + "score": 1.0, + "content": "controls the model complexity, and weight sharing that relaxes the requirement of increasing the", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 506, + 659 + ], + "score": 1.0, + "content": "training data scale and reduces the model parameters, as well as dynamic weight prediction that", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 657, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 657, + 505, + 669 + ], + "score": 1.0, + "content": "increases the model capability, to study the local attention mechanism. We rephrase local attention", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "as a channel-wise spatially-locally connected layer with dynamic connection weights. The main", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 679, + 507, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 507, + 691 + ], + "score": 1.0, + "content": "properties are summarized as follows. (i) Sparse connectivity: there is no connection across channels,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 691, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 505, + 702 + ], + "score": 1.0, + "content": "and each output position is only connected to the input positions within a local window. (ii) Weight", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "sharing: the connection weights are shared across channels or within each group of channels. (iii)", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 107 + ], + "score": 1.0, + "content": "Dynamic weight: the connection weights are dynamically predicted according to each image instance.", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 624, + 507, + 702 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 82, + 505, + 105 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "sharing: the connection weights are shared across channels or within each group of channels. (iii)", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 107 + ], + "score": 1.0, + "content": "Dynamic weight: the connection weights are dynamically predicted according to each image instance.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 110, + 505, + 199 + ], + "lines": [ + { + "bbox": [ + 105, + 111, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 111, + 505, + 123 + ], + "score": 1.0, + "content": "We connect local attention with depth-wise convolution (Chollet, 2017; Howard et al., 2017) and its", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 122, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 134 + ], + "score": 1.0, + "content": "dynamic variants that are also a channel-wise spatially-locally connected layer with optional dynamic", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "score": 1.0, + "content": "connection weights. They are similar in sparse connectivity. The main differences lie in (i) weight", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "sharing - depth-wise convolution shares connection weights (kernel weights) across spatial positions", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 505, + 166 + ], + "score": 1.0, + "content": "and attention shares the connection weights across channels, and (ii) dynamic weight computation", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "manners - local attention is based on dot-products between pairwise positions in the local window,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "and dynamic convolution is based on linear projections conducted on the center representation or the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 233, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 233, + 201 + ], + "score": 1.0, + "content": "globally pooled representation.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 204, + 505, + 259 + ], + "lines": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "score": 1.0, + "content": "We further present the empirical verification for the connection. We take the recently-developed Local", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 215, + 505, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 227 + ], + "score": 1.0, + "content": "Vision Transformer, Swin Transformer (Liu et al., 2021b), as an example, and study the empirical", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 225, + 506, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 506, + 240 + ], + "score": 1.0, + "content": "performance of local attention and (dynamic) depth-wise convolution in the same training settings as", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 236, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 505, + 250 + ], + "score": 1.0, + "content": "Swin Transformer. 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The ablation studies imply that weight sharing and dynamic weight improves the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "model capability. 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In the spatial dimension, we use 1D to illustrate the local-connectivity pattern for clarity.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 192, + 424, + 204 + ], + "lines": [ + { + "bbox": [ + 105, + 192, + 426, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 426, + 205 + ], + "score": 1.0, + "content": "2.2 SPARSE CONNECTIVITY, WEIGHT SHARING, AND DYNAMIC WEIGHT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 210, + 502, + 243 + ], + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 505, + 222 + ], + "score": 1.0, + "content": "We give a brief introduction of two regularization forms, sparse connectivity and weight sharing, and", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 221, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 233 + ], + "score": 1.0, + "content": "dynamic weight, and their benefits. We will use the three forms to analyze local attention and connect", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 232, + 259, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 259, + 244 + ], + "score": 1.0, + "content": "it to dynamic depth-wise convolution.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 249, + 504, + 282 + ], + "lines": [ + { + "bbox": [ + 106, + 249, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 261 + ], + "score": 1.0, + "content": "Sparse connectivity means that there are no connections between some output neurons (variables)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "score": 1.0, + "content": "and some input neurons in a layer. It reduces the model complexity without decreasing the number of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 271, + 322, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 322, + 284 + ], + "score": 1.0, + "content": "neurons, e.g., the size of the (hidden) representations.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 288, + 505, + 321 + ], + "lines": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "Weight sharing indicates that some connection weights are equal. It lowers the number of model", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 298, + 506, + 313 + ], + "spans": [ + { + "bbox": [ + 104, + 298, + 506, + 313 + ], + "score": 1.0, + "content": "parameters and increases the network size without requiring a corresponding increase in training", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 310, + 231, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 310, + 231, + 322 + ], + "score": 1.0, + "content": "data (Goodfellow et al., 2016).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 371 + ], + "lines": [ + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "score": 1.0, + "content": "Dynamic weight refers to learning specialized connection weights for each instance. It generally", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 338, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 506, + 350 + ], + "score": 1.0, + "content": "aims to increase the model capacity. If regarding the learned connection weights as hidden variables,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 349, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 506, + 361 + ], + "score": 1.0, + "content": "dynamic weight can be viewed as introducing second-order operations that increase the capability of", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 360, + 468, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 468, + 372 + ], + "score": 1.0, + "content": "the network. The connection to Hopfield networks is discussed in (Ramsauer et al., 2020).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5 + }, + { + "type": "title", + "bbox": [ + 108, + 381, + 266, + 393 + ], + "lines": [ + { + "bbox": [ + 106, + 381, + 267, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 267, + 394 + ], + "score": 1.0, + "content": "2.3 ANALYZING LOCAL ATTENTION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 399, + 504, + 422 + ], + "lines": [ + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "score": 1.0, + "content": "We show that local attention is a channel-wise spatially-locally connected layer with dynamic weight", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 409, + 457, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 457, + 423 + ], + "score": 1.0, + "content": "computation, and discuss its properties. Figure 1 (c) illustrates the connectivity pattern.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 504, + 449 + ], + "lines": [ + { + "bbox": [ + 105, + 425, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 441 + ], + "score": 1.0, + "content": "The aggregation processes (Equation 1 and Equation 3) for local attention can be rewritten equivalently", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 438, + 272, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 272, + 450 + ], + "score": 1.0, + "content": "in a form of element-wise multiplication:", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "interline_equation", + "bbox": [ + 255, + 450, + 354, + 474 + ], + "lines": [ + { + "bbox": [ + 255, + 450, + 354, + 474 + ], + "spans": [ + { + "bbox": [ + 255, + 450, + 354, + 474 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\mathbf { y } _ { i } = \\displaystyle \\sum _ { j = 1 } ^ { N _ { k } } \\mathbf { w } _ { i j } \\odot \\mathbf { x } _ { i j } , } \\end{array}", + "type": "interline_equation", + "image_path": "a462fe232582eedd83388ce2ef6fafc72f1d7f418a68f39e30177abe0a616832.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 255, + 450, + 354, + 474 + ], + "spans": [], + "index": 25 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 477, + 505, + 502 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 133, + 491 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 479, + 143, + 489 + ], + "score": 0.82, + "content": "\\odot", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 477, + 343, + 491 + ], + "score": 1.0, + "content": "is the element-wise multiplication operator, and", + "type": "text" + }, + { + "bbox": [ + 343, + 477, + 387, + 490 + ], + "score": 0.95, + "content": "\\mathbf { w } _ { i j } \\in \\mathbb { R } ^ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 477, + 505, + 491 + ], + "score": 1.0, + "content": "is the weight vector formed", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 487, + 330, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 210, + 504 + ], + "score": 1.0, + "content": "from the attention weight", + "type": "text" + }, + { + "bbox": [ + 210, + 490, + 223, + 502 + ], + "score": 0.88, + "content": "a _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 487, + 236, + 504 + ], + "score": 1.0, + "content": "or", + "type": "text" + }, + { + "bbox": [ + 236, + 489, + 326, + 502 + ], + "score": 0.92, + "content": "\\{ a _ { i j 1 } , a _ { i j 2 } , . . . , a _ { i j M } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 487, + 330, + 504 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5 + }, + { + "type": "text", + "bbox": [ + 106, + 506, + 505, + 562 + ], + "lines": [ + { + "bbox": [ + 106, + 506, + 504, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 489, + 518 + ], + "score": 1.0, + "content": "Sparse connectivity. The local attention layer is spatially sparse: each position is connected to the", + "type": "text" + }, + { + "bbox": [ + 490, + 506, + 504, + 517 + ], + "score": 0.88, + "content": "N _ { k }", + "type": "inline_equation" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "positions in a small local window. There are also no connections across channels. 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The weights are shared with respect to channels. 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We rewrite it as:", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38.5 + }, + { + "type": "interline_equation", + "bbox": [ + 200, + 654, + 410, + 667 + ], + "lines": [ + { + "bbox": [ + 200, + 654, + 410, + 667 + ], + "spans": [ + { + "bbox": [ + 200, + 654, + 410, + 667 + ], + "score": 0.89, + "content": "\\begin{array} { r } { \\{ \\mathbf { w } _ { i 1 } , \\mathbf { w } _ { i 2 } , \\dots , \\mathbf { w } _ { i N _ { k } } \\} = f ( \\mathbf { x } _ { i } ; \\mathbf { x } _ { i 1 } , \\mathbf { x } _ { i 2 } , \\dots , \\mathbf { x } _ { i N _ { k } } ) . } \\end{array}", + "type": "interline_equation", + "image_path": "c0b985aa7f9b6c60a158fc5ea229622b113b4f8d557b5b148535dd5d61afea1a.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 200, + 654, + 410, + 667 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 671, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 670, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 505, + 683 + ], + "score": 1.0, + "content": "Each weight may obtain the information across all the channels in one head, and serves as a bridge to", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 681, + 357, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 681, + 357, + 693 + ], + "score": 1.0, + "content": "deliver the across-channel information to each output channel.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "Translation equivalence. Different from convolution which satisfies translation equivalence through", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "sharing weights across positions, the equivalence to translation for local attention, depends if the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 721, + 504, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 504, + 732 + ], + "score": 1.0, + "content": "keys/values are changed, i.e., the attention weights are changed, when the feature map is translated.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 44 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 75, + 501, + 149 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 75, + 501, + 149 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 75, + 501, + 149 + ], + "spans": [ + { + "bbox": [ + 109, + 75, + 501, + 149 + ], + "score": 0.961, + "type": "image", + "image_path": "2ba0278d1ad365ab4ed1a5c39815468edc419def2f96349e877503015fafd44a.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 75, + 501, + 99.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 99.66666666666667, + 501, + 124.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 124.33333333333334, + 501, + 149.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 156, + 505, + 187 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "score": 1.0, + "content": "Figure 1: Illustration of connectivity for (a) convolution, (b) global attention and spatial mixing MLP, (c) local", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 166, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 166, + 326, + 178 + ], + "score": 1.0, + "content": "attention and depth-wise convolution, (d) point-wise MLP or", + "type": "text" + }, + { + "bbox": [ + 326, + 167, + 348, + 176 + ], + "score": 0.9, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 166, + 506, + 178 + ], + "score": 1.0, + "content": "convolution, and (e) MLP (fully-connected", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 176, + 452, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 452, + 188 + ], + "score": 1.0, + "content": "layer). In the spatial dimension, we use 1D to illustrate the local-connectivity pattern for clarity.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 192, + 424, + 204 + ], + "lines": [ + { + "bbox": [ + 105, + 192, + 426, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 426, + 205 + ], + "score": 1.0, + "content": "2.2 SPARSE CONNECTIVITY, WEIGHT SHARING, AND DYNAMIC WEIGHT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 192, + 426, + 205 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 210, + 502, + 243 + ], + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 505, + 222 + ], + "score": 1.0, + "content": "We give a brief introduction of two regularization forms, sparse connectivity and weight sharing, and", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 221, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 233 + ], + "score": 1.0, + "content": "dynamic weight, and their benefits. We will use the three forms to analyze local attention and connect", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 232, + 259, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 259, + 244 + ], + "score": 1.0, + "content": "it to dynamic depth-wise convolution.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 210, + 505, + 244 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 249, + 504, + 282 + ], + "lines": [ + { + "bbox": [ + 106, + 249, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 261 + ], + "score": 1.0, + "content": "Sparse connectivity means that there are no connections between some output neurons (variables)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 272 + ], + "score": 1.0, + "content": "and some input neurons in a layer. It reduces the model complexity without decreasing the number of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 271, + 322, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 322, + 284 + ], + "score": 1.0, + "content": "neurons, e.g., the size of the (hidden) representations.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 249, + 506, + 284 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 288, + 505, + 321 + ], + "lines": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "Weight sharing indicates that some connection weights are equal. It lowers the number of model", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 298, + 506, + 313 + ], + "spans": [ + { + "bbox": [ + 104, + 298, + 506, + 313 + ], + "score": 1.0, + "content": "parameters and increases the network size without requiring a corresponding increase in training", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 310, + 231, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 310, + 231, + 322 + ], + "score": 1.0, + "content": "data (Goodfellow et al., 2016).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14, + "bbox_fs": [ + 104, + 287, + 506, + 322 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 371 + ], + "lines": [ + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "score": 1.0, + "content": "Dynamic weight refers to learning specialized connection weights for each instance. It generally", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 338, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 506, + 350 + ], + "score": 1.0, + "content": "aims to increase the model capacity. If regarding the learned connection weights as hidden variables,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 349, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 506, + 361 + ], + "score": 1.0, + "content": "dynamic weight can be viewed as introducing second-order operations that increase the capability of", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 360, + 468, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 468, + 372 + ], + "score": 1.0, + "content": "the network. The connection to Hopfield networks is discussed in (Ramsauer et al., 2020).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 327, + 506, + 372 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 381, + 266, + 393 + ], + "lines": [ + { + "bbox": [ + 106, + 381, + 267, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 267, + 394 + ], + "score": 1.0, + "content": "2.3 ANALYZING LOCAL ATTENTION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 399, + 504, + 422 + ], + "lines": [ + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 505, + 412 + ], + "score": 1.0, + "content": "We show that local attention is a channel-wise spatially-locally connected layer with dynamic weight", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 409, + 457, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 457, + 423 + ], + "score": 1.0, + "content": "computation, and discuss its properties. Figure 1 (c) illustrates the connectivity pattern.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 398, + 505, + 423 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 504, + 449 + ], + "lines": [ + { + "bbox": [ + 105, + 425, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 441 + ], + "score": 1.0, + "content": "The aggregation processes (Equation 1 and Equation 3) for local attention can be rewritten equivalently", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 438, + 272, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 272, + 450 + ], + "score": 1.0, + "content": "in a form of element-wise multiplication:", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 425, + 505, + 450 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 255, + 450, + 354, + 474 + ], + "lines": [ + { + "bbox": [ + 255, + 450, + 354, + 474 + ], + "spans": [ + { + "bbox": [ + 255, + 450, + 354, + 474 + ], + "score": 0.94, + "content": "\\begin{array} { r } { \\mathbf { y } _ { i } = \\displaystyle \\sum _ { j = 1 } ^ { N _ { k } } \\mathbf { w } _ { i j } \\odot \\mathbf { x } _ { i j } , } \\end{array}", + "type": "interline_equation", + "image_path": "a462fe232582eedd83388ce2ef6fafc72f1d7f418a68f39e30177abe0a616832.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 255, + 450, + 354, + 474 + ], + "spans": [], + "index": 25 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 477, + 505, + 502 + ], + "lines": [ + { + "bbox": [ + 105, + 477, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 133, + 491 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 479, + 143, + 489 + ], + "score": 0.82, + "content": "\\odot", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 477, + 343, + 491 + ], + "score": 1.0, + "content": "is the element-wise multiplication operator, and", + "type": "text" + }, + { + "bbox": [ + 343, + 477, + 387, + 490 + ], + "score": 0.95, + "content": "\\mathbf { w } _ { i j } \\in \\mathbb { R } ^ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 477, + 505, + 491 + ], + "score": 1.0, + "content": "is the weight vector formed", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 487, + 330, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 210, + 504 + ], + "score": 1.0, + "content": "from the attention weight", + "type": "text" + }, + { + "bbox": [ + 210, + 490, + 223, + 502 + ], + "score": 0.88, + "content": "a _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 487, + 236, + 504 + ], + "score": 1.0, + "content": "or", + "type": "text" + }, + { + "bbox": [ + 236, + 489, + 326, + 502 + ], + "score": 0.92, + "content": "\\{ a _ { i j 1 } , a _ { i j 2 } , . . . , a _ { i j M } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 487, + 330, + 504 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 477, + 505, + 504 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 506, + 505, + 562 + ], + "lines": [ + { + "bbox": [ + 106, + 506, + 504, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 489, + 518 + ], + "score": 1.0, + "content": "Sparse connectivity. The local attention layer is spatially sparse: each position is connected to the", + "type": "text" + }, + { + "bbox": [ + 490, + 506, + 504, + 517 + ], + "score": 0.88, + "content": "N _ { k }", + "type": "inline_equation" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "positions in a small local window. There are also no connections across channels. The element-wise", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 525, + 504, + 543 + ], + "spans": [ + { + "bbox": [ + 104, + 525, + 490, + 543 + ], + "score": 1.0, + "content": "multiplication in Equation 4 indicates that given the attention weights, each output element, e.g.,", + "type": "text" + }, + { + "bbox": [ + 490, + 530, + 504, + 540 + ], + "score": 0.83, + "content": "y _ { i d }", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 539, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 505, + 551 + ], + "score": 1.0, + "content": "(the ith position for the dth channel), is only dependent on the corresponding input elements from the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 550, + 459, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 224, + 563 + ], + "score": 1.0, + "content": "same channel in the window,", + "type": "text" + }, + { + "bbox": [ + 225, + 550, + 320, + 562 + ], + "score": 0.92, + "content": "\\{ x _ { i 1 d } , x _ { i 2 d } , \\ldots , x _ { i N _ { k } d } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 550, + 459, + 563 + ], + "score": 1.0, + "content": ", and not related to other channels.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30, + "bbox_fs": [ + 104, + 506, + 505, + 563 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 566, + 505, + 623 + ], + "lines": [ + { + "bbox": [ + 106, + 567, + 504, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 504, + 578 + ], + "score": 1.0, + "content": "Weight sharing. The weights are shared with respect to channels. In the single-head attention case, all", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 576, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 159, + 592 + ], + "score": 1.0, + "content": "the elements", + "type": "text" + }, + { + "bbox": [ + 159, + 578, + 253, + 590 + ], + "score": 0.91, + "content": "\\{ w _ { i j 1 } , w _ { i j 2 } , \\ldots , w _ { i j D } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 576, + 335, + 592 + ], + "score": 1.0, + "content": "in the weight vector", + "type": "text" + }, + { + "bbox": [ + 335, + 579, + 351, + 590 + ], + "score": 0.89, + "content": "\\mathbf { w } _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 576, + 407, + 592 + ], + "score": 1.0, + "content": "are the same:", + "type": "text" + }, + { + "bbox": [ + 408, + 579, + 452, + 590 + ], + "score": 0.85, + "content": "w _ { i j d } = a _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 576, + 456, + 592 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 456, + 578, + 503, + 589 + ], + "score": 0.85, + "content": "1 \\leqslant d \\leqslant D", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 576, + 506, + 592 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 504, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 308, + 603 + ], + "score": 1.0, + "content": "In the multi-head attention case, the weight vector", + "type": "text" + }, + { + "bbox": [ + 308, + 590, + 325, + 601 + ], + "score": 0.88, + "content": "\\mathbf { w } _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 588, + 408, + 603 + ], + "score": 1.0, + "content": "is group-wise same:", + "type": "text" + }, + { + "bbox": [ + 409, + 591, + 425, + 601 + ], + "score": 0.87, + "content": "{ \\bf w } _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 588, + 492, + 603 + ], + "score": 1.0, + "content": "is partitioned to", + "type": "text" + }, + { + "bbox": [ + 492, + 589, + 504, + 599 + ], + "score": 0.75, + "content": "M", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 599, + 507, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 321, + 615 + ], + "score": 1.0, + "content": "subvectors each corresponding to one attention head,", + "type": "text" + }, + { + "bbox": [ + 322, + 600, + 421, + 612 + ], + "score": 0.91, + "content": "\\left\\{ \\mathbf { w } _ { i j 1 } , \\mathbf { w } _ { i j 2 } , \\ldots , \\mathbf { w } _ { i j M } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 599, + 507, + 615 + ], + "score": 1.0, + "content": ", and the elements in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 609, + 439, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 168, + 625 + ], + "score": 1.0, + "content": "each subvector", + "type": "text" + }, + { + "bbox": [ + 168, + 612, + 192, + 623 + ], + "score": 0.9, + "content": "\\mathbf { w } _ { i j m }", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 609, + 325, + 625 + ], + "score": 1.0, + "content": "are the same and are equal to the", + "type": "text" + }, + { + "bbox": [ + 326, + 613, + 335, + 621 + ], + "score": 0.47, + "content": "m", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 609, + 414, + 625 + ], + "score": 1.0, + "content": "th attention weight,", + "type": "text" + }, + { + "bbox": [ + 415, + 613, + 434, + 623 + ], + "score": 0.89, + "content": "a _ { i j m }", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 609, + 439, + 625 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35, + "bbox_fs": [ + 105, + 567, + 507, + 625 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 502, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 504, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 231, + 641 + ], + "score": 1.0, + "content": "Dynamic weight. The weights,", + "type": "text" + }, + { + "bbox": [ + 231, + 627, + 322, + 640 + ], + "score": 0.91, + "content": "\\left\\{ \\mathbf { w } _ { i 1 } , \\mathbf { w } _ { i 2 } , \\ldots , \\mathbf { w } _ { i N _ { k } } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 626, + 493, + 641 + ], + "score": 1.0, + "content": ", are dynamically predicted from the query", + "type": "text" + }, + { + "bbox": [ + 493, + 630, + 504, + 639 + ], + "score": 0.83, + "content": "\\mathbf { x } _ { i }", + "type": "inline_equation" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 638, + 492, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 159, + 652 + ], + "score": 1.0, + "content": "and the keys", + "type": "text" + }, + { + "bbox": [ + 159, + 639, + 243, + 651 + ], + "score": 0.91, + "content": "\\left\\{ \\mathbf { x } _ { i 1 } , \\mathbf { x } _ { i 2 } , \\ldots , \\mathbf { x } _ { i N _ { k } } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 638, + 492, + 652 + ], + "score": 1.0, + "content": "in the local window as shown in Equation 2. 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Each position is only connected to the positions in a small local window", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 582, + 177, + 593 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 177, + 593 + ], + "score": 1.0, + "content": "for each channel.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 560, + 505, + 593 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 599, + 505, + 655 + ], + "lines": [ + { + "bbox": [ + 106, + 599, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 599, + 505, + 611 + ], + "score": 1.0, + "content": "Difference. 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Depth-wise convolution benefits from the weight sharing across positions to reduce the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 643, + 341, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 341, + 657 + ], + "score": 1.0, + "content": "parameter complexity and increase the network capability.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 599, + 506, + 657 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 660, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 659, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 506, + 673 + ], + "score": 1.0, + "content": "The second difference is that the connection weights for depth-wise convolution are static and learned", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "as model parameters, while the connection weights for local attention are dynamic and predicted from", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 682, + 506, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 506, + 694 + ], + "score": 1.0, + "content": "each instance. The dynamic variants of depth-wise convolution also benefit from the dynamic weight.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 44, + "bbox_fs": [ + 105, + 659, + 506, + 694 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 114, + 123, + 494, + 201 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 81, + 505, + 121 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 80, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 505, + 94 + ], + "score": 1.0, + "content": "Table 1: The comparison of attention, local MLP (non-dynamic version of local attention, the attention weights", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 505, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 505, + 102 + ], + "score": 1.0, + "content": "are learned as static model parameters), local attention, convolution, depth-wise convolution (DW-Conv.) and", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "score": 1.0, + "content": "the dynamic variant (D-DW-Conv.) in terms of the patterns of sparse connectivity, weight sharing, and dynamic", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 111, + 364, + 123 + ], + "spans": [ + { + "bbox": [ + 106, + 111, + 364, + 123 + ], + "score": 1.0, + "content": "weight. Please refer to Figure 1 for the connectivity pattern illustration.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "table_body", + "bbox": [ + 114, + 123, + 494, + 201 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 114, + 123, + 494, + 201 + ], + "spans": [ + { + "bbox": [ + 114, + 123, + 494, + 201 + ], + "score": 0.98, + "html": "
Sparse between positionsSparse between channelsWeight sharing acrossDynamic weight
non-localfullpositionchannel
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Local attention√：√
DW-Conv.√：
D-DW-Conv.√√√
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In addition, we study the effects of weight sharing and dynamic weight in the two structures.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 367, + 366, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 366, + 380 + ], + "score": 1.0, + "content": "The results for large scale pre-training are given in the appendix.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17.5 + }, + { + "type": "title", + "bbox": [ + 107, + 383, + 205, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 205, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 205, + 396 + ], + "score": 1.0, + "content": "3.1 ARCHITECTURES", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 398, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "score": 1.0, + "content": "We use the recently-developed Swin Transformer as the example of local attention-based networks", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "score": 1.0, + "content": "and study the performance over the tiny and base networks: Swin-T and Swin-B, provided by the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "score": 1.0, + "content": "authors (Liu et al., 2021b) We follow the tiny and base networks to build two depth-wise convolution-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "score": 1.0, + "content": "based networks, DW-Conv.-T and DW-Conv.-B so that the overall architectures are the same, making", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "score": 1.0, + "content": "the comparison fair. We also build two dynamic versions, D-DW-Conv. and I-D-DW-Conv., by", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "score": 1.0, + "content": "predicting the dynamic weights as described in Section 2.4. We simply replace local attention in", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 464, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 506, + 477 + ], + "score": 1.0, + "content": "Swin Transformer by depth-wise convolution of the same window size, where the pre- and post-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 308, + 487 + ], + "score": 1.0, + "content": "linear projections over the values are replaced by", + "type": "text" + }, + { + "bbox": [ + 308, + 475, + 332, + 485 + ], + "score": 0.9, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "convolutions. We adopt the convolutional", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "network design pattern to append BN (Ioffe & Szegedy, 2015) and ReLU (Nair & Hinton, 2010) to", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "the convolution. The details are available in the Appendix. In terms of parameter and computation", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "score": 1.0, + "content": "complexity, the depth-wise convolution-based networks are lower (Table 2) because there are linear", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 519, + 304, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 304, + 531 + ], + "score": 1.0, + "content": "projections for keys and values in local attention.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 27.5 + }, + { + "type": "title", + "bbox": [ + 107, + 541, + 317, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 540, + 318, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 318, + 552 + ], + "score": 1.0, + "content": "3.2 DATASETS AND IMPLEMENTATION DETAILS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 106, + 555, + 505, + 633 + ], + "lines": [ + { + "bbox": [ + 106, + 554, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 506, + 568 + ], + "score": 1.0, + "content": "ImageNet classification. The ImageNet-1K recognition dataset (Deng et al., 2009) contains 1.28M", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 566, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 505, + 578 + ], + "score": 1.0, + "content": "training images and 50K validation images with totally 1,000 classes. We use the exactly-same", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "score": 1.0, + "content": "training setting as Swin Transformer (Liu et al., 2021b). The AdamW (Loshchilov & Hutter, 2019)", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "score": 1.0, + "content": "optimizer for 300 epochs is adopted, with a cosine decay learning rate scheduler and 20 epochs of", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 599, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 599, + 505, + 612 + ], + "score": 1.0, + "content": "linear warm-up. The weight decay is 0.05, and the initial learning rate is 0.001. 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The COCO 2017 dataset (Lin et al., 2014) contains 118K training and 5K", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 648, + 506, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 506, + 661 + ], + "score": 1.0, + "content": "validation images. We follow Swin Transformer to adopt Cascade Mask R-CNN (Cai & Vasconcelos,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 660, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 506, + 673 + ], + "score": 1.0, + "content": "2019) for comparing backbones. 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The ADE20K (Zhou et al., 2017) dataset contains 25K images, 20K", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 718, + 505, + 735 + ], + "spans": [ + { + "bbox": [ + 105, + 718, + 505, + 735 + ], + "score": 1.0, + "content": "for training, 2K for validation, and 3K for testing, with 150 semantic categories. The same setting", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 114, + 123, + 494, + 201 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 81, + 505, + 121 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 80, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 505, + 94 + ], + "score": 1.0, + "content": "Table 1: The comparison of attention, local MLP (non-dynamic version of local attention, the attention weights", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 505, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 505, + 102 + ], + "score": 1.0, + "content": "are learned as static model parameters), local attention, convolution, depth-wise convolution (DW-Conv.) and", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "score": 1.0, + "content": "the dynamic variant (D-DW-Conv.) in terms of the patterns of sparse connectivity, weight sharing, and dynamic", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 111, + 364, + 123 + ], + "spans": [ + { + "bbox": [ + 106, + 111, + 364, + 123 + ], + "score": 1.0, + "content": "weight. Please refer to Figure 1 for the connectivity pattern illustration.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "table_body", + "bbox": [ + 114, + 123, + 494, + 201 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 114, + 123, + 494, + 201 + ], + "spans": [ + { + "bbox": [ + 114, + 123, + 494, + 201 + ], + "score": 0.98, + "html": "
Sparse between positionsSparse between channelsWeight sharing acrossDynamic weight
non-localfullpositionchannel
Local MLP√√”
Local attention√：√
DW-Conv.√：
D-DW-Conv.√√√
Conv.√√
", + "type": "table", + "image_path": "904077d03e0620e83fc86a626857fb39ffe6dbac4f46220acd0740e882b7177d.jpg" + } + ] + } + ], + "index": 5, + "virtual_lines": [ + { + "bbox": [ + 114, + 123, + 494, + 149.0 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 114, + 149.0, + 494, + 175.0 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 114, + 175.0, + 494, + 201.0 + ], + "spans": [], + "index": 6 + } + ] + } + ], + "index": 3.25 + }, + { + "type": "text", + "bbox": [ + 106, + 203, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 106, + 202, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 202, + 505, + 216 + ], + "score": 1.0, + "content": "One more difference lies in window representation. Local attention represents the positions in", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 214, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 506, + 227 + ], + "score": 1.0, + "content": "a window by utilizing a set form with spatial-order information lost. It explores the spatial-order", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 224, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 506, + 238 + ], + "score": 1.0, + "content": "information implicitly using the positional embedding or explicitly using the learned so-called relative", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 236, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 506, + 249 + ], + "score": 1.0, + "content": "positional embedding. Depth-wise convolution exploits a vector form: aggregate the representations", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 245, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 505, + 261 + ], + "score": 1.0, + "content": "within a local window with the weights indexed by the relative position (see Equation 6); keep", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 258, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 506, + 271 + ], + "score": 1.0, + "content": "spatial correspondence between the positions for different windows, thus exploring the spatial-order", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 268, + 198, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 198, + 282 + ], + "score": 1.0, + "content": "information explicitly.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 202, + 506, + 282 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 293, + 245, + 306 + ], + "lines": [ + { + "bbox": [ + 105, + 292, + 247, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 247, + 308 + ], + "score": 1.0, + "content": "3 EXPERIMENTAL STUDY", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 506, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "We conduct empirical comparisons between local attention and depth-wise convolutions on three", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "visual recognition tasks: ImageNet classification, COCO object detection, and ADE semantic", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 334, + 507, + 347 + ], + "spans": [ + { + "bbox": [ + 104, + 334, + 507, + 347 + ], + "score": 1.0, + "content": "segmentation. We follow the structure of Swin Transformer to build the depth-wise convolution-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "based networks. We apply the same training and evaluation settings from Swin Transformer to our", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 356, + 507, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 507, + 369 + ], + "score": 1.0, + "content": "models. In addition, we study the effects of weight sharing and dynamic weight in the two structures.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 367, + 366, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 366, + 380 + ], + "score": 1.0, + "content": "The results for large scale pre-training are given in the appendix.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17.5, + "bbox_fs": [ + 104, + 312, + 507, + 380 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 383, + 205, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 205, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 205, + 396 + ], + "score": 1.0, + "content": "3.1 ARCHITECTURES", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 398, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 505, + 410 + ], + "score": 1.0, + "content": "We use the recently-developed Swin Transformer as the example of local attention-based networks", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "score": 1.0, + "content": "and study the performance over the tiny and base networks: Swin-T and Swin-B, provided by the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "score": 1.0, + "content": "authors (Liu et al., 2021b) We follow the tiny and base networks to build two depth-wise convolution-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "score": 1.0, + "content": "based networks, DW-Conv.-T and DW-Conv.-B so that the overall architectures are the same, making", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "score": 1.0, + "content": "the comparison fair. We also build two dynamic versions, D-DW-Conv. and I-D-DW-Conv., by", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 465 + ], + "score": 1.0, + "content": "predicting the dynamic weights as described in Section 2.4. We simply replace local attention in", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 464, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 506, + 477 + ], + "score": 1.0, + "content": "Swin Transformer by depth-wise convolution of the same window size, where the pre- and post-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 308, + 487 + ], + "score": 1.0, + "content": "linear projections over the values are replaced by", + "type": "text" + }, + { + "bbox": [ + 308, + 475, + 332, + 485 + ], + "score": 0.9, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "convolutions. We adopt the convolutional", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "network design pattern to append BN (Ioffe & Szegedy, 2015) and ReLU (Nair & Hinton, 2010) to", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "the convolution. The details are available in the Appendix. In terms of parameter and computation", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "score": 1.0, + "content": "complexity, the depth-wise convolution-based networks are lower (Table 2) because there are linear", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 519, + 304, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 304, + 531 + ], + "score": 1.0, + "content": "projections for keys and values in local attention.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 398, + 506, + 531 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 541, + 317, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 540, + 318, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 318, + 552 + ], + "score": 1.0, + "content": "3.2 DATASETS AND IMPLEMENTATION DETAILS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 106, + 555, + 505, + 633 + ], + "lines": [ + { + "bbox": [ + 106, + 554, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 506, + 568 + ], + "score": 1.0, + "content": "ImageNet classification. The ImageNet-1K recognition dataset (Deng et al., 2009) contains 1.28M", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 566, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 505, + 578 + ], + "score": 1.0, + "content": "training images and 50K validation images with totally 1,000 classes. We use the exactly-same", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "score": 1.0, + "content": "training setting as Swin Transformer (Liu et al., 2021b). The AdamW (Loshchilov & Hutter, 2019)", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 600 + ], + "score": 1.0, + "content": "optimizer for 300 epochs is adopted, with a cosine decay learning rate scheduler and 20 epochs of", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 599, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 599, + 505, + 612 + ], + "score": 1.0, + "content": "linear warm-up. The weight decay is 0.05, and the initial learning rate is 0.001. 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The same setting", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48.5, + "bbox_fs": [ + 105, + 710, + 505, + 735 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 100, + 504, + 451 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 81, + 504, + 101 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 80, + 505, + 93 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 505, + 93 + ], + "score": 1.0, + "content": "Table 2: ImageNet classification comparison for ResNet, Mixer and ResMLP, ViT and DeiT, Swin (Swin", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 91, + 486, + 102 + ], + "spans": [ + { + "bbox": [ + 106, + 91, + 486, + 102 + ], + "score": 1.0, + "content": "Transformer), DW-Conv. (depth-wise convolution), and D-DW-Conv. 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methodimg. size #param. FLOPs throughput (img./s) top-1 acc.real acc.
Bottleneck:convolution with low rank
ResNet-50 (He et al.,2016)224226M4.1G1128.376.282.5
ResNet-101 (He et al., 2016)224²45M7.9G652.077.483.7
ResNet-152 (He et al., 2016)224260M11.6G456.778.384.1
Channel and spatial separable MLP, spatial separable MLP=point-wise1 ×1 convolution
Mixer-B/16 (Tolstikhin et al.,2021)224246M--76.482.4
Mixer-L/16(Tolstikhin et al.,2021)224²189M-71.877.1
ResMLP-12 (Touvron et al., 2021)224²15M3.0G=76.683.3
ResMLP-24 (Touvron et al., 2021)224²30M6.0G79.485.3
ResMLP-36 (Touvron et al.,2021)224245M8.9G-79.785.6
Global attention:dynamicchannel separable MLP+ spatial separable MLP
ViT-B/16 (Dosovitskiy et al.,2021)384286M55.4G83.477.983.6
ViT-L/16 (Dosovitskiy et al.,2021)3842307M190.7G26.576.582.2
DeiT-S (Touvron et al., 2020)224²22M4.6G947.379.885.7
DeiT-B (Touvron et al.,2020)224²86M17.5G298.281.886.7
DeiT-B (Touvron et al., 2020)384286M55.4G82.783.187.7
Local MLP: perform static separable MLP in local small windows
Swin-Local MLP-T224226M3.8G861.080.386.1
Swin-Local MLP-B224²79M12.9G321.282.286.9
Local attention:perform attention inlocal small windows
Swin-T (Liu et al.,2021b)224²28M4.5G713.581.386.6
Swin-B (Liu et al., 2021b)224288M15.4G263.083.387.9
Depth-wise convolution + point-wise 1 ×1 convolution
DW-Conv.-T224224M3.8G928.781.386.8
DW-Conv.-B224274M12.9G327.683.287.9
D-DW-Conv.-T224²51M3.8G897.081.987.3
D-DW-Conv.-B224²162M13.0G322.483.287.9
I-D-DW-Conv.-T224226M4.4G685.381.887.1
I-D-DW-Conv.-B224280M14.3G244.983.488.0
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methodimg. size #param. FLOPs throughput (img./s) top-1 acc.real acc.
Bottleneck:convolution with low rank
ResNet-50 (He et al.,2016)224226M4.1G1128.376.282.5
ResNet-101 (He et al., 2016)224²45M7.9G652.077.483.7
ResNet-152 (He et al., 2016)224260M11.6G456.778.384.1
Channel and spatial separable MLP, spatial separable MLP=point-wise1 ×1 convolution
Mixer-B/16 (Tolstikhin et al.,2021)224246M--76.482.4
Mixer-L/16(Tolstikhin et al.,2021)224²189M-71.877.1
ResMLP-12 (Touvron et al., 2021)224²15M3.0G=76.683.3
ResMLP-24 (Touvron et al., 2021)224²30M6.0G79.485.3
ResMLP-36 (Touvron et al.,2021)224245M8.9G-79.785.6
Global attention:dynamicchannel separable MLP+ spatial separable MLP
ViT-B/16 (Dosovitskiy et al.,2021)384286M55.4G83.477.983.6
ViT-L/16 (Dosovitskiy et al.,2021)3842307M190.7G26.576.582.2
DeiT-S (Touvron et al., 2020)224²22M4.6G947.379.885.7
DeiT-B (Touvron et al.,2020)224²86M17.5G298.281.886.7
DeiT-B (Touvron et al., 2020)384286M55.4G82.783.187.7
Local MLP: perform static separable MLP in local small windows
Swin-Local MLP-T224226M3.8G861.080.386.1
Swin-Local MLP-B224²79M12.9G321.282.286.9
Local attention:perform attention inlocal small windows
Swin-T (Liu et al.,2021b)224²28M4.5G713.581.386.6
Swin-B (Liu et al., 2021b)224288M15.4G263.083.387.9
Depth-wise convolution + point-wise 1 ×1 convolution
DW-Conv.-T224224M3.8G928.781.386.8
DW-Conv.-B224274M12.9G327.683.287.9
D-DW-Conv.-T224²51M3.8G897.081.987.3
D-DW-Conv.-B224²162M13.0G322.483.287.9
I-D-DW-Conv.-T224226M4.4G685.381.887.1
I-D-DW-Conv.-B224280M14.3G244.983.488.0
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In the base model case, the performances are similar3.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 669, + 506, + 704 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 93, + 503, + 211 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 141, + 81, + 468, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 140, + 79, + 469, + 93 + ], + "spans": [ + { + "bbox": [ + 140, + 79, + 469, + 93 + ], + "score": 1.0, + "content": "Table 3: Comparison results on COCO object detection and ADE semantic segmentation.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 93, + 503, + 211 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 93, + 503, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 503, + 211 + ], + "score": 0.953, + "html": "
COCO Object DetectionADE20K Semantic Segmentation
#param.FLOPsApbotAPAPPApmask#param. FLOPsmIoU
Swin-T86M747G50.569.354.943.760M 947G44.5
DW Conv.-T82M730G 49.968.654.343.456M928G45.5
D-DW Conv.-T108M730G 50.569.554.643.783M 928G45.7
I-D-DW Conv.-T84M741G50.869.555.344.058M 939G46.2
Swin-B145M986G51.970.956.545.0121M 1192G48.1
DW Conv.-B132M924G51.169.655.444.2108M 1129G48.3
D-DW Conv.-B219M924G 51.270.055.444.4195M 1129G48.0
I-D-DW Conv.-B137M948G51.870.356.144.8114M 1153G47.8
", + "type": "table", + "image_path": "c0159f99a1094eda16cd883e0bc3650eb141a2ac46ee86268f9e305ddb158d2e.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 106, + 93, + 503, + 132.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 132.33333333333334, + 503, + 171.66666666666669 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 106, + 171.66666666666669, + 503, + 211.00000000000003 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 107, + 211, + 503, + 233 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 210, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 505, + 223 + ], + "score": 1.0, + "content": "Table 4: Effects of weight sharing across channels and positions. The results are reported on the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 222, + 458, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 222, + 212, + 234 + ], + "score": 1.0, + "content": "ImageNet top-1 accuracy.", + "type": "text" + }, + { + "bbox": [ + 212, + 222, + 235, + 232 + ], + "score": 0.67, + "content": "\\mathbf { S } \\mathbf { C } =", + "type": "inline_equation" + }, + { + "bbox": [ + 236, + 222, + 336, + 234 + ], + "score": 1.0, + "content": "Sharing across channels.", + "type": "text" + }, + { + "bbox": [ + 336, + 222, + 358, + 232 + ], + "score": 0.77, + "content": "\\mathrm { S P = }", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 222, + 458, + 234 + ], + "score": 1.0, + "content": "sharing across positions.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5 + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 107, + 235, + 503, + 283 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 107, + 235, + 503, + 283 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 107, + 235, + 503, + 283 + ], + "spans": [ + { + "bbox": [ + 107, + 235, + 503, + 283 + ], + "score": 0.931, + "html": "
SCSPAcc.#param.SCSPAcc.#param.
Local MLPX>80.235.3MDW Conv.X √√81.324.2M
√X80.326.2M×80.326.2M
√√80.324.3M√√81.123.9M
", + "type": "table", + "image_path": "7e62411f3761e8910ac8cdf91ddea921d58f9985711e23a877d9d46ae50b6a6f.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 107, + 235, + 503, + 251.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 107, + 251.0, + 503, + 267.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 107, + 267.0, + 503, + 283.0 + ], + "spans": [], + "index": 8 + } + ] + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 108, + 292, + 227, + 303 + ], + "lines": [ + { + "bbox": [ + 105, + 290, + 228, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 228, + 305 + ], + "score": 1.0, + "content": "3.4 EMPIRICAL ANALYSIS", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 307, + 505, + 362 + ], + "lines": [ + { + "bbox": [ + 106, + 307, + 505, + 319 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 505, + 319 + ], + "score": 1.0, + "content": "Local and channel-separable connection has been shown to be helpful for visual recognition. The", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 317, + 506, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 506, + 330 + ], + "score": 1.0, + "content": "empirical results in Table 2, e.g., local attention performs better than global attention (local connection)", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 329, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 342 + ], + "score": 1.0, + "content": "and depth-wise convolution performs better than convolution (channel-separable connection), also", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 339, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 505, + 354 + ], + "score": 1.0, + "content": "verify it. In the following, we present empirical results for weight sharing and dynamic weight by", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 351, + 251, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 251, + 364 + ], + "score": 1.0, + "content": "taking the tiny models as examples.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 106, + 367, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 367, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 381 + ], + "score": 1.0, + "content": "Weight sharing. We study how the performance is affected by the number of channels in each group", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "score": 1.0, + "content": "across which the weights are shared (the numbers of attention heads at each stage are accordingly", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 390, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 402 + ], + "score": 1.0, + "content": "changed) for local attention and local MLP (learn the weights in each window as model parameters", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "score": 1.0, + "content": "and not shared across windows). Figure 2 shows the effect for (a) local MLP - static weights, and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 412, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "(b) local attention - dynamic weights. One can see that for local attention, too many channels and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 422, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 506, + 435 + ], + "score": 1.0, + "content": "too few channels in each group perform similarly, but do not lead to the best. For local MLP, weight", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "score": 1.0, + "content": "sharing significantly reduces model parameters. These indicate proper weight sharing across channels", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 445, + 303, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 303, + 456 + ], + "score": 1.0, + "content": "is helpful for both local attention and local MLP.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 475 + ], + "score": 1.0, + "content": "We further study the effect of combining the weight sharing pattern for local MLP and depth-wise", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "score": 1.0, + "content": "convolution. For local MLP, Weight sharing across positions means the connection weight is shared", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "for different spatial blocks in local MLP. For convolution, the scheme of sharing weights across", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "score": 1.0, + "content": "channels is similar to the multi-head manner in local attention. The results in Table 4 suggest that:", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "(i) for local MLP, sharing weight across channels reduces the model parameters and sharing across", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "spatial blocks do not have big impact; (ii) For depth-wise convolution, sharing weight across channels", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "score": 1.0, + "content": "does not have big impact, but sharing weight across positions significantly increase the performance.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 544, + 505, + 610 + ], + "lines": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "The window sampling scheme for local MLP and depth-wise convolution is different: local MLP", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 555, + 507, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 507, + 568 + ], + "score": 1.0, + "content": "sparsely samples the windows using the way in Swin Transformer, for reducing the high memory cost,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "score": 1.0, + "content": "and depth-wise convolution densely sample the windows. Weight sharing across positions in local", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "score": 1.0, + "content": "MLP is insufficient for learning translation-equivalent representation, explaining why local MLP", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "score": 1.0, + "content": "with weight sharing across both channels and positions performs lower than depth-wise convolution", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 600, + 297, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 297, + 611 + ], + "score": 1.0, + "content": "with additional weight sharing across channels.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32.5 + }, + { + "type": "text", + "bbox": [ + 107, + 616, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "score": 1.0, + "content": "Dynamic weight. We study how dynamic weight in local attention affects performance. As seen", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 627, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 325, + 639 + ], + "score": 1.0, + "content": "from Table 2, local MLP achieves, the static version,", + "type": "text" + }, + { + "bbox": [ + 325, + 627, + 353, + 637 + ], + "score": 0.88, + "content": "8 0 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 627, + 371, + 639 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 372, + 627, + 399, + 637 + ], + "score": 0.89, + "content": "8 2 . 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 627, + 506, + 639 + ], + "score": 1.0, + "content": "for tiny and base models,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 506, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 257, + 650 + ], + "score": 1.0, + "content": "lower than Swin, the dynamic version,", + "type": "text" + }, + { + "bbox": [ + 258, + 638, + 285, + 649 + ], + "score": 0.88, + "content": "8 1 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 639, + 302, + 650 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 302, + 638, + 329, + 649 + ], + "score": 0.87, + "content": "8 3 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 639, + 506, + 650 + ], + "score": 1.0, + "content": ". This implies that dynamic weight is helpful.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 649, + 493, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 493, + 662 + ], + "score": 1.0, + "content": "The improvements from dynamic weight are also observed for depth-wise convolution (Table 2).", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5 + }, + { + "type": "text", + "bbox": [ + 106, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "We further study the effects of the attention scheme and the linear-projection scheme for dynamic", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "weight computation. The observations from in Table 5 include: the attention mechanism for shifted", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "and sliding window sampling performs similarly; the inhomogeneous dynamic weight computa-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "tion way is better than the attention mechanism (81.8 vs 81.4). We think that the reasons for the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 710, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 504, + 721 + ], + "score": 1.0, + "content": "latter observation include: for the attention mechanism the representation is only block translation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "equivalent other than any translation equivalent; the linear projection-based dynamic weight scheme", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 42.5 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 93, + 503, + 211 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 141, + 81, + 468, + 92 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 140, + 79, + 469, + 93 + ], + "spans": [ + { + "bbox": [ + 140, + 79, + 469, + 93 + ], + "score": 1.0, + "content": "Table 3: Comparison results on COCO object detection and ADE semantic segmentation.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 106, + 93, + 503, + 211 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 93, + 503, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 503, + 211 + ], + "score": 0.953, + "html": "
COCO Object DetectionADE20K Semantic Segmentation
#param.FLOPsApbotAPAPPApmask#param. FLOPsmIoU
Swin-T86M747G50.569.354.943.760M 947G44.5
DW Conv.-T82M730G 49.968.654.343.456M928G45.5
D-DW Conv.-T108M730G 50.569.554.643.783M 928G45.7
I-D-DW Conv.-T84M741G50.869.555.344.058M 939G46.2
Swin-B145M986G51.970.956.545.0121M 1192G48.1
DW Conv.-B132M924G51.169.655.444.2108M 1129G48.3
D-DW Conv.-B219M924G 51.270.055.444.4195M 1129G48.0
I-D-DW Conv.-B137M948G51.870.356.144.8114M 1153G47.8
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SCSPAcc.#param.SCSPAcc.#param.
Local MLPX>80.235.3MDW Conv.X √√81.324.2M
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√√80.324.3M√√81.123.9M
", + "type": "table", + "image_path": "7e62411f3761e8910ac8cdf91ddea921d58f9985711e23a877d9d46ae50b6a6f.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 107, + 235, + 503, + 251.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 107, + 251.0, + 503, + 267.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 107, + 267.0, + 503, + 283.0 + ], + "spans": [], + "index": 8 + } + ] + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 108, + 292, + 227, + 303 + ], + "lines": [ + { + "bbox": [ + 105, + 290, + 228, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 228, + 305 + ], + "score": 1.0, + "content": "3.4 EMPIRICAL ANALYSIS", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 307, + 505, + 362 + ], + "lines": [ + { + "bbox": [ + 106, + 307, + 505, + 319 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 505, + 319 + ], + "score": 1.0, + "content": "Local and channel-separable connection has been shown to be helpful for visual recognition. The", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 317, + 506, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 506, + 330 + ], + "score": 1.0, + "content": "empirical results in Table 2, e.g., local attention performs better than global attention (local connection)", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 329, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 342 + ], + "score": 1.0, + "content": "and depth-wise convolution performs better than convolution (channel-separable connection), also", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 339, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 505, + 354 + ], + "score": 1.0, + "content": "verify it. In the following, we present empirical results for weight sharing and dynamic weight by", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 351, + 251, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 251, + 364 + ], + "score": 1.0, + "content": "taking the tiny models as examples.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 307, + 506, + 364 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 367, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 367, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 381 + ], + "score": 1.0, + "content": "Weight sharing. We study how the performance is affected by the number of channels in each group", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 392 + ], + "score": 1.0, + "content": "across which the weights are shared (the numbers of attention heads at each stage are accordingly", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 390, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 402 + ], + "score": 1.0, + "content": "changed) for local attention and local MLP (learn the weights in each window as model parameters", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "score": 1.0, + "content": "and not shared across windows). Figure 2 shows the effect for (a) local MLP - static weights, and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 412, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "(b) local attention - dynamic weights. One can see that for local attention, too many channels and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 422, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 506, + 435 + ], + "score": 1.0, + "content": "too few channels in each group perform similarly, but do not lead to the best. For local MLP, weight", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "score": 1.0, + "content": "sharing significantly reduces model parameters. These indicate proper weight sharing across channels", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 445, + 303, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 303, + 456 + ], + "score": 1.0, + "content": "is helpful for both local attention and local MLP.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 367, + 506, + 456 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 475 + ], + "score": 1.0, + "content": "We further study the effect of combining the weight sharing pattern for local MLP and depth-wise", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "score": 1.0, + "content": "convolution. For local MLP, Weight sharing across positions means the connection weight is shared", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "for different spatial blocks in local MLP. For convolution, the scheme of sharing weights across", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 508 + ], + "score": 1.0, + "content": "channels is similar to the multi-head manner in local attention. The results in Table 4 suggest that:", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "(i) for local MLP, sharing weight across channels reduces the model parameters and sharing across", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "spatial blocks do not have big impact; (ii) For depth-wise convolution, sharing weight across channels", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 506, + 540 + ], + "score": 1.0, + "content": "does not have big impact, but sharing weight across positions significantly increase the performance.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 460, + 506, + 540 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 544, + 505, + 610 + ], + "lines": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "The window sampling scheme for local MLP and depth-wise convolution is different: local MLP", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 555, + 507, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 507, + 568 + ], + "score": 1.0, + "content": "sparsely samples the windows using the way in Swin Transformer, for reducing the high memory cost,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "score": 1.0, + "content": "and depth-wise convolution densely sample the windows. Weight sharing across positions in local", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "score": 1.0, + "content": "MLP is insufficient for learning translation-equivalent representation, explaining why local MLP", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "score": 1.0, + "content": "with weight sharing across both channels and positions performs lower than depth-wise convolution", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 600, + 297, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 297, + 611 + ], + "score": 1.0, + "content": "with additional weight sharing across channels.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 545, + 507, + 611 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 616, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 505, + 628 + ], + "score": 1.0, + "content": "Dynamic weight. We study how dynamic weight in local attention affects performance. As seen", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 627, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 325, + 639 + ], + "score": 1.0, + "content": "from Table 2, local MLP achieves, the static version,", + "type": "text" + }, + { + "bbox": [ + 325, + 627, + 353, + 637 + ], + "score": 0.88, + "content": "8 0 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 627, + 371, + 639 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 372, + 627, + 399, + 637 + ], + "score": 0.89, + "content": "8 2 . 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 627, + 506, + 639 + ], + "score": 1.0, + "content": "for tiny and base models,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 506, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 257, + 650 + ], + "score": 1.0, + "content": "lower than Swin, the dynamic version,", + "type": "text" + }, + { + "bbox": [ + 258, + 638, + 285, + 649 + ], + "score": 0.88, + "content": "8 1 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 639, + 302, + 650 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 302, + 638, + 329, + 649 + ], + "score": 0.87, + "content": "8 3 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 639, + 506, + 650 + ], + "score": 1.0, + "content": ". This implies that dynamic weight is helpful.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 649, + 493, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 493, + 662 + ], + "score": 1.0, + "content": "The improvements from dynamic weight are also observed for depth-wise convolution (Table 2).", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5, + "bbox_fs": [ + 105, + 616, + 506, + 662 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "We further study the effects of the attention scheme and the linear-projection scheme for dynamic", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "weight computation. The observations from in Table 5 include: the attention mechanism for shifted", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "and sliding window sampling performs similarly; the inhomogeneous dynamic weight computa-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "tion way is better than the attention mechanism (81.8 vs 81.4). We think that the reasons for the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 710, + 504, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 504, + 721 + ], + "score": 1.0, + "content": "latter observation include: for the attention mechanism the representation is only block translation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "equivalent other than any translation equivalent; the linear projection-based dynamic weight scheme", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 297, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 297, + 505, + 309 + ], + "score": 1.0, + "content": "(vector representation for the window) learns better weights than the attention-based scheme (set", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 308, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 505, + 320 + ], + "score": 1.0, + "content": "representation for the window). 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#param.FLOPstop-1 acc.
Twins-PCPVT (Chu et al.,2021a)24M3.8G81.2
Twins-SVT (Chu et al.,2021a)24M2.9G81.7
CoaT-Lite (Xu et al.,2021)20M4.0G81.9
CoaT (Xu et al., 2021)22M12.6G82.1
PVT-v2 (Wang et al., 2021a)25M4.0G82.0
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I-D-DW Conv.26M4.4G81.8
I-D-DW Conv. + DW27M4.4G82.3
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#param.FLOPstop-1 acc.
Twins-PCPVT (Chu et al.,2021a)24M3.8G81.2
Twins-SVT (Chu et al.,2021a)24M2.9G81.7
CoaT-Lite (Xu et al.,2021)20M4.0G81.9
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I-D-DW Conv.26M4.4G81.8
I-D-DW Conv. + DW27M4.4G82.3
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Table 7", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 107, + 186, + 505, + 241 + ], + "lines": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "Multilayer perceptron (MLP) is a fully-connected layer: each neuron (an element at each position", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 196, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 505, + 210 + ], + "score": 1.0, + "content": "and each channel) in one layer is connected with all the neurons in the previous layer5. Convolution", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 208, + 505, + 220 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 505, + 220 + ], + "score": 1.0, + "content": "and separable MLP are sparse versions of MLP. The connection weights can be formulated as a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 219, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 506, + 232 + ], + "score": 1.0, + "content": "tensor (e.g., 3D tensor, two dimension for space and one dimension for channel) and the low-rank", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 230, + 360, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 230, + 360, + 243 + ], + "score": 1.0, + "content": "approximation of the tensor can be used to regularize the MLP.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 246, + 505, + 313 + ], + "lines": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "score": 1.0, + "content": "Convolution is a locally-connected layer, formed by connecting each neuron to the neurons in a small", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 257, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 505, + 271 + ], + "score": 1.0, + "content": "local window with the weights shared across the spatial positions. Depth-wise separable convolution", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 269, + 506, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 431, + 281 + ], + "score": 1.0, + "content": "is formed by decomposing the convolution into two components: one is point-wise", + "type": "text" + }, + { + "bbox": [ + 432, + 269, + 454, + 279 + ], + "score": 0.9, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 269, + 506, + 281 + ], + "score": 1.0, + "content": "convolution,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 280, + 506, + 293 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 506, + 293 + ], + "score": 1.0, + "content": "mixing the information across channels, and the other is depth-wise convolution, mixing the spatial", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 290, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 506, + 303 + ], + "score": 1.0, + "content": "information. Other variants of convolution, such as bottleneck, multi-scale convolution or pyramid,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 302, + 256, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 256, + 314 + ], + "score": 1.0, + "content": "can be regarded as low-rank variants.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 505, + 396 + ], + "lines": [ + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "score": 1.0, + "content": "Separable MLP (e.g., MLP-Mixer and ResMLP) reshapes the 3D tensor into a 2D format with the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 330, + 506, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 506, + 342 + ], + "score": 1.0, + "content": "spatial dimension and channel dimension. 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Regarding", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 352, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 505, + 364 + ], + "score": 1.0, + "content": "channel sparsity, the neurons in the same channel form a group, and an MLP is performed over each", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "group with the MLP parameters shared across groups, forming the first sparse MLP (spatial/token", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 372, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 505, + 387 + ], + "score": 1.0, + "content": "mixing). 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Local Vision Transformer is a", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "spatially-sparser version of Vision Transformer: each output neuron is connected to the input neurons", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 434, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 447 + ], + "score": 1.0, + "content": "in a local window. PVT (Wang et al., 2021b) is a pyramid (spatial sampling/ low-rank) variant of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 444, + 189, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 189, + 458 + ], + "score": 1.0, + "content": "Vision Transformer.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 461, + 505, + 506 + ], + "lines": [ + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "Depth-wise separable convolution can also be regarded as a spatially-sparser version of separable", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "MLP. 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There might be other definitions.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 80, + 183, + 96 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 187, + 100 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 187, + 100 + ], + "score": 1.0, + "content": "APPENDIX", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 108, + 110, + 222, + 124 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 224, + 126 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 224, + 126 + ], + "score": 1.0, + "content": "A RELATION GRAPH", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 107, + 136, + 505, + 181 + ], + "lines": [ + { + "bbox": [ + 105, + 136, + 506, + 148 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 506, + 148 + ], + "score": 1.0, + "content": "We present a relation graph in Figure 3 to describe the relation between convolution, depth-wise", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 147, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 300, + 159 + ], + "score": 1.0, + "content": "separable convolution (depth-wise convolution", + "type": "text" + }, + { + "bbox": [ + 301, + 147, + 335, + 158 + ], + "score": 0.89, + "content": "+ 1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 147, + 505, + 159 + ], + "score": 1.0, + "content": "convolution), Vision Transformer, Local", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 158, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 505, + 171 + ], + "score": 1.0, + "content": "Vision Transformer, as well as multilayer perceptron (MLP), Separable MLP in terms of sparse", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 170, + 342, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 342, + 181 + ], + "score": 1.0, + "content": "connectivity, weight sharing, and dynamic weight. Table 7", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3.5, + "bbox_fs": [ + 105, + 136, + 506, + 181 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 186, + 505, + 241 + ], + "lines": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "Multilayer perceptron (MLP) is a fully-connected layer: each neuron (an element at each position", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 196, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 505, + 210 + ], + "score": 1.0, + "content": "and each channel) in one layer is connected with all the neurons in the previous layer5. Convolution", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 208, + 505, + 220 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 505, + 220 + ], + "score": 1.0, + "content": "and separable MLP are sparse versions of MLP. The connection weights can be formulated as a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 219, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 506, + 232 + ], + "score": 1.0, + "content": "tensor (e.g., 3D tensor, two dimension for space and one dimension for channel) and the low-rank", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 230, + 360, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 230, + 360, + 243 + ], + "score": 1.0, + "content": "approximation of the tensor can be used to regularize the MLP.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 187, + 506, + 243 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 246, + 505, + 313 + ], + "lines": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 505, + 259 + ], + "score": 1.0, + "content": "Convolution is a locally-connected layer, formed by connecting each neuron to the neurons in a small", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 257, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 505, + 271 + ], + "score": 1.0, + "content": "local window with the weights shared across the spatial positions. 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Sparse between positionsSparse between channelsWeight sharing acrossDynamic weight
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Local attention√
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D-DW-Conv.<√√√
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MLP Attention√
Spatial-mixing MLP†1
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The weight depends", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 258, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 276, + 272 + ], + "score": 1.0, + "content": "on the features at the same position, e.g.,", + "type": "text" + }, + { + "bbox": [ + 277, + 261, + 299, + 270 + ], + "score": 0.89, + "content": "w _ { i - k }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 258, + 362, + 272 + ], + "score": 1.0, + "content": "corresponds to", + "type": "text" + }, + { + "bbox": [ + 363, + 260, + 384, + 270 + ], + "score": 0.91, + "content": "\\mathbf { x } _ { i - k }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 258, + 505, + 272 + ], + "score": 1.0, + "content": ". 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The weight depends", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 258, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 276, + 272 + ], + "score": 1.0, + "content": "on the features at the same position, e.g.,", + "type": "text" + }, + { + "bbox": [ + 277, + 261, + 299, + 270 + ], + "score": 0.89, + "content": "w _ { i - k }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 258, + 362, + 272 + ], + "score": 1.0, + "content": "corresponds to", + "type": "text" + }, + { + "bbox": [ + 363, + 260, + 384, + 270 + ], + "score": 0.91, + "content": "\\mathbf { x } _ { i - k }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 258, + 505, + 272 + ], + "score": 1.0, + "content": ". It in some sense regards the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 270, + 405, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 405, + 282 + ], + "score": 1.0, + "content": "positions in the window as a set form, losing the spatial order information.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 104, + 244, + 507, + 282 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 286, + 226, + 298 + ], + "lines": [ + { + "bbox": [ + 106, + 284, + 227, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 227, + 300 + ], + "score": 1.0, + "content": "We rewrite it as the following", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10, + "bbox_fs": [ + 106, + 284, + 227, + 300 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 250, + 304, + 360, + 394 + ], + "lines": [ + { + "bbox": [ + 250, + 304, + 360, + 394 + ], + "spans": [ + { + "bbox": [ + 250, + 304, + 360, + 394 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\Theta _ { d } = \\left[ \\begin{array} { c } { ( \\mathbf { x } _ { i - K } ) ^ { \\top } } \\\\ { \\vdots } \\\\ { ( \\mathbf { x } _ { i } ) ^ { \\top } } \\\\ { \\vdots } \\\\ { ( \\mathbf { x } _ { i + K } ) ^ { \\top } } \\end{array} \\right] \\mathbf { P } _ { k } ^ { \\top } \\mathbf { P } _ { q } , } \\end{array}", + "type": "interline_equation", + "image_path": "3ae446499be6857a0d3f848c2ebf201d562a2b6c03433b7aa5e3dc505c4859c5.jpg" + } + ] + } + ], + "index": 11.5, + "virtual_lines": [ + { + "bbox": [ + 250, + 304, + 360, + 349.0 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 250, + 349.0, + 360, + 394.0 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 399, + 505, + 423 + ], + "lines": [ + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 277, + 412 + ], + "score": 1.0, + "content": "from which we can see that the parameters", + "type": "text" + }, + { + "bbox": [ + 277, + 400, + 291, + 411 + ], + "score": 0.9, + "content": "\\Theta _ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "is dynamically predicted. 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K - 1 } \\right) ^ { \\top } } \\\\ { \\left( \\mathbf { x } _ { i - K } \\right) ^ { \\top } } \\\\ { \\vdots } \\\\ { \\left( \\mathbf { x } _ { i } \\right) ^ { \\top } } \\\\ { \\vdots } \\\\ { \\left( \\mathbf { x } _ { i + K } \\right) ^ { \\top } } \\end{array} \\right] \\mathbf { P } _ { k } ^ { \\top } \\mathbf { P } _ { q } \\left[ \\mathbf { x } _ { i - 1 } \\quad \\mathbf { x } _ { i } \\quad \\mathbf { x } _ { i + 1 } \\right] \\left[ \\begin{array} { c } { a _ { 1 } } \\\\ { a _ { 2 } } \\\\ { a _ { 3 } } \\end{array} \\right] . } \\end{array}", + "type": "interline_equation", + "image_path": "b0ec78a82f578aa30284350c03f778c5923f45dbae40674b5fb7bfca065ee01f.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 111, + 278, + 502, + 317.6666666666667 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 111, + 317.6666666666667, + 502, + 357.33333333333337 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 111, + 357.33333333333337, + 502, + 397.00000000000006 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 412, + 308, + 425 + ], + "lines": [ + { + "bbox": [ + 105, + 412, + 309, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 309, + 426 + ], + "score": 1.0, + "content": "It can be generalized to using normal convolution:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "interline_equation", + "bbox": [ + 156, + 430, + 456, + 543 + ], + "lines": [ + { + "bbox": [ + 156, + 430, + 456, + 543 + ], + "spans": [ + { + "bbox": [ + 156, + 430, + 456, + 543 + ], + "score": 0.95, + "content": "\\left[ \\begin{array} { c } { \\boldsymbol { w } _ { i - 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downsp.rate(output size)SwinDW Conv.
stage 14×(56×56)concat 4×4, linear 96-d, LNconcat 4×4, linear 96-d, LN
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stage 28×(28×28)concat 2×2, linear 192-d,LNconcat 2×2, linear 192-d,LN
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stage 316×(14×14)concat 2×2, linear 384-d,LNconcat 2×2,linear 384-d,LN
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stage 432×(7×7)concat 2×2, linear 768-d,LNconcat 2×2, linear 768-d,LN
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stage 41×1LN, AvgPool. 1 ×1linear classifierLN, AvgPool. 1 ×1linear classifier
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downsp.rate(output size)SwinDW Conv.
stage 14×(56×56)concat 4×4, linear 96-d, LNconcat 4×4, linear 96-d, LN
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methodimg.size #param.FLOPs throughput (img./s)top-1 acc. real acc.
Convolution: local connection
ResNet-38 † (Wang et al.,2020)224²28M3.8G2123.775.4-
ResNet-72 † (Wang et al.,2020)224248M7.5G623.076.7-
ResNet-106 † (Wang et al., 2020)224265M11.1G452.877.3-
Bottleneck: convolution with low rank
ResNet-50 (He et al.,2016)224226M4.1G1128.376.282.5
ResNet-101 (He et al.,2016)224²45M7.9G652.077.483.7
ResNet-152 (He et al.,2016)224260M11.6G456.778.384.1
Pyramid: convolution with pyramid (spatial low rank) features.
HRNet-W18 (Wang et al., 2020)224221M4.0G-76.8-
HRNet-W32 (Wang et al.,2020)224241M8.3G78.5-
HRNet-W48 (Wang et al., 2020)224278M16.1G179.31
Channel and spatial separable MLP, spatial separable MLP = point-wise 1 ×1 convolution
Mixer-B/16 (Tolstikhin et al.,2021)22446M1-76.482.4
Mixer-L/16 (Tolstikhin et al.,2021)224²189M171.877.1
ResMLP-12(Touvron et al., 2021)224²15M3.0G76.683.3
ResMLP-24 (Touvron et al., 2021)224230M6.0G79.485.3
ResMLP-36 (Touvron et al.,2021)224²45M8.9G79.785.6
gMLP-Ti (Liu et al., 2021a)2242 224²6M1.4G72.01
gMLP-S (Liu et al.,2021a)224220M4.5G79.41
gMLP-B (Liu et al., 2021a)73M15.8G=81.6-
Global attention: dynamic channel separable MLP + spatial separable MLP
ViT-B/16 (Dosovitskiy et al., 2021)384286M55.4G83.477.983.6
ViT-L/16 (Dosovitskiy et al., 2021)3842307M190.7G26.576.582.2
DeiT-S (Touvron et al.,2020)224²22M4.6G947.379.885.7
DeiT-B (Touvron et al., 2020)224²86M17.5G298.281.886.7
DeiT-B (Touvron et al., 2020)384286M55.4G82.783.187.7
Pyramid attention: perform attention with spatial low rank
PVT-S (Wang et al., 2021b)22425M3.8G-79.8-
PVT-M (Wang et al., 2021b)224²44M6.7G=81.2-
PVT-L (Wang et al., 2021b)224261M9.8G=81.71
Local MLP: perform static separable MLP in local small windows
Swin-Local MLP-T224226M3.8G861.080.386.1
Swin-Local MLP-B224279M12.9G321.282.286.9
Local attention:perform attention in local small windows
Swin-T (Liu et al., 2021b)22428M4.5G713.581.386.6
Swin-B (Liu et al.,2021b)224288M15.4G263.083.387.9
Depth-wise convolution + point-wise 1 ×1 convolution
DW-Conv.-T224224M3.8G928.781.386.8
DW-Conv.-B224274M12.9G327.683.287.9
D-DW-Conv.-T224²51M3.8G897.081.987.3
D-DW-Conv.-B224²162M13.0G322.483.287.9
I-D-DW-Conv.-T224226M4.4G685.381.887.1
I-D-DW-Conv.-B224280M14.3G244.983.488.0
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methodimg.size #param.FLOPs throughput (img./s)top-1 acc. real acc.
Convolution: local connection
ResNet-38 † (Wang et al.,2020)224²28M3.8G2123.775.4-
ResNet-72 † (Wang et al.,2020)224248M7.5G623.076.7-
ResNet-106 † (Wang et al., 2020)224265M11.1G452.877.3-
Bottleneck: convolution with low rank
ResNet-50 (He et al.,2016)224226M4.1G1128.376.282.5
ResNet-101 (He et al.,2016)224²45M7.9G652.077.483.7
ResNet-152 (He et al.,2016)224260M11.6G456.778.384.1
Pyramid: convolution with pyramid (spatial low rank) features.
HRNet-W18 (Wang et al., 2020)224221M4.0G-76.8-
HRNet-W32 (Wang et al.,2020)224241M8.3G78.5-
HRNet-W48 (Wang et al., 2020)224278M16.1G179.31
Channel and spatial separable MLP, spatial separable MLP = point-wise 1 ×1 convolution
Mixer-B/16 (Tolstikhin et al.,2021)22446M1-76.482.4
Mixer-L/16 (Tolstikhin et al.,2021)224²189M171.877.1
ResMLP-12(Touvron et al., 2021)224²15M3.0G76.683.3
ResMLP-24 (Touvron et al., 2021)224230M6.0G79.485.3
ResMLP-36 (Touvron et al.,2021)224²45M8.9G79.785.6
gMLP-Ti (Liu et al., 2021a)2242 224²6M1.4G72.01
gMLP-S (Liu et al.,2021a)224220M4.5G79.41
gMLP-B (Liu et al., 2021a)73M15.8G=81.6-
Global attention: dynamic channel separable MLP + spatial separable MLP
ViT-B/16 (Dosovitskiy et al., 2021)384286M55.4G83.477.983.6
ViT-L/16 (Dosovitskiy et al., 2021)3842307M190.7G26.576.582.2
DeiT-S (Touvron et al.,2020)224²22M4.6G947.379.885.7
DeiT-B (Touvron et al., 2020)224²86M17.5G298.281.886.7
DeiT-B (Touvron et al., 2020)384286M55.4G82.783.187.7
Pyramid attention: perform attention with spatial low rank
PVT-S (Wang et al., 2021b)22425M3.8G-79.8-
PVT-M (Wang et al., 2021b)224²44M6.7G=81.2-
PVT-L (Wang et al., 2021b)224261M9.8G=81.71
Local MLP: perform static separable MLP in local small windows
Swin-Local MLP-T224226M3.8G861.080.386.1
Swin-Local MLP-B224279M12.9G321.282.286.9
Local attention:perform attention in local small windows
Swin-T (Liu et al., 2021b)22428M4.5G713.581.386.6
Swin-B (Liu et al.,2021b)224288M15.4G263.083.387.9
Depth-wise convolution + point-wise 1 ×1 convolution
DW-Conv.-T224224M3.8G928.781.386.8
DW-Conv.-B224274M12.9G327.683.287.9
D-DW-Conv.-T224²51M3.8G897.081.987.3
D-DW-Conv.-B224²162M13.0G322.483.287.9
I-D-DW-Conv.-T224226M4.4G685.381.887.1
I-D-DW-Conv.-B224280M14.3G244.983.488.0
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These results also verify that locality-based sparsity pattern", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "score": 1.0, + "content": "(adopted in depth-wise convolution and local attention) besides sparsity between channels/spatial", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 460, + 360, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 360, + 473 + ], + "score": 1.0, + "content": "positions still facilitates the network training for ImageNet-1K.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27.5 + }, + { + "type": "text", + "bbox": [ + 107, + 477, + 505, + 565 + ], + "lines": [ + { + "bbox": [ + 106, + 477, + 506, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 506, + 489 + ], + "score": 1.0, + "content": "Results on large scale pre-training. 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We use learning", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 358, + 504, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 123, + 371 + ], + "score": 1.0, + "content": "rate", + "type": "text" + }, + { + "bbox": [ + 123, + 358, + 145, + 369 + ], + "score": 0.9, + "content": "1 0 ^ { - 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 145, + 358, + 203, + 371 + ], + "score": 1.0, + "content": ", weight decay", + "type": "text" + }, + { + "bbox": [ + 203, + 358, + 225, + 369 + ], + "score": 0.91, + "content": "1 \\bar { 0 } ^ { - 8 }", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 358, + 432, + 371 + ], + "score": 1.0, + "content": "and stochastic depth ratio 0.1 for 30 epochs for both", + "type": "text" + }, + { + "bbox": [ + 432, + 359, + 454, + 369 + ], + "score": 0.89, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 358, + 471, + 371 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 472, + 359, + 504, + 369 + ], + "score": 0.89, + "content": "1 2 \\times 1 2", + "type": "inline_equation" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 369, + 148, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 148, + 381 + ], + "score": 1.0, + "content": "windows.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 336, + 505, + 381 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 400, + 352, + 412 + ], + "lines": [ + { + "bbox": [ + 105, + 399, + 353, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 353, + 415 + ], + "score": 1.0, + "content": "F ADDITIONAL EXPERIMENTS AND ANALYSIS", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 426, + 505, + 471 + ], + "lines": [ + { + "bbox": [ + 105, + 427, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 505, + 440 + ], + "score": 1.0, + "content": "More results on ImageNet classification. We give more experimental results with different sparse", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 437, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 451 + ], + "score": 1.0, + "content": "connection strategies, as shown in Table 9. These results also verify that locality-based sparsity pattern", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "score": 1.0, + "content": "(adopted in depth-wise convolution and local attention) besides sparsity between channels/spatial", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 460, + 360, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 360, + 473 + ], + "score": 1.0, + "content": "positions still facilitates the network training for ImageNet-1K.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 427, + 505, + 473 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 477, + 505, + 565 + ], + "lines": [ + { + "bbox": [ + 106, + 477, + 506, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 506, + 489 + ], + "score": 1.0, + "content": "Results on large scale pre-training. Transformers (Liu et al., 2021b; Dosovitskiy et al., 2021)", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 488, + 507, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 488, + 507, + 500 + ], + "score": 1.0, + "content": "show higher performance compared with the previous convolutional networks with large scale pre-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "training. We further study the performance on ImageNet-22K pre-training. We first train the model", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 510, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 522 + ], + "score": 1.0, + "content": "on ImageNet-22K dataset which has about 14.2 million images, and then fine-tune the model on", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "score": 1.0, + "content": "ImageNet-1K classification, downstream detection and segmentation tasks. The same training settings", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 531, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 505, + 544 + ], + "score": 1.0, + "content": "with Swin transformer are used in all tasks. The fine-tuning results in Table 10 and Table 11 indicate", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 543, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 505, + 555 + ], + "score": 1.0, + "content": "the (dynamic) depth-wise convolution based networks could get the performance comparable to Swin", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 554, + 272, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 272, + 567 + ], + "score": 1.0, + "content": "transformer with large scale pre-training.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 477, + 507, + 567 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 570, + 505, + 615 + ], + "lines": [ + { + "bbox": [ + 106, + 571, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 571, + 506, + 583 + ], + "score": 1.0, + "content": "Cooperating with different normalization functions. 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ImageNet-1K fine-tuning
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COCO fine-tuningADE20K fine-tuning
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Layer Norm.Batch Norm.Centering calibrated Batch Norm.Top-1 Acc.
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The remaining structures are unchanged", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "and the same training setting is used as the original papers. The experimental results are shown in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 428, + 403, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 403, + 442 + ], + "score": 1.0, + "content": "Tab 13 and the observations are the same as the Swin Transformer design.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 506, + 490 + ], + "lines": [ + { + "bbox": [ + 105, + 445, + 507, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 168, + 458 + ], + "score": 1.0, + "content": "Retraining on", + "type": "text" + }, + { + "bbox": [ + 168, + 446, + 212, + 456 + ], + "score": 0.88, + "content": "3 8 4 \\times 3 8 4", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 445, + 507, + 458 + ], + "score": 1.0, + "content": "images. Similar to (Liu et al., 2021b), we study the performance of fine-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 456, + 507, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 246, + 469 + ], + "score": 1.0, + "content": "tuning the models: first learn with", + "type": "text" + }, + { + "bbox": [ + 246, + 457, + 290, + 467 + ], + "score": 0.89, + "content": "2 2 4 \\times 2 2 4", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 456, + 460, + 469 + ], + "score": 1.0, + "content": "images, then fine-tune on large images of", + "type": "text" + }, + { + "bbox": [ + 460, + 457, + 503, + 467 + ], + "score": 0.89, + "content": "3 8 4 \\times 3 8 4", + "type": "inline_equation" + }, + { + "bbox": [ + 504, + 456, + 507, + 469 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 288, + 480 + ], + "score": 1.0, + "content": "We study two cases: (1) keep the window size", + "type": "text" + }, + { + "bbox": [ + 289, + 468, + 312, + 478 + ], + "score": 0.89, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "unchanged; and (2) upsample the kernel weights", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 477, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 128, + 492 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 128, + 479, + 150, + 489 + ], + "score": 0.89, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 477, + 160, + 492 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 160, + 479, + 192, + 489 + ], + "score": 0.91, + "content": "1 2 \\times 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 477, + 506, + 492 + ], + "score": 1.0, + "content": "as done in (Liu et al., 2021b) for upsampling the relative positional embeddings.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 495, + 505, + 550 + ], + "lines": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 204, + 507 + ], + "score": 1.0, + "content": "The results are in Table", + "type": "text" + }, + { + "bbox": [ + 204, + 495, + 219, + 506 + ], + "score": 0.86, + "content": "1 4 ^ { 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 495, + 384, + 507 + ], + "score": 1.0, + "content": ". In the case of keeping the window size", + "type": "text" + }, + { + "bbox": [ + 384, + 496, + 408, + 506 + ], + "score": 0.88, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "unchanged, depth-wise", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 506, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 376, + 519 + ], + "score": 1.0, + "content": "convolution (DW) performs better. 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We suspect that this is because upsampling the kernel weights is not a good", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "score": 1.0, + "content": "starting for fine-tuning. In Swin Transformer, using a larger window size improves the performance.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 539, + 502, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 502, + 552 + ], + "score": 1.0, + "content": "We believe that this is because the local attention mechanism is suitable for variable window sizes.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 556, + 505, + 612 + ], + "lines": [ + { + "bbox": [ + 106, + 556, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 505, + 568 + ], + "score": 1.0, + "content": "Cooperating with SE. 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COCO fine-tuningADE20K fine-tuning
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Layer Norm.Batch Norm.Centering calibrated Batch Norm.Top-1 Acc.
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The remaining structures are unchanged", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "and the same training setting is used as the original papers. The experimental results are shown in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 428, + 403, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 403, + 442 + ], + "score": 1.0, + "content": "Tab 13 and the observations are the same as the Swin Transformer design.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 352, + 506, + 442 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 506, + 490 + ], + "lines": [ + { + "bbox": [ + 105, + 445, + 507, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 168, + 458 + ], + "score": 1.0, + "content": "Retraining on", + "type": "text" + }, + { + "bbox": [ + 168, + 446, + 212, + 456 + ], + "score": 0.88, + "content": "3 8 4 \\times 3 8 4", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 445, + 507, + 458 + ], + "score": 1.0, + "content": "images. Similar to (Liu et al., 2021b), we study the performance of fine-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 456, + 507, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 246, + 469 + ], + "score": 1.0, + "content": "tuning the models: first learn with", + "type": "text" + }, + { + "bbox": [ + 246, + 457, + 290, + 467 + ], + "score": 0.89, + "content": "2 2 4 \\times 2 2 4", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 456, + 460, + 469 + ], + "score": 1.0, + "content": "images, then fine-tune on large images of", + "type": "text" + }, + { + "bbox": [ + 460, + 457, + 503, + 467 + ], + "score": 0.89, + "content": "3 8 4 \\times 3 8 4", + "type": "inline_equation" + }, + { + "bbox": [ + 504, + 456, + 507, + 469 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 288, + 480 + ], + "score": 1.0, + "content": "We study two cases: (1) keep the window size", + "type": "text" + }, + { + "bbox": [ + 289, + 468, + 312, + 478 + ], + "score": 0.89, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "unchanged; and (2) upsample the kernel weights", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 477, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 128, + 492 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 128, + 479, + 150, + 489 + ], + "score": 0.89, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 150, + 477, + 160, + 492 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 160, + 479, + 192, + 489 + ], + "score": 0.91, + "content": "1 2 \\times 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 477, + 506, + 492 + ], + "score": 1.0, + "content": "as done in (Liu et al., 2021b) for upsampling the relative positional embeddings.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 445, + 507, + 492 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 495, + 505, + 550 + ], + "lines": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 204, + 507 + ], + "score": 1.0, + "content": "The results are in Table", + "type": "text" + }, + { + "bbox": [ + 204, + 495, + 219, + 506 + ], + "score": 0.86, + "content": "1 4 ^ { 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 495, + 384, + 507 + ], + "score": 1.0, + "content": ". In the case of keeping the window size", + "type": "text" + }, + { + "bbox": [ + 384, + 496, + 408, + 506 + ], + "score": 0.88, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "unchanged, depth-wise", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 506, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 376, + 519 + ], + "score": 1.0, + "content": "convolution (DW) performs better. When using a larger window size", + "type": "text" + }, + { + "bbox": [ + 376, + 507, + 408, + 517 + ], + "score": 0.9, + "content": "1 2 \\times 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 506, + 506, + 519 + ], + "score": 1.0, + "content": ", depth-wise convolution", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 517, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 188, + 531 + ], + "score": 1.0, + "content": "performs worse than", + "type": "text" + }, + { + "bbox": [ + 188, + 518, + 209, + 528 + ], + "score": 0.88, + "content": "7 \\times 7", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 517, + 505, + 531 + ], + "score": 1.0, + "content": ". We suspect that this is because upsampling the kernel weights is not a good", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "score": 1.0, + "content": "starting for fine-tuning. In Swin Transformer, using a larger window size improves the performance.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 539, + 502, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 502, + 552 + ], + "score": 1.0, + "content": "We believe that this is because the local attention mechanism is suitable for variable window sizes.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 495, + 506, + 552 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 556, + 505, + 612 + ], + "lines": [ + { + "bbox": [ + 106, + 556, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 505, + 568 + ], + "score": 1.0, + "content": "Cooperating with SE. Squeeze-and-excitation (Hu et al., 2018b) (SE) is a parameter- and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 568, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 506, + 580 + ], + "score": 1.0, + "content": "computation-efficient dynamic module, initially designed for improving the ResNet performance.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "The results in Table 15 show that depth-wise convolution (DW), a static module, benefits from the SE", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 590, + 504, + 602 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 504, + 602 + ], + "score": 1.0, + "content": "module, while Swin Transformer, already a dynamic module, does not benefit from dynamic module", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 600, + 365, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 365, + 613 + ], + "score": 1.0, + "content": "SE. The reason is still unclear, and might lie in the optimization.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 556, + 506, + 613 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 629, + 236, + 642 + ], + "lines": [ + { + "bbox": [ + 106, + 628, + 237, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 237, + 644 + ], + "score": 1.0, + "content": "G POTENTIAL STUDIES", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 505, + 700 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 279, + 668 + ], + "score": 1.0, + "content": "Complexity balance between point-wise", + "type": "text" + }, + { + "bbox": [ + 280, + 656, + 307, + 666 + ], + "score": 0.82, + "content": "( 1 \\times 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 308, + 655, + 506, + 668 + ], + "score": 1.0, + "content": "convolution and depth-wise (spatial) convolu-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 667, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 292, + 678 + ], + "score": 1.0, + "content": "tion. Depth-wise convolution takes only about", + "type": "text" + }, + { + "bbox": [ + 293, + 667, + 307, + 677 + ], + "score": 0.86, + "content": "2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 308, + 667, + 505, + 678 + ], + "score": 1.0, + "content": "computation in the depth-wise convolution-based", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 355, + 690 + ], + "score": 1.0, + "content": "architecture. The major computation complexity comes from", + "type": "text" + }, + { + "bbox": [ + 356, + 678, + 379, + 688 + ], + "score": 0.89, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 678, + 505, + 690 + ], + "score": 1.0, + "content": "convolutions. The solutions to", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 689, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 209, + 700 + ], + "score": 1.0, + "content": "this issue could be: group", + "type": "text" + }, + { + "bbox": [ + 209, + 689, + 232, + 699 + ], + "score": 0.89, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 689, + 505, + 700 + ], + "score": 1.0, + "content": "convolution studied in IGC (Zhang et al., 2017; Sun et al., 2018), and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 368, + 506, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 368, + 506, + 381 + ], + "score": 1.0, + "content": "channel-wise weighting (like SENet) studied in Lite-HRNet (Yu et al., 2021) and EfficientNet (Tan &", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 380, + 393, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 393, + 393 + ], + "score": 1.0, + "content": "Le, 2019; 2021), or simply add more depth-wise (spatial) convolutions.", + "type": "text", + "cross_page": true + } + ], + "index": 19 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 655, + 506, + 700 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 185, + 123, + 426, + 196 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 80, + 506, + 113 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 79, + 507, + 93 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 507, + 93 + ], + "score": 1.0, + "content": "Table 13: Comparison between local attention and depth-wise convolution in VOLO (Yuan et al.,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 91, + 505, + 104 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 505, + 104 + ], + "score": 1.0, + "content": "2021c) and SVT (Chu et al., 2021a) architecture. 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#param.FLOPstop-1 acc.
VOLO-d1 (Yuan et al.,2021c)27M7.0G84.1
VOLO (Local SA)-d127M7.2G84.2
DW Conv.-d126M6.9G84.2
SVT-S (Chu et al., 2021a)24M2.8G81.7
DW Conv.-S22M2.7G81.9
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modelws.#param.FLOPsAcc.
Swin7×7 12×1228M 28M14.4G 14.2G81.8 82.4
DW Conv.7×7 12×1224M 25M11.1G 11.5G82.2 82.1
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modelSE#param.FLOPsAcc.
Swin√28M4.5G81.3
29M4.5G81.2
DW Conv.√24M3.8G81.3
24M3.8G81.7
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Attention weights in attention can be regarded as channel maps.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "The operations, such as convolution or simple weighting, can be applied to the attention weights. The", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 418, + 503, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 297, + 432 + ], + "score": 1.0, + "content": "resT approach (Zhang & Yang, 2021) performs", + "type": "text" + }, + { + "bbox": [ + 297, + 419, + 321, + 429 + ], + "score": 0.89, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 418, + 503, + 432 + ], + "score": 1.0, + "content": "convolutions over the attention weight maps.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 435, + 505, + 480 + ], + "lines": [ + { + "bbox": [ + 106, + 435, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 506, + 448 + ], + "score": 1.0, + "content": "Dynamic weights. 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#param.FLOPstop-1 acc.
VOLO-d1 (Yuan et al.,2021c)27M7.0G84.1
VOLO (Local SA)-d127M7.2G84.2
DW Conv.-d126M6.9G84.2
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modelws.#param.FLOPsAcc.
Swin7×7 12×1228M 28M14.4G 14.2G81.8 82.4
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modelSE#param.FLOPsAcc.
Swin√28M4.5G81.3
29M4.5G81.2
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methodimg. size #param. FLOPs throughput (img./s) top-1 acc.real acc.
Bottleneck:convolution with low rank
ResNet-50 (He et al.,2016)224226M4.1G1128.376.282.5
ResNet-101 (He et al., 2016)224²45M7.9G652.077.483.7
ResNet-152 (He et al., 2016)224260M11.6G456.778.384.1
Channel and spatial separable MLP, spatial separable MLP=point-wise1 ×1 convolution
Mixer-B/16 (Tolstikhin et al.,2021)224246M--76.482.4
Mixer-L/16(Tolstikhin et al.,2021)224²189M-71.877.1
ResMLP-12 (Touvron et al., 2021)224²15M3.0G=76.683.3
ResMLP-24 (Touvron et al., 2021)224²30M6.0G79.485.3
ResMLP-36 (Touvron et al.,2021)224245M8.9G-79.785.6
Global attention:dynamicchannel separable MLP+ spatial separable MLP
ViT-B/16 (Dosovitskiy et al.,2021)384286M55.4G83.477.983.6
ViT-L/16 (Dosovitskiy et al.,2021)3842307M190.7G26.576.582.2
DeiT-S (Touvron et al., 2020)224²22M4.6G947.379.885.7
DeiT-B (Touvron et al.,2020)224²86M17.5G298.281.886.7
DeiT-B (Touvron et al., 2020)384286M55.4G82.783.187.7
Local MLP: perform static separable MLP in local small windows
Swin-Local MLP-T224226M3.8G861.080.386.1
Swin-Local MLP-B224²79M12.9G321.282.286.9
Local attention:perform attention inlocal small windows
Swin-T (Liu et al.,2021b)224²28M4.5G713.581.386.6
Swin-B (Liu et al., 2021b)224288M15.4G263.083.387.9
Depth-wise convolution + point-wise 1 ×1 convolution
DW-Conv.-T224224M3.8G928.781.386.8
DW-Conv.-B224274M12.9G327.683.287.9
D-DW-Conv.-T224²51M3.8G897.081.987.3
D-DW-Conv.-B224²162M13.0G322.483.287.9
I-D-DW-Conv.-T224226M4.4G685.381.887.1
I-D-DW-Conv.-B224280M14.3G244.983.488.0
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COCO Object DetectionADE20K Semantic Segmentation
#param.FLOPsApbotAPAPPApmask#param. FLOPsmIoU
Swin-T86M747G50.569.354.943.760M 947G44.5
DW Conv.-T82M730G 49.968.654.343.456M928G45.5
D-DW Conv.-T108M730G 50.569.554.643.783M 928G45.7
I-D-DW Conv.-T84M741G50.869.555.344.058M 939G46.2
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DW Conv.-B132M924G51.169.655.444.2108M 1129G48.3
D-DW Conv.-B219M924G 51.270.055.444.4195M 1129G48.0
I-D-DW Conv.-B137M948G51.870.356.144.8114M 1153G47.8
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SCSPAcc.#param.SCSPAcc.#param.
Local MLPX>80.235.3MDW Conv.X √√81.324.2M
√X80.326.2M×80.326.2M
√√80.324.3M√√81.123.9M
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#param.FLOPstop-1 acc.
Twins-PCPVT (Chu et al.,2021a)24M3.8G81.2
Twins-SVT (Chu et al.,2021a)24M2.9G81.7
CoaT-Lite (Xu et al.,2021)20M4.0G81.9
CoaT (Xu et al., 2021)22M12.6G82.1
PVT-v2 (Wang et al., 2021a)25M4.0G82.0
Shuffle Transformer (Huang et al.,2021)29M4.6G82.5
I-D-DW Conv.26M4.4G81.8
I-D-DW Conv. + DW27M4.4G82.3
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Sparse between positionsSparse between channelsWeight sharing acrossDynamic weight
non-localfullpositionchannel
Local MLP√√公
Local attention√
DW-Conv.<</v√√
D-DW-Conv.<√√√
Conv.√
MLP Attention√
Spatial-mixing MLP†1
1 ×1 Conv.‡：
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downsp.rate(output size)SwinDW Conv.
stage 14×(56×56)concat 4×4, linear 96-d, LNconcat 4×4, linear 96-d, LN
LN, linear 96x3-dlocal sa. 7×7,head 3linear 96-dLN, linear 384-dGELU, linear 96-d×2linear 96-d, BN, ReLUdepthwise conv.7×7,BN,ReLUlinear 96-d, BNBN, linear 384-dGELU, linear 96-d×2
stage 28×(28×28)concat 2×2, linear 192-d,LNconcat 2×2, linear 192-d,LN
LN, linear 192x3-dlocal sa. 7×7, head 6linear 192-dLN, linear 768-dGELU, linear 192-d×2linear 192-d, BN,ReLUdepthwise conv. 7×7, BN,ReLUlinear 192-d, BNBN, linear 768-dGELU, linear 192-d×2
stage 316×(14×14)concat 2×2, linear 384-d,LNconcat 2×2,linear 384-d,LN
LN, linear 384x3-dlocal sa. 7×7, head 12linear 384-dLN,linear 1536-dGELU, linear 384-d×6linear 384-d, BN,ReLUdepthwise conv. 7×7, BN, ReLUlinear 384-d, BNBN, linear 1536-dGELU,linear 384-d×6
stage 432×(7×7)concat 2×2, linear 768-d,LNconcat 2×2, linear 768-d,LN
LN, linear 768x3-dlocal sa. 7×7, head 24linear 768-dLN, linear 3072-dGELU,linear 768-d×2linear 768-d,BN,ReLUdepthwise conv.7×7,BN, ReLUlinear 768-d,BNBN, linear 3072-dGELU, linear 768-d×2
stage 41×1LN, AvgPool. 1 ×1linear classifierLN, AvgPool. 1 ×1linear classifier
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methodimg.size #param.FLOPs throughput (img./s)top-1 acc. real acc.
Convolution: local connection
ResNet-38 † (Wang et al.,2020)224²28M3.8G2123.775.4-
ResNet-72 † (Wang et al.,2020)224248M7.5G623.076.7-
ResNet-106 † (Wang et al., 2020)224265M11.1G452.877.3-
Bottleneck: convolution with low rank
ResNet-50 (He et al.,2016)224226M4.1G1128.376.282.5
ResNet-101 (He et al.,2016)224²45M7.9G652.077.483.7
ResNet-152 (He et al.,2016)224260M11.6G456.778.384.1
Pyramid: convolution with pyramid (spatial low rank) features.
HRNet-W18 (Wang et al., 2020)224221M4.0G-76.8-
HRNet-W32 (Wang et al.,2020)224241M8.3G78.5-
HRNet-W48 (Wang et al., 2020)224278M16.1G179.31
Channel and spatial separable MLP, spatial separable MLP = point-wise 1 ×1 convolution
Mixer-B/16 (Tolstikhin et al.,2021)22446M1-76.482.4
Mixer-L/16 (Tolstikhin et al.,2021)224²189M171.877.1
ResMLP-12(Touvron et al., 2021)224²15M3.0G76.683.3
ResMLP-24 (Touvron et al., 2021)224230M6.0G79.485.3
ResMLP-36 (Touvron et al.,2021)224²45M8.9G79.785.6
gMLP-Ti (Liu et al., 2021a)2242 224²6M1.4G72.01
gMLP-S (Liu et al.,2021a)224220M4.5G79.41
gMLP-B (Liu et al., 2021a)73M15.8G=81.6-
Global attention: dynamic channel separable MLP + spatial separable MLP
ViT-B/16 (Dosovitskiy et al., 2021)384286M55.4G83.477.983.6
ViT-L/16 (Dosovitskiy et al., 2021)3842307M190.7G26.576.582.2
DeiT-S (Touvron et al.,2020)224²22M4.6G947.379.885.7
DeiT-B (Touvron et al., 2020)224²86M17.5G298.281.886.7
DeiT-B (Touvron et al., 2020)384286M55.4G82.783.187.7
Pyramid attention: perform attention with spatial low rank
PVT-S (Wang et al., 2021b)22425M3.8G-79.8-
PVT-M (Wang et al., 2021b)224²44M6.7G=81.2-
PVT-L (Wang et al., 2021b)224261M9.8G=81.71
Local MLP: perform static separable MLP in local small windows
Swin-Local MLP-T224226M3.8G861.080.386.1
Swin-Local MLP-B224279M12.9G321.282.286.9
Local attention:perform attention in local small windows
Swin-T (Liu et al., 2021b)22428M4.5G713.581.386.6
Swin-B (Liu et al.,2021b)224288M15.4G263.083.387.9
Depth-wise convolution + point-wise 1 ×1 convolution
DW-Conv.-T224224M3.8G928.781.386.8
DW-Conv.-B224274M12.9G327.683.287.9
D-DW-Conv.-T224²51M3.8G897.081.987.3
D-DW-Conv.-B224²162M13.0G322.483.287.9
I-D-DW-Conv.-T224226M4.4G685.381.887.1
I-D-DW-Conv.-B224280M14.3G244.983.488.0
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ImageNet-1K fine-tuning
#param.FLOPstop-1 acc.
Swin-B88M15.4G85.2
DW-Conv.-B74M12.9G84.8
D-DW-Conv.-B162M13.0G85.0
I-D-DW-Conv.-B80M14.3G85.2
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COCO fine-tuningADE20K fine-tuning
#param.FLOPsAPboxAPAPAPmask#param.FLOPsmIoU
Swin-B145M986G53.472.158.146.1121M1192G49.4
DW Conv.-B132M924G52.070.456.345.0108M1129G50.1
D-DW Conv.-B219M924G51.970.756.245.0195M1129G49.6
I-D-DW Conv.-B137M948G52.971.257.245.8114M1153G51.3
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Layer Norm.Batch Norm.Centering calibrated Batch Norm.Top-1 Acc.
Swin<【81.3
Swin80.9
Swin√81.2
DW Conv.181.2
DW Conv.√81.3
√
DW Conv.81.7
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#param.FLOPstop-1 acc.
VOLO-d1 (Yuan et al.,2021c)27M7.0G84.1
VOLO (Local SA)-d127M7.2G84.2
DW Conv.-d126M6.9G84.2
SVT-S (Chu et al., 2021a)24M2.8G81.7
DW Conv.-S22M2.7G81.9
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modelws.#param.FLOPsAcc.
Swin7×7 12×1228M 28M14.4G 14.2G81.8 82.4
DW Conv.7×7 12×1224M 25M11.1G 11.5G82.2 82.1
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modelSE#param.FLOPsAcc.
Swin√28M4.5G81.3
29M4.5G81.2
DW Conv.√24M3.8G81.3
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Smith1,3 Luke Zettlemoyer1, + +1Paul G. Allen School of Computer Science & Engineering, University of Washington 2Meta AI Research 3Allen Institute for Artificial Intelligence hilagnn@gmail.com sviyer@meta.com {blvns,nasmith,lsz}@cs.washington.edu + +# Abstract + +Language models can be prompted to perform a wide variety of tasks with zero- and few-shot incontext learning. However, performance varies significantly with the choice of prompt, and we do not yet understand why this happens. In this paper, we analyze the factors that contribute to this variance and establish a new empirical hypothesis: the performance of a prompt is predicted by the extent to which the model is familiar with the language it contains. Over a wide range of tasks, we show that the lower the perplexity of the prompt, the better it is able to perform the task, when considering reasonable prompts that are related to it. As part of our analysis, we also devise a method to automatically extend a small seed set of manually written prompts by paraphrasing with GPT3 and backtranslation. This larger set allows us to verify that perplexity is a strong predictor of the success of a prompt and we show that the lowest perplexity prompts are consistently effective. + +# 1 Introduction + +Language models can be prompted to perform a wide range of zero- and few-shot learning tasks (Brown et al., 2020; Schick and Schütze, 2020). However, there is significant variance in the performance of seemingly similar prompts (Chen et al., 2022): for AG News (Zhang et al., 2015), we find an over 30 point accuracy gap between different manually curated prompts (see Table 1) on OPT 175B (Zhang et al., 2022). Despite efforts to improve prompt engineering (Shin et al., 2020; Li and Liang, 2021; Gao et al., 2021), it is still challenging to develop high-quality prompts for new tasks, and little is known about why this phenomenon occurs. + +We are interested in understanding what makes some prompts better than others, and using this understanding to create better prompts for given tasks and models. We hypothesize that the lower the perplexity of a prompt is, the better its performance on the task will be, when considering reasonable prompts that are related to the task. This is based on the intuition that the more frequently the prompt (or very similar phrases) appears in the training data, the more the model is familiar with it and is able to perform the described task. We refrain from using the training data directly as it is often unavailable, expensive to search due to its size, and hard to use for approximate matching of similar prompts. Instead, we focus on the perplexity of the prompt as a proxy for its occurrences in the data. + +![](images/4ff36496e07000f2d3b941c7008cf5afb10d1b32105a220ab3e483f827d67b6a.jpg) +Figure 1: Accuracy vs. perplexity for the AG News dataset with OPT 175B. The $x$ axis is in log scale. Each point stands for a different prompt. + +To enable more complete analysis, we automatically expand the set of manually created prompts for the task by paraphrasing, resulting in a much larger and diverse set of prompts. We focus on prompts in English that reasonably describe the task for two reasons: (a) our main motivation is to understand what lies under the variance of performance in this type of prompt; (b) we aim to devise a useful method for creating prompts that are consistently effective, that could be easily adopted and interpreted by future, potentially non-expert users. + +We show empirically that our hypothesis holds across a diverse set of tasks (including classification and word prediction), models, and model sizes, providing us some insights about the underlying mechanism of prompting (see Figure 1). As a result, we devise a method, SPELL (Selecting Prompts by Estimating LM Likelihood), for creating prompts in an informed manner. We show that using SPELL to choose prompts results in less variability in performance as well as in accuracy gains (1.8 accuracy points with OPT and 2.3 accuracy points with Bloom on average). Importantly, our method does not require labels at all, only a small sample of inputs for the task. + +Our contributions can be summarized as follows: (a) we formalize the notion that better familiarity of the model with the prompt correlates with better performance (Section 2); (b) we automatically elaborate a given set of seed prompts using paraphrasing (Section 3); (c) we establish experimentally the hypothesis that lower perplexity of the prompt correlates well with better performance (Section 5); (d) we devise a method to create a more consistent set of prompts, that also improve results even with no labels for the task (Section 7). + +# 2 Why are prompts not all created equal? + +Despite the popularity of prompting as a method for using language models (Shin et al., 2020; Li and Liang, 2021; Gao et al., 2021), the cause for the different behavior of various prompts remains unclear so far. Table 1 shows four example prompts for a news topic classification task (AG News) and their respective accuracies when used to prompt OPT 175B (Zhang et al., 2022). The accuracy gap between the different prompts is not trivial, and it is not possible to predict from the prompts alone. + +Table 1: Example prompts for the task AG News (news classification) that vary considerably in accuracy. + +
PromptAccuracy
What is this piece of news regarding?40.9
What is this article about?52.4
What is the best way to describe this article?68.2
What is the most accurate label for this news article?71.2
+ +We propose that the more frequently a prompt appears in some variation in the data, the better it works for the task. The intuition behind this is that a sequence that is more expected by the model is more likely to aid the model to extract the relevant information. However, this premise is hard to measure accurately: most language models use huge amounts of training data (e.g., OPT uses a corpus of roughly 180B tokens, and Bloom uses roughly 366B tokens), and in addition, this training data is not always publicly available (e.g., GPT3; Brown et al. 2020). Our initial attempts to estimate exact-match occurrences of prompts in the data resulted in very sparse counts, which led us to look for a softer formalization.1 + +Instead of considering the training data directly, we propose to focus on the perplexity of the prompt as a proxy for its occurrences in some form in the data – essentially indicating to what extent the model expects this prompt. This perplexity-based framing helps to avoid the challenge of exact match in the data, and takes into account variations of the prompt that the model is also exposed to and might be influenced by. In addition, it helps overcome the challenges mentioned above as it requires neither access to the pretraining data (which is not always publicly available for LMs) nor matching over huge amounts of text. + +Hypothesis: lower perplexity correlates with better performance. We hypothesize that on average, lower-perplexity prompts perform better. We are interested in establishing this hypothesis by experimentally showing a significant negative correlation between the perplexity of the prompt and its performance on the task, across a diverse set of tasks and models. + +We define the perplexity of the prompt as the perplexity of the full prompt sequence, including the input itself, and without the label, averaged over 1,000 examples (see Section 4 for details). The input is a part of the prompt in the case of the word prediction tasks by design (e.g., “The opposite of the word good is”). Inclusion of the task input as part of the prompt for classification tasks as well is intentional: we want to ground the prompt to the task (without the input, we are testing the hypothesis that lower perplexity prompts across all tasks work better on every task). The label is not considered a part of the prompt and is not taken into consideration when computing the prompt. In practice, this also results in a huge advantage of our method, SPELL (Section 7), which aims to find better prompts—it does not require any labels. + +For performance measures, we use the loglikelihood score assigned by the model to the correct label given that prompt. We choose this metric over accuracy as it gives a more fine-grained distinction between prompts and because accuracy can be unstable, as explained in more detail in Section 4. For classification tasks, we also report correlation with accuracy, which is the main evaluation metric for this type of task. + +# 3 Automatic Expansion of Seed Prompts + +We are interested in expanding our pool of prompts in order to: (a) have a more diverse set of prompts, making it more likely to find a better prompt for our task, and (b) support better analysis to validate our prompt quality hypothesis. In this section, we describe our method for automatically expanding a seed set of manually created prompts using paraphrasing. + +Step 0: Creating a seed set of manually-written prompts We first write/collect a small set of human written prompts that describe the task. For classification tasks we assume that the input appears before the prompt, with no choices appearing as part of the prompt (to help in smooth paraphrasing of the prompt itself). + +Step 1: Paraphrasing with GPT3 We use the text-davinci-002 version of GPT3 (Brown et al., 2020) to generate paraphrases for each of the manual prompts in our seed set. We prompt it with a meta-prompt for paraphrasing to generate variations of one of our seed prompts. An example of such a meta-prompt is: Write a paraphrase for the following sentence: Paraphrase:. The 7 meta-prompts used in this step are listed in Table 2. + +We choose GPT3 as our paraphrasing model because of its well-documented generation abilities. This is also to ensure that there is a separation between the model we use to create the prompts and the models we use to rank them (OPT and Bloom, see Section 4 for details), to avoid confounding the experimental setup. + +Step 2: Paraphrasing using backtranslation Our second step takes as input the paraphrases from GPT3 (in addition to the seed set of prompts) and translates them into different languages and back into English to get additional prompt paraphrases (Wieting et al., 2017). We use a set of 8 languages available in the NLLB translation model (Costajussà et al., 2022) that are relatively high resource and close to English,2 to reduce the risk of noise. Since we aim to get about 100 prompts per task, we add 8 additional languages3 in the case where the basic 8 languages yielded too few alternatives. For word prediction tasks, we use the sequence of the created prompt up to the index of the label, not including the label, for example: The word “dog” in French is “. Depending on the task, we enforce the existence of specific words (e.g., the name of the language, and the source word, in word-level translation) or enforce the prompt to be a question. + +Examples and Statistics Table 4 lists all 4 manually created prompts we use for the AG News task (news classification), alongside a few sampled prompts created automatically using our method. As was typically the case, we are able to get prompts that are rather different in phrasing and structure from those included in the seed set. + +The statistics of the prompts in the manually created seed set (Step 0) as well as the prompts after Step 1 and Step 2 for each task (see Section 4.1 for details about the tasks) are detailed in Table 3. + +# 4 Experimental Setup + +# 4.1 Models, Tasks and Datasets + +We study four auto-regressive models: OPT (Zhang et al., 2022) of different sizes (1.3B, 30B, 175B parameters), all trained mainly on English,4 and Bloom (176B parameters; Luccioni et al. 2022), which is trained on 46 natural languages and 13 programming languages. We experiment with two types of tasks: word prediction tasks and classification tasks, as detailed below. + +Word Prediction Tasks The first task in this category is word-level translation. Given a source word in English and a target language, we expect the model to predict the correct translation. For this task we use NorthEuraLex5 (Dellert et al., 2019), a lexical database providing translations of 1016 words into 107 languages. We experiment with 9 languages that use the Latin script. For Bloom, we use 5 additional languages that do not use the + +Table 2: Meta prompts used in Step 1 of our method for paraphrasing using GPT3. + +
Meta prompts
Write a paraphrase for the following sentence: <seed-prompt> Paraphrase: <seed-prompt> Paraphrase:
Write a likely paraphrase of the text: <seed-prompt> Paraphrase:
Write a sentence similar to the following one: <seed-prompt> Paraphrase:
Paraphrase the following sentence: <seed-prompt> Paraphrase:
Write a variation of this sentence: <seed-prompt> How would you say the following sentence in a different way? <seed-prompt>
+ +Table 3: Number of prompts for the different tasks: prompts after step 0 (creating prompts manually), prompts after step 1 (GPT3 paraphrasing), and prompts after step 2 (backtranslation). + +
Task# Step 0# Step 1 # Step 2
Word-Level Translation12 59118
Antonyms12 85176
GLUE Cola4 27144
Newspop13 43119
AG News4 23108
IMDB10 45178
DBpedia8 23103
Emotion4 1494
Tweet Offensive5 41119
+ +Latin script (since Bloom is multilingual). Note that only 5 of the languages we experiment with are officially covered by Bloom.6 + +We also consider antonym prediction where, given a word, the model is expected to predict its antonym. For this task, we use data from Kaggle,7 which is based on WordNet (Miller, 1995). We choose 1,000 word pairs at random. + +Classification Tasks We choose classification tasks from Huggingface Datasets,8 with an attempt to have a set of diverse tasks that use relatively short inputs, with some prompts available in PromptSource (Bach et al., 2022):9 (a) GLUE Cola (grammaticality; Warstadt et al. 2018); (b) Newspop (news classification; Moniz and Torgo 2018); (c) AG News (news classification; Zhang et al. 2015); (d) IMDB (movie review classification; Maas et al. 2011); (e) DBpedia (topic classification; Lehmann et al. 2015); (f) Emotion (classification to emotions; Saravia et al. 2018); (g) Tweet Offensive (classification to offensive vs. not offensive tweets; Barbieri et al. 2020). We use 1,000 random examples from each dataset. + +The full set of manual prompts is listed in Section A in the Appendix. In these tasks, the prompt follows the input, and at the end of each prompt we add the choices of classes (i.e., we provide the possible labels explicitly in the prompt by listing the possible answers as defined by the dataset itself.): “Choices: X, Y, Z. Answer:” as we find it helps in terms of accuracy. Defining the label space likely helps in our zero-shot setting because there are no previous demonstrations from which the model can learn the possible classes. Additionally, adding class options to the prompt helps to reduce the effect of the surface form competition (Holtzman et al., 2021). The option of generating the answer and comparing it with the gold label was not reasonable here, since we cannot expect the model to generate the exact label as the first choice often enough. + +# 4.2 Implementation Details + +In all experiments we evaluate zero-shot performance. To avoid noise when computing perplexity, we instantiate the prompts with 1,000 examples of the dataset, compute the perplexity of the prompt with each example, and calculate the average across all instantiated prompts. + +To estimate the performance of the prompt, we look at two measures: (a) the language model score (log probability) of the correct label, averaged across 1,000 examples; (b) the accuracy on the task, computed over the 1,000 examples. To compute accuracy, for each example we score all classes and choose the highest ranking class as the prediction of the model. The score of a label of multiple tokens is defined by the sum of the token + +Table 4: Prompts for the task AG News (news classification): the manually created prompts and a sample of automatically created prompts using our method. + +
All Manually Created PromptsExamples of Similar Automatically Created Prompts
What label best describes this news article?What's the most accurate label for this news article?
What is this piece of news regarding? Which newspaper section would this article likely appear in?What does this piece of news concern?
What topic is this news article about?In what section of the newspaper could this article be published? What category does this article fall into?
+ +Table 5: Correlation results for the different tasks, with OPT (different sizes) and Bloom. Correlations with $p < 0 . 0 5$ are marked with \*. Correlations with $p < 0 . 0 0 6 2 5$ (according to Bonferroni correction for multiple hypotheses) are marked with $^ { * * }$ . Dark and light blue colored cells stand for negative correlations $< - 0 . 2$ and $> - 0 . 2$ , respectively. Dark and light orange colored cells stand for positive correlations $> 0 . 2$ and $< 0 . 2$ , respectively. Average accuracy across all prompts and average accuracy of best $50 \%$ prompts are also reported for reference (Avg Acc and Acc $50 \%$ , respectively). + +
ModelTaskPerplexity-score corr. Pearson SpearmanPerplexity-acc corr. Pearson Spearman Avg Acc Acc 50%
OPT175BAntonyms**-0.41**-0.53
GLUE Cola-0.15-0.14-0.041 -0.021 47.71 57.1
Newspop*-0.24**-0.26 *-0.20-0.1866.472.9
AG News**-0.63 **-0.68 **-0.77**-0.8157.568.7
IMDB**0.35**0.400.14*0.2086.291.0
DBpedia **-0.50**-0.44 **-0.51**-0.4246.755.2
Emotion-0.14-0.19 **-0.30 **-0.3216.423.0
Tweet Offensive*-0.190.070.18*0.2351.355.8
Bloom 176BAntonyms**-0.37**-0.2311
GLUE Cola0.070.11**-0.25**-0.2655.565.6
Newspop**-0.50**-0.42 **-0.59 **-0.5178.987.8
AG News**-0.62 **-0.54**-0.44**-0.4450.359.4
IMDB0.040.09-0.08-0.1489.392.2
DBpedia**-0.47 *-0.27**-0.35*-0.2127.233.4
Emotion**-0.33 **-0.42**-0.48**-0.5529.331.7
Tweet Offensive0.14*0.24 *-0.20-0.0341.646.2
OPT 30B Antonyms **-0.54**-0.701111
GLUE Cola-0.050.03-0.130.0232.235.5
Newspop*-0.23 *-0.25*-0.18-0.1260.366.6
AG News**-0.66 **-0.71 **-0.81**-0.8049.360.7
IMDB-0.06*0.170.04**0.2281.686.1
DBpedia **-0.41 **-0.34*-0.21*-0.2535.942.4
Emotion0.00-0.030.180.1312.316.2
Tweet Offensive**-0.44**-0.39-0.11-0.0554.660.2
OPT 1.3BAntonyms **-0.45**-0.531
GLUE Cola **-0.39 **-0.36-0.09*-0.1960.31 65.9
Newspop**0.33*0.21-0.07-0.0737.640.3
AG News**-0.33**-0.29 **-0.56 **-0.4931.937.6
IMDB-0.11-0.07**0.24**0.2286.089.1
DBpedia-0.16-0.14-0.02-0.018.79.2
Emotion0.080.08**-0.29**-0.307.09.1
Tweet Offensive**-0.42**-0.35 **-0.50**-0.3858.662.6
+ +scores. + +For the word prediction tasks we only report scores, since accuracy in general is less stable, suffers more from the surface form competition (Holtzman et al., 2021), and is usually quite low for these tasks in our setting (the chances the model will generate an exact match of the label are low). Hence, the score of the correct label gives a better estimate of the actual performance of the model. + +Table 6: Correlation results for word-level translation, with OPT 175B and Bloom 176B. All correlations are statistically significant also according to Bonferroni correction for multiple hypotheses for OPT $( p < 0 . 0 0 5 5 )$ . Same for Bloom $( p \textless 0 . 0 0 3 5 7 )$ , except for Catalan (Pearson) and Japanese (Spearman). + +
LangOPT175BBloom 176B PearsonSpear.
PearsonSpear.
ita-0.44-0.57-0.37-0.63
spa-0.47-0.61-0.51-0.66
cat-0.47-0.58-0.24-0.31
fra-0.48-0.57-0.48-0.64
deu-0.44-0.60-0.46-0.65
fin-0.44-0.62-0.34-0.56
por-0.45-0.62-0.46-0.61
eus-0.47-0.61-0.45-0.61
tur-0.44-0.62-0.33-0.62
jpn-0.33-0.26
arb-0.36-0.47
rus1-0.54-0.69
kor-0.42-0.58
ell-0.40-0.51
+ +# 5 Results + +Classification Tasks and Antonym Prediction Table 5 depicts the Pearson and Spearman correlation results on the classification tasks and the antonym task, with both OPT 175B and Bloom (two upper blocks). We see that most correlations are negative and statistically significant, as we expect. This validates our hypothesis and shows that in the majority of tasks we indeed get a strong correlation between low perplexity of the prompt and better performance on the task.10 For each task we also report the average accuracy. + +Word-Level Translation The results of the wordlevel translation task are reported in Table 6. Here the correlations are extremely consistent across all languages and across models, with statistical significance for all languages except for Catalan and Japanese (in Bloom). + +Results across Different Model Sizes We repeat the same experiment with the OPT models of sizes 1.3B and 30B, to investigate whether these correlations are also consistent across model sizes or whether this is a phenomenon we should expect only in large language models. Table 5 (two lower blocks) shows these results for all classification tasks and antonym prediction. We do see that in general the trend appears to be the same in the smaller models as well; however, the correlations seem to be slightly weaker. We hypothesize that this might be due to the overall lower performance of these smaller models, making the performance results we use for correlation less stable and reliable. For word-level translation, however, all correlations with the 30B and 1.3B models are similar to those with the 175B model, and are all statistically significant (also after Bonferroni correction for multiple hypotheses). + +# 6 Analysis + +Next, we further explore the observed relationship between model perplexity and prompt performance. Despite the consistently high correlation between these two factors, the structure of this relationship varies across tasks (Section 6.1). Additionally, we find that the automatically added prompts are highquality and not a significant source of noise (Section 6.2), and that the best prompts selected by our approach vary across models (Section 6.3). + +# 6.1 Visualizing the Relationship between Perplexity and Performance + +To visualize the correlations we get between the perplexity and the performance of the prompts across the different settings, we plot a few examples for different tasks and languages. Figures 1 and 2 show some of the results for selected tasks, as detailed in the captions. The negative trend of the correlation is clearly visible in all plots. Interestingly, the structure of the plots for word-level translation are very similar across all the language pairs, suggesting that prompts get consistent perplexity and performance across languages (possibly at different scales). Indeed, the intersection of the 10 lowest perplexity prompts between any two different languages is 8.6 and 8.4 on average (for OPT 175B and Bloom, respectively), which is extremely high. This is not very surprising since we know that the only differences between the prompts in the different languages are the names of the target languages (e.g., The word for “dog” in French is “). Additionally, the intersection of 10 prompts with the highest label score between any two different languages is 7 and 6.5 on average (for OPT 175B and Bloom, respectively). + +A notable finding that appears in the word-level translation plots is the clear separation between prompts that include or do not include quotation marks for the label (usually aligns with whether the prompt uses quotation marks for the source word) – three example prompts appear on the plot. Prompts with quotation marks for the words tend to have both lower perplexity and better performance, consistently. We further analyze the results for OPT 175B within clusters (with/without quotations marks). In the cluster with quotation marks, we get negative correlations (in the range of $- 0 . 2 8$ to –0.38) that are statistically significant for almost all languages. The correlations within the other cluster are weaker and less significant (this is expected given the overall lower performance of that cluster). + +![](images/75ad713163e05245c30b6d7c7488af8e438550f2577006fad2670d68d0418ccd.jpg) +Figure 2: Score of correct label vs. perplexity for the word-level translation task in French with OPT 175B. The $x$ axis is in log scale. The blue points stand for prompts with quotation marks for the words, while the yellow points are of prompts without quotation marks. + +# 6.2 Effect of Noisy Prompts + +We expect our automatic method for expanding the set of prompts to also introduce some noise. Though our focus is on the lower perplexity prompts, since we want to benefit from this analysis and be able to devise a method for creating better prompts, we do want to make sure that this potential noise is not the cause for the strong correlations we get. In other words, one might claim that some noisy prompts have particularly high perplexity and also perform badly, thus, supporting our hypothesis in an undesirable and uncontrolled manner. + +We turn to inspect the $10 \%$ highest perplexity prompts in the different tasks and find subjectively that they are not noisy, and are usually valid prompts for the tasks. The 5 highest perplexity prompts for the GLUE Cola task are listed in Table 7 as an example. + +Table 7: Example of the 5 highest perplexity prompts for GLUE Cola, using OPT 175B. + +
promptppl
Is this example correct English usage?25.79
Is this example using English correctly?25.46
Is this example correct English?25.33
Is this the example in correct English?25.00
Is English in this example correct?24.90
+ +Table 8: Correlations before and after filtering out noisy prompts, with AG News and Word-Level Translation (WLT). + +
TaskLangBefore filteringAfter filtering
PearsonSpearmanPearsonSpearman
AG News--0.63-0.68-0.62-0.54
WLTita-0.44-0.58-0.44-0.57
spa-0.47-0.61-0.47-0.61
cat-0.45-0.57-0.47-0.58
fra-0.47-0.57-0.48-0.57
deu-0.43-0.60-0.44-0.60
fin-0.41-0.60-0.44-0.62
por-0.43-0.61-0.45-0.62
eus-0.45-0.60-0.47-0.61
tur-0.43-0.61-0.44-0.62
+ +As a sanity check, we choose two tasks: wordlevel translation and AG News, manually filter out the noisy prompts, and compute the correlations again. The annotation is done by external annotators (NLP researchers) that were presented with the tasks and asked to label whether the prompt is reasonable to use for the task. The new correlations with OPT 175B are reported in Table 8. We find that all correlations remain strong and statistically significant when noise is manually removed from the analysis. We get the same trends with Bloom as well. + +# 6.3 Best Performing Prompts + +Table 9 lists the 5 lowest perplexity prompts for the task of antonym prediction, as an example. Similar lists for the rest of the tasks are listed in Section B in the Appendix. + +A closer look at the lowest perplexity prompts reveals that the intersection of 10 lowest perplexity prompts between OPT 175B and Bloom is 7.1 on average, across the classification tasks. When looking at the 10 highest accuracy prompts across models we get an average intersection of 3.1 across the classification tasks. + +Table 9: Lowest perplexity prompts for the antonym prediction task, using OPT 175B. + +
promptppl
The following two words are antonyms:“good"and “10.24
The antonym of the word“good’is“10.32
The word that has the opposite meaning of the word “good"is “10.43
The word“good’is the antithesis of the word “10.85
The word “good"is the opposite of the word “11.15
+ +# 7 SPELL: Selecting Prompts by Estimating LM Likelihood + +The primary contribution of this work is the analysis of the relationship between prompt perplexity and downstream task performance (Section 5). As one potential application of our findings, we also present a new method, SPELL, for generating and selecting consistently effective prompts. + +Assuming a fixed computational budget for finding effective prompts for a given task, and that the search space might be quite large, we devise the following straightforward procedure: + +1. Obtain a small set of manually created prompts for the task. +2. Expand the set of prompts with automatic paraphrasing using a LM (e.g., GPT3) and backtranslation (see Section 3). +3. Rank the list of prompts by perplexity (averaged on a representative sample of task inputs, e.g., 1,000). +4. Choose the $k$ (e.g., 3) lowest perplexity prompts. + +Using this algorithm, we show empirically that it is best to prioritize experimenting with the lowest perplexity prompts, as they are more stable (exhibit less variation in performance) and perform better than manual prompts on average. This method also does not require any labels for the task, and is applicable to any task, also by non-experts, given example inputs only. + +# 7.1 Empirical Validation of SPELL + +To show the effectiveness of our method, we report the results we get using SPELL across the different tasks. In Table 10 we report the average accuracy with the manual prompts compared to the average accuracy with the 3 lowest-perplexity prompts, for both OPT 175B and Bloom. Indeed, in most cases, the average accuracy using the 3 lowest perplexity prompts outperforms the average accuracy of the manual prompts, with an average of 1.8 accuracy points across tasks with OPT and 2.3 accuracy points with Bloom, demonstrating the effectiveness of our method. + +Table 10: The average accuracy with the manual prompts (manual) compared to the average accuracy with the 3 lowest-perplexity prompts (low-ppl), for both OPT 175B and Bloom, across tasks. + +
OPTBloom
Tasklow-pplmanual△low-pplmanual△
GLUE Cola51.748.53.164.560.93.6
Newspop80.670.410.290.080.010.0
AG News68.461.96.551.063.5-12.5
IMDB90.488.91.491.388.82.5
DBpedia46.051.7-5.731.230.21.0
Emotion21.622.6-1.135.832.13.6
Tweet Offensive48.450.6-2.348.640.87.8
+ +The variability in accuracy of the 3 lowest perplexity prompts is also much lower than that of the manually created prompts: with OPT 175B, the average standard deviation within the 3 lowest perplexity prompts (across tasks) is 5.07, vs. 6.86 for the manual prompts, and with Bloom the gap is much bigger, with an average of 2.6 for the 3 lowest perplexity prompts vs. 7.47 for the manual ones.11 This further shows that SPELL is more stable and reliable compared to using an arbitrary set of manually created prompts. SPELL sets the stage for further development in this direction, and serves as an initial indication of the benefits of involving perplexity estimation in the process of generating effective prompts. + +# 8 Related Work + +Relation between performance and training data Previous work looking directly into the relation between the training data and the performance is limited. Razeghi et al. (2022) study numeric deduction tasks, and examine the correlations between the model performance on specific test instances and the frequency of terms from those instances in the pretraining data. They find that the models are more accurate on instances whose terms are more prevalent in the training data. Additionally, Han and Tsvetkov (2022) propose a method to effectively identify a very small subset of pretraining data that directly supports the model in performing a specific task. Elazar et al. (2022) use causal inference to measure the effect of pretraining data statistics on factual knowledge performance, and + +Kandpal et al. (2022) show correlational and causal relationships between accuracy and relevant document count (from training data) for QA datasets. + +Prompt tuning and analysis There is a very rich line of work trying to find prompts automatically. Shin et al. (2020) present an automated method to create discrete prompts for a diverse set of tasks, based on a gradient-guided search, and they demonstrate their method on masked LMs. Other work also focuses on discrete prompts, aiming to improve zero-shot performance (Gao et al., 2021; Le Scao and Rush, 2021; Deng et al., 2022; Shi et al., 2022), or trains continuous prompts (Li and Liang, 2021; Lester et al., 2021; Qin and Eisner, 2021). + +On top of works that suggest a variety of methods for creating better prompts, some work also analyzes those prompts to try and get some insights about them: Khashabi et al. (2022a) find that model performance is highly sensitive to small changes in wordings and Khashabi et al. (2022b) point to a surprising disconnect between continuous and discrete prompts. + +# Limitations + +Searching for human-readable prompts We limit our search space to human-readable prompts that are fluent and accurately describe the task at hand, as we are primarily motivated in understanding why some relevant prompts work better than others. We do this by using manually created prompts and their automatically created paraphrases. Our findings may not hold when the possible prompt space is expanded to include any token sequence; we leave this direction to future work. + +Generality of our analysis and of the SPELL method We perform our analysis on and build our method around specific models, namely OPT and Bloom. Additionally, our study is limited to the specific tasks we experiment with and to English. It is possible that our analysis and SPELL method do not generalize to other pretrained models or tasks; however, we consider models of various sizes and from different sources, and a wide range of tasks to mitigate this risk. + +# Acknowledgements + +We thank Alisa Liu and Orevaoghene Ahia for their help in annotating noisy prompts. We also thank the reviewers for their valuable comments on the paper. + +# 9 Conclusion + +We investigate the phenomenon where some prompts perform better than others despite appearing similar to the human users of LMs. Specifically, we hypothesize that the perplexity of a prompt under a given LM is closely tied to its task performance. We test this theory on a large number of tasks and autoregressive LMs, and the resulting correlation study validates our hypothesis. Further analysis of this relationship demonstrates that the best prompts differ across models, highlighting the importance of model-specific analysis, and that the underlying structure of the relationship between perplexity and performance varies across tasks. + +In light of these findings, we then propose a method, SPELL, to help users find wellperforming prompts for new tasks. Empirical validation of the proposed procedure shows that SPELL generates effective prompts with low variability in performance, and produces small gains of 1.8 (2.3) accuracy points with OPT (Bloom) over manual prompts. We therefore conclude that SPELL provides a general and interpretable approach for applying LMs to new tasks while requiring minimal human effort, and no labels. + +# References + +Stephen H. Bach, Victor Sanh, Zheng-Xin Yong, Albert Webson, Colin Raffel, Nihal V. Nayak, Abheesht Sharma, Taewoon Kim, M Saiful Bari, Thibault Fevry, Zaid Alyafeai, Manan Dey, Andrea Santilli, Zhiqing Sun, Srulik Ben-David, Canwen Xu, Gunjan Chhablani, Han Wang, Jason Alan Fries, Maged S. Al-shaibani, Shanya Sharma, Urmish Thakker, Khalid Almubarak, Xiangru Tang, Xiangru Tang, Mike Tian-Jian Jiang, and Alexander M. Rush. 2022. Promptsource: An integrated development environment and repository for natural language prompts. + +Francesco Barbieri, Jose Camacho-Collados, Luis Espinosa-Anke, and Leonardo Neves. 2020. TweetEval:Unified Benchmark and Comparative Evaluation for Tweet Classification. In Proceedings of Findings of EMNLP. + +Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. 2020. Language models are few-shot learners. Advances in neural information processing systems, 33:1877–1901. + +Yanda Chen, Chen Zhao, Zhou Yu, Kathleen McKeown, and He He. 2022. On the relation between sensitivity and accuracy in in-context learning. arXiv e-prints, pages arXiv–2209. + +Marta R Costa-jussà, James Cross, Onur Çelebi, Maha Elbayad, Kenneth Heafield, Kevin Heffernan, Elahe Kalbassi, Janice Lam, Daniel Licht, Jean Maillard, et al. 2022. No language left behind: Scaling human-centered machine translation. arXiv preprint arXiv:2207.04672. + +Johannes Dellert, Thora Daneyko, Alla Münch, Alina Ladygina, Armin Buch, Natalie Clarius, Ilja Grigorjew, Mohamed Balabel, Hizniye Isabella Boga, Zalina Baysarova, et al. 2019. Northeuralex: a widecoverage lexical database of northern eurasia. Language Resources and Evaluation, pages 1–29. + +Mingkai Deng, Jianyu Wang, Cheng-Ping Hsieh, Yihan Wang, Han Guo, Tianmin Shu, Meng Song, Eric P Xing, and Zhiting Hu. 2022. Rlprompt: Optimizing discrete text prompts with reinforcement learning. arXiv preprint arXiv:2205.12548. + +Yanai Elazar, Nora Kassner, Shauli Ravfogel, Amir Feder, Abhilasha Ravichander, Marius Mosbach, Yonatan Belinkov, Hinrich Schütze, and Yoav Goldberg. 2022. Measuring causal effects of data statistics on language model’sfactual’predictions. arXiv preprint arXiv:2207.14251. + +Tianyu Gao, Adam Fisch, and Danqi Chen. 2021. Making pre-trained language models better few-shot learners. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 3816–3830. + +Xiaochuang Han and Yulia Tsvetkov. 2022. Orca: Interpreting prompted language models via locating supporting data evidence in the ocean of pretraining data. arXiv preprint arXiv:2205.12600. + +Ari Holtzman, Peter West, Vered Shwartz, Yejin Choi, and Luke Zettlemoyer. 2021. Surface form competition: Why the highest probability answer isn’t always right. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 7038–7051. + +Nikhil Kandpal, Haikang Deng, Adam Roberts, Eric Wallace, and Colin Raffel. 2022. Large language models struggle to learn long-tail knowledge. arXiv preprint arXiv:2211.08411. + +Daniel Khashabi, Chitta Baral, Yejin Choi, and Hannaneh Hajishirzi. 2022a. Reframing instructional prompts to gptk’s language. In Findings of the Association for Computational Linguistics: ACL 2022, pages 589–612. + +Daniel Khashabi, Xinxi Lyu, Sewon Min, Lianhui Qin, Kyle Richardson, Sean Welleck, Hannaneh Hajishirzi, Tushar Khot, Ashish Sabharwal, Sameer + +Singh, and Yejin Choi. 2022b. Prompt waywardness: The curious case of discretized interpretation of continuous prompts. In Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. + +Teven Le Scao and Alexander Rush. 2021. How many data points is a prompt worth? In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. Association for Computational Linguistics. + +Jens Lehmann, Robert Isele, Max Jakob, Anja Jentzsch, Dimitris Kontokostas, Pablo N Mendes, Sebastian Hellmann, Mohamed Morsey, Patrick Van Kleef, Sören Auer, et al. 2015. Dbpedia–a large-scale, multilingual knowledge base extracted from wikipedia. Semantic web, 6(2):167–195. + +Brian Lester, Rami Al-Rfou, and Noah Constant. 2021. The power of scale for parameter-efficient prompt tuning. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pages 3045–3059. + +Xiang Lisa Li and Percy Liang. 2021. Prefix-tuning: Optimizing continuous prompts for generation. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 4582– 4597. + +Alexandra Sasha Luccioni, Sylvain Viguier, and AnneLaure Ligozat. 2022. Estimating the carbon footprint of bloom, a 176b parameter language model. arXiv preprint arXiv:2211.02001. + +Andrew L. Maas, Raymond E. Daly, Peter T. Pham, Dan Huang, Andrew Y. Ng, and Christopher Potts. 2011. Learning word vectors for sentiment analysis. In Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies, pages 142–150, Portland, Oregon, USA. Association for Computational Linguistics. + +George A Miller. 1995. Wordnet: a lexical database for english. Communications of the ACM, 38(11):39–41. + +N. Moniz and L. Torgo. 2018. Multi-source social feedback of online news feeds. ArXiv, abs/1801.07055. + +Guanghui Qin and Jason Eisner. 2021. Learning how to ask: Querying lms with mixtures of soft prompts. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 5203–5212. + +Yasaman Razeghi, Robert L Logan IV, Matt Gardner, and Sameer Singh. 2022. Impact of pretraining term frequencies on few-shot reasoning. arXiv preprint arXiv:2202.07206. + +Elvis Saravia, Hsien-Chi Toby Liu, Yen-Hao Huang, Junlin Wu, and Yi-Shin Chen. 2018. CARER: Contextualized affect representations for emotion recognition. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 3687–3697, Brussels, Belgium. Association for Computational Linguistics. + +Timo Schick and Hinrich Schütze. 2020. It’s not just size that matters: Small language models are also few-shot learners. arXiv preprint arXiv:2009.07118. + +Weijia Shi, Xiaochuang Han, Hila Gonen, Ari Holtzman, Yulia Tsvetkov, and Luke Zettlemoyer. 2022. Toward human readable prompt tuning: Kubrick’s the shining is a good movie, and a good prompt too? arXiv preprint arXiv:2212.10539. + +Taylor Shin, Yasaman Razeghi, Robert L Logan IV, Eric Wallace, and Sameer Singh. 2020. Autoprompt: Eliciting knowledge from language models with automatically generated prompts. arXiv preprint arXiv:2010.15980. + +Alex Warstadt, Amanpreet Singh, and Samuel R Bowman. 2018. Neural network acceptability judgments. arXiv preprint arXiv:1805.12471. + +John Wieting, Jonathan Mallinson, and Kevin Gimpel. 2017. Learning paraphrastic sentence embeddings from back-translated bitext. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 274–285. + +Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher Dewan, Mona Diab, Xian Li, Xi Victoria Lin, et al. 2022. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068. + +Xiang Zhang, Junbo Jake Zhao, and Yann LeCun. 2015. Character-level convolutional networks for text classification. In NIPS. + +# A Manually Created Prompts + +Table 11 lists the manually created prompts we use for the different tasks. We manually add, remove and edit prompts for some of these tasks, to make them fit for our setting. For example, the following prompt for AG News, taken from Promptsource, does not fit our setting: Would you recommend the following article to a politician, an athlete, business executive, or a scientist? + +# B Lowest Perplexity Prompts + +Table 12 lists the 5 lowest perplexity prompts for each task, using OPT 175B. + +Table 11: The set of manually created prompts for each task. + +
Task Manual Prompts
AntonymsThe antonym of the word “good”is“ The opposite meaning of the word “good”is “ “Good”is the opposite of“ “Good”is the negation of“ The following are opposites of each other:“good"and “ The word “good"contradicts the word “ The antonym of the word good is The opposite meaning of the word good is Good is the opposite of
GLUE ColaThe following are opposites of each other: good and The word good contradicts the word Does the this sentence make sense and use correct English? Is this example grammatically correct and sensible? Does this sentence make sense and is it grammatically correct?
NewspopDoes this example use correct English? What is the article about? What is this news about? What is the topic of this news piece? What does this article discuss? What is the topic of this sentence? What category does the article belong to? Pick one category forthis news piece. Pick the category that fits the text. The article refers to which category? What topic does the article belong to? What category fits this article? What topic does this news piece belong to? Choose the correct category for this article.
AG NewsWhat label best describes this news article? What is this piece of news regarding? Which newspaper section would this article likely appear in? What topic is this news article about? This movie review expresses what sentiment? Did the reviewer find this movie good or bad?
IMDBIs this review positive or negative? How does the viewer feel about the movie? What sentiment does the writer express for the movie? What sentiment is expressed for the movie? What is the sentiment expressed in this text? Did the reviewer enjoy the movie? What is the sentiment expressed by the reviewer for the movie? How does the reviewer feel about the movie? What category does the paragraph belong to? Pick one category for the text.
DBpediaPick the category that fits the text. The text refers to which category? What category does the title belong to? What category fits this text? What topic does this text belong to? Choose the correct category for the text. What is the emotion expressed in this message?
EmotionWhat emotion does this message express? How will you feel about the message? What emotion does the writer express for the message? Is this tweet offensive? Can the tweet be removed for being offensive?
Tweet OffensiveIs the author's tweet offensive? Task: Identify if the tweetor text is offensive. Is this an offensive tweet? The translation of the word “dog"to French is“ The translation of the word dog to French is The word “dog”in French is“
Word-Level Translation“dog”(In French: “ Translate the word dog into French: The translation of dog to French is “dog”(French: “ The word dog in French is Translate the word“dog”into French: “ dog (In French: dog (French: The translation of“dog”to French is “
+ +Table 12: The 5 lowest perplexity prompts for each task, using OPT 175B. + +
TaskLowest Perplexity PromptsPerplexity
AntonymsThe following two words are antonyms:“good”and “10.24
The antonym of the word“good"is“10.32
The word that has the opposite meaning of the word “good" is “10.43
The word“good”is the antithesis of the word“10.85
The word “good” is the opposite of the word “11.15
GLUE ColaIs this an example of the proper use of the English language?11.63
Does the sentence make sense and does it follow the rules of grammar?11.76
Is this sentence an example of the correct use of the English language?12.10
Does this sentence make sense and is it grammatically correct?12.15
Is this sentence grammatically correct and does it make sense?12.68
NewspopWhat is the main subject of the article?10.01
What is the main topic of the article?10.01
What is the subject matter of the article?10.17
What is the subject of the article?10.21
What is the main idea of this article?10.21
AG NewsIn what section of the newspaper would you expect to find this article?7.51
In which section of the newspaper would you expect to find this article?7.52
In which section of the newspaper would this article be most likely to appear?7.60
In what section of the newspaper do you expect to find this article?7.80
In what section of the newspaper would this article most likely appear?7.87
IMDBWhat is the opinion of the review? Is it positive or negative?7.19
Is this a positive or negative review?7.31
What do you think of the movie?7.33
What do you think of the film?7.35
Is that a positive or a negative?7.35
DBpediaWhat is the category to which the text refers?8.99
What is the subject of the text?9.15
What category does the title belong to?9.18
Which category does the text refer to?9.19
What is the subject of this text?9.20
EmotionHow do you feel when you hear this message?12.72
What is the writer's emotional reaction to this news?13.18
What is the emotion expressed in this message?13.20
How does this message make you feel?13.32
How do you feel about this message?13.50
Tweet OffensiveIf someone said this to you, would you be offended?13.00
If someone said that to you, would you be offended?13.10
Would you be offended if someone said that to you?13.73
Would it offend you if someone said that to you?14.79
If someone told you that, would you be offended?14.93
Word-Level TranslationThe word for“dog"in French is“7.73
The French word for“dog”is“8.16
The French translation of the word“dog”is“8.24
The translation of the word “dog”in French is “8.35
The translation of the word “dog” into French is “8.91
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Allen School of Computer Science & Engineering, University of Washington 2Meta AI Research 3Allen Institute for Artificial Intelligence hilagnn@gmail.com sviyer@meta.com {blvns,nasmith,lsz}@cs.washington.edu ", + "bbox": [ + 154, + 142, + 852, + 225 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 263, + 252, + 339, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Language models can be prompted to perform a wide variety of tasks with zero- and few-shot incontext learning. However, performance varies significantly with the choice of prompt, and we do not yet understand why this happens. In this paper, we analyze the factors that contribute to this variance and establish a new empirical hypothesis: the performance of a prompt is predicted by the extent to which the model is familiar with the language it contains. Over a wide range of tasks, we show that the lower the perplexity of the prompt, the better it is able to perform the task, when considering reasonable prompts that are related to it. As part of our analysis, we also devise a method to automatically extend a small seed set of manually written prompts by paraphrasing with GPT3 and backtranslation. This larger set allows us to verify that perplexity is a strong predictor of the success of a prompt and we show that the lowest perplexity prompts are consistently effective. ", + "bbox": [ + 146, + 279, + 457, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 117, + 605, + 257, + 620 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Language models can be prompted to perform a wide range of zero- and few-shot learning tasks (Brown et al., 2020; Schick and Schütze, 2020). However, there is significant variance in the performance of seemingly similar prompts (Chen et al., 2022): for AG News (Zhang et al., 2015), we find an over 30 point accuracy gap between different manually curated prompts (see Table 1) on OPT 175B (Zhang et al., 2022). Despite efforts to improve prompt engineering (Shin et al., 2020; Li and Liang, 2021; Gao et al., 2021), it is still challenging to develop high-quality prompts for new tasks, and little is known about why this phenomenon occurs. ", + "bbox": [ + 117, + 631, + 487, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We are interested in understanding what makes some prompts better than others, and using this understanding to create better prompts for given tasks and models. We hypothesize that the lower the perplexity of a prompt is, the better its performance on the task will be, when considering reasonable prompts that are related to the task. This is based on the intuition that the more frequently the prompt (or very similar phrases) appears in the training data, the more the model is familiar with it and is able to perform the described task. We refrain from using the training data directly as it is often unavailable, expensive to search due to its size, and hard to use for approximate matching of similar prompts. Instead, we focus on the perplexity of the prompt as a proxy for its occurrences in the data. ", + "bbox": [ + 115, + 840, + 487, + 920 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4ff36496e07000f2d3b941c7008cf5afb10d1b32105a220ab3e483f827d67b6a.jpg", + "image_caption": [ + "Figure 1: Accuracy vs. perplexity for the AG News dataset with OPT 175B. The $x$ axis is in log scale. Each point stands for a different prompt. " + ], + "image_footnote": [], + "bbox": [ + 517, + 256, + 870, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 516, + 882, + 692 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enable more complete analysis, we automatically expand the set of manually created prompts for the task by paraphrasing, resulting in a much larger and diverse set of prompts. We focus on prompts in English that reasonably describe the task for two reasons: (a) our main motivation is to understand what lies under the variance of performance in this type of prompt; (b) we aim to devise a useful method for creating prompts that are consistently effective, that could be easily adopted and interpreted by future, potentially non-expert users. ", + "bbox": [ + 512, + 695, + 882, + 870 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We show empirically that our hypothesis holds across a diverse set of tasks (including classification and word prediction), models, and model sizes, providing us some insights about the underlying mechanism of prompting (see Figure 1). As a result, we devise a method, SPELL (Selecting Prompts by Estimating LM Likelihood), for creating prompts in an informed manner. We show that using SPELL to choose prompts results in less variability in performance as well as in accuracy gains (1.8 accuracy points with OPT and 2.3 accuracy points with Bloom on average). Importantly, our method does not require labels at all, only a small sample of inputs for the task. ", + "bbox": [ + 512, + 872, + 882, + 919 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 84, + 487, + 260 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows: (a) we formalize the notion that better familiarity of the model with the prompt correlates with better performance (Section 2); (b) we automatically elaborate a given set of seed prompts using paraphrasing (Section 3); (c) we establish experimentally the hypothesis that lower perplexity of the prompt correlates well with better performance (Section 5); (d) we devise a method to create a more consistent set of prompts, that also improve results even with no labels for the task (Section 7). ", + "bbox": [ + 115, + 262, + 487, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Why are prompts not all created equal? ", + "text_level": 1, + "bbox": [ + 115, + 450, + 487, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the popularity of prompting as a method for using language models (Shin et al., 2020; Li and Liang, 2021; Gao et al., 2021), the cause for the different behavior of various prompts remains unclear so far. Table 1 shows four example prompts for a news topic classification task (AG News) and their respective accuracies when used to prompt OPT 175B (Zhang et al., 2022). The accuracy gap between the different prompts is not trivial, and it is not possible to predict from the prompts alone. ", + "bbox": [ + 117, + 476, + 485, + 637 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/ea68510e63399b4380ccc0f73bc5f0646153fcf98376e15ebd683a5a241ad974.jpg", + "table_caption": [ + "Table 1: Example prompts for the task AG News (news classification) that vary considerably in accuracy. " + ], + "table_footnote": [], + "table_body": "
PromptAccuracy
What is this piece of news regarding?40.9
What is this article about?52.4
What is the best way to describe this article?68.2
What is the most accurate label for this news article?71.2
", + "bbox": [ + 117, + 649, + 487, + 720 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose that the more frequently a prompt appears in some variation in the data, the better it works for the task. The intuition behind this is that a sequence that is more expected by the model is more likely to aid the model to extract the relevant information. However, this premise is hard to measure accurately: most language models use huge amounts of training data (e.g., OPT uses a corpus of roughly 180B tokens, and Bloom uses roughly 366B tokens), and in addition, this training data is not always publicly available (e.g., GPT3; Brown et al. 2020). Our initial attempts to estimate exact-match occurrences of prompts in the data resulted in very sparse counts, which led us to look for a softer formalization.1 ", + "bbox": [ + 117, + 776, + 485, + 919 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 85, + 882, + 179 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instead of considering the training data directly, we propose to focus on the perplexity of the prompt as a proxy for its occurrences in some form in the data – essentially indicating to what extent the model expects this prompt. This perplexity-based framing helps to avoid the challenge of exact match in the data, and takes into account variations of the prompt that the model is also exposed to and might be influenced by. In addition, it helps overcome the challenges mentioned above as it requires neither access to the pretraining data (which is not always publicly available for LMs) nor matching over huge amounts of text. ", + "bbox": [ + 512, + 183, + 882, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Hypothesis: lower perplexity correlates with better performance. We hypothesize that on average, lower-perplexity prompts perform better. We are interested in establishing this hypothesis by experimentally showing a significant negative correlation between the perplexity of the prompt and its performance on the task, across a diverse set of tasks and models. ", + "bbox": [ + 512, + 399, + 882, + 526 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We define the perplexity of the prompt as the perplexity of the full prompt sequence, including the input itself, and without the label, averaged over 1,000 examples (see Section 4 for details). The input is a part of the prompt in the case of the word prediction tasks by design (e.g., “The opposite of the word good is”). Inclusion of the task input as part of the prompt for classification tasks as well is intentional: we want to ground the prompt to the task (without the input, we are testing the hypothesis that lower perplexity prompts across all tasks work better on every task). The label is not considered a part of the prompt and is not taken into consideration when computing the prompt. In practice, this also results in a huge advantage of our method, SPELL (Section 7), which aims to find better prompts—it does not require any labels. ", + "bbox": [ + 512, + 529, + 882, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For performance measures, we use the loglikelihood score assigned by the model to the correct label given that prompt. We choose this metric over accuracy as it gives a more fine-grained distinction between prompts and because accuracy can be unstable, as explained in more detail in Section 4. For classification tasks, we also report correlation with accuracy, which is the main evaluation metric for this type of task. ", + "bbox": [ + 510, + 803, + 882, + 850 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 85, + 487, + 180 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 Automatic Expansion of Seed Prompts ", + "text_level": 1, + "bbox": [ + 115, + 198, + 480, + 215 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We are interested in expanding our pool of prompts in order to: (a) have a more diverse set of prompts, making it more likely to find a better prompt for our task, and (b) support better analysis to validate our prompt quality hypothesis. In this section, we describe our method for automatically expanding a seed set of manually created prompts using paraphrasing. ", + "bbox": [ + 115, + 229, + 487, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Step 0: Creating a seed set of manually-written prompts We first write/collect a small set of human written prompts that describe the task. For classification tasks we assume that the input appears before the prompt, with no choices appearing as part of the prompt (to help in smooth paraphrasing of the prompt itself). ", + "bbox": [ + 115, + 373, + 487, + 485 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Step 1: Paraphrasing with GPT3 We use the text-davinci-002 version of GPT3 (Brown et al., 2020) to generate paraphrases for each of the manual prompts in our seed set. We prompt it with a meta-prompt for paraphrasing to generate variations of one of our seed prompts. An example of such a meta-prompt is: Write a paraphrase for the following sentence: Paraphrase:. The 7 meta-prompts used in this step are listed in Table 2. ", + "bbox": [ + 115, + 500, + 487, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We choose GPT3 as our paraphrasing model because of its well-documented generation abilities. This is also to ensure that there is a separation between the model we use to create the prompts and the models we use to rank them (OPT and Bloom, see Section 4 for details), to avoid confounding the experimental setup. ", + "bbox": [ + 115, + 664, + 487, + 776 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Step 2: Paraphrasing using backtranslation Our second step takes as input the paraphrases from GPT3 (in addition to the seed set of prompts) and translates them into different languages and back into English to get additional prompt paraphrases (Wieting et al., 2017). We use a set of 8 languages available in the NLLB translation model (Costajussà et al., 2022) that are relatively high resource and close to English,2 to reduce the risk of noise. Since we aim to get about 100 prompts per task, we add 8 additional languages3 in the case where the basic 8 languages yielded too few alternatives. For word prediction tasks, we use the sequence of the created prompt up to the index of the label, not including the label, for example: The word “dog” in French is “. Depending on the task, we enforce the existence of specific words (e.g., the name of the language, and the source word, in word-level translation) or enforce the prompt to be a question. ", + "bbox": [ + 115, + 791, + 485, + 919 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 84, + 884, + 261 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Examples and Statistics Table 4 lists all 4 manually created prompts we use for the AG News task (news classification), alongside a few sampled prompts created automatically using our method. As was typically the case, we are able to get prompts that are rather different in phrasing and structure from those included in the seed set. ", + "bbox": [ + 512, + 272, + 882, + 384 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The statistics of the prompts in the manually created seed set (Step 0) as well as the prompts after Step 1 and Step 2 for each task (see Section 4.1 for details about the tasks) are detailed in Table 3. ", + "bbox": [ + 512, + 386, + 882, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4 Experimental Setup ", + "text_level": 1, + "bbox": [ + 514, + 463, + 715, + 480 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1 Models, Tasks and Datasets ", + "text_level": 1, + "bbox": [ + 514, + 491, + 771, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We study four auto-regressive models: OPT (Zhang et al., 2022) of different sizes (1.3B, 30B, 175B parameters), all trained mainly on English,4 and Bloom (176B parameters; Luccioni et al. 2022), which is trained on 46 natural languages and 13 programming languages. We experiment with two types of tasks: word prediction tasks and classification tasks, as detailed below. ", + "bbox": [ + 512, + 513, + 882, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Word Prediction Tasks The first task in this category is word-level translation. Given a source word in English and a target language, we expect the model to predict the correct translation. For this task we use NorthEuraLex5 (Dellert et al., 2019), a lexical database providing translations of 1016 words into 107 languages. We experiment with 9 languages that use the Latin script. For Bloom, we use 5 additional languages that do not use the ", + "bbox": [ + 510, + 652, + 882, + 796 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/d21b84152ca0a15d718817bca473b356a29419b24ca03eb2dec7132513e6feb8.jpg", + "table_caption": [ + "Table 2: Meta prompts used in Step 1 of our method for paraphrasing using GPT3. " + ], + "table_footnote": [], + "table_body": "
Meta prompts
Write a paraphrase for the following sentence: <seed-prompt> Paraphrase: <seed-prompt> Paraphrase:
Write a likely paraphrase of the text: <seed-prompt> Paraphrase:
Write a sentence similar to the following one: <seed-prompt> Paraphrase:
Paraphrase the following sentence: <seed-prompt> Paraphrase:
Write a variation of this sentence: <seed-prompt> How would you say the following sentence in a different way? <seed-prompt>
", + "bbox": [ + 200, + 83, + 796, + 227 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/80ac122f9a0b4355fd95af79e2d54827e9019d8a349901617b3e349b892d64c2.jpg", + "table_caption": [ + "Table 3: Number of prompts for the different tasks: prompts after step 0 (creating prompts manually), prompts after step 1 (GPT3 paraphrasing), and prompts after step 2 (backtranslation). " + ], + "table_footnote": [], + "table_body": "
Task# Step 0# Step 1 # Step 2
Word-Level Translation12 59118
Antonyms12 85176
GLUE Cola4 27144
Newspop13 43119
AG News4 23108
IMDB10 45178
DBpedia8 23103
Emotion4 1494
Tweet Offensive5 41119
", + "bbox": [ + 121, + 275, + 485, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Latin script (since Bloom is multilingual). Note that only 5 of the languages we experiment with are officially covered by Bloom.6 ", + "bbox": [ + 115, + 517, + 485, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also consider antonym prediction where, given a word, the model is expected to predict its antonym. For this task, we use data from Kaggle,7 which is based on WordNet (Miller, 1995). We choose 1,000 word pairs at random. ", + "bbox": [ + 115, + 565, + 485, + 644 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Classification Tasks We choose classification tasks from Huggingface Datasets,8 with an attempt to have a set of diverse tasks that use relatively short inputs, with some prompts available in PromptSource (Bach et al., 2022):9 (a) GLUE Cola (grammaticality; Warstadt et al. 2018); (b) Newspop (news classification; Moniz and Torgo 2018); (c) AG News (news classification; Zhang et al. 2015); (d) IMDB (movie review classification; Maas et al. 2011); (e) DBpedia (topic classification; Lehmann et al. 2015); (f) Emotion (classification to emotions; Saravia et al. 2018); (g) Tweet Offensive (classification to offensive vs. not offensive tweets; Barbieri et al. 2020). We use 1,000 random examples from each dataset. ", + "bbox": [ + 115, + 656, + 487, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 510, + 279, + 882, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The full set of manual prompts is listed in Section A in the Appendix. In these tasks, the prompt follows the input, and at the end of each prompt we add the choices of classes (i.e., we provide the possible labels explicitly in the prompt by listing the possible answers as defined by the dataset itself.): “Choices: X, Y, Z. Answer:” as we find it helps in terms of accuracy. Defining the label space likely helps in our zero-shot setting because there are no previous demonstrations from which the model can learn the possible classes. Additionally, adding class options to the prompt helps to reduce the effect of the surface form competition (Holtzman et al., 2021). The option of generating the answer and comparing it with the gold label was not reasonable here, since we cannot expect the model to generate the exact label as the first choice often enough. ", + "bbox": [ + 512, + 344, + 882, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2 Implementation Details ", + "text_level": 1, + "bbox": [ + 514, + 652, + 739, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In all experiments we evaluate zero-shot performance. To avoid noise when computing perplexity, we instantiate the prompts with 1,000 examples of the dataset, compute the perplexity of the prompt with each example, and calculate the average across all instantiated prompts. ", + "bbox": [ + 512, + 677, + 882, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To estimate the performance of the prompt, we look at two measures: (a) the language model score (log probability) of the correct label, averaged across 1,000 examples; (b) the accuracy on the task, computed over the 1,000 examples. To compute accuracy, for each example we score all classes and choose the highest ranking class as the prediction of the model. The score of a label of multiple tokens is defined by the sum of the token ", + "bbox": [ + 512, + 776, + 882, + 919 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/4ef2732c58de75405c34d56b0a95216e2af13aa77680db7cab619512d10bb8bd.jpg", + "table_caption": [ + "Table 4: Prompts for the task AG News (news classification): the manually created prompts and a sample of automatically created prompts using our method. " + ], + "table_footnote": [], + "table_body": "
All Manually Created PromptsExamples of Similar Automatically Created Prompts
What label best describes this news article?What's the most accurate label for this news article?
What is this piece of news regarding? Which newspaper section would this article likely appear in?What does this piece of news concern?
What topic is this news article about?In what section of the newspaper could this article be published? What category does this article fall into?
", + "bbox": [ + 121, + 83, + 880, + 159 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2564a9d6aca6404d8b57aa3b0b8806b272e11caa0ac3eafaa2eacc890fd98f87.jpg", + "table_caption": [ + "Table 5: Correlation results for the different tasks, with OPT (different sizes) and Bloom. Correlations with $p < 0 . 0 5$ are marked with \\*. Correlations with $p < 0 . 0 0 6 2 5$ (according to Bonferroni correction for multiple hypotheses) are marked with $^ { * * }$ . Dark and light blue colored cells stand for negative correlations $< - 0 . 2$ and $> - 0 . 2$ , respectively. Dark and light orange colored cells stand for positive correlations $> 0 . 2$ and $< 0 . 2$ , respectively. Average accuracy across all prompts and average accuracy of best $50 \\%$ prompts are also reported for reference (Avg Acc and Acc $50 \\%$ , respectively). " + ], + "table_footnote": [], + "table_body": "
ModelTaskPerplexity-score corr. Pearson SpearmanPerplexity-acc corr. Pearson Spearman Avg Acc Acc 50%
OPT175BAntonyms**-0.41**-0.53
GLUE Cola-0.15-0.14-0.041 -0.021 47.71 57.1
Newspop*-0.24**-0.26 *-0.20-0.1866.472.9
AG News**-0.63 **-0.68 **-0.77**-0.8157.568.7
IMDB**0.35**0.400.14*0.2086.291.0
DBpedia **-0.50**-0.44 **-0.51**-0.4246.755.2
Emotion-0.14-0.19 **-0.30 **-0.3216.423.0
Tweet Offensive*-0.190.070.18*0.2351.355.8
Bloom 176BAntonyms**-0.37**-0.2311
GLUE Cola0.070.11**-0.25**-0.2655.565.6
Newspop**-0.50**-0.42 **-0.59 **-0.5178.987.8
AG News**-0.62 **-0.54**-0.44**-0.4450.359.4
IMDB0.040.09-0.08-0.1489.392.2
DBpedia**-0.47 *-0.27**-0.35*-0.2127.233.4
Emotion**-0.33 **-0.42**-0.48**-0.5529.331.7
Tweet Offensive0.14*0.24 *-0.20-0.0341.646.2
OPT 30B Antonyms **-0.54**-0.701111
GLUE Cola-0.050.03-0.130.0232.235.5
Newspop*-0.23 *-0.25*-0.18-0.1260.366.6
AG News**-0.66 **-0.71 **-0.81**-0.8049.360.7
IMDB-0.06*0.170.04**0.2281.686.1
DBpedia **-0.41 **-0.34*-0.21*-0.2535.942.4
Emotion0.00-0.030.180.1312.316.2
Tweet Offensive**-0.44**-0.39-0.11-0.0554.660.2
OPT 1.3BAntonyms **-0.45**-0.531
GLUE Cola **-0.39 **-0.36-0.09*-0.1960.31 65.9
Newspop**0.33*0.21-0.07-0.0737.640.3
AG News**-0.33**-0.29 **-0.56 **-0.4931.937.6
IMDB-0.11-0.07**0.24**0.2286.089.1
DBpedia-0.16-0.14-0.02-0.018.79.2
Emotion0.080.08**-0.29**-0.307.09.1
Tweet Offensive**-0.42**-0.35 **-0.50**-0.3858.662.6
", + "bbox": [ + 156, + 209, + 845, + 711 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "scores. ", + "bbox": [ + 117, + 834, + 168, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the word prediction tasks we only report scores, since accuracy in general is less stable, suffers more from the surface form competition (Holtzman et al., 2021), and is usually quite low for these tasks in our setting (the chances the model will generate an exact match of the label are low). Hence, the score of the correct label gives a better estimate of the actual performance of the model. ", + "bbox": [ + 115, + 856, + 487, + 919 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 510, + 831, + 884, + 894 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b3cba6af752cb82670186ce9f9013f8469ef2cf9ec5f5cc7cefe20d8c12f210f.jpg", + "table_caption": [ + "Table 6: Correlation results for word-level translation, with OPT 175B and Bloom 176B. All correlations are statistically significant also according to Bonferroni correction for multiple hypotheses for OPT $( p < 0 . 0 0 5 5 )$ . Same for Bloom $( p \\textless 0 . 0 0 3 5 7 )$ , except for Catalan (Pearson) and Japanese (Spearman). " + ], + "table_footnote": [], + "table_body": "
LangOPT175BBloom 176B PearsonSpear.
PearsonSpear.
ita-0.44-0.57-0.37-0.63
spa-0.47-0.61-0.51-0.66
cat-0.47-0.58-0.24-0.31
fra-0.48-0.57-0.48-0.64
deu-0.44-0.60-0.46-0.65
fin-0.44-0.62-0.34-0.56
por-0.45-0.62-0.46-0.61
eus-0.47-0.61-0.45-0.61
tur-0.44-0.62-0.33-0.62
jpn-0.33-0.26
arb-0.36-0.47
rus1-0.54-0.69
kor-0.42-0.58
ell-0.40-0.51
", + "bbox": [ + 156, + 83, + 452, + 302 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5 Results ", + "text_level": 1, + "bbox": [ + 117, + 424, + 211, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Classification Tasks and Antonym Prediction Table 5 depicts the Pearson and Spearman correlation results on the classification tasks and the antonym task, with both OPT 175B and Bloom (two upper blocks). We see that most correlations are negative and statistically significant, as we expect. This validates our hypothesis and shows that in the majority of tasks we indeed get a strong correlation between low perplexity of the prompt and better performance on the task.10 For each task we also report the average accuracy. ", + "bbox": [ + 115, + 450, + 487, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Word-Level Translation The results of the wordlevel translation task are reported in Table 6. Here the correlations are extremely consistent across all languages and across models, with statistical significance for all languages except for Catalan and Japanese (in Bloom). ", + "bbox": [ + 115, + 637, + 487, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results across Different Model Sizes We repeat the same experiment with the OPT models of sizes 1.3B and 30B, to investigate whether these correlations are also consistent across model sizes or whether this is a phenomenon we should expect only in large language models. Table 5 (two lower blocks) shows these results for all classification tasks and antonym prediction. We do see that in general the trend appears to be the same in the smaller models as well; however, the correlations seem to be slightly weaker. We hypothesize that this might be due to the overall lower performance of these smaller models, making the performance results we use for correlation less stable and reliable. For word-level translation, however, all correlations with the 30B and 1.3B models are similar to those with the 175B model, and are all statistically significant (also after Bonferroni correction for multiple hypotheses). ", + "bbox": [ + 115, + 744, + 485, + 871 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 85, + 882, + 261 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6 Analysis ", + "text_level": 1, + "bbox": [ + 512, + 275, + 616, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we further explore the observed relationship between model perplexity and prompt performance. Despite the consistently high correlation between these two factors, the structure of this relationship varies across tasks (Section 6.1). Additionally, we find that the automatically added prompts are highquality and not a significant source of noise (Section 6.2), and that the best prompts selected by our approach vary across models (Section 6.3). ", + "bbox": [ + 512, + 304, + 882, + 447 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1 Visualizing the Relationship between Perplexity and Performance ", + "text_level": 1, + "bbox": [ + 512, + 462, + 843, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To visualize the correlations we get between the perplexity and the performance of the prompts across the different settings, we plot a few examples for different tasks and languages. Figures 1 and 2 show some of the results for selected tasks, as detailed in the captions. The negative trend of the correlation is clearly visible in all plots. Interestingly, the structure of the plots for word-level translation are very similar across all the language pairs, suggesting that prompts get consistent perplexity and performance across languages (possibly at different scales). Indeed, the intersection of the 10 lowest perplexity prompts between any two different languages is 8.6 and 8.4 on average (for OPT 175B and Bloom, respectively), which is extremely high. This is not very surprising since we know that the only differences between the prompts in the different languages are the names of the target languages (e.g., The word for “dog” in French is “). Additionally, the intersection of 10 prompts with the highest label score between any two different languages is 7 and 6.5 on average (for OPT 175B and Bloom, respectively). ", + "bbox": [ + 512, + 500, + 882, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A notable finding that appears in the word-level translation plots is the clear separation between prompts that include or do not include quotation marks for the label (usually aligns with whether the prompt uses quotation marks for the source word) – three example prompts appear on the plot. Prompts with quotation marks for the words tend to have both lower perplexity and better performance, consistently. We further analyze the results for OPT 175B within clusters (with/without quotations marks). In the cluster with quotation marks, we get negative correlations (in the range of $- 0 . 2 8$ to –0.38) that are statistically significant for almost all languages. The correlations within the other cluster are weaker and less significant (this is expected given the overall lower performance of that cluster). ", + "bbox": [ + 510, + 872, + 880, + 920 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 84, + 487, + 293 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/75ad713163e05245c30b6d7c7488af8e438550f2577006fad2670d68d0418ccd.jpg", + "image_caption": [ + "Figure 2: Score of correct label vs. perplexity for the word-level translation task in French with OPT 175B. The $x$ axis is in log scale. The blue points stand for prompts with quotation marks for the words, while the yellow points are of prompts without quotation marks. " + ], + "image_footnote": [], + "bbox": [ + 119, + 311, + 473, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2 Effect of Noisy Prompts ", + "text_level": 1, + "bbox": [ + 117, + 606, + 347, + 620 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We expect our automatic method for expanding the set of prompts to also introduce some noise. Though our focus is on the lower perplexity prompts, since we want to benefit from this analysis and be able to devise a method for creating better prompts, we do want to make sure that this potential noise is not the cause for the strong correlations we get. In other words, one might claim that some noisy prompts have particularly high perplexity and also perform badly, thus, supporting our hypothesis in an undesirable and uncontrolled manner. ", + "bbox": [ + 115, + 629, + 487, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We turn to inspect the $10 \\%$ highest perplexity prompts in the different tasks and find subjectively that they are not noisy, and are usually valid prompts for the tasks. The 5 highest perplexity prompts for the GLUE Cola task are listed in Table 7 as an example. ", + "bbox": [ + 115, + 824, + 487, + 920 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0676c167016e601752cbf9cf576b41c3f00970b48aace957a068b4c8db70d3fb.jpg", + "table_caption": [ + "Table 7: Example of the 5 highest perplexity prompts for GLUE Cola, using OPT 175B. " + ], + "table_footnote": [], + "table_body": "
promptppl
Is this example correct English usage?25.79
Is this example using English correctly?25.46
Is this example correct English?25.33
Is this the example in correct English?25.00
Is English in this example correct?24.90
", + "bbox": [ + 547, + 82, + 852, + 173 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4939bb9ff9bdb5824103cf27fa0b652f5bf028a68c2ee989473913a65f55fb34.jpg", + "table_caption": [ + "Table 8: Correlations before and after filtering out noisy prompts, with AG News and Word-Level Translation (WLT). " + ], + "table_footnote": [], + "table_body": "
TaskLangBefore filteringAfter filtering
PearsonSpearmanPearsonSpearman
AG News--0.63-0.68-0.62-0.54
WLTita-0.44-0.58-0.44-0.57
spa-0.47-0.61-0.47-0.61
cat-0.45-0.57-0.47-0.58
fra-0.47-0.57-0.48-0.57
deu-0.43-0.60-0.44-0.60
fin-0.41-0.60-0.44-0.62
por-0.43-0.61-0.45-0.62
eus-0.45-0.60-0.47-0.61
tur-0.43-0.61-0.44-0.62
", + "bbox": [ + 514, + 227, + 882, + 374 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As a sanity check, we choose two tasks: wordlevel translation and AG News, manually filter out the noisy prompts, and compute the correlations again. The annotation is done by external annotators (NLP researchers) that were presented with the tasks and asked to label whether the prompt is reasonable to use for the task. The new correlations with OPT 175B are reported in Table 8. We find that all correlations remain strong and statistically significant when noise is manually removed from the analysis. We get the same trends with Bloom as well. ", + "bbox": [ + 512, + 455, + 882, + 646 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3 Best Performing Prompts ", + "text_level": 1, + "bbox": [ + 512, + 659, + 756, + 675 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 9 lists the 5 lowest perplexity prompts for the task of antonym prediction, as an example. Similar lists for the rest of the tasks are listed in Section B in the Appendix. ", + "bbox": [ + 510, + 682, + 880, + 745 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A closer look at the lowest perplexity prompts reveals that the intersection of 10 lowest perplexity prompts between OPT 175B and Bloom is 7.1 on average, across the classification tasks. When looking at the 10 highest accuracy prompts across models we get an average intersection of 3.1 across the classification tasks. ", + "bbox": [ + 512, + 747, + 882, + 777 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8a34ea5b354451180d9db62eda8e50dbc7cce6d832a3d346f164a1dd2489bb33.jpg", + "table_caption": [ + "Table 9: Lowest perplexity prompts for the antonym prediction task, using OPT 175B. " + ], + "table_footnote": [], + "table_body": "
promptppl
The following two words are antonyms:“good"and “10.24
The antonym of the word“good’is“10.32
The word that has the opposite meaning of the word “good"is “10.43
The word“good’is the antithesis of the word “10.85
The word “good"is the opposite of the word “11.15
", + "bbox": [ + 514, + 800, + 882, + 877 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 84, + 487, + 164 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7 SPELL: Selecting Prompts by Estimating LM Likelihood ", + "text_level": 1, + "bbox": [ + 115, + 178, + 410, + 211 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The primary contribution of this work is the analysis of the relationship between prompt perplexity and downstream task performance (Section 5). As one potential application of our findings, we also present a new method, SPELL, for generating and selecting consistently effective prompts. ", + "bbox": [ + 115, + 222, + 487, + 318 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Assuming a fixed computational budget for finding effective prompts for a given task, and that the search space might be quite large, we devise the following straightforward procedure: ", + "bbox": [ + 115, + 321, + 487, + 384 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "1. Obtain a small set of manually created prompts for the task. \n2. Expand the set of prompts with automatic paraphrasing using a LM (e.g., GPT3) and backtranslation (see Section 3). \n3. Rank the list of prompts by perplexity (averaged on a representative sample of task inputs, e.g., 1,000). \n4. Choose the $k$ (e.g., 3) lowest perplexity prompts. ", + "bbox": [ + 131, + 399, + 487, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using this algorithm, we show empirically that it is best to prioritize experimenting with the lowest perplexity prompts, as they are more stable (exhibit less variation in performance) and perform better than manual prompts on average. This method also does not require any labels for the task, and is applicable to any task, also by non-experts, given example inputs only. ", + "bbox": [ + 117, + 595, + 485, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7.1 Empirical Validation of SPELL ", + "text_level": 1, + "bbox": [ + 117, + 737, + 408, + 752 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To show the effectiveness of our method, we report the results we get using SPELL across the different tasks. In Table 10 we report the average accuracy with the manual prompts compared to the average accuracy with the 3 lowest-perplexity prompts, for both OPT 175B and Bloom. Indeed, in most cases, the average accuracy using the 3 lowest perplexity prompts outperforms the average accuracy of the manual prompts, with an average of 1.8 accuracy points across tasks with OPT and 2.3 accuracy points with Bloom, demonstrating the effectiveness of our method. ", + "bbox": [ + 115, + 759, + 487, + 919 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f413625d6c4e09e95cee13f18621cc7605e4ba78b2045a51a59caa4f433489b6.jpg", + "table_caption": [ + "Table 10: The average accuracy with the manual prompts (manual) compared to the average accuracy with the 3 lowest-perplexity prompts (low-ppl), for both OPT 175B and Bloom, across tasks. " + ], + "table_footnote": [], + "table_body": "
OPTBloom
Tasklow-pplmanual△low-pplmanual△
GLUE Cola51.748.53.164.560.93.6
Newspop80.670.410.290.080.010.0
AG News68.461.96.551.063.5-12.5
IMDB90.488.91.491.388.82.5
DBpedia46.051.7-5.731.230.21.0
Emotion21.622.6-1.135.832.13.6
Tweet Offensive48.450.6-2.348.640.87.8
", + "bbox": [ + 514, + 83, + 880, + 189 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 510, + 285, + 880, + 315 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The variability in accuracy of the 3 lowest perplexity prompts is also much lower than that of the manually created prompts: with OPT 175B, the average standard deviation within the 3 lowest perplexity prompts (across tasks) is 5.07, vs. 6.86 for the manual prompts, and with Bloom the gap is much bigger, with an average of 2.6 for the 3 lowest perplexity prompts vs. 7.47 for the manual ones.11 This further shows that SPELL is more stable and reliable compared to using an arbitrary set of manually created prompts. SPELL sets the stage for further development in this direction, and serves as an initial indication of the benefits of involving perplexity estimation in the process of generating effective prompts. ", + "bbox": [ + 512, + 317, + 882, + 558 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8 Related Work ", + "text_level": 1, + "bbox": [ + 512, + 573, + 663, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Relation between performance and training data Previous work looking directly into the relation between the training data and the performance is limited. Razeghi et al. (2022) study numeric deduction tasks, and examine the correlations between the model performance on specific test instances and the frequency of terms from those instances in the pretraining data. They find that the models are more accurate on instances whose terms are more prevalent in the training data. Additionally, Han and Tsvetkov (2022) propose a method to effectively identify a very small subset of pretraining data that directly supports the model in performing a specific task. Elazar et al. (2022) use causal inference to measure the effect of pretraining data statistics on factual knowledge performance, and ", + "bbox": [ + 510, + 601, + 884, + 858 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Kandpal et al. (2022) show correlational and causal relationships between accuracy and relevant document count (from training data) for QA datasets. ", + "bbox": [ + 115, + 85, + 487, + 131 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Prompt tuning and analysis There is a very rich line of work trying to find prompts automatically. Shin et al. (2020) present an automated method to create discrete prompts for a diverse set of tasks, based on a gradient-guided search, and they demonstrate their method on masked LMs. Other work also focuses on discrete prompts, aiming to improve zero-shot performance (Gao et al., 2021; Le Scao and Rush, 2021; Deng et al., 2022; Shi et al., 2022), or trains continuous prompts (Li and Liang, 2021; Lester et al., 2021; Qin and Eisner, 2021). ", + "bbox": [ + 115, + 152, + 487, + 343 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "On top of works that suggest a variety of methods for creating better prompts, some work also analyzes those prompts to try and get some insights about them: Khashabi et al. (2022a) find that model performance is highly sensitive to small changes in wordings and Khashabi et al. (2022b) point to a surprising disconnect between continuous and discrete prompts. ", + "bbox": [ + 115, + 348, + 485, + 475 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Limitations ", + "text_level": 1, + "bbox": [ + 512, + 84, + 613, + 99 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Searching for human-readable prompts We limit our search space to human-readable prompts that are fluent and accurately describe the task at hand, as we are primarily motivated in understanding why some relevant prompts work better than others. We do this by using manually created prompts and their automatically created paraphrases. Our findings may not hold when the possible prompt space is expanded to include any token sequence; we leave this direction to future work. ", + "bbox": [ + 512, + 110, + 882, + 269 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Generality of our analysis and of the SPELL method We perform our analysis on and build our method around specific models, namely OPT and Bloom. Additionally, our study is limited to the specific tasks we experiment with and to English. It is possible that our analysis and SPELL method do not generalize to other pretrained models or tasks; however, we consider models of various sizes and from different sources, and a wide range of tasks to mitigate this risk. ", + "bbox": [ + 512, + 281, + 882, + 441 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Acknowledgements ", + "text_level": 1, + "bbox": [ + 514, + 455, + 680, + 470 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We thank Alisa Liu and Orevaoghene Ahia for their help in annotating noisy prompts. We also thank the reviewers for their valuable comments on the paper. ", + "bbox": [ + 512, + 481, + 880, + 543 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "9 Conclusion ", + "text_level": 1, + "bbox": [ + 115, + 498, + 243, + 513 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We investigate the phenomenon where some prompts perform better than others despite appearing similar to the human users of LMs. Specifically, we hypothesize that the perplexity of a prompt under a given LM is closely tied to its task performance. We test this theory on a large number of tasks and autoregressive LMs, and the resulting correlation study validates our hypothesis. Further analysis of this relationship demonstrates that the best prompts differ across models, highlighting the importance of model-specific analysis, and that the underlying structure of the relationship between perplexity and performance varies across tasks. ", + "bbox": [ + 117, + 532, + 487, + 739 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In light of these findings, we then propose a method, SPELL, to help users find wellperforming prompts for new tasks. Empirical validation of the proposed procedure shows that SPELL generates effective prompts with low variability in performance, and produces small gains of 1.8 (2.3) accuracy points with OPT (Bloom) over manual prompts. We therefore conclude that SPELL provides a general and interpretable approach for applying LMs to new tasks while requiring minimal human effort, and no labels. ", + "bbox": [ + 117, + 744, + 487, + 919 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "References ", + "text_level": 1, + "bbox": [ + 514, + 573, + 606, + 588 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Stephen H. Bach, Victor Sanh, Zheng-Xin Yong, Albert Webson, Colin Raffel, Nihal V. 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", + "bbox": [ + 115, + 187, + 487, + 227 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Weijia Shi, Xiaochuang Han, Hila Gonen, Ari Holtzman, Yulia Tsvetkov, and Luke Zettlemoyer. 2022. Toward human readable prompt tuning: Kubrick’s the shining is a good movie, and a good prompt too? arXiv preprint arXiv:2212.10539. ", + "bbox": [ + 115, + 237, + 487, + 303 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Taylor Shin, Yasaman Razeghi, Robert L Logan IV, Eric Wallace, and Sameer Singh. 2020. Autoprompt: Eliciting knowledge from language models with automatically generated prompts. arXiv preprint arXiv:2010.15980. ", + "bbox": [ + 117, + 313, + 487, + 378 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Alex Warstadt, Amanpreet Singh, and Samuel R Bowman. 2018. Neural network acceptability judgments. arXiv preprint arXiv:1805.12471. ", + "bbox": [ + 115, + 388, + 487, + 429 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "John Wieting, Jonathan Mallinson, and Kevin Gimpel. 2017. Learning paraphrastic sentence embeddings from back-translated bitext. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 274–285. ", + "bbox": [ + 115, + 438, + 487, + 505 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher Dewan, Mona Diab, Xian Li, Xi Victoria Lin, et al. 2022. Opt: Open pre-trained transformer language models. arXiv preprint arXiv:2205.01068. ", + "bbox": [ + 115, + 514, + 487, + 580 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Xiang Zhang, Junbo Jake Zhao, and Yann LeCun. 2015. Character-level convolutional networks for text classification. In NIPS. ", + "bbox": [ + 115, + 590, + 487, + 630 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "A Manually Created Prompts ", + "text_level": 1, + "bbox": [ + 117, + 643, + 388, + 659 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Table 11 lists the manually created prompts we use for the different tasks. We manually add, remove and edit prompts for some of these tasks, to make them fit for our setting. For example, the following prompt for AG News, taken from Promptsource, does not fit our setting: Would you recommend the following article to a politician, an athlete, business executive, or a scientist? ", + "bbox": [ + 115, + 669, + 487, + 795 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "B Lowest Perplexity Prompts ", + "text_level": 1, + "bbox": [ + 117, + 808, + 384, + 825 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Table 12 lists the 5 lowest perplexity prompts for each task, using OPT 175B. ", + "bbox": [ + 115, + 835, + 485, + 866 + ], + "page_idx": 10 + }, + { + "type": "table", + "img_path": "images/612ece7565d834a2a16a0597f73565c3c5e8c306e876beb3cc91113f8998a7b1.jpg", + "table_caption": [ + "Table 11: The set of manually created prompts for each task. " + ], + "table_footnote": [], + "table_body": "
Task Manual Prompts
AntonymsThe antonym of the word “good”is“ The opposite meaning of the word “good”is “ “Good”is the opposite of“ “Good”is the negation of“ The following are opposites of each other:“good"and “ The word “good"contradicts the word “ The antonym of the word good is The opposite meaning of the word good is Good is the opposite of
GLUE ColaThe following are opposites of each other: good and The word good contradicts the word Does the this sentence make sense and use correct English? Is this example grammatically correct and sensible? Does this sentence make sense and is it grammatically correct?
NewspopDoes this example use correct English? What is the article about? What is this news about? What is the topic of this news piece? What does this article discuss? What is the topic of this sentence? What category does the article belong to? Pick one category forthis news piece. Pick the category that fits the text. The article refers to which category? What topic does the article belong to? What category fits this article? What topic does this news piece belong to? Choose the correct category for this article.
AG NewsWhat label best describes this news article? What is this piece of news regarding? Which newspaper section would this article likely appear in? What topic is this news article about? This movie review expresses what sentiment? Did the reviewer find this movie good or bad?
IMDBIs this review positive or negative? How does the viewer feel about the movie? What sentiment does the writer express for the movie? What sentiment is expressed for the movie? What is the sentiment expressed in this text? Did the reviewer enjoy the movie? What is the sentiment expressed by the reviewer for the movie? How does the reviewer feel about the movie? What category does the paragraph belong to? Pick one category for the text.
DBpediaPick the category that fits the text. The text refers to which category? What category does the title belong to? What category fits this text? What topic does this text belong to? Choose the correct category for the text. What is the emotion expressed in this message?
EmotionWhat emotion does this message express? How will you feel about the message? What emotion does the writer express for the message? Is this tweet offensive? Can the tweet be removed for being offensive?
Tweet OffensiveIs the author's tweet offensive? Task: Identify if the tweetor text is offensive. Is this an offensive tweet? The translation of the word “dog"to French is“ The translation of the word dog to French is The word “dog”in French is“
Word-Level Translation“dog”(In French: “ Translate the word dog into French: The translation of dog to French is “dog”(French: “ The word dog in French is Translate the word“dog”into French: “ dog (In French: dog (French: The translation of“dog”to French is “
", + "bbox": [ + 275, + 71, + 727, + 906 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/45d19f9d0823cbb9eeb63ab25dd750b457ac6ef2d6939218d35ded145a99986c.jpg", + "table_caption": [ + "Table 12: The 5 lowest perplexity prompts for each task, using OPT 175B. " + ], + "table_footnote": [], + "table_body": "
TaskLowest Perplexity PromptsPerplexity
AntonymsThe following two words are antonyms:“good”and “10.24
The antonym of the word“good"is“10.32
The word that has the opposite meaning of the word “good" is “10.43
The word“good”is the antithesis of the word“10.85
The word “good” is the opposite of the word “11.15
GLUE ColaIs this an example of the proper use of the English language?11.63
Does the sentence make sense and does it follow the rules of grammar?11.76
Is this sentence an example of the correct use of the English language?12.10
Does this sentence make sense and is it grammatically correct?12.15
Is this sentence grammatically correct and does it make sense?12.68
NewspopWhat is the main subject of the article?10.01
What is the main topic of the article?10.01
What is the subject matter of the article?10.17
What is the subject of the article?10.21
What is the main idea of this article?10.21
AG NewsIn what section of the newspaper would you expect to find this article?7.51
In which section of the newspaper would you expect to find this article?7.52
In which section of the newspaper would this article be most likely to appear?7.60
In what section of the newspaper do you expect to find this article?7.80
In what section of the newspaper would this article most likely appear?7.87
IMDBWhat is the opinion of the review? Is it positive or negative?7.19
Is this a positive or negative review?7.31
What do you think of the movie?7.33
What do you think of the film?7.35
Is that a positive or a negative?7.35
DBpediaWhat is the category to which the text refers?8.99
What is the subject of the text?9.15
What category does the title belong to?9.18
Which category does the text refer to?9.19
What is the subject of this text?9.20
EmotionHow do you feel when you hear this message?12.72
What is the writer's emotional reaction to this news?13.18
What is the emotion expressed in this message?13.20
How does this message make you feel?13.32
How do you feel about this message?13.50
Tweet OffensiveIf someone said this to you, would you be offended?13.00
If someone said that to you, would you be offended?13.10
Would you be offended if someone said that to you?13.73
Would it offend you if someone said that to you?14.79
If someone told you that, would you be offended?14.93
Word-Level TranslationThe word for“dog"in French is“7.73
The French word for“dog”is“8.16
The French translation of the word“dog”is“8.24
The translation of the word “dog”in French is “8.35
The translation of the word “dog” into French is “8.91
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This larger set allows us", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 86, + 451, + 273, + 463 + ], + "spans": [ + { + "bbox": [ + 86, + 451, + 273, + 463 + ], + "score": 1.0, + "content": "to verify that perplexity is a strong predictor", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 86, + 463, + 273, + 474 + ], + "spans": [ + { + "bbox": [ + 86, + 463, + 273, + 474 + ], + "score": 1.0, + "content": "of the success of a prompt and we show that", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 86, + 474, + 273, + 487 + ], + "spans": [ + { + "bbox": [ + 86, + 474, + 273, + 487 + ], + "score": 1.0, + "content": "the lowest perplexity prompts are consistently", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 86, + 486, + 126, + 499 + ], + "spans": [ + { + "bbox": [ + 86, + 486, + 126, + 499 + ], + "score": 1.0, + "content": "effective.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 70, + 509, + 153, + 522 + ], + "lines": [ + { + "bbox": [ + 67, + 507, + 155, + 524 + ], + "spans": [ + { + "bbox": [ + 67, + 507, + 155, + 524 + ], + "score": 1.0, + "content": "1 Introduction", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 70, + 531, + 290, + 705 + ], + "lines": [ + { + "bbox": [ + 68, + 531, + 290, + 544 + ], + "spans": [ + { + "bbox": [ + 68, + 531, + 290, + 544 + ], + "score": 1.0, + "content": "Language models can be prompted to perform", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 543, + 290, + 558 + ], + "spans": [ + { + "bbox": [ + 68, + 543, + 290, + 558 + ], + "score": 1.0, + "content": "a wide range of zero- and few-shot learning", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 69, + 557, + 291, + 570 + ], + "spans": [ + { + "bbox": [ + 69, + 557, + 291, + 570 + ], + "score": 1.0, + "content": "tasks (Brown et al., 2020; Schick and Schütze,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 68, + 570, + 291, + 585 + ], + "spans": [ + { + "bbox": [ + 68, + 570, + 291, + 585 + ], + "score": 1.0, + "content": "2020). 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Despite efforts to im-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 68, + 654, + 290, + 665 + ], + "spans": [ + { + "bbox": [ + 68, + 654, + 290, + 665 + ], + "score": 1.0, + "content": "prove prompt engineering (Shin et al., 2020; Li and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "spans": [ + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "score": 1.0, + "content": "Liang, 2021; Gao et al., 2021), it is still challenging", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 680, + 291, + 693 + ], + "spans": [ + { + "bbox": [ + 68, + 680, + 291, + 693 + ], + "score": 1.0, + "content": "to develop high-quality prompts for new tasks, and", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 69, + 693, + 292, + 706 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 292, + 706 + ], + "score": 1.0, + "content": "little is known about why this phenomenon occurs.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 69, + 707, + 290, + 774 + ], + "lines": [ + { + "bbox": [ + 80, + 707, + 290, + 720 + ], + "spans": [ + { + "bbox": [ + 80, + 707, + 290, + 720 + ], + "score": 1.0, + "content": "We are interested in understanding what makes", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 69, + 721, + 291, + 734 + ], + "spans": [ + { + "bbox": [ + 69, + 721, + 291, + 734 + ], + "score": 1.0, + "content": "some prompts better than others, and using this un-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 69, + 734, + 291, + 748 + ], + "spans": [ + { + "bbox": [ + 69, + 734, + 291, + 748 + ], + "score": 1.0, + "content": "derstanding to create better prompts for given tasks", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 68, + 747, + 291, + 761 + ], + "spans": [ + { + "bbox": [ + 68, + 747, + 291, + 761 + ], + "score": 1.0, + "content": "and models. 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This is based", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 303, + 461, + 527, + 475 + ], + "spans": [ + { + "bbox": [ + 303, + 461, + 527, + 475 + ], + "score": 1.0, + "content": "on the intuition that the more frequently the prompt", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 303, + 475, + 525, + 488 + ], + "spans": [ + { + "bbox": [ + 303, + 475, + 525, + 488 + ], + "score": 1.0, + "content": "(or very similar phrases) appears in the training", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 488, + 526, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 526, + 501 + ], + "score": 1.0, + "content": "data, the more the model is familiar with it and", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 303, + 502, + 525, + 514 + ], + "spans": [ + { + "bbox": [ + 303, + 502, + 525, + 514 + ], + "score": 1.0, + "content": "is able to perform the described task. 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As part of", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 86, + 404, + 274, + 415 + ], + "spans": [ + { + "bbox": [ + 86, + 404, + 274, + 415 + ], + "score": 1.0, + "content": "our analysis, we also devise a method to auto-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 86, + 415, + 273, + 427 + ], + "spans": [ + { + "bbox": [ + 86, + 415, + 273, + 427 + ], + "score": 1.0, + "content": "matically extend a small seed set of manually", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 86, + 428, + 273, + 439 + ], + "spans": [ + { + "bbox": [ + 86, + 428, + 273, + 439 + ], + "score": 1.0, + "content": "written prompts by paraphrasing with GPT3", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 86, + 438, + 273, + 452 + ], + "spans": [ + { + "bbox": [ + 86, + 438, + 273, + 452 + ], + "score": 1.0, + "content": "and backtranslation. This larger set allows us", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 86, + 451, + 273, + 463 + ], + "spans": [ + { + "bbox": [ + 86, + 451, + 273, + 463 + ], + "score": 1.0, + "content": "to verify that perplexity is a strong predictor", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 86, + 463, + 273, + 474 + ], + "spans": [ + { + "bbox": [ + 86, + 463, + 273, + 474 + ], + "score": 1.0, + "content": "of the success of a prompt and we show that", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 86, + 474, + 273, + 487 + ], + "spans": [ + { + "bbox": [ + 86, + 474, + 273, + 487 + ], + "score": 1.0, + "content": "the lowest perplexity prompts are consistently", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 86, + 486, + 126, + 499 + ], + "spans": [ + { + "bbox": [ + 86, + 486, + 126, + 499 + ], + "score": 1.0, + "content": "effective.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 18.5, + "bbox_fs": [ + 85, + 236, + 274, + 499 + ] + }, + { + "type": "title", + "bbox": [ + 70, + 509, + 153, + 522 + ], + "lines": [ + { + "bbox": [ + 67, + 507, + 155, + 524 + ], + "spans": [ + { + "bbox": [ + 67, + 507, + 155, + 524 + ], + "score": 1.0, + "content": "1 Introduction", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 70, + 531, + 290, + 705 + ], + "lines": [ + { + "bbox": [ + 68, + 531, + 290, + 544 + ], + "spans": [ + { + "bbox": [ + 68, + 531, + 290, + 544 + ], + "score": 1.0, + "content": "Language models can be prompted to perform", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 543, + 290, + 558 + ], + "spans": [ + { + "bbox": [ + 68, + 543, + 290, + 558 + ], + "score": 1.0, + "content": "a wide range of zero- and few-shot learning", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 69, + 557, + 291, + 570 + ], + "spans": [ + { + "bbox": [ + 69, + 557, + 291, + 570 + ], + "score": 1.0, + "content": "tasks (Brown et al., 2020; Schick and Schütze,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 68, + 570, + 291, + 585 + ], + "spans": [ + { + "bbox": [ + 68, + 570, + 291, + 585 + ], + "score": 1.0, + "content": "2020). However, there is significant variance in the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 585, + 290, + 598 + ], + "spans": [ + { + "bbox": [ + 69, + 585, + 290, + 598 + ], + "score": 1.0, + "content": "performance of seemingly similar prompts (Chen", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 68, + 599, + 290, + 611 + ], + "spans": [ + { + "bbox": [ + 68, + 599, + 290, + 611 + ], + "score": 1.0, + "content": "et al., 2022): for AG News (Zhang et al., 2015), we", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 69, + 612, + 291, + 626 + ], + "spans": [ + { + "bbox": [ + 69, + 612, + 291, + 626 + ], + "score": 1.0, + "content": "find an over 30 point accuracy gap between differ-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 69, + 626, + 290, + 638 + ], + "spans": [ + { + "bbox": [ + 69, + 626, + 290, + 638 + ], + "score": 1.0, + "content": "ent manually curated prompts (see Table 1) on OPT", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 69, + 639, + 291, + 651 + ], + "spans": [ + { + "bbox": [ + 69, + 639, + 291, + 651 + ], + "score": 1.0, + "content": "175B (Zhang et al., 2022). Despite efforts to im-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 68, + 654, + 290, + 665 + ], + "spans": [ + { + "bbox": [ + 68, + 654, + 290, + 665 + ], + "score": 1.0, + "content": "prove prompt engineering (Shin et al., 2020; Li and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "spans": [ + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "score": 1.0, + "content": "Liang, 2021; Gao et al., 2021), it is still challenging", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 680, + 291, + 693 + ], + "spans": [ + { + "bbox": [ + 68, + 680, + 291, + 693 + ], + "score": 1.0, + "content": "to develop high-quality prompts for new tasks, and", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 69, + 693, + 292, + 706 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 292, + 706 + ], + "score": 1.0, + "content": "little is known about why this phenomenon occurs.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 37, + "bbox_fs": [ + 68, + 531, + 292, + 706 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 707, + 290, + 774 + ], + "lines": [ + { + "bbox": [ + 80, + 707, + 290, + 720 + ], + "spans": [ + { + "bbox": [ + 80, + 707, + 290, + 720 + ], + "score": 1.0, + "content": "We are interested in understanding what makes", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 69, + 721, + 291, + 734 + ], + "spans": [ + { + "bbox": [ + 69, + 721, + 291, + 734 + ], + "score": 1.0, + "content": "some prompts better than others, and using this un-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 69, + 734, + 291, + 748 + ], + "spans": [ + { + "bbox": [ + 69, + 734, + 291, + 748 + ], + "score": 1.0, + "content": "derstanding to create better prompts for given tasks", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 68, + 747, + 291, + 761 + ], + "spans": [ + { + "bbox": [ + 68, + 747, + 291, + 761 + ], + "score": 1.0, + "content": "and models. We hypothesize that the lower the per-", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 69, + 761, + 290, + 775 + ], + "spans": [ + { + "bbox": [ + 69, + 761, + 290, + 775 + ], + "score": 1.0, + "content": "plexity of a prompt is, the better its performance", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 434, + 525, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 525, + 447 + ], + "score": 1.0, + "content": "on the task will be, when considering reasonable", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 303, + 448, + 526, + 460 + ], + "spans": [ + { + "bbox": [ + 303, + 448, + 526, + 460 + ], + "score": 1.0, + "content": "prompts that are related to the task. This is based", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 303, + 461, + 527, + 475 + ], + "spans": [ + { + "bbox": [ + 303, + 461, + 527, + 475 + ], + "score": 1.0, + "content": "on the intuition that the more frequently the prompt", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 303, + 475, + 525, + 488 + ], + "spans": [ + { + "bbox": [ + 303, + 475, + 525, + 488 + ], + "score": 1.0, + "content": "(or very similar phrases) appears in the training", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 488, + 526, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 526, + 501 + ], + "score": 1.0, + "content": "data, the more the model is familiar with it and", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 303, + 502, + 525, + 514 + ], + "spans": [ + { + "bbox": [ + 303, + 502, + 525, + 514 + ], + "score": 1.0, + "content": "is able to perform the described task. We refrain", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 304, + 515, + 525, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 525, + 528 + ], + "score": 1.0, + "content": "from using the training data directly as it is often", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 303, + 529, + 525, + 541 + ], + "spans": [ + { + "bbox": [ + 303, + 529, + 525, + 541 + ], + "score": 1.0, + "content": "unavailable, expensive to search due to its size, and", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 303, + 542, + 526, + 556 + ], + "spans": [ + { + "bbox": [ + 303, + 542, + 526, + 556 + ], + "score": 1.0, + "content": "hard to use for approximate matching of similar", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 303, + 556, + 525, + 569 + ], + "spans": [ + { + "bbox": [ + 303, + 556, + 525, + 569 + ], + "score": 1.0, + "content": "prompts. Instead, we focus on the perplexity of the", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 303, + 570, + 522, + 582 + ], + "spans": [ + { + "bbox": [ + 303, + 570, + 522, + 582 + ], + "score": 1.0, + "content": "prompt as a proxy for its occurrences in the data.", + "type": "text" + } + ], + "index": 72 + } + ], + "index": 46, + "bbox_fs": [ + 68, + 707, + 291, + 775 + ] + }, + { + "type": "image", + "bbox": [ + 308, + 216, + 518, + 358 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 308, + 216, + 518, + 358 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 308, + 216, + 518, + 358 + ], + "spans": [ + { + "bbox": [ + 308, + 216, + 518, + 358 + ], + "score": 0.967, + "type": "image", + "image_path": "4ff36496e07000f2d3b941c7008cf5afb10d1b32105a220ab3e483f827d67b6a.jpg" + } + ] + } + ], + "index": 53.5, + "virtual_lines": [ + { + "bbox": [ + 308, + 216, + 518, + 230.2 + ], + "spans": [], + "index": 49 + }, + { + "bbox": [ + 308, + 230.2, + 518, + 244.39999999999998 + ], + "spans": [], + "index": 50 + }, + { + "bbox": [ + 308, + 244.39999999999998, + 518, + 258.59999999999997 + ], + "spans": [], + "index": 51 + }, + { + "bbox": [ + 308, + 258.59999999999997, + 518, + 272.79999999999995 + ], + "spans": [], + "index": 52 + }, + { + "bbox": [ + 308, + 272.79999999999995, + 518, + 286.99999999999994 + ], + "spans": [], + "index": 53 + }, + { + "bbox": [ + 308, + 286.99999999999994, + 518, + 301.19999999999993 + ], + "spans": [], + "index": 54 + }, + { + "bbox": [ + 308, + 301.19999999999993, + 518, + 315.3999999999999 + ], + "spans": [], + "index": 55 + }, + { + "bbox": [ + 308, + 315.3999999999999, + 518, + 329.5999999999999 + ], + "spans": [], + "index": 56 + }, + { + "bbox": [ + 308, + 329.5999999999999, + 518, + 343.7999999999999 + ], + "spans": [], + "index": 57 + }, + { + "bbox": [ + 308, + 343.7999999999999, + 518, + 357.9999999999999 + ], + "spans": [], + "index": 58 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 304, + 374, + 525, + 410 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 525, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 525, + 386 + ], + "score": 1.0, + "content": "Figure 1: Accuracy vs. perplexity for the AG News", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 304, + 385, + 525, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 418, + 399 + ], + "score": 1.0, + "content": "dataset with OPT 175B. The", + "type": "text" + }, + { + "bbox": [ + 418, + 388, + 425, + 396 + ], + "score": 0.73, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 385, + 525, + 399 + ], + "score": 1.0, + "content": "axis is in log scale. Each", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 304, + 399, + 446, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 446, + 412 + ], + "score": 1.0, + "content": "point stands for a different prompt.", + "type": "text" + } + ], + "index": 61 + } + ], + "index": 60 + } + ], + "index": 56.75 + }, + { + "type": "text", + "bbox": [ + 305, + 434, + 525, + 582 + ], + "lines": [], + "index": 67, + "bbox_fs": [ + 303, + 434, + 527, + 582 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 305, + 585, + 525, + 732 + ], + "lines": [ + { + "bbox": [ + 316, + 584, + 526, + 597 + ], + "spans": [ + { + "bbox": [ + 316, + 584, + 526, + 597 + ], + "score": 1.0, + "content": "To enable more complete analysis, we automati-", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 596, + 525, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 525, + 612 + ], + "score": 1.0, + "content": "cally expand the set of manually created prompts", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 611, + 525, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 525, + 624 + ], + "score": 1.0, + "content": "for the task by paraphrasing, resulting in a much", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 625, + 525, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 525, + 638 + ], + "score": 1.0, + "content": "larger and diverse set of prompts. 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As", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 98, + 291, + 113 + ], + "spans": [ + { + "bbox": [ + 68, + 98, + 291, + 113 + ], + "score": 1.0, + "content": "a result, we devise a method, SPELL (Selecting", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 113, + 291, + 125 + ], + "spans": [ + { + "bbox": [ + 69, + 113, + 291, + 125 + ], + "score": 1.0, + "content": "Prompts by Estimating LM Likelihood), for cre-", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 127, + 290, + 139 + ], + "spans": [ + { + "bbox": [ + 68, + 127, + 290, + 139 + ], + "score": 1.0, + "content": "ating prompts in an informed manner. We show", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 140, + 290, + 153 + ], + "spans": [ + { + "bbox": [ + 68, + 140, + 290, + 153 + ], + "score": 1.0, + "content": "that using SPELL to choose prompts results in less", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 152, + 291, + 167 + ], + "spans": [ + { + "bbox": [ + 68, + 152, + 291, + 167 + ], + "score": 1.0, + "content": "variability in performance as well as in accuracy", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 167, + 292, + 180 + ], + "spans": [ + { + "bbox": [ + 68, + 167, + 292, + 180 + ], + "score": 1.0, + "content": "gains (1.8 accuracy points with OPT and 2.3 accu-", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 181, + 291, + 194 + ], + "spans": [ + { + "bbox": [ + 69, + 181, + 291, + 194 + ], + "score": 1.0, + "content": "racy points with Bloom on average). 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As", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 98, + 291, + 113 + ], + "spans": [ + { + "bbox": [ + 68, + 98, + 291, + 113 + ], + "score": 1.0, + "content": "a result, we devise a method, SPELL (Selecting", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 113, + 291, + 125 + ], + "spans": [ + { + "bbox": [ + 69, + 113, + 291, + 125 + ], + "score": 1.0, + "content": "Prompts by Estimating LM Likelihood), for cre-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 127, + 290, + 139 + ], + "spans": [ + { + "bbox": [ + 68, + 127, + 290, + 139 + ], + "score": 1.0, + "content": "ating prompts in an informed manner. We show", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 140, + 290, + 153 + ], + "spans": [ + { + "bbox": [ + 68, + 140, + 290, + 153 + ], + "score": 1.0, + "content": "that using SPELL to choose prompts results in less", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 152, + 291, + 167 + ], + "spans": [ + { + "bbox": [ + 68, + 152, + 291, + 167 + ], + "score": 1.0, + "content": "variability in performance as well as in accuracy", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 167, + 292, + 180 + ], + "spans": [ + { + "bbox": [ + 68, + 167, + 292, + 180 + ], + "score": 1.0, + "content": "gains (1.8 accuracy points with OPT and 2.3 accu-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 181, + 291, + 194 + ], + "spans": [ + { + "bbox": [ + 69, + 181, + 291, + 194 + ], + "score": 1.0, + "content": "racy points with Bloom on average). Importantly,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 194, + 291, + 207 + ], + "spans": [ + { + "bbox": [ + 69, + 194, + 291, + 207 + ], + "score": 1.0, + "content": "our method does not require labels at all, only a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 208, + 225, + 220 + ], + "spans": [ + { + "bbox": [ + 69, + 208, + 225, + 220 + ], + "score": 1.0, + "content": "small sample of inputs for the task.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 69, + 221, + 290, + 369 + ], + "lines": [ + { + "bbox": [ + 80, + 221, + 292, + 233 + ], + "spans": [ + { + "bbox": [ + 80, + 221, + 292, + 233 + ], + "score": 1.0, + "content": "Our contributions can be summarized as follows:", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 234, + 290, + 248 + ], + "spans": [ + { + "bbox": [ + 69, + 234, + 290, + 248 + ], + "score": 1.0, + "content": "(a) we formalize the notion that better familiarity", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 69, + 248, + 291, + 261 + ], + "spans": [ + { + "bbox": [ + 69, + 248, + 291, + 261 + ], + "score": 1.0, + "content": "of the model with the prompt correlates with better", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 69, + 262, + 291, + 275 + ], + "spans": [ + { + "bbox": [ + 69, + 262, + 291, + 275 + ], + "score": 1.0, + "content": "performance (Section 2); (b) we automatically elab-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 69, + 276, + 291, + 289 + ], + "spans": [ + { + "bbox": [ + 69, + 276, + 291, + 289 + ], + "score": 1.0, + "content": "orate a given set of seed prompts using paraphras-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 69, + 289, + 290, + 302 + ], + "spans": [ + { + "bbox": [ + 69, + 289, + 290, + 302 + ], + "score": 1.0, + "content": "ing (Section 3); (c) we establish experimentally the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 69, + 302, + 292, + 316 + ], + "spans": [ + { + "bbox": [ + 69, + 302, + 292, + 316 + ], + "score": 1.0, + "content": "hypothesis that lower perplexity of the prompt cor-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 68, + 315, + 291, + 329 + ], + "spans": [ + { + "bbox": [ + 68, + 315, + 291, + 329 + ], + "score": 1.0, + "content": "relates well with better performance (Section 5);", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 69, + 330, + 291, + 342 + ], + "spans": [ + { + "bbox": [ + 69, + 330, + 291, + 342 + ], + "score": 1.0, + "content": "(d) we devise a method to create a more consistent", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 68, + 343, + 290, + 356 + ], + "spans": [ + { + "bbox": [ + 68, + 343, + 290, + 356 + ], + "score": 1.0, + "content": "set of prompts, that also improve results even with", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 69, + 356, + 216, + 369 + ], + "spans": [ + { + "bbox": [ + 69, + 356, + 216, + 369 + ], + "score": 1.0, + "content": "no labels for the task (Section 7).", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 16 + }, + { + "type": "title", + "bbox": [ + 69, + 379, + 290, + 393 + ], + "lines": [ + { + "bbox": [ + 66, + 377, + 291, + 397 + ], + "spans": [ + { + "bbox": [ + 66, + 377, + 291, + 397 + ], + "score": 1.0, + "content": "2 Why are prompts not all created equal?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 70, + 401, + 289, + 536 + ], + "lines": [ + { + "bbox": [ + 69, + 401, + 290, + 414 + ], + "spans": [ + { + "bbox": [ + 69, + 401, + 290, + 414 + ], + "score": 1.0, + "content": "Despite the popularity of prompting as a method", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 68, + 415, + 290, + 428 + ], + "spans": [ + { + "bbox": [ + 68, + 415, + 290, + 428 + ], + "score": 1.0, + "content": "for using language models (Shin et al., 2020; Li", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 69, + 429, + 290, + 441 + ], + "spans": [ + { + "bbox": [ + 69, + 429, + 290, + 441 + ], + "score": 1.0, + "content": "and Liang, 2021; Gao et al., 2021), the cause for", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 69, + 441, + 290, + 456 + ], + "spans": [ + { + "bbox": [ + 69, + 441, + 290, + 456 + ], + "score": 1.0, + "content": "the different behavior of various prompts remains", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 69, + 455, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 69, + 455, + 290, + 469 + ], + "score": 1.0, + "content": "unclear so far. Table 1 shows four example prompts", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 69, + 469, + 290, + 482 + ], + "spans": [ + { + "bbox": [ + 69, + 469, + 290, + 482 + ], + "score": 1.0, + "content": "for a news topic classification task (AG News) and", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 482, + 291, + 496 + ], + "spans": [ + { + "bbox": [ + 68, + 482, + 291, + 496 + ], + "score": 1.0, + "content": "their respective accuracies when used to prompt", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 68, + 495, + 291, + 510 + ], + "spans": [ + { + "bbox": [ + 68, + 495, + 291, + 510 + ], + "score": 1.0, + "content": "OPT 175B (Zhang et al., 2022). The accuracy gap", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 69, + 510, + 290, + 522 + ], + "spans": [ + { + "bbox": [ + 69, + 510, + 290, + 522 + ], + "score": 1.0, + "content": "between the different prompts is not trivial, and it", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 523, + 286, + 537 + ], + "spans": [ + { + "bbox": [ + 68, + 523, + 286, + 537 + ], + "score": 1.0, + "content": "is not possible to predict from the prompts alone.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27.5 + }, + { + "type": "table", + "bbox": [ + 70, + 546, + 290, + 606 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 70, + 546, + 290, + 606 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 70, + 546, + 290, + 606 + ], + "spans": [ + { + "bbox": [ + 70, + 546, + 290, + 606 + ], + "score": 0.978, + "html": "
PromptAccuracy
What is this piece of news regarding?40.9
What is this article about?52.4
What is the best way to describe this article?68.2
What is the most accurate label for this news article?71.2
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The intuition behind this", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 693, + 290, + 707 + ], + "spans": [ + { + "bbox": [ + 68, + 693, + 290, + 707 + ], + "score": 1.0, + "content": "is that a sequence that is more expected by the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 69, + 707, + 291, + 719 + ], + "spans": [ + { + "bbox": [ + 69, + 707, + 291, + 719 + ], + "score": 1.0, + "content": "model is more likely to aid the model to extract", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 720, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 69, + 720, + 290, + 733 + ], + "score": 1.0, + "content": "the relevant information. 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Our initial attempts to estimate", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 113, + 526, + 125 + ], + "spans": [ + { + "bbox": [ + 304, + 113, + 526, + 125 + ], + "score": 1.0, + "content": "exact-match occurrences of prompts in the data", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 303, + 126, + 526, + 139 + ], + "spans": [ + { + "bbox": [ + 303, + 126, + 526, + 139 + ], + "score": 1.0, + "content": "resulted in very sparse counts, which led us to look", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 305, + 140, + 422, + 151 + ], + "spans": [ + { + "bbox": [ + 305, + 140, + 422, + 151 + ], + "score": 1.0, + "content": "for a softer formalization.1", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 50.5 + }, + { + "type": "text", + "bbox": [ + 305, + 154, + 525, + 327 + ], + "lines": [ + { + "bbox": [ + 315, + 152, + 527, + 167 + ], + "spans": [ + { + "bbox": [ + 315, + 152, + 527, + 167 + ], + "score": 1.0, + "content": "Instead of considering the training data directly,", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 167, + 526, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 526, + 180 + ], + "score": 1.0, + "content": "we propose to focus on the perplexity of the prompt", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 181, + 525, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 525, + 192 + ], + "score": 1.0, + "content": "as a proxy for its occurrences in some form in", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 194, + 526, + 207 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 526, + 207 + ], + "score": 1.0, + "content": "the data – essentially indicating to what extent the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 207, + 526, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 526, + 221 + ], + "score": 1.0, + "content": "model expects this prompt. This perplexity-based", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 304, + 221, + 525, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 525, + 234 + ], + "score": 1.0, + "content": "framing helps to avoid the challenge of exact match", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 304, + 234, + 525, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 525, + 247 + ], + "score": 1.0, + "content": "in the data, and takes into account variations of the", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 303, + 249, + 525, + 261 + ], + "spans": [ + { + "bbox": [ + 303, + 249, + 525, + 261 + ], + "score": 1.0, + "content": "prompt that the model is also exposed to and might", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 262, + 525, + 274 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 525, + 274 + ], + "score": 1.0, + "content": "be influenced by. In addition, it helps overcome the", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 275, + 527, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 527, + 289 + ], + "score": 1.0, + "content": "challenges mentioned above as it requires neither", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 290, + 525, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 525, + 302 + ], + "score": 1.0, + "content": "access to the pretraining data (which is not always", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 303, + 302, + 526, + 317 + ], + "spans": [ + { + "bbox": [ + 303, + 302, + 526, + 317 + ], + "score": 1.0, + "content": "publicly available for LMs) nor matching over huge", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 316, + 377, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 377, + 327 + ], + "score": 1.0, + "content": "amounts of text.", + "type": "text" + } + ], + "index": 66 + } + ], + "index": 60 + }, + { + "type": "text", + "bbox": [ + 305, + 336, + 525, + 443 + ], + "lines": [ + { + "bbox": [ + 305, + 337, + 527, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 527, + 350 + ], + "score": 1.0, + "content": "Hypothesis: lower perplexity correlates with bet-", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 304, + 350, + 527, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 527, + 363 + ], + "score": 1.0, + "content": "ter performance. We hypothesize that on aver-", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 304, + 365, + 526, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 526, + 377 + ], + "score": 1.0, + "content": "age, lower-perplexity prompts perform better. We", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 303, + 376, + 526, + 392 + ], + "spans": [ + { + "bbox": [ + 303, + 376, + 526, + 392 + ], + "score": 1.0, + "content": "are interested in establishing this hypothesis by", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 392, + 527, + 404 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 527, + 404 + ], + "score": 1.0, + "content": "experimentally showing a significant negative cor-", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 303, + 403, + 526, + 418 + ], + "spans": [ + { + "bbox": [ + 303, + 403, + 526, + 418 + ], + "score": 1.0, + "content": "relation between the perplexity of the prompt and", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 304, + 418, + 526, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 526, + 431 + ], + "score": 1.0, + "content": "its performance on the task, across a diverse set of", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 431, + 385, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 385, + 444 + ], + "score": 1.0, + "content": "tasks and models.", + "type": "text" + } + ], + "index": 74 + } + ], + "index": 70.5 + }, + { + "type": "text", + "bbox": [ + 305, + 445, + 525, + 674 + ], + "lines": [ + { + "bbox": [ + 315, + 444, + 526, + 459 + ], + "spans": [ + { + "bbox": [ + 315, + 444, + 526, + 459 + ], + "score": 1.0, + "content": "We define the perplexity of the prompt as the", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 303, + 458, + 526, + 472 + ], + "spans": [ + { + "bbox": [ + 303, + 458, + 526, + 472 + ], + "score": 1.0, + "content": "perplexity of the full prompt sequence, including", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 304, + 472, + 526, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 526, + 485 + ], + "score": 1.0, + "content": "the input itself, and without the label, averaged", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 304, + 486, + 527, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 527, + 498 + ], + "score": 1.0, + "content": "over 1,000 examples (see Section 4 for details).", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 303, + 499, + 527, + 513 + ], + "spans": [ + { + "bbox": [ + 303, + 499, + 527, + 513 + ], + "score": 1.0, + "content": "The input is a part of the prompt in the case of", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 304, + 513, + 525, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 525, + 525 + ], + "score": 1.0, + "content": "the word prediction tasks by design (e.g., “The", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 303, + 527, + 525, + 540 + ], + "spans": [ + { + "bbox": [ + 303, + 527, + 525, + 540 + ], + "score": 1.0, + "content": "opposite of the word good is”). Inclusion of the", + "type": "text" + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 540, + 525, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 525, + 552 + ], + "score": 1.0, + "content": "task input as part of the prompt for classification", + "type": "text" + } + ], + "index": 82 + }, + { + "bbox": [ + 303, + 553, + 526, + 567 + ], + "spans": [ + { + "bbox": [ + 303, + 553, + 526, + 567 + ], + "score": 1.0, + "content": "tasks as well is intentional: we want to ground the", + "type": "text" + } + ], + "index": 83 + }, + { + "bbox": [ + 303, + 567, + 526, + 581 + ], + "spans": [ + { + "bbox": [ + 303, + 567, + 526, + 581 + ], + "score": 1.0, + "content": "prompt to the task (without the input, we are testing", + "type": "text" + } + ], + "index": 84 + }, + { + "bbox": [ + 304, + 580, + 526, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 526, + 594 + ], + "score": 1.0, + "content": "the hypothesis that lower perplexity prompts across", + "type": "text" + } + ], + "index": 85 + }, + { + "bbox": [ + 304, + 594, + 525, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 525, + 606 + ], + "score": 1.0, + "content": "all tasks work better on every task). The label is", + "type": "text" + } + ], + "index": 86 + }, + { + "bbox": [ + 304, + 608, + 525, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 525, + 620 + ], + "score": 1.0, + "content": "not considered a part of the prompt and is not taken", + "type": "text" + } + ], + "index": 87 + }, + { + "bbox": [ + 304, + 621, + 526, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 526, + 635 + ], + "score": 1.0, + "content": "into consideration when computing the prompt. In", + "type": "text" + } + ], + "index": 88 + }, + { + "bbox": [ + 303, + 635, + 526, + 648 + ], + "spans": [ + { + "bbox": [ + 303, + 635, + 526, + 648 + ], + "score": 1.0, + "content": "practice, this also results in a huge advantage of our", + "type": "text" + } + ], + "index": 89 + }, + { + "bbox": [ + 304, + 648, + 525, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 648, + 525, + 661 + ], + "score": 1.0, + "content": "method, SPELL (Section 7), which aims to find", + "type": "text" + } + ], + "index": 90 + }, + { + "bbox": [ + 304, + 662, + 509, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 509, + 675 + ], + "score": 1.0, + "content": "better prompts—it does not require any labels.", + "type": "text" + } + ], + "index": 91 + } + ], + "index": 83 + }, + { + "type": "text", + "bbox": [ + 304, + 676, + 525, + 715 + ], + "lines": [ + { + "bbox": [ + 314, + 673, + 527, + 690 + ], + "spans": [ + { + "bbox": [ + 314, + 673, + 527, + 690 + ], + "score": 1.0, + "content": "For performance measures, we use the log-", + "type": "text" + } + ], + "index": 92 + }, + { + "bbox": [ + 304, + 688, + 527, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 688, + 527, + 702 + ], + "score": 1.0, + "content": "likelihood score assigned by the model to the cor-", + "type": "text" + } + ], + "index": 93 + }, + { + "bbox": [ + 304, + 703, + 525, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 703, + 525, + 715 + ], + "score": 1.0, + "content": "rect label given that prompt. We choose this metric", + "type": "text" + } + ], + "index": 94 + } + ], + "index": 93 + } + ], + "page_idx": 1, + "page_size": [ + 595, + 841 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 304, + 722, + 525, + 773 + ], + "lines": [ + { + "bbox": [ + 316, + 721, + 527, + 734 + ], + "spans": [ + { + "bbox": [ + 316, + 721, + 527, + 734 + ], + "score": 1.0, + "content": "1We experimented with the task of AG News (see Sec-", + "type": "text" + } + ] + }, + { + "bbox": [ + 304, + 732, + 526, + 744 + ], + "spans": [ + { + "bbox": [ + 304, + 732, + 526, + 744 + ], + "score": 1.0, + "content": "tion 4.1), and looked for all of its prompts (using exact match)", + "type": "text" + } + ] + }, + { + "bbox": [ + 304, + 742, + 525, + 754 + ], + "spans": [ + { + "bbox": [ + 304, + 742, + 525, + 754 + ], + "score": 1.0, + "content": "in the OPT training data. Indeed, only 9/108 of the prompts", + "type": "text" + } + ] + }, + { + "bbox": [ + 304, + 753, + 525, + 763 + ], + "spans": [ + { + "bbox": [ + 304, + 753, + 525, + 763 + ], + "score": 1.0, + "content": "appear in the training data. Such sparse counts do not allow", + "type": "text" + } + ] + }, + { + "bbox": [ + 304, + 762, + 504, + 774 + ], + "spans": [ + { + "bbox": [ + 304, + 762, + 504, + 774 + ], + "score": 1.0, + "content": "for any useful or reliable analysis of prompt behaviour.", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 69, + 71, + 290, + 219 + ], + "lines": [], + "index": 5, + "bbox_fs": [ + 68, + 71, + 292, + 220 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 69, + 221, + 290, + 369 + ], + "lines": [ + { + "bbox": [ + 80, + 221, + 292, + 233 + ], + "spans": [ + { + "bbox": [ + 80, + 221, + 292, + 233 + ], + "score": 1.0, + "content": "Our contributions can be summarized as follows:", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 234, + 290, + 248 + ], + "spans": [ + { + "bbox": [ + 69, + 234, + 290, + 248 + ], + "score": 1.0, + "content": "(a) we formalize the notion that better familiarity", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 69, + 248, + 291, + 261 + ], + "spans": [ + { + "bbox": [ + 69, + 248, + 291, + 261 + ], + "score": 1.0, + "content": "of the model with the prompt correlates with better", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 69, + 262, + 291, + 275 + ], + "spans": [ + { + "bbox": [ + 69, + 262, + 291, + 275 + ], + "score": 1.0, + "content": "performance (Section 2); (b) we automatically elab-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 69, + 276, + 291, + 289 + ], + "spans": [ + { + "bbox": [ + 69, + 276, + 291, + 289 + ], + "score": 1.0, + "content": "orate a given set of seed prompts using paraphras-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 69, + 289, + 290, + 302 + ], + "spans": [ + { + "bbox": [ + 69, + 289, + 290, + 302 + ], + "score": 1.0, + "content": "ing (Section 3); (c) we establish experimentally the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 69, + 302, + 292, + 316 + ], + "spans": [ + { + "bbox": [ + 69, + 302, + 292, + 316 + ], + "score": 1.0, + "content": "hypothesis that lower perplexity of the prompt cor-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 68, + 315, + 291, + 329 + ], + "spans": [ + { + "bbox": [ + 68, + 315, + 291, + 329 + ], + "score": 1.0, + "content": "relates well with better performance (Section 5);", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 69, + 330, + 291, + 342 + ], + "spans": [ + { + "bbox": [ + 69, + 330, + 291, + 342 + ], + "score": 1.0, + "content": "(d) we devise a method to create a more consistent", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 68, + 343, + 290, + 356 + ], + "spans": [ + { + "bbox": [ + 68, + 343, + 290, + 356 + ], + "score": 1.0, + "content": "set of prompts, that also improve results even with", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 69, + 356, + 216, + 369 + ], + "spans": [ + { + "bbox": [ + 69, + 356, + 216, + 369 + ], + "score": 1.0, + "content": "no labels for the task (Section 7).", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 16, + "bbox_fs": [ + 68, + 221, + 292, + 369 + ] + }, + { + "type": "title", + "bbox": [ + 69, + 379, + 290, + 393 + ], + "lines": [ + { + "bbox": [ + 66, + 377, + 291, + 397 + ], + "spans": [ + { + "bbox": [ + 66, + 377, + 291, + 397 + ], + "score": 1.0, + "content": "2 Why are prompts not all created equal?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 70, + 401, + 289, + 536 + ], + "lines": [ + { + "bbox": [ + 69, + 401, + 290, + 414 + ], + "spans": [ + { + "bbox": [ + 69, + 401, + 290, + 414 + ], + "score": 1.0, + "content": "Despite the popularity of prompting as a method", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 68, + 415, + 290, + 428 + ], + "spans": [ + { + "bbox": [ + 68, + 415, + 290, + 428 + ], + "score": 1.0, + "content": "for using language models (Shin et al., 2020; Li", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 69, + 429, + 290, + 441 + ], + "spans": [ + { + "bbox": [ + 69, + 429, + 290, + 441 + ], + "score": 1.0, + "content": "and Liang, 2021; Gao et al., 2021), the cause for", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 69, + 441, + 290, + 456 + ], + "spans": [ + { + "bbox": [ + 69, + 441, + 290, + 456 + ], + "score": 1.0, + "content": "the different behavior of various prompts remains", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 69, + 455, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 69, + 455, + 290, + 469 + ], + "score": 1.0, + "content": "unclear so far. 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The accuracy gap", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 69, + 510, + 290, + 522 + ], + "spans": [ + { + "bbox": [ + 69, + 510, + 290, + 522 + ], + "score": 1.0, + "content": "between the different prompts is not trivial, and it", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 523, + 286, + 537 + ], + "spans": [ + { + "bbox": [ + 68, + 523, + 286, + 537 + ], + "score": 1.0, + "content": "is not possible to predict from the prompts alone.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27.5, + "bbox_fs": [ + 68, + 401, + 291, + 537 + ] + }, + { + "type": "table", + "bbox": [ + 70, + 546, + 290, + 606 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 70, + 546, + 290, + 606 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 70, + 546, + 290, + 606 + ], + "spans": [ + { + "bbox": [ + 70, + 546, + 290, + 606 + ], + "score": 0.978, + "html": "
PromptAccuracy
What is this piece of news regarding?40.9
What is this article about?52.4
What is the best way to describe this article?68.2
What is the most accurate label for this news article?71.2
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Our initial attempts to estimate", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 113, + 526, + 125 + ], + "spans": [ + { + "bbox": [ + 304, + 113, + 526, + 125 + ], + "score": 1.0, + "content": "exact-match occurrences of prompts in the data", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 303, + 126, + 526, + 139 + ], + "spans": [ + { + "bbox": [ + 303, + 126, + 526, + 139 + ], + "score": 1.0, + "content": "resulted in very sparse counts, which led us to look", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 305, + 140, + 422, + 151 + ], + "spans": [ + { + "bbox": [ + 305, + 140, + 422, + 151 + ], + "score": 1.0, + "content": "for a softer formalization.1", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 43, + "bbox_fs": [ + 68, + 651, + 291, + 774 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 72, + 525, + 151 + ], + "lines": [], + "index": 50.5, + "bbox_fs": [ + 303, + 70, + 527, + 151 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 305, + 154, + 525, + 327 + ], + "lines": [ + { + "bbox": [ + 315, + 152, + 527, + 167 + ], + "spans": [ + { + "bbox": [ + 315, + 152, + 527, + 167 + ], + "score": 1.0, + "content": "Instead of considering the training data directly,", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 167, + 526, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 526, + 180 + ], + "score": 1.0, + "content": "we propose to focus on the perplexity of the prompt", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 181, + 525, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 525, + 192 + ], + "score": 1.0, + "content": "as a proxy for its occurrences in some form in", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 194, + 526, + 207 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 526, + 207 + ], + "score": 1.0, + "content": "the data – essentially indicating to what extent the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 207, + 526, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 526, + 221 + ], + "score": 1.0, + "content": "model expects this prompt. This perplexity-based", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 304, + 221, + 525, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 525, + 234 + ], + "score": 1.0, + "content": "framing helps to avoid the challenge of exact match", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 304, + 234, + 525, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 525, + 247 + ], + "score": 1.0, + "content": "in the data, and takes into account variations of the", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 303, + 249, + 525, + 261 + ], + "spans": [ + { + "bbox": [ + 303, + 249, + 525, + 261 + ], + "score": 1.0, + "content": "prompt that the model is also exposed to and might", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 262, + 525, + 274 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 525, + 274 + ], + "score": 1.0, + "content": "be influenced by. In addition, it helps overcome the", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 275, + 527, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 527, + 289 + ], + "score": 1.0, + "content": "challenges mentioned above as it requires neither", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 290, + 525, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 525, + 302 + ], + "score": 1.0, + "content": "access to the pretraining data (which is not always", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 303, + 302, + 526, + 317 + ], + "spans": [ + { + "bbox": [ + 303, + 302, + 526, + 317 + ], + "score": 1.0, + "content": "publicly available for LMs) nor matching over huge", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 316, + 377, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 377, + 327 + ], + "score": 1.0, + "content": "amounts of text.", + "type": "text" + } + ], + "index": 66 + } + ], + "index": 60, + "bbox_fs": [ + 303, + 152, + 527, + 327 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 336, + 525, + 443 + ], + "lines": [ + { + "bbox": [ + 305, + 337, + 527, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 527, + 350 + ], + "score": 1.0, + "content": "Hypothesis: lower perplexity correlates with bet-", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 304, + 350, + 527, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 527, + 363 + ], + "score": 1.0, + "content": "ter performance. We hypothesize that on aver-", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 304, + 365, + 526, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 526, + 377 + ], + "score": 1.0, + "content": "age, lower-perplexity prompts perform better. We", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 303, + 376, + 526, + 392 + ], + "spans": [ + { + "bbox": [ + 303, + 376, + 526, + 392 + ], + "score": 1.0, + "content": "are interested in establishing this hypothesis by", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 392, + 527, + 404 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 527, + 404 + ], + "score": 1.0, + "content": "experimentally showing a significant negative cor-", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 303, + 403, + 526, + 418 + ], + "spans": [ + { + "bbox": [ + 303, + 403, + 526, + 418 + ], + "score": 1.0, + "content": "relation between the perplexity of the prompt and", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 304, + 418, + 526, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 526, + 431 + ], + "score": 1.0, + "content": "its performance on the task, across a diverse set of", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 431, + 385, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 385, + 444 + ], + "score": 1.0, + "content": "tasks and models.", + "type": "text" + } + ], + "index": 74 + } + ], + "index": 70.5, + "bbox_fs": [ + 303, + 337, + 527, + 444 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 445, + 525, + 674 + ], + "lines": [ + { + "bbox": [ + 315, + 444, + 526, + 459 + ], + "spans": [ + { + "bbox": [ + 315, + 444, + 526, + 459 + ], + "score": 1.0, + "content": "We define the perplexity of the prompt as the", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 303, + 458, + 526, + 472 + ], + "spans": [ + { + "bbox": [ + 303, + 458, + 526, + 472 + ], + "score": 1.0, + "content": "perplexity of the full prompt sequence, including", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 304, + 472, + 526, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 526, + 485 + ], + "score": 1.0, + "content": "the input itself, and without the label, averaged", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 304, + 486, + 527, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 527, + 498 + ], + "score": 1.0, + "content": "over 1,000 examples (see Section 4 for details).", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 303, + 499, + 527, + 513 + ], + "spans": [ + { + "bbox": [ + 303, + 499, + 527, + 513 + ], + "score": 1.0, + "content": "The input is a part of the prompt in the case of", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 304, + 513, + 525, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 525, + 525 + ], + "score": 1.0, + "content": "the word prediction tasks by design (e.g., “The", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 303, + 527, + 525, + 540 + ], + "spans": [ + { + "bbox": [ + 303, + 527, + 525, + 540 + ], + "score": 1.0, + "content": "opposite of the word good is”). 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The label is", + "type": "text" + } + ], + "index": 86 + }, + { + "bbox": [ + 304, + 608, + 525, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 525, + 620 + ], + "score": 1.0, + "content": "not considered a part of the prompt and is not taken", + "type": "text" + } + ], + "index": 87 + }, + { + "bbox": [ + 304, + 621, + 526, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 526, + 635 + ], + "score": 1.0, + "content": "into consideration when computing the prompt. In", + "type": "text" + } + ], + "index": 88 + }, + { + "bbox": [ + 303, + 635, + 526, + 648 + ], + "spans": [ + { + "bbox": [ + 303, + 635, + 526, + 648 + ], + "score": 1.0, + "content": "practice, this also results in a huge advantage of our", + "type": "text" + } + ], + "index": 89 + }, + { + "bbox": [ + 304, + 648, + 525, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 648, + 525, + 661 + ], + "score": 1.0, + "content": "method, SPELL (Section 7), which aims to find", + "type": "text" + } + ], + "index": 90 + }, + { + "bbox": [ + 304, + 662, + 509, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 509, + 675 + ], + "score": 1.0, + "content": "better prompts—it does not require any labels.", + "type": "text" + } + ], + "index": 91 + } + ], + "index": 83, + "bbox_fs": [ + 303, + 444, + 527, + 675 + ] + }, + { + "type": "text", + "bbox": [ + 304, + 676, + 525, + 715 + ], + "lines": [ + { + "bbox": [ + 314, + 673, + 527, + 690 + ], + "spans": [ + { + "bbox": [ + 314, + 673, + 527, + 690 + ], + "score": 1.0, + "content": "For performance measures, we use the log-", + "type": "text" + } + ], + "index": 92 + }, + { + "bbox": [ + 304, + 688, + 527, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 688, + 527, + 702 + ], + "score": 1.0, + "content": "likelihood score assigned by the model to the cor-", + "type": "text" + } + ], + "index": 93 + }, + { + "bbox": [ + 304, + 703, + 525, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 703, + 525, + 715 + ], + "score": 1.0, + "content": "rect label given that prompt. 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For", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 69, + 354, + 292, + 369 + ], + "spans": [ + { + "bbox": [ + 69, + 354, + 292, + 369 + ], + "score": 1.0, + "content": "classification tasks we assume that the input ap-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 68, + 368, + 291, + 383 + ], + "spans": [ + { + "bbox": [ + 68, + 368, + 291, + 383 + ], + "score": 1.0, + "content": "pears before the prompt, with no choices appearing", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 68, + 382, + 291, + 396 + ], + "spans": [ + { + "bbox": [ + 68, + 382, + 291, + 396 + ], + "score": 1.0, + "content": "as part of the prompt (to help in smooth paraphras-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 68, + 396, + 178, + 409 + ], + "spans": [ + { + "bbox": [ + 68, + 396, + 178, + 409 + ], + "score": 1.0, + "content": "ing of the prompt itself).", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 69, + 421, + 290, + 555 + ], + "lines": [ + { + "bbox": [ + 69, + 421, + 290, + 434 + ], + "spans": [ + { + "bbox": [ + 69, + 421, + 290, + 434 + ], + "score": 1.0, + "content": "Step 1: Paraphrasing with GPT3 We use the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 68, + 435, + 291, + 448 + ], + "spans": [ + { + "bbox": [ + 68, + 435, + 291, + 448 + ], + "score": 1.0, + "content": "text-davinci-002 version of GPT3 (Brown et al.,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 68, + 448, + 291, + 464 + ], + "spans": [ + { + "bbox": [ + 68, + 448, + 291, + 464 + ], + "score": 1.0, + "content": "2020) to generate paraphrases for each of the man-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 69, + 463, + 290, + 475 + ], + "spans": [ + { + "bbox": [ + 69, + 463, + 290, + 475 + ], + "score": 1.0, + "content": "ual prompts in our seed set. We prompt it with", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 68, + 476, + 291, + 489 + ], + "spans": [ + { + "bbox": [ + 68, + 476, + 291, + 489 + ], + "score": 1.0, + "content": "a meta-prompt for paraphrasing to generate varia-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 69, + 490, + 291, + 502 + ], + "spans": [ + { + "bbox": [ + 69, + 490, + 291, + 502 + ], + "score": 1.0, + "content": "tions of one of our seed prompts. An example of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 69, + 504, + 290, + 516 + ], + "spans": [ + { + "bbox": [ + 69, + 504, + 290, + 516 + ], + "score": 1.0, + "content": "such a meta-prompt is: Write a paraphrase for the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 516, + 291, + 531 + ], + "spans": [ + { + "bbox": [ + 68, + 516, + 291, + 531 + ], + "score": 1.0, + "content": "following sentence: Paraphrase:.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 67, + 529, + 290, + 544 + ], + "spans": [ + { + "bbox": [ + 67, + 529, + 290, + 544 + ], + "score": 1.0, + "content": "The 7 meta-prompts used in this step are listed in", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 542, + 106, + 556 + ], + "spans": [ + { + "bbox": [ + 68, + 542, + 106, + 556 + ], + "score": 1.0, + "content": "Table 2.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26.5 + }, + { + "type": "text", + "bbox": [ + 69, + 559, + 290, + 653 + ], + "lines": [ + { + "bbox": [ + 80, + 558, + 290, + 572 + ], + "spans": [ + { + "bbox": [ + 80, + 558, + 290, + 572 + ], + "score": 1.0, + "content": "We choose GPT3 as our paraphrasing model", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 68, + 572, + 292, + 585 + ], + "spans": [ + { + "bbox": [ + 68, + 572, + 292, + 585 + ], + "score": 1.0, + "content": "because of its well-documented generation abilities.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 68, + 585, + 290, + 599 + ], + "spans": [ + { + "bbox": [ + 68, + 585, + 290, + 599 + ], + "score": 1.0, + "content": "This is also to ensure that there is a separation", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 68, + 599, + 291, + 613 + ], + "spans": [ + { + "bbox": [ + 68, + 599, + 291, + 613 + ], + "score": 1.0, + "content": "between the model we use to create the prompts and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 69, + 613, + 291, + 626 + ], + "spans": [ + { + "bbox": [ + 69, + 613, + 291, + 626 + ], + "score": 1.0, + "content": "the models we use to rank them (OPT and Bloom,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 69, + 626, + 290, + 640 + ], + "spans": [ + { + "bbox": [ + 69, + 626, + 290, + 640 + ], + "score": 1.0, + "content": "see Section 4 for details), to avoid confounding the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 69, + 640, + 157, + 654 + ], + "spans": [ + { + "bbox": [ + 69, + 640, + 157, + 654 + ], + "score": 1.0, + "content": "experimental setup.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 69, + 666, + 289, + 773 + ], + "lines": [ + { + "bbox": [ + 69, + 667, + 290, + 679 + ], + "spans": [ + { + "bbox": [ + 69, + 667, + 290, + 679 + ], + "score": 1.0, + "content": "Step 2: Paraphrasing using backtranslation", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 69, + 680, + 290, + 693 + ], + "spans": [ + { + "bbox": [ + 69, + 680, + 290, + 693 + ], + "score": 1.0, + "content": "Our second step takes as input the paraphrases from", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 693, + 290, + 707 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 290, + 707 + ], + "score": 1.0, + "content": "GPT3 (in addition to the seed set of prompts) and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 707, + 291, + 720 + ], + "spans": [ + { + "bbox": [ + 68, + 707, + 291, + 720 + ], + "score": 1.0, + "content": "translates them into different languages and back", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 68, + 720, + 290, + 735 + ], + "spans": [ + { + "bbox": [ + 68, + 720, + 290, + 735 + ], + "score": 1.0, + "content": "into English to get additional prompt paraphrases", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 734, + 290, + 748 + ], + "spans": [ + { + "bbox": [ + 69, + 734, + 290, + 748 + ], + "score": 1.0, + "content": "(Wieting et al., 2017). 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We experiment with two", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 303, + 513, + 527, + 525 + ], + "spans": [ + { + "bbox": [ + 303, + 513, + 527, + 525 + ], + "score": 1.0, + "content": "types of tasks: word prediction tasks and classifica-", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 305, + 527, + 432, + 539 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 432, + 539 + ], + "score": 1.0, + "content": "tion tasks, as detailed below.", + "type": "text" + } + ], + "index": 78 + } + ], + "index": 74.5 + }, + { + "type": "text", + "bbox": [ + 304, + 549, + 525, + 670 + ], + "lines": [ + { + "bbox": [ + 305, + 549, + 526, + 561 + ], + "spans": [ + { + "bbox": [ + 305, + 549, + 526, + 561 + ], + "score": 1.0, + "content": "Word Prediction Tasks The first task in this cat-", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 304, + 563, + 526, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 526, + 576 + ], + "score": 1.0, + "content": "egory is word-level translation. 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We prompt it with", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 68, + 476, + 291, + 489 + ], + "spans": [ + { + "bbox": [ + 68, + 476, + 291, + 489 + ], + "score": 1.0, + "content": "a meta-prompt for paraphrasing to generate varia-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 69, + 490, + 291, + 502 + ], + "spans": [ + { + "bbox": [ + 69, + 490, + 291, + 502 + ], + "score": 1.0, + "content": "tions of one of our seed prompts. An example of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 69, + 504, + 290, + 516 + ], + "spans": [ + { + "bbox": [ + 69, + 504, + 290, + 516 + ], + "score": 1.0, + "content": "such a meta-prompt is: Write a paraphrase for the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 516, + 291, + 531 + ], + "spans": [ + { + "bbox": [ + 68, + 516, + 291, + 531 + ], + "score": 1.0, + "content": "following sentence: Paraphrase:.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 67, + 529, + 290, + 544 + ], + "spans": [ + { + "bbox": [ + 67, + 529, + 290, + 544 + ], + "score": 1.0, + "content": "The 7 meta-prompts used in this step are listed in", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 542, + 106, + 556 + ], + "spans": [ + { + "bbox": [ + 68, + 542, + 106, + 556 + ], + "score": 1.0, + "content": "Table 2.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26.5, + "bbox_fs": [ + 67, + 421, + 291, + 556 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 559, + 290, + 653 + ], + "lines": [ + { + "bbox": [ + 80, + 558, + 290, + 572 + ], + "spans": [ + { + "bbox": [ + 80, + 558, + 290, + 572 + ], + "score": 1.0, + "content": "We choose GPT3 as our paraphrasing model", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 68, + 572, + 292, + 585 + ], + "spans": [ + { + "bbox": [ + 68, + 572, + 292, + 585 + ], + "score": 1.0, + "content": "because of its well-documented generation abilities.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 68, + 585, + 290, + 599 + ], + "spans": [ + { + "bbox": [ + 68, + 585, + 290, + 599 + ], + "score": 1.0, + "content": "This is also to ensure that there is a separation", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 68, + 599, + 291, + 613 + ], + "spans": [ + { + "bbox": [ + 68, + 599, + 291, + 613 + ], + "score": 1.0, + "content": "between the model we use to create the prompts and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 69, + 613, + 291, + 626 + ], + "spans": [ + { + "bbox": [ + 69, + 613, + 291, + 626 + ], + "score": 1.0, + "content": "the models we use to rank them (OPT and Bloom,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 69, + 626, + 290, + 640 + ], + "spans": [ + { + "bbox": [ + 69, + 626, + 290, + 640 + ], + "score": 1.0, + "content": "see Section 4 for details), to avoid confounding the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 69, + 640, + 157, + 654 + ], + "spans": [ + { + "bbox": [ + 69, + 640, + 157, + 654 + ], + "score": 1.0, + "content": "experimental setup.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35, + "bbox_fs": [ + 68, + 558, + 292, + 654 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 666, + 289, + 773 + ], + "lines": [ + { + "bbox": [ + 69, + 667, + 290, + 679 + ], + "spans": [ + { + "bbox": [ + 69, + 667, + 290, + 679 + ], + "score": 1.0, + "content": "Step 2: Paraphrasing using backtranslation", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 69, + 680, + 290, + 693 + ], + "spans": [ + { + "bbox": [ + 69, + 680, + 290, + 693 + ], + "score": 1.0, + "content": "Our second step takes as input the paraphrases from", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 693, + 290, + 707 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 290, + 707 + ], + "score": 1.0, + "content": "GPT3 (in addition to the seed set of prompts) and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 707, + 291, + 720 + ], + "spans": [ + { + "bbox": [ + 68, + 707, + 291, + 720 + ], + "score": 1.0, + "content": "translates them into different languages and back", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 68, + 720, + 290, + 735 + ], + "spans": [ + { + "bbox": [ + 68, + 720, + 290, + 735 + ], + "score": 1.0, + "content": "into English to get additional prompt paraphrases", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 734, + 290, + 748 + ], + "spans": [ + { + "bbox": [ + 69, + 734, + 290, + 748 + ], + "score": 1.0, + "content": "(Wieting et al., 2017). 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Meta prompts
Write a paraphrase for the following sentence: <seed-prompt> Paraphrase: <seed-prompt> Paraphrase:
Write a likely paraphrase of the text: <seed-prompt> Paraphrase:
Write a sentence similar to the following one: <seed-prompt> Paraphrase:
Paraphrase the following sentence: <seed-prompt> Paraphrase:
Write a variation of this sentence: <seed-prompt> How would you say the following sentence in a different way? <seed-prompt>
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Task# Step 0# Step 1 # Step 2
Word-Level Translation12 59118
Antonyms12 85176
GLUE Cola4 27144
Newspop13 43119
AG News4 23108
IMDB10 45178
DBpedia8 23103
Emotion4 1494
Tweet Offensive5 41119
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We", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 69, + 530, + 227, + 543 + ], + "spans": [ + { + "bbox": [ + 69, + 530, + 227, + 543 + ], + "score": 1.0, + "content": "choose 1,000 word pairs at random.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 69, + 552, + 290, + 700 + ], + "lines": [ + { + "bbox": [ + 70, + 552, + 290, + 565 + ], + "spans": [ + { + "bbox": [ + 70, + 552, + 290, + 565 + ], + "score": 1.0, + "content": "Classification Tasks We choose classification", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 69, + 566, + 290, + 580 + ], + "spans": [ + { + "bbox": [ + 69, + 566, + 290, + 580 + ], + "score": 1.0, + "content": "tasks from Huggingface Datasets,8 with an attempt", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 69, + 579, + 290, + 592 + ], + "spans": [ + { + "bbox": [ + 69, + 579, + 290, + 592 + ], + "score": 1.0, + "content": "to have a set of diverse tasks that use relatively short", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 68, + 593, + 292, + 607 + ], + "spans": [ + { + "bbox": [ + 68, + 593, + 292, + 607 + ], + "score": 1.0, + "content": "inputs, with some prompts available in Prompt-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 605, + 292, + 621 + ], + "spans": [ + { + "bbox": [ + 68, + 605, + 292, + 621 + ], + "score": 1.0, + "content": "Source (Bach et al., 2022):9 (a) GLUE Cola (gram-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 68, + 619, + 291, + 635 + ], + "spans": [ + { + "bbox": [ + 68, + 619, + 291, + 635 + ], + "score": 1.0, + "content": "maticality; Warstadt et al. 2018); (b) Newspop", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 633, + 291, + 647 + ], + "spans": [ + { + "bbox": [ + 68, + 633, + 291, + 647 + ], + "score": 1.0, + "content": "(news classification; Moniz and Torgo 2018); (c)", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 647, + 292, + 661 + ], + "spans": [ + { + "bbox": [ + 68, + 647, + 292, + 661 + ], + "score": 1.0, + "content": "AG News (news classification; Zhang et al. 2015);", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 68, + 661, + 291, + 673 + ], + "spans": [ + { + "bbox": [ + 68, + 661, + 291, + 673 + ], + "score": 1.0, + "content": "(d) IMDB (movie review classification; Maas et al.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 69, + 675, + 290, + 687 + ], + "spans": [ + { + "bbox": [ + 69, + 675, + 290, + 687 + ], + "score": 1.0, + "content": "2011); (e) DBpedia (topic classification; Lehmann", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 689, + 291, + 701 + ], + "spans": [ + { + "bbox": [ + 69, + 689, + 291, + 701 + ], + "score": 1.0, + "content": "et al. 2015); (f) Emotion (classification to emo-", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 304, + 235, + 525, + 288 + ], + "lines": [ + { + "bbox": [ + 303, + 234, + 526, + 248 + ], + "spans": [ + { + "bbox": [ + 303, + 234, + 526, + 248 + ], + "score": 1.0, + "content": "tions; Saravia et al. 2018); (g) Tweet Offensive", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 248, + 526, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 526, + 261 + ], + "score": 1.0, + "content": "(classification to offensive vs. not offensive tweets;", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 261, + 527, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 527, + 275 + ], + "score": 1.0, + "content": "Barbieri et al. 2020). 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The score of a label of", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 304, + 761, + 525, + 774 + ], + "spans": [ + { + "bbox": [ + 304, + 761, + 525, + 774 + ], + "score": 1.0, + "content": "multiple tokens is defined by the sum of the token", + "type": "text" + } + ], + "index": 81 + } + ], + "index": 77 + } + ], + "page_idx": 3, + "page_size": [ + 595, + 841 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 69, + 710, + 276, + 773 + ], + "lines": [ + { + "bbox": [ + 81, + 709, + 267, + 722 + ], + "spans": [ + { + "bbox": [ + 81, + 709, + 267, + 722 + ], + "score": 1.0, + "content": "6Basque, French, Portuguese, Spanish, and Arabic.", + "type": "text" + } + ] + }, + { + "bbox": [ + 82, + 719, + 276, + 732 + ], + "spans": [ + { + "bbox": [ + 82, + 719, + 276, + 732 + ], + "score": 1.0, + "content": "7https://www.kaggle.com/datasets/duketemon/", + "type": "text" + } + ] + }, + { + "bbox": [ + 69, + 731, + 144, + 741 + ], + "spans": [ + { + "bbox": [ + 69, + 731, + 144, + 741 + ], + "score": 1.0, + "content": "antonyms-wordnet", + "type": "text" + } + ] + }, + { + "bbox": [ + 81, + 740, + 277, + 754 + ], + "spans": [ + { + "bbox": [ + 81, + 740, + 277, + 754 + ], + "score": 1.0, + "content": "8https://huggingface.co/docs/datasets/index", + "type": "text" + } + ] + }, + { + "bbox": [ + 81, + 751, + 263, + 764 + ], + "spans": [ + { + "bbox": [ + 81, + 751, + 263, + 764 + ], + "score": 1.0, + "content": "9https://github.com/bigscience-workshop/", + "type": "text" + } + ] + }, + { + "bbox": [ + 69, + 763, + 126, + 773 + ], + "spans": [ + { + "bbox": [ + 69, + 763, + 126, + 773 + ], + "score": 1.0, + "content": "promptsource", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 119, + 70, + 474, + 191 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 119, + 70, + 474, + 191 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 119, + 70, + 474, + 191 + ], + "spans": [ + { + "bbox": [ + 119, + 70, + 474, + 191 + ], + "score": 0.915, + "html": "
Meta prompts
Write a paraphrase for the following sentence: <seed-prompt> Paraphrase: <seed-prompt> Paraphrase:
Write a likely paraphrase of the text: <seed-prompt> Paraphrase:
Write a sentence similar to the following one: <seed-prompt> Paraphrase:
Paraphrase the following sentence: <seed-prompt> Paraphrase:
Write a variation of this sentence: <seed-prompt> How would you say the following sentence in a different way? <seed-prompt>
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Task# Step 0# Step 1 # Step 2
Word-Level Translation12 59118
Antonyms12 85176
GLUE Cola4 27144
Newspop13 43119
AG News4 23108
IMDB10 45178
DBpedia8 23103
Emotion4 1494
Tweet Offensive5 41119
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Note", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 68, + 448, + 290, + 462 + ], + "spans": [ + { + "bbox": [ + 68, + 448, + 290, + 462 + ], + "score": 1.0, + "content": "that only 5 of the languages we experiment with", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 69, + 461, + 216, + 475 + ], + "spans": [ + { + "bbox": [ + 69, + 461, + 216, + 475 + ], + "score": 1.0, + "content": "are officially covered by Bloom.6", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 68, + 434, + 290, + 475 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 476, + 289, + 542 + ], + "lines": [ + { + "bbox": [ + 80, + 475, + 292, + 489 + ], + "spans": [ + { + "bbox": [ + 80, + 475, + 292, + 489 + ], + "score": 1.0, + "content": "We also consider antonym prediction where,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 68, + 490, + 290, + 502 + ], + "spans": [ + { + "bbox": [ + 68, + 490, + 290, + 502 + ], + "score": 1.0, + "content": "given a word, the model is expected to predict its", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 68, + 503, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 68, + 503, + 290, + 515 + ], + "score": 1.0, + "content": "antonym. For this task, we use data from Kaggle,7", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 68, + 517, + 290, + 529 + ], + "spans": [ + { + "bbox": [ + 68, + 517, + 290, + 529 + ], + "score": 1.0, + "content": "which is based on WordNet (Miller, 1995). We", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 69, + 530, + 227, + 543 + ], + "spans": [ + { + "bbox": [ + 69, + 530, + 227, + 543 + ], + "score": 1.0, + "content": "choose 1,000 word pairs at random.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22, + "bbox_fs": [ + 68, + 475, + 292, + 543 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 552, + 290, + 700 + ], + "lines": [ + { + "bbox": [ + 70, + 552, + 290, + 565 + ], + "spans": [ + { + "bbox": [ + 70, + 552, + 290, + 565 + ], + "score": 1.0, + "content": "Classification Tasks We choose classification", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 69, + 566, + 290, + 580 + ], + "spans": [ + { + "bbox": [ + 69, + 566, + 290, + 580 + ], + "score": 1.0, + "content": "tasks from Huggingface Datasets,8 with an attempt", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 69, + 579, + 290, + 592 + ], + "spans": [ + { + "bbox": [ + 69, + 579, + 290, + 592 + ], + "score": 1.0, + "content": "to have a set of diverse tasks that use relatively short", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 68, + 593, + 292, + 607 + ], + "spans": [ + { + "bbox": [ + 68, + 593, + 292, + 607 + ], + "score": 1.0, + "content": "inputs, with some prompts available in Prompt-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 605, + 292, + 621 + ], + "spans": [ + { + "bbox": [ + 68, + 605, + 292, + 621 + ], + "score": 1.0, + "content": "Source (Bach et al., 2022):9 (a) GLUE Cola (gram-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 68, + 619, + 291, + 635 + ], + "spans": [ + { + "bbox": [ + 68, + 619, + 291, + 635 + ], + "score": 1.0, + "content": "maticality; Warstadt et al. 2018); (b) Newspop", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 633, + 291, + 647 + ], + "spans": [ + { + "bbox": [ + 68, + 633, + 291, + 647 + ], + "score": 1.0, + "content": "(news classification; Moniz and Torgo 2018); (c)", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 647, + 292, + 661 + ], + "spans": [ + { + "bbox": [ + 68, + 647, + 292, + 661 + ], + "score": 1.0, + "content": "AG News (news classification; Zhang et al. 2015);", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 68, + 661, + 291, + 673 + ], + "spans": [ + { + "bbox": [ + 68, + 661, + 291, + 673 + ], + "score": 1.0, + "content": "(d) IMDB (movie review classification; Maas et al.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 69, + 675, + 290, + 687 + ], + "spans": [ + { + "bbox": [ + 69, + 675, + 290, + 687 + ], + "score": 1.0, + "content": "2011); (e) DBpedia (topic classification; Lehmann", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 689, + 291, + 701 + ], + "spans": [ + { + "bbox": [ + 69, + 689, + 291, + 701 + ], + "score": 1.0, + "content": "et al. 2015); (f) Emotion (classification to emo-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 303, + 234, + 526, + 248 + ], + "spans": [ + { + "bbox": [ + 303, + 234, + 526, + 248 + ], + "score": 1.0, + "content": "tions; Saravia et al. 2018); (g) Tweet Offensive", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 248, + 526, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 526, + 261 + ], + "score": 1.0, + "content": "(classification to offensive vs. not offensive tweets;", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 261, + 527, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 527, + 275 + ], + "score": 1.0, + "content": "Barbieri et al. 2020). We use 1,000 random exam-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 276, + 407, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 407, + 288 + ], + "score": 1.0, + "content": "ples from each dataset.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 30, + "bbox_fs": [ + 68, + 552, + 292, + 701 + ] + }, + { + "type": "text", + "bbox": [ + 304, + 235, + 525, + 288 + ], + "lines": [], + "index": 45.5, + "bbox_fs": [ + 303, + 234, + 527, + 288 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 305, + 290, + 525, + 533 + ], + "lines": [ + { + "bbox": [ + 315, + 290, + 527, + 303 + ], + "spans": [ + { + "bbox": [ + 315, + 290, + 527, + 303 + ], + "score": 1.0, + "content": "The full set of manual prompts is listed in Sec-", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 303, + 526, + 318 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 526, + 318 + ], + "score": 1.0, + "content": "tion A in the Appendix. In these tasks, the prompt", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 317, + 526, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 526, + 331 + ], + "score": 1.0, + "content": "follows the input, and at the end of each prompt", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 303, + 331, + 526, + 344 + ], + "spans": [ + { + "bbox": [ + 303, + 331, + 526, + 344 + ], + "score": 1.0, + "content": "we add the choices of classes (i.e., we provide the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 303, + 344, + 527, + 359 + ], + "spans": [ + { + "bbox": [ + 303, + 344, + 527, + 359 + ], + "score": 1.0, + "content": "possible labels explicitly in the prompt by listing", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 358, + 526, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 526, + 371 + ], + "score": 1.0, + "content": "the possible answers as defined by the dataset it-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 372, + 526, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 526, + 384 + ], + "score": 1.0, + "content": "self.): “Choices: X, Y, Z. Answer:” as we find it", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 384, + 525, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 525, + 399 + ], + "score": 1.0, + "content": "helps in terms of accuracy. Defining the label space", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 398, + 525, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 525, + 412 + ], + "score": 1.0, + "content": "likely helps in our zero-shot setting because there", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 303, + 414, + 525, + 425 + ], + "spans": [ + { + "bbox": [ + 303, + 414, + 525, + 425 + ], + "score": 1.0, + "content": "are no previous demonstrations from which the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 425, + 527, + 439 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 527, + 439 + ], + "score": 1.0, + "content": "model can learn the possible classes. Additionally,", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 305, + 440, + 525, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 440, + 525, + 453 + ], + "score": 1.0, + "content": "adding class options to the prompt helps to reduce", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 304, + 452, + 526, + 466 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 526, + 466 + ], + "score": 1.0, + "content": "the effect of the surface form competition (Holtz-", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 303, + 466, + 525, + 480 + ], + "spans": [ + { + "bbox": [ + 303, + 466, + 525, + 480 + ], + "score": 1.0, + "content": "man et al., 2021). The option of generating the", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 481, + 525, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 525, + 493 + ], + "score": 1.0, + "content": "answer and comparing it with the gold label was", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 494, + 525, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 525, + 507 + ], + "score": 1.0, + "content": "not reasonable here, since we cannot expect the", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 508, + 525, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 525, + 519 + ], + "score": 1.0, + "content": "model to generate the exact label as the first choice", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 520, + 367, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 367, + 535 + ], + "score": 1.0, + "content": "often enough.", + "type": "text" + } + ], + "index": 65 + } + ], + "index": 56.5, + "bbox_fs": [ + 303, + 290, + 527, + 535 + ] + }, + { + "type": "title", + "bbox": [ + 306, + 549, + 440, + 561 + ], + "lines": [ + { + "bbox": [ + 303, + 548, + 442, + 563 + ], + "spans": [ + { + "bbox": [ + 303, + 548, + 442, + 563 + ], + "score": 1.0, + "content": "4.2 Implementation Details", + "type": "text" + } + ], + "index": 66 + } + ], + "index": 66 + }, + { + "type": "text", + "bbox": [ + 305, + 570, + 525, + 650 + ], + "lines": [ + { + "bbox": [ + 304, + 570, + 527, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 527, + 583 + ], + "score": 1.0, + "content": "In all experiments we evaluate zero-shot perfor-", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 303, + 582, + 527, + 597 + ], + "spans": [ + { + "bbox": [ + 303, + 582, + 527, + 597 + ], + "score": 1.0, + "content": "mance. To avoid noise when computing perplexity,", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 304, + 597, + 526, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 526, + 610 + ], + "score": 1.0, + "content": "we instantiate the prompts with 1,000 examples of", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 304, + 610, + 526, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 610, + 526, + 624 + ], + "score": 1.0, + "content": "the dataset, compute the perplexity of the prompt", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 624, + 525, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 525, + 637 + ], + "score": 1.0, + "content": "with each example, and calculate the average across", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 304, + 636, + 412, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 636, + 412, + 652 + ], + "score": 1.0, + "content": "all instantiated prompts.", + "type": "text" + } + ], + "index": 72 + } + ], + "index": 69.5, + "bbox_fs": [ + 303, + 570, + 527, + 652 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 653, + 525, + 773 + ], + "lines": [ + { + "bbox": [ + 315, + 651, + 526, + 667 + ], + "spans": [ + { + "bbox": [ + 315, + 651, + 526, + 667 + ], + "score": 1.0, + "content": "To estimate the performance of the prompt, we", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 666, + 525, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 525, + 680 + ], + "score": 1.0, + "content": "look at two measures: (a) the language model", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 681, + 527, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 681, + 527, + 693 + ], + "score": 1.0, + "content": "score (log probability) of the correct label, aver-", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 693, + 527, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 693, + 527, + 708 + ], + "score": 1.0, + "content": "aged across 1,000 examples; (b) the accuracy on", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 304, + 707, + 526, + 720 + ], + "spans": [ + { + "bbox": [ + 304, + 707, + 526, + 720 + ], + "score": 1.0, + "content": "the task, computed over the 1,000 examples. To", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 303, + 721, + 526, + 733 + ], + "spans": [ + { + "bbox": [ + 303, + 721, + 526, + 733 + ], + "score": 1.0, + "content": "compute accuracy, for each example we score all", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 304, + 734, + 526, + 747 + ], + "spans": [ + { + "bbox": [ + 304, + 734, + 526, + 747 + ], + "score": 1.0, + "content": "classes and choose the highest ranking class as the", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 304, + 748, + 526, + 759 + ], + "spans": [ + { + "bbox": [ + 304, + 748, + 526, + 759 + ], + "score": 1.0, + "content": "prediction of the model. 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All Manually Created PromptsExamples of Similar Automatically Created Prompts
What label best describes this news article?What's the most accurate label for this news article?
What is this piece of news regarding? Which newspaper section would this article likely appear in?What does this piece of news concern?
What topic is this news article about?In what section of the newspaper could this article be published? What category does this article fall into?
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ModelTaskPerplexity-score corr. Pearson SpearmanPerplexity-acc corr. Pearson Spearman Avg Acc Acc 50%
OPT175BAntonyms**-0.41**-0.53
GLUE Cola-0.15-0.14-0.041 -0.021 47.71 57.1
Newspop*-0.24**-0.26 *-0.20-0.1866.472.9
AG News**-0.63 **-0.68 **-0.77**-0.8157.568.7
IMDB**0.35**0.400.14*0.2086.291.0
DBpedia **-0.50**-0.44 **-0.51**-0.4246.755.2
Emotion-0.14-0.19 **-0.30 **-0.3216.423.0
Tweet Offensive*-0.190.070.18*0.2351.355.8
Bloom 176BAntonyms**-0.37**-0.2311
GLUE Cola0.070.11**-0.25**-0.2655.565.6
Newspop**-0.50**-0.42 **-0.59 **-0.5178.987.8
AG News**-0.62 **-0.54**-0.44**-0.4450.359.4
IMDB0.040.09-0.08-0.1489.392.2
DBpedia**-0.47 *-0.27**-0.35*-0.2127.233.4
Emotion**-0.33 **-0.42**-0.48**-0.5529.331.7
Tweet Offensive0.14*0.24 *-0.20-0.0341.646.2
OPT 30B Antonyms **-0.54**-0.701111
GLUE Cola-0.050.03-0.130.0232.235.5
Newspop*-0.23 *-0.25*-0.18-0.1260.366.6
AG News**-0.66 **-0.71 **-0.81**-0.8049.360.7
IMDB-0.06*0.170.04**0.2281.686.1
DBpedia **-0.41 **-0.34*-0.21*-0.2535.942.4
Emotion0.00-0.030.180.1312.316.2
Tweet Offensive**-0.44**-0.39-0.11-0.0554.660.2
OPT 1.3BAntonyms **-0.45**-0.531
GLUE Cola **-0.39 **-0.36-0.09*-0.1960.31 65.9
Newspop**0.33*0.21-0.07-0.0737.640.3
AG News**-0.33**-0.29 **-0.56 **-0.4931.937.6
IMDB-0.11-0.07**0.24**0.2286.089.1
DBpedia-0.16-0.14-0.02-0.018.79.2
Emotion0.080.08**-0.29**-0.307.09.1
Tweet Offensive**-0.42**-0.35 **-0.50**-0.3858.662.6
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All Manually Created PromptsExamples of Similar Automatically Created Prompts
What label best describes this news article?What's the most accurate label for this news article?
What is this piece of news regarding? Which newspaper section would this article likely appear in?What does this piece of news concern?
What topic is this news article about?In what section of the newspaper could this article be published? What category does this article fall into?
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ModelTaskPerplexity-score corr. Pearson SpearmanPerplexity-acc corr. Pearson Spearman Avg Acc Acc 50%
OPT175BAntonyms**-0.41**-0.53
GLUE Cola-0.15-0.14-0.041 -0.021 47.71 57.1
Newspop*-0.24**-0.26 *-0.20-0.1866.472.9
AG News**-0.63 **-0.68 **-0.77**-0.8157.568.7
IMDB**0.35**0.400.14*0.2086.291.0
DBpedia **-0.50**-0.44 **-0.51**-0.4246.755.2
Emotion-0.14-0.19 **-0.30 **-0.3216.423.0
Tweet Offensive*-0.190.070.18*0.2351.355.8
Bloom 176BAntonyms**-0.37**-0.2311
GLUE Cola0.070.11**-0.25**-0.2655.565.6
Newspop**-0.50**-0.42 **-0.59 **-0.5178.987.8
AG News**-0.62 **-0.54**-0.44**-0.4450.359.4
IMDB0.040.09-0.08-0.1489.392.2
DBpedia**-0.47 *-0.27**-0.35*-0.2127.233.4
Emotion**-0.33 **-0.42**-0.48**-0.5529.331.7
Tweet Offensive0.14*0.24 *-0.20-0.0341.646.2
OPT 30B Antonyms **-0.54**-0.701111
GLUE Cola-0.050.03-0.130.0232.235.5
Newspop*-0.23 *-0.25*-0.18-0.1260.366.6
AG News**-0.66 **-0.71 **-0.81**-0.8049.360.7
IMDB-0.06*0.170.04**0.2281.686.1
DBpedia **-0.41 **-0.34*-0.21*-0.2535.942.4
Emotion0.00-0.030.180.1312.316.2
Tweet Offensive**-0.44**-0.39-0.11-0.0554.660.2
OPT 1.3BAntonyms **-0.45**-0.531
GLUE Cola **-0.39 **-0.36-0.09*-0.1960.31 65.9
Newspop**0.33*0.21-0.07-0.0737.640.3
AG News**-0.33**-0.29 **-0.56 **-0.4931.937.6
IMDB-0.11-0.07**0.24**0.2286.089.1
DBpedia-0.16-0.14-0.02-0.018.79.2
Emotion0.080.08**-0.29**-0.307.09.1
Tweet Offensive**-0.42**-0.35 **-0.50**-0.3858.662.6
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LangOPT175BBloom 176B PearsonSpear.
PearsonSpear.
ita-0.44-0.57-0.37-0.63
spa-0.47-0.61-0.51-0.66
cat-0.47-0.58-0.24-0.31
fra-0.48-0.57-0.48-0.64
deu-0.44-0.60-0.46-0.65
fin-0.44-0.62-0.34-0.56
por-0.45-0.62-0.46-0.61
eus-0.47-0.61-0.45-0.61
tur-0.44-0.62-0.33-0.62
jpn-0.33-0.26
arb-0.36-0.47
rus1-0.54-0.69
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We see that most correlations", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 69, + 447, + 291, + 460 + ], + "spans": [ + { + "bbox": [ + 69, + 447, + 291, + 460 + ], + "score": 1.0, + "content": "are negative and statistically significant, as we ex-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 68, + 460, + 291, + 473 + ], + "spans": [ + { + "bbox": [ + 68, + 460, + 291, + 473 + ], + "score": 1.0, + "content": "pect. This validates our hypothesis and shows that", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 68, + 473, + 292, + 488 + ], + "spans": [ + { + "bbox": [ + 68, + 473, + 292, + 488 + ], + "score": 1.0, + "content": "in the majority of tasks we indeed get a strong cor-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 487, + 291, + 501 + ], + "spans": [ + { + "bbox": [ + 68, + 487, + 291, + 501 + ], + "score": 1.0, + "content": "relation between low perplexity of the prompt and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 69, + 501, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 69, + 501, + 290, + 514 + ], + "score": 1.0, + "content": "better performance on the task.10 For each task we", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 69, + 514, + 214, + 528 + ], + "spans": [ + { + "bbox": [ + 69, + 514, + 214, + 528 + ], + "score": 1.0, + "content": "also report the average accuracy.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 69, + 536, + 290, + 617 + ], + "lines": [ + { + "bbox": [ + 70, + 536, + 291, + 549 + ], + "spans": [ + { + "bbox": [ + 70, + 536, + 291, + 549 + ], + "score": 1.0, + "content": "Word-Level Translation The results of the word-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 69, + 550, + 290, + 563 + ], + "spans": [ + { + "bbox": [ + 69, + 550, + 290, + 563 + ], + "score": 1.0, + "content": "level translation task are reported in Table 6. Here", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 69, + 564, + 290, + 576 + ], + "spans": [ + { + "bbox": [ + 69, + 564, + 290, + 576 + ], + "score": 1.0, + "content": "the correlations are extremely consistent across all", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 578, + 291, + 590 + ], + "spans": [ + { + "bbox": [ + 69, + 578, + 291, + 590 + ], + "score": 1.0, + "content": "languages and across models, with statistical sig-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 68, + 590, + 291, + 604 + ], + "spans": [ + { + "bbox": [ + 68, + 590, + 291, + 604 + ], + "score": 1.0, + "content": "nificance for all languages except for Catalan and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 69, + 605, + 163, + 618 + ], + "spans": [ + { + "bbox": [ + 69, + 605, + 163, + 618 + ], + "score": 1.0, + "content": "Japanese (in Bloom).", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 69, + 626, + 289, + 733 + ], + "lines": [ + { + "bbox": [ + 69, + 626, + 290, + 639 + ], + "spans": [ + { + "bbox": [ + 69, + 626, + 290, + 639 + ], + "score": 1.0, + "content": "Results across Different Model Sizes We repeat", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 68, + 640, + 290, + 652 + ], + "spans": [ + { + "bbox": [ + 68, + 640, + 290, + 652 + ], + "score": 1.0, + "content": "the same experiment with the OPT models of sizes", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 69, + 653, + 291, + 666 + ], + "spans": [ + { + "bbox": [ + 69, + 653, + 291, + 666 + ], + "score": 1.0, + "content": "1.3B and 30B, to investigate whether these corre-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 666, + 291, + 680 + ], + "spans": [ + { + "bbox": [ + 69, + 666, + 291, + 680 + ], + "score": 1.0, + "content": "lations are also consistent across model sizes or", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 680, + 291, + 694 + ], + "spans": [ + { + "bbox": [ + 68, + 680, + 291, + 694 + ], + "score": 1.0, + "content": "whether this is a phenomenon we should expect", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 68, + 693, + 291, + 708 + ], + "spans": [ + { + "bbox": [ + 68, + 693, + 291, + 708 + ], + "score": 1.0, + "content": "only in large language models. Table 5 (two lower", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 708, + 290, + 720 + ], + "spans": [ + { + "bbox": [ + 69, + 708, + 290, + 720 + ], + "score": 1.0, + "content": "blocks) shows these results for all classification", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 68, + 721, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 68, + 721, + 290, + 733 + ], + "score": 1.0, + "content": "tasks and antonym prediction. We do see that in", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 305, + 72, + 525, + 220 + ], + "lines": [ + { + "bbox": [ + 304, + 72, + 526, + 84 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 526, + 84 + ], + "score": 1.0, + "content": "general the trend appears to be the same in the", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 85, + 525, + 98 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 525, + 98 + ], + "score": 1.0, + "content": "smaller models as well; however, the correlations", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 99, + 526, + 112 + ], + "spans": [ + { + "bbox": [ + 304, + 99, + 526, + 112 + ], + "score": 1.0, + "content": "seem to be slightly weaker. We hypothesize that", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 112, + 526, + 126 + ], + "spans": [ + { + "bbox": [ + 304, + 112, + 526, + 126 + ], + "score": 1.0, + "content": "this might be due to the overall lower performance", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 125, + 526, + 140 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 526, + 140 + ], + "score": 1.0, + "content": "of these smaller models, making the performance", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 140, + 526, + 151 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 526, + 151 + ], + "score": 1.0, + "content": "results we use for correlation less stable and reli-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 153, + 527, + 165 + ], + "spans": [ + { + "bbox": [ + 304, + 153, + 527, + 165 + ], + "score": 1.0, + "content": "able. For word-level translation, however, all corre-", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 167, + 526, + 178 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 526, + 178 + ], + "score": 1.0, + "content": "lations with the 30B and 1.3B models are similar", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 180, + 527, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 527, + 192 + ], + "score": 1.0, + "content": "to those with the 175B model, and are all statisti-", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 194, + 525, + 207 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 525, + 207 + ], + "score": 1.0, + "content": "cally significant (also after Bonferroni correction", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 207, + 416, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 416, + 221 + ], + "score": 1.0, + "content": "for multiple hypotheses).", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 53 + }, + { + "type": "title", + "bbox": [ + 305, + 232, + 367, + 246 + ], + "lines": [ + { + "bbox": [ + 302, + 230, + 370, + 250 + ], + "spans": [ + { + "bbox": [ + 302, + 230, + 370, + 250 + ], + "score": 1.0, + "content": "6 Analysis", + "type": "text" + } + ], + "index": 59 + } + ], + "index": 59 + }, + { + "type": "text", + "bbox": [ + 305, + 256, + 525, + 376 + ], + "lines": [ + { + "bbox": [ + 304, + 255, + 525, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 525, + 269 + ], + "score": 1.0, + "content": "Next, we further explore the observed relationship", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 303, + 269, + 528, + 283 + ], + "spans": [ + { + "bbox": [ + 303, + 269, + 528, + 283 + ], + "score": 1.0, + "content": "between model perplexity and prompt performance.", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 283, + 526, + 296 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 526, + 296 + ], + "score": 1.0, + "content": "Despite the consistently high correlation between", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 296, + 525, + 310 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 525, + 310 + ], + "score": 1.0, + "content": "these two factors, the structure of this relationship", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 311, + 525, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 525, + 323 + ], + "score": 1.0, + "content": "varies across tasks (Section 6.1). Additionally, we", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 323, + 527, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 527, + 337 + ], + "score": 1.0, + "content": "find that the automatically added prompts are high-", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 338, + 527, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 527, + 351 + ], + "score": 1.0, + "content": "quality and not a significant source of noise (Sec-", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 304, + 351, + 526, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 526, + 365 + ], + "score": 1.0, + "content": "tion 6.2), and that the best prompts selected by our", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 304, + 365, + 495, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 495, + 376 + ], + "score": 1.0, + "content": "approach vary across models (Section 6.3).", + "type": "text" + } + ], + "index": 68 + } + ], + "index": 64 + }, + { + "type": "title", + "bbox": [ + 305, + 389, + 502, + 416 + ], + "lines": [ + { + "bbox": [ + 304, + 389, + 502, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 322, + 402 + ], + "score": 1.0, + "content": "6.1", + "type": "text" + }, + { + "bbox": [ + 327, + 389, + 502, + 403 + ], + "score": 1.0, + "content": "Visualizing the Relationship between", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 328, + 403, + 463, + 417 + ], + "spans": [ + { + "bbox": [ + 328, + 403, + 463, + 417 + ], + "score": 1.0, + "content": "Perplexity and Performance", + "type": "text" + } + ], + "index": 70 + } + ], + "index": 69.5 + }, + { + "type": "text", + "bbox": [ + 305, + 421, + 525, + 731 + ], + "lines": [ + { + "bbox": [ + 304, + 420, + 527, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 527, + 435 + ], + "score": 1.0, + "content": "To visualize the correlations we get between the per-", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 304, + 435, + 525, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 525, + 449 + ], + "score": 1.0, + "content": "plexity and the performance of the prompts across", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 303, + 448, + 526, + 462 + ], + "spans": [ + { + "bbox": [ + 303, + 448, + 526, + 462 + ], + "score": 1.0, + "content": "the different settings, we plot a few examples for", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 462, + 525, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 525, + 475 + ], + "score": 1.0, + "content": "different tasks and languages. Figures 1 and 2 show", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 477, + 525, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 525, + 488 + ], + "score": 1.0, + "content": "some of the results for selected tasks, as detailed", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 490, + 527, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 527, + 502 + ], + "score": 1.0, + "content": "in the captions. The negative trend of the corre-", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 304, + 502, + 526, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 526, + 517 + ], + "score": 1.0, + "content": "lation is clearly visible in all plots. 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Indeed, the intersection of the 10 lowest", + "type": "text" + } + ], + "index": 82 + }, + { + "bbox": [ + 303, + 585, + 527, + 597 + ], + "spans": [ + { + "bbox": [ + 303, + 585, + 527, + 597 + ], + "score": 1.0, + "content": "perplexity prompts between any two different lan-", + "type": "text" + } + ], + "index": 83 + }, + { + "bbox": [ + 303, + 598, + 525, + 610 + ], + "spans": [ + { + "bbox": [ + 303, + 598, + 525, + 610 + ], + "score": 1.0, + "content": "guages is 8.6 and 8.4 on average (for OPT 175B", + "type": "text" + } + ], + "index": 84 + }, + { + "bbox": [ + 304, + 612, + 527, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 612, + 527, + 624 + ], + "score": 1.0, + "content": "and Bloom, respectively), which is extremely high.", + "type": "text" + } + ], + "index": 85 + }, + { + "bbox": [ + 303, + 624, + 526, + 639 + ], + "spans": [ + { + "bbox": [ + 303, + 624, + 526, + 639 + ], + "score": 1.0, + "content": "This is not very surprising since we know that the", + "type": "text" + } + ], + "index": 86 + }, + { + "bbox": [ + 305, + 639, + 526, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 639, + 526, + 651 + ], + "score": 1.0, + "content": "only differences between the prompts in the differ-", + "type": "text" + } + ], + "index": 87 + }, + { + "bbox": [ + 303, + 651, + 526, + 667 + ], + "spans": [ + { + "bbox": [ + 303, + 651, + 526, + 667 + ], + "score": 1.0, + "content": "ent languages are the names of the target languages", + "type": "text" + } + ], + "index": 88 + }, + { + "bbox": [ + 304, + 666, + 527, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 527, + 678 + ], + "score": 1.0, + "content": "(e.g., The word for “dog” in French is “). 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Here", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 69, + 564, + 290, + 576 + ], + "spans": [ + { + "bbox": [ + 69, + 564, + 290, + 576 + ], + "score": 1.0, + "content": "the correlations are extremely consistent across all", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 578, + 291, + 590 + ], + "spans": [ + { + "bbox": [ + 69, + 578, + 291, + 590 + ], + "score": 1.0, + "content": "languages and across models, with statistical sig-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 68, + 590, + 291, + 604 + ], + "spans": [ + { + "bbox": [ + 68, + 590, + 291, + 604 + ], + "score": 1.0, + "content": "nificance for all languages except for Catalan and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 69, + 605, + 163, + 618 + ], + "spans": [ + { + "bbox": [ + 69, + 605, + 163, + 618 + ], + "score": 1.0, + "content": "Japanese (in Bloom).", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 34.5, + "bbox_fs": [ + 68, + 536, + 291, + 618 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 626, + 289, + 733 + ], + "lines": [ + { + "bbox": [ + 69, + 626, + 290, + 639 + ], + "spans": [ + { + "bbox": [ + 69, + 626, + 290, + 639 + ], + "score": 1.0, + "content": "Results across Different Model Sizes We repeat", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 68, + 640, + 290, + 652 + ], + "spans": [ + { + "bbox": [ + 68, + 640, + 290, + 652 + ], + "score": 1.0, + "content": "the same experiment with the OPT models of sizes", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 69, + 653, + 291, + 666 + ], + "spans": [ + { + "bbox": [ + 69, + 653, + 291, + 666 + ], + "score": 1.0, + "content": "1.3B and 30B, to investigate whether these corre-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 666, + 291, + 680 + ], + "spans": [ + { + "bbox": [ + 69, + 666, + 291, + 680 + ], + "score": 1.0, + "content": "lations are also consistent across model sizes or", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 68, + 680, + 291, + 694 + ], + "spans": [ + { + "bbox": [ + 68, + 680, + 291, + 694 + ], + "score": 1.0, + "content": "whether this is a phenomenon we should expect", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 68, + 693, + 291, + 708 + ], + "spans": [ + { + "bbox": [ + 68, + 693, + 291, + 708 + ], + "score": 1.0, + "content": "only in large language models. Table 5 (two lower", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 708, + 290, + 720 + ], + "spans": [ + { + "bbox": [ + 69, + 708, + 290, + 720 + ], + "score": 1.0, + "content": "blocks) shows these results for all classification", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 68, + 721, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 68, + 721, + 290, + 733 + ], + "score": 1.0, + "content": "tasks and antonym prediction. We do see that in", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 72, + 526, + 84 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 526, + 84 + ], + "score": 1.0, + "content": "general the trend appears to be the same in the", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 85, + 525, + 98 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 525, + 98 + ], + "score": 1.0, + "content": "smaller models as well; however, the correlations", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 99, + 526, + 112 + ], + "spans": [ + { + "bbox": [ + 304, + 99, + 526, + 112 + ], + "score": 1.0, + "content": "seem to be slightly weaker. We hypothesize that", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 112, + 526, + 126 + ], + "spans": [ + { + "bbox": [ + 304, + 112, + 526, + 126 + ], + "score": 1.0, + "content": "this might be due to the overall lower performance", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 125, + 526, + 140 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 526, + 140 + ], + "score": 1.0, + "content": "of these smaller models, making the performance", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 140, + 526, + 151 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 526, + 151 + ], + "score": 1.0, + "content": "results we use for correlation less stable and reli-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 153, + 527, + 165 + ], + "spans": [ + { + "bbox": [ + 304, + 153, + 527, + 165 + ], + "score": 1.0, + "content": "able. For word-level translation, however, all corre-", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 167, + 526, + 178 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 526, + 178 + ], + "score": 1.0, + "content": "lations with the 30B and 1.3B models are similar", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 180, + 527, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 527, + 192 + ], + "score": 1.0, + "content": "to those with the 175B model, and are all statisti-", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 194, + 525, + 207 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 525, + 207 + ], + "score": 1.0, + "content": "cally significant (also after Bonferroni correction", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 207, + 416, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 416, + 221 + ], + "score": 1.0, + "content": "for multiple hypotheses).", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 41.5, + "bbox_fs": [ + 68, + 626, + 291, + 733 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 72, + 525, + 220 + ], + "lines": [], + "index": 53, + "bbox_fs": [ + 304, + 72, + 527, + 221 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 305, + 232, + 367, + 246 + ], + "lines": [ + { + "bbox": [ + 302, + 230, + 370, + 250 + ], + "spans": [ + { + "bbox": [ + 302, + 230, + 370, + 250 + ], + "score": 1.0, + "content": "6 Analysis", + "type": "text" + } + ], + "index": 59 + } + ], + "index": 59 + }, + { + "type": "text", + "bbox": [ + 305, + 256, + 525, + 376 + ], + "lines": [ + { + "bbox": [ + 304, + 255, + 525, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 525, + 269 + ], + "score": 1.0, + "content": "Next, we further explore the observed relationship", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 303, + 269, + 528, + 283 + ], + "spans": [ + { + "bbox": [ + 303, + 269, + 528, + 283 + ], + "score": 1.0, + "content": "between model perplexity and prompt performance.", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 283, + 526, + 296 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 526, + 296 + ], + "score": 1.0, + "content": "Despite the consistently high correlation between", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 296, + 525, + 310 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 525, + 310 + ], + "score": 1.0, + "content": "these two factors, the structure of this relationship", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 311, + 525, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 525, + 323 + ], + "score": 1.0, + "content": "varies across tasks (Section 6.1). Additionally, we", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 323, + 527, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 527, + 337 + ], + "score": 1.0, + "content": "find that the automatically added prompts are high-", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 338, + 527, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 527, + 351 + ], + "score": 1.0, + "content": "quality and not a significant source of noise (Sec-", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 304, + 351, + 526, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 526, + 365 + ], + "score": 1.0, + "content": "tion 6.2), and that the best prompts selected by our", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 304, + 365, + 495, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 495, + 376 + ], + "score": 1.0, + "content": "approach vary across models (Section 6.3).", + "type": "text" + } + ], + "index": 68 + } + ], + "index": 64, + "bbox_fs": [ + 303, + 255, + 528, + 376 + ] + }, + { + "type": "title", + "bbox": [ + 305, + 389, + 502, + 416 + ], + "lines": [ + { + "bbox": [ + 304, + 389, + 502, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 322, + 402 + ], + "score": 1.0, + "content": "6.1", + "type": "text" + }, + { + "bbox": [ + 327, + 389, + 502, + 403 + ], + "score": 1.0, + "content": "Visualizing the Relationship between", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 328, + 403, + 463, + 417 + ], + "spans": [ + { + "bbox": [ + 328, + 403, + 463, + 417 + ], + "score": 1.0, + "content": "Perplexity and Performance", + "type": "text" + } + ], + "index": 70 + } + ], + "index": 69.5 + }, + { + "type": "text", + "bbox": [ + 305, + 421, + 525, + 731 + ], + "lines": [ + { + "bbox": [ + 304, + 420, + 527, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 527, + 435 + ], + "score": 1.0, + "content": "To visualize the correlations we get between the per-", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 304, + 435, + 525, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 525, + 449 + ], + "score": 1.0, + "content": "plexity and the performance of the prompts across", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 303, + 448, + 526, + 462 + ], + "spans": [ + { + "bbox": [ + 303, + 448, + 526, + 462 + ], + "score": 1.0, + "content": "the different settings, we plot a few examples for", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 462, + 525, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 525, + 475 + ], + "score": 1.0, + "content": "different tasks and languages. Figures 1 and 2 show", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 477, + 525, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 525, + 488 + ], + "score": 1.0, + "content": "some of the results for selected tasks, as detailed", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 490, + 527, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 527, + 502 + ], + "score": 1.0, + "content": "in the captions. The negative trend of the corre-", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 304, + 502, + 526, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 526, + 517 + ], + "score": 1.0, + "content": "lation is clearly visible in all plots. Interestingly,", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 304, + 516, + 526, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 526, + 529 + ], + "score": 1.0, + "content": "the structure of the plots for word-level translation", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 304, + 531, + 527, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 527, + 543 + ], + "score": 1.0, + "content": "are very similar across all the language pairs, sug-", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 304, + 544, + 526, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 526, + 557 + ], + "score": 1.0, + "content": "gesting that prompts get consistent perplexity and", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 304, + 558, + 525, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 525, + 570 + ], + "score": 1.0, + "content": "performance across languages (possibly at different", + "type": "text" + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 571, + 526, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 526, + 583 + ], + "score": 1.0, + "content": "scales). Indeed, the intersection of the 10 lowest", + "type": "text" + } + ], + "index": 82 + }, + { + "bbox": [ + 303, + 585, + 527, + 597 + ], + "spans": [ + { + "bbox": [ + 303, + 585, + 527, + 597 + ], + "score": 1.0, + "content": "perplexity prompts between any two different lan-", + "type": "text" + } + ], + "index": 83 + }, + { + "bbox": [ + 303, + 598, + 525, + 610 + ], + "spans": [ + { + "bbox": [ + 303, + 598, + 525, + 610 + ], + "score": 1.0, + "content": "guages is 8.6 and 8.4 on average (for OPT 175B", + "type": "text" + } + ], + "index": 84 + }, + { + "bbox": [ + 304, + 612, + 527, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 612, + 527, + 624 + ], + "score": 1.0, + "content": "and Bloom, respectively), which is extremely high.", + "type": "text" + } + ], + "index": 85 + }, + { + "bbox": [ + 303, + 624, + 526, + 639 + ], + "spans": [ + { + "bbox": [ + 303, + 624, + 526, + 639 + ], + "score": 1.0, + "content": "This is not very surprising since we know that the", + "type": "text" + } + ], + "index": 86 + }, + { + "bbox": [ + 305, + 639, + 526, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 639, + 526, + 651 + ], + "score": 1.0, + "content": "only differences between the prompts in the differ-", + "type": "text" + } + ], + "index": 87 + }, + { + "bbox": [ + 303, + 651, + 526, + 667 + ], + "spans": [ + { + "bbox": [ + 303, + 651, + 526, + 667 + ], + "score": 1.0, + "content": "ent languages are the names of the target languages", + "type": "text" + } + ], + "index": 88 + }, + { + "bbox": [ + 304, + 666, + 527, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 527, + 678 + ], + "score": 1.0, + "content": "(e.g., The word for “dog” in French is “). Addition-", + "type": "text" + } + ], + "index": 89 + }, + { + "bbox": [ + 304, + 678, + 526, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 526, + 693 + ], + "score": 1.0, + "content": "ally, the intersection of 10 prompts with the highest", + "type": "text" + } + ], + "index": 90 + }, + { + "bbox": [ + 303, + 692, + 526, + 707 + ], + "spans": [ + { + "bbox": [ + 303, + 692, + 526, + 707 + ], + "score": 1.0, + "content": "label score between any two different languages is", + "type": "text" + } + ], + "index": 91 + }, + { + "bbox": [ + 304, + 707, + 527, + 719 + ], + "spans": [ + { + "bbox": [ + 304, + 707, + 527, + 719 + ], + "score": 1.0, + "content": "7 and 6.5 on average (for OPT 175B and Bloom,", + "type": "text" + } + ], + "index": 92 + }, + { + "bbox": [ + 304, + 720, + 365, + 733 + ], + "spans": [ + { + "bbox": [ + 304, + 720, + 365, + 733 + ], + "score": 1.0, + "content": "respectively).", + "type": "text" + } + ], + "index": 93 + } + ], + "index": 82, + "bbox_fs": [ + 303, + 420, + 527, + 733 + ] + }, + { + "type": "text", + "bbox": [ + 304, + 734, + 524, + 774 + ], + "lines": [ + { + "bbox": [ + 316, + 734, + 525, + 746 + ], + "spans": [ + { + "bbox": [ + 316, + 734, + 525, + 746 + ], + "score": 1.0, + "content": "A notable finding that appears in the word-level", + "type": "text" + } + ], + "index": 94 + }, + { + "bbox": [ + 304, + 748, + 525, + 760 + ], + "spans": [ + { + "bbox": [ + 304, + 748, + 525, + 760 + ], + "score": 1.0, + "content": "translation plots is the clear separation between", + "type": "text" + } + ], + "index": 95 + }, + { + "bbox": [ + 303, + 761, + 525, + 774 + ], + "spans": [ + { + "bbox": [ + 303, + 761, + 525, + 774 + ], + "score": 1.0, + "content": "prompts that include or do not include quotation", + "type": "text" + } + ], + "index": 96 + }, + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "score": 1.0, + "content": "marks for the label (usually aligns with whether", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 86, + 290, + 98 + ], + "spans": [ + { + "bbox": [ + 69, + 86, + 290, + 98 + ], + "score": 1.0, + "content": "the prompt uses quotation marks for the source", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 100, + 291, + 112 + ], + "spans": [ + { + "bbox": [ + 69, + 100, + 291, + 112 + ], + "score": 1.0, + "content": "word) – three example prompts appear on the plot.", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 113, + 290, + 125 + ], + "spans": [ + { + "bbox": [ + 69, + 113, + 290, + 125 + ], + "score": 1.0, + "content": "Prompts with quotation marks for the words tend to", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 125, + 291, + 140 + ], + "spans": [ + { + "bbox": [ + 68, + 125, + 291, + 140 + ], + "score": 1.0, + "content": "have both lower perplexity and better performance,", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 141, + 290, + 152 + ], + "spans": [ + { + "bbox": [ + 69, + 141, + 290, + 152 + ], + "score": 1.0, + "content": "consistently. We further analyze the results for", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 153, + 290, + 166 + ], + "spans": [ + { + "bbox": [ + 69, + 153, + 290, + 166 + ], + "score": 1.0, + "content": "OPT 175B within clusters (with/without quotations", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 167, + 290, + 180 + ], + "spans": [ + { + "bbox": [ + 69, + 167, + 290, + 180 + ], + "score": 1.0, + "content": "marks). In the cluster with quotation marks, we", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 68, + 180, + 290, + 194 + ], + "spans": [ + { + "bbox": [ + 68, + 180, + 250, + 194 + ], + "score": 1.0, + "content": "get negative correlations (in the range of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 251, + 180, + 278, + 192 + ], + "score": 0.53, + "content": "- 0 . 2 8", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 278, + 180, + 290, + 194 + ], + "score": 1.0, + "content": "to", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 194, + 290, + 207 + ], + "spans": [ + { + "bbox": [ + 69, + 194, + 290, + 207 + ], + "score": 1.0, + "content": "–0.38) that are statistically significant for almost all", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 208, + 290, + 219 + ], + "spans": [ + { + "bbox": [ + 69, + 208, + 290, + 219 + ], + "score": 1.0, + "content": "languages. The correlations within the other cluster", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 221, + 290, + 234 + ], + "spans": [ + { + "bbox": [ + 69, + 221, + 290, + 234 + ], + "score": 1.0, + "content": "are weaker and less significant (this is expected", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 234, + 292, + 248 + ], + "spans": [ + { + "bbox": [ + 69, + 234, + 292, + 248 + ], + "score": 1.0, + "content": "given the overall lower performance of that cluster).", + "type": "text", + "cross_page": true + } + ], + "index": 12 + } + ], + "index": 95, + "bbox_fs": [ + 303, + 734, + 525, + 774 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 69, + 71, + 290, + 247 + ], + "lines": [ + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "score": 1.0, + "content": "marks for the label (usually aligns with whether", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 86, + 290, + 98 + ], + "spans": [ + { + "bbox": [ + 69, + 86, + 290, + 98 + ], + "score": 1.0, + "content": "the prompt uses quotation marks for the source", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 100, + 291, + 112 + ], + "spans": [ + { + "bbox": [ + 69, + 100, + 291, + 112 + ], + "score": 1.0, + "content": "word) – three example prompts appear on the plot.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 113, + 290, + 125 + ], + "spans": [ + { + "bbox": [ + 69, + 113, + 290, + 125 + ], + "score": 1.0, + "content": "Prompts with quotation marks for the words tend to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 125, + 291, + 140 + ], + "spans": [ + { + "bbox": [ + 68, + 125, + 291, + 140 + ], + "score": 1.0, + "content": "have both lower perplexity and better performance,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 141, + 290, + 152 + ], + "spans": [ + { + "bbox": [ + 69, + 141, + 290, + 152 + ], + "score": 1.0, + "content": "consistently. We further analyze the results for", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 153, + 290, + 166 + ], + "spans": [ + { + "bbox": [ + 69, + 153, + 290, + 166 + ], + "score": 1.0, + "content": "OPT 175B within clusters (with/without quotations", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 167, + 290, + 180 + ], + "spans": [ + { + "bbox": [ + 69, + 167, + 290, + 180 + ], + "score": 1.0, + "content": "marks). In the cluster with quotation marks, we", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 68, + 180, + 290, + 194 + ], + "spans": [ + { + "bbox": [ + 68, + 180, + 250, + 194 + ], + "score": 1.0, + "content": "get negative correlations (in the range of", + "type": "text" + }, + { + "bbox": [ + 251, + 180, + 278, + 192 + ], + "score": 0.53, + "content": "- 0 . 2 8", + "type": "inline_equation" + }, + { + "bbox": [ + 278, + 180, + 290, + 194 + ], + "score": 1.0, + "content": "to", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 194, + 290, + 207 + ], + "spans": [ + { + "bbox": [ + 69, + 194, + 290, + 207 + ], + "score": 1.0, + "content": "–0.38) that are statistically significant for almost all", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 208, + 290, + 219 + ], + "spans": [ + { + "bbox": [ + 69, + 208, + 290, + 219 + ], + "score": 1.0, + "content": "languages. 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The blue points stand for", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 67, + 457, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 67, + 457, + 290, + 469 + ], + "score": 1.0, + "content": "prompts with quotation marks for the words, while the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 68, + 470, + 288, + 482 + ], + "spans": [ + { + "bbox": [ + 68, + 470, + 288, + 482 + ], + "score": 1.0, + "content": "yellow points are of prompts without quotation marks.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26 + } + ], + "index": 22.0 + }, + { + "type": "title", + "bbox": [ + 70, + 510, + 207, + 522 + ], + "lines": [ + { + "bbox": [ + 67, + 507, + 208, + 525 + ], + "spans": [ + { + "bbox": [ + 67, + 507, + 208, + 525 + ], + "score": 1.0, + "content": "6.2 Effect of Noisy Prompts", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 69, + 529, + 290, + 691 + ], + "lines": [ + { + "bbox": [ + 69, + 529, + 291, + 543 + ], + "spans": [ + { + "bbox": [ + 69, + 529, + 291, + 543 + ], + "score": 1.0, + "content": "We expect our automatic method for expand-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 543, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 68, + 543, + 290, + 555 + ], + "score": 1.0, + "content": "ing the set of prompts to also introduce some", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 69, + 557, + 290, + 570 + ], + "spans": [ + { + "bbox": [ + 69, + 557, + 290, + 570 + ], + "score": 1.0, + "content": "noise. 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promptppl
Is this example correct English usage?25.79
Is this example using English correctly?25.46
Is this example correct English?25.33
Is this the example in correct English?25.00
Is English in this example correct?24.90
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TaskLangBefore filteringAfter filtering
PearsonSpearmanPearsonSpearman
AG News--0.63-0.68-0.62-0.54
WLTita-0.44-0.58-0.44-0.57
spa-0.47-0.61-0.47-0.61
cat-0.45-0.57-0.47-0.58
fra-0.47-0.57-0.48-0.57
deu-0.43-0.60-0.44-0.60
fin-0.41-0.60-0.44-0.62
por-0.43-0.61-0.45-0.62
eus-0.45-0.60-0.47-0.61
tur-0.43-0.61-0.44-0.62
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Similar", + "type": "text" + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 601, + 525, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 525, + 613 + ], + "score": 1.0, + "content": "lists for the rest of the tasks are listed in Section B", + "type": "text" + } + ], + "index": 82 + }, + { + "bbox": [ + 303, + 614, + 380, + 628 + ], + "spans": [ + { + "bbox": [ + 303, + 614, + 380, + 628 + ], + "score": 1.0, + "content": "in the Appendix.", + "type": "text" + } + ], + "index": 83 + } + ], + "index": 81.5 + }, + { + "type": "text", + "bbox": [ + 305, + 629, + 525, + 654 + ], + "lines": [ + { + "bbox": [ + 315, + 628, + 525, + 642 + ], + "spans": [ + { + "bbox": [ + 315, + 628, + 525, + 642 + ], + "score": 1.0, + "content": "A closer look at the lowest perplexity prompts", + "type": "text" + } + ], + "index": 84 + }, + { + "bbox": [ + 303, + 642, + 526, + 656 + ], + "spans": [ + { + "bbox": [ + 303, + 642, + 526, + 656 + ], + "score": 1.0, + "content": "reveals that the intersection of 10 lowest perplex-", + "type": "text" + } + ], + "index": 85 + } + ], + "index": 84.5 + }, + { + "type": "table", + "bbox": [ + 306, + 673, + 525, + 738 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 306, + 673, + 525, + 738 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 306, + 673, + 525, + 738 + ], + "spans": [ + { + "bbox": [ + 306, + 673, + 525, + 738 + ], + "score": 0.976, + "html": "
promptppl
The following two words are antonyms:“good"and “10.24
The antonym of the word“good’is“10.32
The word that has the opposite meaning of the word “good"is “10.43
The word“good’is the antithesis of the word “10.85
The word “good"is the opposite of the word “11.15
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The blue points stand for", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 67, + 457, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 67, + 457, + 290, + 469 + ], + "score": 1.0, + "content": "prompts with quotation marks for the words, while the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 68, + 470, + 288, + 482 + ], + "spans": [ + { + "bbox": [ + 68, + 470, + 288, + 482 + ], + "score": 1.0, + "content": "yellow points are of prompts without quotation marks.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26 + } + ], + "index": 22.0 + }, + { + "type": "title", + "bbox": [ + 70, + 510, + 207, + 522 + ], + "lines": [ + { + "bbox": [ + 67, + 507, + 208, + 525 + ], + "spans": [ + { + "bbox": [ + 67, + 507, + 208, + 525 + ], + "score": 1.0, + "content": "6.2 Effect of Noisy Prompts", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 69, + 529, + 290, + 691 + ], + "lines": [ + { + "bbox": [ + 69, + 529, + 291, + 543 + ], + "spans": [ + { + "bbox": [ + 69, + 529, + 291, + 543 + ], + "score": 1.0, + "content": "We expect our automatic method for expand-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 543, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 68, + 543, + 290, + 555 + ], + "score": 1.0, + "content": "ing the set of prompts to also introduce some", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 69, + 557, + 290, + 570 + ], + "spans": [ + { + "bbox": [ + 69, + 557, + 290, + 570 + ], + "score": 1.0, + "content": "noise. 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promptppl
Is this example correct English usage?25.79
Is this example using English correctly?25.46
Is this example correct English?25.33
Is this the example in correct English?25.00
Is English in this example correct?24.90
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TaskLangBefore filteringAfter filtering
PearsonSpearmanPearsonSpearman
AG News--0.63-0.68-0.62-0.54
WLTita-0.44-0.58-0.44-0.57
spa-0.47-0.61-0.47-0.61
cat-0.45-0.57-0.47-0.58
fra-0.47-0.57-0.48-0.57
deu-0.43-0.60-0.44-0.60
fin-0.41-0.60-0.44-0.62
por-0.43-0.61-0.45-0.62
eus-0.45-0.60-0.47-0.61
tur-0.43-0.61-0.44-0.62
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promptppl
The following two words are antonyms:“good"and “10.24
The antonym of the word“good’is“10.32
The word that has the opposite meaning of the word “good"is “10.43
The word“good’is the antithesis of the word “10.85
The word “good"is the opposite of the word “11.15
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As", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 230, + 290, + 242 + ], + "spans": [ + { + "bbox": [ + 69, + 230, + 290, + 242 + ], + "score": 1.0, + "content": "one potential application of our findings, we also", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 68, + 243, + 290, + 256 + ], + "spans": [ + { + "bbox": [ + 68, + 243, + 290, + 256 + ], + "score": 1.0, + "content": "present a new method, SPELL, for generating and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 255, + 246, + 270 + ], + "spans": [ + { + "bbox": [ + 69, + 255, + 246, + 270 + ], + "score": 1.0, + "content": "selecting consistently effective prompts.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 69, + 270, + 290, + 323 + ], + "lines": [ + { + "bbox": [ + 80, + 269, + 291, + 282 + ], + "spans": [ + { + "bbox": [ + 80, + 269, + 291, + 282 + ], + "score": 1.0, + "content": "Assuming a fixed computational budget for find-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 69, + 284, + 290, + 297 + ], + "spans": [ + { + "bbox": [ + 69, + 284, + 290, + 297 + ], + "score": 1.0, + "content": "ing effective prompts for a given task, and that the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 69, + 297, + 290, + 310 + ], + "spans": [ + { + "bbox": [ + 69, + 297, + 290, + 310 + ], + "score": 1.0, + "content": "search space might be quite large, we devise the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 69, + 310, + 233, + 324 + ], + "spans": [ + { + "bbox": [ + 69, + 310, + 233, + 324 + ], + "score": 1.0, + "content": "following straightforward procedure:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 78, + 336, + 290, + 488 + ], + "lines": [ + { + "bbox": [ + 78, + 335, + 290, + 350 + ], + "spans": [ + { + "bbox": [ + 78, + 335, + 290, + 350 + ], + "score": 1.0, + "content": "1. 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Rank the list of prompts by perplexity (aver-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 91, + 429, + 291, + 443 + ], + "spans": [ + { + "bbox": [ + 91, + 429, + 291, + 443 + ], + "score": 1.0, + "content": "aged on a representative sample of task inputs,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 90, + 443, + 146, + 456 + ], + "spans": [ + { + "bbox": [ + 90, + 443, + 146, + 456 + ], + "score": 1.0, + "content": "e.g., 1,000).", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 76, + 461, + 290, + 476 + ], + "spans": [ + { + "bbox": [ + 76, + 461, + 150, + 476 + ], + "score": 1.0, + "content": "4. Choose the", + "type": "text" + }, + { + "bbox": [ + 150, + 462, + 158, + 473 + ], + "score": 0.75, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 461, + 290, + 476 + ], + "score": 1.0, + "content": "(e.g., 3) lowest perplexity", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 89, + 476, + 132, + 489 + ], + "spans": [ + { + "bbox": [ + 89, + 476, + 132, + 489 + ], + "score": 1.0, + "content": "prompts.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 70, + 501, + 289, + 609 + ], + "lines": [ + { + "bbox": [ + 80, + 502, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 80, + 502, + 290, + 515 + ], + "score": 1.0, + "content": "Using this algorithm, we show empirically that", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 69, + 515, + 291, + 528 + ], + "spans": [ + { + "bbox": [ + 69, + 515, + 291, + 528 + ], + "score": 1.0, + "content": "it is best to prioritize experimenting with the lowest", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 529, + 290, + 541 + ], + "spans": [ + { + "bbox": [ + 68, + 529, + 290, + 541 + ], + "score": 1.0, + "content": "perplexity prompts, as they are more stable (exhibit", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 68, + 542, + 291, + 555 + ], + "spans": [ + { + "bbox": [ + 68, + 542, + 291, + 555 + ], + "score": 1.0, + "content": "less variation in performance) and perform better", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 555, + 291, + 569 + ], + "spans": [ + { + "bbox": [ + 68, + 555, + 291, + 569 + ], + "score": 1.0, + "content": "than manual prompts on average. 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OPTBloom
Tasklow-pplmanual△low-pplmanual△
GLUE Cola51.748.53.164.560.93.6
Newspop80.670.410.290.080.010.0
AG News68.461.96.551.063.5-12.5
IMDB90.488.91.491.388.82.5
DBpedia46.051.7-5.731.230.21.0
Emotion21.622.6-1.135.832.13.6
Tweet Offensive48.450.6-2.348.640.87.8
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OPTBloom
Tasklow-pplmanual△low-pplmanual△
GLUE Cola51.748.53.164.560.93.6
Newspop80.670.410.290.080.010.0
AG News68.461.96.551.063.5-12.5
IMDB90.488.91.491.388.82.5
DBpedia46.051.7-5.731.230.21.0
Emotion21.622.6-1.135.832.13.6
Tweet Offensive48.450.6-2.348.640.87.8
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Our findings may not hold when the possi-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 202, + 525, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 525, + 215 + ], + "score": 1.0, + "content": "ble prompt space is expanded to include any token", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 303, + 216, + 518, + 228 + ], + "spans": [ + { + "bbox": [ + 303, + 216, + 518, + 228 + ], + "score": 1.0, + "content": "sequence; we leave this direction to future work.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 305, + 237, + 525, + 371 + ], + "lines": [ + { + "bbox": [ + 304, + 237, + 525, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 237, + 525, + 249 + ], + "score": 1.0, + "content": "Generality of our analysis and of the SPELL", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 303, + 250, + 526, + 263 + ], + "spans": [ + { + "bbox": [ + 303, + 250, + 526, + 263 + ], + "score": 1.0, + "content": "method We perform our analysis on and build", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 303, + 264, + 526, + 277 + ], + "spans": [ + { + "bbox": [ + 303, + 264, + 526, + 277 + ], + "score": 1.0, + "content": "our method around specific models, namely OPT", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 278, + 525, + 290 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 525, + 290 + ], + "score": 1.0, + "content": "and Bloom. 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It", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 305, + 525, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 525, + 317 + ], + "score": 1.0, + "content": "is possible that our analysis and SPELL method do", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 303, + 318, + 527, + 331 + ], + "spans": [ + { + "bbox": [ + 303, + 318, + 527, + 331 + ], + "score": 1.0, + "content": "not generalize to other pretrained models or tasks;", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 303, + 331, + 526, + 344 + ], + "spans": [ + { + "bbox": [ + 303, + 331, + 526, + 344 + ], + "score": 1.0, + "content": "however, we consider models of various sizes and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 345, + 525, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 525, + 359 + ], + "score": 1.0, + "content": "from different sources, and a wide range of tasks", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 303, + 359, + 394, + 371 + ], + "spans": [ + { + "bbox": [ + 303, + 359, + 394, + 371 + ], + "score": 1.0, + "content": "to mitigate this risk.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38.5 + }, + { + "type": "title", + "bbox": [ + 306, + 383, + 405, + 396 + ], + "lines": [ + { + "bbox": [ + 304, + 380, + 406, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 406, + 398 + ], + "score": 1.0, + "content": "Acknowledgements", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 305, + 405, + 524, + 457 + ], + "lines": [ + { + "bbox": [ + 304, + 405, + 526, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 526, + 417 + ], + "score": 1.0, + "content": "We thank Alisa Liu and Orevaoghene Ahia for their", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 303, + 418, + 527, + 432 + ], + "spans": [ + { + "bbox": [ + 303, + 418, + 527, + 432 + ], + "score": 1.0, + "content": "help in annotating noisy prompts. We also thank", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 432, + 525, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 525, + 444 + ], + "score": 1.0, + "content": "the reviewers for their valuable comments on the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 302, + 447, + 334, + 460 + ], + "spans": [ + { + "bbox": [ + 302, + 447, + 334, + 460 + ], + "score": 1.0, + "content": "paper.", + "type": "text" + } + ], + "index": 73 + } + ], + "index": 46.5 + }, + { + "type": "title", + "bbox": [ + 69, + 419, + 145, + 432 + ], + "lines": [ + { + "bbox": [ + 67, + 417, + 147, + 436 + ], + "spans": [ + { + "bbox": [ + 67, + 417, + 147, + 436 + ], + "score": 1.0, + "content": "9 Conclusion", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 48 + }, + { + "type": "text", + "bbox": [ + 70, + 448, + 290, + 622 + ], + "lines": [ + { + "bbox": [ + 69, + 447, + 290, + 460 + ], + "spans": [ + { + "bbox": [ + 69, + 447, + 290, + 460 + ], + "score": 1.0, + "content": "We investigate the phenomenon where some", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 68, + 460, + 292, + 475 + ], + "spans": [ + { + "bbox": [ + 68, + 460, + 292, + 475 + ], + "score": 1.0, + "content": "prompts perform better than others despite appear-", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 68, + 474, + 292, + 488 + ], + "spans": [ + { + "bbox": [ + 68, + 474, + 292, + 488 + ], + "score": 1.0, + "content": "ing similar to the human users of LMs. Specifically,", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 68, + 488, + 292, + 502 + ], + "spans": [ + { + "bbox": [ + 68, + 488, + 292, + 502 + ], + "score": 1.0, + "content": "we hypothesize that the perplexity of a prompt un-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 69, + 501, + 292, + 514 + ], + "spans": [ + { + "bbox": [ + 69, + 501, + 292, + 514 + ], + "score": 1.0, + "content": "der a given LM is closely tied to its task perfor-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 68, + 515, + 291, + 527 + ], + "spans": [ + { + "bbox": [ + 68, + 515, + 291, + 527 + ], + "score": 1.0, + "content": "mance. We test this theory on a large number of", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 69, + 527, + 291, + 542 + ], + "spans": [ + { + "bbox": [ + 69, + 527, + 291, + 542 + ], + "score": 1.0, + "content": "tasks and autoregressive LMs, and the resulting", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 69, + 542, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 69, + 542, + 290, + 555 + ], + "score": 1.0, + "content": "correlation study validates our hypothesis. Further", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 69, + 556, + 290, + 569 + ], + "spans": [ + { + "bbox": [ + 69, + 556, + 290, + 569 + ], + "score": 1.0, + "content": "analysis of this relationship demonstrates that the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 68, + 569, + 290, + 582 + ], + "spans": [ + { + "bbox": [ + 68, + 569, + 290, + 582 + ], + "score": 1.0, + "content": "best prompts differ across models, highlighting the", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 69, + 583, + 290, + 596 + ], + "spans": [ + { + "bbox": [ + 69, + 583, + 290, + 596 + ], + "score": 1.0, + "content": "importance of model-specific analysis, and that the", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 69, + 597, + 290, + 609 + ], + "spans": [ + { + "bbox": [ + 69, + 597, + 290, + 609 + ], + "score": 1.0, + "content": "underlying structure of the relationship between", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 68, + 610, + 278, + 622 + ], + "spans": [ + { + "bbox": [ + 68, + 610, + 278, + 622 + ], + "score": 1.0, + "content": "perplexity and performance varies across tasks.", + "type": "text" + } + ], + "index": 61 + } + ], + "index": 55 + }, + { + "type": "text", + "bbox": [ + 70, + 626, + 290, + 773 + ], + "lines": [ + { + "bbox": [ + 79, + 625, + 291, + 640 + ], + "spans": [ + { + "bbox": [ + 79, + 625, + 291, + 640 + ], + "score": 1.0, + "content": "In light of these findings, we then propose", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 68, + 639, + 291, + 651 + ], + "spans": [ + { + "bbox": [ + 68, + 639, + 291, + 651 + ], + "score": 1.0, + "content": "a method, SPELL, to help users find well-", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 68, + 652, + 291, + 667 + ], + "spans": [ + { + "bbox": [ + 68, + 652, + 291, + 667 + ], + "score": 1.0, + "content": "performing prompts for new tasks. 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It", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 305, + 525, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 525, + 317 + ], + "score": 1.0, + "content": "is possible that our analysis and SPELL method do", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 303, + 318, + 527, + 331 + ], + "spans": [ + { + "bbox": [ + 303, + 318, + 527, + 331 + ], + "score": 1.0, + "content": "not generalize to other pretrained models or tasks;", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 303, + 331, + 526, + 344 + ], + "spans": [ + { + "bbox": [ + 303, + 331, + 526, + 344 + ], + "score": 1.0, + "content": "however, we consider models of various sizes and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 345, + 525, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 525, + 359 + ], + "score": 1.0, + "content": "from different sources, and a wide range of tasks", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 303, + 359, + 394, + 371 + ], + "spans": [ + { + "bbox": [ + 303, + 359, + 394, + 371 + ], + "score": 1.0, + "content": "to mitigate this risk.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38.5, + "bbox_fs": [ + 303, + 237, + 527, + 371 + ] + }, + { + "type": "title", + "bbox": [ + 306, + 383, + 405, + 396 + ], + "lines": [ + { + "bbox": [ + 304, + 380, + 406, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 406, + 398 + ], + "score": 1.0, + "content": "Acknowledgements", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 305, + 405, + 524, + 457 + ], + "lines": [ + { + "bbox": [ + 304, + 405, + 526, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 526, + 417 + ], + "score": 1.0, + "content": "We thank Alisa Liu and Orevaoghene Ahia for their", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 303, + 418, + 527, + 432 + ], + "spans": [ + { + "bbox": [ + 303, + 418, + 527, + 432 + ], + "score": 1.0, + "content": "help in annotating noisy prompts. We also thank", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 432, + 525, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 525, + 444 + ], + "score": 1.0, + "content": "the reviewers for their valuable comments on the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 302, + 447, + 334, + 460 + ], + "spans": [ + { + "bbox": [ + 302, + 447, + 334, + 460 + ], + "score": 1.0, + "content": "paper.", + "type": "text" + } + ], + "index": 73 + } + ], + "index": 46.5, + "bbox_fs": [ + 302, + 405, + 527, + 460 + ] + }, + { + "type": "title", + "bbox": [ + 69, + 419, + 145, + 432 + ], + "lines": [ + { + "bbox": [ + 67, + 417, + 147, + 436 + ], + "spans": [ + { + "bbox": [ + 67, + 417, + 147, + 436 + ], + "score": 1.0, + "content": "9 Conclusion", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 48 + }, + { + "type": "text", + "bbox": [ + 70, + 448, + 290, + 622 + ], + "lines": [ + { + "bbox": [ + 69, + 447, + 290, + 460 + ], + "spans": [ + { + "bbox": [ + 69, + 447, + 290, + 460 + ], + "score": 1.0, + "content": "We investigate the phenomenon where some", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 68, + 460, + 292, + 475 + ], + "spans": [ + { + "bbox": [ + 68, + 460, + 292, + 475 + ], + "score": 1.0, + "content": "prompts perform better than others despite appear-", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 68, + 474, + 292, + 488 + ], + "spans": [ + { + "bbox": [ + 68, + 474, + 292, + 488 + ], + "score": 1.0, + "content": "ing similar to the human users of LMs. Specifically,", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 68, + 488, + 292, + 502 + ], + "spans": [ + { + "bbox": [ + 68, + 488, + 292, + 502 + ], + "score": 1.0, + "content": "we hypothesize that the perplexity of a prompt un-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 69, + 501, + 292, + 514 + ], + "spans": [ + { + "bbox": [ + 69, + 501, + 292, + 514 + ], + "score": 1.0, + "content": "der a given LM is closely tied to its task perfor-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 68, + 515, + 291, + 527 + ], + "spans": [ + { + "bbox": [ + 68, + 515, + 291, + 527 + ], + "score": 1.0, + "content": "mance. We test this theory on a large number of", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 69, + 527, + 291, + 542 + ], + "spans": [ + { + "bbox": [ + 69, + 527, + 291, + 542 + ], + "score": 1.0, + "content": "tasks and autoregressive LMs, and the resulting", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 69, + 542, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 69, + 542, + 290, + 555 + ], + "score": 1.0, + "content": "correlation study validates our hypothesis. Further", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 69, + 556, + 290, + 569 + ], + "spans": [ + { + "bbox": [ + 69, + 556, + 290, + 569 + ], + "score": 1.0, + "content": "analysis of this relationship demonstrates that the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 68, + 569, + 290, + 582 + ], + "spans": [ + { + "bbox": [ + 68, + 569, + 290, + 582 + ], + "score": 1.0, + "content": "best prompts differ across models, highlighting the", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 69, + 583, + 290, + 596 + ], + "spans": [ + { + "bbox": [ + 69, + 583, + 290, + 596 + ], + "score": 1.0, + "content": "importance of model-specific analysis, and that the", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 69, + 597, + 290, + 609 + ], + "spans": [ + { + "bbox": [ + 69, + 597, + 290, + 609 + ], + "score": 1.0, + "content": "underlying structure of the relationship between", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 68, + 610, + 278, + 622 + ], + "spans": [ + { + "bbox": [ + 68, + 610, + 278, + 622 + ], + "score": 1.0, + "content": "perplexity and performance varies across tasks.", + "type": "text" + } + ], + "index": 61 + } + ], + "index": 55, + "bbox_fs": [ + 68, + 447, + 292, + 622 + ] + }, + { + "type": "text", + "bbox": [ + 70, + 626, + 290, + 773 + ], + "lines": [ + { + "bbox": [ + 79, + 625, + 291, + 640 + ], + "spans": [ + { + "bbox": [ + 79, + 625, + 291, + 640 + ], + "score": 1.0, + "content": "In light of these findings, we then propose", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 68, + 639, + 291, + 651 + ], + "spans": [ + { + "bbox": [ + 68, + 639, + 291, + 651 + ], + "score": 1.0, + "content": "a method, SPELL, to help users find well-", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 68, + 652, + 291, + 667 + ], + "spans": [ + { + "bbox": [ + 68, + 652, + 291, + 667 + ], + "score": 1.0, + "content": "performing prompts for new tasks. Empirical", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 68, + 666, + 291, + 680 + ], + "spans": [ + { + "bbox": [ + 68, + 666, + 291, + 680 + ], + "score": 1.0, + "content": "validation of the proposed procedure shows that", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 69, + 680, + 291, + 693 + ], + "spans": [ + { + "bbox": [ + 69, + 680, + 291, + 693 + ], + "score": 1.0, + "content": "SPELL generates effective prompts with low vari-", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 69, + 693, + 291, + 707 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 291, + 707 + ], + "score": 1.0, + "content": "ability in performance, and produces small gains", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 69, + 707, + 291, + 720 + ], + "spans": [ + { + "bbox": [ + 69, + 707, + 291, + 720 + ], + "score": 1.0, + "content": "of 1.8 (2.3) accuracy points with OPT (Bloom)", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 68, + 721, + 291, + 733 + ], + "spans": [ + { + "bbox": [ + 68, + 721, + 291, + 733 + ], + "score": 1.0, + "content": "over manual prompts. 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In Proceedings of the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 79, + 401, + 291, + 415 + ], + "spans": [ + { + "bbox": [ + 79, + 401, + 291, + 415 + ], + "score": 1.0, + "content": "2017 Conference on Empirical Methods in Natural", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 79, + 413, + 236, + 426 + ], + "spans": [ + { + "bbox": [ + 79, + 413, + 236, + 426 + ], + "score": 1.0, + "content": "Language Processing, pages 274–285.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25, + "bbox_fs": [ + 69, + 369, + 291, + 426 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 433, + 290, + 488 + ], + "lines": [ + { + "bbox": [ + 69, + 432, + 291, + 445 + ], + "spans": [ + { + "bbox": [ + 69, + 432, + 291, + 445 + ], + "score": 1.0, + "content": "Susan Zhang, Stephen Roller, Naman Goyal, Mikel", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 79, + 444, + 292, + 456 + ], + "spans": [ + { + "bbox": [ + 79, + 444, + 292, + 456 + ], + "score": 1.0, + "content": "Artetxe, Moya Chen, Shuohui Chen, Christopher De-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 79, + 455, + 292, + 467 + ], + "spans": [ + { + "bbox": [ + 79, + 455, + 292, + 467 + ], + "score": 1.0, + "content": "wan, Mona Diab, Xian Li, Xi Victoria Lin, et al. 2022.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 80, + 466, + 292, + 479 + ], + "spans": [ + { + "bbox": [ + 80, + 466, + 292, + 479 + ], + "score": 1.0, + "content": "Opt: Open pre-trained transformer language models.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 79, + 478, + 218, + 488 + ], + "spans": [ + { + "bbox": [ + 79, + 478, + 218, + 488 + ], + "score": 1.0, + "content": "arXiv preprint arXiv:2205.01068.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30, + "bbox_fs": [ + 69, + 432, + 292, + 488 + ] + }, + { + "type": "text", + "bbox": [ + 69, + 497, + 290, + 530 + ], + "lines": [ + { + "bbox": [ + 68, + 497, + 292, + 508 + ], + "spans": [ + { + "bbox": [ + 68, + 497, + 292, + 508 + ], + "score": 1.0, + "content": "Xiang Zhang, Junbo Jake Zhao, and Yann LeCun. 2015.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 79, + 508, + 292, + 519 + ], + "spans": [ + { + "bbox": [ + 79, + 508, + 292, + 519 + ], + "score": 1.0, + "content": "Character-level convolutional networks for text clas-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 80, + 519, + 159, + 530 + ], + "spans": [ + { + "bbox": [ + 80, + 519, + 159, + 530 + ], + "score": 1.0, + "content": "sification. In NIPS.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34, + "bbox_fs": [ + 68, + 497, + 292, + 530 + ] + }, + { + "type": "title", + "bbox": [ + 70, + 541, + 231, + 555 + ], + "lines": [ + { + "bbox": [ + 68, + 540, + 233, + 558 + ], + "spans": [ + { + "bbox": [ + 68, + 540, + 233, + 558 + ], + "score": 1.0, + "content": "A Manually Created Prompts", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 69, + 563, + 290, + 669 + ], + "lines": [ + { + "bbox": [ + 68, + 562, + 290, + 577 + ], + "spans": [ + { + "bbox": [ + 68, + 562, + 290, + 577 + ], + "score": 1.0, + "content": "Table 11 lists the manually created prompts we use", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 69, + 577, + 290, + 590 + ], + "spans": [ + { + "bbox": [ + 69, + 577, + 290, + 590 + ], + "score": 1.0, + "content": "for the different tasks. We manually add, remove", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 69, + 591, + 290, + 603 + ], + "spans": [ + { + "bbox": [ + 69, + 591, + 290, + 603 + ], + "score": 1.0, + "content": "and edit prompts for some of these tasks, to make", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 68, + 603, + 291, + 617 + ], + "spans": [ + { + "bbox": [ + 68, + 603, + 291, + 617 + ], + "score": 1.0, + "content": "them fit for our setting. For example, the following", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 618, + 291, + 630 + ], + "spans": [ + { + "bbox": [ + 69, + 618, + 291, + 630 + ], + "score": 1.0, + "content": "prompt for AG News, taken from Promptsource,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 69, + 630, + 290, + 644 + ], + "spans": [ + { + "bbox": [ + 69, + 630, + 290, + 644 + ], + "score": 1.0, + "content": "does not fit our setting: Would you recommend the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 68, + 644, + 292, + 657 + ], + "spans": [ + { + "bbox": [ + 68, + 644, + 292, + 657 + ], + "score": 1.0, + "content": "following article to a politician, an athlete, busi-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 659, + 200, + 669 + ], + "spans": [ + { + "bbox": [ + 69, + 659, + 200, + 669 + ], + "score": 1.0, + "content": "ness executive, or a scientist?", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 40.5, + "bbox_fs": [ + 68, + 562, + 292, + 669 + ] + }, + { + "type": "title", + "bbox": [ + 70, + 680, + 229, + 694 + ], + "lines": [ + { + "bbox": [ + 67, + 678, + 230, + 697 + ], + "spans": [ + { + "bbox": [ + 67, + 678, + 230, + 697 + ], + "score": 1.0, + "content": "B Lowest Perplexity Prompts", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 45 + }, + { + "type": "text", + "bbox": [ + 69, + 703, + 289, + 729 + ], + "lines": [ + { + "bbox": [ + 68, + 701, + 290, + 717 + ], + "spans": [ + { + "bbox": [ + 68, + 701, + 290, + 717 + ], + "score": 1.0, + "content": "Table 12 lists the 5 lowest perplexity prompts for", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 68, + 716, + 195, + 730 + ], + "spans": [ + { + "bbox": [ + 68, + 716, + 195, + 730 + ], + "score": 1.0, + "content": "each task, using OPT 175B.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46.5, + "bbox_fs": [ + 68, + 701, + 290, + 730 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 164, + 60, + 433, + 762 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 164, + 60, + 433, + 762 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 164, + 60, + 433, + 762 + ], + "spans": [ + { + "bbox": [ + 164, + 60, + 433, + 762 + ], + "score": 0.969, + "html": "
Task Manual Prompts
AntonymsThe antonym of the word “good”is“ The opposite meaning of the word “good”is “ “Good”is the opposite of“ “Good”is the negation of“ The following are opposites of each other:“good"and “ The word “good"contradicts the word “ The antonym of the word good is The opposite meaning of the word good is Good is the opposite of
GLUE ColaThe following are opposites of each other: good and The word good contradicts the word Does the this sentence make sense and use correct English? Is this example grammatically correct and sensible? Does this sentence make sense and is it grammatically correct?
NewspopDoes this example use correct English? What is the article about? What is this news about? What is the topic of this news piece? What does this article discuss? What is the topic of this sentence? What category does the article belong to? Pick one category forthis news piece. Pick the category that fits the text. The article refers to which category? What topic does the article belong to? What category fits this article? What topic does this news piece belong to? Choose the correct category for this article.
AG NewsWhat label best describes this news article? What is this piece of news regarding? Which newspaper section would this article likely appear in? What topic is this news article about? This movie review expresses what sentiment? Did the reviewer find this movie good or bad?
IMDBIs this review positive or negative? How does the viewer feel about the movie? What sentiment does the writer express for the movie? What sentiment is expressed for the movie? What is the sentiment expressed in this text? Did the reviewer enjoy the movie? What is the sentiment expressed by the reviewer for the movie? How does the reviewer feel about the movie? What category does the paragraph belong to? Pick one category for the text.
DBpediaPick the category that fits the text. The text refers to which category? What category does the title belong to? What category fits this text? What topic does this text belong to? Choose the correct category for the text. What is the emotion expressed in this message?
EmotionWhat emotion does this message express? How will you feel about the message? What emotion does the writer express for the message? Is this tweet offensive? Can the tweet be removed for being offensive?
Tweet OffensiveIs the author's tweet offensive? Task: Identify if the tweetor text is offensive. Is this an offensive tweet? The translation of the word “dog"to French is“ The translation of the word dog to French is The word “dog”in French is“
Word-Level Translation“dog”(In French: “ Translate the word dog into French: The translation of dog to French is “dog”(French: “ The word dog in French is Translate the word“dog”into French: “ dog (In French: dog (French: The translation of“dog”to French is “
", + "type": "table", + "image_path": "612ece7565d834a2a16a0597f73565c3c5e8c306e876beb3cc91113f8998a7b1.jpg" + } + ] + } + ], + "index": 24.5, + "virtual_lines": [ + { + "bbox": [ + 164, + 60, + 433, + 74.03999999999999 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 164, + 74.03999999999999, + 433, + 88.07999999999998 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 164, + 88.07999999999998, + 433, + 102.11999999999998 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 164, + 102.11999999999998, + 433, + 116.15999999999997 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 164, + 116.15999999999997, + 433, + 130.19999999999996 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 164, + 130.19999999999996, + 433, + 144.23999999999995 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 164, + 144.23999999999995, + 433, + 158.27999999999994 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 164, + 158.27999999999994, + 433, + 172.31999999999994 + ], + 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Task Manual Prompts
AntonymsThe antonym of the word “good”is“ The opposite meaning of the word “good”is “ “Good”is the opposite of“ “Good”is the negation of“ The following are opposites of each other:“good"and “ The word “good"contradicts the word “ The antonym of the word good is The opposite meaning of the word good is Good is the opposite of
GLUE ColaThe following are opposites of each other: good and The word good contradicts the word Does the this sentence make sense and use correct English? Is this example grammatically correct and sensible? Does this sentence make sense and is it grammatically correct?
NewspopDoes this example use correct English? What is the article about? What is this news about? What is the topic of this news piece? What does this article discuss? What is the topic of this sentence? What category does the article belong to? Pick one category forthis news piece. Pick the category that fits the text. The article refers to which category? What topic does the article belong to? What category fits this article? What topic does this news piece belong to? Choose the correct category for this article.
AG NewsWhat label best describes this news article? What is this piece of news regarding? Which newspaper section would this article likely appear in? What topic is this news article about? This movie review expresses what sentiment? Did the reviewer find this movie good or bad?
IMDBIs this review positive or negative? How does the viewer feel about the movie? What sentiment does the writer express for the movie? What sentiment is expressed for the movie? What is the sentiment expressed in this text? Did the reviewer enjoy the movie? What is the sentiment expressed by the reviewer for the movie? How does the reviewer feel about the movie? What category does the paragraph belong to? Pick one category for the text.
DBpediaPick the category that fits the text. The text refers to which category? What category does the title belong to? What category fits this text? What topic does this text belong to? Choose the correct category for the text. What is the emotion expressed in this message?
EmotionWhat emotion does this message express? How will you feel about the message? What emotion does the writer express for the message? Is this tweet offensive? Can the tweet be removed for being offensive?
Tweet OffensiveIs the author's tweet offensive? Task: Identify if the tweetor text is offensive. Is this an offensive tweet? The translation of the word “dog"to French is“ The translation of the word dog to French is The word “dog”in French is“
Word-Level Translation“dog”(In French: “ Translate the word dog into French: The translation of dog to French is “dog”(French: “ The word dog in French is Translate the word“dog”into French: “ dog (In French: dog (French: The translation of“dog”to French is “
", + "type": "table", + "image_path": "612ece7565d834a2a16a0597f73565c3c5e8c306e876beb3cc91113f8998a7b1.jpg" + } + ] + } + ], + "index": 24.5, + "virtual_lines": [ + { + "bbox": [ + 164, + 60, + 433, + 74.03999999999999 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 164, + 74.03999999999999, + 433, + 88.07999999999998 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 164, + 88.07999999999998, + 433, + 102.11999999999998 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 164, + 102.11999999999998, + 433, + 116.15999999999997 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 164, + 116.15999999999997, + 433, + 130.19999999999996 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 164, + 130.19999999999996, + 433, + 144.23999999999995 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 164, + 144.23999999999995, + 433, + 158.27999999999994 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 164, + 158.27999999999994, + 433, + 172.31999999999994 + ], + 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TaskLowest Perplexity PromptsPerplexity
AntonymsThe following two words are antonyms:“good”and “10.24
The antonym of the word“good"is“10.32
The word that has the opposite meaning of the word “good" is “10.43
The word“good”is the antithesis of the word“10.85
The word “good” is the opposite of the word “11.15
GLUE ColaIs this an example of the proper use of the English language?11.63
Does the sentence make sense and does it follow the rules of grammar?11.76
Is this sentence an example of the correct use of the English language?12.10
Does this sentence make sense and is it grammatically correct?12.15
Is this sentence grammatically correct and does it make sense?12.68
NewspopWhat is the main subject of the article?10.01
What is the main topic of the article?10.01
What is the subject matter of the article?10.17
What is the subject of the article?10.21
What is the main idea of this article?10.21
AG NewsIn what section of the newspaper would you expect to find this article?7.51
In which section of the newspaper would you expect to find this article?7.52
In which section of the newspaper would this article be most likely to appear?7.60
In what section of the newspaper do you expect to find this article?7.80
In what section of the newspaper would this article most likely appear?7.87
IMDBWhat is the opinion of the review? Is it positive or negative?7.19
Is this a positive or negative review?7.31
What do you think of the movie?7.33
What do you think of the film?7.35
Is that a positive or a negative?7.35
DBpediaWhat is the category to which the text refers?8.99
What is the subject of the text?9.15
What category does the title belong to?9.18
Which category does the text refer to?9.19
What is the subject of this text?9.20
EmotionHow do you feel when you hear this message?12.72
What is the writer's emotional reaction to this news?13.18
What is the emotion expressed in this message?13.20
How does this message make you feel?13.32
How do you feel about this message?13.50
Tweet OffensiveIf someone said this to you, would you be offended?13.00
If someone said that to you, would you be offended?13.10
Would you be offended if someone said that to you?13.73
Would it offend you if someone said that to you?14.79
If someone told you that, would you be offended?14.93
Word-Level TranslationThe word for“dog"in French is“7.73
The French word for“dog”is“8.16
The French translation of the word“dog”is“8.24
The translation of the word “dog”in French is “8.35
The translation of the word “dog” into French is “8.91
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TaskLowest Perplexity PromptsPerplexity
AntonymsThe following two words are antonyms:“good”and “10.24
The antonym of the word“good"is“10.32
The word that has the opposite meaning of the word “good" is “10.43
The word“good”is the antithesis of the word“10.85
The word “good” is the opposite of the word “11.15
GLUE ColaIs this an example of the proper use of the English language?11.63
Does the sentence make sense and does it follow the rules of grammar?11.76
Is this sentence an example of the correct use of the English language?12.10
Does this sentence make sense and is it grammatically correct?12.15
Is this sentence grammatically correct and does it make sense?12.68
NewspopWhat is the main subject of the article?10.01
What is the main topic of the article?10.01
What is the subject matter of the article?10.17
What is the subject of the article?10.21
What is the main idea of this article?10.21
AG NewsIn what section of the newspaper would you expect to find this article?7.51
In which section of the newspaper would you expect to find this article?7.52
In which section of the newspaper would this article be most likely to appear?7.60
In what section of the newspaper do you expect to find this article?7.80
In what section of the newspaper would this article most likely appear?7.87
IMDBWhat is the opinion of the review? Is it positive or negative?7.19
Is this a positive or negative review?7.31
What do you think of the movie?7.33
What do you think of the film?7.35
Is that a positive or a negative?7.35
DBpediaWhat is the category to which the text refers?8.99
What is the subject of the text?9.15
What category does the title belong to?9.18
Which category does the text refer to?9.19
What is the subject of this text?9.20
EmotionHow do you feel when you hear this message?12.72
What is the writer's emotional reaction to this news?13.18
What is the emotion expressed in this message?13.20
How does this message make you feel?13.32
How do you feel about this message?13.50
Tweet OffensiveIf someone said this to you, would you be offended?13.00
If someone said that to you, would you be offended?13.10
Would you be offended if someone said that to you?13.73
Would it offend you if someone said that to you?14.79
If someone told you that, would you be offended?14.93
Word-Level TranslationThe word for“dog"in French is“7.73
The French word for“dog”is“8.16
The French translation of the word“dog”is“8.24
The translation of the word “dog”in French is “8.35
The translation of the word “dog” into French is “8.91
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Task# Step 0# Step 1 # Step 2
Word-Level Translation12 59118
Antonyms12 85176
GLUE Cola4 27144
Newspop13 43119
AG News4 23108
IMDB10 45178
DBpedia8 23103
Emotion4 1494
Tweet Offensive5 41119
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ModelTaskPerplexity-score corr. Pearson SpearmanPerplexity-acc corr. Pearson Spearman Avg Acc Acc 50%
OPT175BAntonyms**-0.41**-0.53
GLUE Cola-0.15-0.14-0.041 -0.021 47.71 57.1
Newspop*-0.24**-0.26 *-0.20-0.1866.472.9
AG News**-0.63 **-0.68 **-0.77**-0.8157.568.7
IMDB**0.35**0.400.14*0.2086.291.0
DBpedia **-0.50**-0.44 **-0.51**-0.4246.755.2
Emotion-0.14-0.19 **-0.30 **-0.3216.423.0
Tweet Offensive*-0.190.070.18*0.2351.355.8
Bloom 176BAntonyms**-0.37**-0.2311
GLUE Cola0.070.11**-0.25**-0.2655.565.6
Newspop**-0.50**-0.42 **-0.59 **-0.5178.987.8
AG News**-0.62 **-0.54**-0.44**-0.4450.359.4
IMDB0.040.09-0.08-0.1489.392.2
DBpedia**-0.47 *-0.27**-0.35*-0.2127.233.4
Emotion**-0.33 **-0.42**-0.48**-0.5529.331.7
Tweet Offensive0.14*0.24 *-0.20-0.0341.646.2
OPT 30B Antonyms **-0.54**-0.701111
GLUE Cola-0.050.03-0.130.0232.235.5
Newspop*-0.23 *-0.25*-0.18-0.1260.366.6
AG News**-0.66 **-0.71 **-0.81**-0.8049.360.7
IMDB-0.06*0.170.04**0.2281.686.1
DBpedia **-0.41 **-0.34*-0.21*-0.2535.942.4
Emotion0.00-0.030.180.1312.316.2
Tweet Offensive**-0.44**-0.39-0.11-0.0554.660.2
OPT 1.3BAntonyms **-0.45**-0.531
GLUE Cola **-0.39 **-0.36-0.09*-0.1960.31 65.9
Newspop**0.33*0.21-0.07-0.0737.640.3
AG News**-0.33**-0.29 **-0.56 **-0.4931.937.6
IMDB-0.11-0.07**0.24**0.2286.089.1
DBpedia-0.16-0.14-0.02-0.018.79.2
Emotion0.080.08**-0.29**-0.307.09.1
Tweet Offensive**-0.42**-0.35 **-0.50**-0.3858.662.6
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All Manually Created PromptsExamples of Similar Automatically Created Prompts
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LangOPT175BBloom 176B PearsonSpear.
PearsonSpear.
ita-0.44-0.57-0.37-0.63
spa-0.47-0.61-0.51-0.66
cat-0.47-0.58-0.24-0.31
fra-0.48-0.57-0.48-0.64
deu-0.44-0.60-0.46-0.65
fin-0.44-0.62-0.34-0.56
por-0.45-0.62-0.46-0.61
eus-0.47-0.61-0.45-0.61
tur-0.44-0.62-0.33-0.62
jpn-0.33-0.26
arb-0.36-0.47
rus1-0.54-0.69
kor-0.42-0.58
ell-0.40-0.51
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TaskLangBefore filteringAfter filtering
PearsonSpearmanPearsonSpearman
AG News--0.63-0.68-0.62-0.54
WLTita-0.44-0.58-0.44-0.57
spa-0.47-0.61-0.47-0.61
cat-0.45-0.57-0.47-0.58
fra-0.47-0.57-0.48-0.57
deu-0.43-0.60-0.44-0.60
fin-0.41-0.60-0.44-0.62
por-0.43-0.61-0.45-0.62
eus-0.45-0.60-0.47-0.61
tur-0.43-0.61-0.44-0.62
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promptppl
The following two words are antonyms:“good"and “10.24
The antonym of the word“good’is“10.32
The word that has the opposite meaning of the word “good"is “10.43
The word“good’is the antithesis of the word “10.85
The word “good"is the opposite of the word “11.15
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promptppl
Is this example correct English usage?25.79
Is this example using English correctly?25.46
Is this example correct English?25.33
Is this the example in correct English?25.00
Is English in this example correct?24.90
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OPTBloom
Tasklow-pplmanual△low-pplmanual△
GLUE Cola51.748.53.164.560.93.6
Newspop80.670.410.290.080.010.0
AG News68.461.96.551.063.5-12.5
IMDB90.488.91.491.388.82.5
DBpedia46.051.7-5.731.230.21.0
Emotion21.622.6-1.135.832.13.6
Tweet Offensive48.450.6-2.348.640.87.8
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Task Manual Prompts
AntonymsThe antonym of the word “good”is“ The opposite meaning of the word “good”is “ “Good”is the opposite of“ “Good”is the negation of“ The following are opposites of each other:“good"and “ The word “good"contradicts the word “ The antonym of the word good is The opposite meaning of the word good is Good is the opposite of
GLUE ColaThe following are opposites of each other: good and The word good contradicts the word Does the this sentence make sense and use correct English? Is this example grammatically correct and sensible? Does this sentence make sense and is it grammatically correct?
NewspopDoes this example use correct English? What is the article about? What is this news about? What is the topic of this news piece? What does this article discuss? What is the topic of this sentence? What category does the article belong to? Pick one category forthis news piece. Pick the category that fits the text. The article refers to which category? What topic does the article belong to? What category fits this article? What topic does this news piece belong to? Choose the correct category for this article.
AG NewsWhat label best describes this news article? What is this piece of news regarding? Which newspaper section would this article likely appear in? What topic is this news article about? This movie review expresses what sentiment? Did the reviewer find this movie good or bad?
IMDBIs this review positive or negative? How does the viewer feel about the movie? What sentiment does the writer express for the movie? What sentiment is expressed for the movie? What is the sentiment expressed in this text? Did the reviewer enjoy the movie? What is the sentiment expressed by the reviewer for the movie? How does the reviewer feel about the movie? What category does the paragraph belong to? Pick one category for the text.
DBpediaPick the category that fits the text. The text refers to which category? What category does the title belong to? What category fits this text? What topic does this text belong to? Choose the correct category for the text. What is the emotion expressed in this message?
EmotionWhat emotion does this message express? How will you feel about the message? What emotion does the writer express for the message? Is this tweet offensive? Can the tweet be removed for being offensive?
Tweet OffensiveIs the author's tweet offensive? Task: Identify if the tweetor text is offensive. Is this an offensive tweet? The translation of the word “dog"to French is“ The translation of the word dog to French is The word “dog”in French is“
Word-Level Translation“dog”(In French: “ Translate the word dog into French: The translation of dog to French is “dog”(French: “ The word dog in French is Translate the word“dog”into French: “ dog (In French: dog (French: The translation of“dog”to French is “
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TaskLowest Perplexity PromptsPerplexity
AntonymsThe following two words are antonyms:“good”and “10.24
The antonym of the word“good"is“10.32
The word that has the opposite meaning of the word “good" is “10.43
The word“good”is the antithesis of the word“10.85
The word “good” is the opposite of the word “11.15
GLUE ColaIs this an example of the proper use of the English language?11.63
Does the sentence make sense and does it follow the rules of grammar?11.76
Is this sentence an example of the correct use of the English language?12.10
Does this sentence make sense and is it grammatically correct?12.15
Is this sentence grammatically correct and does it make sense?12.68
NewspopWhat is the main subject of the article?10.01
What is the main topic of the article?10.01
What is the subject matter of the article?10.17
What is the subject of the article?10.21
What is the main idea of this article?10.21
AG NewsIn what section of the newspaper would you expect to find this article?7.51
In which section of the newspaper would you expect to find this article?7.52
In which section of the newspaper would this article be most likely to appear?7.60
In what section of the newspaper do you expect to find this article?7.80
In what section of the newspaper would this article most likely appear?7.87
IMDBWhat is the opinion of the review? Is it positive or negative?7.19
Is this a positive or negative review?7.31
What do you think of the movie?7.33
What do you think of the film?7.35
Is that a positive or a negative?7.35
DBpediaWhat is the category to which the text refers?8.99
What is the subject of the text?9.15
What category does the title belong to?9.18
Which category does the text refer to?9.19
What is the subject of this text?9.20
EmotionHow do you feel when you hear this message?12.72
What is the writer's emotional reaction to this news?13.18
What is the emotion expressed in this message?13.20
How does this message make you feel?13.32
How do you feel about this message?13.50
Tweet OffensiveIf someone said this to you, would you be offended?13.00
If someone said that to you, would you be offended?13.10
Would you be offended if someone said that to you?13.73
Would it offend you if someone said that to you?14.79
If someone told you that, would you be offended?14.93
Word-Level TranslationThe word for“dog"in French is“7.73
The French word for“dog”is“8.16
The French translation of the word“dog”is“8.24
The translation of the word “dog”in French is “8.35
The translation of the word “dog” into French is “8.91
" + }, + { + "category_id": 6, + "poly": [ + 410, + 1922, + 1240, + 1922, + 1240, + 1956, + 410, + 1956 + ], + "score": 0.75 + }, + { + "category_id": 15, + "poly": [ + 409.0, + 1920.0, + 1243.0, + 1920.0, + 1243.0, + 1960.0, + 409.0, + 1960.0 + ], + "score": 1.0, + "text": "" + } + ], + "page_info": { + "page_no": 12, + "width": 1654, + "height": 2339 + } + } +] \ No newline at end of file diff --git a/parse/dev/R8sQPpGCv0/R8sQPpGCv0.md b/parse/dev/R8sQPpGCv0/R8sQPpGCv0.md new file mode 100644 index 0000000000000000000000000000000000000000..5902f08f7bd6f06b53467637375a82341f403b4f --- /dev/null +++ b/parse/dev/R8sQPpGCv0/R8sQPpGCv0.md @@ -0,0 +1,411 @@ +# TRAIN SHORT, TEST LONG: ATTENTION WITH LINEAR BIASES ENABLES INPUT LENGTH EXTRAPOLATION + +Ofir Press1,2 Noah A. Smith1,3 Mike Lewis2 + +1Paul G. Allen School of Computer Science & Engineering, University of Washington +2Facebook AI Research +3Allen Institute for AI +ofirp@cs.washington.edu + +# ABSTRACT + +Since the introduction of the transformer model by Vaswani et al. (2017), a fundamental question has yet to be answered: how does a model achieve extrapolation at inference time for sequences that are longer than it saw during training? We first show that extrapolation can be enabled by simply changing the position representation method, though we find that current methods do not allow for efficient extrapolation. We therefore introduce a simpler and more efficient position method, Attention with Linear Biases (ALiBi). ALiBi does not add positional embeddings to word embeddings; instead, it biases query-key attention scores with a penalty that is proportional to their distance. We show that this method trains a 1.3 billion parameter model on input sequences of length 1024 that extrapolates to input sequences of length 2048, achieving the same perplexity as a sinusoidal position embedding model trained on inputs of length 2048 but training $11 \%$ faster and using $11 \%$ less memory. ALiBi’s inductive bias towards recency also leads it to outperform multiple strong position methods on the WikiText-103 benchmark.1 + +# 1 INTRODUCTION + +When constructing a transformer-based language model, a major design decision is the length of training sequences, denoted $L$ herein, which has to date been equivalent to the length of inference sequences. More context, achieved by larger $L$ , improves predictions at inference time. But longer sequences are more expensive to train on.2 + +Before transformers, RNN language models were trained on shorter- $L$ sequences and assumed to generalize to longer contexts at inference time (Mikolov et al., 2010; Mikolov & Zweig, 2012; Zaremba et al., 2014). Vaswani et al. (2017), introducing the transformer, speculated that it “may [...] extrapolate to sequence lengths longer than the ones encountered during training.” We define extrapolation as a model’s ability to continue performing well as the number of input tokens during validation increases beyond the number of tokens on which the the model was trained. We find that transformer language models (LMs) that use sinusoidal position embeddings have very weak extrapolation abilities; see Figure 1. + +We demonstrate that this failure to extrapolate is caused by the position embedding method. As shown in Figure 1, recent alternatives to the original sinusoidal position method (Su et al., 2021; Raffel et al., 2020) have improved extrapolation. However, the better of these, the T5 bias, is considerably slower than the sinusoidal approach and uses extra memory and parameters (Figure 2). + +We therefore introduce Attention with Linear Biases (ALiBi) to facilitate efficient extrapolation. ALiBi negatively biases attention scores with a linearly decreasing penalty proportional to the distance between the relevant key and query. Our simple approach eliminates position embeddings. + +![](images/7c2de5b2ccea4aa444e71cd10921636105b41bcb27c830339ed09ce9eab36dcd.jpg) +Figure 1: Extrapolation: as the (validation-set’s) input sequence gets longer $x$ -axis), current position methods (sinusoidal, rotary, and T5) show degraded perplexity $y$ -axis, lower is better), but our method (§3) does not. Models were trained on WikiText-103 with sequences of $L = 5 1 2$ (left) or $L = 1 { , } 0 2 4$ (right) tokens. T5 ran out of memory on our 32GB GPU. For more detail on exact perplexities and runtimes, see Tables 2 and 3 in the appendix. + +Compared to a sinusoidal model trained on the same input length, our method requires no additional runtime or parameters and incurs a negligible $( 0 - 0 . 7 \% )$ memory increase. ALiBi can be implemented by changing only a few lines of existing transformer code. + +Using ALiBi, a transformer LM can be trained on short- $L$ sequences and therefore at much lower cost, and it can still be reliably applied to long sequences at runtime. For example, a 1.3 billion parameter LM trained on $L = 1 0 2 4$ tokens with ALiBi achieves the same perplexity as a sinusoidal model trained on $L = 2 0 4 8$ when both are tested on sequences of 2048 tokens, even though our model is $11 \%$ faster and uses $11 \%$ less memory. + +Though performance peaks at around two times the number of tokens that the model was trained on, ALiBi maintains strong performance even on sequences of length 10,000. In recently explored settings where NLP training examples are given as context to an LM (Brown et al., 2020), our approach will allow exposure to more examples. Additionally, it enables generation of longer outputs. + +# 2 CURRENT APPROACHES DO NOT EXTRAPOLATE EFFICIENTLY + +We show for the first time that the sinusoidal position method, which technically should be able to extrapolate, in practice has very limited extrapolation capabilities. Though the rotary position method improves over the sinusoidal one, it still does not achieve satisfying results. Holding everything else constant, we are the first to observe that the T5 bias method leads to better extrapolation than either of these, and so we conclude that extrapolation ability depends heavily on the position embedding. Unfortunately, the T5 bias is computationally costly (Figure 2). + +# 2.1 BACKGROUND AND EXPERIMENTAL SETUP + +A transformer LM receives a list of tokens and outputs a probability distribution representing its prediction for the next token. We call the input list the current input subsequence since the inputs to language models are typically subsequences from (much longer) training or evaluation sequences. During both training and perplexity evaluation (i.e., scoring a fixed sequence), many predictions can be calculated at once; this is done using a “causal mask” that ensures each position’s prediction is influenced only by tokens to its left. Let $L$ be the length of each input subsequence during training; it includes $L$ predictions, which on average have access to $\textstyle { \frac { L + 1 } { 2 } }$ tokens of (left) context. To explore a model’s extrapolation abilities, we are interested in cases where sequences of length $L _ { \nu a l i d } > L$ are considered at evaluation time. When $L$ differs between inference and training, we use $L$ to refer to the length of subsequences during training and $L _ { \nu a l i d }$ to refer to their length at validation. + +![](images/9f29b550e905335c294f61b8464d4c694992982177b7482612f4886e33a397ed.jpg) +Figure 2: A comparison of batched training, inference speed and memory use of the sinusoidal, rotary, T5 bias, and our ALiBi position methods. The speed differences between our method and the sinusoidal are within $1 \%$ during training and $3 \%$ for inference, which is insignificant on our hardware. ALiBi uses 100MB of extra memory when training on input lengths 1024 and 3072 in this setting. Memory usage is lower in all approaches when training on 3072 tokens (compared to 1024) since we break batches into multiple updates. See Table 1 in the appendix for exact numbers. + +Nonoverlapping Inference To train on or evaluate a sequence longer than $L$ tokens, it is typical to segment the sequence into $L$ -length subsequences and train on or evaluate them independently. Unless otherwise stated, we use nonoverlapping inference to report perplexity scores. + +Extrapolation During Inference Formally, the functions that define a transformer layer are agnostic to input length;3 they map from some arbitrary, unfixed number of input vectors to the same number of output vectors. When transformers are applied to data that is inherently sequential, like text, positional information is injected into the inputs in various ways. + +Vaswani et al. (2017) discussed two options for embedding positions into vectors to be added to word embeddings: learning embeddings for specific positions and unlearned sinusoidal embeddings. They observed similar performance between these two but preferred the sinusoidal approach, which they argued might extrapolate to longer input sequences during inference. We find that this model cannot extrapolate to more than a few dozen tokens beyond $L$ . 4 + +Experiment Setup We first test the extrapolation abilities of various position methods on the WikiText-103 corpus (Merity et al., 2016) using the transformer language model of Baevski & Auli (2018). We use this model because of its prominent role in recent language modeling developments (Khandelwal et al., 2020; Press et al., 2021). The training set is about 103 million tokens from English Wikipedia (half a gigabyte). The model has 16 transformer layers of dimension 1024, with 8 heads, and a feedforward inner dimension of 4096. This model ties the word embedding and softmax matrices (Press & Wolf, 2017; Inan et al., 2017). In our experiments, other than varying the position method and training subsequence length, we modify no other hyperparameters, including the random seed and number of training epochs (205). + +# 2.2 MEASURING EXTRAPOLATION + +Sinusoidal Position Embeddings Sinusoidal position embeddings (Vaswani et al., 2017; $\ S 3 . 5 \AA$ ) are constant, non-learned vectors that are added to token embeddings on input to the first layer of the transformer. They are frequently used in transformer language modeling (Baevski & Auli, 2018; Lewis et al., 2021) and machine translation (Vaswani et al., 2017; Ott et al., 2018) models. We first consider the unmodified model of Baevski & Auli (2018), which uses sinusoidal position embeddings, and train it on $L = 5 1 2$ tokens; we then run inference with it on the validation set on $L + k$ tokens, with $k$ ranging from 0 to 15,000. Figure 1 (left) and the corresponding Table 2 (in the appendix) show that while the model improves perplexity up to $k = 2 0$ , performance stops improving and stays steady from $k = 2 0$ to $k = 5 0$ and then begins degrading. Similar results are obtained for a model trained with $L = 1 0 2 4$ tokens (Figure 1 (right) and Table 3 in the appendix). That model improves for up to $L _ { \nu a l i d } = L + 5 0$ tokens, after which performance declines. + +Rotary Position Embeddings The rotary method was introduced by Su et al. (2021) and has recently been popularized by the open source GPT-3 (Brown et al., 2020) implementation GPTJ (Wang & Komatsuzaki, 2021). Instead of adding sinusoidal embeddings at the bottom of the transformer, they multiply the keys and queries of every attention layer by sinusoidal embeddings. + +Unlike the sinusoidal or learned positional embedding approach, the rotary method injects position information into the model at every layer, not just at the initial one. In addition, it adds no position information to the values of the self-attention sublayer. The output of a self-attention sublayer is a linearly transformed, weighted sum of the input value vectors; therefore, by not inserting position information into the values, the outputs of each transformer-layer contain no explicit position information. We suspect that this segregation of position information may be beneficial for extrapolation, and we draw inspiration from it in the design of our method (§3). + +We apply the rotary position embedding method to our Baevski & Auli baseline.5 The perplexity results (Figure 1 and Appendix Tables 2 and 3) are better than the sinusoidal approach: the model with $L = 5 1 2$ $L = 1 0 2 4 )$ ) improves perplexity with up to $k = 2 0 0$ $k = 1 0 0$ ) more tokens than it saw during training, but this comes at the cost of slower training and inference (Figure 2). + +T5 Bias Though most models use trained or sinusoidal position embeddings, the T5 model of Raffel et al. (2020) uses a relative position method (Shaw et al., 2018; Huang et al., 2019) that adds no position information to word embeddings (as in the previous method). Instead, it modifies the way attention values are computed. We refer to this as the “T5 bias” method.6 To compute attention values in the unmodified transformer, we compute the dot product of every query with every relevant key and then softmax these attention values. In this method, we compute the attention values as before, but then we add a learned, shared bias to each query-key score that is dependent on just the distance between the query and key. Therefore, all query-key scores where the query and key distance are zero (i.e., the query and key represent the same token) get a specific learned bias, all scores where the query and key are one word away get a different learned bias, and so on, up to a certain point, from where multiple different distances share the same learned bias (which might be beneficial for extrapolation). As in the rotary method, the T5 bias injects position information into the model at every layer and integrates no explicit position information into the self-attention value vectors. + +Raffel et al. (2020) propose that the T5 bias may allow extrapolation, but they did not report experiments testing this. Here, we show that the T5 bias does allow language models to extrapolate. We do this by again modifying the Baevski & Auli model, this time to insert the T5 bias into it.7 + +As Figure 1 shows, the T5 bias improves perplexity with longer sequences than the ones it was trained on, i.e., $k = 6 0 0$ $k = 8 0 0$ ) extra tokens for a model trained on $L = 5 1 2$ $L = 1 0 2 4 )$ ) input tokens. Unfortunately, this impressive performance comes at a cost: training is at least twice as slow as with the sinusoidal model. Therefore, this model’s extrapolation ability provides no efficiency advantage. For example, to do inference on 1024 tokens, we could either train the sinusoidal model with $L = 1 0 2 4$ or train the T5 bias model on $L = 5 1 2$ tokens and extrapolate to 1024 for inference. However, the $L = 1 0 2 4$ sinusoidal model runs at $2 8 . 5 \mathrm { k }$ words per second (WPS), while the $L =$ 512 T5 bias model runs at $1 4 . 4 \mathrm { k }$ WPS (Appendix Table 1), so there is no speedup when training on shorter sequences with this method.8 + +![](images/8454a7f642bfe7c9c8ba601f447d89325a8b662f0a3982b8163a3c9e341f4b1d.jpg) +Figure 3: When computing attention scores for each head, our linearly biased attention method, ALiBi, adds a constant bias (right) to each attention score $( { \bf q } _ { i } \cdot { \bf k } _ { j }$ , left). As in the unmodified attention sublayer, the softmax function is then applied to these scores, and the rest of the computation is unmodified. m is a head-specific scalar that is set and not learned throughout training. We show that our method for setting $m$ values generalizes to multiple text domains, models and training compute budgets. When using ALiBi, we do not add positional embeddings at the bottom of the network. + +# 3 ATTENTION WITH LINEAR BIASES (ALIBI) + +In the transformer model of Vaswani et al. (2017), position embeddings are added to the word embeddings at the bottom of the network. For an input subsequence of length $L$ , the attention sublayer computes the attention scores for the $i$ th query $\mathbf { \bar { q } } _ { i } \in \mathbb { R } ^ { 1 \times \bar { d } }$ , $( 1 \leq i \leq L )$ in each head, given the first $i$ keys $\mathbf { K } \in \mathbb { R } ^ { i \times d }$ , where $d$ is the head dimension: + +$$ +\operatorname { s o f t m a x } ( \mathbf { q } _ { i } \mathbf { K } ^ { \top } ) +$$ + +These attention scores are then multiplied by the values to return the output of the attention sublayer.9 + +When using ALiBi, we do not add position embeddings at any point in the network. The only modification we apply is after the query-key dot product, where we add a static, non-learned bias:10 + +$$ +\mathrm { s o f t m a x } ( \mathbf { q } _ { i } \mathbf { K } ^ { \top } + m \cdot [ - ( i - 1 ) , . . . , - 2 , - 1 , 0 ] ) , +$$ + +where scalar $m$ is a head-specific slope fixed before training. Figure 3 offers a visualization. + +For our models with 8 heads, the slopes that we used are the geometric sequence: ${ \frac { 1 } { 2 ^ { 1 } } } , { \frac { 1 } { 2 ^ { 2 } } } , . . . , { \frac { 1 } { 2 ^ { 8 } } }$ . For models that require 16 heads, we interpolate those 8 slopes by geometrically averaging every consecutive pair, resulting in the geometric sequence that starts at $\frac { 1 } { \sqrt { 2 } }$ and has the ratio of $\frac { 1 } { \sqrt { 2 } }$ $\textstyle { \frac { 1 } { 2 ^ { 0 . 5 } } } , { \frac { 1 } { 2 ^ { 1 } } } , { \frac { 1 } { 2 ^ { 1 . 5 } } } , \dotsc , { \frac { 1 } { 2 ^ { 8 } } }$ . In general, for $n$ heads, our set of slopes is the geometric sequence that starts at $2 ^ { \frac { - 8 } { n } }$ and uses that same value as its ratio. + +In $\ S 4$ , we observe that this set of slopes works on a wide variety of text domains and model sizes. Therefore, we do not believe that it is necessary to tune these slope values every time a new model is trained on a new dataset. This makes our method similar to the sinusoidal approach, where the hyperparameters (the start and end of the geometric progression of wavelengths) were set once by Vaswani et al. (2017) and then reused in different models of different sizes on different datasets. + +ALiBi has an inductive bias towards recency; it penalizes attention scores between distant query-key pairs, with the penalty increasing as the distance between a key and a query grows. The different heads increase their penalties at different rates, depending on the slope magnitude. + +We initially experimented with making the slopes trainable, but this did not yield strong extrapolation results.11 A brief manual exploration of around ten slope sets led us to discover the set of slopes that we finally picked. Our main insight from this exploration is that the slope sets that work best are those with slopes in the $( 0 , 1 )$ range, with the slopes’ density increasing as we get closer to 0. We also found our method to be robust to slope choice. Even randomly sampling from the exponential distribution worked well in some cases (although that method had high variance). + +Since ALiBi is a relative position method, we add position information at every layer to the keys and queries but not to the values, as is done in the T5 bias and rotary methods. We hypothesize that these properties might be beneficial for extrapolation. + +Implementation. ALiBi is easy to implement, with all changes accomplished in a few lines of code. We implement it by modifying the mask matrix by adding the linear biases to it (in practice, when training a transformer LM, query $\mathbf { q } _ { i }$ attends only to keys 1 to $i$ ; this is implemented by adding a mask matrix to the query-key dot product before the softmax operation is applied). This means that there is no runtime penalty when using our method since we add no operations to the network. + +Compared to the sinusoidal model trained on the same input lengths, AliBi incurs a memory increase (up to 100MB in some of our experiments): in the unmodified transformer, the mask is of size $L \times L$ ; when using ALiBi, the mask is a slightly larger $n \times L \times L$ (where $n$ is the number of heads) since the linear biases added for each head uses a different slope. But, as we show, ALiBi enables training on much smaller sequences while still achieving (and occasionally surpassing) results obtained using sinusoidal embeddings on longer sequences, which saves multiple gigabytes of memory. + +# 4 RESULTS + +We first show that on WikiText103 ALiBi is efficient and enables training models with short input subsequences that outperform strong baselines even when the ALiBi models extrapolate to more than six times the number of tokens that they were trained on. We then take the same hyperparameters for our method (the set of slopes) that worked on WikiText-103 and show that – with no modification – they provide strong results on a dataset in a very different domain: books. Finally, we show that a 1.3B parameter model trained with AliBi on a much larger (461 GB) dataset with much more compute provides a superior alternative to the sinusoidal method since it achieves similar perplexity scores while running faster and using less memory (since it is trained on shorter inputs). + +While multiple alternatives to the position methods presented in Vaswani et al. (2017) have been proposed, few have been adopted in large (1B or more parameter) LMs since that setting is much more challenging than the smaller scale experiments. GPT-3 and Jurassic-1 (Lieber et al., 2021) use the learned position embedding method from Vaswani et al., and GPT-J uses the rotary method. Our results on the 1.3B parameter model show our method’s ability to generalize to larger models, dataset sizes and training durations without retuning the hyperparameter. + +# 4.1 RESULTS ON WIKITEXT-103 AND TORONTO BOOKCORPUS + +![](images/d39db463b0572a503ac269bc7ea4d3cf74b4273f25d3fc6a30263194d063c4e9.jpg) +Figure 4: ALiBi models trained and evaluated on varying sequence lengths on the WikiText-103 validation set and the sinusoidal baseline (not evaluated on longer sequences). All of our models outperform the sinusoidal ones even when trained on fewer tokens. Appendix Table 5 has exact perplexities, more ALiBi models (trained on fewer tokens), and results for rotary and T5 bias models. + +We first develop our method on the WikiText-103 corpus (Merity et al., 2016), replacing the sinusoidal position embeddings in the language model of Baevski & Auli (2018) with ALiBi. + +Figure 4 (and the corresponding Appendix Table 5) show our results for models trained with varying numbers of input subsequence tokens $( L )$ , extrapolating to longer subsequence lengths on the validation dataset. Our first observation is that, without extrapolation, for every $L$ , our models outperform those using the sinusoidal method, sometimes by a significant amount. For example, the Baevski & Auli model achieves $1 8 . 6 7 { \scriptstyle \pm 0 . 2 4 }$ (std. dev.) perplexity when trained with $L = 3 0 7 2$ input tokens, but our $L = 3 0 7 2$ model achieves 17.60 perplexity (when both models evaluate with $L _ { \nu a l i d } = 3 0 7 2$ ). + +Our second observation is that all of our models can extrapolate, and they obtain improved perplexity scores when handling more tokens than they observed during training. For example, our model trained on 512 tokens (which achieves 19.73 perplexity when evaluating subsequences of length 512 in the development set) achieves a perplexity score of 18.40 on the development set when extrapolating to subsequences of length 3072. Surprisingly, this surpasses the score that the $L =$ 3072 sinusoidal model obtains on the development set by a statistically significant margin. Note that all our models trained on $L = 5 1 2$ to $L = 2 0 4 8$ outperform the sinusoidal baseline trained on $L = 3 0 7 2$ when extrapolating to $L _ { \nu a l i d } = 3 0 7 2$ even though those models all take much less time to train since they train on shorter subsequences (Appendix Figure 8 compares training speed to perplexity for these models)! The $L \ = \ 5 1 2$ model is 1.84 times faster to train and yet still outperforms the $L = 3 0 7 2$ sinusoidal model when extrapolating to $L _ { \nu a l i d } = 3 0 7 2$ . In addition, training the $L = 3 0 7 2$ sinusoidal model requires a GPU with more than 16 GB of memory to fit the large attention matrices, which our $L = 5 1 2$ outperforms even though it can be trained on a GPU with much less memory due to much smaller attention matrices. + +Additionally, Table 5 (in the appendix) also shows that, for $L s$ of 1024 and 3072, our method performs better than the rotary and T5 bias models even when $L _ { \nu a l i d } = L$ (i.e., no extrapolation is occurring). Figure 1 (and the corresponding Appendix Tables 2 and 3) more broadly explore our method vs. the other position methods. They show that the T5 bias (the best of the baselines) improves perplexity until $L _ { \nu a l i d }$ is around $2 L$ , but on the WikiText-103 dataset our method continually improves perplexity until at least around $3 L$ , with the $L = 5 1 2$ model improving perplexity even when $L _ { \nu a l i d }$ exceeds $1 2 \mathrm { k }$ tokens. Even when unable to improve perplexity given longer sequences, ALiBi always maintains strong performance as more tokens are added. + +Appendix Table 6 shows that our results on the validation set also transfer to the test set of WikiText103. Currently, almost all models that present results on WikiText-103 use sliding window evaluation (defined in $\ S \mathbf { B } _ { \varepsilon }$ ) to compute perplexities. We apply that method to our (and to the sinusoidal, rotary and T5 bias) models in Appendix Table 7. We find that our $\mathrm { L } = 3 0 7 2$ model surpasses the performance of Transformer-XL (Dai et al., 2019), the Sandwich (Press et al., 2020), and Shortformer (Press et al., 2021) models. Our results are similar to the ones obtained with staged training (Press et al., 2021) but fall short of results obtained by Routing Transformer (Roy et al., 2020) and kNN-LM (Khandelwal et al., 2020). The methods used in those models are orthogonal to ours, and we hypothesize that combining them with ours might lead to even larger performance increases. + +After developing our method on WikiText-103, in Appendix Section A.3, we run one set of experiments on a different domain (books) using a similar model architecture and without modifying any of the ALiBi hyperparameters (the slopes) and show that our results fully transfer to this new domain. Our models are able to both surpass the sinusoidal baseline when not extrapolating while also outperforming it when extrapolating to longer sequences. + +# 4.2 RESULTS ON THE CC100+ROBERTA CORPUS + +Our final set of experiments investigates whether ALiBi transfers to a larger model trained with a larger computational budget on a larger dataset than the ones we previously used. We show that our method achieves strong results in this more challenging setting, obtaining similar performance to the sinusoidal baseline while using significantly less memory, since we train on shorter subsequences. + +The dataset we choose is a combination of the datasets used to train the RoBERTa (Liu et al., 2019) implementation of BERT (Devlin et al., 2019) and the English part of the CC-100 corpus introduced in Conneau et al. (2020), for a total of 461 GB. The RoBERTa training corpus—i.e., the Toronto Book Corpus (Zhu et al., 2015), English Wikipedia, CC-News (Nagel, 2016), OpenWebText (Gokaslan & Cohen, 2019) and Stories (Trinh & Le, 2018))—is 161 gigabytes, and the English part of the CC-100 corpus is 300 gigabytes. The validation set contains 649K tokens. + +Our models for this dataset have 25 transformer layers with 16 heads and a dimension of 2048, with an 8192 hidden dimension of the feedforward sublayers. These models have 1.3B parameters. We train our models for one epoch, which is $5 0 \mathrm { k }$ updates on 128 V100 GPUs. + +In Figure 5 (left), we compare the validation perplexity for $L _ { \nu a l i d } = 1 0 2 4$ throughout the training process for an ALiBi model trained with $L = 5 1 2$ compared to the sinusoidal model trained with $L = 1 0 2 4$ . Since our model is trained on shorter sequences, it is $7 \%$ faster and uses 1.6 GB less memory. We halt training of the sinusoidal baseline when our model reaches the end of its training (one epoch). At that time, our model is just 0.06 perplexity away from the baseline even though it was trained on sequences that are half the length of those the baseline used and requires less memory. + +![](images/62e1ddb45dd45ac9aad501c22f605e26e185a1d9f475f7db8b3e49274186cebf.jpg) +Figure 5: On the left (right), a 1.3B-parameter ALiBi model trained on 512 (1024) and evaluated on 1024 (2048) tokens during training, compared to the sinusoidal baseline trained on 1024 (2048) tokens. The ALiBi models obtain strong results even though they use $6 \% - 1 1 \%$ less memory since they train on shorter sequences. Appendix Table 11 shows memory use and end-of-training perplexities. + +In Figure 5 (right), results become even more impressive, showing that our model trained on $L =$ 1024 outperforms by 0.09 perplexity the sinusoidal model trained on $L = 2 0 4 8$ (when evaluating with $L _ { \nu a l i d } = 2 0 4 8$ ) even though our model uses 3.1 GB less memory. Our model maintains a lead in perplexity over the sinusoidal model during the entire training process. By sampling five evenly distributed points across the training process, we compute that our $L = 1 0 2 4$ model reaches a given perplexity value, on average, $11 \%$ faster than the sinusoidal model does. + +Since our models in these comparisons use much less memory, they allow for stacking more layers, which would further improve performance (with negligible, if any, runtime cost). To keep our experiments as straightforward as possible, however, we do not add layers to our models. + +Appendix Table 12 presents additional results comparing our models to the sinusoidal baseline when both are trained on the same $L$ , showing that ALiBi performs similarly to the sinusoidal baseline when not extrapolating. This contrasts with the results presented on the smaller datasets, where ALiBi consistently outperforms other position methods even when not extrapolating, suggesting that ALiBi’s inductive bias provides additional benefits for lower-resource language modeling. + +![](images/37d9ab2edddd1d80138da0ecfd8dddb54afcb0124c12608fe09965316d4b2445.jpg) +Figure 6: The ALiBi and sinusoidal models (with both $L = 5 1 2$ and 1024) trained for $5 0 \mathrm { k }$ updates (1 epoch) on the CC100+RoBERTa corpus, extrapolating on the validation set. ALiBi achieves the best results at around $2 L$ but maintains strong performance even up to 10000 tokens in these experiments. + +Figure 6 shows that our models trained on $L = 5 1 2$ and $L = 1 0 2 4$ achieve the best results when extrapolating to about double the tokens that they were trained on. Specifically, the $L = 5 1 2$ model (that obtains 9.79 perplexity when $L _ { \nu a l i d } = 5 1 2$ ) achieves its best score (9.3) when extrapolating to + +1012 tokens, and the $L = 1 0 2 4$ model (that obtains 9.16 perplexity when $L _ { \nu a l i d } = 1 0 2 4 )$ achieves its best score (8.9) when extrapolating to 2024 tokens. + +One possible explanation is that the subsequences the model observes during training are up to $L$ tokens long. When performing inference on subsequences of length $2 L$ , half of the subsequences the model consumes are as long as the examples seen during training. When inference is performed on subsequences of length $2 L + 1$ or longer, less than half of the predictions the model makes are on subsequences of lengths seen during training, and that might degrade performance. + +The sinusoidal model cannot extrapolate at all in this setting, with its performance degrading for both the $L = 5 1 2$ and 1024 models as soon as one token more than $L$ is added during evaluation. + +In Appendix B, we find that ALiBi’s edge over sinusoidal embeddings is largely explained by its improved avoidance of the early token curse. We posit that future work building on ALiBi might achieve further gains by more efficiently exploiting longer histories. + +# 5 RELATED WORK + +In parallel with our work, Wennberg & Henter (2021) introduce a relative position method that, like our method, adds a bias to attention scores that is a function of the distance between the key and query elements. Unlike our ALiBi method, which uses a non-learned linear function, their method uses a radial-basis function, with multiple trainable parameters (in our experiments, this led to a slight decrease in runtime). In addition, they present experiments on text classification, not on language modeling. They do not explore extrapolation. The Distance Aware Transformer (Wu et al., 2021) multiplies attention scores by a bias that is a function of the distance between the key and query. This function uses a different, learned parameter in every head. They show results only on text classification. In our experiments (not presented), multiplying attention scores by the bias (instead of adding, as in ALiBi) degraded performance. + +Transformer-XL (Dai et al., 2019) presented a language model that uses a cache and can attend to more tokens during inference than it was trained on (by increasing the length of the cache). However, this work presents results only where output length is limited to the $L$ (the training length), and their relative position method is very slow (Press et al., 2021). The Longformer (Beltagy et al., 2020) adapts models trained on shorter sequences to document-level tasks. However, to achieve this they had to partially train their models on longer sequences. Our ALiBi method enables extrapolation without any additional training on longer sequences. + +To our knowledge, extrapolation has not been previously explored in transformer language modeling, but it has been investigated previously and concurrently with transformers on other tasks, such as machine translation (Rosendahl et al., 2019; Neishi & Yoshinaga, 2019; Newman et al., 2020; Kiyono et al., 2021), sequence-to-sequence models trained on an artificial dataset (Hupkes et al., 2020), pretrained sequence-to-sequence models tested on arithmetic tasks (Nogueira et al., 2021, Appendix C), models trained with reinforcement learning (Lampinen et al., 2021), image, speech recognition, and machine translation models (Likhomanenko et al., 2021), and protein structure prediction (Jumper et al., 2021, Appendix 1.5). + +# 6 CONCLUSION + +We showed that the sinusoidal position embedding approach does not enable transformers to extrapolate to inputs longer than the ones they were trained on. We then established that extrapolation in transformers can be enabled by just changing the position method. We showed that our ALiBi method offers an extremely simple replacement for existing position approaches and allow models to extrapolate. In addition, when not extrapolating, our method achieves either better perplexity than the sinusoidal method (in models smaller than 1B parameters, trained on less data) or similar perplexity (in larger, billion parameter models trained on much more data). ALiBi is simple to implement and does not slow down runtime or require extra parameters (but does occasionally require a negligible amount of extra memory). Using our method, we sped up the training of a 1.3 billion parameter model evaluated on the same input sequence length as GPT-3 (2048). + +# ACKNOWLEDGMENTS + +We thank Tim Dettmers, Gabriel Ilharco, Jungo Kasai, Hao Peng, Sewon Min, Sofia Serrano, Sam Shleifer, Luke Zettlemoyer, Julian Michael, Nikolaos Pappas, Yizhong Wang, and the anonymous reviewers for their valuable feedback and fruitful discussions. + +# REFERENCES + +Alexei Baevski and Michael Auli. Adaptive input representations for neural language modeling. CoRR, abs/1809.10853, 2018. URL http://arxiv.org/abs/1809.10853. + +Iz Beltagy, Matthew E. Peters, and Arman Cohan. Longformer: The long-document transformer. arXiv:2004.05150, 2020. + +Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. 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In Proceedings of the IEEE international conference on computer vision, pp. 19–27, 2015. + +# A APPENDIX + +# A.1 INTRODUCTION + +The training speed of transformer LMs gets slower as the input subsequence length $L$ increases. +Figure 7 visualizes this. + +![](images/7eb8dd2190ae75b0f8d7168c460e942ce528e59251864b16b1ee56e6ecaa8990.jpg) + +Figure 7: Training speed of our model and the sinusoidal baseline trained on different amounts of input subsequence tokens $L$ . + +Table 1 contains the runtimes and memory use statistics for models using the various position methods discussed in this work. + +Table 1: The speed (during training and evaluation, in words per second) and memory usage (during training) of the rotary, T5 bias, and ALiBi models compared to the sinusoidal baseline on WikiText103. Training and inference are batched, and speeds are shown for one V100 GPU. + +
Position MethodTrain LengthSpeed (↑)Memory (↓)
TrainEval.
Sinusoidal51228.5k82.1k15.3 GB
102426.0k77.8k19.2 GB
307215.3k42.4k15.1 GB
Rotary51220.0k43.4k17.8 GB
102417.7k39.4k22.8 GB
307211.5k29.5k17.8 GB
T5 Bias51214.4k21.8k16.9 GB
102413.0k20.2k20.9 GB
30724.3k4.9k15.9 GB
ALiBi51228.3k85.8k15.3 GB
102425.8k76.4k19.3 GB
307215.5k42.2k15.2 GB
+ +Tables 2, 3, and 4 show the perplexity and runtime of models using the sinusoidal, rotary T5 bias, and ALiBi position methods when extrapolating to sequences longer than the ones they were trained on. The models used in these tables were trained on $L = 5 1 2$ , 1024 and 3072 tokens. + +Table 2: The sinusoidal, rotary, T5 bias and ALiBi models trained on $L = 5 1 2$ on WikiText-103 and evaluated with different values of $L _ { \nu a l i d }$ on the validation set. Bold shows the best score for each model. Inference speeds (in words per second) are from inference on a GPU with batch size of one. + +
SinusoidalRotaryT5 BiasALiBi
InputsPPL (↓)WPS (↑)PPL (↓)WPS (↑)PPL (↓)WPS (↑)PPL (↓)WPS (↑)
51220.051504620.071083919.651172419.7314726
51319.981492520.011080619.571049119.6214965
52219.931511620.021129519.57997019.6415316
53219.911535819.981085419.531038219.6115383
54219.911507619.941079519.471227019.5715301
55219.911639419.931226719.471300019.5416540
56219.911664619.871248119.391220119.4916385
57219.951693419.831266819.361285119.4616881
58220.131696119.881259419.411390419.4817064
59220.181724319.841300719.361370619.4317289
60220.401750219.811278819.331410219.3817141
61220.591763719.811260119.271457319.3817661
71224.861561419.791267619.101381819.1415637
81230.821715120.171395418.941437718.9917210
91237.421720020.731388718.861534518.8817619
101243.541630421.371375918.791424018.7316059
111250.361642422.011389118.771401418.6816659
121258.011729423.021524518.871458918.6717372
131263.621531423.931369818.841313818.6015698
141270.751566324.811392818.871285718.5915860
151276.231581225.991424818.911375218.5216225
2512132.411525431.581345620.41994818.4115204
3512178.971329335.541185022.91784718.4013329
4512209.371176739.151048525.91614618.4111738
5512240.441016843.14902029.54530918.369986
6512271.40905247.81810834.48468018.359022
7512293.02831551.12748339.29410218.338324
8512305.65725954.98671843.08366018.347366
9512336.02667257.85621148.90337018.346555
10512341.53612660.77557552.95301018.326030
11512362.74599466.62544561.38287318.325882
12512373.17542169.70498864.94260218.315287
13512382.91517473.274692OOM18.314962
14512399.98435175.524103OOM= =18.314352
15512406.01429179.253969OOM18.314289
+ +Table 3: The sinusoidal, rotary, T5 bias and ALiBi models trained on $L = { \bf 1 0 2 4 }$ on WikiText-103 and evaluated with different values of $L _ { \nu a l i d }$ on the validation set. Bold shows the best score for each model. Inference speeds (in words per second) are from inference on a GPU with batch size of one. + +
SinusoidalRotaryT5 BiasALiBi
InputsPPL (↓)WPS (↑)PPL (↓)WPS (↑)PPL (↓)WPS (↑)PPL (↓)WPS (↑)
102419.341700219.331469018.801497318.6616951
102519.331663019.341442318.821463518.6716690
103419.271658919.281435118.741443518.6016707
104419.261676019.271449118.721464418.6016667
105419.231674719.261450318.711480018.5816833
106419.211667619.221462318.701449818.5516941
107419.191687919.191446418.651467018.4916936
108419.221694219.231465018.701460718.5617090
109419.241677119.221462918.691451718.5416880
110419.281687019.271483718.691463518.5217009
111419.291679519.271487918.691454018.5217050
112419.261731219.181512118.621448018.4617571
122420.541790119.381558418.581495618.4018013
132423.131630819.961438618.521372618.3316422
142426.451621721.271438518.481351618.2816121
152429.821637722.591469318.421358718.2216659
162434.271592824.341422818.401297918.1716053
172438.241664025.661468618.351297618.1516607
182442.231684027.631491818.301307118.0816846
192446.461507129.641345218.311184318.0815118
202451.091559131.171370618.341190618.0515557
302496.461363935.671225618.62848017.9213668
4024144.001244144.301120319.44744317.9512402
5024182.311143148.311032420.47638417.9211394
6024214.021023854.78911721.76557718.0110119
7024261.86878562.83795023.64486717.938779
8024284.88813264.91735525.79437717.968086
9024310.04704571.91638027.54378717.987001
10024337.48663377.70601629.54358217.976583
11024358.43572281.15521931.94317018.025641
12024375.95556087.51507233.35294018.015294
13024393.57469194.744383OOM17.984621
14024403.52490596.104546OOM-18.014827
15024431.66451899.784170OOM=17.964447
16024453.324239106.993878OOM17.984153
+ +Table 4: The sinusoidal, rotary, T5 bias and ALiBi models trained on $L = 3 0 7 2$ on WikiText-103 and evaluated with different values of $L _ { \nu a l i d }$ on the validation set. Bold shows the best score for each model. Inference speeds (in words per second) are from inference on a GPU with batch size of one. + +
InputsSinusoidalRotaryT5BiasALiBi
PPL (↓)WPS (↑)PPL (↓)WPS (↑)PPL (↓)WPS (↑)PPL (↓)WPS (↑)
307218.671338018.571254818.01882817.6013866
307318.671377318.571247418.01848317.5913793
308218.621374118.541238817.95869817.5913778
309218.601374218.481245817.92836117.5513783
310218.651370118.521236517.94876417.5913747
311218.641380918.511244917.96866517.5913827
312218.681372218.521243217.98843717.5813795
313218.671382518.541249017.97865317.5813784
314218.691354318.521223017.97828217.6113572
315218.661352018.561224017.98860817.5913523
316218.711350118.561225318.04858917.6213598
317218.721356318.551229717.99858317.5913625
327218.871345318.551214817.93814417.5913482
337219.461353318.501225417.88844217.5213565
347220.551304718.521186817.95785717.5413107
357221.841312818.501188217.86781417.5013170
367223.041310618.491185917.87771917.4813196
377224.471328718.541194217.85757917.4913312
387225.851262118.401127217.82758117.4112566
397227.211237918.481115117.84748317.4112324
407228.591217818.591101917.88697417.4812212
507245.531107618.80988717.76623017.3310938
607265.011011419.50904917.68555417.2610133
707285.96864720.60786117.83482017.228670
8072102.74775521.60699118.06428117.307729
9072125.99695322.14636018.12382317.266939
10072133.68664623.21606818.37357917.286597
11072161.29566324.39515818.64311917.265585
12072169.55556726.70511118.93292017.245397
13072189.43504429.33465819.10273517.154809
14072203.86491532.214616OOM17.224866
15072221.14456133.474292OOM- =17.234491
16072231.29438234.514099OOM=17.224312
+ +# A.2 ALIBI RESULTS ON WIKITEXT-103 + +![](images/03e1e3f377a9207d455228489bc857a42f02c2d3588934f12ec12ce2fcb9d8a3.jpg) +Figure 8: The training speed and validation perplexity (with $L _ { \nu a l i d } = 3 0 7 2 )$ for ALiBi models and the sinusoidal model trained with $L = 3 0 7 2$ . All our models trained on 512 or more tokens achieve better perplexity than the sinusoidal model even though all of them (except the $L = 3 0 7 2$ ) require less time and memory to train. + +Figure 8 depicts a cross section of Figure 4, showing our models with different train lengths and the sinusoidal baseline, all evaluated on $L _ { \nu a l i d } = 3 0 7 2$ tokens. We observe that all our models with $5 1 2 \leq L < 3 0 7 2$ are faster to train than the sinusoidal model with $L = 3 0 7 2$ , but they all achieve greater perplexity scores on the validation set. Our model with $L = 3 0 7 2$ trains just as fast as the sinusoidal one but bests its score by more than one perplexity point; (the standard deviation for the the sinusoidal model with $L = 3 0 7 2$ is 0.24). + +Table 5 shows the perplexity values obtained when 8 different ALiBi models, trained on $L$ values between 64 and 3072, extrapolating to $L _ { \nu a l i d }$ values longer than the ones they were trained on. In addition, we present results for the sinusoidal, rotary and T5 bias models, with $L _ { \nu a l i d } = L$ . + +Table 5: Perplexity when ALiBi extrapolates on the WikiText-103 development set. ∗For results we present for the sinusoidal, rotary and T5 bias models, $L = L _ { v a l i d }$ (so we do not test the extrapolation abilities of those baselines here). + +
ALiBiEvaluation Length
Train Length641282565121024153620483072
6428.4624.7022.8822.0921.7321.6321.5921.53
128123.9821.7020.6720.3620.2920.3120.28
2561121.2919.8919.2919.1319.1019.03
512--19.7318.8118.5018.4818.40
1024=-18.6618.2018.0517.96
1536===18.1217.9017.72
2048===17.9117.64
30721====-117.60
Sinusoidal*28.0323.8121.4520.0519.3419.0518.8718.67
Rotary*11-20.0719.331118.57
T5 Bias*==119.6518.801=18.01
+ +Table 6 compares ALiBi to the sinusoidal, rotary and T5 bias baselines on the test set of WikiText103, and Table 7 compares ALiBi to the current state of the art models on that test set. + +Table 6: Test perplexity and runtime on WikiText-103 for two of our ALiBi models and models that use the sinusoidal, rotary and T5 bias methods. + +
ModelParam.↓TrainInference
Speed↑Speed ↑Valid ↓Test↓
Sinusoidal, L = 3072247M15.3k13.6k18.6719.38
Rotary,L = 3072247M11.5k12.2k18.5719.28
T5 Bias,L = 3072247M4.3k7.3k18.0118.73
L = 512,Lvalid = 3072247M28.3k13.6k18.4019.08
A L=3072,Lvalid =3072247M15.5k13.6k17.6018.30
+ +Table 7: Valid and test perplexity scores on WikiText-103 for two of our ALiBi models and models that use the sinusoidal, rotary and T5 bias methods with sliding window evaluation ( $\mathrm { \ S B }$ and $\scriptstyle \mathbf { S } = 5 1 2$ following (Baevski & Auli, 2018; Khandelwal et al., 2020; Press et al., 2021)). The sinusoidal model presents our results from training and inference with the model of Baevski & Auli. + +
ModelParam.↓Valid↓Test↓
Adaptive Inputs (Baevski & Auli, 2018)247M17.9718.70
Transformer-XL (Dai et al., 2019)257M118.3
Shortformer (Press et al.,2021)247M17.4718.15
Sandwich Transformer (Press et al., 2020)247M117.96
Staged Training (Press et al.,2021)247M17.56
Compressive Transformer (Rae et al., 2020)329M17.1
Routing Transformer (Roy et al., 2020)=15.8
kNN-LM (Khandelwal et al., 2020)247M15.8115.79
Sinusoidal, L = 3072247M17.9518.67
Rotary,L = 3072247M17.9818.72
T5 Bias,L = 3072247M17.3718.12
L = 512,Lyalid = 3072247M18.3019.01
L = 3072,Lvalid = 3072247M16.9717.66
+ +# A.3 RESULTS ON THE TORONTO BOOK CORPUS + +To ensure that our results are not specific to the WikiText-103 corpus, we next apply our model and the baselines to a different domain while using a similar model architecture and the same ALiBi slopes as those used in the previous subsection. + +We emphasize that our set of slopes was chosen by running experiments on the WikiText-103 corpus, and here we apply that set of slopes to a model trained on a very different text domain. Throughout the entire process of developing this method, we ran only one set of experiments on this domain using the previously selected set of slopes. + +Specifically, we use the Toronto BooksCorpus (Zhu et al., 2015), which has been used to train BERT (Devlin et al., 2019) (in conjuction with the English Wikipedia). The corpus is about 700M tokens (2.9 GB). + +We use the same train/validation/test split as Khandelwal et al. (2020) and their tokenization, which uses BERT’s vocabulary of 29K byte-pair encodings. Since the vocabulary is much smaller than WikiText-103’s, we replace the adaptive word embedding and softmax of Baevski & Auli (2018) with a tied word embedding and softmax matrix (Press & Wolf, 2017; Inan et al., 2017). + +Our results in Figure 9 (and Table 8) replicate our success on the WikiText-103 dataset. Our model surpasses the sinusoidal baseline when trained on the same amount of input tokens $( L )$ and, in addition, our model is able to extrapolate to longer sequences at inference. This occurs even though our set of slopes was not tuned on this dataset. This result establishes the generality of ALiBi and the particular set of slopes we found and suggests that they may be used on different text domains without further hyperparameter tuning. + +![](images/5d2b57b38065977c1ee49f4412f8f13fc2f5d4c03b7b10ce48b0b3cb02da17e1.jpg) +Figure 9: ALiBi-enabled models evaluated on different input lengths on the Toronto BookCorpus. Our models extrapolate to longer sequence lengths and outperform the sinusoidal baseline even when trained on much shorter sequences. + +Tables 9 and 10 present the perplexities for our ALiBi models, the baselines, and the current state of the art on the Toronto BookCorpus validation and test sets. Our results here mirror our results on WikiText-103: we improve over the sinusoidal baseline even when AliBi is trained on fewer tokens. + +Table 8: ALiBi models extrapolating on the Toronto BookCorpus development set. ∗For the results of the sinusoidal models, $L = L _ { \nu a l i d }$ (so we do not test the extrapolation abilities of those models here). + +Table 9: Validation and test perplexities on the Toronto Book Corpus dataset. + +
Train Length 512Evaluation Length 1024 3072
51214.2913.6413.55
1024113.8613.52
30721113.15
Sinusoidal*14.8014.7314.46
+ +
ModelParam.↓Valid ↓Test↓
Sinusoidal,L = 3072247M14.4611.67
B Ltrain =512,Lvalid =3072247M13.5510.98
A Ltrain =3072,Lvalid=3072247M13.1510.73
+ +# A.4 RESULTS ON THE CC $^ { 1 0 0 + }$ ROBERTA CORPUS + +Table 11 compares our 1.3 billion parameter ALiBi models when extrapolating to two times the number of tokens that they were trained on. We use the sinusoidal model as our baseline, and train it for the same amount of time as we train the ALiBi model that we compare it to (and so since our ALiBi models run faster in this setting, the sinusoidal models complete less updates). + +Table 10: Validation and test perplexities on the Toronto Book Corpus dataset with a sliding window $( \ S \mathbf { B } )$ . Following (Baevski & Auli, 2018; Khandelwal et al., 2020; Press et al., 2020; 2021), we set the sliding window stride $S { = } 5 1 2$ . + +
ModelParam.↓Valid ↓Test↓
kNN-LM (Khandelwal et al., 2020)247M14.2010.89
Shortformer (Press et al.,2021)247M13.4010.88
Sandwich (Press et al., 2020)247M=10.83
Staged Training (Press et al., 2021)247M12.8010.48
Sinusoidal,L = 3072247M14.0611.40
L =512,Lyalid = 3072247M13.7611.11
L= 3072,Lalid = 3072247M12.7010.40
+ +Table 11: Perplexity, memory, and train time on the $\mathrm { C C 1 0 0 + }$ RoBERTa corpus for our ALiBi models and the sinusoidal baseline. We run our $L = 5 1 2$ (1024) model and the sinusoidal model with $L =$ 1024 (2048) for the same amount of time. We show that our models achieve strong results even though they use $6 { - } 1 1 \%$ less memory. + +
TrainingValid PPL↓
Memory↓UpdatesHours↓Lvalid = 1024Lvalid = 2048
Sinusoidal, Ltrain = 102426.2 GB46.7k5.5k9.241
ALiBi, Ltrain = 51224.6 GB50.0k5.5k9.301
Sinusoidal, Ltrain = 204829.3 GB44.2k5.9k19.01
ALiBi,Ltrain = 102426.2 GB50.0k5.9k8.92
+ +Table 12 compares our 1.3 billion parameter ALiBi models to the sinusoidal baselines, with and without extrapolation, with all models completing 50,000 updates. + +Table 12: Perplexity, train time and memory use of the sinusoidal and ALiBi models on the CC100+RoBERTa corpus when all models are trained with $5 0 \mathrm { k }$ updates. + +
TrainingValid PPL ↓
Memory↓UpdatesHours←Lvalid =512 Lvalid =1024 Lvalid=2048
Sinusoidal, Ltrain = 512 ALiBi,Ltrain = 51224.6 GB50.0k5.5k9.7137.05105.42
24.6 GB50.0k5.5k9.799.309.54
Sinusoidal, Ltrain = 1024 ALiBi,Ltrain = 102426.2 GB50.0k5.9k19.1548.85
26.2 GB50.0k5.9k=9.168.92
Sinusoidal, Ltrain = 2048 ALiBi,Ltrain = 204829.3 GB50.0k6.7k-8.83
29.4 GB50.0k6.7k18.84
+ +# B ANALYSIS + +In this section we investigate why ALiBi works so effectively. We find that ALiBi’s decrease in perplexity when given longer sequences is largely explained by its improved avoidance of the early token curse. We hypothesize that future work building on ALiBi might achieve further gains by more efficiently exploiting longer histories. + +![](images/d4ac4d21ebb896e9182b2f88806590481ddff892b612e79f3a70592e627367b3.jpg) +Figure 10: Sliding window evaluation (top; blue) compared to nonoverlapping evaluation (bottom; red) on a sequence of 8 words using a model with $L _ { \nu a l i d } = 4$ . Nonoverlapping evaluation is much faster since it requires just two inference passes (as opposed to the five passes required by the siding window approach). But the sliding window approach provides more context for each prediction. + +Sliding Window Inference As mentioned in Section 2, nonoverlapping inference is commonly used to evaluate sequences longer than $L$ (the number of tokens in each training subsequence). An alternative is to use a sliding window during evaluation (Baevski & Auli, 2018). + +A stride $S$ is picked between 1 and $L - 1$ , and the window is advanced by $S$ tokens after each forward pass.12 This means that $L - S$ tokens from the previous subsequence are re-encoded, and only $S$ new tokens are output. The advantage is that all outputs in each subsequence after the first have at least $L - S$ previous tokens to condition on. However, since tokens must be re-encoded multiple times, this approach is much slower than the nonoverlapping one. When $S = 1$ , we output one token every inference pass, each using the maximal context window that the model can handle; however, this is the slowest approach. Figure 10 is a visualization of the nonoverlapping and sliding window evaluation approaches. + +We use sliding window inference as a tool to analyze our models, but we note that it is normally prohibitively slow in practice (Press et al., 2021). + +Early Token Curse Splitting an evaluation set into subsequences means that predictions occuring early in each subsequence cannot access many previous context tokens (appearing at the end of the previous subsequence). The result, referred to as the early token curse (Press et al., 2021), increases (i.e., degrades) perplexity scores. A workaround is to evaluate the model using a sliding window, giving each prediction more context. This solution is slow since it requires many more forward passes of the model. + +# B.2 EXTRAPOLATION REDUCES THE EARLY TOKEN CURSE + +We presented results showing that our ALiBi method (and, to a lesser extent, the T5 bias) allows LMs to extrapolate during inference. Two reasons could explain why these methods enable LMs to achieve better perplexity given longer input subsequences: + +1. Performance improves because the models can use longer contexts to make more accurate predictions. For example, the average article length in the WikiText-103 corpus is about 3600 tokens; therefore, if a model trained on $L \ = \ 5 1 2$ tokens extrapolates to $L _ { \nu a l i d } =$ 3072 tokens during inference and achieves better results, that might be because it can spot patterns occurring across more than 512 tokens. 2. Performance improves because longer input sequences mean the early token curse is reduced. For example, during nonoverlapping evaluation on sequences of length $L _ { \nu a l i d } =$ 1000, $10 \%$ of predictions have 100 tokens of context or less. If we rerun nonoverlapping evaluation on that model with $L _ { \nu a l i d } = 2 0 0 0$ tokens, now only $5 \%$ of predictions have 100 tokens of context or less. So, by simply being able to handle longer sequences, a model can substantially reduce the early token curse and improve performance.13 + +To better understand what might be occurring, we re-evaluate the development set of WikiText-103 with our models and the sinusoidal baseline with $L = 5 1 2$ , 1024, 3072. However, this time we use sliding window evaluation with a stride of $S = 1$ , meaning that we move the sliding window just one token after every inference pass, giving each prediction the maximum number of context tokens that the model can use. + +![](images/5f91f6bdf10f91e9df60fe8a82792a8da3426e81d9d9493ba58fb5c39b32bcae.jpg) +Figure 11: ALiBi models evaluated on different input lengths on WikiText-103 with sliding window evaluation (with stride $S = 1 { \dot { } }$ ). Unlike results shown in Figure 4, where performance improves in each of our models as we increase the validation sequence length, here performance stays relatively flat as we increase $L _ { \nu a l i d }$ . This might mean that ALiBi increases performance when $L _ { \nu a l i d } > L$ not because it uses longer contexts, but because fewer tokens suffer from the early token curse. Note that as in $\ S 2$ , the perplexity of the sinusoidal model explodes when $L _ { \nu a l i d } > L$ even when using sliding window evaluation. + +The results are shown in Figure 11 and in the corresponding Tables 13 (sinusoidal) and 15 (ALiBi). + +Unsurprisingly, for the sinusoidal model, as in $\ S 2$ , increasing $L _ { \nu a l i d }$ causes an explosion in perplexity even when using sliding window evaluation. Our ALiBi models cannot improve perplexity when looking at longer sequences in this setting, but they keep perplexity flat when $L _ { \nu a l i d }$ increases. + +This leads us to believe that our perplexity improvement when increasing $L _ { \nu a l i d }$ and using nonoverlapping evaluation is caused by explanation 2, not explanation 1. Because sliding window evaluation provides long context windows for every prediction made, it curtails the early token curse. In this setting, ALiBi’s performance remains flat when $L _ { \nu a l i d }$ increases, leading us to hypothesize that the gains seen while increasing $L _ { \nu a l i d }$ in $\ S 4$ were the result of larger $L _ { \nu a l i d }$ values mitigating the early token curse. + +Our ALiBi results mirror what occurs in the model using the T5 bias: when using sliding window evaluation, perplexity remains relatively flat when evaluating longer sequences (see Table 14). + +Our analysis reveals that when $L _ { \nu a l i d } > L$ , ALiBi might not be using contexts longer than the ones it was trained on. This highlights a research direction that could be pursued in future work. + +These findings do not lessen the value of ALiBi. When $L _ { \nu a l i d } = L$ , ALiBi achieves either superior or similar results to the sinusoidal method and other alternatives even though it is simpler and requires no learned parameters. When evaluating $L _ { \nu a l i d } > L$ tokens, even if ALiBi does not attend to more than $L$ tokens, it yields better results than the other alternatives that can be used in this case, i.e., standard nonoverlapping inference (which is cheap, but does not perform as well) and the more accurate sliding window approach (which is very slow). + +Table 13: Perplexities of the sinusoidal models evaluated with sliding window evaluation with stride $S = 1$ on the WikiText-103 validation dataset. + +
Evaluation Length (S = 1)3072
Train Length512102415362048
51218.35204.42264.74306.19360.12
1024118.05206.55302.6393.71
3072-11118.03
+ +Table 14: Perplexities of the T5 bias models evaluated with sliding window evaluation with stride $S = 1$ on the WikiText-103 validation dataset. + +
Evaluation Length (S = 1)
Train Length5121024153620483072
51217.9218.5120.3622.6230.77
1024117.6517.8718.5120.66
3072111117.41
+ +Table 15: Perplexities of the ALiBi models evaluated with sliding window evaluation with stride $S = 1$ on the WikiText-103 validation dataset. + +
Evaluation Length (S = 1)
Train Length5121024153620483072
51217.9817.9218.218.2818.3
1024117.4617.4717.6217.92
3072111116.96
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1: procedure SA({0i},i=1..n,n ≥ 2)Goal:minimize the barrier between n solutions
2:Ti= πo,∀i=1..n
3:for k=O; k <kmax; k++ do
4:T←temperature( k+1
5:Pick random candidate permutations {πi},∀i= 1..n
6:if亚(P(0i,πi))<亚(P(0i,πi)) then亚:barrier objective function
7:Ti←
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Hyper-parametersMLPShallow CNNVGGResNet
Learning RateFixed 0.011, Fixed 0.001²Cosine 0.02Cosine 0.02Cosine 0.02
Batch Size64256256256
Epochs3000100010001000
Momentum0.90.90.90.9
Weight Decay1-=
Data AugmentationNormalizationNormalizationNormalizationNormalization
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width=16width=32width=64
stepsbarrier△barrierstepsbarrier△barrierstepsbarrier△barrier
100.470=100.430-100.2711
1000.3311.42×11000.3021.43×1000.2021.35×
1K0.1901.73×1K0.1751.71×1K0.1211.41×
10K0.1051.80×10K0.9951.75×10K0.0851.71×
50K0.0551.90×50K0.0551.80×50K0.0481.77×
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// Simulated Annealing from simanneal import Annealer def barrier_SA(arch，model，sd1，sd2，w2，init_state，tmax，tmin，steps，train_inputs,
deftrain_targets，train_avg_org_models，nchannels，nclasses，nunits):
class BarrierCalculationProblem(Annealer): """anealer with a travelling salesman problem. 11 11 11
__init__(self，state): super(BarrierCalculationProblem，self).__init__(state）# important!
def move(self):
"""Swaps two cities in the route."""
initial_energy = self.energy()
for j in range(5):
fori in range(len(self.state[j])): X = self.state[j][i] a = random.randint(O，len(x)- 1)
b = random.randint(o，len(x)- 1)
self.state[j][i][a]，self.state[j][i][b]=self.state[j][i][b],
self.state[j][i][a]
return self.energy()- initial_energy
def energy(self):
"""Calculates the cost for proposed permutation.""
permuted_models = []
for i in range(5):
permuted_models.append(permute(arch，model，self.state[i]，sd2[i]，w2[i],
nchannels，nclasses,nunits))
#### form one model which is the average of 5 permuted models
permuted_avg = copy.deepcopy(model)
new_params = OrderedDict()
for key in sd2[O].keys():
param = 0
fori in range(len(permuted_models)):
param = param + permuted_models[i][key]
new_params[key]= param /len(permuted_models)
permuted_avg.load_state_dict(new_params)
eval_train = evaluate_model(permuted_avg，train_inputs，train_targets)['top1'
cost = 1 - eval_train
return cost
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index 0000000000000000000000000000000000000000..43e85038f767141f897e845c0342cb71c753574b --- /dev/null +++ b/parse/dev/ePZsWeGJXyp/ePZsWeGJXyp.md @@ -0,0 +1,194 @@ +# VICRegL: Self-Supervised Learning of Local Visual Features + +Adrien Bardes1,2 + +Jean Ponce2,4 + +Yann LeCun1,3,4 + +1Meta, FAIR +2Inria, École normale supérieure, CNRS, PSL Research University +3Courant Institute, New York University +4Center for Data Science, New York University + +# Abstract + +Most recent self-supervised methods for learning image representations focus on either producing a global feature with invariance properties, or producing a set of local features. The former works best for classification tasks while the latter is best for detection and segmentation tasks. This paper explores the fundamental tradeoff between learning local and global features. A new method called VICRegL is proposed that learns good global and local features simultaneously, yielding excellent performance on detection and segmentation tasks while maintaining good performance on classification tasks. Concretely, two identical branches of a standard convolutional net architecture are fed two differently distorted versions of the same image. The VICReg criterion is applied to pairs of global feature vectors. Simultaneously, the VICReg criterion is applied to pairs of local feature vectors occurring before the last pooling layer. Two local feature vectors are attracted to each other if their $l ^ { 2 }$ -distance is below a threshold or if their relative locations are consistent with a known geometric transformation between the two input images. We demonstrate strong performance on linear classification and segmentation transfer tasks. Code and pretrained models are publicly available at: https://github.com/facebookresearch/VICRegL + +# 1 Introduction + +Recent advances in self-supervised learning for computer vision have been largely driven by downstream proxy tasks such as image categorization, with convolutional backbones [Chen et al., 2020a,b, Grill et al., 2020, Lee et al., 2021, Caron et al., 2020, Zbontar et al., 2021, Bardes et al., 2022, Tomasev et al., 2022], or vision transformers [Caron et al., 2021, Chen et al., 2021, Li et al., 2022, Zhou et al., 2022a]. Current approaches rely on a joint embedding architecture and a loss function that forces the learned features to be invariant to a sampling process selecting pairs of different views of the same image, obtained by transformation such as cropping, rescaling, or color jittering [Misra and Maaten, 2020, Chen et al., 2020a, He et al., 2020, Grill et al., 2020]. These methods learn to eliminate the irrelevant part of position and color information, in order to satisfy the invariance criterion, and perform well on image classification benchmarks. Some recent approaches go beyond learning global features: to tackle tasks such as semantic segmentation where spatial information plays a key role, [Yang et al., 2021, Xie et al., 2021, Hénaff et al., 2021, Yang et al., 2022, Hénaff et al., 2022, El-Nouby et al., 2022] also learn image models with more emphasis on local image structure. In the end most recent approaches to self-supervised learning of visual features learn the corresponding image model using either a (possibly quite sophisticated) global criterion, or a (necessarily) different one exploiting local image characteristics and spatial information. The best performing local methods require a non-parametric pre-processing step that compute unsupervised segmentation masks [Hénaff et al., 2021], which can be done online [Hénaff et al., 2022], but with an additional computational burden. + +We argue that more complex reasoning systems should be structured in a hierarchical way, by learning at several scales. To this end, we propose VICRegL, a method that learn features at a global scale, and that additionally uses spatial information, and matches feature vectors that are either pooled from close-by regions in the original input image, or close in the embedding space, therefore learning features at a local scale. In practice, the global VICReg criterion [Bardes et al., 2022] is applied to pairs of feature vectors, before and after the final pooling layer of a convolutional network, thus learning local and global features at the same time. When a segmentation mask is available as in [Hénaff et al., 2021], feature vectors that correspond to the same region in the mask can be pooled together, and compared using a contrastive loss function, which allows spatial vectors far away in the original image to be pooled together if they belong to the same object. In our case, segmentation masks are not available, and we therefore face two challenges: (1) there is no a priori information on how to pool vectors from the same object together, thus long-range matching should be learned in a self-supervised manner, and (2) contrasting negatively feature vectors corresponding to far away locations can have a negative effect, as these vectors could have been pooled from locations that represent the same object in the image. In order to address these issues, VICRegL (1) matches feature vectors according to a $l ^ { 2 }$ nearest-neighbor criterion exploiting both the distances between features and image locations, properly weighted, and (2) uses the VICReg criterion between matched feature vectors. We use VICReg for its simplicity and its non-contrastive nature, which alleviates the need for negative samples and therefore does not have an explicit negative contrasting effect between feature vectors that could have been potential matches. + +We demonstrate the effectiveness of VICRegL by evaluating the learned representations on vision tasks such as image classification on ImageNet and semantic segmentation on various datasets. Our evaluation is (mostly) done in the setting where the backbone learned by VICRegL is frozen, with only a linear classification or segmentation head tuned to the task at hand. We believe that this setting is a much better evaluation metric than the commonly used fine-tuning benchmarks, as the performance can not be attributed to the use of a complex head, or to the availability of the ground truth masks. Our results show that learning local features, in addition to global features, does not hurt the classification performance, but significantly improves segmentation accuracy. On the Pascal VOC linear frozen semantic segmentation task, VICRegL achieves 55.9 mIoU with a ResNet-50 backbone, which is a ${ \bf + 8 . 1 }$ mIoU improvement over VICReg, and 67.5 mIoU with a ConvNeXt-S backbone, which is a $+ 6 . 6$ mIoU improvement. + +# 2 Related work + +Global features. Most recent methods for global feature learning are based on a joint embedding architecture that learns representations that are invariant to various views. These methods differ in the way collapsing solutions are avoided. Contrastive methods [Hjelm et al., 2019, Chen et al., 2020a, He et al., 2020, Chen et al., 2020b, Mitrovic et al., 2021, Dwibedi et al., 2021, Chen et al., 2021, Tomasev et al., 2022] uses negative samples to push dissimilar samples apart from each other. Clustering methods [Caron et al., 2018, 2020, 2021] ensure a balanced partition of the samples within a set of clusters. Non-contrastive methods, which are dual to contrastive ones [Garrido et al., 2022], rely on maintaining the informational content of the representations by either explicit regularization [Zbontar et al., 2021, Bardes et al., 2022] or architectural design [Chen and He, 2020, Grill et al., 2020, Richemond et al., 2020, Lee et al., 2021]. Finally, the best performing methods today are based on vision transformers [Caron et al., 2021, Chen et al., 2021, Li et al., 2022, Zhou et al., 2022a,b] and deliver strong results in both downstream classification and segmentation tasks. + +Local features. In opposition to global methods, local one focus on explicitly learning a set of local features that describe small parts of the image, which global methods do implicitly [Chen et al., 2022], and are therefore better suited for segmentation tasks. Indeed these methods commonly only evaluate on segmentation benchmarks. A contrastive loss function can be applied directly: (1) at the pixel level [Xie et al., 2021], which forces consistency between pixels at similar locations; (2) at the feature map level [Wang et al., 2021], which forces consistency between groups of pixels: (3) at the image region level [Xiao et al., 2021], which forces consistency between large regions that overlap in different views of an image. Similar to [Wang et al., 2021], our method VICRegL operates at the feature map level but with a more advanced matching criterion that takes into account the distance in pixel space between the objects. Copy pasting a patch on a random background [Yang et al., 2021, Wang et al., 2022] has also shown to be effective for learning to localize an object without relying on spurious correlations with the background. Aggregating multiple images corresponding to several object instances into a single image can also help the localization task [Yang et al., 2022]. These approaches rely on carefully and handcrafted constructions of new images with modified background or with aggregation of semantic content from several other images, which is not satisfactory, while our method simply rely on the classical augmentations commonly used in self-supervised learning. The best current approaches consist in using the information from unsupervised segmentation masks, which can be computed as a pre-processing step [Hénaff et al., 2021] or computed online [Hénaff et al., 2022]. The feature vectors coming from the same region in the mask are pooled together and the resulting vectors are contrasted between each other with a contrastive loss function. These approaches explicitly construct semantic segmentation masks using k-means for every input image, which is computationally not efficient, and is a strong inductive bias in the architecture. Our method does not rely on these masks and therefore learns less specialized features. + +# 3 Method + +Background. VICReg was introduced as a self-supervised method for learning image representations that avoid the collapse problem by design. Its loss function is composed of three terms: a variance term, that preserves the variance of the embeddings, and consists in a hinge loss function on the standard deviation, on each component of the vectors individually and along the batch dimension; an invariance term, which is simply an $l ^ { 2 }$ distance between the embeddings from the two branches of a siamese architecture; and finally a covariance term, that decorrelates the different dimensions of the embeddings, by bringing to 0 the off-diagonal coefficients of the empirical covariance matrix of the embeddings. + +For completeness, we describe how the VICReg framework works [Bardes et al., 2022]. A seed image $I$ is first sampled in the unlabelled training dataset. Two views $x$ and $x ^ { \prime }$ are obtained by a rectangular crop at random locations in $I$ , rescaling them to a fixed size $( R , S )$ and applying various color jitters with random parameters. The views are fed to an encoder $\dot { f } _ { \theta } : \mathbb { R } ^ { C \times R \times S } \xrightarrow { } \mathbb { R } ^ { \tilde { C } }$ producing their representations $y = f _ { \boldsymbol { \theta } } ( x )$ and $y ^ { \prime } = f _ { \theta } ( x ^ { \prime } ) \in \mathbb R ^ { C }$ , which are mapped by an expander $\mathbf { \Sigma } \dot { h } _ { \phi } : \mathbb { R } ^ { C } \overset { \mathbf { \Sigma } } { } \mathbb { R } ^ { D }$ onto the embeddings $z = h _ { \phi } ( y )$ and $z ^ { \prime } = h _ { \phi } ( y ^ { \prime } ) \in \mathbb { R } ^ { D }$ . The VICReg loss function is defined as follows: + +$$ +\ell ( z , z ^ { \prime } ) = \lambda s ( z , z ^ { \prime } ) + \mu [ v ( z ) + v ( z ^ { \prime } ) ] + \nu [ c ( z ) + c ( z ^ { \prime } ) ] , +$$ + +where $s , v$ and $c$ are the invariance, variance and covariance terms as described in [Bardes et al., 2022], and $\lambda$ , $\mu$ and $\nu$ are scalar coefficients weighting the terms. + +# 3.1 VICRegL: feature vectors matching + +When the encoder $f _ { \theta }$ is a convolutional neural network, the final representations are obtained by performing an average pooling operation $\oplus : \mathbb { R } ^ { C \times H \times W } \mathbb { R } ^ { C }$ on the output feature maps, with $C$ the number of channels and $( H , W )$ the spatial dimensions. We now denote the pooled representations $y _ { \oplus }$ and $y _ { \oplus } ^ { \prime } \in \mathbb { R } ^ { C }$ and the unpooled representations $y$ and $y ^ { \prime } \in \mathbb { R } ^ { C \times H \times W }$ . We denote $y _ { i , j }$ and $y _ { i , j } ^ { \prime } \in \mathbb { R } ^ { C }$ the feature vectors at position $( i , j )$ in their corresponding feature maps. The main idea is to apply the VICReg criterion between pairs of feature vectors from $y$ and $y ^ { \prime }$ , by matching an element of $y$ to one from $y ^ { \prime }$ , using spatial and $l ^ { 2 }$ -distance based information. We introduce a local projector network $h _ { \phi } ^ { l } : \mathbb { R } ^ { \tilde { C } \times H \times W } \to \mathbb { R } ^ { D \times H \times W }$ , that embed the feature maps $y$ and $y ^ { \prime } \in \mathbb { R } ^ { C \times H \times W }$ onto feature maps embeddings $z = h _ { \phi } ^ { l } ( y )$ and $z ^ { \prime } = h _ { \phi } ^ { l } ( y ^ { \prime } ) \in \mathbb { R } ^ { D \times H \times W }$ . The standard expander of VICReg is now the global expander $h _ { \psi } ^ { g } : \mathbb { R } ^ { C } \mathbb { R } ^ { D }$ , which maps the pooled representations $y _ { \oplus }$ and $y _ { \oplus } ^ { \prime } \in \mathbb { R } ^ { C }$ to the embeddings $z _ { \oplus } = h _ { \psi } ^ { g } ( z _ { \oplus } )$ and $z _ { \oplus } ^ { \prime } = h _ { \psi } ^ { g } ( z _ { \oplus } ^ { \prime } ) \in \mathbb { R } ^ { D }$ . We describe now how we perform the matching, and introduce our loss functions. + +Location-based matching. In order to take into account the transformation that occurs between the views $x$ and $x ^ { \prime }$ of an image $I$ , and thus matching features from similar locations, we compute the absolute position in $I$ that corresponds to the coordinate of each feature vector in its feature map. Each feature vector $z _ { p }$ at position $p$ in the feature map is matched to its spatial nearest neighbor according the the absolute position in $I$ , and among the $H \times W$ resulting pairs, only the top- $\gamma$ pairs are kept. The location-based matching loss function is defined as follows: + +![](images/b98233657e067d35a65c70938c5e8214eab10ae5de06ddb23153174e73a35926.jpg) +Figure 1: Overview of VICRegL: Learning local and global features with VICReg. Given a seed image, two views are produced and fed to an encoder that produces local features. The features are further processed by a local projector that embed them into a smaller space, without destroying the localization information. Two matchings, one based on the spatial information provided by the transformation between the views, the other one based on the $l ^ { 2 }$ -distance in the embedding space are computed, and the VICReg criterion is then applied between matched spatial embeddings. Additionally, the local features from the encoder are pooled together, and the pooled features are fed to a global expander. The VICReg criterion is finally applied between the two resulting embeddings. + +$$ +\mathcal { L } _ { s } ( z , z ^ { \prime } ) = \sum _ { p \in P } l ( z _ { p } , z _ { \mathrm { N N } ( p ) } ^ { \prime } ) , +$$ + +where the sum is over coordinates $p$ in $P = \{ ( h , w ) \mid ( h , w ) \in [ 1 , . . . , H ] \times [ 1 , . . . , W ] \}$ the set of all coordinates in the feature map, and $\mathrm { N N } ( p )$ denotes the (spatially) closest coordinate $p ^ { \prime }$ to $p$ according to the actual distance in the seed image. + +Feature-based matching. In addition to matching features that are close in terms of location in the original image, we match features that are close in the embedding space. Each feature vector $z _ { p }$ at position $p$ is matched to its nearest neighbor in $z ^ { \prime }$ according to the $l ^ { 2 }$ distance in the embedding space, and among the $H \times W$ resulting pairs, only the top- $\gamma$ pairs are kept. The feature-based matching loss function is defined as follows: + +$$ +\mathcal { L } _ { d } ( z , z ^ { \prime } ) = \sum _ { p \in P } l ( z _ { p } , \mathrm { N N } ^ { \prime } ( z _ { p } ) ) , +$$ + +where the sum is over coordinates $p$ in $P$ and $\mathrm { N N } ^ { \prime } ( z _ { p } )$ denotes the closest feature vector to $z _ { p }$ in the feature maps $z ^ { \prime }$ , in terms of the $l ^ { 2 }$ -distance. Similar to the location-based loss function, the featurebased loss function enforces invariance on a local scale, but between vectors that are close in the embedding space, and not necessarily pooled from the same location in the seed image. The purpose of this loss function is mainly to capture long-range interactions not captured by the location-based matching. + +The general idea of top- $\gamma$ filtering is to eliminate the mismatched pairs of feature vectors that are too far away in the image for the location-based matching, and that therefore probably do not represent the same objects, but most importantly that are probably mismatched for the feature-based matching, especially at the beginning of the training when the network matches feature vectors representing different objects or textures. Sometime, two views don’t or barely overlap, for the feature-based matching this is not an issue, as the purpose of this matching is to capture long-range interactions not captured by location-based matching. For the location-based matching, given the parameters we use to generate the views (each view covers between $8 \%$ and $100 \%$ of the image, chosen uniformly), the probability for the views to not overlap is small, and even in that case matching the closest points between the views does not degrade the final performance. Indeed, we have tried to use a variable number of matches and a threshold value used to compute the matches, which did not improve the performance compared to using a fixed number of matches. In practice, there are with high probability always good local features to match as the views have a low probability of not overlapping, and this explains why always matching the top- $\gamma$ pairs, compared to introducing a threshold value at which the pair is considered a match, does not degrade the performance. + +Our final loss function is a combination of the location-based and feature-based loss functions, which form the local criterion, with in addition a standard VICReg loss function applied on the pooled representations, which is the global criterion. Both location and feature-based loss functions are symmetrized, because for both, the search for the best match is not a symmetric operation. Our final loss function is described as follows: + +$$ +\mathcal { L } ( z , z ^ { \prime } ) = \alpha \ell ( z _ { \oplus } , z _ { \oplus } ^ { \prime } ) + ( 1 - \alpha ) \{ \mathcal { L } _ { s } ( z , z ^ { \prime } ) + \mathcal { L } _ { s } ( z ^ { \prime } , z ) + \mathcal { L } _ { d } ( z , z ^ { \prime } ) + \mathcal { L } _ { d } ( z ^ { \prime } , z ) \} , +$$ + +where $\alpha$ is an hyper-parameter controlling the importance one wants to put on learning global rather than local features. We study later in Section 4.2 the influence of $\alpha$ on the downstream performance, and show that there exists a trade-off such that the learned representations contain local and global information at the same time, and therefore transfer well on both image classification and segmentation tasks. + +# 3.2 VICRegL with the ConvNeXt backbone + +The feature matching procedure is designed to work with any kind of convolutional neural network. In the experimental section, we provide results with a standard ResNet-50 backbone. However, one can considerably improve the performance on downstream tasks by using a more sophisticated backbone. We propose to use the recently introduced ConvNeXt architecture [Liu et al., 2022], that is very similar to the ResNet one, but with many simple modifications to the original architecture, which make it work as well as modern vision transformers. To the best of our knowledge, this is the first time ConvNeXts have been used in self-supervised learning, and our work shows that convolutional neural networks are still able to deliver state-of-the-art performances in most standard self-supervised learning benchmarks. In order to make the performance competitive with recent approaches, we use the multi-crop strategy introduced in [Caron et al., 2020]. Surprisingly, we found that the combination of multi-crop with encoders from the ResNet family and the VICReg criterion is extremely difficult to optimize, and haven’t been able to make it work properly. However, multi-crop shows very good results when combined with ConvNeXts. Our intuitive explanation is based on a study of the optimal batch size. The VICReg criterion regularizes the empirical covariance matrix of the embeddings, computed using the current batch, and we hypothesize that there is a link between the size of the batch, and the dimensionality of the representations. VICReg combined with a ResNet-50 has shown to have an optimal batch size of 2048, which is exactly the dimensionality of the representations of a ResNet-50. We found that the optimal batch size when working with ConvNeXts is 512 which is much smaller, and correlates with the fact that ConvNeXts also have smaller representations (768 for ConvNeXt-S and 1024 for ConvNeXt-B). The optimal batch size might therefore be close to the dimensionality of the representations. Now, the multi-crop strategy artificially increases the size of the batch, which is much easier to handle when the size of the batch before multi-crop is small. Indeed the effective batch size otherwise becomes too large, which causes optimization issues. + +We now describe how the matching loss functions are adapted in order to work with multi-crop. Instead of generating only two views of the seed image, $N$ views (2 large, and $N - 2$ small), resized $z ^ { 1 }$ twoand $z ^ { 2 }$ ferent resolutions arfor large views, and $\{ \bar { z } ^ { n } \} _ { n = 3 } ^ { N }$ ed, and further encoded into the feature maps embeddingsfor small views. The spatial matching loss function is then defined as follows: + +$$ +\mathcal { L } _ { s } ( \{ z ^ { n } \} _ { n = 1 } ^ { N } ) = \sum _ { m = 1 } ^ { 2 } \sum _ { n \neq m } ^ { N } \{ \sum _ { p \in P } l ( z _ { p } ^ { m } , z _ { \mathrm { N N } ( p ) } ^ { n } ) + \sum _ { p \in P } l ( z _ { p } ^ { n } , z _ { \mathrm { N N } ( p ) } ^ { m } ) \} , +$$ + +where only the top- $\gamma _ { 1 }$ and top- $\gamma _ { 2 }$ pairs of feature vectors of large and small views respectively are kept in the computation of the loss. The feature-based loss function, and the global criterion are adapted in a very similar way, one large view is matched to the other large views and to the small views, and the final loss function is defined as follows: + +$$ +\mathscr { L } ( \{ z ^ { n } \} _ { n = 1 } ^ { N } ) = \alpha \ell ( \{ z _ { \oplus } ^ { n } \} _ { n = 1 } ^ { N } ) + ( 1 - \alpha ) \{ \mathscr { L } _ { s } ( \{ z ^ { n } \} _ { n = 1 } ^ { N } ) + \mathscr { L } _ { d } ( \{ z ^ { n } \} _ { n = 1 } ^ { N } ) \} . +$$ + +Table 1: Comparison of various global and local self-supervised learning methods on different linear evaluation benchmarks. Evaluation of the features learned from a ResNet-50 backbone trained with different methods on: (1) linear classification accuracy $( \% )$ (frozen) on the validation set of ImageNet (2) Linear segmentation (mIoU) (frozen and fine-tuning) on Pascal VOC, (3) Linear segmentation (mIoU) (frozen) on Cityscapes. $\alpha$ is the weight of Eq. (4) balancing the importance given to the global criterion, compared to the local criterion. The best result for each benchmark is bold font. VICRegL consistently improves the linear segmentation mIoU over the VICReg baseline, which shows that introducing a local criterion is beneficial for a localized understanding of the image. + +
Linear Cls. (%)Linear Seg. (mIoU)
MethodEpochsImageNet FrozenPascal VOC FrozenFine-TunedCityscapes Frozen
Global features
MoCo v2 [Chen et al., 2020b]20067.535.664.814.3
SimCLR[Chen et al., 2020a]40068.245.965.417.9
BYOL [Grill et al., 2020]30072.347.165.722.6
VICReg [Bardes et al.,2022]30071.547.865.523.5
Local features
PixPro [Xie et al., 2021]40060.652.867.522.6
DenseCL [Wang et al., 2021]20065.045.366.811.2
DetCon [Hénaff et al., 2021]100066.353.667.416.2
InsLoc [Yang et al., 2022]40045.024.164.47.0
CP² [Wang et al., 2022]82053.121.765.28.4
ReSim [Xiao et al., 2021]40059.551.967.312.3
Ours
VICRegL α = 0.930071.254.066.625.1
VICRegL α = 0.7530070.4 55.967.625.2
+ +# 3.3 Implementation details + +We provide here the implementation details necessary to reproduce the results obtained with our best ResNet-50 and ConvNeXts models. All the models are pretrained on the 1000-class unlabelled ImageNet dataset. Most hyper-parameters are kept unchanged compared to the implementation provided by [Bardes et al., 2022], the VICReg loss variance, invariance and covariance coefficients are set to 25, 25 and 1. The global expander is a 3-layers fully-connected network with dimensions (2048-8192-8192-8192). The local projector is much smaller, due to memory limitations, and has dimensions (2048-512-512-512). With the ResNet-50 backbone, we train our models on 32 Nvidia Tesla V100-32Gb GPUs, with the LARS optimizer [You et al., 2017, Goyal et al., 2017], a weight decay of $1 0 ^ { - 6 }$ , a batch size of 2048 and a learning rate of 0.1. The learning rate follows a cosine decay schedule [Loshchilov and Hutter, 2017], starting from 0 with 10 warmup epochs and with final value of 0.002. The number of selected best matches $\gamma$ of Eq. (2) and (3) is set to 20. With ConvNeXts backbones, we noticed that much smaller batch sizes actually improve the performance, we therefore train our ConvNeXt-S models on 8 Nvidia Tesla V100-32Gb GPUs, with the AdamW optimizer [Loshchilov and Hutter, 2019], a weight decay of $1 0 ^ { - 6 }$ , a batch size of 384 and a learning rate of 0.001, and our ConvNeXt-B models on 16 Nvidia Tesla V100-32Gb GPUs with a batch size of 572 and the same other hyper-parameters. The learning rate follows a cosine decay schedule, starting from 0 with 10 warmup epochs and with final value of 0.00001. The number of selected best matches $\gamma _ { 1 }$ and $\gamma _ { 2 }$ of Eq. (5) are set to 20 for feature maps from large views and 4 for feature maps from small views. + +# 4 Experimental Results + +In this section, we evaluate the representations obtained after pretraining VICRegL with a ResNet-50, and ConvNeXt backbones [Liu et al., 2022] of various size, on linear classification on ImageNet1k [Deng et al., 2009], and linear semantic segmentation on Pacal VOC [Everingham et al., 2010], Cityscapes [Cordts et al., 2016] and ADE20k [Zhou et al., 2019]. We demonstrate that VICRegL strongly improves on segmentation results over VICReg while preserving the classification performance, and is competitive with other local and global self-supervised learning methods. We choose the linear evaluation with frozen weights as our main evaluation metrics, as we believe it is a much better way of evaluating the learned representations. Indeed, the performance can not be attributed to the use of a complex segmentation head, or to the availability of the ground truth masks, and contrary to the frozen setting, the fine-tuning setting measures whether the relevant information is present in the representation, but does not measure if the information is easily extractable from it. We perform the linear evaluation using the protocol introduced by [Zhou et al., 2022a], where the learned feature maps are fed to a linear classifier that outputs a vector with the same size as the number of target classes in the dataset, and is then upsampled to the resolution of the image to produce the predicted mask. The results are averaged over 3 runs with randomly initialized parameters and we found that the difference in performance between worse and best runs is always lower than $0 . 2 \%$ . + +Table 2: Comparison of various global and local self-supervised learning methods on different linear evaluation benchmarks. Evaluation of the features learned from ConvNeXt and ViT backbones trained with different methods on: (1) linear classification accuracy $( \% )$ (frozen) on the validation set of ImageNet (2) Linear segmentation (mIoU) (frozen and fine-tuning) on Pascal VOC, (3) Linear segmentation (mIoU) (frozen) on ADE20k. $\alpha$ is the weight of Eq. (4) balancing the importance given to the global criterion, compared to the local criterion. The best result for each benchmark is bold font. $\dagger$ denotes pretraining on ImageNet-22k. + +
Linear Cls. (%)Linear Seg. (mloU)
MethodBackbone ParamsEpochsImageNet FrozenPascal VOC FrozenFTADE20k Frozen
Global features
MoCo v3 [Chen et al., 2021]ViT-S21M30073.257.175.923.7
DINO [Caron et al., 2021]ViT-S21M40077.065.279.530.5
IBOT[Zhou et al., 2022a]ViT-S21M40077.968.279.933.2
VICReg [Bardes et al., 2022]CNX-S50M40076.260.177.828.6
MoCo v3ViT-B85M30076.764.878.928.7
DINOViT-B85M40078.270.182.034.5
IBOT [Zhou et al., 2022a]ViT-B85M40079.573.082.438.3
MAE [He et al., 2022]ViT-B85M40068.059.682.427.0
VICRegCNX-B85M40077.667.281.132.7
Local features
CP² [Wang et al., 2022]ViT-S21M32062.863.579.625.3
Ours
VICRegL α = 0.9CNX-S50M40075.966.780.030.8
VICRegL α = 0.75CNX-S50M40074.667.580.631.2
VICRegL α = 0.9CNX-B85M40077.169.381.233.5
VICRegL α = 0.75CNX-B85M40076.370.482.535.3
VICRegL α = 0.75+ CNX-XL350M15079.478.784.143.2
+ +# 4.1 Comparison with prior work + +ResNet-50 backbone. Table 1 presents our results against several other global and local selfsupervised learning methods, all pretrained with a ResNet-50 backbone [He et al., 2016]. The main observation we make is the improvement of VICRegL over VICReg on linear segmentation. On Pascal VOC, when the weights of the backbone are frozen, VICRegL $\alpha = 0 . 9$ improves by $+ 6 . 2$ mIoU while only loosing $0 . 3 \%$ classification accuracy, and VICRegL $\alpha = 0 . 7 5$ improves by $\mathbf { + 8 . 1 }$ mIoU. On fine-tuning the improvement is less significative, which we attribute to the non-informative nature of fine-tuning benchmarks. Indeed, some methods like InsLoc and $\mathrm { C P ^ { 2 } }$ that seem competitive on fine-tuning significantly underperform in the frozen regime, which shows that the actual performance of these methods can be attributed to the fact that the weights of the backbone benefit form the availability of the labels during the fine-tuning phase. On Cityscapes, which is much harder, most methods do not perform very well in the linear frozen regime, which sets a new challenge for selfsupervised learning of local features. VICRegL outperforms the VICReg baseline by ${ + 1 . 7 }$ mIoU, as well as every other local features methods by a significant margin. The second observation we make is the robustness of VICRegL in classification, which indicates that it learns both local and global features at the same time. The performance of most local methods is greatly impacted on classification where they all perform around 10 to $20 \%$ below global methods. Global methods on the contrary are efficient for classification but underperform in segmentation compared to VICRegL. + +![](images/b27d297dccbb3e53bb7dc837d75a74a2dfbedc5ed13a2978a8a5752c500cd92a.jpg) +Figure 2: Study of the trade-off between local and global criteria. Evaluation on linear classification on ImageNet and on linear Segmentation on Pascal VOC of VICRegL pretrained with various $\alpha$ coefficients of Eq. (4), controlling the importance of the global criterion against the local criterion. + +Table 3: Ablation: matching criterion. Comparison between using the feature-based matching loss $( \mathcal { L } _ { d } )$ , the location-based matching loss $( \mathcal { L } _ { s } )$ none of the two (Baseline), or both at the same time. + +
MethodCls. (%)Seg. (mIoU)
Baseline73.856.0
Ls73.558.9
Ld73.657.7
Ls-Ld73.660.3
+ +![](images/6852a7b2a0ccd830c64b94fcc62b87381c43a2bc1a13d57f9be9426d2a5722fe.jpg) +Figure 3: Selected matches: visualization of the locations of the best local matches selected by VICRegL. Left image is the seed image, with in red and blue the crop locations for the two views. Left column are the feature-based matches. Right column are the location-based matches. Only 10 matches are visualized for better clarity, but the actual number of selected matches is 20. We display the matches according to the location of the feature vectors in the feature maps. Note that the receptive field of these feature vectors is much larger than only the patch represented by one square of the grid in the figure. Best viewed in color with zoom. + +ConvNeXt backbone. Table 2 presents our results when pretraining with ConvNeXts backbones against several other global and local self-supervised learning methods pretrained with vision transformers [Dosovitskiy et al., 2021]. Similar to our experiments with a ResNet-50 backbone, the main observation we make is the improvement on segmentation tasks provided by the introduction of the local criterion. With a ConvNeXt-S backbone, in the linear frozen regime, VICRegL $\alpha = 0 . 9$ improves over VICReg by $+ 6 . 6$ mIoU on the Pascal VOC, and by $+ 2 . 2$ mIoU on the ADE20K, while preserving most of the classification accuracy. VICRegL $\alpha = 0 . 7 5$ further improves by $\mathbf { + 7 . 4 }$ mIoU and $\mathbf { + 3 . 6 }$ over VICReg on these two benchmarks respectively. With a ConvNeXt-B backbone, the performance improvement remain consistent over VICReg, and VICRegL $\alpha = 0 . 7 5$ is competitive with other strong methods such as DINO and IBOT. The improvement also remain consistent in linear fine-tuning where VICRegL also achieves a strong performance. Finally, we report the performance of a much larger ConvNeXt-XL backbone, pretrained in ImageNet-22k, which is significantly improved on segmentation tasks and set a new state-of-the art in linear segmentation. Our results highlight the trade-off between classification and segmentation performance, which can be controlled by the weight given to the local criterion. + +# 4.2 Ablations + +For all the experiments done in this section, unless specified otherwise, we pretrain a ConvNeXt-S on ImageNet over 100 epochs, with the hyper-parameters described in Section 3.3, and report both the linear classification accuracy on ImageNet, and the linear frozen segmentation mIoU on Pascal VOC. + +Table 4: Ablation: SSL criterion. Introducing our local criterion with VICReg gives a stronger improvement compared to SimCLR, which is contrastive. (ResNet-50, 300 epochs) + +
MethodCls. (%)Seg. (mIoU)
VICReg71.147.8
VICRegL70.4 55.9
SimCLR67.545.9
SimCLR-L66.651.3
+ +Table 5: Ablation: impact of multi-crop. Introducing our local criterion yields an improved performance with or without the usage of multicrop. + +
MethodMulti-cropCls. (%)Seg. (mIoU)
VICReg70.152.9
VICRegL69.957.8
VICReg√73.954.4
VICRegL√73.660.3
+ +Table 6: Ablation: number of selected matches. The large feature maps are of size $7 \times 7$ and the small ones are of size $3 \times 3$ . There are therefore a total number of 49 large and 9 small feature vectors and as many possible matches, and only the top- $\gamma _ { 1 }$ large and top- $\gamma _ { 2 }$ small are kept. + +
Y1γ2Cls. (%)Seg. (mIoU)
10273.459.2
20473.660.3
49973.559.6
+ +Table 7: Ablation: VICReg local criterion. The collapse problem is automatically prevented with the global criterion. We study here how regularizing the local feature vectors influence the performance. V: variance criterion is used, I: invariance criterion is used, C: covariance criterion is used. + +
CriterionCls. (%)Seg. (mIoU)
I73.459.0
VI73.358.2
VIC73.660.3
+ +Trade-off between the local and global criterion. The parameter $\alpha$ of Eq. (4) controls the importance that is given to the global criterion, compared to the local criterion. Figure 2 shows that there exists a fundamental trade-off between the ability of a model to learn global visual features, as opposed to learning local features. In the case $\alpha = 1 . 0$ , which is simply VICReg, the model is very efficient at producing global representations of the image, as demonstrated by the performance of $7 3 . 9 \%$ in classification accuracy. When $\alpha < 1$ , which introduces the local criterion, the performance in segmentation is greatly increased, by $+ 3 . 4$ mIoU when $\alpha = 0 . 9$ , $\pm 4 . 3$ mIoU when $\alpha = 0 . 7 5$ and $+ 4 . 6$ mIoU when the local and global criteria are weighted equally. At the same time, the classification accuracy only drops by respectively $0 . 2 \%$ , $1 . 2 \%$ and $2 . 9 \%$ . This highlights the existence of a sweet spot, where the model is strongly performing at both classification and segmentation, which indicates that it has learned both meaningful local and global features. When $\alpha$ decreases too much, the model starts to lose its performance in both tasks, which shows that having a global understanding of the image is necessary, even for localized tasks. + +Study of the importance between feature-based and location-based local criteria. VICRegL matches feature vectors according to a location-based criterion $\mathcal { L } _ { s }$ of Eq. (2) and a feature-based criterion $\mathcal { L } _ { d }$ of Eq. (3). Table 3 study the importance of these criterion. Baseline in the table means that no local criterion is used, and is simply VICReg. The location-based criterion gives the best improvement by $\mathbf { + 2 . 9 }$ mIoU over the baseline, compared to only ${ + 1 . 7 }$ mIoU for the feature-based criterion, but it is the combination of the two that significantly improves over the baseline by $\mathbf { + 4 . 3 }$ mIoU, which shows that using both the learned distance in the embedding space in combination with the actual distance in the pixel space produces local features with the best quality. In all cases, the classification accuracy is not affected, which is expected as the local criterion has little effect on the quality of the global features, and therefore on the downstream classification accuracy. + +Study of the number of matches. We study here the influence of changing the number of selected best matches $\gamma _ { 1 }$ and $\gamma _ { 2 }$ of Eq. (5), to keep for the computation of the local losses. For our experiments with multi-crop, the size of the feature maps is $( 2 0 4 8 \times 7 \times 7 )$ for the large crops and $( 2 0 4 8 \times 3 \times 3 )$ for the small crops. There are therefore in one branch of the siamese architecture 49 feature maps for large crops, and 9 for small crops. Tables 6 shows that there is a trade-off between keeping all the matches $\gamma _ { 1 } = 4 9$ and $\gamma _ { 2 } = 9$ ), and keeping a small number of matches $\gamma _ { 1 } = 1 0$ and $\gamma _ { 2 } = 2 \quad ,$ ), and that the best segmentation performance is obtained with an in-between number of matches, $\gamma _ { 1 } = 2 0$ and $\gamma _ { 2 } = 4$ ), which improves by $\mathbf { + 0 . 7 \ m I o U }$ compared to keeping all the matches. Similar to the study on the influence of the local losses, the classification accuracy is not affected, as the local criterion does not improve or degrade the global features. + +Study of VICReg components for the local criterion. The global criterion is sufficient for the vectors to not collapse to trivial solutions. We therefore investigate if introducing the variance (V) and covariance (C) criterion, in addition to the invariance (I) criterion, applied by the local loss functions on the feature vectors, is useful or not. Table 7 shows that these regularization criteria are actually helping the performance, introducing the variance criterion improves on segmentation by $\mathbf { + 0 . 8 \ m I o U }$ , and additionally adding the covariance criterion further improves the performance by $\mathbf { + 1 . 3 }$ mIoU over the baseline. Similar to other ablations on the local loss functions, the classification accuracy is not significantly impacted. + +Study of a different collapse prevention method. Our collapse-prevention mechanism is the variance and covariance regularization of VICReg, which is a non-contrastive criterion that therefore does not contrast negatively on potential positive matchings. We study however the incorporation of our local criterion with a contrastive criterion, SimCLR [Chen et al., 2020a]. We simply replace VICReg by SimCLR in Eq. (2) and Eq. (3) and refer this new method as SimCLR-L. Table 4 reports the performance, and we observe that although there is a gap in performance between regular SimCLR and VICReg, the additional benefit provided by the local criterion is much stronger with VICReg. + +Impact of multi-crop. We study the impact of using the multi-crop strategy for the data augmentation, by comparing VICReg to VICRegL. Table 5 reports our results. Whether multi-crop is used or not, introducing the local criterion always improve significantly the segmentation results, while preserving again most of the classification performance. + +# 4.3 Visualization + +We provide in Figure 3, a visualization of the pairs of matched feature vectors selected by VICRegL. Right to the seed image, the left column shows the feature-based matches, and the right column shows the location-based matches. Each case in the the grid represents a position in the feature map, and a match between two feature vectors is represented by a yellow line. The receptive field of these feature vectors is larger than a single case in the grid, and actually spans the entire image, but we observe that the embedding space is shaped such that the feature-based matching is coherent regarding the semantic content at a position in the image where a feature vector is pooled. A feature vector that is located at a position corresponding to a texture representing "sky" or "grass" in one view is matched to another one on the other view located at a position corresponding to a similar "sky" or "grass" texture. Additional visualizations are available in Appendix ??. + +# 5 Conclusion + +In this work, we introduced VICRegL, a method for learning both local and global visual features at the same time, by matching feature vectors with respect to their distance in the pixel space and in the embedding space. We show that introducing a local criterion significantly improves the performance on segmentation tasks, while preserving the classification accuracy. We also demonstrate that convolutional networks are competitive to vision transformers in self-supervised learning, by using the ConvNeXt backbone. + +Limitations and Future work. Convolutional neural networks by design produce feature maps that have a receptive field that covers the entire image. It is not clear to which extent a feature vector at a given position in the feature maps actually contains mainly information about the objects located at the corresponding location in the input image. The learned tokens of a vision transformers are also good candidates for local features, and a detailed study of the actual local nature of both the feature vectors of a convolutional network and the tokens of a vision transformer, would provide useful insights for future directions of self-supervised learning of local features. Future work will also tackle the problem of learning hierarchical features, by applying a criterion not only at a local and a global scale, but also at multiple levels in the encoder network. + +Acknowledgement. Jean Ponce was supported in part by the French government under management of Agence Nationale de la Recherche as part of the ”Investissements d’avenir” program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), the Louis Vuitton/ENS Chair in Artificial Intelligence and the Inria/NYU collaboration. Adrien Bardes was supported in part by a FAIR/Prairie CIFRE PhD Fellowship. The authors wish to thank Li Jing, Randall Balestriero, Amir Bar, Grégoire Mialon, Jiachen Zhu, Quentin Garrido, Florian Bordes, Bobak Kiani, Surya Ganguli, Megi Dervichi, Yubei Chen, Mido Assran, Nicolas Ballas and Pascal Vincent for useful discussions. + +# References + +A. Bardes, J. Ponce, and Y. LeCun. Vicreg: Variance-invariance-covariance regularization for self-supervised learning. In ICLR, 2022. 1, 2, 3, 6, 7 +M. Caron, P. Bojanowski, A. Joulin, and M. Douze. Deep clustering for unsupervised learning. In ECCV, 2018. 2 +M. Caron, I. Misra, J. Mairal, P. Goyal, P. Bojanowski, and A. Joulin. Unsupervised learning of visual features by contrasting cluster assignments. In NeurIPS, 2020. 1, 2, 5 +M. Caron, H. Touvron, I. Misra, H. Jegou, and J. M. P. B. A. Joulin. Emerging properties in self-supervised vision transformers. In ICCV, 2021. 1, 2, 7 +T. Chen, S. Kornblith, M. Norouzi, and G. E. Hinton. A simple framework for contrastive learning of visual representations. 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Yuille, and T. Kong. ibot: Image bert pre-training with online tokenizer. In ICLR, 2022a. 1, 2, 7 P. Zhou, Y. Zhou, C. Si, W. Yu, T. K. Ng, and S. Yan. Mugs: A multi-granular self-supervised learning framework. arXiv preprint arXiv:2203.14415, 2022b. 2 \ No newline at end of file diff --git a/parse/dev/ePZsWeGJXyp/ePZsWeGJXyp_content_list.json b/parse/dev/ePZsWeGJXyp/ePZsWeGJXyp_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..24013a235bf61a5aaee0e735ba926162eb16be7c --- /dev/null +++ b/parse/dev/ePZsWeGJXyp/ePZsWeGJXyp_content_list.json @@ -0,0 +1,933 @@ +[ + { + "type": "text", + "text": "VICRegL: Self-Supervised Learning of Local Visual Features ", + "text_level": 1, + "bbox": [ + 184, + 122, + 815, + 171 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adrien Bardes1,2 ", + "bbox": [ + 253, + 222, + 369, + 236 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jean Ponce2,4 ", + "bbox": [ + 452, + 220, + 550, + 236 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yann LeCun1,3,4 ", + "bbox": [ + 632, + 220, + 750, + 236 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Meta, FAIR \n2Inria, École normale supérieure, CNRS, PSL Research University \n3Courant Institute, New York University \n4Center for Data Science, New York University ", + "bbox": [ + 279, + 238, + 718, + 296 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 332, + 535, + 348 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most recent self-supervised methods for learning image representations focus on either producing a global feature with invariance properties, or producing a set of local features. The former works best for classification tasks while the latter is best for detection and segmentation tasks. This paper explores the fundamental tradeoff between learning local and global features. A new method called VICRegL is proposed that learns good global and local features simultaneously, yielding excellent performance on detection and segmentation tasks while maintaining good performance on classification tasks. Concretely, two identical branches of a standard convolutional net architecture are fed two differently distorted versions of the same image. The VICReg criterion is applied to pairs of global feature vectors. Simultaneously, the VICReg criterion is applied to pairs of local feature vectors occurring before the last pooling layer. Two local feature vectors are attracted to each other if their $l ^ { 2 }$ -distance is below a threshold or if their relative locations are consistent with a known geometric transformation between the two input images. We demonstrate strong performance on linear classification and segmentation transfer tasks. Code and pretrained models are publicly available at: https://github.com/facebookresearch/VICRegL ", + "bbox": [ + 233, + 364, + 766, + 601 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 174, + 630, + 312, + 647 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advances in self-supervised learning for computer vision have been largely driven by downstream proxy tasks such as image categorization, with convolutional backbones [Chen et al., 2020a,b, Grill et al., 2020, Lee et al., 2021, Caron et al., 2020, Zbontar et al., 2021, Bardes et al., 2022, Tomasev et al., 2022], or vision transformers [Caron et al., 2021, Chen et al., 2021, Li et al., 2022, Zhou et al., 2022a]. Current approaches rely on a joint embedding architecture and a loss function that forces the learned features to be invariant to a sampling process selecting pairs of different views of the same image, obtained by transformation such as cropping, rescaling, or color jittering [Misra and Maaten, 2020, Chen et al., 2020a, He et al., 2020, Grill et al., 2020]. These methods learn to eliminate the irrelevant part of position and color information, in order to satisfy the invariance criterion, and perform well on image classification benchmarks. Some recent approaches go beyond learning global features: to tackle tasks such as semantic segmentation where spatial information plays a key role, [Yang et al., 2021, Xie et al., 2021, Hénaff et al., 2021, Yang et al., 2022, Hénaff et al., 2022, El-Nouby et al., 2022] also learn image models with more emphasis on local image structure. In the end most recent approaches to self-supervised learning of visual features learn the corresponding image model using either a (possibly quite sophisticated) global criterion, or a (necessarily) different one exploiting local image characteristics and spatial information. The best performing local methods require a non-parametric pre-processing step that compute unsupervised segmentation masks [Hénaff et al., 2021], which can be done online [Hénaff et al., 2022], but with an additional computational burden. ", + "bbox": [ + 174, + 664, + 825, + 898 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 823, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We argue that more complex reasoning systems should be structured in a hierarchical way, by learning at several scales. To this end, we propose VICRegL, a method that learn features at a global scale, and that additionally uses spatial information, and matches feature vectors that are either pooled from close-by regions in the original input image, or close in the embedding space, therefore learning features at a local scale. In practice, the global VICReg criterion [Bardes et al., 2022] is applied to pairs of feature vectors, before and after the final pooling layer of a convolutional network, thus learning local and global features at the same time. When a segmentation mask is available as in [Hénaff et al., 2021], feature vectors that correspond to the same region in the mask can be pooled together, and compared using a contrastive loss function, which allows spatial vectors far away in the original image to be pooled together if they belong to the same object. In our case, segmentation masks are not available, and we therefore face two challenges: (1) there is no a priori information on how to pool vectors from the same object together, thus long-range matching should be learned in a self-supervised manner, and (2) contrasting negatively feature vectors corresponding to far away locations can have a negative effect, as these vectors could have been pooled from locations that represent the same object in the image. In order to address these issues, VICRegL (1) matches feature vectors according to a $l ^ { 2 }$ nearest-neighbor criterion exploiting both the distances between features and image locations, properly weighted, and (2) uses the VICReg criterion between matched feature vectors. We use VICReg for its simplicity and its non-contrastive nature, which alleviates the need for negative samples and therefore does not have an explicit negative contrasting effect between feature vectors that could have been potential matches. ", + "bbox": [ + 174, + 126, + 825, + 401 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the effectiveness of VICRegL by evaluating the learned representations on vision tasks such as image classification on ImageNet and semantic segmentation on various datasets. Our evaluation is (mostly) done in the setting where the backbone learned by VICRegL is frozen, with only a linear classification or segmentation head tuned to the task at hand. We believe that this setting is a much better evaluation metric than the commonly used fine-tuning benchmarks, as the performance can not be attributed to the use of a complex head, or to the availability of the ground truth masks. Our results show that learning local features, in addition to global features, does not hurt the classification performance, but significantly improves segmentation accuracy. On the Pascal VOC linear frozen semantic segmentation task, VICRegL achieves 55.9 mIoU with a ResNet-50 backbone, which is a ${ \\bf + 8 . 1 }$ mIoU improvement over VICReg, and 67.5 mIoU with a ConvNeXt-S backbone, which is a $+ 6 . 6$ mIoU improvement. ", + "bbox": [ + 174, + 409, + 825, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Related work ", + "text_level": 1, + "bbox": [ + 174, + 582, + 316, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Global features. Most recent methods for global feature learning are based on a joint embedding architecture that learns representations that are invariant to various views. These methods differ in the way collapsing solutions are avoided. Contrastive methods [Hjelm et al., 2019, Chen et al., 2020a, He et al., 2020, Chen et al., 2020b, Mitrovic et al., 2021, Dwibedi et al., 2021, Chen et al., 2021, Tomasev et al., 2022] uses negative samples to push dissimilar samples apart from each other. Clustering methods [Caron et al., 2018, 2020, 2021] ensure a balanced partition of the samples within a set of clusters. Non-contrastive methods, which are dual to contrastive ones [Garrido et al., 2022], rely on maintaining the informational content of the representations by either explicit regularization [Zbontar et al., 2021, Bardes et al., 2022] or architectural design [Chen and He, 2020, Grill et al., 2020, Richemond et al., 2020, Lee et al., 2021]. Finally, the best performing methods today are based on vision transformers [Caron et al., 2021, Chen et al., 2021, Li et al., 2022, Zhou et al., 2022a,b] and deliver strong results in both downstream classification and segmentation tasks. ", + "bbox": [ + 174, + 614, + 825, + 780 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Local features. In opposition to global methods, local one focus on explicitly learning a set of local features that describe small parts of the image, which global methods do implicitly [Chen et al., 2022], and are therefore better suited for segmentation tasks. Indeed these methods commonly only evaluate on segmentation benchmarks. A contrastive loss function can be applied directly: (1) at the pixel level [Xie et al., 2021], which forces consistency between pixels at similar locations; (2) at the feature map level [Wang et al., 2021], which forces consistency between groups of pixels: (3) at the image region level [Xiao et al., 2021], which forces consistency between large regions that overlap in different views of an image. Similar to [Wang et al., 2021], our method VICRegL operates at the feature map level but with a more advanced matching criterion that takes into account the distance in pixel space between the objects. Copy pasting a patch on a random background [Yang et al., 2021, Wang et al., 2022] has also shown to be effective for learning to localize an object without relying on spurious correlations with the background. Aggregating multiple images corresponding to several object instances into a single image can also help the localization task [Yang et al., 2022]. These approaches rely on carefully and handcrafted constructions of new images with modified background or with aggregation of semantic content from several other images, which is not satisfactory, while our method simply rely on the classical augmentations commonly used in self-supervised learning. The best current approaches consist in using the information from unsupervised segmentation masks, which can be computed as a pre-processing step [Hénaff et al., 2021] or computed online [Hénaff et al., 2022]. The feature vectors coming from the same region in the mask are pooled together and the resulting vectors are contrasted between each other with a contrastive loss function. These approaches explicitly construct semantic segmentation masks using k-means for every input image, which is computationally not efficient, and is a strong inductive bias in the architecture. Our method does not rely on these masks and therefore learns less specialized features. ", + "bbox": [ + 174, + 786, + 825, + 911 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 90, + 826, + 285 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 Method ", + "text_level": 1, + "bbox": [ + 174, + 304, + 271, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Background. VICReg was introduced as a self-supervised method for learning image representations that avoid the collapse problem by design. Its loss function is composed of three terms: a variance term, that preserves the variance of the embeddings, and consists in a hinge loss function on the standard deviation, on each component of the vectors individually and along the batch dimension; an invariance term, which is simply an $l ^ { 2 }$ distance between the embeddings from the two branches of a siamese architecture; and finally a covariance term, that decorrelates the different dimensions of the embeddings, by bringing to 0 the off-diagonal coefficients of the empirical covariance matrix of the embeddings. ", + "bbox": [ + 173, + 335, + 825, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For completeness, we describe how the VICReg framework works [Bardes et al., 2022]. A seed image $I$ is first sampled in the unlabelled training dataset. Two views $x$ and $x ^ { \\prime }$ are obtained by a rectangular crop at random locations in $I$ , rescaling them to a fixed size $( R , S )$ and applying various color jitters with random parameters. The views are fed to an encoder $\\dot { f } _ { \\theta } : \\mathbb { R } ^ { C \\times R \\times S } \\xrightarrow { } \\mathbb { R } ^ { \\tilde { C } }$ producing their representations $y = f _ { \\boldsymbol { \\theta } } ( x )$ and $y ^ { \\prime } = f _ { \\theta } ( x ^ { \\prime } ) \\in \\mathbb R ^ { C }$ , which are mapped by an expander $\\mathbf { \\Sigma } \\dot { h } _ { \\phi } : \\mathbb { R } ^ { C } \\overset { \\mathbf { \\Sigma } } { } \\mathbb { R } ^ { D }$ onto the embeddings $z = h _ { \\phi } ( y )$ and $z ^ { \\prime } = h _ { \\phi } ( y ^ { \\prime } ) \\in \\mathbb { R } ^ { D }$ . The VICReg loss function is defined as follows: ", + "bbox": [ + 173, + 453, + 825, + 550 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/7e5008688d3dd8e9727406b81a904336fcd0e0596727075a525f922b083c8ba9.jpg", + "text": "$$\n\\ell ( z , z ^ { \\prime } ) = \\lambda s ( z , z ^ { \\prime } ) + \\mu [ v ( z ) + v ( z ^ { \\prime } ) ] + \\nu [ c ( z ) + c ( z ^ { \\prime } ) ] ,\n$$", + "text_format": "latex", + "bbox": [ + 308, + 558, + 689, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $s , v$ and $c$ are the invariance, variance and covariance terms as described in [Bardes et al., 2022], and $\\lambda$ , $\\mu$ and $\\nu$ are scalar coefficients weighting the terms. ", + "bbox": [ + 173, + 583, + 823, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 VICRegL: feature vectors matching ", + "text_level": 1, + "bbox": [ + 174, + 627, + 462, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "When the encoder $f _ { \\theta }$ is a convolutional neural network, the final representations are obtained by performing an average pooling operation $\\oplus : \\mathbb { R } ^ { C \\times H \\times W } \\mathbb { R } ^ { C }$ on the output feature maps, with $C$ the number of channels and $( H , W )$ the spatial dimensions. We now denote the pooled representations $y _ { \\oplus }$ and $y _ { \\oplus } ^ { \\prime } \\in \\mathbb { R } ^ { C }$ and the unpooled representations $y$ and $y ^ { \\prime } \\in \\mathbb { R } ^ { C \\times H \\times W }$ . We denote $y _ { i , j }$ and $y _ { i , j } ^ { \\prime } \\in \\mathbb { R } ^ { C }$ the feature vectors at position $( i , j )$ in their corresponding feature maps. The main idea is to apply the VICReg criterion between pairs of feature vectors from $y$ and $y ^ { \\prime }$ , by matching an element of $y$ to one from $y ^ { \\prime }$ , using spatial and $l ^ { 2 }$ -distance based information. We introduce a local projector network $h _ { \\phi } ^ { l } : \\mathbb { R } ^ { \\tilde { C } \\times H \\times W } \\to \\mathbb { R } ^ { D \\times H \\times W }$ , that embed the feature maps $y$ and $y ^ { \\prime } \\in \\mathbb { R } ^ { C \\times H \\times W }$ onto feature maps embeddings $z = h _ { \\phi } ^ { l } ( y )$ and $z ^ { \\prime } = h _ { \\phi } ^ { l } ( y ^ { \\prime } ) \\in \\mathbb { R } ^ { D \\times H \\times W }$ . The standard expander of VICReg is now the global expander $h _ { \\psi } ^ { g } : \\mathbb { R } ^ { C } \\mathbb { R } ^ { D }$ , which maps the pooled representations $y _ { \\oplus }$ and $y _ { \\oplus } ^ { \\prime } \\in \\mathbb { R } ^ { C }$ to the embeddings $z _ { \\oplus } = h _ { \\psi } ^ { g } ( z _ { \\oplus } )$ and $z _ { \\oplus } ^ { \\prime } = h _ { \\psi } ^ { g } ( z _ { \\oplus } ^ { \\prime } ) \\in \\mathbb { R } ^ { D }$ . We describe now how we perform the matching, and introduce our loss functions. ", + "bbox": [ + 173, + 654, + 825, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Location-based matching. In order to take into account the transformation that occurs between the views $x$ and $x ^ { \\prime }$ of an image $I$ , and thus matching features from similar locations, we compute the absolute position in $I$ that corresponds to the coordinate of each feature vector in its feature map. Each feature vector $z _ { p }$ at position $p$ in the feature map is matched to its spatial nearest neighbor according the the absolute position in $I$ , and among the $H \\times W$ resulting pairs, only the top- $\\gamma$ pairs are kept. The location-based matching loss function is defined as follows: ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b98233657e067d35a65c70938c5e8214eab10ae5de06ddb23153174e73a35926.jpg", + "image_caption": [ + "Figure 1: Overview of VICRegL: Learning local and global features with VICReg. Given a seed image, two views are produced and fed to an encoder that produces local features. The features are further processed by a local projector that embed them into a smaller space, without destroying the localization information. Two matchings, one based on the spatial information provided by the transformation between the views, the other one based on the $l ^ { 2 }$ -distance in the embedding space are computed, and the VICReg criterion is then applied between matched spatial embeddings. Additionally, the local features from the encoder are pooled together, and the pooled features are fed to a global expander. The VICReg criterion is finally applied between the two resulting embeddings. " + ], + "image_footnote": [], + "bbox": [ + 178, + 89, + 823, + 308 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 458, + 655, + 473 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/4525d0fcb9b2ab6ad72f485902d43b4a30db18214bf3fd0173530dcff313e8ec.jpg", + "text": "$$\n\\mathcal { L } _ { s } ( z , z ^ { \\prime } ) = \\sum _ { p \\in P } l ( z _ { p } , z _ { \\mathrm { N N } ( p ) } ^ { \\prime } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 398, + 478, + 598, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the sum is over coordinates $p$ in $P = \\{ ( h , w ) \\mid ( h , w ) \\in [ 1 , . . . , H ] \\times [ 1 , . . . , W ] \\}$ the set of all coordinates in the feature map, and $\\mathrm { N N } ( p )$ denotes the (spatially) closest coordinate $p ^ { \\prime }$ to $p$ according to the actual distance in the seed image. ", + "bbox": [ + 174, + 518, + 825, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature-based matching. In addition to matching features that are close in terms of location in the original image, we match features that are close in the embedding space. Each feature vector $z _ { p }$ at position $p$ is matched to its nearest neighbor in $z ^ { \\prime }$ according to the $l ^ { 2 }$ distance in the embedding space, and among the $H \\times W$ resulting pairs, only the top- $\\gamma$ pairs are kept. The feature-based matching loss function is defined as follows: ", + "bbox": [ + 173, + 566, + 825, + 637 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/dff4eac298853f1f27cd88c99dfb726466c604035ccee6be93d9b970c109ba56.jpg", + "text": "$$\n\\mathcal { L } _ { d } ( z , z ^ { \\prime } ) = \\sum _ { p \\in P } l ( z _ { p } , \\mathrm { N N } ^ { \\prime } ( z _ { p } ) ) ,\n$$", + "text_format": "latex", + "bbox": [ + 392, + 640, + 606, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the sum is over coordinates $p$ in $P$ and $\\mathrm { N N } ^ { \\prime } ( z _ { p } )$ denotes the closest feature vector to $z _ { p }$ in the feature maps $z ^ { \\prime }$ , in terms of the $l ^ { 2 }$ -distance. Similar to the location-based loss function, the featurebased loss function enforces invariance on a local scale, but between vectors that are close in the embedding space, and not necessarily pooled from the same location in the seed image. The purpose of this loss function is mainly to capture long-range interactions not captured by the location-based matching. ", + "bbox": [ + 173, + 680, + 825, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The general idea of top- $\\gamma$ filtering is to eliminate the mismatched pairs of feature vectors that are too far away in the image for the location-based matching, and that therefore probably do not represent the same objects, but most importantly that are probably mismatched for the feature-based matching, especially at the beginning of the training when the network matches feature vectors representing different objects or textures. Sometime, two views don’t or barely overlap, for the feature-based matching this is not an issue, as the purpose of this matching is to capture long-range interactions not captured by location-based matching. For the location-based matching, given the parameters we use to generate the views (each view covers between $8 \\%$ and $100 \\%$ of the image, chosen uniformly), the probability for the views to not overlap is small, and even in that case matching the closest points between the views does not degrade the final performance. Indeed, we have tried to use a variable number of matches and a threshold value used to compute the matches, which did not improve the performance compared to using a fixed number of matches. In practice, there are with high probability always good local features to match as the views have a low probability of not overlapping, and this explains why always matching the top- $\\gamma$ pairs, compared to introducing a threshold value at which the pair is considered a match, does not degrade the performance. ", + "bbox": [ + 173, + 772, + 825, + 911 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 825, + 161 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our final loss function is a combination of the location-based and feature-based loss functions, which form the local criterion, with in addition a standard VICReg loss function applied on the pooled representations, which is the global criterion. Both location and feature-based loss functions are symmetrized, because for both, the search for the best match is not a symmetric operation. Our final loss function is described as follows: ", + "bbox": [ + 173, + 166, + 825, + 236 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/96e5220d2dd0348141b4b6d3be021dbd3ec1a21e7527f4f0e2c1385d930abb94.jpg", + "text": "$$\n\\mathcal { L } ( z , z ^ { \\prime } ) = \\alpha \\ell ( z _ { \\oplus } , z _ { \\oplus } ^ { \\prime } ) + ( 1 - \\alpha ) \\{ \\mathcal { L } _ { s } ( z , z ^ { \\prime } ) + \\mathcal { L } _ { s } ( z ^ { \\prime } , z ) + \\mathcal { L } _ { d } ( z , z ^ { \\prime } ) + \\mathcal { L } _ { d } ( z ^ { \\prime } , z ) \\} ,\n$$", + "text_format": "latex", + "bbox": [ + 227, + 243, + 767, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ is an hyper-parameter controlling the importance one wants to put on learning global rather than local features. We study later in Section 4.2 the influence of $\\alpha$ on the downstream performance, and show that there exists a trade-off such that the learned representations contain local and global information at the same time, and therefore transfer well on both image classification and segmentation tasks. ", + "bbox": [ + 174, + 268, + 825, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2 VICRegL with the ConvNeXt backbone ", + "text_level": 1, + "bbox": [ + 174, + 354, + 490, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The feature matching procedure is designed to work with any kind of convolutional neural network. In the experimental section, we provide results with a standard ResNet-50 backbone. However, one can considerably improve the performance on downstream tasks by using a more sophisticated backbone. We propose to use the recently introduced ConvNeXt architecture [Liu et al., 2022], that is very similar to the ResNet one, but with many simple modifications to the original architecture, which make it work as well as modern vision transformers. To the best of our knowledge, this is the first time ConvNeXts have been used in self-supervised learning, and our work shows that convolutional neural networks are still able to deliver state-of-the-art performances in most standard self-supervised learning benchmarks. In order to make the performance competitive with recent approaches, we use the multi-crop strategy introduced in [Caron et al., 2020]. Surprisingly, we found that the combination of multi-crop with encoders from the ResNet family and the VICReg criterion is extremely difficult to optimize, and haven’t been able to make it work properly. However, multi-crop shows very good results when combined with ConvNeXts. Our intuitive explanation is based on a study of the optimal batch size. The VICReg criterion regularizes the empirical covariance matrix of the embeddings, computed using the current batch, and we hypothesize that there is a link between the size of the batch, and the dimensionality of the representations. VICReg combined with a ResNet-50 has shown to have an optimal batch size of 2048, which is exactly the dimensionality of the representations of a ResNet-50. We found that the optimal batch size when working with ConvNeXts is 512 which is much smaller, and correlates with the fact that ConvNeXts also have smaller representations (768 for ConvNeXt-S and 1024 for ConvNeXt-B). The optimal batch size might therefore be close to the dimensionality of the representations. Now, the multi-crop strategy artificially increases the size of the batch, which is much easier to handle when the size of the batch before multi-crop is small. Indeed the effective batch size otherwise becomes too large, which causes optimization issues. ", + "bbox": [ + 173, + 380, + 825, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now describe how the matching loss functions are adapted in order to work with multi-crop. Instead of generating only two views of the seed image, $N$ views (2 large, and $N - 2$ small), resized $z ^ { 1 }$ twoand $z ^ { 2 }$ ferent resolutions arfor large views, and $\\{ \\bar { z } ^ { n } \\} _ { n = 3 } ^ { N }$ ed, and further encoded into the feature maps embeddingsfor small views. The spatial matching loss function is then defined as follows: ", + "bbox": [ + 174, + 705, + 826, + 775 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/64d13d5221fedde969cf80a2e1c8c74d4d71ca2dae6aaffeba9064887e14b837.jpg", + "text": "$$\n\\mathcal { L } _ { s } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) = \\sum _ { m = 1 } ^ { 2 } \\sum _ { n \\neq m } ^ { N } \\{ \\sum _ { p \\in P } l ( z _ { p } ^ { m } , z _ { \\mathrm { N N } ( p ) } ^ { n } ) + \\sum _ { p \\in P } l ( z _ { p } ^ { n } , z _ { \\mathrm { N N } ( p ) } ^ { m } ) \\} ,\n$$", + "text_format": "latex", + "bbox": [ + 276, + 779, + 720, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where only the top- $\\gamma _ { 1 }$ and top- $\\gamma _ { 2 }$ pairs of feature vectors of large and small views respectively are kept in the computation of the loss. The feature-based loss function, and the global criterion are adapted in a very similar way, one large view is matched to the other large views and to the small views, and the final loss function is defined as follows: ", + "bbox": [ + 174, + 832, + 825, + 887 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/8cd42f3fe48b7a24a93597e2706e23a4c85ce58d2a028fee9e13ac850191d6cb.jpg", + "text": "$$\n\\mathscr { L } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) = \\alpha \\ell ( \\{ z _ { \\oplus } ^ { n } \\} _ { n = 1 } ^ { N } ) + ( 1 - \\alpha ) \\{ \\mathscr { L } _ { s } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) + \\mathscr { L } _ { d } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) \\} .\n$$", + "text_format": "latex", + "bbox": [ + 253, + 893, + 745, + 914 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7869cba0b8099e1665f7747b4481f1790612ebd9a4922f2ed2598975df10c83f.jpg", + "table_caption": [ + "Table 1: Comparison of various global and local self-supervised learning methods on different linear evaluation benchmarks. Evaluation of the features learned from a ResNet-50 backbone trained with different methods on: (1) linear classification accuracy $( \\% )$ (frozen) on the validation set of ImageNet (2) Linear segmentation (mIoU) (frozen and fine-tuning) on Pascal VOC, (3) Linear segmentation (mIoU) (frozen) on Cityscapes. $\\alpha$ is the weight of Eq. (4) balancing the importance given to the global criterion, compared to the local criterion. The best result for each benchmark is bold font. VICRegL consistently improves the linear segmentation mIoU over the VICReg baseline, which shows that introducing a local criterion is beneficial for a localized understanding of the image. " + ], + "table_footnote": [], + "table_body": "
Linear Cls. (%)Linear Seg. (mIoU)
MethodEpochsImageNet FrozenPascal VOC FrozenFine-TunedCityscapes Frozen
Global features
MoCo v2 [Chen et al., 2020b]20067.535.664.814.3
SimCLR[Chen et al., 2020a]40068.245.965.417.9
BYOL [Grill et al., 2020]30072.347.165.722.6
VICReg [Bardes et al.,2022]30071.547.865.523.5
Local features
PixPro [Xie et al., 2021]40060.652.867.522.6
DenseCL [Wang et al., 2021]20065.045.366.811.2
DetCon [Hénaff et al., 2021]100066.353.667.416.2
InsLoc [Yang et al., 2022]40045.024.164.47.0
CP² [Wang et al., 2022]82053.121.765.28.4
ReSim [Xiao et al., 2021]40059.551.967.312.3
Ours
VICRegL α = 0.930071.254.066.625.1
VICRegL α = 0.7530070.4 55.967.625.2
", + "bbox": [ + 210, + 222, + 785, + 478 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3 Implementation details ", + "text_level": 1, + "bbox": [ + 174, + 503, + 374, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide here the implementation details necessary to reproduce the results obtained with our best ResNet-50 and ConvNeXts models. All the models are pretrained on the 1000-class unlabelled ImageNet dataset. Most hyper-parameters are kept unchanged compared to the implementation provided by [Bardes et al., 2022], the VICReg loss variance, invariance and covariance coefficients are set to 25, 25 and 1. The global expander is a 3-layers fully-connected network with dimensions (2048-8192-8192-8192). The local projector is much smaller, due to memory limitations, and has dimensions (2048-512-512-512). With the ResNet-50 backbone, we train our models on 32 Nvidia Tesla V100-32Gb GPUs, with the LARS optimizer [You et al., 2017, Goyal et al., 2017], a weight decay of $1 0 ^ { - 6 }$ , a batch size of 2048 and a learning rate of 0.1. The learning rate follows a cosine decay schedule [Loshchilov and Hutter, 2017], starting from 0 with 10 warmup epochs and with final value of 0.002. The number of selected best matches $\\gamma$ of Eq. (2) and (3) is set to 20. With ConvNeXts backbones, we noticed that much smaller batch sizes actually improve the performance, we therefore train our ConvNeXt-S models on 8 Nvidia Tesla V100-32Gb GPUs, with the AdamW optimizer [Loshchilov and Hutter, 2019], a weight decay of $1 0 ^ { - 6 }$ , a batch size of 384 and a learning rate of 0.001, and our ConvNeXt-B models on 16 Nvidia Tesla V100-32Gb GPUs with a batch size of 572 and the same other hyper-parameters. The learning rate follows a cosine decay schedule, starting from 0 with 10 warmup epochs and with final value of 0.00001. The number of selected best matches $\\gamma _ { 1 }$ and $\\gamma _ { 2 }$ of Eq. (5) are set to 20 for feature maps from large views and 4 for feature maps from small views. ", + "bbox": [ + 173, + 530, + 825, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 Experimental Results ", + "text_level": 1, + "bbox": [ + 174, + 810, + 385, + 828 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the representations obtained after pretraining VICRegL with a ResNet-50, and ConvNeXt backbones [Liu et al., 2022] of various size, on linear classification on ImageNet1k [Deng et al., 2009], and linear semantic segmentation on Pacal VOC [Everingham et al., 2010], Cityscapes [Cordts et al., 2016] and ADE20k [Zhou et al., 2019]. We demonstrate that VICRegL strongly improves on segmentation results over VICReg while preserving the classification performance, and is competitive with other local and global self-supervised learning methods. We choose the linear evaluation with frozen weights as our main evaluation metrics, as we believe it is a much better way of evaluating the learned representations. Indeed, the performance can not be attributed to the use of a complex segmentation head, or to the availability of the ground truth masks, and contrary to the frozen setting, the fine-tuning setting measures whether the relevant information is present in the representation, but does not measure if the information is easily extractable from it. We perform the linear evaluation using the protocol introduced by [Zhou et al., 2022a], where the learned feature maps are fed to a linear classifier that outputs a vector with the same size as the number of target classes in the dataset, and is then upsampled to the resolution of the image to produce the predicted mask. The results are averaged over 3 runs with randomly initialized parameters and we found that the difference in performance between worse and best runs is always lower than $0 . 2 \\%$ . ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c6fc33382d61a1b21918bf06a2351504aaa07191adb334271f96b811a366ec92.jpg", + "table_caption": [ + "Table 2: Comparison of various global and local self-supervised learning methods on different linear evaluation benchmarks. Evaluation of the features learned from ConvNeXt and ViT backbones trained with different methods on: (1) linear classification accuracy $( \\% )$ (frozen) on the validation set of ImageNet (2) Linear segmentation (mIoU) (frozen and fine-tuning) on Pascal VOC, (3) Linear segmentation (mIoU) (frozen) on ADE20k. $\\alpha$ is the weight of Eq. (4) balancing the importance given to the global criterion, compared to the local criterion. The best result for each benchmark is bold font. $\\dagger$ denotes pretraining on ImageNet-22k. " + ], + "table_footnote": [], + "table_body": "
Linear Cls. (%)Linear Seg. (mloU)
MethodBackbone ParamsEpochsImageNet FrozenPascal VOC FrozenFTADE20k Frozen
Global features
MoCo v3 [Chen et al., 2021]ViT-S21M30073.257.175.923.7
DINO [Caron et al., 2021]ViT-S21M40077.065.279.530.5
IBOT[Zhou et al., 2022a]ViT-S21M40077.968.279.933.2
VICReg [Bardes et al., 2022]CNX-S50M40076.260.177.828.6
MoCo v3ViT-B85M30076.764.878.928.7
DINOViT-B85M40078.270.182.034.5
IBOT [Zhou et al., 2022a]ViT-B85M40079.573.082.438.3
MAE [He et al., 2022]ViT-B85M40068.059.682.427.0
VICRegCNX-B85M40077.667.281.132.7
Local features
CP² [Wang et al., 2022]ViT-S21M32062.863.579.625.3
Ours
VICRegL α = 0.9CNX-S50M40075.966.780.030.8
VICRegL α = 0.75CNX-S50M40074.667.580.631.2
VICRegL α = 0.9CNX-B85M40077.169.381.233.5
VICRegL α = 0.75CNX-B85M40076.370.482.535.3
VICRegL α = 0.75+ CNX-XL350M15079.478.784.143.2
", + "bbox": [ + 189, + 200, + 802, + 497 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 522, + 825, + 675 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1 Comparison with prior work ", + "text_level": 1, + "bbox": [ + 176, + 693, + 413, + 707 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ResNet-50 backbone. Table 1 presents our results against several other global and local selfsupervised learning methods, all pretrained with a ResNet-50 backbone [He et al., 2016]. The main observation we make is the improvement of VICRegL over VICReg on linear segmentation. On Pascal VOC, when the weights of the backbone are frozen, VICRegL $\\alpha = 0 . 9$ improves by $+ 6 . 2$ mIoU while only loosing $0 . 3 \\%$ classification accuracy, and VICRegL $\\alpha = 0 . 7 5$ improves by $\\mathbf { + 8 . 1 }$ mIoU. On fine-tuning the improvement is less significative, which we attribute to the non-informative nature of fine-tuning benchmarks. Indeed, some methods like InsLoc and $\\mathrm { C P ^ { 2 } }$ that seem competitive on fine-tuning significantly underperform in the frozen regime, which shows that the actual performance of these methods can be attributed to the fact that the weights of the backbone benefit form the availability of the labels during the fine-tuning phase. On Cityscapes, which is much harder, most methods do not perform very well in the linear frozen regime, which sets a new challenge for selfsupervised learning of local features. VICRegL outperforms the VICReg baseline by ${ + 1 . 7 }$ mIoU, as well as every other local features methods by a significant margin. The second observation we make is the robustness of VICRegL in classification, which indicates that it learns both local and global features at the same time. The performance of most local methods is greatly impacted on classification where they all perform around 10 to $20 \\%$ below global methods. Global methods on the contrary are efficient for classification but underperform in segmentation compared to VICRegL. ", + "bbox": [ + 173, + 718, + 825, + 911 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b27d297dccbb3e53bb7dc837d75a74a2dfbedc5ed13a2978a8a5752c500cd92a.jpg", + "image_caption": [ + "Figure 2: Study of the trade-off between local and global criteria. Evaluation on linear classification on ImageNet and on linear Segmentation on Pascal VOC of VICRegL pretrained with various $\\alpha$ coefficients of Eq. (4), controlling the importance of the global criterion against the local criterion. " + ], + "image_footnote": [], + "bbox": [ + 181, + 99, + 491, + 276 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1e58d41a7fd33898268373339ea4b9dbbd52d3d1fe7cdfe39835a0d762250bcb.jpg", + "table_caption": [ + "Table 3: Ablation: matching criterion. Comparison between using the feature-based matching loss $( \\mathcal { L } _ { d } )$ , the location-based matching loss $( \\mathcal { L } _ { s } )$ none of the two (Baseline), or both at the same time. " + ], + "table_footnote": [], + "table_body": "
MethodCls. (%)Seg. (mIoU)
Baseline73.856.0
Ls73.558.9
Ld73.657.7
Ls-Ld73.660.3
", + "bbox": [ + 222, + 462, + 441, + 540 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6852a7b2a0ccd830c64b94fcc62b87381c43a2bc1a13d57f9be9426d2a5722fe.jpg", + "image_caption": [ + "Figure 3: Selected matches: visualization of the locations of the best local matches selected by VICRegL. Left image is the seed image, with in red and blue the crop locations for the two views. Left column are the feature-based matches. Right column are the location-based matches. Only 10 matches are visualized for better clarity, but the actual number of selected matches is 20. We display the matches according to the location of the feature vectors in the feature maps. Note that the receptive field of these feature vectors is much larger than only the patch represented by one square of the grid in the figure. Best viewed in color with zoom. " + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 821, + 337 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 176, + 571, + 825, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ConvNeXt backbone. Table 2 presents our results when pretraining with ConvNeXts backbones against several other global and local self-supervised learning methods pretrained with vision transformers [Dosovitskiy et al., 2021]. Similar to our experiments with a ResNet-50 backbone, the main observation we make is the improvement on segmentation tasks provided by the introduction of the local criterion. With a ConvNeXt-S backbone, in the linear frozen regime, VICRegL $\\alpha = 0 . 9$ improves over VICReg by $+ 6 . 6$ mIoU on the Pascal VOC, and by $+ 2 . 2$ mIoU on the ADE20K, while preserving most of the classification accuracy. VICRegL $\\alpha = 0 . 7 5$ further improves by $\\mathbf { + 7 . 4 }$ mIoU and $\\mathbf { + 3 . 6 }$ over VICReg on these two benchmarks respectively. With a ConvNeXt-B backbone, the performance improvement remain consistent over VICReg, and VICRegL $\\alpha = 0 . 7 5$ is competitive with other strong methods such as DINO and IBOT. The improvement also remain consistent in linear fine-tuning where VICRegL also achieves a strong performance. Finally, we report the performance of a much larger ConvNeXt-XL backbone, pretrained in ImageNet-22k, which is significantly improved on segmentation tasks and set a new state-of-the art in linear segmentation. Our results highlight the trade-off between classification and segmentation performance, which can be controlled by the weight given to the local criterion. ", + "bbox": [ + 174, + 619, + 825, + 827 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2 Ablations ", + "text_level": 1, + "bbox": [ + 174, + 843, + 279, + 858 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For all the experiments done in this section, unless specified otherwise, we pretrain a ConvNeXt-S on ImageNet over 100 epochs, with the hyper-parameters described in Section 3.3, and report both the linear classification accuracy on ImageNet, and the linear frozen segmentation mIoU on Pascal VOC. ", + "bbox": [ + 176, + 869, + 825, + 911 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/409848c646a89deb8fa54431ca4712e19c7b61851245a711e8335be4e6a1605c.jpg", + "table_caption": [ + "Table 4: Ablation: SSL criterion. Introducing our local criterion with VICReg gives a stronger improvement compared to SimCLR, which is contrastive. (ResNet-50, 300 epochs) " + ], + "table_footnote": [], + "table_body": "
MethodCls. (%)Seg. (mIoU)
VICReg71.147.8
VICRegL70.4 55.9
SimCLR67.545.9
SimCLR-L66.651.3
", + "bbox": [ + 230, + 159, + 429, + 227 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/706e5a44fdde824daafe5b3d117b9934634d0bdeb103bd669872e36190c9d9b7.jpg", + "table_caption": [ + "Table 5: Ablation: impact of multi-crop. Introducing our local criterion yields an improved performance with or without the usage of multicrop. " + ], + "table_footnote": [], + "table_body": "
MethodMulti-cropCls. (%)Seg. (mIoU)
VICReg70.152.9
VICRegL69.957.8
VICReg√73.954.4
VICRegL√73.660.3
", + "bbox": [ + 531, + 159, + 787, + 227 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/046625e3f141d75d864af03611b553837aa9ff9f8816060d2f65a499c608d96c.jpg", + "table_caption": [ + "Table 6: Ablation: number of selected matches. The large feature maps are of size $7 \\times 7$ and the small ones are of size $3 \\times 3$ . There are therefore a total number of 49 large and 9 small feature vectors and as many possible matches, and only the top- $\\gamma _ { 1 }$ large and top- $\\gamma _ { 2 }$ small are kept. " + ], + "table_footnote": [], + "table_body": "
Y1γ2Cls. (%)Seg. (mIoU)
10273.459.2
20473.660.3
49973.559.6
", + "bbox": [ + 236, + 332, + 423, + 388 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/0e249ecaa4c8fd8ebece63953f3b73ae580e04deab1399d13b01e1993b3a2283.jpg", + "table_caption": [ + "Table 7: Ablation: VICReg local criterion. The collapse problem is automatically prevented with the global criterion. We study here how regularizing the local feature vectors influence the performance. V: variance criterion is used, I: invariance criterion is used, C: covariance criterion is used. " + ], + "table_footnote": [], + "table_body": "
CriterionCls. (%)Seg. (mIoU)
I73.459.0
VI73.358.2
VIC73.660.3
", + "bbox": [ + 563, + 330, + 751, + 388 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Trade-off between the local and global criterion. The parameter $\\alpha$ of Eq. (4) controls the importance that is given to the global criterion, compared to the local criterion. Figure 2 shows that there exists a fundamental trade-off between the ability of a model to learn global visual features, as opposed to learning local features. In the case $\\alpha = 1 . 0$ , which is simply VICReg, the model is very efficient at producing global representations of the image, as demonstrated by the performance of $7 3 . 9 \\%$ in classification accuracy. When $\\alpha < 1$ , which introduces the local criterion, the performance in segmentation is greatly increased, by $+ 3 . 4$ mIoU when $\\alpha = 0 . 9$ , $\\pm 4 . 3$ mIoU when $\\alpha = 0 . 7 5$ and $+ 4 . 6$ mIoU when the local and global criteria are weighted equally. At the same time, the classification accuracy only drops by respectively $0 . 2 \\%$ , $1 . 2 \\%$ and $2 . 9 \\%$ . This highlights the existence of a sweet spot, where the model is strongly performing at both classification and segmentation, which indicates that it has learned both meaningful local and global features. When $\\alpha$ decreases too much, the model starts to lose its performance in both tasks, which shows that having a global understanding of the image is necessary, even for localized tasks. ", + "bbox": [ + 174, + 407, + 825, + 588 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Study of the importance between feature-based and location-based local criteria. VICRegL matches feature vectors according to a location-based criterion $\\mathcal { L } _ { s }$ of Eq. (2) and a feature-based criterion $\\mathcal { L } _ { d }$ of Eq. (3). Table 3 study the importance of these criterion. Baseline in the table means that no local criterion is used, and is simply VICReg. The location-based criterion gives the best improvement by $\\mathbf { + 2 . 9 }$ mIoU over the baseline, compared to only ${ + 1 . 7 }$ mIoU for the feature-based criterion, but it is the combination of the two that significantly improves over the baseline by $\\mathbf { + 4 . 3 }$ mIoU, which shows that using both the learned distance in the embedding space in combination with the actual distance in the pixel space produces local features with the best quality. In all cases, the classification accuracy is not affected, which is expected as the local criterion has little effect on the quality of the global features, and therefore on the downstream classification accuracy. ", + "bbox": [ + 173, + 593, + 825, + 732 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Study of the number of matches. We study here the influence of changing the number of selected best matches $\\gamma _ { 1 }$ and $\\gamma _ { 2 }$ of Eq. (5), to keep for the computation of the local losses. For our experiments with multi-crop, the size of the feature maps is $( 2 0 4 8 \\times 7 \\times 7 )$ for the large crops and $( 2 0 4 8 \\times 3 \\times 3 )$ for the small crops. There are therefore in one branch of the siamese architecture 49 feature maps for large crops, and 9 for small crops. Tables 6 shows that there is a trade-off between keeping all the matches $\\gamma _ { 1 } = 4 9$ and $\\gamma _ { 2 } = 9$ ), and keeping a small number of matches $\\gamma _ { 1 } = 1 0$ and $\\gamma _ { 2 } = 2 \\quad ,$ ), and that the best segmentation performance is obtained with an in-between number of matches, $\\gamma _ { 1 } = 2 0$ and $\\gamma _ { 2 } = 4$ ), which improves by $\\mathbf { + 0 . 7 \\ m I o U }$ compared to keeping all the matches. Similar to the study on the influence of the local losses, the classification accuracy is not affected, as the local criterion does not improve or degrade the global features. ", + "bbox": [ + 173, + 738, + 825, + 877 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Study of VICReg components for the local criterion. The global criterion is sufficient for the vectors to not collapse to trivial solutions. We therefore investigate if introducing the variance (V) and covariance (C) criterion, in addition to the invariance (I) criterion, applied by the local loss functions on the feature vectors, is useful or not. Table 7 shows that these regularization criteria are actually helping the performance, introducing the variance criterion improves on segmentation by $\\mathbf { + 0 . 8 \\ m I o U }$ , and additionally adding the covariance criterion further improves the performance by $\\mathbf { + 1 . 3 }$ mIoU over the baseline. Similar to other ablations on the local loss functions, the classification accuracy is not significantly impacted. ", + "bbox": [ + 174, + 883, + 821, + 911 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 825, + 174 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Study of a different collapse prevention method. Our collapse-prevention mechanism is the variance and covariance regularization of VICReg, which is a non-contrastive criterion that therefore does not contrast negatively on potential positive matchings. We study however the incorporation of our local criterion with a contrastive criterion, SimCLR [Chen et al., 2020a]. We simply replace VICReg by SimCLR in Eq. (2) and Eq. (3) and refer this new method as SimCLR-L. Table 4 reports the performance, and we observe that although there is a gap in performance between regular SimCLR and VICReg, the additional benefit provided by the local criterion is much stronger with VICReg. ", + "bbox": [ + 173, + 181, + 825, + 279 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Impact of multi-crop. We study the impact of using the multi-crop strategy for the data augmentation, by comparing VICReg to VICRegL. Table 5 reports our results. Whether multi-crop is used or not, introducing the local criterion always improve significantly the segmentation results, while preserving again most of the classification performance. ", + "bbox": [ + 174, + 284, + 825, + 339 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "4.3 Visualization ", + "text_level": 1, + "bbox": [ + 174, + 356, + 303, + 371 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We provide in Figure 3, a visualization of the pairs of matched feature vectors selected by VICRegL. Right to the seed image, the left column shows the feature-based matches, and the right column shows the location-based matches. Each case in the the grid represents a position in the feature map, and a match between two feature vectors is represented by a yellow line. The receptive field of these feature vectors is larger than a single case in the grid, and actually spans the entire image, but we observe that the embedding space is shaped such that the feature-based matching is coherent regarding the semantic content at a position in the image where a feature vector is pooled. A feature vector that is located at a position corresponding to a texture representing \"sky\" or \"grass\" in one view is matched to another one on the other view located at a position corresponding to a similar \"sky\" or \"grass\" texture. Additional visualizations are available in Appendix ??. ", + "bbox": [ + 174, + 381, + 825, + 520 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5 Conclusion ", + "text_level": 1, + "bbox": [ + 174, + 539, + 299, + 556 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In this work, we introduced VICRegL, a method for learning both local and global visual features at the same time, by matching feature vectors with respect to their distance in the pixel space and in the embedding space. We show that introducing a local criterion significantly improves the performance on segmentation tasks, while preserving the classification accuracy. We also demonstrate that convolutional networks are competitive to vision transformers in self-supervised learning, by using the ConvNeXt backbone. ", + "bbox": [ + 174, + 570, + 825, + 654 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Limitations and Future work. Convolutional neural networks by design produce feature maps that have a receptive field that covers the entire image. It is not clear to which extent a feature vector at a given position in the feature maps actually contains mainly information about the objects located at the corresponding location in the input image. The learned tokens of a vision transformers are also good candidates for local features, and a detailed study of the actual local nature of both the feature vectors of a convolutional network and the tokens of a vision transformer, would provide useful insights for future directions of self-supervised learning of local features. Future work will also tackle the problem of learning hierarchical features, by applying a criterion not only at a local and a global scale, but also at multiple levels in the encoder network. ", + "bbox": [ + 174, + 660, + 825, + 785 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Acknowledgement. Jean Ponce was supported in part by the French government under management of Agence Nationale de la Recherche as part of the ”Investissements d’avenir” program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), the Louis Vuitton/ENS Chair in Artificial Intelligence and the Inria/NYU collaboration. Adrien Bardes was supported in part by a FAIR/Prairie CIFRE PhD Fellowship. The authors wish to thank Li Jing, Randall Balestriero, Amir Bar, Grégoire Mialon, Jiachen Zhu, Quentin Garrido, Florian Bordes, Bobak Kiani, Surya Ganguli, Megi Dervichi, Yubei Chen, Mido Assran, Nicolas Ballas and Pascal Vincent for useful discussions. ", + "bbox": [ + 174, + 791, + 825, + 888 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "References ", + "text_level": 1, + "bbox": [ + 174, + 90, + 267, + 106 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "A. Bardes, J. Ponce, and Y. LeCun. Vicreg: Variance-invariance-covariance regularization for self-supervised learning. 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We demonstrate strong performance on linear classification and", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 452, + 471, + 467 + ], + "spans": [ + { + "bbox": [ + 141, + 452, + 471, + 467 + ], + "score": 1.0, + "content": "segmentation transfer tasks. 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Current approaches rely on a joint embedding architecture and a loss function", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 580, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 505, + 593 + ], + "score": 1.0, + "content": "that forces the learned features to be invariant to a sampling process selecting pairs of different views", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 590, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 506, + 604 + ], + "score": 1.0, + "content": "of the same image, obtained by transformation such as cropping, rescaling, or color jittering [Misra", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "score": 1.0, + "content": "and Maaten, 2020, Chen et al., 2020a, He et al., 2020, Grill et al., 2020]. These methods learn", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "score": 1.0, + "content": "to eliminate the irrelevant part of position and color information, in order to satisfy the invariance", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 623, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 505, + 636 + ], + "score": 1.0, + "content": "criterion, and perform well on image classification benchmarks. Some recent approaches go beyond", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 635, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 647 + ], + "score": 1.0, + "content": "learning global features: to tackle tasks such as semantic segmentation where spatial information", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 506, + 658 + ], + "score": 1.0, + "content": "plays a key role, [Yang et al., 2021, Xie et al., 2021, Hénaff et al., 2021, Yang et al., 2022, Hénaff", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 655, + 505, + 670 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 670 + ], + "score": 1.0, + "content": "et al., 2022, El-Nouby et al., 2022] also learn image models with more emphasis on local image", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "structure. 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The best", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 700, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 505, + 713 + ], + "score": 1.0, + "content": "performing local methods require a non-parametric pre-processing step that compute unsupervised", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 72, + 506, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 506, + 85 + ], + "score": 1.0, + "content": "segmentation masks [Hénaff et al., 2021], which can be done online [Hénaff et al., 2022], but with an", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 84, + 240, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 240, + 95 + ], + "score": 1.0, + "content": "additional computational burden.", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 526, + 506, + 713 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 504, + 95 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 506, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 506, + 85 + ], + "score": 1.0, + "content": "segmentation masks [Hénaff et al., 2021], which can be done online [Hénaff et al., 2022], but with an", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 84, + 240, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 240, + 95 + ], + "score": 1.0, + "content": "additional computational burden.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 105, + 98, + 505, + 114 + ], + "spans": [ + { + "bbox": [ + 105, + 98, + 505, + 114 + ], + "score": 1.0, + "content": "We argue that more complex reasoning systems should be structured in a hierarchical way, by learning", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 110, + 507, + 124 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 507, + 124 + ], + "score": 1.0, + "content": "at several scales. To this end, we propose VICRegL, a method that learn features at a global scale,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 121, + 506, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 506, + 135 + ], + "score": 1.0, + "content": "and that additionally uses spatial information, and matches feature vectors that are either pooled from", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 131, + 505, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 505, + 146 + ], + "score": 1.0, + "content": "close-by regions in the original input image, or close in the embedding space, therefore learning", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 143, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 506, + 156 + ], + "score": 1.0, + "content": "features at a local scale. In practice, the global VICReg criterion [Bardes et al., 2022] is applied", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 155, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 506, + 167 + ], + "score": 1.0, + "content": "to pairs of feature vectors, before and after the final pooling layer of a convolutional network, thus", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "learning local and global features at the same time. When a segmentation mask is available as", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 177, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 177, + 506, + 189 + ], + "score": 1.0, + "content": "in [Hénaff et al., 2021], feature vectors that correspond to the same region in the mask can be pooled", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "together, and compared using a contrastive loss function, which allows spatial vectors far away in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "the original image to be pooled together if they belong to the same object. In our case, segmentation", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "masks are not available, and we therefore face two challenges: (1) there is no a priori information on", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 220, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 233 + ], + "score": 1.0, + "content": "how to pool vectors from the same object together, thus long-range matching should be learned in", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 230, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 104, + 230, + 505, + 245 + ], + "score": 1.0, + "content": "a self-supervised manner, and (2) contrasting negatively feature vectors corresponding to far away", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "score": 1.0, + "content": "locations can have a negative effect, as these vectors could have been pooled from locations that", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 253, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 506, + 265 + ], + "score": 1.0, + "content": "represent the same object in the image. In order to address these issues, VICRegL (1) matches feature", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 263, + 506, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 198, + 276 + ], + "score": 1.0, + "content": "vectors according to a", + "type": "text" + }, + { + "bbox": [ + 198, + 263, + 207, + 273 + ], + "score": 0.84, + "content": "l ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 263, + 506, + 276 + ], + "score": 1.0, + "content": "nearest-neighbor criterion exploiting both the distances between features", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 275, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 506, + 287 + ], + "score": 1.0, + "content": "and image locations, properly weighted, and (2) uses the VICReg criterion between matched feature", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "vectors. We use VICReg for its simplicity and its non-contrastive nature, which alleviates the need", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 297, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 505, + 309 + ], + "score": 1.0, + "content": "for negative samples and therefore does not have an explicit negative contrasting effect between", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 307, + 327, + 319 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 327, + 319 + ], + "score": 1.0, + "content": "feature vectors that could have been potential matches.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 11.5 + }, + { + "type": "text", + "bbox": [ + 107, + 324, + 505, + 444 + ], + "lines": [ + { + "bbox": [ + 105, + 324, + 504, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 504, + 336 + ], + "score": 1.0, + "content": "We demonstrate the effectiveness of VICRegL by evaluating the learned representations on vision", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "tasks such as image classification on ImageNet and semantic segmentation on various datasets. Our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 346, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 346, + 504, + 357 + ], + "score": 1.0, + "content": "evaluation is (mostly) done in the setting where the backbone learned by VICRegL is frozen, with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "only a linear classification or segmentation head tuned to the task at hand. We believe that this", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 367, + 504, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 504, + 379 + ], + "score": 1.0, + "content": "setting is a much better evaluation metric than the commonly used fine-tuning benchmarks, as the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 379, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 506, + 391 + ], + "score": 1.0, + "content": "performance can not be attributed to the use of a complex head, or to the availability of the ground", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "score": 1.0, + "content": "truth masks. Our results show that learning local features, in addition to global features, does not hurt", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "score": 1.0, + "content": "the classification performance, but significantly improves segmentation accuracy. On the Pascal VOC", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "linear frozen semantic segmentation task, VICRegL achieves 55.9 mIoU with a ResNet-50 backbone,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 422, + 507, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 150, + 435 + ], + "score": 1.0, + "content": "which is a", + "type": "text" + }, + { + "bbox": [ + 150, + 422, + 171, + 432 + ], + "score": 0.82, + "content": "{ \\bf + 8 . 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 422, + 507, + 435 + ], + "score": 1.0, + "content": "mIoU improvement over VICReg, and 67.5 mIoU with a ConvNeXt-S backbone,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 433, + 253, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 149, + 445 + ], + "score": 1.0, + "content": "which is a", + "type": "text" + }, + { + "bbox": [ + 149, + 433, + 169, + 444 + ], + "score": 0.79, + "content": "+ 6 . 6", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 434, + 253, + 445 + ], + "score": 1.0, + "content": "mIoU improvement.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27 + }, + { + "type": "title", + "bbox": [ + 107, + 461, + 194, + 474 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 196, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 196, + 476 + ], + "score": 1.0, + "content": "2 Related work", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 487, + 505, + 618 + ], + "lines": [ + { + "bbox": [ + 106, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "Global features. Most recent methods for global feature learning are based on a joint embedding", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "score": 1.0, + "content": "architecture that learns representations that are invariant to various views. These methods differ", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 509, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 505, + 520 + ], + "score": 1.0, + "content": "in the way collapsing solutions are avoided. Contrastive methods [Hjelm et al., 2019, Chen et al.,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "score": 1.0, + "content": "2020a, He et al., 2020, Chen et al., 2020b, Mitrovic et al., 2021, Dwibedi et al., 2021, Chen et al.,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 530, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 506, + 543 + ], + "score": 1.0, + "content": "2021, Tomasev et al., 2022] uses negative samples to push dissimilar samples apart from each other.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 542, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 553 + ], + "score": 1.0, + "content": "Clustering methods [Caron et al., 2018, 2020, 2021] ensure a balanced partition of the samples within", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 553, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 505, + 564 + ], + "score": 1.0, + "content": "a set of clusters. Non-contrastive methods, which are dual to contrastive ones [Garrido et al., 2022],", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "rely on maintaining the informational content of the representations by either explicit regularization", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "score": 1.0, + "content": "[Zbontar et al., 2021, Bardes et al., 2022] or architectural design [Chen and He, 2020, Grill et al.,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "score": 1.0, + "content": "2020, Richemond et al., 2020, Lee et al., 2021]. Finally, the best performing methods today are based", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 596, + 504, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 504, + 607 + ], + "score": 1.0, + "content": "on vision transformers [Caron et al., 2021, Chen et al., 2021, Li et al., 2022, Zhou et al., 2022a,b] and", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 607, + 425, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 425, + 619 + ], + "score": 1.0, + "content": "deliver strong results in both downstream classification and segmentation tasks.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 39.5 + }, + { + "type": "text", + "bbox": [ + 107, + 623, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 623, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 505, + 635 + ], + "score": 1.0, + "content": "Local features. In opposition to global methods, local one focus on explicitly learning a set of local", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 635, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 505, + 646 + ], + "score": 1.0, + "content": "features that describe small parts of the image, which global methods do implicitly [Chen et al.,", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 644, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 658 + ], + "score": 1.0, + "content": "2022], and are therefore better suited for segmentation tasks. Indeed these methods commonly only", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 655, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 668 + ], + "score": 1.0, + "content": "evaluate on segmentation benchmarks. A contrastive loss function can be applied directly: (1) at the", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "pixel level [Xie et al., 2021], which forces consistency between pixels at similar locations; (2) at the", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "feature map level [Wang et al., 2021], which forces consistency between groups of pixels: (3) at the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 688, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 702 + ], + "score": 1.0, + "content": "image region level [Xiao et al., 2021], which forces consistency between large regions that overlap in", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "different views of an image. Similar to [Wang et al., 2021], our method VICRegL operates at the", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "score": 1.0, + "content": "feature map level but with a more advanced matching criterion that takes into account the distance in", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 50 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 741, + 310, + 753 + ], + "spans": [ + { + "bbox": [ + 301, + 741, + 310, + 753 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 504, + 95 + ], + "lines": [], + "index": 0.5, + "bbox_fs": [ + 105, + 72, + 506, + 95 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 105, + 98, + 505, + 114 + ], + "spans": [ + { + "bbox": [ + 105, + 98, + 505, + 114 + ], + "score": 1.0, + "content": "We argue that more complex reasoning systems should be structured in a hierarchical way, by learning", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 110, + 507, + 124 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 507, + 124 + ], + "score": 1.0, + "content": "at several scales. To this end, we propose VICRegL, a method that learn features at a global scale,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 121, + 506, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 506, + 135 + ], + "score": 1.0, + "content": "and that additionally uses spatial information, and matches feature vectors that are either pooled from", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 131, + 505, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 505, + 146 + ], + "score": 1.0, + "content": "close-by regions in the original input image, or close in the embedding space, therefore learning", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 143, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 506, + 156 + ], + "score": 1.0, + "content": "features at a local scale. In practice, the global VICReg criterion [Bardes et al., 2022] is applied", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 155, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 506, + 167 + ], + "score": 1.0, + "content": "to pairs of feature vectors, before and after the final pooling layer of a convolutional network, thus", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "learning local and global features at the same time. When a segmentation mask is available as", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 177, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 177, + 506, + 189 + ], + "score": 1.0, + "content": "in [Hénaff et al., 2021], feature vectors that correspond to the same region in the mask can be pooled", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "together, and compared using a contrastive loss function, which allows spatial vectors far away in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "the original image to be pooled together if they belong to the same object. In our case, segmentation", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "masks are not available, and we therefore face two challenges: (1) there is no a priori information on", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 220, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 233 + ], + "score": 1.0, + "content": "how to pool vectors from the same object together, thus long-range matching should be learned in", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 230, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 104, + 230, + 505, + 245 + ], + "score": 1.0, + "content": "a self-supervised manner, and (2) contrasting negatively feature vectors corresponding to far away", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 254 + ], + "score": 1.0, + "content": "locations can have a negative effect, as these vectors could have been pooled from locations that", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 253, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 506, + 265 + ], + "score": 1.0, + "content": "represent the same object in the image. In order to address these issues, VICRegL (1) matches feature", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 263, + 506, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 198, + 276 + ], + "score": 1.0, + "content": "vectors according to a", + "type": "text" + }, + { + "bbox": [ + 198, + 263, + 207, + 273 + ], + "score": 0.84, + "content": "l ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 263, + 506, + 276 + ], + "score": 1.0, + "content": "nearest-neighbor criterion exploiting both the distances between features", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 275, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 506, + 287 + ], + "score": 1.0, + "content": "and image locations, properly weighted, and (2) uses the VICReg criterion between matched feature", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "vectors. We use VICReg for its simplicity and its non-contrastive nature, which alleviates the need", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 297, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 505, + 309 + ], + "score": 1.0, + "content": "for negative samples and therefore does not have an explicit negative contrasting effect between", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 307, + 327, + 319 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 327, + 319 + ], + "score": 1.0, + "content": "feature vectors that could have been potential matches.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 11.5, + "bbox_fs": [ + 104, + 98, + 507, + 319 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 324, + 505, + 444 + ], + "lines": [ + { + "bbox": [ + 105, + 324, + 504, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 504, + 336 + ], + "score": 1.0, + "content": "We demonstrate the effectiveness of VICRegL by evaluating the learned representations on vision", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "tasks such as image classification on ImageNet and semantic segmentation on various datasets. Our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 346, + 504, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 346, + 504, + 357 + ], + "score": 1.0, + "content": "evaluation is (mostly) done in the setting where the backbone learned by VICRegL is frozen, with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "only a linear classification or segmentation head tuned to the task at hand. We believe that this", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 367, + 504, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 504, + 379 + ], + "score": 1.0, + "content": "setting is a much better evaluation metric than the commonly used fine-tuning benchmarks, as the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 379, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 506, + 391 + ], + "score": 1.0, + "content": "performance can not be attributed to the use of a complex head, or to the availability of the ground", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "score": 1.0, + "content": "truth masks. Our results show that learning local features, in addition to global features, does not hurt", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 413 + ], + "score": 1.0, + "content": "the classification performance, but significantly improves segmentation accuracy. On the Pascal VOC", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "linear frozen semantic segmentation task, VICRegL achieves 55.9 mIoU with a ResNet-50 backbone,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 422, + 507, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 150, + 435 + ], + "score": 1.0, + "content": "which is a", + "type": "text" + }, + { + "bbox": [ + 150, + 422, + 171, + 432 + ], + "score": 0.82, + "content": "{ \\bf + 8 . 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 422, + 507, + 435 + ], + "score": 1.0, + "content": "mIoU improvement over VICReg, and 67.5 mIoU with a ConvNeXt-S backbone,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 433, + 253, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 149, + 445 + ], + "score": 1.0, + "content": "which is a", + "type": "text" + }, + { + "bbox": [ + 149, + 433, + 169, + 444 + ], + "score": 0.79, + "content": "+ 6 . 6", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 434, + 253, + 445 + ], + "score": 1.0, + "content": "mIoU improvement.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 324, + 507, + 445 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 461, + 194, + 474 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 196, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 196, + 476 + ], + "score": 1.0, + "content": "2 Related work", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 487, + 505, + 618 + ], + "lines": [ + { + "bbox": [ + 106, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "Global features. Most recent methods for global feature learning are based on a joint embedding", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 505, + 509 + ], + "score": 1.0, + "content": "architecture that learns representations that are invariant to various views. These methods differ", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 509, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 505, + 520 + ], + "score": 1.0, + "content": "in the way collapsing solutions are avoided. Contrastive methods [Hjelm et al., 2019, Chen et al.,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "score": 1.0, + "content": "2020a, He et al., 2020, Chen et al., 2020b, Mitrovic et al., 2021, Dwibedi et al., 2021, Chen et al.,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 530, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 506, + 543 + ], + "score": 1.0, + "content": "2021, Tomasev et al., 2022] uses negative samples to push dissimilar samples apart from each other.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 542, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 553 + ], + "score": 1.0, + "content": "Clustering methods [Caron et al., 2018, 2020, 2021] ensure a balanced partition of the samples within", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 553, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 505, + 564 + ], + "score": 1.0, + "content": "a set of clusters. Non-contrastive methods, which are dual to contrastive ones [Garrido et al., 2022],", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "rely on maintaining the informational content of the representations by either explicit regularization", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "score": 1.0, + "content": "[Zbontar et al., 2021, Bardes et al., 2022] or architectural design [Chen and He, 2020, Grill et al.,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "score": 1.0, + "content": "2020, Richemond et al., 2020, Lee et al., 2021]. Finally, the best performing methods today are based", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 596, + 504, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 504, + 607 + ], + "score": 1.0, + "content": "on vision transformers [Caron et al., 2021, Chen et al., 2021, Li et al., 2022, Zhou et al., 2022a,b] and", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 607, + 425, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 425, + 619 + ], + "score": 1.0, + "content": "deliver strong results in both downstream classification and segmentation tasks.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 486, + 506, + 619 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 623, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 623, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 505, + 635 + ], + "score": 1.0, + "content": "Local features. In opposition to global methods, local one focus on explicitly learning a set of local", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 635, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 505, + 646 + ], + "score": 1.0, + "content": "features that describe small parts of the image, which global methods do implicitly [Chen et al.,", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 644, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 658 + ], + "score": 1.0, + "content": "2022], and are therefore better suited for segmentation tasks. Indeed these methods commonly only", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 655, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 668 + ], + "score": 1.0, + "content": "evaluate on segmentation benchmarks. A contrastive loss function can be applied directly: (1) at the", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "pixel level [Xie et al., 2021], which forces consistency between pixels at similar locations; (2) at the", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "feature map level [Wang et al., 2021], which forces consistency between groups of pixels: (3) at the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 688, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 702 + ], + "score": 1.0, + "content": "image region level [Xiao et al., 2021], which forces consistency between large regions that overlap in", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "different views of an image. Similar to [Wang et al., 2021], our method VICRegL operates at the", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "score": 1.0, + "content": "feature map level but with a more advanced matching criterion that takes into account the distance in", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "score": 1.0, + "content": "pixel space between the objects. Copy pasting a patch on a random background [Yang et al., 2021,", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "score": 1.0, + "content": "Wang et al., 2022] has also shown to be effective for learning to localize an object without relying on", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 94, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 104, + 94, + 506, + 107 + ], + "score": 1.0, + "content": "spurious correlations with the background. Aggregating multiple images corresponding to several", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "object instances into a single image can also help the localization task [Yang et al., 2022]. These", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "score": 1.0, + "content": "approaches rely on carefully and handcrafted constructions of new images with modified background", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 127, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 505, + 138 + ], + "score": 1.0, + "content": "or with aggregation of semantic content from several other images, which is not satisfactory, while", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 136, + 507, + 152 + ], + "spans": [ + { + "bbox": [ + 104, + 136, + 507, + 152 + ], + "score": 1.0, + "content": "our method simply rely on the classical augmentations commonly used in self-supervised learning.", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 148, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 506, + 162 + ], + "score": 1.0, + "content": "The best current approaches consist in using the information from unsupervised segmentation masks,", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "score": 1.0, + "content": "which can be computed as a pre-processing step [Hénaff et al., 2021] or computed online [Hénaff", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "score": 1.0, + "content": "et al., 2022]. The feature vectors coming from the same region in the mask are pooled together", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "score": 1.0, + "content": "and the resulting vectors are contrasted between each other with a contrastive loss function. These", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 191, + 507, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 507, + 207 + ], + "score": 1.0, + "content": "approaches explicitly construct semantic segmentation masks using k-means for every input image,", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 204, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 215 + ], + "score": 1.0, + "content": "which is computationally not efficient, and is a strong inductive bias in the architecture. Our method", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 214, + 406, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 406, + 227 + ], + "score": 1.0, + "content": "does not rely on these masks and therefore learns less specialized features.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + } + ], + "index": 50, + "bbox_fs": [ + 105, + 623, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 72, + 506, + 226 + ], + "lines": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "score": 1.0, + "content": "pixel space between the objects. Copy pasting a patch on a random background [Yang et al., 2021,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "score": 1.0, + "content": "Wang et al., 2022] has also shown to be effective for learning to localize an object without relying on", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 94, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 104, + 94, + 506, + 107 + ], + "score": 1.0, + "content": "spurious correlations with the background. Aggregating multiple images corresponding to several", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "object instances into a single image can also help the localization task [Yang et al., 2022]. These", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "score": 1.0, + "content": "approaches rely on carefully and handcrafted constructions of new images with modified background", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 127, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 505, + 138 + ], + "score": 1.0, + "content": "or with aggregation of semantic content from several other images, which is not satisfactory, while", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 136, + 507, + 152 + ], + "spans": [ + { + "bbox": [ + 104, + 136, + 507, + 152 + ], + "score": 1.0, + "content": "our method simply rely on the classical augmentations commonly used in self-supervised learning.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 148, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 506, + 162 + ], + "score": 1.0, + "content": "The best current approaches consist in using the information from unsupervised segmentation masks,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 173 + ], + "score": 1.0, + "content": "which can be computed as a pre-processing step [Hénaff et al., 2021] or computed online [Hénaff", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "score": 1.0, + "content": "et al., 2022]. The feature vectors coming from the same region in the mask are pooled together", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "score": 1.0, + "content": "and the resulting vectors are contrasted between each other with a contrastive loss function. These", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 191, + 507, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 507, + 207 + ], + "score": 1.0, + "content": "approaches explicitly construct semantic segmentation masks using k-means for every input image,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 204, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 215 + ], + "score": 1.0, + "content": "which is computationally not efficient, and is a strong inductive bias in the architecture. Our method", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 214, + 406, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 406, + 227 + ], + "score": 1.0, + "content": "does not rely on these masks and therefore learns less specialized features.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 6.5 + }, + { + "type": "title", + "bbox": [ + 107, + 241, + 166, + 255 + ], + "lines": [ + { + "bbox": [ + 104, + 240, + 168, + 257 + ], + "spans": [ + { + "bbox": [ + 104, + 240, + 168, + 257 + ], + "score": 1.0, + "content": "3 Method", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 106, + 266, + 505, + 355 + ], + "lines": [ + { + "bbox": [ + 105, + 266, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 280 + ], + "score": 1.0, + "content": "Background. VICReg was introduced as a self-supervised method for learning image representations", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "score": 1.0, + "content": "that avoid the collapse problem by design. 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We denote", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 107, + 562, + 506, + 577 + ], + "spans": [ + { + "bbox": [ + 107, + 565, + 122, + 576 + ], + "score": 0.83, + "content": "y _ { i , j }", + "type": "inline_equation" + }, + { + "bbox": [ + 122, + 562, + 139, + 577 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 140, + 563, + 181, + 577 + ], + "score": 0.93, + "content": "y _ { i , j } ^ { \\prime } \\in \\mathbb { R } ^ { C }", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 562, + 299, + 577 + ], + "score": 1.0, + "content": "the feature vectors at position", + "type": "text" + }, + { + "bbox": [ + 300, + 563, + 320, + 576 + ], + "score": 0.92, + "content": "( i , j )", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 562, + 506, + 577 + ], + "score": 1.0, + "content": "in their corresponding feature maps. The main", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 575, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 404, + 588 + ], + "score": 1.0, + "content": "idea is to apply the VICReg criterion between pairs of feature vectors from", + "type": "text" + }, + { + "bbox": [ + 404, + 577, + 411, + 587 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 575, + 428, + 588 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 429, + 576, + 438, + 587 + ], + "score": 0.87, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 575, + 505, + 588 + ], + "score": 1.0, + "content": ", by matching an", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 586, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 152, + 599 + ], + "score": 1.0, + "content": "element of", + "type": "text" + }, + { + "bbox": [ + 152, + 588, + 159, + 599 + ], + "score": 0.82, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 586, + 210, + 599 + ], + "score": 1.0, + "content": "to one from", + "type": "text" + }, + { + "bbox": [ + 210, + 587, + 218, + 598 + ], + "score": 0.82, + "content": "y ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 586, + 293, + 599 + ], + "score": 1.0, + "content": ", using spatial and", + "type": "text" + }, + { + "bbox": [ + 294, + 587, + 302, + 596 + ], + "score": 0.85, + "content": "l ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 586, + 506, + 599 + ], + "score": 1.0, + "content": "-distance based information. We introduce a local", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 103, + 593, + 503, + 613 + ], + "spans": [ + { + "bbox": [ + 103, + 593, + 178, + 613 + ], + "score": 1.0, + "content": "projector network", + "type": "text" + }, + { + "bbox": [ + 179, + 597, + 299, + 612 + ], + "score": 0.88, + "content": "h _ { \\phi } ^ { l } : \\mathbb { R } ^ { \\tilde { C } \\times H \\times W } \\to \\mathbb { R } ^ { D \\times H \\times W }", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 593, + 415, + 613 + ], + "score": 1.0, + "content": ", that embed the feature maps", + "type": "text" + }, + { + "bbox": [ + 416, + 599, + 423, + 609 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 423, + 593, + 440, + 613 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 441, + 597, + 503, + 609 + ], + "score": 0.91, + "content": "y ^ { \\prime } \\in \\mathbb { R } ^ { C \\times H \\times W }", + "type": "inline_equation" + } + ], + "index": 41 + }, + { + "bbox": [ + 103, + 608, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 103, + 608, + 234, + 626 + ], + "score": 1.0, + "content": "onto feature maps embeddings", + "type": "text" + }, + { + "bbox": [ + 235, + 610, + 279, + 625 + ], + "score": 0.92, + "content": "z = h _ { \\phi } ^ { l } ( y )", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 608, + 298, + 626 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 299, + 610, + 405, + 625 + ], + "score": 0.93, + "content": "z ^ { \\prime } = h _ { \\phi } ^ { l } ( y ^ { \\prime } ) \\in \\mathbb { R } ^ { D \\times H \\times W }", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 608, + 506, + 626 + ], + "score": 1.0, + "content": ". The standard expander", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 622, + 504, + 641 + ], + "spans": [ + { + "bbox": [ + 104, + 622, + 263, + 641 + ], + "score": 1.0, + "content": "of VICReg is now the global expander", + "type": "text" + }, + { + "bbox": [ + 264, + 624, + 328, + 638 + ], + "score": 0.9, + "content": "h _ { \\psi } ^ { g } : \\mathbb { R } ^ { C } \\mathbb { R } ^ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 622, + 491, + 641 + ], + "score": 1.0, + "content": ", which maps the pooled representations", + "type": "text" + }, + { + "bbox": [ + 491, + 627, + 504, + 637 + ], + "score": 0.87, + "content": "y _ { \\oplus }", + "type": "inline_equation" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 636, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 123, + 653 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 123, + 637, + 162, + 651 + ], + "score": 0.92, + "content": "y _ { \\oplus } ^ { \\prime } \\in \\mathbb { R } ^ { C }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 636, + 239, + 653 + ], + "score": 1.0, + "content": "to the embeddings", + "type": "text" + }, + { + "bbox": [ + 239, + 639, + 295, + 652 + ], + "score": 0.93, + "content": "z _ { \\oplus } = h _ { \\psi } ^ { g } ( z _ { \\oplus } )", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 636, + 313, + 653 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 314, + 637, + 397, + 653 + ], + "score": 0.93, + "content": "z _ { \\oplus } ^ { \\prime } = h _ { \\psi } ^ { g } ( z _ { \\oplus } ^ { \\prime } ) \\in \\mathbb { R } ^ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 636, + 506, + 653 + ], + "score": 1.0, + "content": ". We describe now how we", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 651, + 331, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 331, + 663 + ], + "score": 1.0, + "content": "perform the matching, and introduce our loss functions.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 39.5, + "bbox_fs": [ + 103, + 518, + 508, + 663 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 504, + 678 + ], + "score": 1.0, + "content": "Location-based matching. 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Given a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 266, + 506, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 506, + 278 + ], + "score": 1.0, + "content": "seed image, two views are produced and fed to an encoder that produces local features. The features", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 104, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "are further processed by a local projector that embed them into a smaller space, without destroying", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 286, + 506, + 301 + ], + "spans": [ + { + "bbox": [ + 104, + 286, + 506, + 301 + ], + "score": 1.0, + "content": "the localization information. Two matchings, one based on the spatial information provided by", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 297, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 104, + 297, + 382, + 312 + ], + "score": 1.0, + "content": "the transformation between the views, the other one based on the", + "type": "text" + }, + { + "bbox": [ + 383, + 298, + 391, + 308 + ], + "score": 0.84, + "content": "l ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 297, + 506, + 312 + ], + "score": 1.0, + "content": "-distance in the embedding", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 309, + 507, + 322 + ], + "spans": [ + { + "bbox": [ + 104, + 309, + 507, + 322 + ], + "score": 1.0, + "content": "space are computed, and the VICReg criterion is then applied between matched spatial embeddings.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "Additionally, the local features from the encoder are pooled together, and the pooled features are fed", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 104, + 331, + 505, + 344 + ], + "score": 1.0, + "content": "to a global expander. The VICReg criterion is finally applied between the two resulting embeddings.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "text", + "bbox": [ + 106, + 363, + 401, + 375 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 402, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 402, + 376 + ], + "score": 1.0, + "content": "are kept. 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Both location and feature-based loss functions are", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 164, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 104, + 164, + 506, + 178 + ], + "score": 1.0, + "content": "symmetrized, because for both, the search for the best match is not a symmetric operation. Our final", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 176, + 256, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 256, + 189 + ], + "score": 1.0, + "content": "loss function is described as follows:", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7 + }, + { + "type": "interline_equation", + "bbox": [ + 139, + 193, + 470, + 208 + ], + "lines": [ + { + "bbox": [ + 139, + 193, + 470, + 208 + ], + "spans": [ + { + "bbox": [ + 139, + 193, + 470, + 208 + ], + "score": 0.87, + "content": "\\mathcal { L } ( z , z ^ { \\prime } ) = \\alpha \\ell ( z _ { \\oplus } , z _ { \\oplus } ^ { \\prime } ) + ( 1 - \\alpha ) \\{ \\mathcal { L } _ { s } ( z , z ^ { \\prime } ) + \\mathcal { L } _ { s } ( z ^ { \\prime } , z ) + \\mathcal { L } _ { d } ( z , z ^ { \\prime } ) + \\mathcal { L } _ { d } ( z ^ { \\prime } , z ) \\} ,", + "type": "interline_equation", + "image_path": "96e5220d2dd0348141b4b6d3be021dbd3ec1a21e7527f4f0e2c1385d930abb94.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 139, + 193, + 470, + 208 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 213, + 505, + 268 + ], + "lines": [ + { + "bbox": [ + 105, + 213, + 506, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 134, + 226 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 135, + 216, + 142, + 223 + ], + "score": 0.79, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 213, + 506, + 226 + ], + "score": 1.0, + "content": "is an hyper-parameter controlling the importance one wants to put on learning global", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 413, + 236 + ], + "score": 1.0, + "content": "rather than local features. We study later in Section 4.2 the influence of", + "type": "text" + }, + { + "bbox": [ + 414, + 226, + 421, + 235 + ], + "score": 0.78, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 422, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "on the downstream", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 234, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 104, + 234, + 506, + 248 + ], + "score": 1.0, + "content": "performance, and show that there exists a trade-off such that the learned representations contain local", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "score": 1.0, + "content": "and global information at the same time, and therefore transfer well on both image classification and", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 258, + 186, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 186, + 269 + ], + "score": 1.0, + "content": "segmentation tasks.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 107, + 281, + 300, + 294 + ], + "lines": [ + { + "bbox": [ + 105, + 281, + 300, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 300, + 296 + ], + "score": 1.0, + "content": "3.2 VICRegL with the ConvNeXt backbone", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 301, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 106, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "The feature matching procedure is designed to work with any kind of convolutional neural network.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 313, + 507, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 507, + 326 + ], + "score": 1.0, + "content": "In the experimental section, we provide results with a standard ResNet-50 backbone. However,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 325, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 336 + ], + "score": 1.0, + "content": "one can considerably improve the performance on downstream tasks by using a more sophisticated", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 335, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 347 + ], + "score": 1.0, + "content": "backbone. We propose to use the recently introduced ConvNeXt architecture [Liu et al., 2022], that is", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 346, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 358 + ], + "score": 1.0, + "content": "very similar to the ResNet one, but with many simple modifications to the original architecture, which", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 358, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 506, + 369 + ], + "score": 1.0, + "content": "make it work as well as modern vision transformers. To the best of our knowledge, this is the first", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "time ConvNeXts have been used in self-supervised learning, and our work shows that convolutional", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 506, + 392 + ], + "score": 1.0, + "content": "neural networks are still able to deliver state-of-the-art performances in most standard self-supervised", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "learning benchmarks. In order to make the performance competitive with recent approaches, we use", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 506, + 414 + ], + "score": 1.0, + "content": "the multi-crop strategy introduced in [Caron et al., 2020]. Surprisingly, we found that the combination", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "of multi-crop with encoders from the ResNet family and the VICReg criterion is extremely difficult", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 422, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 506, + 436 + ], + "score": 1.0, + "content": "to optimize, and haven’t been able to make it work properly. However, multi-crop shows very good", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "results when combined with ConvNeXts. Our intuitive explanation is based on a study of the optimal", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 444, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 506, + 457 + ], + "score": 1.0, + "content": "batch size. The VICReg criterion regularizes the empirical covariance matrix of the embeddings,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "computed using the current batch, and we hypothesize that there is a link between the size of the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "batch, and the dimensionality of the representations. VICReg combined with a ResNet-50 has shown", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 478, + 506, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 506, + 489 + ], + "score": 1.0, + "content": "to have an optimal batch size of 2048, which is exactly the dimensionality of the representations of a", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 488, + 506, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 506, + 501 + ], + "score": 1.0, + "content": "ResNet-50. We found that the optimal batch size when working with ConvNeXts is 512 which is", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "much smaller, and correlates with the fact that ConvNeXts also have smaller representations (768", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 509, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 506, + 523 + ], + "score": 1.0, + "content": "for ConvNeXt-S and 1024 for ConvNeXt-B). The optimal batch size might therefore be close to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "the dimensionality of the representations. Now, the multi-crop strategy artificially increases the size", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "of the batch, which is much easier to handle when the size of the batch before multi-crop is small.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 542, + 485, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 485, + 555 + ], + "score": 1.0, + "content": "Indeed the effective batch size otherwise becomes too large, which causes optimization issues.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 559, + 506, + 614 + ], + "lines": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "We now describe how the matching loss functions are adapted in order to work with multi-crop.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 328, + 581 + ], + "score": 1.0, + "content": "Instead of generating only two views of the seed image,", + "type": "text" + }, + { + "bbox": [ + 328, + 570, + 338, + 580 + ], + "score": 0.79, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 569, + 416, + 581 + ], + "score": 1.0, + "content": "views (2 large, and", + "type": "text" + }, + { + "bbox": [ + 417, + 570, + 444, + 581 + ], + "score": 0.85, + "content": "N - 2", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "small), resized", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 107, + 579, + 509, + 608 + ], + "spans": [ + { + "bbox": [ + 107, + 591, + 117, + 602 + ], + "score": 0.86, + "content": "z ^ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 118, + 579, + 135, + 608 + ], + "score": 1.0, + "content": "twoand", + "type": "text" + }, + { + "bbox": [ + 136, + 591, + 146, + 602 + ], + "score": 0.87, + "content": "z ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 579, + 230, + 608 + ], + "score": 1.0, + "content": "ferent resolutions arfor large views, and", + "type": "text" + }, + { + "bbox": [ + 230, + 591, + 266, + 604 + ], + "score": 0.93, + "content": "\\{ \\bar { z } ^ { n } \\} _ { n = 3 } ^ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 579, + 509, + 608 + ], + "score": 1.0, + "content": "ed, and further encoded into the feature maps embeddingsfor small views. The spatial matching loss function is then", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 602, + 184, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 184, + 615 + ], + "score": 1.0, + "content": "defined as follows:", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41.5 + }, + { + "type": "interline_equation", + "bbox": [ + 169, + 617, + 441, + 654 + ], + "lines": [ + { + "bbox": [ + 169, + 617, + 441, + 654 + ], + "spans": [ + { + "bbox": [ + 169, + 617, + 441, + 654 + ], + "score": 0.94, + "content": "\\mathcal { L } _ { s } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) = \\sum _ { m = 1 } ^ { 2 } \\sum _ { n \\neq m } ^ { N } \\{ \\sum _ { p \\in P } l ( z _ { p } ^ { m } , z _ { \\mathrm { N N } ( p ) } ^ { n } ) + \\sum _ { p \\in P } l ( z _ { p } ^ { n } , z _ { \\mathrm { N N } ( p ) } ^ { m } ) \\} ,", + "type": "interline_equation", + "image_path": "64d13d5221fedde969cf80a2e1c8c74d4d71ca2dae6aaffeba9064887e14b837.jpg" + } + ] + } + ], + "index": 45, + "virtual_lines": [ + { + "bbox": [ + 169, + 617, + 441, + 629.3333333333334 + ], + "spans": [], + "index": 44 + }, + { + "bbox": [ + 169, + 629.3333333333334, + 441, + 641.6666666666667 + ], + "spans": [], + "index": 45 + }, + { + "bbox": [ + 169, + 641.6666666666667, + 441, + 654.0000000000001 + ], + "spans": [], + "index": 46 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 658, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 185, + 672 + ], + "score": 1.0, + "content": "where only the top-", + "type": "text" + }, + { + "bbox": [ + 185, + 661, + 196, + 671 + ], + "score": 0.83, + "content": "\\gamma _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 658, + 231, + 672 + ], + "score": 1.0, + "content": "and top-", + "type": "text" + }, + { + "bbox": [ + 231, + 661, + 241, + 671 + ], + "score": 0.84, + "content": "\\gamma _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 658, + 505, + 672 + ], + "score": 1.0, + "content": "pairs of feature vectors of large and small views respectively are", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "score": 1.0, + "content": "kept in the computation of the loss. The feature-based loss function, and the global criterion are", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 681, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 694 + ], + "score": 1.0, + "content": "adapted in a very similar way, one large view is matched to the other large views and to the small", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 693, + 326, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 326, + 703 + ], + "score": 1.0, + "content": "views, and the final loss function is defined as follows:", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 48.5 + }, + { + "type": "interline_equation", + "bbox": [ + 155, + 708, + 456, + 724 + ], + "lines": [ + { + "bbox": [ + 155, + 708, + 456, + 724 + ], + "spans": [ + { + "bbox": [ + 155, + 708, + 456, + 724 + ], + "score": 0.89, + "content": "\\mathscr { L } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) = \\alpha \\ell ( \\{ z _ { \\oplus } ^ { n } \\} _ { n = 1 } ^ { N } ) + ( 1 - \\alpha ) \\{ \\mathscr { L } _ { s } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) + \\mathscr { L } _ { d } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) \\} .", + "type": "interline_equation", + "image_path": "8cd42f3fe48b7a24a93597e2706e23a4c85ce58d2a028fee9e13ac850191d6cb.jpg" + } + ] + } + ], + "index": 51, + "virtual_lines": [ + { + "bbox": [ + 155, + 708, + 456, + 724 + ], + "spans": [], + "index": 51 + } + ] + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 753 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 753 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 128 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 105, + 73, + 506, + 130 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 132, + 505, + 187 + ], + "lines": [ + { + "bbox": [ + 106, + 133, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 145 + ], + "score": 1.0, + "content": "Our final loss function is a combination of the location-based and feature-based loss functions, which", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "form the local criterion, with in addition a standard VICReg loss function applied on the pooled", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "representations, which is the global criterion. Both location and feature-based loss functions are", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 164, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 104, + 164, + 506, + 178 + ], + "score": 1.0, + "content": "symmetrized, because for both, the search for the best match is not a symmetric operation. Our final", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 176, + 256, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 256, + 189 + ], + "score": 1.0, + "content": "loss function is described as follows:", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7, + "bbox_fs": [ + 104, + 133, + 506, + 189 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 139, + 193, + 470, + 208 + ], + "lines": [ + { + "bbox": [ + 139, + 193, + 470, + 208 + ], + "spans": [ + { + "bbox": [ + 139, + 193, + 470, + 208 + ], + "score": 0.87, + "content": "\\mathcal { L } ( z , z ^ { \\prime } ) = \\alpha \\ell ( z _ { \\oplus } , z _ { \\oplus } ^ { \\prime } ) + ( 1 - \\alpha ) \\{ \\mathcal { L } _ { s } ( z , z ^ { \\prime } ) + \\mathcal { L } _ { s } ( z ^ { \\prime } , z ) + \\mathcal { L } _ { d } ( z , z ^ { \\prime } ) + \\mathcal { L } _ { d } ( z ^ { \\prime } , z ) \\} ,", + "type": "interline_equation", + "image_path": "96e5220d2dd0348141b4b6d3be021dbd3ec1a21e7527f4f0e2c1385d930abb94.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 139, + 193, + 470, + 208 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 213, + 505, + 268 + ], + "lines": [ + { + "bbox": [ + 105, + 213, + 506, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 134, + 226 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 135, + 216, + 142, + 223 + ], + "score": 0.79, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 213, + 506, + 226 + ], + "score": 1.0, + "content": "is an hyper-parameter controlling the importance one wants to put on learning global", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 413, + 236 + ], + "score": 1.0, + "content": "rather than local features. We study later in Section 4.2 the influence of", + "type": "text" + }, + { + "bbox": [ + 414, + 226, + 421, + 235 + ], + "score": 0.78, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 422, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "on the downstream", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 234, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 104, + 234, + 506, + 248 + ], + "score": 1.0, + "content": "performance, and show that there exists a trade-off such that the learned representations contain local", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 505, + 258 + ], + "score": 1.0, + "content": "and global information at the same time, and therefore transfer well on both image classification and", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 258, + 186, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 186, + 269 + ], + "score": 1.0, + "content": "segmentation tasks.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13, + "bbox_fs": [ + 104, + 213, + 506, + 269 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 281, + 300, + 294 + ], + "lines": [ + { + "bbox": [ + 105, + 281, + 300, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 300, + 296 + ], + "score": 1.0, + "content": "3.2 VICRegL with the ConvNeXt backbone", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 301, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 106, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "The feature matching procedure is designed to work with any kind of convolutional neural network.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 313, + 507, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 507, + 326 + ], + "score": 1.0, + "content": "In the experimental section, we provide results with a standard ResNet-50 backbone. However,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 325, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 336 + ], + "score": 1.0, + "content": "one can considerably improve the performance on downstream tasks by using a more sophisticated", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 335, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 347 + ], + "score": 1.0, + "content": "backbone. We propose to use the recently introduced ConvNeXt architecture [Liu et al., 2022], that is", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 346, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 358 + ], + "score": 1.0, + "content": "very similar to the ResNet one, but with many simple modifications to the original architecture, which", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 358, + 506, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 506, + 369 + ], + "score": 1.0, + "content": "make it work as well as modern vision transformers. To the best of our knowledge, this is the first", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "time ConvNeXts have been used in self-supervised learning, and our work shows that convolutional", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 506, + 392 + ], + "score": 1.0, + "content": "neural networks are still able to deliver state-of-the-art performances in most standard self-supervised", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "learning benchmarks. In order to make the performance competitive with recent approaches, we use", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 506, + 414 + ], + "score": 1.0, + "content": "the multi-crop strategy introduced in [Caron et al., 2020]. Surprisingly, we found that the combination", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "of multi-crop with encoders from the ResNet family and the VICReg criterion is extremely difficult", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 422, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 506, + 436 + ], + "score": 1.0, + "content": "to optimize, and haven’t been able to make it work properly. However, multi-crop shows very good", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "results when combined with ConvNeXts. Our intuitive explanation is based on a study of the optimal", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 444, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 506, + 457 + ], + "score": 1.0, + "content": "batch size. The VICReg criterion regularizes the empirical covariance matrix of the embeddings,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "computed using the current batch, and we hypothesize that there is a link between the size of the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "batch, and the dimensionality of the representations. VICReg combined with a ResNet-50 has shown", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 478, + 506, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 506, + 489 + ], + "score": 1.0, + "content": "to have an optimal batch size of 2048, which is exactly the dimensionality of the representations of a", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 488, + 506, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 506, + 501 + ], + "score": 1.0, + "content": "ResNet-50. We found that the optimal batch size when working with ConvNeXts is 512 which is", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "much smaller, and correlates with the fact that ConvNeXts also have smaller representations (768", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 509, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 506, + 523 + ], + "score": 1.0, + "content": "for ConvNeXt-S and 1024 for ConvNeXt-B). The optimal batch size might therefore be close to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "the dimensionality of the representations. Now, the multi-crop strategy artificially increases the size", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "of the batch, which is much easier to handle when the size of the batch before multi-crop is small.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 542, + 485, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 485, + 555 + ], + "score": 1.0, + "content": "Indeed the effective batch size otherwise becomes too large, which causes optimization issues.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 28, + "bbox_fs": [ + 105, + 302, + 507, + 555 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 559, + 506, + 614 + ], + "lines": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "We now describe how the matching loss functions are adapted in order to work with multi-crop.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 328, + 581 + ], + "score": 1.0, + "content": "Instead of generating only two views of the seed image,", + "type": "text" + }, + { + "bbox": [ + 328, + 570, + 338, + 580 + ], + "score": 0.79, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 569, + 416, + 581 + ], + "score": 1.0, + "content": "views (2 large, and", + "type": "text" + }, + { + "bbox": [ + 417, + 570, + 444, + 581 + ], + "score": 0.85, + "content": "N - 2", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "small), resized", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 107, + 579, + 509, + 608 + ], + "spans": [ + { + "bbox": [ + 107, + 591, + 117, + 602 + ], + "score": 0.86, + "content": "z ^ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 118, + 579, + 135, + 608 + ], + "score": 1.0, + "content": "twoand", + "type": "text" + }, + { + "bbox": [ + 136, + 591, + 146, + 602 + ], + "score": 0.87, + "content": "z ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 579, + 230, + 608 + ], + "score": 1.0, + "content": "ferent resolutions arfor large views, and", + "type": "text" + }, + { + "bbox": [ + 230, + 591, + 266, + 604 + ], + "score": 0.93, + "content": "\\{ \\bar { z } ^ { n } \\} _ { n = 3 } ^ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 579, + 509, + 608 + ], + "score": 1.0, + "content": "ed, and further encoded into the feature maps embeddingsfor small views. The spatial matching loss function is then", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 602, + 184, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 184, + 615 + ], + "score": 1.0, + "content": "defined as follows:", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 558, + 509, + 615 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 169, + 617, + 441, + 654 + ], + "lines": [ + { + "bbox": [ + 169, + 617, + 441, + 654 + ], + "spans": [ + { + "bbox": [ + 169, + 617, + 441, + 654 + ], + "score": 0.94, + "content": "\\mathcal { L } _ { s } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) = \\sum _ { m = 1 } ^ { 2 } \\sum _ { n \\neq m } ^ { N } \\{ \\sum _ { p \\in P } l ( z _ { p } ^ { m } , z _ { \\mathrm { N N } ( p ) } ^ { n } ) + \\sum _ { p \\in P } l ( z _ { p } ^ { n } , z _ { \\mathrm { N N } ( p ) } ^ { m } ) \\} ,", + "type": "interline_equation", + "image_path": "64d13d5221fedde969cf80a2e1c8c74d4d71ca2dae6aaffeba9064887e14b837.jpg" + } + ] + } + ], + "index": 45, + "virtual_lines": [ + { + "bbox": [ + 169, + 617, + 441, + 629.3333333333334 + ], + "spans": [], + "index": 44 + }, + { + "bbox": [ + 169, + 629.3333333333334, + 441, + 641.6666666666667 + ], + "spans": [], + "index": 45 + }, + { + "bbox": [ + 169, + 641.6666666666667, + 441, + 654.0000000000001 + ], + "spans": [], + "index": 46 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 659, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 658, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 185, + 672 + ], + "score": 1.0, + "content": "where only the top-", + "type": "text" + }, + { + "bbox": [ + 185, + 661, + 196, + 671 + ], + "score": 0.83, + "content": "\\gamma _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 658, + 231, + 672 + ], + "score": 1.0, + "content": "and top-", + "type": "text" + }, + { + "bbox": [ + 231, + 661, + 241, + 671 + ], + "score": 0.84, + "content": "\\gamma _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 658, + 505, + 672 + ], + "score": 1.0, + "content": "pairs of feature vectors of large and small views respectively are", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 682 + ], + "score": 1.0, + "content": "kept in the computation of the loss. The feature-based loss function, and the global criterion are", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 681, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 694 + ], + "score": 1.0, + "content": "adapted in a very similar way, one large view is matched to the other large views and to the small", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 693, + 326, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 326, + 703 + ], + "score": 1.0, + "content": "views, and the final loss function is defined as follows:", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 48.5, + "bbox_fs": [ + 105, + 658, + 505, + 703 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 155, + 708, + 456, + 724 + ], + "lines": [ + { + "bbox": [ + 155, + 708, + 456, + 724 + ], + "spans": [ + { + "bbox": [ + 155, + 708, + 456, + 724 + ], + "score": 0.89, + "content": "\\mathscr { L } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) = \\alpha \\ell ( \\{ z _ { \\oplus } ^ { n } \\} _ { n = 1 } ^ { N } ) + ( 1 - \\alpha ) \\{ \\mathscr { L } _ { s } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) + \\mathscr { L } _ { d } ( \\{ z ^ { n } \\} _ { n = 1 } ^ { N } ) \\} .", + "type": "interline_equation", + "image_path": "8cd42f3fe48b7a24a93597e2706e23a4c85ce58d2a028fee9e13ac850191d6cb.jpg" + } + ] + } + ], + "index": 51, + "virtual_lines": [ + { + "bbox": [ + 155, + 708, + 456, + 724 + ], + "spans": [], + "index": 51 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 129, + 176, + 481, + 379 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 82, + 506, + 171 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "Table 1: Comparison of various global and local self-supervised learning methods on different", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 95, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 505, + 105 + ], + "score": 1.0, + "content": "linear evaluation benchmarks. Evaluation of the features learned from a ResNet-50 backbone", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 372, + 117 + ], + "score": 1.0, + "content": "trained with different methods on: (1) linear classification accuracy", + "type": "text" + }, + { + "bbox": [ + 373, + 105, + 388, + 116 + ], + "score": 0.67, + "content": "( \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 105, + 506, + 117 + ], + "score": 1.0, + "content": "(frozen) on the validation set", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "score": 1.0, + "content": "of ImageNet (2) Linear segmentation (mIoU) (frozen and fine-tuning) on Pascal VOC, (3) Linear", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 294, + 140 + ], + "score": 1.0, + "content": "segmentation (mIoU) (frozen) on Cityscapes.", + "type": "text" + }, + { + "bbox": [ + 294, + 129, + 302, + 137 + ], + "score": 0.69, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 127, + 505, + 140 + ], + "score": 1.0, + "content": "is the weight of Eq. (4) balancing the importance", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 138, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 150 + ], + "score": 1.0, + "content": "given to the global criterion, compared to the local criterion. The best result for each benchmark is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 149, + 506, + 161 + ], + "spans": [ + { + "bbox": [ + 106, + 149, + 506, + 161 + ], + "score": 1.0, + "content": "bold font. VICRegL consistently improves the linear segmentation mIoU over the VICReg baseline,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 173 + ], + "score": 1.0, + "content": "which shows that introducing a local criterion is beneficial for a localized understanding of the image.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 3.5 + }, + { + "type": "table_body", + "bbox": [ + 129, + 176, + 481, + 379 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 129, + 176, + 481, + 379 + ], + "spans": [ + { + "bbox": [ + 129, + 176, + 481, + 379 + ], + "score": 0.985, + "html": "
Linear Cls. (%)Linear Seg. (mIoU)
MethodEpochsImageNet FrozenPascal VOC FrozenFine-TunedCityscapes Frozen
Global features
MoCo v2 [Chen et al., 2020b]20067.535.664.814.3
SimCLR[Chen et al., 2020a]40068.245.965.417.9
BYOL [Grill et al., 2020]30072.347.165.722.6
VICReg [Bardes et al.,2022]30071.547.865.523.5
Local features
PixPro [Xie et al., 2021]40060.652.867.522.6
DenseCL [Wang et al., 2021]20065.045.366.811.2
DetCon [Hénaff et al., 2021]100066.353.667.416.2
InsLoc [Yang et al., 2022]40045.024.164.47.0
CP² [Wang et al., 2022]82053.121.765.28.4
ReSim [Xiao et al., 2021]40059.551.967.312.3
Ours
VICRegL α = 0.930071.254.066.625.1
VICRegL α = 0.7530070.4 55.967.625.2
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VICRegL consistently improves the linear segmentation mIoU over the VICReg baseline,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 173 + ], + "score": 1.0, + "content": "which shows that introducing a local criterion is beneficial for a localized understanding of the image.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 3.5 + }, + { + "type": "table_body", + "bbox": [ + 129, + 176, + 481, + 379 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 129, + 176, + 481, + 379 + ], + "spans": [ + { + "bbox": [ + 129, + 176, + 481, + 379 + ], + "score": 0.985, + "html": "
Linear Cls. (%)Linear Seg. (mIoU)
MethodEpochsImageNet FrozenPascal VOC FrozenFine-TunedCityscapes Frozen
Global features
MoCo v2 [Chen et al., 2020b]20067.535.664.814.3
SimCLR[Chen et al., 2020a]40068.245.965.417.9
BYOL [Grill et al., 2020]30072.347.165.722.6
VICReg [Bardes et al.,2022]30071.547.865.523.5
Local features
PixPro [Xie et al., 2021]40060.652.867.522.6
DenseCL [Wang et al., 2021]20065.045.366.811.2
DetCon [Hénaff et al., 2021]100066.353.667.416.2
InsLoc [Yang et al., 2022]40045.024.164.47.0
CP² [Wang et al., 2022]82053.121.765.28.4
ReSim [Xiao et al., 2021]40059.551.967.312.3
Ours
VICRegL α = 0.930071.254.066.625.1
VICRegL α = 0.7530070.4 55.967.625.2
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We demonstrate that VICRegL", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 710, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 507, + 723 + ], + "score": 1.0, + "content": "strongly improves on segmentation results over VICReg while preserving the classification perfor-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 415, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 505, + 426 + ], + "score": 1.0, + "content": "mance, and is competitive with other local and global self-supervised learning methods. We choose", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 426, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 505, + 438 + ], + "score": 1.0, + "content": "the linear evaluation with frozen weights as our main evaluation metrics, as we believe it is a much", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 449 + ], + "score": 1.0, + "content": "better way of evaluating the learned representations. 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Linear Cls. (%)Linear Seg. (mloU)
MethodBackbone ParamsEpochsImageNet FrozenPascal VOC FrozenFTADE20k Frozen
Global features
MoCo v3 [Chen et al., 2021]ViT-S21M30073.257.175.923.7
DINO [Caron et al., 2021]ViT-S21M40077.065.279.530.5
IBOT[Zhou et al., 2022a]ViT-S21M40077.968.279.933.2
VICReg [Bardes et al., 2022]CNX-S50M40076.260.177.828.6
MoCo v3ViT-B85M30076.764.878.928.7
DINOViT-B85M40078.270.182.034.5
IBOT [Zhou et al., 2022a]ViT-B85M40079.573.082.438.3
MAE [He et al., 2022]ViT-B85M40068.059.682.427.0
VICRegCNX-B85M40077.667.281.132.7
Local features
CP² [Wang et al., 2022]ViT-S21M32062.863.579.625.3
Ours
VICRegL α = 0.9CNX-S50M40075.966.780.030.8
VICRegL α = 0.75CNX-S50M40074.667.580.631.2
VICRegL α = 0.9CNX-B85M40077.169.381.233.5
VICRegL α = 0.75CNX-B85M40076.370.482.535.3
VICRegL α = 0.75+ CNX-XL350M15079.478.784.143.2
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On", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 601, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 375, + 614 + ], + "score": 1.0, + "content": "Pascal VOC, when the weights of the backbone are frozen, VICRegL", + "type": "text" + }, + { + "bbox": [ + 375, + 602, + 409, + 612 + ], + "score": 0.89, + "content": "\\alpha = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 601, + 459, + 614 + ], + "score": 1.0, + "content": "improves by", + "type": "text" + }, + { + "bbox": [ + 460, + 602, + 479, + 612 + ], + "score": 0.8, + "content": "+ 6 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 601, + 505, + 614 + ], + "score": 1.0, + "content": "mIoU", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 184, + 625 + ], + "score": 1.0, + "content": "while only loosing", + "type": "text" + }, + { + "bbox": [ + 185, + 613, + 207, + 623 + ], + "score": 0.86, + "content": "0 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 612, + 363, + 625 + ], + "score": 1.0, + "content": "classification accuracy, and VICRegL", + "type": "text" + }, + { + "bbox": [ + 364, + 613, + 403, + 623 + ], + "score": 0.87, + "content": "\\alpha = 0 . 7 5", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 612, + 456, + 625 + ], + "score": 1.0, + "content": "improves by", + "type": "text" + }, + { + "bbox": [ + 457, + 613, + 477, + 623 + ], + "score": 0.81, + "content": "\\mathbf { + 8 . 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 612, + 506, + 625 + ], + "score": 1.0, + "content": "mIoU.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 623, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 506, + 636 + ], + "score": 1.0, + "content": "On fine-tuning the improvement is less significative, which we attribute to the non-informative nature", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 633, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 380, + 648 + ], + "score": 1.0, + "content": "of fine-tuning benchmarks. 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Linear Cls. (%)Linear Seg. (mloU)
MethodBackbone ParamsEpochsImageNet FrozenPascal VOC FrozenFTADE20k Frozen
Global features
MoCo v3 [Chen et al., 2021]ViT-S21M30073.257.175.923.7
DINO [Caron et al., 2021]ViT-S21M40077.065.279.530.5
IBOT[Zhou et al., 2022a]ViT-S21M40077.968.279.933.2
VICReg [Bardes et al., 2022]CNX-S50M40076.260.177.828.6
MoCo v3ViT-B85M30076.764.878.928.7
DINOViT-B85M40078.270.182.034.5
IBOT [Zhou et al., 2022a]ViT-B85M40079.573.082.438.3
MAE [He et al., 2022]ViT-B85M40068.059.682.427.0
VICRegCNX-B85M40077.667.281.132.7
Local features
CP² [Wang et al., 2022]ViT-S21M32062.863.579.625.3
Ours
VICRegL α = 0.9CNX-S50M40075.966.780.030.8
VICRegL α = 0.75CNX-S50M40074.667.580.631.2
VICRegL α = 0.9CNX-B85M40077.169.381.233.5
VICRegL α = 0.75CNX-B85M40076.370.482.535.3
VICRegL α = 0.75+ CNX-XL350M15079.478.784.143.2
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MethodCls. (%)Seg. (mIoU)
Baseline73.856.0
Ls73.558.9
Ld73.657.7
Ls-Ld73.660.3
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MethodCls. (%)Seg. (mIoU)
Baseline73.856.0
Ls73.558.9
Ld73.657.7
Ls-Ld73.660.3
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Only 10", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 308, + 343, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 308, + 343, + 505, + 354 + ], + "score": 1.0, + "content": "matches are visualized for better clarity, but the", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 308, + 354, + 506, + 365 + ], + "spans": [ + { + "bbox": [ + 308, + 354, + 506, + 365 + ], + "score": 1.0, + "content": "actual number of selected matches is 20. We dis-", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 307, + 365, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 307, + 365, + 505, + 376 + ], + "score": 1.0, + "content": "play the matches according to the location of the", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 308, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 308, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "feature vectors in the feature maps. 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Our results highlight", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 646 + ], + "score": 1.0, + "content": "the trade-off between classification and segmentation performance, which can be controlled by the", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 106, + 645, + 245, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 245, + 656 + ], + "score": 1.0, + "content": "weight given to the local criterion.", + "type": "text" + } + ], + "index": 72 + } + ], + "index": 65, + "bbox_fs": [ + 105, + 491, + 507, + 656 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 668, + 171, + 680 + ], + "lines": [ + { + "bbox": [ + 105, + 667, + 173, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 173, + 682 + ], + "score": 1.0, + "content": "4.2 Ablations", + "type": "text" + } + ], + "index": 73 + } + ], + "index": 73 + }, + { + "type": "text", + "bbox": [ + 108, + 689, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "For all the experiments done in this section, unless specified otherwise, we pretrain a ConvNeXt-S on", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "score": 1.0, + "content": "ImageNet over 100 epochs, with the hyper-parameters described in Section 3.3, and report both the", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "score": 1.0, + "content": "linear classification accuracy on ImageNet, and the linear frozen segmentation mIoU on Pascal VOC.", + "type": "text" + } + ], + "index": 76 + } + ], + "index": 75, + "bbox_fs": [ + 105, + 689, + 507, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 141, + 126, + 263, + 180 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 77, + 303, + 121 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 76, + 303, + 90 + ], + "spans": [ + { + "bbox": [ + 105, + 76, + 303, + 90 + ], + "score": 1.0, + "content": "Table 4: Ablation: SSL criterion. Introducing", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 88, + 304, + 101 + ], + "spans": [ + { + "bbox": [ + 106, + 88, + 304, + 101 + ], + "score": 1.0, + "content": "our local criterion with VICReg gives a stronger", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 100, + 304, + 110 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 304, + 110 + ], + "score": 1.0, + "content": "improvement compared to SimCLR, which is con-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 109, + 243, + 122 + ], + "spans": [ + { + "bbox": [ + 106, + 109, + 243, + 122 + ], + "score": 1.0, + "content": "trastive. 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MethodCls. (%)Seg. (mIoU)
VICReg71.147.8
VICRegL70.4 55.9
SimCLR67.545.9
SimCLR-L66.651.3
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MethodMulti-cropCls. (%)Seg. (mIoU)
VICReg70.152.9
VICRegL69.957.8
VICReg√73.954.4
VICRegL√73.660.3
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Y1γ2Cls. (%)Seg. (mIoU)
10273.459.2
20473.660.3
49973.559.6
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CriterionCls. (%)Seg. (mIoU)
I73.459.0
VI73.358.2
VIC73.660.3
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This highlights the existence of a sweet", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "spot, where the model is strongly performing at both classification and segmentation, which indicates", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 433, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 372, + 444 + ], + "score": 1.0, + "content": "that it has learned both meaningful local and global features. When", + "type": "text" + }, + { + "bbox": [ + 373, + 434, + 381, + 442 + ], + "score": 0.69, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 433, + 505, + 444 + ], + "score": 1.0, + "content": "decreases too much, the model", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "starts to lose its performance in both tasks, which shows that having a global understanding of the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 454, + 284, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 284, + 467 + ], + "score": 1.0, + "content": "image is necessary, even for localized tasks.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 505, + 580 + ], + "lines": [ + { + "bbox": [ + 106, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "Study of the importance between feature-based and location-based local criteria. 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Table 3 study the importance of these criterion. Baseline in the table means", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 504, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 506, + 516 + ], + "score": 1.0, + "content": "that no local criterion is used, and is simply VICReg. 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In all cases, the", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "score": 1.0, + "content": "classification accuracy is not affected, which is expected as the local criterion has little effect on the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 569, + 454, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 454, + 583 + ], + "score": 1.0, + "content": "quality of the global features, and therefore on the downstream classification accuracy.", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 47.5 + }, + { + "type": "text", + "bbox": [ + 106, + 585, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 505, + 597 + ], + "score": 1.0, + "content": "Study of the number of matches. 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For our experiments", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 106, + 607, + 504, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 291, + 619 + ], + "score": 1.0, + "content": "with multi-crop, the size of the feature maps is", + "type": "text" + }, + { + "bbox": [ + 291, + 607, + 352, + 618 + ], + "score": 0.89, + "content": "( 2 0 4 8 \\times 7 \\times 7 )", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 607, + 444, + 619 + ], + "score": 1.0, + "content": "for the large crops and", + "type": "text" + }, + { + "bbox": [ + 445, + 607, + 504, + 618 + ], + "score": 0.87, + "content": "( 2 0 4 8 \\times 3 \\times 3 )", + "type": "inline_equation" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "score": 1.0, + "content": "for the small crops. There are therefore in one branch of the siamese architecture 49 feature maps for", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 629, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 506, + 641 + ], + "score": 1.0, + "content": "large crops, and 9 for small crops. 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Similar to the", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 106, + 672, + 506, + 685 + ], + "spans": [ + { + "bbox": [ + 106, + 672, + 506, + 685 + ], + "score": 1.0, + "content": "study on the influence of the local losses, the classification accuracy is not affected, as the local", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 106, + 683, + 337, + 696 + ], + "spans": [ + { + "bbox": [ + 106, + 683, + 337, + 696 + ], + "score": 1.0, + "content": "criterion does not improve or degrade the global features.", + "type": "text" + } + ], + "index": 62 + } + ], + "index": 57.5 + }, + { + "type": "text", + "bbox": [ + 107, + 700, + 503, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "Study of VICReg components for the local criterion. The global criterion is sufficient for the", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "vectors to not collapse to trivial solutions. 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Introducing", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 88, + 304, + 101 + ], + "spans": [ + { + "bbox": [ + 106, + 88, + 304, + 101 + ], + "score": 1.0, + "content": "our local criterion with VICReg gives a stronger", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 100, + 304, + 110 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 304, + 110 + ], + "score": 1.0, + "content": "improvement compared to SimCLR, which is con-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 109, + 243, + 122 + ], + "spans": [ + { + "bbox": [ + 106, + 109, + 243, + 122 + ], + "score": 1.0, + "content": "trastive. (ResNet-50, 300 epochs)", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "table_body", + "bbox": [ + 141, + 126, + 263, + 180 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 141, + 126, + 263, + 180 + ], + "spans": [ + { + "bbox": [ + 141, + 126, + 263, + 180 + ], + "score": 0.971, + "html": "
MethodCls. (%)Seg. (mIoU)
VICReg71.147.8
VICRegL70.4 55.9
SimCLR67.545.9
SimCLR-L66.651.3
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MethodMulti-cropCls. (%)Seg. (mIoU)
VICReg70.152.9
VICRegL69.957.8
VICReg√73.954.4
VICRegL√73.660.3
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Y1γ2Cls. (%)Seg. (mIoU)
10273.459.2
20473.660.3
49973.559.6
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CriterionCls. (%)Seg. (mIoU)
I73.459.0
VI73.358.2
VIC73.660.3
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(4) controls the importance", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 335, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 505, + 346 + ], + "score": 1.0, + "content": "that is given to the global criterion, compared to the local criterion. Figure 2 shows that there exists", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 344, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 358 + ], + "score": 1.0, + "content": "a fundamental trade-off between the ability of a model to learn global visual features, as opposed", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 357, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 256, + 368 + ], + "score": 1.0, + "content": "to learning local features. In the case", + "type": "text" + }, + { + "bbox": [ + 257, + 357, + 290, + 367 + ], + "score": 0.9, + "content": "\\alpha = 1 . 0", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 357, + 505, + 368 + ], + "score": 1.0, + "content": ", which is simply VICReg, the model is very efficient", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 367, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 477, + 379 + ], + "score": 1.0, + "content": "at producing global representations of the image, as demonstrated by the performance of", + "type": "text" + }, + { + "bbox": [ + 477, + 367, + 505, + 378 + ], + "score": 0.88, + "content": "7 3 . 9 \\%", + "type": "inline_equation" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 378, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 242, + 390 + ], + "score": 1.0, + "content": "in classification accuracy. When", + "type": "text" + }, + { + "bbox": [ + 243, + 379, + 270, + 388 + ], + "score": 0.9, + "content": "\\alpha < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 378, + 505, + 390 + ], + "score": 1.0, + "content": ", which introduces the local criterion, the performance in", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 389, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 253, + 401 + ], + "score": 1.0, + "content": "segmentation is greatly increased, by", + "type": "text" + }, + { + "bbox": [ + 253, + 389, + 273, + 399 + ], + "score": 0.84, + "content": "+ 3 . 4", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 389, + 322, + 401 + ], + "score": 1.0, + "content": "mIoU when", + "type": "text" + }, + { + "bbox": [ + 322, + 389, + 356, + 399 + ], + "score": 0.87, + "content": "\\alpha = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 389, + 359, + 401 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 359, + 389, + 379, + 399 + ], + "score": 0.79, + "content": "\\pm 4 . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 389, + 428, + 401 + ], + "score": 1.0, + "content": "mIoU when", + "type": "text" + }, + { + "bbox": [ + 428, + 389, + 467, + 399 + ], + "score": 0.89, + "content": "\\alpha = 0 . 7 5", + "type": "inline_equation" + }, + { + "bbox": [ + 468, + 389, + 484, + 401 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 484, + 389, + 505, + 399 + ], + "score": 0.86, + "content": "+ 4 . 6", + "type": "inline_equation" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "mIoU when the local and global criteria are weighted equally. At the same time, the classification", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 252, + 423 + ], + "score": 1.0, + "content": "accuracy only drops by respectively", + "type": "text" + }, + { + "bbox": [ + 252, + 411, + 274, + 421 + ], + "score": 0.86, + "content": "0 . 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 411, + 278, + 423 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 279, + 411, + 300, + 421 + ], + "score": 0.87, + "content": "1 . 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 411, + 318, + 423 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 318, + 411, + 340, + 421 + ], + "score": 0.86, + "content": "2 . 9 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 341, + 411, + 506, + 423 + ], + "score": 1.0, + "content": ". This highlights the existence of a sweet", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "spot, where the model is strongly performing at both classification and segmentation, which indicates", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 433, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 372, + 444 + ], + "score": 1.0, + "content": "that it has learned both meaningful local and global features. When", + "type": "text" + }, + { + "bbox": [ + 373, + 434, + 381, + 442 + ], + "score": 0.69, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 433, + 505, + 444 + ], + "score": 1.0, + "content": "decreases too much, the model", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "starts to lose its performance in both tasks, which shows that having a global understanding of the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 454, + 284, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 284, + 467 + ], + "score": 1.0, + "content": "image is necessary, even for localized tasks.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 322, + 506, + 467 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 505, + 580 + ], + "lines": [ + { + "bbox": [ + 106, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "Study of the importance between feature-based and location-based local criteria. VICRegL", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 482, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 366, + 493 + ], + "score": 1.0, + "content": "matches feature vectors according to a location-based criterion", + "type": "text" + }, + { + "bbox": [ + 366, + 482, + 379, + 493 + ], + "score": 0.89, + "content": "\\mathcal { L } _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 482, + 505, + 493 + ], + "score": 1.0, + "content": "of Eq. (2) and a feature-based", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 492, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 143, + 505 + ], + "score": 1.0, + "content": "criterion", + "type": "text" + }, + { + "bbox": [ + 143, + 493, + 156, + 504 + ], + "score": 0.89, + "content": "\\mathcal { L } _ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 492, + 506, + 505 + ], + "score": 1.0, + "content": "of Eq. (3). Table 3 study the importance of these criterion. Baseline in the table means", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 504, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 506, + 516 + ], + "score": 1.0, + "content": "that no local criterion is used, and is simply VICReg. The location-based criterion gives the best", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 514, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 175, + 526 + ], + "score": 1.0, + "content": "improvement by", + "type": "text" + }, + { + "bbox": [ + 176, + 514, + 196, + 525 + ], + "score": 0.79, + "content": "\\mathbf { + 2 . 9 }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 514, + 370, + 526 + ], + "score": 1.0, + "content": "mIoU over the baseline, compared to only", + "type": "text" + }, + { + "bbox": [ + 371, + 514, + 391, + 525 + ], + "score": 0.82, + "content": "{ + 1 . 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 514, + 506, + 526 + ], + "score": 1.0, + "content": "mIoU for the feature-based", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 524, + 504, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 483, + 538 + ], + "score": 1.0, + "content": "criterion, but it is the combination of the two that significantly improves over the baseline by", + "type": "text" + }, + { + "bbox": [ + 484, + 525, + 504, + 536 + ], + "score": 0.84, + "content": "\\mathbf { + 4 . 3 }", + "type": "inline_equation" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 535, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 506, + 549 + ], + "score": 1.0, + "content": "mIoU, which shows that using both the learned distance in the embedding space in combination with", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 546, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 505, + 559 + ], + "score": 1.0, + "content": "the actual distance in the pixel space produces local features with the best quality. In all cases, the", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "score": 1.0, + "content": "classification accuracy is not affected, which is expected as the local criterion has little effect on the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 569, + 454, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 454, + 583 + ], + "score": 1.0, + "content": "quality of the global features, and therefore on the downstream classification accuracy.", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 47.5, + "bbox_fs": [ + 105, + 470, + 506, + 583 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 585, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 505, + 597 + ], + "score": 1.0, + "content": "Study of the number of matches. We study here the influence of changing the number of selected", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 158, + 609 + ], + "score": 1.0, + "content": "best matches", + "type": "text" + }, + { + "bbox": [ + 158, + 598, + 169, + 608 + ], + "score": 0.85, + "content": "\\gamma _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 596, + 186, + 609 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 187, + 597, + 198, + 608 + ], + "score": 0.85, + "content": "\\gamma _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 596, + 506, + 609 + ], + "score": 1.0, + "content": "of Eq. (5), to keep for the computation of the local losses. For our experiments", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 106, + 607, + 504, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 291, + 619 + ], + "score": 1.0, + "content": "with multi-crop, the size of the feature maps is", + "type": "text" + }, + { + "bbox": [ + 291, + 607, + 352, + 618 + ], + "score": 0.89, + "content": "( 2 0 4 8 \\times 7 \\times 7 )", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 607, + 444, + 619 + ], + "score": 1.0, + "content": "for the large crops and", + "type": "text" + }, + { + "bbox": [ + 445, + 607, + 504, + 618 + ], + "score": 0.87, + "content": "( 2 0 4 8 \\times 3 \\times 3 )", + "type": "inline_equation" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "score": 1.0, + "content": "for the small crops. There are therefore in one branch of the siamese architecture 49 feature maps for", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 629, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 506, + 641 + ], + "score": 1.0, + "content": "large crops, and 9 for small crops. Tables 6 shows that there is a trade-off between keeping all the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 105, + 640, + 506, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 145, + 652 + ], + "score": 1.0, + "content": "matches", + "type": "text" + }, + { + "bbox": [ + 145, + 640, + 180, + 651 + ], + "score": 0.9, + "content": "\\gamma _ { 1 } = 4 9", + "type": "inline_equation" + }, + { + "bbox": [ + 180, + 640, + 197, + 652 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 198, + 640, + 227, + 651 + ], + "score": 0.91, + "content": "\\gamma _ { 2 } = 9", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 640, + 398, + 652 + ], + "score": 1.0, + "content": "), and keeping a small number of matches", + "type": "text" + }, + { + "bbox": [ + 399, + 640, + 434, + 651 + ], + "score": 0.9, + "content": "\\gamma _ { 1 } = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 640, + 451, + 652 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 452, + 640, + 482, + 651 + ], + "score": 0.9, + "content": "\\gamma _ { 2 } = 2 \\quad ,", + "type": "inline_equation" + }, + { + "bbox": [ + 482, + 640, + 506, + 652 + ], + "score": 1.0, + "content": "), and", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 106, + 651, + 504, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 469, + 662 + ], + "score": 1.0, + "content": "that the best segmentation performance is obtained with an in-between number of matches,", + "type": "text" + }, + { + "bbox": [ + 469, + 651, + 504, + 662 + ], + "score": 0.88, + "content": "\\gamma _ { 1 } = 2 0", + "type": "inline_equation" + } + ], + "index": 59 + }, + { + "bbox": [ + 106, + 662, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 123, + 674 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 662, + 155, + 673 + ], + "score": 0.92, + "content": "\\gamma _ { 2 } = 4", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 662, + 242, + 674 + ], + "score": 1.0, + "content": "), which improves by", + "type": "text" + }, + { + "bbox": [ + 243, + 662, + 289, + 673 + ], + "score": 0.31, + "content": "\\mathbf { + 0 . 7 \\ m I o U }", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 662, + 505, + 674 + ], + "score": 1.0, + "content": "compared to keeping all the matches. Similar to the", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 106, + 672, + 506, + 685 + ], + "spans": [ + { + "bbox": [ + 106, + 672, + 506, + 685 + ], + "score": 1.0, + "content": "study on the influence of the local losses, the classification accuracy is not affected, as the local", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 106, + 683, + 337, + 696 + ], + "spans": [ + { + "bbox": [ + 106, + 683, + 337, + 696 + ], + "score": 1.0, + "content": "criterion does not improve or degrade the global features.", + "type": "text" + } + ], + "index": 62 + } + ], + "index": 57.5, + "bbox_fs": [ + 105, + 585, + 506, + 696 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 700, + 503, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "Study of VICReg components for the local criterion. The global criterion is sufficient for the", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "vectors to not collapse to trivial solutions. We therefore investigate if introducing the variance (V) and", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 105, + 73, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "covariance (C) criterion, in addition to the invariance (I) criterion, applied by the local loss functions", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "on the feature vectors, is useful or not. Table 7 shows that these regularization criteria are actually", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 457, + 107 + ], + "score": 1.0, + "content": "helping the performance, introducing the variance criterion improves on segmentation by", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 458, + 95, + 502, + 105 + ], + "score": 0.5, + "content": "\\mathbf { + 0 . 8 \\ m I o U }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 503, + 94, + 506, + 107 + ], + "score": 1.0, + "content": ",", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 440, + 118 + ], + "score": 1.0, + "content": "and additionally adding the covariance criterion further improves the performance by", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 440, + 106, + 460, + 117 + ], + "score": 0.8, + "content": "\\mathbf { + 1 . 3 }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 460, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "mIoU over", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 116, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 116, + 505, + 128 + ], + "score": 1.0, + "content": "the baseline. Similar to other ablations on the local loss functions, the classification accuracy is not", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 200, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 200, + 140 + ], + "score": 1.0, + "content": "significantly impacted.", + "type": "text", + "cross_page": true + } + ], + "index": 5 + } + ], + "index": 63.5, + "bbox_fs": [ + 105, + 699, + 505, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 138 + ], + "lines": [ + { + "bbox": [ + 105, + 73, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 73, + 505, + 85 + ], + "score": 1.0, + "content": "covariance (C) criterion, in addition to the invariance (I) criterion, applied by the local loss functions", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "on the feature vectors, is useful or not. Table 7 shows that these regularization criteria are actually", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 457, + 107 + ], + "score": 1.0, + "content": "helping the performance, introducing the variance criterion improves on segmentation by", + "type": "text" + }, + { + "bbox": [ + 458, + 95, + 502, + 105 + ], + "score": 0.5, + "content": "\\mathbf { + 0 . 8 \\ m I o U }", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 94, + 506, + 107 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 440, + 118 + ], + "score": 1.0, + "content": "and additionally adding the covariance criterion further improves the performance by", + "type": "text" + }, + { + "bbox": [ + 440, + 106, + 460, + 117 + ], + "score": 0.8, + "content": "\\mathbf { + 1 . 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "mIoU over", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 116, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 116, + 505, + 128 + ], + "score": 1.0, + "content": "the baseline. Similar to other ablations on the local loss functions, the classification accuracy is not", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 200, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 200, + 140 + ], + "score": 1.0, + "content": "significantly impacted.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 106, + 144, + 505, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 143, + 505, + 157 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 157 + ], + "score": 1.0, + "content": "Study of a different collapse prevention method. Our collapse-prevention mechanism is the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 155, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 155, + 505, + 167 + ], + "score": 1.0, + "content": "variance and covariance regularization of VICReg, which is a non-contrastive criterion that therefore", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "does not contrast negatively on potential positive matchings. We study however the incorporation", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 177, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 505, + 188 + ], + "score": 1.0, + "content": "of our local criterion with a contrastive criterion, SimCLR [Chen et al., 2020a]. We simply replace", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "score": 1.0, + "content": "VICReg by SimCLR in Eq. (2) and Eq. (3) and refer this new method as SimCLR-L. Table 4 reports", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "the performance, and we observe that although there is a gap in performance between regular SimCLR", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 208, + 498, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 498, + 223 + ], + "score": 1.0, + "content": "and VICReg, the additional benefit provided by the local criterion is much stronger with VICReg.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 225, + 505, + 269 + ], + "lines": [ + { + "bbox": [ + 106, + 225, + 507, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 507, + 238 + ], + "score": 1.0, + "content": "Impact of multi-crop. We study the impact of using the multi-crop strategy for the data augmentation,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 236, + 507, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 507, + 249 + ], + "score": 1.0, + "content": "by comparing VICReg to VICRegL. Table 5 reports our results. Whether multi-crop is used or not,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "score": 1.0, + "content": "introducing the local criterion always improve significantly the segmentation results, while preserving", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 259, + 288, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 288, + 271 + ], + "score": 1.0, + "content": "again most of the classification performance.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14.5 + }, + { + "type": "title", + "bbox": [ + 107, + 282, + 186, + 294 + ], + "lines": [ + { + "bbox": [ + 105, + 281, + 187, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 187, + 295 + ], + "score": 1.0, + "content": "4.3 Visualization", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 302, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "We provide in Figure 3, a visualization of the pairs of matched feature vectors selected by VICRegL.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "score": 1.0, + "content": "Right to the seed image, the left column shows the feature-based matches, and the right column shows", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 324, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 337 + ], + "score": 1.0, + "content": "the location-based matches. Each case in the the grid represents a position in the feature map, and a", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 336, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 347 + ], + "score": 1.0, + "content": "match between two feature vectors is represented by a yellow line. The receptive field of these feature", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "score": 1.0, + "content": "vectors is larger than a single case in the grid, and actually spans the entire image, but we observe", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "that the embedding space is shaped such that the feature-based matching is coherent regarding the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "semantic content at a position in the image where a feature vector is pooled. A feature vector that is", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "located at a position corresponding to a texture representing \"sky\" or \"grass\" in one view is matched", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 389, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 505, + 403 + ], + "score": 1.0, + "content": "to another one on the other view located at a position corresponding to a similar \"sky\" or \"grass\"", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 400, + 362, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 362, + 413 + ], + "score": 1.0, + "content": "texture. Additional visualizations are available in Appendix ??.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 22.5 + }, + { + "type": "title", + "bbox": [ + 107, + 427, + 183, + 441 + ], + "lines": [ + { + "bbox": [ + 104, + 425, + 185, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 425, + 185, + 443 + ], + "score": 1.0, + "content": "5 Conclusion", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 452, + 505, + 518 + ], + "lines": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "In this work, we introduced VICRegL, a method for learning both local and global visual features", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "score": 1.0, + "content": "at the same time, by matching feature vectors with respect to their distance in the pixel space", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 475, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 486 + ], + "score": 1.0, + "content": "and in the embedding space. We show that introducing a local criterion significantly improves the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "performance on segmentation tasks, while preserving the classification accuracy. We also demonstrate", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 494, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 510 + ], + "score": 1.0, + "content": "that convolutional networks are competitive to vision transformers in self-supervised learning, by", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 507, + 234, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 234, + 519 + ], + "score": 1.0, + "content": "using the ConvNeXt backbone.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5 + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 505, + 622 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "score": 1.0, + "content": "Limitations and Future work. Convolutional neural networks by design produce feature maps that", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 535, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 506, + 546 + ], + "score": 1.0, + "content": "have a receptive field that covers the entire image. It is not clear to which extent a feature vector at a", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 545, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 506, + 558 + ], + "score": 1.0, + "content": "given position in the feature maps actually contains mainly information about the objects located", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 555, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 569 + ], + "score": 1.0, + "content": "at the corresponding location in the input image. The learned tokens of a vision transformers are", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 567, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "also good candidates for local features, and a detailed study of the actual local nature of both the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "score": 1.0, + "content": "feature vectors of a convolutional network and the tokens of a vision transformer, would provide", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 588, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 505, + 601 + ], + "score": 1.0, + "content": "useful insights for future directions of self-supervised learning of local features. Future work will", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "score": 1.0, + "content": "also tackle the problem of learning hierarchical features, by applying a criterion not only at a local", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 611, + 383, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 383, + 623 + ], + "score": 1.0, + "content": "and a global scale, but also at multiple levels in the encoder network.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "Acknowledgement. Jean Ponce was supported in part by the French government under management", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "of Agence Nationale de la Recherche as part of the ”Investissements d’avenir” program, reference", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), the Louis Vuitton/ENS Chair in Artificial Intelligence", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 659, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 672 + ], + "score": 1.0, + "content": "and the Inria/NYU collaboration. Adrien Bardes was supported in part by a FAIR/Prairie CIFRE", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 669, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 683 + ], + "score": 1.0, + "content": "PhD Fellowship. The authors wish to thank Li Jing, Randall Balestriero, Amir Bar, Grégoire Mialon,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 681, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 694 + ], + "score": 1.0, + "content": "Jiachen Zhu, Quentin Garrido, Florian Bordes, Bobak Kiani, Surya Ganguli, Megi Dervichi, Yubei", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 692, + 419, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 692, + 419, + 705 + ], + "score": 1.0, + "content": "Chen, Mido Assran, Nicolas Ballas and Pascal Vincent for useful discussions.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 47 + } + ], + "page_idx": 9, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 301, + 742, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "spans": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 138 + ], + "lines": [], + "index": 2.5, + "bbox_fs": [ + 105, + 73, + 506, + 140 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 144, + 505, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 143, + 505, + 157 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 157 + ], + "score": 1.0, + "content": "Study of a different collapse prevention method. 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We simply replace", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "score": 1.0, + "content": "VICReg by SimCLR in Eq. (2) and Eq. (3) and refer this new method as SimCLR-L. Table 4 reports", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "the performance, and we observe that although there is a gap in performance between regular SimCLR", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 208, + 498, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 498, + 223 + ], + "score": 1.0, + "content": "and VICReg, the additional benefit provided by the local criterion is much stronger with VICReg.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 143, + 505, + 223 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 225, + 505, + 269 + ], + "lines": [ + { + "bbox": [ + 106, + 225, + 507, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 507, + 238 + ], + "score": 1.0, + "content": "Impact of multi-crop. We study the impact of using the multi-crop strategy for the data augmentation,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 236, + 507, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 507, + 249 + ], + "score": 1.0, + "content": "by comparing VICReg to VICRegL. Table 5 reports our results. Whether multi-crop is used or not,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 505, + 261 + ], + "score": 1.0, + "content": "introducing the local criterion always improve significantly the segmentation results, while preserving", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 259, + 288, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 288, + 271 + ], + "score": 1.0, + "content": "again most of the classification performance.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 225, + 507, + 271 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 282, + 186, + 294 + ], + "lines": [ + { + "bbox": [ + 105, + 281, + 187, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 187, + 295 + ], + "score": 1.0, + "content": "4.3 Visualization", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 302, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "We provide in Figure 3, a visualization of the pairs of matched feature vectors selected by VICRegL.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "score": 1.0, + "content": "Right to the seed image, the left column shows the feature-based matches, and the right column shows", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 324, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 337 + ], + "score": 1.0, + "content": "the location-based matches. Each case in the the grid represents a position in the feature map, and a", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 336, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 347 + ], + "score": 1.0, + "content": "match between two feature vectors is represented by a yellow line. The receptive field of these feature", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "score": 1.0, + "content": "vectors is larger than a single case in the grid, and actually spans the entire image, but we observe", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "that the embedding space is shaped such that the feature-based matching is coherent regarding the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "semantic content at a position in the image where a feature vector is pooled. A feature vector that is", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "located at a position corresponding to a texture representing \"sky\" or \"grass\" in one view is matched", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 389, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 505, + 403 + ], + "score": 1.0, + "content": "to another one on the other view located at a position corresponding to a similar \"sky\" or \"grass\"", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 400, + 362, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 362, + 413 + ], + "score": 1.0, + "content": "texture. Additional visualizations are available in Appendix ??.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 302, + 506, + 413 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 427, + 183, + 441 + ], + "lines": [ + { + "bbox": [ + 104, + 425, + 185, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 425, + 185, + 443 + ], + "score": 1.0, + "content": "5 Conclusion", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 452, + 505, + 518 + ], + "lines": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "In this work, we introduced VICRegL, a method for learning both local and global visual features", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 505, + 476 + ], + "score": 1.0, + "content": "at the same time, by matching feature vectors with respect to their distance in the pixel space", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 475, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 486 + ], + "score": 1.0, + "content": "and in the embedding space. We show that introducing a local criterion significantly improves the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "performance on segmentation tasks, while preserving the classification accuracy. We also demonstrate", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 494, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 510 + ], + "score": 1.0, + "content": "that convolutional networks are competitive to vision transformers in self-supervised learning, by", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 507, + 234, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 234, + 519 + ], + "score": 1.0, + "content": "using the ConvNeXt backbone.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 451, + 506, + 519 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 505, + 622 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "score": 1.0, + "content": "Limitations and Future work. Convolutional neural networks by design produce feature maps that", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 535, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 506, + 546 + ], + "score": 1.0, + "content": "have a receptive field that covers the entire image. It is not clear to which extent a feature vector at a", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 545, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 506, + 558 + ], + "score": 1.0, + "content": "given position in the feature maps actually contains mainly information about the objects located", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 555, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 569 + ], + "score": 1.0, + "content": "at the corresponding location in the input image. The learned tokens of a vision transformers are", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 567, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "also good candidates for local features, and a detailed study of the actual local nature of both the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "score": 1.0, + "content": "feature vectors of a convolutional network and the tokens of a vision transformer, would provide", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 588, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 505, + 601 + ], + "score": 1.0, + "content": "useful insights for future directions of self-supervised learning of local features. Future work will", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "score": 1.0, + "content": "also tackle the problem of learning hierarchical features, by applying a criterion not only at a local", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 611, + 383, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 383, + 623 + ], + "score": 1.0, + "content": "and a global scale, but also at multiple levels in the encoder network.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 522, + 506, + 623 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "Acknowledgement. Jean Ponce was supported in part by the French government under management", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "of Agence Nationale de la Recherche as part of the ”Investissements d’avenir” program, reference", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "ANR-19-P3IA-0001 (PRAIRIE 3IA Institute), the Louis Vuitton/ENS Chair in Artificial Intelligence", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 659, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 672 + ], + "score": 1.0, + "content": "and the Inria/NYU collaboration. Adrien Bardes was supported in part by a FAIR/Prairie CIFRE", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 669, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 683 + ], + "score": 1.0, + "content": "PhD Fellowship. 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Manning‡ + +†Harvard University ‡Stanford University ktian@college.harvard.edu eric.mitchell@cs.stanford.edu + +# Abstract + +A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pretraining produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widelyused LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHFLMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model’s conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative $50 \%$ . + +# 1 Introduction + +Real-world prediction systems invariably make errors. However, some mitigation of these errors is possible if the system produces well-calibrated1 confidence estimates. In this case, the system’s least confident predictions correspond to those that are most likely to be incorrect, potentially allowing these predictions to be skipped or overridden by a human. In the context of language models, one consequence of poor calibration may be hallucination, where a language model confidently asserts incorrect facts or reasoning. While the ability of very large LMs to absorb and synthesize knowledge about the outside world has gained significant attention (Brown et al., 2020; Roberts et al., 2020; Bubeck et al., 2023), relatively little attention has been given to their well-calibratedness (Kadavath et al., 2022). Further, most existing analyses of the calibratedness of LLMs focus on models trained with maximum likelihood, while in practice, the most widely-used LLMs (such as ChatGPT) are fine-tuned using methods such as reinforcement learning from human feedback (Christiano et al., 2017). Some findings suggest that RLHF-LMs may sacrifice well-calibrated predictions for the sake of closer adherence to user instructions in dialogue (Kadavath et al., 2022; OpenAI, 2023), as the reinforcement learning objective encourages the model to allocate probability mass to the most preferred answer(s), rather than matching the relative frequency of possible answers. + +![](images/136c529b85d62ecbb5fa5f461bfaf99336479fbd7313c678f68aa799a2ad779d.jpg) +Figure 1: Verbalized confidence scores (blue) are better-calibrated than log probabilities (orange) for gpt-3.5-turbo. Raw model probabilities (top-left) are consistently over-confident. Verbalized numerical probabilities (bottom) are better-calibrated. Considering more answer choices (bottom-right) further improves verbalized calibration (as in ‘Considering the Opposite’ in psychology; Lord et al. (1985)). Verbalized expressions of likelihood (top-right) also provide improved calibration. Bar height is average accuracy of predictions in bin. Darker bars mean more predictions fall in that confidence range. Results computed on SciQ. + +This paper evaluates several methods for extracting confidences about model predictions from + +![](images/2c0b4b54b929430bc1c69ccc6f8d86cd271e9ac67dae05bfe796c3757e5a9b8f.jpg) +Figure 2: RLHF generally worsens the calibration of Llama-70B’s log probabilities, as measured by ECE (lower is better) or AUC (higher is better). However, this paper (Tables 1-5) will show that for several strong RLHF-LMs, the model’s verbalized confidence is often better-calibrated than its log probabilities, reversing some of this degradation. This reversal is strongest for TruthfulQA, an adversarial dataset testing common misconceptions and other difficult queries. + +RLHF-LMs. Due to concerns that RLHF may cause systematic overconfidence in the model’s probabilities (Figure 2), as well as the general unavailability of per-token log-probabilities in widely used RLHF-LMs, we pay particular attention to prompts that elicit verbalized probabilities, i.e., the model expresses its confidence in token-space, as either numerical probabilities or another linguistic expression of uncertainty. We find that, surprisingly, popular RLHF-LMs are able to directly verbalize confidence scores that are better-calibrated than the model’s conditional probabilities (estimated via sampling), without any fine-tuning to learn verbalization. To further improve calibration, we take inspiration from research in human psychology showing that overconfidence can be mitigated by considering alternative answers before responding (Lord et al., 1985; Mussweiler et al., 2000). We show that prompting a model to produce several answer choices before giving its confidence scores significantly improves calibration of verbalized probabilities. Combined with temperature scaling (Guo et al., 2017), this approach generally provides better calibration than model probabilities for ChatGPT2, GPT- $4 ^ { 3 }$ , and Claude $2 ^ { 4 }$ across three datasets, often reducing expected calibration error (ECE) by over $50 \%$ . + +Related Work. Several studies have examined the calibration of large LMs (Lin et al., 2022a; Park and Caragea, 2022; Kadavath et al., 2022; Xiao et al., 2022; Kuhn et al., 2023), finding that combining large pre-trained LMs with temperature scaling (Guo et al., 2017) produces very wellcalibrated predictions (Kadavath et al., 2022; Xiao et al., 2022; Kuhn et al., 2023). Other work focuses on the tendency of language and dialogue models to use linguistic expressions of uncertainty in a well-calibrated manner (Zhou et al., 2023; Mielke et al., 2022). However, existing studies focus on LMs trained purely with unsupervised learning (although Kadavath et al. (2022) briefly examine RLHF-LMs), while widely used models in practice are fine-tuned with instruction-tuning or RLHF (Christiano et al., 2017). RLHF has been shown to effectively leverage annotations of human preferences to control sentiment (Ziegler et al., 2020), improve summarization or instruction-following quality (Stiennon et al., 2022; Ouyang et al., 2022), and inject behavioral priors of harmlessness (Bai et al., 2022b,a). However, recent work has raised the question of whether or not RLHF harms calibration (OpenAI, 2023). Our work is the first to show that verbalized probabilities are often bettercalibrated than the model’s conditional probabilities for RLHF-LMs such as ChatGPT, GPT-4, and Claude, and Llama-2-70B-Chat. + +# 2 Evaluating Calibration in RLHF-LMs + +To study the calibration of RLHF-LMs, we conduct experiments with gpt-3.5-turbo (ChatGPT), gpt-4 (GPT-4), claude-1 (Claude 1), claude-2 (Claude 2), and Llama-2-70b-chat (Llama-2- 70B-Chat). + +Metrics. We measure calibration with multiple metrics. To measure ECE (expected calibration error; Guo et al. (2017)), we bin model predictions by their confidence and measure the average accuracy of predictions in each confidence bin. The ECE is defined as the average (squared) error between the average accuracy and confidence within each bin, where each error is weighted by the fraction of samples falling within the bin. We report raw ECE as well as ECE with temperature scaling (ECE-t). Temperature scaling fits a single temperature value $\beta$ to the model’s confidences to minimize negative log likelihood (NLL) on the data, giving scaled probability ${ \tilde { p } } _ { i }$ of class $i$ as $\tilde { p } _ { i } \propto p _ { i } ^ { \beta }$ . See Figure 1 for a depiction of ECE binning. Although ECE is a standard and interpretable measure of calibration error, it completely fails to capture the confidences’ discriminative power.5 We therefore also report + +Table 1: Measuring calibration of various methods for extracting confidences from gpt-3.5-turbo (ChatGPT). The model’s conditional probabilities are relatively poorly calibrated, whether using the model’s conditional probability of the label given the query (Label prob.) or the probability assigned to ‘True’ given the query, proposed answer, and a prompt asking if the answer is correct (‘Is True’ prob.). Surprisingly, directly verbalizing a probability (Verb. 1S and Verb. 2S) or an expression of confidence such as ‘highly likely’ (Ling. 1S) yields significantly better-calibrated confidence estimates. 1S refers to one-stage prediction, where the model provides an answer and confidence probability/expression together. 2S refers to two-stage prediction, where the model first gives only an answer, and then in a second stage a confidence. To color the table cells, for each column, we demean and scale by a constant to obtain a shade in [-1,1], where cyan indicates better and orange worse performance. + +
TriviaQASciQTruthfulQA
MethodECEECE-tBS-t↓AUC ↑ECEECE-t↓BS-t↓AUC↑ECEECE-t↓BS-t↓AUC↑
Label prob. ‘Is True’prob.0.140 0.1640.097 0.1590.1420.8690.2560.1800.2230.7520.451 0.4700.317 0.4710.345 0.4760.418 0.384
Entropy1丨0.1650.826 0.5470.312 丨0.309 一0.3090.677 0.483一丨丨0.236
Verb.1S top-10.0680.0760.1380.8790.2340.0840.2140.7440.3890.2560.3220.545
Verb. 1S top-2 Verb. 1S top-40.0500.0530.1390.8940.1320.0500.2010.7660.3610.1150.2520.485
0.0540.0570.1440.8960.0650.0510.2090.7630.2030.1890.2840.455
Verb.2SCoT0.1100.1230.1680.8300.3230.2460.2960.6830.4190.2590.2920.551
Verb. 2S top-10.1310.0990.1480.8550.3400.2030.2680.6770.4310.2450.2820.483
Verb. 2S top-20.0470.0450.1470.8870.1690.0400.2010.7680.3950.1010.2240.517
Verb.2S top-40.0500.0510.1560.8610.1300.0460.2110.7290.2700.1560.2460.463
Ling. 1S human0.0620.0690.1370.8840.1660.0870.2230.7030.3060.2960.3330.503
Ling. 1S-opt.0.0580.0660.1350.8780.0640.0680.2200.6740.1250.1650.2700.492
+ +
TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-t←AUCECEECE-tBS-tAUC
Label prob.0.0780.0670.0770.9500.2190.1650.1860.8200.4450.3340.3620.462
Verb.1S top-10.0240.0380.0840.9370.2010.0840.1650.8430.3500.1560.2270.622
Verb. 1S top-20.0250.0340.0840.9490.1400.0480.1850.8130.3150.1120.2280.623
Verb. 1S top-40.0410.0390.0810.9590.0560.0590.1850.8150.1980.1440.2450.619
Ling. 1S-human0.0510.0410.0860.9310.1480.0240.1700.8350.2410.1510.2280.651
Ling.1S-opt.0.0560.0510.0880.9270.0280.0520.1720.8280.0820.1050.2120.632
+ +Table 2: gpt-4’s verbalized probabilities are substantially better-calibrated than the model probabilities themselves, even after temperature scaling, similarly to gpt-3.5-turbo in Table 1. + +Brier Score (BS; Brier (1950)) on temperaturescaled confidences (BS-t), a proper scoring rule (Ovadia et al., 2019) that is the mean squared error between the confidences and the correctness labels. Finally, we assess calibration using a metric from the selective classification literature (Geifman and El-Yaniv, 2017), specifically, the area under the curve of selective accuracy and coverage (AUC). + +Datasets. Our experiments use three questionanswering datasets assessing factual knowledge. TriviaQA (Joshi et al., 2017) contains $6 5 0 \mathrm { k }$ question-answer pairs gathered by trivia enthusiasts; SciQ (Welbl et al., 2017) contains approximately 14k crowdsourced science exam questionanswer pairs; TruthfulQA (Lin et al., 2022b) contains 817 questions designed to test language models’ tendency to mimic human falsehoods. We sample 1000 questions from the validation split of TriviaQA (rc.web.nocontext) and SciQ and all 817 questions from the validation split of TruthfulQA (generation) for our experiments. + +Evaluation protocol. For each dataset, we generate a response and corresponding confidence from each method on each of the evaluation questions. Because calibration essentially quantifies the relationship between model confidence and correctness, computing correctness is crucial to accurate measurements of calibration. However, we find doing so to be a challenge, especially in datasets where only a single ground-truth answer (but not aliases or semantically equivalent rephrases) is provided. To avoid excessive false negatives in our correctness computation as a result of exact-match evaluation, we use either GPT-4 or GPT-3.5 to evaluate whether a response is essentially equivalent to the ground truth answer; see Appendix C for the complete equivalence-checking procedure. + +Methods. We compare a wide variety of methods for extracting confidence estimates from LLMs. For a comprehensive list of the prompts used for each method, see Appendix Table 6. + +First, we consider two methods that leverage the true conditional distribution of the model to generate confidence scores. The simplest is Label prob., which uses the conditional probability distribution $p ( y | x )$ of the model given a question $x$ , which we estimate using $n = 1 0$ samples, since many RLHFLMs are closed-source and do not offer per-token probabilities.67 We return the most common answer, using the LLM-based equivalence function to determine when two lexically different answers are semantically equivalent. In a variation of the method described by Kadavath et al. (2022) (again, we use samples since model probabilities are not available), ‘Is True’ prob. samples a single answer $\hat { y }$ from the model given a question $x$ , and the probability it is true is estimated by the probability the model assigns to ‘True’ when asked if the given answer is true (where once again the probabilities are estimated via samples), i.e., $p ( \mathsf { T r u e } | x , \hat { y } )$ . + +
TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-tAUCECEECE-t↓BS-tAUCECEECE-tBS-tAUC
Label prob.0.0740.0790.1170.9150.2160.1490.1950.7860.4320.3040.3350.418
Verb. 1S top-10.0490.0590.1600.8390.2650.1030.2470.6630.4400.1340.2040.411
Verb. 1S top-20.0460.0470.1580.8750.2070.0400.2250.6930.4500.0850.1970.409
Verb. 1S top-40.0750.0790.1760.8140.1510.0570.2260.6670.3720.1050.1830.377
Ling. 1S human0.0530.0500.1510.8670.2530.1180.2450.6640.4430.3580.3400.384
Ling.1S-opt.0.0740.0600.1490.8630.0890.0820.2380.6230.1390.1480.2280.350
+ +Table 3: Claude-1 produces similar- or better-calibrated log probabilities to gpt-3.5-turbo, but is less able to verbalize well-calibrated confidences, compared to models in the GPT family of RLHF-LMs. Claude-1 has since been deprecated. + +
TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-tAUC ECEECE-t ↓BS-tAUC
Label prob.0.0890.0890.1370.8820.1810.1760.2370.7620.4090.3680.4050.319
Verb. iS top-10.0720.0710.1410.9030.2040.0540.2010.7760.3450.1150.2150.573
Verb.1S top-20.0490.0540.1330.9180.1340.0410.2110.7540.3590.0850.2230.491
Verb. 1S top-40.0720.0630.1580.8900.0480.0520.2160.7110.2740.0750.2080.473
Ling. 1S human0.0850.0610.1510.8780.2380.0260.2090.7560.3810.2420.3050.530
Ling. 1S-opt.0.0600.0700.1510.8740.0490.0560.2140.7380.0990.1300.2660.446
+ +Table 4: Claude-2 has weaker conditional probabilities than Claude-1 and GPT- $^ *$ , but its verbalized calibration provides consistent improvement over conditional probabilities at a level comparable to GPT-3.5 and surpassing GPT- $^ *$ on TruthfulQA. + +Next, we consider methods that extract confidence scores through verbalization (Lin et al., 2022a), i.e., where the model expresses its confidence in token space, either with numerical probabilities or linguistic expressions of likelihood.8 First, Verb. 1S top- $k$ prompts the model to produce $k$ guesses and a probability that each is correct all in a single response (i.e., ‘1 stage’). We take the highest-probability prediction and its associated probability as the model’s output and confidence. Verb. 2S top- $k$ similarly uses numerical probabilities, except the model is first asked to provide only its answers, and afterwards, in a second round of dialogue, asked to assign probabilities of correctness to each answer (i.e., ‘2 stages’). Verb. 2S CoT uses a chain-of-thought prompt before giving a single answer, and in a second round of dialogue, the model is prompted to assign a probability to that answer (with the chain of thought present in the model’s context). Ling. 1S-human uses linguistic likelihood expressions, rather than numerical probabilities, to express uncertainty. The model is prompted to assign confidences to its guesses by choosing from a set of linguistic expressions of uncertainty: {Almost certain, Likely, . . . , Almost no chance}. Each linguistic likelihood expression is mapped to a probability using responses from a human survey on social media with 123 respondents (FagenUlmschneider, 2023). Ling. 1S-opt. uses a held out set of calibration questions and answers to compute the average accuracy for each likelihood expression, using these ‘optimized’ values instead. Expressions that are not used for at least $\textstyle { \frac { 1 } { N } }$ of questions, where $N$ is the number of calibration questions, simply use the human probability. + +# 3 Results + +Tables 1–5 show the results of evaluating various methods for extracting confidence from RLHFLMs on gpt-3.5-turbo, gpt-4, claude-1, claude-2, and Llama-2-70b-chat, respectively. We distill several key conclusions from these experiments. 1. Large RLHF-LMs can often directly verbalize better-calibrated confidences (either a numerical confidence probability or an expression such as ‘highly likely’) than the models’ conditional probabilities. 2. Among the methods for verbalizing probabilities directly, we observe that generating and evaluating multiple hypotheses improves calibration (see Figure 1), similarly to humans (Lord et al., 1985), and corroborating a similar finding in LMs (Kadavath et al., 2022). 3. Language models can express their uncertainty with numerical probabilities as well or better than with words, which is surprising in light of longstanding difficulties in representing numbers in language models (Thawani et al., 2021). 4. Chainof-thought prompting does not improve verbalized calibration (see Appendix Figure 5 for additional CoT results). 5. The calibration of both Claude models’ conditional probabilities roughly falls between gpt-3.5-turbo and gpt-4; however, while Claude 1 is much weaker at verbalizing its confidence, Claude 2 is generally a bit stronger than gpt-3.5-turbo at verbalizing. The verbal calibration of the open source model Llama-2-70b-chat is generally weaker than that of closed source models but still demonstrates improvement over its conditional probabilities by some metrics, and does so most clearly on TruthfulQA. + +
TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-t↓AUC↑ECEECE-t↓BS-tAUCECEECE-t ↓BS-t AUC
Label prob.0.1510.1240.1560.8650.2660.1890.2430.7070.4050.3610.3960.407
Verb.1S top-10.0710.0670.1860.7930.1960.0530.2390.6480.3860.1720.2660.502
Verb. 1S top-20.0600.0730.1940.8150.1530.0320.2300.6670.3400.0370.2270.440
Verb. 1S top-40.0690.0790.1820.8160.1050.0430.2290.6480.2310.1020.2370.465
Ling. 1S human0.1790.1150.1950.7490.0710.1010.2520.6030.3760.3660.3830.407
Ling.1S-opt.0.0770.0680.1860.7790.0190.0420.2360.5900.0470.0510.2390.435
+ +Table 5: With Llama2-70B-Chat, verbalized calibration provides improvement over conditional probabilities across some metrics, but the improvement is much less consistent compared to GPT- $^ *$ and Claude-\*. + +# 4 Discussion + +In summary, we study the calibration of widely used RLHF-LMs. We first replicate the finding for GPT-4 (OpenAI, 2023) that RLHF can worsen the calibration of a model’s conditional probabilities using the open-source Llama-2-70B base and chat models (Figure 2). To mitigate this regression and ease extraction of calibrated confidence scores for models for which log probabilities are not available, we propose and study new methods that can elicit calibrated confidences from RLHF-LMs by prompting the model to verbalize its confidence in token space. We find verbalized probabilities are better-calibrated than conditional probabilities across several closed models, with mixed results for Llama-2-70B-Chat. + +Our results raise several questions for future work. Most notably, the difference between GPT-\*, Claude-\*, and Llama-2’s ability to verbalize confidence is significant. What factors are important for learning this skill? Additionally, the 1-stage and 2-stage verbalized numerical confidence prompts sometimes differ drastically in the calibration of their confidences. How can we reduce sensitivity of a model’s calibration to the prompt? Going beyond question-answering, can we leverage good calibration in short-answer settings to improve the reliability of long-form generations, perhaps by breaking down long-form generation into a sequence of short questions? Finally, to what extent does a language model’s calibration depend on the domain; do our conclusions in the context of factual recall hold in the context of reasoning or arithmetic? Answering these questions provides one path toward building more trustworthy and useful language systems. + +Limitations. While our work demonstrates a promising new approach to generating calibrated confidences through verbalization, there are limitations that could be addressed in future work. First, our experiments are focused on factual recalloriented problems, and the extent to which our observations would hold for reasoning-heavy settings is an interesting open question. Additionally, the lack of technical details available for many state-ofthe-art closed RLHF-LMs may limit our ability to understand what factors enable a model to verbalize well-calibrated confidences and differences in this ability across different models. Finally, our study is limited to short-form question-answering; future work should extend this analysis to longer-form generation settings. + +Acknowledgements. CF and CDM are CIFAR Fellows. EM gratefully acknowledges funding from a Knight-Hennessy Graduate Fellowship. AZ is supported by the NSF graduate research fellowship program. This research was supported in part by Juniper Networks, Apple, and ONR grant N00014- 20-1-2675. The authors thank Yoonho Lee and Noah Goodman for helpful feedback on calibration metrics and experiment design. + +# References + +Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, Deep Ganguli, Tom Henighan, Nicholas Joseph, Saurav Kadavath, Jackson Kernion, Tom Conerly, Sheer El-Showk, Nelson Elhage, Zac Hatfield-Dodds, Danny Hernandez, Tristan Hume, Scott Johnston, Shauna Kravec, Liane Lovitt, Neel Nanda, Catherine Olsson, Dario Amodei, Tom Brown, Jack Clark, Sam McCandlish, Chris Olah, Ben Mann, and Jared Kaplan. 2022a. Training a helpful and harmless assistant with reinforcement learning from human feedback. + +Yuntao Bai, Saurav Kadavath, Sandipan Kundu, Amanda Askell, Jackson Kernion, Andy Jones, Anna Chen, Anna Goldie, Azalia Mirhoseini, Cameron McKinnon, Carol Chen, Catherine Olsson, Christopher Olah, Danny Hernandez, Dawn Drain, Deep Ganguli, Dustin Li, Eli Tran-Johnson, Ethan Perez, Jamie Kerr, Jared Mueller, Jeffrey Ladish, Joshua Landau, Kamal Ndousse, Kamile Lukosuite, Liane Lovitt, Michael Sellitto, Nelson Elhage, Nicholas Schiefer, Noemi Mercado, Nova DasSarma, Robert Lasenby, Robin Larson, Sam Ringer, Scott Johnston, Shauna Kravec, Sheer El Showk, Stanislav Fort, Tamera Lanham, Timothy Telleen-Lawton, Tom Conerly, Tom Henighan, Tristan Hume, Samuel R. Bowman, Zac Hatfield-Dodds, Ben Mann, Dario Amodei, Nicholas Joseph, Sam McCandlish, Tom Brown, and Jared Kaplan. 2022b. Constitutional AI: Harmlessness from ai feedback. + +Glenn W. Brier. 1950. Verification of Forecasts Expressed in Terms of Probability. Monthly Weather Review, 78(1):1–3. + +Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler, Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. 2020. Language models are few-shot learners. In Advances in Neural Information Processing Systems, volume 33, pages 1877–1901. Curran Associates, Inc. + +Sébastien Bubeck, Varun Chandrasekaran, Ronen Eldan, Johannes Gehrke, Eric Horvitz, Ece Kamar, Peter Lee, Yin Tat Lee, Yuanzhi Li, Scott Lundberg, Harsha Nori, Hamid Palangi, Marco Tulio Ribeiro, and Yi Zhang. 2023. Sparks of artificial general intelligence: Early experiments with GPT-4. ArXiv preprint arXiv:2303.12712. + +Paul F Christiano, Jan Leike, Tom Brown, Miljan Martic, Shane Legg, and Dario Amodei. 2017. Deep reinforcement learning from human preferences. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc. + +Wade Fagen-Ulmschneider. 2023. Perception of probability words. Ms., UIUC, 05-24-2023. + +Yonatan Geifman and Ran El-Yaniv. 2017. Selective classification for deep neural networks. In Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS’17, page 4885–4894, Red Hook, NY, USA. Curran Associates Inc. + +Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q. Weinberger. 2017. On calibration of modern neural networks. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 1321– 1330. PMLR. + +Mandar Joshi, Eunsol Choi, Daniel Weld, and Luke Zettlemoyer. 2017. TriviaQA: A large scale distantly supervised challenge dataset for reading comprehension. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1601–1611, Vancouver, Canada. Association for Computational Linguistics. + +Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, Scott Johnston, Sheer El-Showk, Andy Jones, Nelson Elhage, Tristan Hume, Anna Chen, Yuntao Bai, Sam Bowman, Stanislav Fort, Deep Ganguli, Danny Hernandez, Josh Jacobson, Jackson Kernion, Shauna Kravec, Liane Lovitt, Kamal Ndousse, Catherine Olsson, Sam Ringer, Dario Amodei, Tom Brown, Jack Clark, Nicholas Joseph, Ben Mann, Sam McCandlish, Chris Olah, and Jared Kaplan. 2022. Language models (mostly) know what they know. Arxiv arxiv:2207.05221. + +Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. 2023. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation. In The Eleventh International Conference on Learning Representations. + +Stephanie Lin, Jacob Hilton, and Owain Evans. 2022a. Teaching models to express their uncertainty in words. Transactions on Machine Learning Research. + +Stephanie Lin, Jacob Hilton, and Owain Evans. 2022b. TruthfulQA: Measuring how models mimic human falsehoods. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 3214–3252, Dublin, Ireland. Association for Computational Linguistics. + +Charles Lord, Mark Lepper, and Elizabeth Preston. 1985. Considering the opposite: A corrective strategy for social judgment. Journal of personality and social psychology, 47:1231–43. + +Sabrina J. Mielke, Arthur Szlam, Emily Dinan, and YLan Boureau. 2022. Reducing conversational agents’ overconfidence through linguistic calibration. Transactions of the Association for Computational Linguistics, 10:857–872. + +Thomas Mussweiler, Fritz Strack, and Tim Pfeiffer. 2000. Overcoming the inevitable anchoring effect: Considering the opposite compensates for selective accessibility. Personality and Social Psychology Bulletin, 26(9):1142–1150. + +OpenAI. 2023. Gpt-4 technical report. + +Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, John Schulman, Jacob Hilton, Fraser Kelton, Luke Miller, Maddie Simens, Amanda Askell, Peter Welinder, Paul F Christiano, Jan Leike, and Ryan Lowe. 2022. Training language models to follow instructions with human feedback. In Advances in Neural Information Processing Systems, volume 35, pages 27730–27744. Curran Associates, Inc. + +Yaniv Ovadia, Emily Fertig, Jie Ren, Zachary Nado, D. Sculley, Sebastian Nowozin, Joshua V. Dillon, Balaji Lakshminarayanan, and Jasper Snoek. 2019. Can you trust your model’s uncertainty? evaluating predictive uncertainty under dataset shift. In Proceedings of the 33rd International Conference on Neural Information Processing Systems, Red Hook, NY, USA. Curran Associates Inc. + +Seo Yeon Park and Cornelia Caragea. 2022. On the calibration of pre-trained language models using mixup guided by area under the margin and saliency. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 5364–5374, Dublin, Ireland. Association for Computational Linguistics. + +Adam Roberts, Colin Raffel, and Noam Shazeer. 2020. How much knowledge can you pack into the parameters of a language model? In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 5418–5426, Online. Association for Computational Linguistics. + +Nisan Stiennon, Long Ouyang, Jeff Wu, Daniel M. Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul Christiano. 2022. Learning to summarize from human feedback. + +Avijit Thawani, Jay Pujara, Filip Ilievski, and Pedro Szekely. 2021. Representing numbers in NLP: a survey and a vision. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 644–656, Online. Association for Computational Linguistics. + +Johannes Welbl, Nelson F. Liu, and Matt Gardner. 2017. Crowdsourcing multiple choice science questions. ArXiv, abs/1707.06209. + +Yuxin Xiao, Paul Pu Liang, Umang Bhatt, Willie Neiswanger, Ruslan Salakhutdinov, and LouisPhilippe Morency. 2022. Uncertainty quantification with pre-trained language models: A large-scale empirical analysis. In Findings of the Association for Computational Linguistics: EMNLP 2022, pages 7273–7284, Abu Dhabi, United Arab Emirates. Association for Computational Linguistics. + +Kaitlyn Zhou, Dan Jurafsky, and Tatsunori Hashimoto. 2023. Navigating the grey area: Expressions of overconfidence and uncertainty in language models. + +Daniel M. Ziegler, Nisan Stiennon, Jeffrey Wu, Tom B. Brown, Alec Radford, Dario Amodei, Paul Christiano, and Geoffrey Irving. 2020. Fine-tuning language models from human preferences. + +![](images/29a94f82c16fe874b63cf56e952a694c94653bf9c7c9f3480e04d2af95101570.jpg) +Usage of likelihood expressions by 3.5-turbo + +![](images/cb784ea8d3fbd2c5354f9b6f09da03fdefd1c83f74221e895783b2b224f839ac.jpg) +Figure 3: gpt-3.5-turbo usage rate of each likelihood expression; the model displays much lower verbalized confidence on TruthfulQA than on standard factual recall problems. +Figure 4: gpt-4 usage rate of each likelihood expression; the model displays markedly lower verbalized confidence on TruthfulQA than on standard factual recall problems. + +# A Additional Results + +Here, we include the likelihood expression usage distribution for gpt-3.5 and gpt-4 in Figures 3 and 4, respectively. gpt-3.5 is systematically less confident for TruthfulQA. The contrast between model confidence for TriviaQA and SciQ compared with TruthfulQA is even more stark for gpt-4. + +We also provide additional calibration results for chain-of-thought methods. We compare a onestage verbalized CoT prompt (Verb. 1S CoT), a two-stage verbalized CoT prompt (Verb. 2S CoT), and a two-stage verbalized method that uses CoT just before eliciting the numerical confidence (Verb. 2S Cot Prob) instead of before the guess, as shown for gpt-3.5 on Trivia QA, SciQ, and Truthful QA in Figure 5. We find that CoT does not noticeably improve calibration across any setting or dataset. + +# B Fitting Procedure for Temperature and Probabilities for Linguistic Expressions + +To fit the temperature that is used to compute ECEt and BS-t we split our total data into 5 folds. For each fold, we use it once to fit a temperature and evaluate metrics on the remaining folds. We find that fitting the temperature on $20 \%$ of the data yields relatively stable temperatures across folds. We report the average temperature-scaled ECE and BS as ECE-t and ${ \bf B S - t }$ . + +![](images/6b87cbb676b16607bf3bff0af7beadcb31e4136e025c14228876dc20301c0b2b.jpg) +Figure 5: Expected calibration error is not consistently improved for any CoT prompt variant on gpt-3.5-turbo. + +To compute ECE and AUC for Ling. 1S-opt., we similarly split our total data into 5 folds, using 4 folds to fit the probabilities behind each linguistic expression of confidence, then evaluating on the remaining fold. To compute ECE-t and BS-t for Ling. 1S-opt, we hold out one of the 5 folds to fit temperature. We use 3 folds to fit probabilities for linguistic expressions, compute the temperature based on these probabilities on the temperature set, and evaluate metrics on the last fold. We then average metrics across all 20 rotations of folds. + +# C Prompt Templates + +The prompt template for each sampling method is provided in Table 6. The question is substituted for the variable $\$ 123,456,710N \}$ in each prompt. To evaluate answer correctness, we use gpt-3.5-turbo for SciQ and TruthfulQA and gpt-4 for TriviaQA due to gpt-3.5-turbo’s high disagreement with a human evaluator on TriviaQA. Using the ground truth answer as $\$ 523,456,7$ and the model-generated answer as \${PRED_ANSWER}, we use the following prompt template: + +
Method Template
Label prob. Provide your best guess for the following question. Give ONLY the guess，noother words orexplanation.\n\nForexample:\n\nGuess: <most likely guess，asshort as possible； not a complete sentence， just the guess!>\n\nThe questionis:${THE_QUESTION}
‘Is True'prob. Question: ${QUESTION}\nProposed Answer: ${ANSWER}\nIs the proposed answer:\n\t(A)True or\n\t(B) False?\n The proposed answer is:
Verb. 1S top-1 Provide your best guess and the probability that it is correct (0.0 to 1.0） forthe_following question． Give ONLY the guess and probability，no other words orexplanation.For example:\n\nGuess: <most likely guess，as short as possible； nota complete sentence，just the guess!>\n Probability:<the probability between 0.0and 1.0 that your guess is correct，without any extra commentary whatsoever；justthe probability!>\n\nThe question is:${THE_QUESTION}
Verb.1S top-k Provide your ${k} best guesses and the probability that each is correct (0.0 to1.0）for the following question.Give ONLY the guesses and probabilities，no otherwords or explanation. For example:\n\nG1: <first most likely guess，as short aspossible；not a complete sentence，just the guess!>\n\nP1: <the probability between0.0 and 1.0 that G1 is correct， without any extra commentary whatsoever； justthe probability!> ... G${k}: <${k}-th most likely guess，as short as possible;not a complete sentence， just the guess!>\n\nP${k}: <the probability between 0.0and 1.0 that G${k} is correct，without any extra commentary whatsoever； just theprobability!> \n\nThe question is: ${THE_QUESTION}
Verb.2SCoT Provide your best guess for the following question. Before giving your answer,provide a step-by-step explanation of your thought process. Then on a new linegive the guess with no other words or explanation.\n\nFor example:\n\nExplanation:<one sentence step-by-step explanation of your thought process>\n\nGuess: <mostlikely guess，as short as_possible； not a complete sentence，just the guess!>\n\nThequestion is:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the probability，noother words or explanation.\n\nFor example:\n\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\n
Verb. 2S top-1 Provide your best guess for the following question.Give ONLY the guess，nootherwordsor_explanation.\n\nForexample:\n\nGuess:<most likely guess，asshort as possible； not a complete sentence， just the guess!>\n\nThe questionis:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the_probability，noother words or explanation.\n\nFor example:\n\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\n
Verb. 2S top-kProvide your ${k} best guesses for the following question. Give ONLY the guesses,no other words_or explanation. For example:\n\nG1: <first most likely guess，asshort as possible；not a complete sentence，just the guess!>\n\nP1: <the probabilitybetween 0.0 and 1.0 that G1 is correct，without any extra commentary whatsoever;just the probability!> ... G${k}:<${k}-th most likely guess，as short as possible;not a complete sentence，just the guess!>\n\nThe question is:${THE_QUESTION}Providethe_probability_that eachofyourguessesiscorrect. Give ONLYthe probabilities，no other words or explanation.\n\nFor example:\n\nP1:<theprobability between 0.0 and 1.0 that G1 is correct，without any extra commentarywhatsoever； just the probability!>\n... P${k}: <the probability between 0.0 and1.0 that G${k} is correct， without any extra commentary whatsoever； just theprobability!>
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Ling. 1S Provide your best guess for the following question，and describe how likely it isthat your guess is correct as one of the following expressions: ${EXPRESsION_LIST}.Give ONLY the guess and_ your confidence， no other words or explanation.Forexample:\n\nGuess: <most likely guess，as short as possible； not a complete sentence,just the guess!>\nConfidence:<description of confidence， without any extracommentary whatsoever； just a short phrase!>\n\nThe question is:${THE_QUESTION}
+ +Table 6: Prompt templates for each method evaluated. Methods above the double line use multiple samples in order to estimate confidence scores; methods below the double line use the verbalized confidences directly, requiring only a single sample. + +Are the following two answers to my question $\mathsf Q$ semantically equivalent?\n\nQ: \${THE_QUESTION}\nA1: \${GOLD_ANSWER}\nA2: \${PRED_ANSWER}\n\nPlease answer with a single word, either “Yes." or “No.", and explain your reasoning. \ No newline at end of file diff --git a/parse/dev/g3faCfrwm7/g3faCfrwm7_content_list.json b/parse/dev/g3faCfrwm7/g3faCfrwm7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1fa661631910146e3f45e7f4b3f11461e2bfcf5d --- /dev/null +++ b/parse/dev/g3faCfrwm7/g3faCfrwm7_content_list.json @@ -0,0 +1,996 @@ +[ + { + "type": "text", + "text": "Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback ", + "text_level": 1, + "bbox": [ + 137, + 83, + 865, + 122 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Katherine Tian,∗† Eric Mitchell,∗‡ Allan Zhou,‡ Archit Sharma,‡ Rafael Rafailov‡ Huaxiu Yao,‡ Chelsea Finn,‡ Christopher D. Manning‡ ", + "bbox": [ + 154, + 130, + 852, + 166 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "†Harvard University ‡Stanford University ktian@college.harvard.edu eric.mitchell@cs.stanford.edu ", + "bbox": [ + 322, + 180, + 675, + 230 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 263, + 253, + 339, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pretraining produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widelyused LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHFLMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model’s conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative $50 \\%$ . ", + "bbox": [ + 146, + 278, + 458, + 618 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 117, + 640, + 257, + 656 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Real-world prediction systems invariably make errors. However, some mitigation of these errors is possible if the system produces well-calibrated1 confidence estimates. In this case, the system’s least confident predictions correspond to those that are most likely to be incorrect, potentially allowing these predictions to be skipped or overridden by a human. In the context of language models, one consequence of poor calibration may be hallucination, where a language model confidently asserts incorrect facts or reasoning. While the ability of very large LMs to absorb and synthesize knowledge about the outside world has gained significant attention (Brown et al., 2020; Roberts et al., 2020; Bubeck et al., 2023), relatively little attention has been given to their well-calibratedness (Kadavath et al., 2022). Further, most existing analyses of the calibratedness of LLMs focus on models trained with maximum likelihood, while in practice, the most widely-used LLMs (such as ChatGPT) are fine-tuned using methods such as reinforcement learning from human feedback (Christiano et al., 2017). Some findings suggest that RLHF-LMs may sacrifice well-calibrated predictions for the sake of closer adherence to user instructions in dialogue (Kadavath et al., 2022; OpenAI, 2023), as the reinforcement learning objective encourages the model to allocate probability mass to the most preferred answer(s), rather than matching the relative frequency of possible answers. ", + "bbox": [ + 115, + 665, + 485, + 873 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/136c529b85d62ecbb5fa5f461bfaf99336479fbd7313c678f68aa799a2ad779d.jpg", + "image_caption": [ + "Figure 1: Verbalized confidence scores (blue) are better-calibrated than log probabilities (orange) for gpt-3.5-turbo. Raw model probabilities (top-left) are consistently over-confident. Verbalized numerical probabilities (bottom) are better-calibrated. Considering more answer choices (bottom-right) further improves verbalized calibration (as in ‘Considering the Opposite’ in psychology; Lord et al. (1985)). Verbalized expressions of likelihood (top-right) also provide improved calibration. Bar height is average accuracy of predictions in bin. Darker bars mean more predictions fall in that confidence range. Results computed on SciQ. " + ], + "image_footnote": [], + "bbox": [ + 515, + 249, + 872, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 608, + 882, + 881 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper evaluates several methods for extracting confidences about model predictions from ", + "bbox": [ + 512, + 889, + 882, + 919 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2c0b4b54b929430bc1c69ccc6f8d86cd271e9ac67dae05bfe796c3757e5a9b8f.jpg", + "image_caption": [ + "Figure 2: RLHF generally worsens the calibration of Llama-70B’s log probabilities, as measured by ECE (lower is better) or AUC (higher is better). However, this paper (Tables 1-5) will show that for several strong RLHF-LMs, the model’s verbalized confidence is often better-calibrated than its log probabilities, reversing some of this degradation. This reversal is strongest for TruthfulQA, an adversarial dataset testing common misconceptions and other difficult queries. " + ], + "image_footnote": [], + "bbox": [ + 119, + 83, + 482, + 185 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "RLHF-LMs. Due to concerns that RLHF may cause systematic overconfidence in the model’s probabilities (Figure 2), as well as the general unavailability of per-token log-probabilities in widely used RLHF-LMs, we pay particular attention to prompts that elicit verbalized probabilities, i.e., the model expresses its confidence in token-space, as either numerical probabilities or another linguistic expression of uncertainty. We find that, surprisingly, popular RLHF-LMs are able to directly verbalize confidence scores that are better-calibrated than the model’s conditional probabilities (estimated via sampling), without any fine-tuning to learn verbalization. To further improve calibration, we take inspiration from research in human psychology showing that overconfidence can be mitigated by considering alternative answers before responding (Lord et al., 1985; Mussweiler et al., 2000). We show that prompting a model to produce several answer choices before giving its confidence scores significantly improves calibration of verbalized probabilities. Combined with temperature scaling (Guo et al., 2017), this approach generally provides better calibration than model probabilities for ChatGPT2, GPT- $4 ^ { 3 }$ , and Claude $2 ^ { 4 }$ across three datasets, often reducing expected calibration error (ECE) by over $50 \\%$ . ", + "bbox": [ + 117, + 317, + 487, + 752 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Related Work. Several studies have examined the calibration of large LMs (Lin et al., 2022a; Park and Caragea, 2022; Kadavath et al., 2022; Xiao et al., 2022; Kuhn et al., 2023), finding that combining large pre-trained LMs with temperature scaling (Guo et al., 2017) produces very wellcalibrated predictions (Kadavath et al., 2022; Xiao et al., 2022; Kuhn et al., 2023). Other work focuses on the tendency of language and dialogue models to use linguistic expressions of uncertainty in a well-calibrated manner (Zhou et al., 2023; Mielke et al., 2022). However, existing studies focus on LMs trained purely with unsupervised learning (although Kadavath et al. (2022) briefly examine RLHF-LMs), while widely used models in practice are fine-tuned with instruction-tuning or RLHF (Christiano et al., 2017). RLHF has been shown to effectively leverage annotations of human preferences to control sentiment (Ziegler et al., 2020), improve summarization or instruction-following quality (Stiennon et al., 2022; Ouyang et al., 2022), and inject behavioral priors of harmlessness (Bai et al., 2022b,a). However, recent work has raised the question of whether or not RLHF harms calibration (OpenAI, 2023). Our work is the first to show that verbalized probabilities are often bettercalibrated than the model’s conditional probabilities for RLHF-LMs such as ChatGPT, GPT-4, and Claude, and Llama-2-70B-Chat. ", + "bbox": [ + 115, + 763, + 487, + 858 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 85, + 882, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Evaluating Calibration in RLHF-LMs ", + "text_level": 1, + "bbox": [ + 510, + 470, + 872, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To study the calibration of RLHF-LMs, we conduct experiments with gpt-3.5-turbo (ChatGPT), gpt-4 (GPT-4), claude-1 (Claude 1), claude-2 (Claude 2), and Llama-2-70b-chat (Llama-2- 70B-Chat). ", + "bbox": [ + 512, + 498, + 882, + 577 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Metrics. We measure calibration with multiple metrics. To measure ECE (expected calibration error; Guo et al. (2017)), we bin model predictions by their confidence and measure the average accuracy of predictions in each confidence bin. The ECE is defined as the average (squared) error between the average accuracy and confidence within each bin, where each error is weighted by the fraction of samples falling within the bin. We report raw ECE as well as ECE with temperature scaling (ECE-t). Temperature scaling fits a single temperature value $\\beta$ to the model’s confidences to minimize negative log likelihood (NLL) on the data, giving scaled probability ${ \\tilde { p } } _ { i }$ of class $i$ as $\\tilde { p } _ { i } \\propto p _ { i } ^ { \\beta }$ . See Figure 1 for a depiction of ECE binning. Although ECE is a standard and interpretable measure of calibration error, it completely fails to capture the confidences’ discriminative power.5 We therefore also report ", + "bbox": [ + 512, + 590, + 882, + 879 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/3eb3c85a66849bba3ea5ac8c3442224a20f3828a601cc97efbbaac663d832915.jpg", + "table_caption": [ + "Table 1: Measuring calibration of various methods for extracting confidences from gpt-3.5-turbo (ChatGPT). The model’s conditional probabilities are relatively poorly calibrated, whether using the model’s conditional probability of the label given the query (Label prob.) or the probability assigned to ‘True’ given the query, proposed answer, and a prompt asking if the answer is correct (‘Is True’ prob.). Surprisingly, directly verbalizing a probability (Verb. 1S and Verb. 2S) or an expression of confidence such as ‘highly likely’ (Ling. 1S) yields significantly better-calibrated confidence estimates. 1S refers to one-stage prediction, where the model provides an answer and confidence probability/expression together. 2S refers to two-stage prediction, where the model first gives only an answer, and then in a second stage a confidence. To color the table cells, for each column, we demean and scale by a constant to obtain a shade in [-1,1], where cyan indicates better and orange worse performance. " + ], + "table_footnote": [], + "table_body": "
TriviaQASciQTruthfulQA
MethodECEECE-tBS-t↓AUC ↑ECEECE-t↓BS-t↓AUC↑ECEECE-t↓BS-t↓AUC↑
Label prob. ‘Is True’prob.0.140 0.1640.097 0.1590.1420.8690.2560.1800.2230.7520.451 0.4700.317 0.4710.345 0.4760.418 0.384
Entropy1丨0.1650.826 0.5470.312 丨0.309 一0.3090.677 0.483一丨丨0.236
Verb.1S top-10.0680.0760.1380.8790.2340.0840.2140.7440.3890.2560.3220.545
Verb. 1S top-2 Verb. 1S top-40.0500.0530.1390.8940.1320.0500.2010.7660.3610.1150.2520.485
0.0540.0570.1440.8960.0650.0510.2090.7630.2030.1890.2840.455
Verb.2SCoT0.1100.1230.1680.8300.3230.2460.2960.6830.4190.2590.2920.551
Verb. 2S top-10.1310.0990.1480.8550.3400.2030.2680.6770.4310.2450.2820.483
Verb. 2S top-20.0470.0450.1470.8870.1690.0400.2010.7680.3950.1010.2240.517
Verb.2S top-40.0500.0510.1560.8610.1300.0460.2110.7290.2700.1560.2460.463
Ling. 1S human0.0620.0690.1370.8840.1660.0870.2230.7030.3060.2960.3330.503
Ling. 1S-opt.0.0580.0660.1350.8780.0640.0680.2200.6740.1250.1650.2700.492
", + "bbox": [ + 115, + 83, + 882, + 274 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/75fa943de8286d705270bc7c6dbcdf53ce6fee40a5f886e64bf2bce5d4830b47.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-t←AUCECEECE-tBS-tAUC
Label prob.0.0780.0670.0770.9500.2190.1650.1860.8200.4450.3340.3620.462
Verb.1S top-10.0240.0380.0840.9370.2010.0840.1650.8430.3500.1560.2270.622
Verb. 1S top-20.0250.0340.0840.9490.1400.0480.1850.8130.3150.1120.2280.623
Verb. 1S top-40.0410.0390.0810.9590.0560.0590.1850.8150.1980.1440.2450.619
Ling. 1S-human0.0510.0410.0860.9310.1480.0240.1700.8350.2410.1510.2280.651
Ling.1S-opt.0.0560.0510.0880.9270.0280.0520.1720.8280.0820.1050.2120.632
", + "bbox": [ + 115, + 386, + 882, + 504 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 2: gpt-4’s verbalized probabilities are substantially better-calibrated than the model probabilities themselves, even after temperature scaling, similarly to gpt-3.5-turbo in Table 1. ", + "bbox": [ + 114, + 513, + 880, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Brier Score (BS; Brier (1950)) on temperaturescaled confidences (BS-t), a proper scoring rule (Ovadia et al., 2019) that is the mean squared error between the confidences and the correctness labels. Finally, we assess calibration using a metric from the selective classification literature (Geifman and El-Yaniv, 2017), specifically, the area under the curve of selective accuracy and coverage (AUC). ", + "bbox": [ + 115, + 549, + 487, + 677 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Datasets. Our experiments use three questionanswering datasets assessing factual knowledge. TriviaQA (Joshi et al., 2017) contains $6 5 0 \\mathrm { k }$ question-answer pairs gathered by trivia enthusiasts; SciQ (Welbl et al., 2017) contains approximately 14k crowdsourced science exam questionanswer pairs; TruthfulQA (Lin et al., 2022b) contains 817 questions designed to test language models’ tendency to mimic human falsehoods. We sample 1000 questions from the validation split of TriviaQA (rc.web.nocontext) and SciQ and all 817 questions from the validation split of TruthfulQA (generation) for our experiments. ", + "bbox": [ + 115, + 712, + 487, + 919 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Evaluation protocol. For each dataset, we generate a response and corresponding confidence from each method on each of the evaluation questions. Because calibration essentially quantifies the relationship between model confidence and correctness, computing correctness is crucial to accurate measurements of calibration. However, we find doing so to be a challenge, especially in datasets where only a single ground-truth answer (but not aliases or semantically equivalent rephrases) is provided. To avoid excessive false negatives in our correctness computation as a result of exact-match evaluation, we use either GPT-4 or GPT-3.5 to evaluate whether a response is essentially equivalent to the ground truth answer; see Appendix C for the complete equivalence-checking procedure. ", + "bbox": [ + 512, + 550, + 882, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Methods. We compare a wide variety of methods for extracting confidence estimates from LLMs. For a comprehensive list of the prompts used for each method, see Appendix Table 6. ", + "bbox": [ + 512, + 822, + 882, + 885 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, we consider two methods that leverage the true conditional distribution of the model to generate confidence scores. The simplest is Label prob., which uses the conditional probability distribution $p ( y | x )$ of the model given a question $x$ , which we estimate using $n = 1 0$ samples, since many RLHFLMs are closed-source and do not offer per-token probabilities.67 We return the most common answer, using the LLM-based equivalence function to determine when two lexically different answers are semantically equivalent. In a variation of the method described by Kadavath et al. (2022) (again, we use samples since model probabilities are not available), ‘Is True’ prob. samples a single answer $\\hat { y }$ from the model given a question $x$ , and the probability it is true is estimated by the probability the model assigns to ‘True’ when asked if the given answer is true (where once again the probabilities are estimated via samples), i.e., $p ( \\mathsf { T r u e } | x , \\hat { y } )$ . ", + "bbox": [ + 512, + 889, + 882, + 919 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/281f9bfa04f3188f1dacb47f3902059926d5453a9635e0935f0021120e5c4db2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-tAUCECEECE-t↓BS-tAUCECEECE-tBS-tAUC
Label prob.0.0740.0790.1170.9150.2160.1490.1950.7860.4320.3040.3350.418
Verb. 1S top-10.0490.0590.1600.8390.2650.1030.2470.6630.4400.1340.2040.411
Verb. 1S top-20.0460.0470.1580.8750.2070.0400.2250.6930.4500.0850.1970.409
Verb. 1S top-40.0750.0790.1760.8140.1510.0570.2260.6670.3720.1050.1830.377
Ling. 1S human0.0530.0500.1510.8670.2530.1180.2450.6640.4430.3580.3400.384
Ling.1S-opt.0.0740.0600.1490.8630.0890.0820.2380.6230.1390.1480.2280.350
", + "bbox": [ + 115, + 82, + 882, + 199 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/51785edaf6b15e7efe91a86f6e05fa58536f60a35bab93babbc4d10a4f598f05.jpg", + "table_caption": [ + "Table 3: Claude-1 produces similar- or better-calibrated log probabilities to gpt-3.5-turbo, but is less able to verbalize well-calibrated confidences, compared to models in the GPT family of RLHF-LMs. Claude-1 has since been deprecated. " + ], + "table_footnote": [ + "Table 4: Claude-2 has weaker conditional probabilities than Claude-1 and GPT- $^ *$ , but its verbalized calibration provides consistent improvement over conditional probabilities at a level comparable to GPT-3.5 and surpassing GPT- $^ *$ on TruthfulQA. " + ], + "table_body": "
TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-tAUC ECEECE-t ↓BS-tAUC
Label prob.0.0890.0890.1370.8820.1810.1760.2370.7620.4090.3680.4050.319
Verb. iS top-10.0720.0710.1410.9030.2040.0540.2010.7760.3450.1150.2150.573
Verb.1S top-20.0490.0540.1330.9180.1340.0410.2110.7540.3590.0850.2230.491
Verb. 1S top-40.0720.0630.1580.8900.0480.0520.2160.7110.2740.0750.2080.473
Ling. 1S human0.0850.0610.1510.8780.2380.0260.2090.7560.3810.2420.3050.530
Ling. 1S-opt.0.0600.0700.1510.8740.0490.0560.2140.7380.0990.1300.2660.446
", + "bbox": [ + 115, + 236, + 882, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 394, + 487, + 668 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we consider methods that extract confidence scores through verbalization (Lin et al., 2022a), i.e., where the model expresses its confidence in token space, either with numerical probabilities or linguistic expressions of likelihood.8 First, Verb. 1S top- $k$ prompts the model to produce $k$ guesses and a probability that each is correct all in a single response (i.e., ‘1 stage’). We take the highest-probability prediction and its associated probability as the model’s output and confidence. Verb. 2S top- $k$ similarly uses numerical probabilities, except the model is first asked to provide only its answers, and afterwards, in a second round of dialogue, asked to assign probabilities of correctness to each answer (i.e., ‘2 stages’). Verb. 2S CoT uses a chain-of-thought prompt before giving a single answer, and in a second round of dialogue, the model is prompted to assign a probability to that answer (with the chain of thought present in the model’s context). Ling. 1S-human uses linguistic likelihood expressions, rather than numerical probabilities, to express uncertainty. The model is prompted to assign confidences to its guesses by choosing from a set of linguistic expressions of uncertainty: {Almost certain, Likely, . . . , Almost no chance}. Each linguistic likelihood expression is mapped to a probability using responses from a human survey on social media with 123 respondents (FagenUlmschneider, 2023). Ling. 1S-opt. uses a held out set of calibration questions and answers to compute the average accuracy for each likelihood expression, using these ‘optimized’ values instead. Expressions that are not used for at least $\\textstyle { \\frac { 1 } { N } }$ of questions, where $N$ is the number of calibration questions, simply use the human probability. ", + "bbox": [ + 115, + 669, + 487, + 813 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 394, + 882, + 827 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 Results ", + "text_level": 1, + "bbox": [ + 512, + 844, + 606, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tables 1–5 show the results of evaluating various methods for extracting confidence from RLHFLMs on gpt-3.5-turbo, gpt-4, claude-1, claude-2, and Llama-2-70b-chat, respectively. We distill several key conclusions from these experiments. 1. Large RLHF-LMs can often directly verbalize better-calibrated confidences (either a numerical confidence probability or an expression such as ‘highly likely’) than the models’ conditional probabilities. 2. Among the methods for verbalizing probabilities directly, we observe that generating and evaluating multiple hypotheses improves calibration (see Figure 1), similarly to humans (Lord et al., 1985), and corroborating a similar finding in LMs (Kadavath et al., 2022). 3. Language models can express their uncertainty with numerical probabilities as well or better than with words, which is surprising in light of longstanding difficulties in representing numbers in language models (Thawani et al., 2021). 4. Chainof-thought prompting does not improve verbalized calibration (see Appendix Figure 5 for additional CoT results). 5. The calibration of both Claude models’ conditional probabilities roughly falls between gpt-3.5-turbo and gpt-4; however, while Claude 1 is much weaker at verbalizing its confidence, Claude 2 is generally a bit stronger than gpt-3.5-turbo at verbalizing. The verbal calibration of the open source model Llama-2-70b-chat is generally weaker than that of closed source models but still demonstrates improvement over its conditional probabilities by some metrics, and does so most clearly on TruthfulQA. ", + "bbox": [ + 512, + 872, + 882, + 920 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/f546fb7553aa771ec93f390451f744a497ab7bd82832fa172941f604c451a604.jpg", + "table_caption": [], + "table_footnote": [ + "Table 5: With Llama2-70B-Chat, verbalized calibration provides improvement over conditional probabilities across some metrics, but the improvement is much less consistent compared to GPT- $^ *$ and Claude-\\*. " + ], + "table_body": "
TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-t↓AUC↑ECEECE-t↓BS-tAUCECEECE-t ↓BS-t AUC
Label prob.0.1510.1240.1560.8650.2660.1890.2430.7070.4050.3610.3960.407
Verb.1S top-10.0710.0670.1860.7930.1960.0530.2390.6480.3860.1720.2660.502
Verb. 1S top-20.0600.0730.1940.8150.1530.0320.2300.6670.3400.0370.2270.440
Verb. 1S top-40.0690.0790.1820.8160.1050.0430.2290.6480.2310.1020.2370.465
Ling. 1S human0.1790.1150.1950.7490.0710.1010.2520.6030.3760.3660.3830.407
Ling.1S-opt.0.0770.0680.1860.7790.0190.0420.2360.5900.0470.0510.2390.435
", + "bbox": [ + 115, + 82, + 882, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 243, + 487, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 Discussion ", + "text_level": 1, + "bbox": [ + 117, + 745, + 238, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, we study the calibration of widely used RLHF-LMs. We first replicate the finding for GPT-4 (OpenAI, 2023) that RLHF can worsen the calibration of a model’s conditional probabilities using the open-source Llama-2-70B base and chat models (Figure 2). To mitigate this regression and ease extraction of calibrated confidence scores for models for which log probabilities are not available, we propose and study new methods that can elicit calibrated confidences from RLHF-LMs by prompting the model to verbalize its confidence in token space. We find verbalized probabilities are better-calibrated than conditional probabilities across several closed models, with mixed results for Llama-2-70B-Chat. ", + "bbox": [ + 117, + 776, + 485, + 919 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 246, + 882, + 341 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our results raise several questions for future work. Most notably, the difference between GPT-\\*, Claude-\\*, and Llama-2’s ability to verbalize confidence is significant. What factors are important for learning this skill? Additionally, the 1-stage and 2-stage verbalized numerical confidence prompts sometimes differ drastically in the calibration of their confidences. How can we reduce sensitivity of a model’s calibration to the prompt? Going beyond question-answering, can we leverage good calibration in short-answer settings to improve the reliability of long-form generations, perhaps by breaking down long-form generation into a sequence of short questions? Finally, to what extent does a language model’s calibration depend on the domain; do our conclusions in the context of factual recall hold in the context of reasoning or arithmetic? Answering these questions provides one path toward building more trustworthy and useful language systems. ", + "bbox": [ + 512, + 349, + 882, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Limitations. While our work demonstrates a promising new approach to generating calibrated confidences through verbalization, there are limitations that could be addressed in future work. First, our experiments are focused on factual recalloriented problems, and the extent to which our observations would hold for reasoning-heavy settings is an interesting open question. Additionally, the lack of technical details available for many state-ofthe-art closed RLHF-LMs may limit our ability to understand what factors enable a model to verbalize well-calibrated confidences and differences in this ability across different models. Finally, our study is limited to short-form question-answering; future work should extend this analysis to longer-form generation settings. ", + "bbox": [ + 512, + 662, + 882, + 919 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Acknowledgements. CF and CDM are CIFAR Fellows. EM gratefully acknowledges funding from a Knight-Hennessy Graduate Fellowship. AZ is supported by the NSF graduate research fellowship program. This research was supported in part by Juniper Networks, Apple, and ONR grant N00014- 20-1-2675. The authors thank Yoonho Lee and Noah Goodman for helpful feedback on calibration metrics and experiment design. 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", + "bbox": [ + 510, + 353, + 882, + 392 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Daniel M. Ziegler, Nisan Stiennon, Jeffrey Wu, Tom B. Brown, Alec Radford, Dario Amodei, Paul Christiano, and Geoffrey Irving. 2020. Fine-tuning language models from human preferences. ", + "bbox": [ + 510, + 403, + 884, + 455 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/29a94f82c16fe874b63cf56e952a694c94653bf9c7c9f3480e04d2af95101570.jpg", + "image_caption": [ + "Usage of likelihood expressions by 3.5-turbo " + ], + "image_footnote": [], + "bbox": [ + 136, + 99, + 468, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb784ea8d3fbd2c5354f9b6f09da03fdefd1c83f74221e895783b2b224f839ac.jpg", + "image_caption": [ + "Figure 3: gpt-3.5-turbo usage rate of each likelihood expression; the model displays much lower verbalized confidence on TruthfulQA than on standard factual recall problems. ", + "Figure 4: gpt-4 usage rate of each likelihood expression; the model displays markedly lower verbalized confidence on TruthfulQA than on standard factual recall problems. " + ], + "image_footnote": [], + "bbox": [ + 152, + 316, + 448, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A Additional Results ", + "text_level": 1, + "bbox": [ + 117, + 548, + 312, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here, we include the likelihood expression usage distribution for gpt-3.5 and gpt-4 in Figures 3 and 4, respectively. gpt-3.5 is systematically less confident for TruthfulQA. The contrast between model confidence for TriviaQA and SciQ compared with TruthfulQA is even more stark for gpt-4. ", + "bbox": [ + 115, + 574, + 485, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also provide additional calibration results for chain-of-thought methods. We compare a onestage verbalized CoT prompt (Verb. 1S CoT), a two-stage verbalized CoT prompt (Verb. 2S CoT), and a two-stage verbalized method that uses CoT just before eliciting the numerical confidence (Verb. 2S Cot Prob) instead of before the guess, as shown for gpt-3.5 on Trivia QA, SciQ, and Truthful QA in Figure 5. We find that CoT does not noticeably improve calibration across any setting or dataset. ", + "bbox": [ + 115, + 671, + 487, + 831 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "B Fitting Procedure for Temperature and Probabilities for Linguistic Expressions ", + "text_level": 1, + "bbox": [ + 115, + 845, + 485, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To fit the temperature that is used to compute ECEt and BS-t we split our total data into 5 folds. For each fold, we use it once to fit a temperature and evaluate metrics on the remaining folds. We find that fitting the temperature on $20 \\%$ of the data yields relatively stable temperatures across folds. We report the average temperature-scaled ECE and BS as ECE-t and ${ \\bf B S - t }$ . ", + "bbox": [ + 115, + 889, + 487, + 919 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6b87cbb676b16607bf3bff0af7beadcb31e4136e025c14228876dc20301c0b2b.jpg", + "image_caption": [ + "Figure 5: Expected calibration error is not consistently improved for any CoT prompt variant on gpt-3.5-turbo. " + ], + "image_footnote": [], + "bbox": [ + 517, + 84, + 873, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 512, + 513, + 882, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To compute ECE and AUC for Ling. 1S-opt., we similarly split our total data into 5 folds, using 4 folds to fit the probabilities behind each linguistic expression of confidence, then evaluating on the remaining fold. To compute ECE-t and BS-t for Ling. 1S-opt, we hold out one of the 5 folds to fit temperature. We use 3 folds to fit probabilities for linguistic expressions, compute the temperature based on these probabilities on the temperature set, and evaluate metrics on the last fold. We then average metrics across all 20 rotations of folds. ", + "bbox": [ + 512, + 609, + 880, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "C Prompt Templates ", + "text_level": 1, + "bbox": [ + 512, + 797, + 707, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The prompt template for each sampling method is provided in Table 6. The question is substituted for the variable $\\$ 123,456,710N \\}$ in each prompt. To evaluate answer correctness, we use gpt-3.5-turbo for SciQ and TruthfulQA and gpt-4 for TriviaQA due to gpt-3.5-turbo’s high disagreement with a human evaluator on TriviaQA. Using the ground truth answer as $\\$ 523,456,7$ and the model-generated answer as \\${PRED_ANSWER}, we use the following prompt template: ", + "bbox": [ + 512, + 824, + 882, + 920 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/53d417f2848e7c864ea722f51d6f29fb757295cddd33aa1b71498ec271051052.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6: Prompt templates for each method evaluated. Methods above the double line use multiple samples in order to estimate confidence scores; methods below the double line use the verbalized confidences directly, requiring only a single sample. " + ], + "table_body": "
Method Template
Label prob. Provide your best guess for the following question. Give ONLY the guess，noother words orexplanation.\\n\\nForexample:\\n\\nGuess: <most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}
‘Is True'prob. Question: ${QUESTION}\\nProposed Answer: ${ANSWER}\\nIs the proposed answer:\\n\\t(A)True or\\n\\t(B) False?\\n The proposed answer is:
Verb. 1S top-1 Provide your best guess and the probability that it is correct (0.0 to 1.0） forthe_following question． Give ONLY the guess and probability，no other words orexplanation.For example:\\n\\nGuess: <most likely guess，as short as possible； nota complete sentence，just the guess!>\\n Probability:<the probability between 0.0and 1.0 that your guess is correct，without any extra commentary whatsoever；justthe probability!>\\n\\nThe question is:${THE_QUESTION}
Verb.1S top-k Provide your ${k} best guesses and the probability that each is correct (0.0 to1.0）for the following question.Give ONLY the guesses and probabilities，no otherwords or explanation. For example:\\n\\nG1: <first most likely guess，as short aspossible；not a complete sentence，just the guess!>\\n\\nP1: <the probability between0.0 and 1.0 that G1 is correct， without any extra commentary whatsoever； justthe probability!> ... G${k}: <${k}-th most likely guess，as short as possible;not a complete sentence， just the guess!>\\n\\nP${k}: <the probability between 0.0and 1.0 that G${k} is correct，without any extra commentary whatsoever； just theprobability!> \\n\\nThe question is: ${THE_QUESTION}
Verb.2SCoT Provide your best guess for the following question. Before giving your answer,provide a step-by-step explanation of your thought process. Then on a new linegive the guess with no other words or explanation.\\n\\nFor example:\\n\\nExplanation:<one sentence step-by-step explanation of your thought process>\\n\\nGuess: <mostlikely guess，as short as_possible； not a complete sentence，just the guess!>\\n\\nThequestion is:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-1 Provide your best guess for the following question.Give ONLY the guess，nootherwordsor_explanation.\\n\\nForexample:\\n\\nGuess:<most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the_probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-kProvide your ${k} best guesses for the following question. Give ONLY the guesses,no other words_or explanation. For example:\\n\\nG1: <first most likely guess，asshort as possible；not a complete sentence，just the guess!>\\n\\nP1: <the probabilitybetween 0.0 and 1.0 that G1 is correct，without any extra commentary whatsoever;just the probability!> ... G${k}:<${k}-th most likely guess，as short as possible;not a complete sentence，just the guess!>\\n\\nThe question is:${THE_QUESTION}Providethe_probability_that eachofyourguessesiscorrect. Give ONLYthe probabilities，no other words or explanation.\\n\\nFor example:\\n\\nP1:<theprobability between 0.0 and 1.0 that G1 is correct，without any extra commentarywhatsoever； just the probability!>\\n... P${k}: <the probability between 0.0 and1.0 that G${k} is correct， without any extra commentary whatsoever； just theprobability!>
therwords
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Ling. 1S Provide your best guess for the following question，and describe how likely it isthat your guess is correct as one of the following expressions: ${EXPRESsION_LIST}.Give ONLY the guess and_ your confidence， no other words or explanation.Forexample:\\n\\nGuess: <most likely guess，as short as possible； not a complete sentence,just the guess!>\\nConfidence:<description of confidence， without any extracommentary whatsoever； just a short phrase!>\\n\\nThe question is:${THE_QUESTION}
", + "bbox": [ + 129, + 103, + 868, + 859 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 115, + 85, + 487, + 164 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Are the following two answers to my question $\\mathsf Q$ semantically equivalent?\\n\\nQ: \\${THE_QUESTION}\\nA1: \\${GOLD_ANSWER}\\nA2: \\${PRED_ANSWER}\\n\\nPlease answer with a single word, either “Yes.\" or “No.\", and explain your reasoning. ", + "bbox": [ + 117, + 166, + 487, + 261 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/parse/dev/g3faCfrwm7/g3faCfrwm7_middle.json b/parse/dev/g3faCfrwm7/g3faCfrwm7_middle.json new file mode 100644 index 0000000000000000000000000000000000000000..a1f2bfda2ab3f9f905277f1d3b85d3af831b0edb --- /dev/null +++ b/parse/dev/g3faCfrwm7/g3faCfrwm7_middle.json @@ -0,0 +1,34318 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 82, + 70, + 515, + 103 + ], + "lines": [ + { + "bbox": [ + 79, + 71, + 514, + 89 + ], + "spans": [ + { + "bbox": [ + 79, + 71, + 514, + 89 + ], + "score": 1.0, + "content": "Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 94, + 87, + 500, + 105 + ], + "spans": [ + { + "bbox": [ + 94, + 87, + 500, + 105 + ], + "score": 1.0, + "content": "Scores from Language Models Fine-Tuned with Human Feedback", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 92, + 110, + 507, + 140 + ], + "lines": [ + { + "bbox": [ + 92, + 110, + 507, + 126 + ], + "spans": [ + { + "bbox": [ + 92, + 110, + 507, + 126 + ], + "score": 1.0, + "content": "Katherine Tian,∗† Eric Mitchell,∗‡ Allan Zhou,‡ Archit Sharma,‡ Rafael Rafailov‡", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 157, + 124, + 438, + 141 + ], + "spans": [ + { + "bbox": [ + 157, + 124, + 438, + 141 + ], + "score": 1.0, + "content": "Huaxiu Yao,‡ Chelsea Finn,‡ Christopher D. Manning‡", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 192, + 152, + 402, + 194 + ], + "lines": [ + { + "bbox": [ + 192, + 151, + 403, + 168 + ], + "spans": [ + { + "bbox": [ + 192, + 151, + 403, + 168 + ], + "score": 1.0, + "content": "†Harvard University ‡Stanford University", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 221, + 167, + 374, + 181 + ], + "spans": [ + { + "bbox": [ + 221, + 167, + 374, + 181 + ], + "score": 1.0, + "content": "ktian@college.harvard.edu", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 209, + 181, + 385, + 194 + ], + "spans": [ + { + "bbox": [ + 209, + 181, + 385, + 194 + ], + "score": 1.0, + "content": "eric.mitchell@cs.stanford.edu", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 157, + 213, + 202, + 226 + ], + "lines": [ + { + "bbox": [ + 155, + 212, + 204, + 228 + ], + "spans": [ + { + "bbox": [ + 155, + 212, + 204, + 228 + ], + "score": 1.0, + "content": "Abstract", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 87, + 234, + 273, + 520 + ], + "lines": [ + { + "bbox": [ + 86, + 234, + 273, + 246 + ], + "spans": [ + { + "bbox": [ + 86, + 234, + 273, + 246 + ], + "score": 1.0, + "content": "A trustworthy real-world prediction system", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 86, + 246, + 273, + 258 + ], + "spans": [ + { + "bbox": [ + 86, + 246, + 273, + 258 + ], + "score": 1.0, + "content": "should produce well-calibrated confidence", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 86, + 259, + 273, + 270 + ], + "spans": [ + { + "bbox": [ + 86, + 259, + 273, + 270 + ], + "score": 1.0, + "content": "scores; that is, its confidence in an answer", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 270, + 273, + 281 + ], + "spans": [ + { + "bbox": [ + 86, + 270, + 273, + 281 + ], + "score": 1.0, + "content": "should be indicative of the likelihood that the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 86, + 282, + 273, + 294 + ], + "spans": [ + { + "bbox": [ + 86, + 282, + 273, + 294 + ], + "score": 1.0, + "content": "answer is correct, enabling deferral to an expert", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 86, + 295, + 274, + 306 + ], + "spans": [ + { + "bbox": [ + 86, + 295, + 274, + 306 + ], + "score": 1.0, + "content": "in cases of low-confidence predictions. Re-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 85, + 305, + 274, + 318 + ], + "spans": [ + { + "bbox": [ + 85, + 305, + 274, + 318 + ], + "score": 1.0, + "content": "cent studies have shown that unsupervised pre-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 86, + 318, + 274, + 330 + ], + "spans": [ + { + "bbox": [ + 86, + 318, + 274, + 330 + ], + "score": 1.0, + "content": "training produces large language models (LMs)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 86, + 330, + 273, + 342 + ], + "spans": [ + { + "bbox": [ + 86, + 330, + 273, + 342 + ], + "score": 1.0, + "content": "whose conditional probabilities are remarkably", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 86, + 341, + 274, + 354 + ], + "spans": [ + { + "bbox": [ + 86, + 341, + 274, + 354 + ], + "score": 1.0, + "content": "well-calibrated. 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Considering more answer", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 304, + 433, + 526, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 526, + 444 + ], + "score": 1.0, + "content": "choices (bottom-right) further improves verbalized calibra-", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 303, + 442, + 526, + 454 + ], + "spans": [ + { + "bbox": [ + 303, + 442, + 526, + 454 + ], + "score": 1.0, + "content": "tion (as in ‘Considering the Opposite’ in psychology; Lord", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 303, + 452, + 526, + 464 + ], + "spans": [ + { + "bbox": [ + 303, + 452, + 526, + 464 + ], + "score": 1.0, + "content": "et al. (1985)). Verbalized expressions of likelihood (top-right)", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 304, + 462, + 527, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 527, + 474 + ], + "score": 1.0, + "content": "also provide improved calibration. Bar height is average accu-", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 473, + 525, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 525, + 484 + ], + "score": 1.0, + "content": "racy of predictions in bin. Darker bars mean more predictions", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 304, + 482, + 509, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 509, + 494 + ], + "score": 1.0, + "content": "fall in that confidence range. Results computed on SciQ.", + "type": "text" + } + ], + "index": 72 + } + ], + "index": 67 + } + ], + "index": 60.75 + }, + { + "type": "text", + "bbox": [ + 305, + 512, + 525, + 741 + ], + "lines": [ + { + "bbox": [ + 304, + 513, + 527, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 527, + 525 + ], + "score": 1.0, + "content": "attention (Brown et al., 2020; Roberts et al., 2020;", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 526, + 526, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 526, + 538 + ], + "score": 1.0, + "content": "Bubeck et al., 2023), relatively little attention has", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 303, + 540, + 525, + 552 + ], + "spans": [ + { + "bbox": [ + 303, + 540, + 525, + 552 + ], + "score": 1.0, + "content": "been given to their well-calibratedness (Kadavath", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 554, + 525, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 525, + 566 + ], + "score": 1.0, + "content": "et al., 2022). 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However, this paper (Ta-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 196, + 290, + 208 + ], + "spans": [ + { + "bbox": [ + 69, + 196, + 290, + 208 + ], + "score": 1.0, + "content": "bles 1-5) will show that for several strong RLHF-LMs, the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 207, + 290, + 217 + ], + "spans": [ + { + "bbox": [ + 69, + 207, + 290, + 217 + ], + "score": 1.0, + "content": "model’s verbalized confidence is often better-calibrated than", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 216, + 290, + 228 + ], + "spans": [ + { + "bbox": [ + 69, + 216, + 290, + 228 + ], + "score": 1.0, + "content": "its log probabilities, reversing some of this degradation. 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However, existing studies focus on", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 303, + 151, + 525, + 167 + ], + "spans": [ + { + "bbox": [ + 303, + 151, + 525, + 167 + ], + "score": 1.0, + "content": "LMs trained purely with unsupervised learning", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 166, + 525, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 166, + 525, + 180 + ], + "score": 1.0, + "content": "(although Kadavath et al. 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However, this paper (Ta-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 196, + 290, + 208 + ], + "spans": [ + { + "bbox": [ + 69, + 196, + 290, + 208 + ], + "score": 1.0, + "content": "bles 1-5) will show that for several strong RLHF-LMs, the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 207, + 290, + 217 + ], + "spans": [ + { + "bbox": [ + 69, + 207, + 290, + 217 + ], + "score": 1.0, + "content": "model’s verbalized confidence is often better-calibrated than", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 69, + 216, + 290, + 228 + ], + "spans": [ + { + "bbox": [ + 69, + 216, + 290, + 228 + ], + "score": 1.0, + "content": "its log probabilities, reversing some of this degradation. 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We find that, surpris-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 68, + 389, + 292, + 404 + ], + "spans": [ + { + "bbox": [ + 68, + 389, + 292, + 404 + ], + "score": 1.0, + "content": "ingly, popular RLHF-LMs are able to directly ver-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 69, + 404, + 291, + 417 + ], + "spans": [ + { + "bbox": [ + 69, + 404, + 291, + 417 + ], + "score": 1.0, + "content": "balize confidence scores that are better-calibrated", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 69, + 417, + 291, + 430 + ], + "spans": [ + { + "bbox": [ + 69, + 417, + 291, + 430 + ], + "score": 1.0, + "content": "than the model’s conditional probabilities (esti-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 68, + 430, + 291, + 445 + ], + "spans": [ + { + "bbox": [ + 68, + 430, + 291, + 445 + ], + "score": 1.0, + "content": "mated via sampling), without any fine-tuning to", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 68, + 444, + 291, + 458 + ], + "spans": [ + { + "bbox": [ + 68, + 444, + 291, + 458 + ], + "score": 1.0, + "content": "learn verbalization. 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Other work focuses", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 99, + 525, + 111 + ], + "spans": [ + { + "bbox": [ + 304, + 99, + 525, + 111 + ], + "score": 1.0, + "content": "on the tendency of language and dialogue models", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 113, + 525, + 125 + ], + "spans": [ + { + "bbox": [ + 304, + 113, + 525, + 125 + ], + "score": 1.0, + "content": "to use linguistic expressions of uncertainty in a", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 126, + 525, + 138 + ], + "spans": [ + { + "bbox": [ + 304, + 126, + 525, + 138 + ], + "score": 1.0, + "content": "well-calibrated manner (Zhou et al., 2023; Mielke", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 140, + 525, + 152 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 525, + 152 + ], + "score": 1.0, + "content": "et al., 2022). However, existing studies focus on", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 303, + 151, + 525, + 167 + ], + "spans": [ + { + "bbox": [ + 303, + 151, + 525, + 167 + ], + "score": 1.0, + "content": "LMs trained purely with unsupervised learning", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 166, + 525, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 166, + 525, + 180 + ], + "score": 1.0, + "content": "(although Kadavath et al. 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RLHF has been shown", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 304, + 221, + 527, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 527, + 234 + ], + "score": 1.0, + "content": "to effectively leverage annotations of human pref-", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 235, + 527, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 527, + 247 + ], + "score": 1.0, + "content": "erences to control sentiment (Ziegler et al., 2020),", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 304, + 249, + 526, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 249, + 526, + 261 + ], + "score": 1.0, + "content": "improve summarization or instruction-following", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 304, + 262, + 526, + 274 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 526, + 274 + ], + "score": 1.0, + "content": "quality (Stiennon et al., 2022; Ouyang et al., 2022),", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 275, + 525, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 525, + 288 + ], + "score": 1.0, + "content": "and inject behavioral priors of harmlessness (Bai", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 289, + 526, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 526, + 301 + ], + "score": 1.0, + "content": "et al., 2022b,a). However, recent work has raised", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 304, + 302, + 527, + 315 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 527, + 315 + ], + "score": 1.0, + "content": "the question of whether or not RLHF harms cali-", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 304, + 316, + 526, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 526, + 328 + ], + "score": 1.0, + "content": "bration (OpenAI, 2023). Our work is the first to", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 304, + 330, + 527, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 527, + 342 + ], + "score": 1.0, + "content": "show that verbalized probabilities are often better-", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 304, + 343, + 527, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 527, + 355 + ], + "score": 1.0, + "content": "calibrated than the model’s conditional probabili-", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 356, + 526, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 526, + 369 + ], + "score": 1.0, + "content": "ties for RLHF-LMs such as ChatGPT, GPT-4, and", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 305, + 370, + 447, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 447, + 381 + ], + "score": 1.0, + "content": "Claude, and Llama-2-70B-Chat.", + "type": "text" + } + ], + "index": 72 + } + ], + "index": 43.5, + "bbox_fs": [ + 68, + 642, + 292, + 723 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 72, + 525, + 382 + ], + "lines": [], + "index": 61, + "bbox_fs": [ + 303, + 72, + 527, + 381 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 304, + 396, + 519, + 410 + ], + "lines": [ + { + "bbox": [ + 302, + 394, + 521, + 411 + ], + "spans": [ + { + "bbox": [ + 302, + 394, + 521, + 411 + ], + "score": 1.0, + "content": "2 Evaluating Calibration in RLHF-LMs", + "type": "text" + } + ], + "index": 73 + } + ], + "index": 73 + }, + { + "type": "text", + "bbox": [ + 305, + 419, + 525, + 486 + ], + "lines": [ + { + "bbox": [ + 303, + 419, + 527, + 433 + ], + "spans": [ + { + "bbox": [ + 303, + 419, + 527, + 433 + ], + "score": 1.0, + "content": "To study the calibration of RLHF-LMs, we con-", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 434, + 527, + 446 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 527, + 446 + ], + "score": 1.0, + "content": "duct experiments with gpt-3.5-turbo (ChatGPT),", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 304, + 448, + 526, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 526, + 459 + ], + "score": 1.0, + "content": "gpt-4 (GPT-4), claude-1 (Claude 1), claude-2", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 304, + 461, + 527, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 527, + 473 + ], + "score": 1.0, + "content": "(Claude 2), and Llama-2-70b-chat (Llama-2-", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 304, + 473, + 356, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 356, + 487 + ], + "score": 1.0, + "content": "70B-Chat).", + "type": "text" + } + ], + "index": 78 + } + ], + "index": 76, + "bbox_fs": [ + 303, + 419, + 527, + 487 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 497, + 525, + 740 + ], + "lines": [ + { + "bbox": [ + 304, + 497, + 525, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 525, + 511 + ], + "score": 1.0, + "content": "Metrics. We measure calibration with multiple", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 304, + 512, + 526, + 524 + ], + "spans": [ + { + "bbox": [ + 304, + 512, + 526, + 524 + ], + "score": 1.0, + "content": "metrics. To measure ECE (expected calibration er-", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 304, + 526, + 525, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 525, + 538 + ], + "score": 1.0, + "content": "ror; Guo et al. (2017)), we bin model predictions by", + "type": "text" + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 538, + 526, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 526, + 552 + ], + "score": 1.0, + "content": "their confidence and measure the average accuracy", + "type": "text" + } + ], + "index": 82 + }, + { + "bbox": [ + 304, + 553, + 525, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 525, + 564 + ], + "score": 1.0, + "content": "of predictions in each confidence bin. The ECE", + "type": "text" + } + ], + "index": 83 + }, + { + "bbox": [ + 303, + 565, + 526, + 580 + ], + "spans": [ + { + "bbox": [ + 303, + 565, + 526, + 580 + ], + "score": 1.0, + "content": "is defined as the average (squared) error between", + "type": "text" + } + ], + "index": 84 + }, + { + "bbox": [ + 304, + 580, + 525, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 525, + 592 + ], + "score": 1.0, + "content": "the average accuracy and confidence within each", + "type": "text" + } + ], + "index": 85 + }, + { + "bbox": [ + 304, + 593, + 526, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 526, + 606 + ], + "score": 1.0, + "content": "bin, where each error is weighted by the fraction of", + "type": "text" + } + ], + "index": 86 + }, + { + "bbox": [ + 303, + 606, + 526, + 621 + ], + "spans": [ + { + "bbox": [ + 303, + 606, + 526, + 621 + ], + "score": 1.0, + "content": "samples falling within the bin. We report raw ECE", + "type": "text" + } + ], + "index": 87 + }, + { + "bbox": [ + 304, + 620, + 527, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 527, + 633 + ], + "score": 1.0, + "content": "as well as ECE with temperature scaling (ECE-t).", + "type": "text" + } + ], + "index": 88 + }, + { + "bbox": [ + 304, + 634, + 525, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 634, + 525, + 647 + ], + "score": 1.0, + "content": "Temperature scaling fits a single temperature value", + "type": "text" + } + ], + "index": 89 + }, + { + "bbox": [ + 304, + 646, + 525, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 313, + 660 + ], + "score": 0.83, + "content": "\\beta", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 646, + 525, + 660 + ], + "score": 1.0, + "content": "to the model’s confidences to minimize negative", + "type": "text" + } + ], + "index": 90 + }, + { + "bbox": [ + 303, + 660, + 526, + 675 + ], + "spans": [ + { + "bbox": [ + 303, + 660, + 526, + 675 + ], + "score": 1.0, + "content": "log likelihood (NLL) on the data, giving scaled", + "type": "text" + } + ], + "index": 91 + }, + { + "bbox": [ + 303, + 672, + 526, + 688 + ], + "spans": [ + { + "bbox": [ + 303, + 674, + 356, + 688 + ], + "score": 1.0, + "content": "probability", + "type": "text" + }, + { + "bbox": [ + 356, + 675, + 367, + 687 + ], + "score": 0.86, + "content": "{ \\tilde { p } } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 674, + 405, + 688 + ], + "score": 1.0, + "content": "of class", + "type": "text" + }, + { + "bbox": [ + 405, + 675, + 411, + 685 + ], + "score": 0.69, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 674, + 424, + 688 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 424, + 672, + 461, + 688 + ], + "score": 0.92, + "content": "\\tilde { p } _ { i } \\propto p _ { i } ^ { \\beta }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 674, + 526, + 688 + ], + "score": 1.0, + "content": ". See Figure 1", + "type": "text" + } + ], + "index": 92 + }, + { + "bbox": [ + 304, + 687, + 525, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 687, + 525, + 700 + ], + "score": 1.0, + "content": "for a depiction of ECE binning. Although ECE is a", + "type": "text" + } + ], + "index": 93 + }, + { + "bbox": [ + 304, + 702, + 525, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 702, + 525, + 714 + ], + "score": 1.0, + "content": "standard and interpretable measure of calibration", + "type": "text" + } + ], + "index": 94 + }, + { + "bbox": [ + 304, + 716, + 526, + 727 + ], + "spans": [ + { + "bbox": [ + 304, + 716, + 526, + 727 + ], + "score": 1.0, + "content": "error, it completely fails to capture the confidences’", + "type": "text" + } + ], + "index": 95 + }, + { + "bbox": [ + 304, + 727, + 526, + 742 + ], + "spans": [ + { + "bbox": [ + 304, + 727, + 526, + 742 + ], + "score": 1.0, + "content": "discriminative power.5 We therefore also report", + "type": "text" + } + ], + "index": 96 + } + ], + "index": 87.5, + "bbox_fs": [ + 303, + 497, + 527, + 742 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 525, + 231 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 69, + 70, + 525, + 231 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 69, + 70, + 525, + 231 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 525, + 231 + ], + "score": 0.985, + "html": "
TriviaQASciQTruthfulQA
MethodECEECE-tBS-t↓AUC ↑ECEECE-t↓BS-t↓AUC↑ECEECE-t↓BS-t↓AUC↑
Label prob. ‘Is True’prob.0.140 0.1640.097 0.1590.1420.8690.2560.1800.2230.7520.451 0.4700.317 0.4710.345 0.4760.418 0.384
Entropy1丨0.1650.826 0.5470.312 丨0.309 一0.3090.677 0.483一丨丨0.236
Verb.1S top-10.0680.0760.1380.8790.2340.0840.2140.7440.3890.2560.3220.545
Verb. 1S top-2 Verb. 1S top-40.0500.0530.1390.8940.1320.0500.2010.7660.3610.1150.2520.485
0.0540.0570.1440.8960.0650.0510.2090.7630.2030.1890.2840.455
Verb.2SCoT0.1100.1230.1680.8300.3230.2460.2960.6830.4190.2590.2920.551
Verb. 2S top-10.1310.0990.1480.8550.3400.2030.2680.6770.4310.2450.2820.483
Verb. 2S top-20.0470.0450.1470.8870.1690.0400.2010.7680.3950.1010.2240.517
Verb.2S top-40.0500.0510.1560.8610.1300.0460.2110.7290.2700.1560.2460.463
Ling. 1S human0.0620.0690.1370.8840.1660.0870.2230.7030.3060.2960.3330.503
Ling. 1S-opt.0.0580.0660.1350.8780.0640.0680.2200.6740.1250.1650.2700.492
", + "type": "table", + "image_path": "3eb3c85a66849bba3ea5ac8c3442224a20f3828a601cc97efbbaac663d832915.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 69, + 70, + 525, + 123.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 69, + 123.66666666666666, + 525, + 177.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 69, + 177.33333333333331, + 525, + 230.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 69, + 239, + 526, + 320 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 68, + 239, + 527, + 252 + ], + "spans": [ + { + "bbox": [ + 68, + 239, + 527, + 252 + ], + "score": 1.0, + "content": "Table 1: Measuring calibration of various methods for extracting confidences from gpt-3.5-turbo (ChatGPT). The model’s", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 250, + 526, + 261 + ], + "spans": [ + { + "bbox": [ + 68, + 250, + 526, + 261 + ], + "score": 1.0, + "content": "conditional probabilities are relatively poorly calibrated, whether using the model’s conditional probability of the label given the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 67, + 258, + 527, + 272 + ], + "spans": [ + { + "bbox": [ + 67, + 258, + 527, + 272 + ], + "score": 1.0, + "content": "query (Label prob.) or the probability assigned to ‘True’ given the query, proposed answer, and a prompt asking if the answer is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 268, + 527, + 281 + ], + "spans": [ + { + "bbox": [ + 68, + 268, + 527, + 281 + ], + "score": 1.0, + "content": "correct (‘Is True’ prob.). Surprisingly, directly verbalizing a probability (Verb. 1S and Verb. 2S) or an expression of confidence", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 279, + 527, + 292 + ], + "spans": [ + { + "bbox": [ + 68, + 279, + 527, + 292 + ], + "score": 1.0, + "content": "such as ‘highly likely’ (Ling. 1S) yields significantly better-calibrated confidence estimates. 1S refers to one-stage prediction,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 68, + 289, + 527, + 302 + ], + "spans": [ + { + "bbox": [ + 68, + 289, + 527, + 302 + ], + "score": 1.0, + "content": "where the model provides an answer and confidence probability/expression together. 2S refers to two-stage prediction, where the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 298, + 526, + 311 + ], + "spans": [ + { + "bbox": [ + 68, + 298, + 526, + 311 + ], + "score": 1.0, + "content": "model first gives only an answer, and then in a second stage a confidence. To color the table cells, for each column, we demean", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 68, + 309, + 466, + 321 + ], + "spans": [ + { + "bbox": [ + 68, + 309, + 466, + 321 + ], + "score": 1.0, + "content": "and scale by a constant to obtain a shade in [-1,1], where cyan indicates better and orange worse performance.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "table", + "bbox": [ + 69, + 325, + 525, + 424 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 69, + 325, + 525, + 424 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 69, + 325, + 525, + 424 + ], + "spans": [ + { + "bbox": [ + 69, + 325, + 525, + 424 + ], + "score": 0.981, + "html": "
TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-t←AUCECEECE-tBS-tAUC
Label prob.0.0780.0670.0770.9500.2190.1650.1860.8200.4450.3340.3620.462
Verb.1S top-10.0240.0380.0840.9370.2010.0840.1650.8430.3500.1560.2270.622
Verb. 1S top-20.0250.0340.0840.9490.1400.0480.1850.8130.3150.1120.2280.623
Verb. 1S top-40.0410.0390.0810.9590.0560.0590.1850.8150.1980.1440.2450.619
Ling. 1S-human0.0510.0410.0860.9310.1480.0240.1700.8350.2410.1510.2280.651
Ling.1S-opt.0.0560.0510.0880.9270.0280.0520.1720.8280.0820.1050.2120.632
", + "type": "table", + "image_path": "75fa943de8286d705270bc7c6dbcdf53ce6fee40a5f886e64bf2bce5d4830b47.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 69, + 325, + 525, + 358.0 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 69, + 358.0, + 525, + 391.0 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 69, + 391.0, + 525, + 424.0 + ], + "spans": [], + "index": 13 + } + ] + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 68, + 432, + 524, + 452 + ], + "lines": [ + { + "bbox": [ + 68, + 431, + 525, + 444 + ], + "spans": [ + { + "bbox": [ + 68, + 431, + 525, + 444 + ], + "score": 1.0, + "content": "Table 2: gpt-4’s verbalized probabilities are substantially better-calibrated than the model probabilities themselves, even after", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 68, + 442, + 289, + 454 + ], + "spans": [ + { + "bbox": [ + 68, + 442, + 289, + 454 + ], + "score": 1.0, + "content": "temperature scaling, similarly to gpt-3.5-turbo in Table 1.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 69, + 462, + 290, + 570 + ], + "lines": [ + { + "bbox": [ + 69, + 461, + 292, + 477 + ], + "spans": [ + { + "bbox": [ + 69, + 461, + 292, + 477 + ], + "score": 1.0, + "content": "Brier Score (BS; Brier (1950)) on temperature-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 69, + 476, + 290, + 490 + ], + "spans": [ + { + "bbox": [ + 69, + 476, + 290, + 490 + ], + "score": 1.0, + "content": "scaled confidences (BS-t), a proper scoring rule", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 69, + 489, + 291, + 503 + ], + "spans": [ + { + "bbox": [ + 69, + 489, + 291, + 503 + ], + "score": 1.0, + "content": "(Ovadia et al., 2019) that is the mean squared error", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 69, + 504, + 292, + 516 + ], + "spans": [ + { + "bbox": [ + 69, + 504, + 292, + 516 + ], + "score": 1.0, + "content": "between the confidences and the correctness labels.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 68, + 517, + 290, + 530 + ], + "spans": [ + { + "bbox": [ + 68, + 517, + 290, + 530 + ], + "score": 1.0, + "content": "Finally, we assess calibration using a metric from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 69, + 530, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 69, + 530, + 290, + 542 + ], + "score": 1.0, + "content": "the selective classification literature (Geifman and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 69, + 543, + 290, + 557 + ], + "spans": [ + { + "bbox": [ + 69, + 543, + 290, + 557 + ], + "score": 1.0, + "content": "El-Yaniv, 2017), specifically, the area under the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 69, + 558, + 285, + 571 + ], + "spans": [ + { + "bbox": [ + 69, + 558, + 285, + 571 + ], + "score": 1.0, + "content": "curve of selective accuracy and coverage (AUC).", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 69, + 599, + 290, + 773 + ], + "lines": [ + { + "bbox": [ + 68, + 598, + 291, + 612 + ], + "spans": [ + { + "bbox": [ + 68, + 598, + 291, + 612 + ], + "score": 1.0, + "content": "Datasets. Our experiments use three question-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 68, + 611, + 292, + 626 + ], + "spans": [ + { + "bbox": [ + 68, + 611, + 292, + 626 + ], + "score": 1.0, + "content": "answering datasets assessing factual knowledge.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 68, + 625, + 290, + 639 + ], + "spans": [ + { + "bbox": [ + 68, + 625, + 265, + 639 + ], + "score": 1.0, + "content": "TriviaQA (Joshi et al., 2017) contains", + "type": "text" + }, + { + "bbox": [ + 265, + 625, + 290, + 638 + ], + "score": 0.34, + "content": "6 5 0 \\mathrm { k }", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 68, + 639, + 291, + 652 + ], + "spans": [ + { + "bbox": [ + 68, + 639, + 291, + 652 + ], + "score": 1.0, + "content": "question-answer pairs gathered by trivia enthusi-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 69, + 653, + 291, + 666 + ], + "spans": [ + { + "bbox": [ + 69, + 653, + 291, + 666 + ], + "score": 1.0, + "content": "asts; SciQ (Welbl et al., 2017) contains approxi-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 69, + 666, + 291, + 680 + ], + "spans": [ + { + "bbox": [ + 69, + 666, + 291, + 680 + ], + "score": 1.0, + "content": "mately 14k crowdsourced science exam question-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 68, + 680, + 291, + 693 + ], + "spans": [ + { + "bbox": [ + 68, + 680, + 291, + 693 + ], + "score": 1.0, + "content": "answer pairs; TruthfulQA (Lin et al., 2022b) con-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 69, + 694, + 291, + 707 + ], + "spans": [ + { + "bbox": [ + 69, + 694, + 291, + 707 + ], + "score": 1.0, + "content": "tains 817 questions designed to test language mod-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 69, + 707, + 291, + 719 + ], + "spans": [ + { + "bbox": [ + 69, + 707, + 291, + 719 + ], + "score": 1.0, + "content": "els’ tendency to mimic human falsehoods. We", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 68, + 720, + 291, + 734 + ], + "spans": [ + { + "bbox": [ + 68, + 720, + 291, + 734 + ], + "score": 1.0, + "content": "sample 1000 questions from the validation split of", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 68, + 733, + 290, + 747 + ], + "spans": [ + { + "bbox": [ + 68, + 733, + 290, + 747 + ], + "score": 1.0, + "content": "TriviaQA (rc.web.nocontext) and SciQ and all", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 747, + 292, + 760 + ], + "spans": [ + { + "bbox": [ + 69, + 747, + 292, + 760 + ], + "score": 1.0, + "content": "817 questions from the validation split of Truth-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 69, + 761, + 256, + 775 + ], + "spans": [ + { + "bbox": [ + 69, + 761, + 256, + 775 + ], + "score": 1.0, + "content": "fulQA (generation) for our experiments.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 305, + 463, + 525, + 678 + ], + "lines": [ + { + "bbox": [ + 304, + 462, + 527, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 527, + 477 + ], + "score": 1.0, + "content": "Evaluation protocol. For each dataset, we gener-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 477, + 525, + 489 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 525, + 489 + ], + "score": 1.0, + "content": "ate a response and corresponding confidence from", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 491, + 527, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 527, + 503 + ], + "score": 1.0, + "content": "each method on each of the evaluation questions.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 504, + 527, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 527, + 516 + ], + "score": 1.0, + "content": "Because calibration essentially quantifies the re-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 305, + 518, + 527, + 530 + ], + "spans": [ + { + "bbox": [ + 305, + 518, + 527, + 530 + ], + "score": 1.0, + "content": "lationship between model confidence and correct-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 532, + 526, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 526, + 543 + ], + "score": 1.0, + "content": "ness, computing correctness is crucial to accurate", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 545, + 525, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 525, + 556 + ], + "score": 1.0, + "content": "measurements of calibration. However, we find", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 304, + 559, + 526, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 526, + 571 + ], + "score": 1.0, + "content": "doing so to be a challenge, especially in datasets", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 572, + 526, + 585 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 526, + 585 + ], + "score": 1.0, + "content": "where only a single ground-truth answer (but not", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 585, + 526, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 526, + 598 + ], + "score": 1.0, + "content": "aliases or semantically equivalent rephrases) is pro-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 598, + 526, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 598, + 526, + 612 + ], + "score": 1.0, + "content": "vided. To avoid excessive false negatives in our", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 613, + 525, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 525, + 624 + ], + "score": 1.0, + "content": "correctness computation as a result of exact-match", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 626, + 527, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 626, + 527, + 637 + ], + "score": 1.0, + "content": "evaluation, we use either GPT-4 or GPT-3.5 to eval-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 640, + 526, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 526, + 653 + ], + "score": 1.0, + "content": "uate whether a response is essentially equivalent to", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 304, + 653, + 525, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 525, + 666 + ], + "score": 1.0, + "content": "the ground truth answer; see Appendix C for the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 667, + 493, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 667, + 493, + 680 + ], + "score": 1.0, + "content": "complete equivalence-checking procedure.", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 44.5 + }, + { + "type": "text", + "bbox": [ + 305, + 692, + 525, + 745 + ], + "lines": [ + { + "bbox": [ + 303, + 691, + 526, + 705 + ], + "spans": [ + { + "bbox": [ + 303, + 691, + 526, + 705 + ], + "score": 1.0, + "content": "Methods. We compare a wide variety of methods", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 706, + 527, + 718 + ], + "spans": [ + { + "bbox": [ + 304, + 706, + 527, + 718 + ], + "score": 1.0, + "content": "for extracting confidence estimates from LLMs.", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 720, + 526, + 732 + ], + "spans": [ + { + "bbox": [ + 304, + 720, + 526, + 732 + ], + "score": 1.0, + "content": "For a comprehensive list of the prompts used for", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 733, + 465, + 745 + ], + "spans": [ + { + "bbox": [ + 304, + 733, + 465, + 745 + ], + "score": 1.0, + "content": "each method, see Appendix Table 6.", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 54.5 + }, + { + "type": "text", + "bbox": [ + 305, + 748, + 525, + 773 + ], + "lines": [ + { + "bbox": [ + 315, + 747, + 525, + 761 + ], + "spans": [ + { + "bbox": [ + 315, + 747, + 525, + 761 + ], + "score": 1.0, + "content": "First, we consider two methods that leverage the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 303, + 760, + 527, + 775 + ], + "spans": [ + { + "bbox": [ + 303, + 760, + 527, + 775 + ], + "score": 1.0, + "content": "true conditional distribution of the model to gener-", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 57.5 + } + ], + "page_idx": 2, + "page_size": [ + 595, + 841 + ], + "discarded_blocks": [], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 525, + 231 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 69, + 70, + 525, + 231 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 69, + 70, + 525, + 231 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 525, + 231 + ], + "score": 0.985, + "html": "
TriviaQASciQTruthfulQA
MethodECEECE-tBS-t↓AUC ↑ECEECE-t↓BS-t↓AUC↑ECEECE-t↓BS-t↓AUC↑
Label prob. ‘Is True’prob.0.140 0.1640.097 0.1590.1420.8690.2560.1800.2230.7520.451 0.4700.317 0.4710.345 0.4760.418 0.384
Entropy1丨0.1650.826 0.5470.312 丨0.309 一0.3090.677 0.483一丨丨0.236
Verb.1S top-10.0680.0760.1380.8790.2340.0840.2140.7440.3890.2560.3220.545
Verb. 1S top-2 Verb. 1S top-40.0500.0530.1390.8940.1320.0500.2010.7660.3610.1150.2520.485
0.0540.0570.1440.8960.0650.0510.2090.7630.2030.1890.2840.455
Verb.2SCoT0.1100.1230.1680.8300.3230.2460.2960.6830.4190.2590.2920.551
Verb. 2S top-10.1310.0990.1480.8550.3400.2030.2680.6770.4310.2450.2820.483
Verb. 2S top-20.0470.0450.1470.8870.1690.0400.2010.7680.3950.1010.2240.517
Verb.2S top-40.0500.0510.1560.8610.1300.0460.2110.7290.2700.1560.2460.463
Ling. 1S human0.0620.0690.1370.8840.1660.0870.2230.7030.3060.2960.3330.503
Ling. 1S-opt.0.0580.0660.1350.8780.0640.0680.2200.6740.1250.1650.2700.492
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TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-t←AUCECEECE-tBS-tAUC
Label prob.0.0780.0670.0770.9500.2190.1650.1860.8200.4450.3340.3620.462
Verb.1S top-10.0240.0380.0840.9370.2010.0840.1650.8430.3500.1560.2270.622
Verb. 1S top-20.0250.0340.0840.9490.1400.0480.1850.8130.3150.1120.2280.623
Verb. 1S top-40.0410.0390.0810.9590.0560.0590.1850.8150.1980.1440.2450.619
Ling. 1S-human0.0510.0410.0860.9310.1480.0240.1700.8350.2410.1510.2280.651
Ling.1S-opt.0.0560.0510.0880.9270.0280.0520.1720.8280.0820.1050.2120.632
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TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-tAUCECEECE-t↓BS-tAUCECEECE-tBS-tAUC
Label prob.0.0740.0790.1170.9150.2160.1490.1950.7860.4320.3040.3350.418
Verb. 1S top-10.0490.0590.1600.8390.2650.1030.2470.6630.4400.1340.2040.411
Verb. 1S top-20.0460.0470.1580.8750.2070.0400.2250.6930.4500.0850.1970.409
Verb. 1S top-40.0750.0790.1760.8140.1510.0570.2260.6670.3720.1050.1830.377
Ling. 1S human0.0530.0500.1510.8670.2530.1180.2450.6640.4430.3580.3400.384
Ling.1S-opt.0.0740.0600.1490.8630.0890.0820.2380.6230.1390.1480.2280.350
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TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-tAUC ECEECE-t ↓BS-tAUC
Label prob.0.0890.0890.1370.8820.1810.1760.2370.7620.4090.3680.4050.319
Verb. iS top-10.0720.0710.1410.9030.2040.0540.2010.7760.3450.1150.2150.573
Verb.1S top-20.0490.0540.1330.9180.1340.0410.2110.7540.3590.0850.2230.491
Verb. 1S top-40.0720.0630.1580.8900.0480.0520.2160.7110.2740.0750.2080.473
Ling. 1S human0.0850.0610.1510.8780.2380.0260.2090.7560.3810.2420.3050.530
Ling. 1S-opt.0.0600.0700.1510.8740.0490.0560.2140.7380.0990.1300.2660.446
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TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-tAUCECEECE-t↓BS-tAUCECEECE-tBS-tAUC
Label prob.0.0740.0790.1170.9150.2160.1490.1950.7860.4320.3040.3350.418
Verb. 1S top-10.0490.0590.1600.8390.2650.1030.2470.6630.4400.1340.2040.411
Verb. 1S top-20.0460.0470.1580.8750.2070.0400.2250.6930.4500.0850.1970.409
Verb. 1S top-40.0750.0790.1760.8140.1510.0570.2260.6670.3720.1050.1830.377
Ling. 1S human0.0530.0500.1510.8670.2530.1180.2450.6640.4430.3580.3400.384
Ling.1S-opt.0.0740.0600.1490.8630.0890.0820.2380.6230.1390.1480.2280.350
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TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-tAUC ECEECE-t ↓BS-tAUC
Label prob.0.0890.0890.1370.8820.1810.1760.2370.7620.4090.3680.4050.319
Verb. iS top-10.0720.0710.1410.9030.2040.0540.2010.7760.3450.1150.2150.573
Verb.1S top-20.0490.0540.1330.9180.1340.0410.2110.7540.3590.0850.2230.491
Verb. 1S top-40.0720.0630.1580.8900.0480.0520.2160.7110.2740.0750.2080.473
Ling. 1S human0.0850.0610.1510.8780.2380.0260.2090.7560.3810.2420.3050.530
Ling. 1S-opt.0.0600.0700.1510.8740.0490.0560.2140.7380.0990.1300.2660.446
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We", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 69, + 671, + 291, + 684 + ], + "spans": [ + { + "bbox": [ + 69, + 671, + 291, + 684 + ], + "score": 1.0, + "content": "take the highest-probability prediction and its as-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 303, + 332, + 527, + 346 + ], + "spans": [ + { + "bbox": [ + 303, + 332, + 527, + 346 + ], + "score": 1.0, + "content": "sociated probability as the model’s output and con-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 303, + 345, + 527, + 360 + ], + "spans": [ + { + "bbox": [ + 303, + 345, + 412, + 360 + ], + "score": 1.0, + "content": "fidence. 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TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-t↓AUC↑ECEECE-t↓BS-tAUCECEECE-t ↓BS-t AUC
Label prob.0.1510.1240.1560.8650.2660.1890.2430.7070.4050.3610.3960.407
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Verb. 1S top-20.0600.0730.1940.8150.1530.0320.2300.6670.3400.0370.2270.440
Verb. 1S top-40.0690.0790.1820.8160.1050.0430.2290.6480.2310.1020.2370.465
Ling. 1S human0.1790.1150.1950.7490.0710.1010.2520.6030.3760.3660.3830.407
Ling.1S-opt.0.0770.0680.1860.7790.0190.0420.2360.5900.0470.0510.2390.435
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The calibration of both Claude", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 69, + 479, + 291, + 490 + ], + "spans": [ + { + "bbox": [ + 69, + 479, + 291, + 490 + ], + "score": 1.0, + "content": "models’ conditional probabilities roughly falls be-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 68, + 492, + 290, + 505 + ], + "spans": [ + { + "bbox": [ + 68, + 492, + 290, + 505 + ], + "score": 1.0, + "content": "tween gpt-3.5-turbo and gpt-4; however, while", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 68, + 504, + 291, + 519 + ], + "spans": [ + { + "bbox": [ + 68, + 504, + 291, + 519 + ], + "score": 1.0, + "content": "Claude 1 is much weaker at verbalizing its con-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 68, + 518, + 290, + 532 + ], + "spans": [ + { + "bbox": [ + 68, + 518, + 290, + 532 + ], + "score": 1.0, + "content": "fidence, Claude 2 is generally a bit stronger than", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 68, + 532, + 291, + 546 + ], + "spans": [ + { + "bbox": [ + 68, + 532, + 291, + 546 + ], + "score": 1.0, + "content": "gpt-3.5-turbo at verbalizing. The verbal calibra-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 69, + 546, + 291, + 559 + ], + "spans": [ + { + "bbox": [ + 69, + 546, + 291, + 559 + ], + "score": 1.0, + "content": "tion of the open source model Llama-2-70b-chat", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 68, + 560, + 292, + 572 + ], + "spans": [ + { + "bbox": [ + 68, + 560, + 292, + 572 + ], + "score": 1.0, + "content": "is generally weaker than that of closed source mod-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 68, + 573, + 291, + 586 + ], + "spans": [ + { + "bbox": [ + 68, + 573, + 291, + 586 + ], + "score": 1.0, + "content": "els but still demonstrates improvement over its con-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 68, + 586, + 291, + 600 + ], + "spans": [ + { + "bbox": [ + 68, + 586, + 291, + 600 + ], + "score": 1.0, + "content": "ditional probabilities by some metrics, and does so", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 69, + 600, + 197, + 613 + ], + "spans": [ + { + "bbox": [ + 69, + 600, + 197, + 613 + ], + "score": 1.0, + "content": "most clearly on TruthfulQA.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 19.5 + }, + { + "type": "title", + "bbox": [ + 70, + 627, + 142, + 641 + ], + "lines": [ + { + "bbox": [ + 67, + 626, + 144, + 643 + ], + "spans": [ + { + "bbox": [ + 67, + 626, + 144, + 643 + ], + "score": 1.0, + "content": "4 Discussion", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 70, + 653, + 289, + 773 + ], + "lines": [ + { + "bbox": [ + 69, + 653, + 290, + 666 + ], + "spans": [ + { + "bbox": [ + 69, + 653, + 290, + 666 + ], + "score": 1.0, + "content": "In summary, we study the calibration of widely", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "spans": [ + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "score": 1.0, + "content": "used RLHF-LMs. We first replicate the finding for", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 69, + 680, + 290, + 692 + ], + "spans": [ + { + "bbox": [ + 69, + 680, + 290, + 692 + ], + "score": 1.0, + "content": "GPT-4 (OpenAI, 2023) that RLHF can worsen the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 69, + 693, + 290, + 706 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 290, + 706 + ], + "score": 1.0, + "content": "calibration of a model’s conditional probabilities", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 68, + 708, + 291, + 720 + ], + "spans": [ + { + "bbox": [ + 68, + 708, + 291, + 720 + ], + "score": 1.0, + "content": "using the open-source Llama-2-70B base and chat", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 721, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 69, + 721, + 290, + 733 + ], + "score": 1.0, + "content": "models (Figure 2). To mitigate this regression and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 69, + 735, + 291, + 746 + ], + "spans": [ + { + "bbox": [ + 69, + 735, + 291, + 746 + ], + "score": 1.0, + "content": "ease extraction of calibrated confidence scores for", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 69, + 748, + 291, + 760 + ], + "spans": [ + { + "bbox": [ + 69, + 748, + 291, + 760 + ], + "score": 1.0, + "content": "models for which log probabilities are not avail-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 762, + 290, + 774 + ], + "spans": [ + { + "bbox": [ + 69, + 762, + 290, + 774 + ], + "score": 1.0, + "content": "able, we propose and study new methods that can", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 305, + 207, + 525, + 287 + ], + "lines": [ + { + "bbox": [ + 304, + 206, + 526, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 526, + 221 + ], + "score": 1.0, + "content": "elicit calibrated confidences from RLHF-LMs by", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 303, + 221, + 526, + 234 + ], + "spans": [ + { + "bbox": [ + 303, + 221, + 526, + 234 + ], + "score": 1.0, + "content": "prompting the model to verbalize its confidence", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 303, + 235, + 526, + 248 + ], + "spans": [ + { + "bbox": [ + 303, + 235, + 526, + 248 + ], + "score": 1.0, + "content": "in token space. We find verbalized probabilities", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 248, + 525, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 525, + 261 + ], + "score": 1.0, + "content": "are better-calibrated than conditional probabilities", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 262, + 525, + 273 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 525, + 273 + ], + "score": 1.0, + "content": "across several closed models, with mixed results", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 274, + 408, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 408, + 287 + ], + "score": 1.0, + "content": "for Llama-2-70B-Chat.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 47.5 + }, + { + "type": "text", + "bbox": [ + 305, + 294, + 525, + 551 + ], + "lines": [ + { + "bbox": [ + 316, + 295, + 525, + 307 + ], + "spans": [ + { + "bbox": [ + 316, + 295, + 525, + 307 + ], + "score": 1.0, + "content": "Our results raise several questions for future", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 307, + 526, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 526, + 320 + ], + "score": 1.0, + "content": "work. Most notably, the difference between GPT-*,", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 321, + 527, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 527, + 334 + ], + "score": 1.0, + "content": "Claude-*, and Llama-2’s ability to verbalize confi-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 335, + 527, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 527, + 349 + ], + "score": 1.0, + "content": "dence is significant. What factors are important for", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 349, + 525, + 362 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 525, + 362 + ], + "score": 1.0, + "content": "learning this skill? 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Answering", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 305, + 525, + 525, + 538 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 525, + 538 + ], + "score": 1.0, + "content": "these questions provides one path toward building", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 304, + 538, + 512, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 512, + 552 + ], + "score": 1.0, + "content": "more trustworthy and useful language systems.", + "type": "text" + } + ], + "index": 69 + } + ], + "index": 60 + }, + { + "type": "text", + "bbox": [ + 305, + 557, + 525, + 773 + ], + "lines": [ + { + "bbox": [ + 304, + 556, + 527, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 527, + 571 + ], + "score": 1.0, + "content": "Limitations. While our work demonstrates a", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 572, + 525, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 525, + 584 + ], + "score": 1.0, + "content": "promising new approach to generating calibrated", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 304, + 585, + 527, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 527, + 597 + ], + "score": 1.0, + "content": "confidences through verbalization, there are lim-", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 304, + 599, + 527, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 527, + 610 + ], + "score": 1.0, + "content": "itations that could be addressed in future work.", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 613, + 527, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 527, + 624 + ], + "score": 1.0, + "content": "First, our experiments are focused on factual recall-", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 626, + 527, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 626, + 527, + 638 + ], + "score": 1.0, + "content": "oriented problems, and the extent to which our ob-", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 303, + 639, + 526, + 653 + ], + "spans": [ + { + "bbox": [ + 303, + 639, + 526, + 653 + ], + "score": 1.0, + "content": "servations would hold for reasoning-heavy settings", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 303, + 652, + 526, + 666 + ], + "spans": [ + { + "bbox": [ + 303, + 652, + 526, + 666 + ], + "score": 1.0, + "content": "is an interesting open question. Additionally, the", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 303, + 666, + 527, + 680 + ], + "spans": [ + { + "bbox": [ + 303, + 666, + 527, + 680 + ], + "score": 1.0, + "content": "lack of technical details available for many state-of-", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 304, + 679, + 525, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 679, + 525, + 693 + ], + "score": 1.0, + "content": "the-art closed RLHF-LMs may limit our ability to", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 305, + 694, + 525, + 705 + ], + "spans": [ + { + "bbox": [ + 305, + 694, + 525, + 705 + ], + "score": 1.0, + "content": "understand what factors enable a model to verbalize", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 304, + 708, + 525, + 719 + ], + "spans": [ + { + "bbox": [ + 304, + 708, + 525, + 719 + ], + "score": 1.0, + "content": "well-calibrated confidences and differences in this", + "type": "text" + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 721, + 525, + 734 + ], + "spans": [ + { + "bbox": [ + 304, + 721, + 525, + 734 + ], + "score": 1.0, + "content": "ability across different models. 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TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-t↓AUC↑ECEECE-t↓BS-tAUCECEECE-t ↓BS-t AUC
Label prob.0.1510.1240.1560.8650.2660.1890.2430.7070.4050.3610.3960.407
Verb.1S top-10.0710.0670.1860.7930.1960.0530.2390.6480.3860.1720.2660.502
Verb. 1S top-20.0600.0730.1940.8150.1530.0320.2300.6670.3400.0370.2270.440
Verb. 1S top-40.0690.0790.1820.8160.1050.0430.2290.6480.2310.1020.2370.465
Ling. 1S human0.1790.1150.1950.7490.0710.1010.2520.6030.3760.3660.3830.407
Ling.1S-opt.0.0770.0680.1860.7790.0190.0420.2360.5900.0470.0510.2390.435
", + "type": "table", + "image_path": "f546fb7553aa771ec93f390451f744a497ab7bd82832fa172941f604c451a604.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 69, + 69, + 525, + 102.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 69, + 102.0, + 525, + 135.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 69, + 135.0, + 525, + 168.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 66, + 176, + 525, + 196 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 69, + 174, + 527, + 189 + ], + "spans": [ + { + "bbox": [ + 69, + 174, + 527, + 189 + ], + "score": 1.0, + "content": "Table 5: With Llama2-70B-Chat, verbalized calibration provides improvement over conditional probabilities across some metrics,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 186, + 355, + 198 + ], + "spans": [ + { + "bbox": [ + 69, + 186, + 296, + 198 + ], + "score": 1.0, + "content": "but the improvement is much less consistent compared to GPT-", + "type": "text" + }, + { + "bbox": [ + 297, + 187, + 302, + 195 + ], + "score": 0.3, + "content": "^ *", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 186, + 355, + 198 + ], + "score": 1.0, + "content": "and Claude-*.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 69, + 205, + 290, + 613 + ], + "lines": [], + "index": 19.5, + "bbox_fs": [ + 68, + 206, + 292, + 613 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 70, + 627, + 142, + 641 + ], + "lines": [ + { + "bbox": [ + 67, + 626, + 144, + 643 + ], + "spans": [ + { + "bbox": [ + 67, + 626, + 144, + 643 + ], + "score": 1.0, + "content": "4 Discussion", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 70, + 653, + 289, + 773 + ], + "lines": [ + { + "bbox": [ + 69, + 653, + 290, + 666 + ], + "spans": [ + { + "bbox": [ + 69, + 653, + 290, + 666 + ], + "score": 1.0, + "content": "In summary, we study the calibration of widely", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "spans": [ + { + "bbox": [ + 68, + 666, + 290, + 680 + ], + "score": 1.0, + "content": "used RLHF-LMs. We first replicate the finding for", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 69, + 680, + 290, + 692 + ], + "spans": [ + { + "bbox": [ + 69, + 680, + 290, + 692 + ], + "score": 1.0, + "content": "GPT-4 (OpenAI, 2023) that RLHF can worsen the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 69, + 693, + 290, + 706 + ], + "spans": [ + { + "bbox": [ + 69, + 693, + 290, + 706 + ], + "score": 1.0, + "content": "calibration of a model’s conditional probabilities", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 68, + 708, + 291, + 720 + ], + "spans": [ + { + "bbox": [ + 68, + 708, + 291, + 720 + ], + "score": 1.0, + "content": "using the open-source Llama-2-70B base and chat", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 69, + 721, + 290, + 733 + ], + "spans": [ + { + "bbox": [ + 69, + 721, + 290, + 733 + ], + "score": 1.0, + "content": "models (Figure 2). To mitigate this regression and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 69, + 735, + 291, + 746 + ], + "spans": [ + { + "bbox": [ + 69, + 735, + 291, + 746 + ], + "score": 1.0, + "content": "ease extraction of calibrated confidence scores for", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 69, + 748, + 291, + 760 + ], + "spans": [ + { + "bbox": [ + 69, + 748, + 291, + 760 + ], + "score": 1.0, + "content": "models for which log probabilities are not avail-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 69, + 762, + 290, + 774 + ], + "spans": [ + { + "bbox": [ + 69, + 762, + 290, + 774 + ], + "score": 1.0, + "content": "able, we propose and study new methods that can", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 206, + 526, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 526, + 221 + ], + "score": 1.0, + "content": "elicit calibrated confidences from RLHF-LMs by", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 303, + 221, + 526, + 234 + ], + "spans": [ + { + "bbox": [ + 303, + 221, + 526, + 234 + ], + "score": 1.0, + "content": "prompting the model to verbalize its confidence", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 303, + 235, + 526, + 248 + ], + "spans": [ + { + "bbox": [ + 303, + 235, + 526, + 248 + ], + "score": 1.0, + "content": "in token space. We find verbalized probabilities", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 248, + 525, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 525, + 261 + ], + "score": 1.0, + "content": "are better-calibrated than conditional probabilities", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 262, + 525, + 273 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 525, + 273 + ], + "score": 1.0, + "content": "across several closed models, with mixed results", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 274, + 408, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 408, + 287 + ], + "score": 1.0, + "content": "for Llama-2-70B-Chat.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 40, + "bbox_fs": [ + 68, + 653, + 291, + 774 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 207, + 525, + 287 + ], + "lines": [], + "index": 47.5, + "bbox_fs": [ + 303, + 206, + 526, + 287 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 305, + 294, + 525, + 551 + ], + "lines": [ + { + "bbox": [ + 316, + 295, + 525, + 307 + ], + "spans": [ + { + "bbox": [ + 316, + 295, + 525, + 307 + ], + "score": 1.0, + "content": "Our results raise several questions for future", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 307, + 526, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 526, + 320 + ], + "score": 1.0, + "content": "work. Most notably, the difference between GPT-*,", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 304, + 321, + 527, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 527, + 334 + ], + "score": 1.0, + "content": "Claude-*, and Llama-2’s ability to verbalize confi-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 335, + 527, + 349 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 527, + 349 + ], + "score": 1.0, + "content": "dence is significant. What factors are important for", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 304, + 349, + 525, + 362 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 525, + 362 + ], + "score": 1.0, + "content": "learning this skill? 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Answering", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 305, + 525, + 525, + 538 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 525, + 538 + ], + "score": 1.0, + "content": "these questions provides one path toward building", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 304, + 538, + 512, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 512, + 552 + ], + "score": 1.0, + "content": "more trustworthy and useful language systems.", + "type": "text" + } + ], + "index": 69 + } + ], + "index": 60, + "bbox_fs": [ + 303, + 295, + 527, + 552 + ] + }, + { + "type": "text", + "bbox": [ + 305, + 557, + 525, + 773 + ], + "lines": [ + { + "bbox": [ + 304, + 556, + 527, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 527, + 571 + ], + "score": 1.0, + "content": "Limitations. While our work demonstrates a", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 304, + 572, + 525, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 525, + 584 + ], + "score": 1.0, + "content": "promising new approach to generating calibrated", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 304, + 585, + 527, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 527, + 597 + ], + "score": 1.0, + "content": "confidences through verbalization, there are lim-", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 304, + 599, + 527, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 527, + 610 + ], + "score": 1.0, + "content": "itations that could be addressed in future work.", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 304, + 613, + 527, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 527, + 624 + ], + "score": 1.0, + "content": "First, our experiments are focused on factual recall-", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 304, + 626, + 527, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 626, + 527, + 638 + ], + "score": 1.0, + "content": "oriented problems, and the extent to which our ob-", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 303, + 639, + 526, + 653 + ], + "spans": [ + { + "bbox": [ + 303, + 639, + 526, + 653 + ], + "score": 1.0, + "content": "servations would hold for reasoning-heavy settings", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 303, + 652, + 526, + 666 + ], + "spans": [ + { + "bbox": [ + 303, + 652, + 526, + 666 + ], + "score": 1.0, + "content": "is an interesting open question. Additionally, the", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 303, + 666, + 527, + 680 + ], + "spans": [ + { + "bbox": [ + 303, + 666, + 527, + 680 + ], + "score": 1.0, + "content": "lack of technical details available for many state-of-", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 304, + 679, + 525, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 679, + 525, + 693 + ], + "score": 1.0, + "content": "the-art closed RLHF-LMs may limit our ability to", + "type": "text" + } + ], + "index": 79 + }, + { + "bbox": [ + 305, + 694, + 525, + 705 + ], + "spans": [ + { + "bbox": [ + 305, + 694, + 525, + 705 + ], + "score": 1.0, + "content": "understand what factors enable a model to verbalize", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 304, + 708, + 525, + 719 + ], + "spans": [ + { + "bbox": [ + 304, + 708, + 525, + 719 + ], + "score": 1.0, + "content": "well-calibrated confidences and differences in this", + "type": "text" + } + ], + "index": 81 + }, + { + "bbox": [ + 304, + 721, + 525, + 734 + ], + "spans": [ + { + "bbox": [ + 304, + 721, + 525, + 734 + ], + "score": 1.0, + "content": "ability across different models. 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CF and CDM are CIFAR Fel-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 86, + 290, + 99 + ], + "spans": [ + { + "bbox": [ + 68, + 86, + 290, + 99 + ], + "score": 1.0, + "content": "lows. EM gratefully acknowledges funding from", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 99, + 291, + 113 + ], + "spans": [ + { + "bbox": [ + 68, + 99, + 291, + 113 + ], + "score": 1.0, + "content": "a Knight-Hennessy Graduate Fellowship. AZ is", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 113, + 290, + 126 + ], + "spans": [ + { + "bbox": [ + 68, + 113, + 290, + 126 + ], + "score": 1.0, + "content": "supported by the NSF graduate research fellowship", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 126, + 291, + 140 + ], + "spans": [ + { + "bbox": [ + 67, + 126, + 291, + 140 + ], + "score": 1.0, + "content": "program. 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To compute ECE-t and BS-t for", + "type": "text" + } + ], + "index": 84 + }, + { + "bbox": [ + 304, + 581, + 526, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 526, + 594 + ], + "score": 1.0, + "content": "Ling. 1S-opt, we hold out one of the 5 folds to", + "type": "text" + } + ], + "index": 85 + }, + { + "bbox": [ + 303, + 594, + 526, + 608 + ], + "spans": [ + { + "bbox": [ + 303, + 594, + 526, + 608 + ], + "score": 1.0, + "content": "fit temperature. 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We then", + "type": "text" + } + ], + "index": 89 + }, + { + "bbox": [ + 304, + 649, + 512, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 649, + 512, + 660 + ], + "score": 1.0, + "content": "average metrics across all 20 rotations of folds.", + "type": "text" + } + ], + "index": 90 + } + ], + "index": 85, + "bbox_fs": [ + 303, + 511, + 526, + 660 + ] + }, + { + "type": "title", + "bbox": [ + 305, + 671, + 421, + 685 + ], + "lines": [ + { + "bbox": [ + 303, + 669, + 423, + 690 + ], + "spans": [ + { + "bbox": [ + 303, + 669, + 423, + 690 + ], + "score": 1.0, + "content": "C Prompt Templates", + "type": "text" + } + ], + "index": 91 + } + ], + "index": 91 + }, + { + "type": "text", + "bbox": [ + 305, + 693, + 525, + 774 + ], + "lines": [ + { + "bbox": [ + 303, + 692, + 526, + 708 + ], + "spans": [ + { + "bbox": [ + 303, + 692, + 526, + 708 + ], + "score": 1.0, + "content": "The prompt template for each sampling method", + "type": "text" + } + ], + "index": 92 + }, + { + "bbox": [ + 302, + 706, + 527, + 720 + ], + "spans": [ + { + "bbox": [ + 302, + 706, + 527, + 720 + ], + "score": 1.0, + "content": "is provided in Table 6. The question is substi-", + "type": "text" + } + ], + "index": 93 + }, + { + "bbox": [ + 304, + 720, + 525, + 734 + ], + "spans": [ + { + "bbox": [ + 304, + 720, + 404, + 732 + ], + "score": 1.0, + "content": "tuted for the variable", + "type": "text" + }, + { + "bbox": [ + 405, + 720, + 488, + 734 + ], + "score": 0.59, + "content": "\\$ 123,456,710N \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 720, + 525, + 732 + ], + "score": 1.0, + "content": "in each", + "type": "text" + } + ], + "index": 94 + }, + { + "bbox": [ + 303, + 735, + 527, + 747 + ], + "spans": [ + { + "bbox": [ + 303, + 735, + 527, + 747 + ], + "score": 1.0, + "content": "prompt. To evaluate answer correctness, we", + "type": "text" + } + ], + "index": 95 + }, + { + "bbox": [ + 303, + 748, + 526, + 760 + ], + "spans": [ + { + "bbox": [ + 303, + 748, + 526, + 760 + ], + "score": 1.0, + "content": "use gpt-3.5-turbo for SciQ and TruthfulQA", + "type": "text" + } + ], + "index": 96 + }, + { + "bbox": [ + 304, + 761, + 526, + 774 + ], + "spans": [ + { + "bbox": [ + 304, + 761, + 526, + 774 + ], + "score": 1.0, + "content": "and gpt-4 for TriviaQA due to gpt-3.5-turbo’s", + "type": "text" + } + ], + "index": 97 + }, + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "score": 1.0, + "content": "high disagreement with a human evaluator on", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 84, + 291, + 99 + ], + "spans": [ + { + "bbox": [ + 68, + 84, + 291, + 99 + ], + "score": 1.0, + "content": "TriviaQA. Using the ground truth answer as", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 99, + 291, + 111 + ], + "spans": [ + { + "bbox": [ + 69, + 99, + 147, + 111 + ], + "score": 0.62, + "content": "\\$ 523,456,7", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 147, + 100, + 291, + 111 + ], + "score": 1.0, + "content": "and the model-generated answer", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 112, + 290, + 126 + ], + "spans": [ + { + "bbox": [ + 68, + 112, + 290, + 126 + ], + "score": 1.0, + "content": "as ${PRED_ANSWER}, we use the following prompt", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 126, + 113, + 140 + ], + "spans": [ + { + "bbox": [ + 68, + 126, + 113, + 140 + ], + "score": 1.0, + "content": "template:", + "type": "text", + "cross_page": true + } + ], + "index": 4 + } + ], + "index": 94.5, + "bbox_fs": [ + 302, + 692, + 527, + 774 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 87, + 517, + 723 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 77, + 87, + 517, + 723 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 77, + 87, + 517, + 723 + ], + "spans": [ + { + "bbox": [ + 77, + 87, + 517, + 723 + ], + "score": 0.972, + "html": "
Method Template
Label prob. Provide your best guess for the following question. Give ONLY the guess，noother words orexplanation.\\n\\nForexample:\\n\\nGuess: <most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}
‘Is True'prob. Question: ${QUESTION}\\nProposed Answer: ${ANSWER}\\nIs the proposed answer:\\n\\t(A)True or\\n\\t(B) False?\\n The proposed answer is:
Verb. 1S top-1 Provide your best guess and the probability that it is correct (0.0 to 1.0） forthe_following question． Give ONLY the guess and probability，no other words orexplanation.For example:\\n\\nGuess: <most likely guess，as short as possible； nota complete sentence，just the guess!>\\n Probability:<the probability between 0.0and 1.0 that your guess is correct，without any extra commentary whatsoever；justthe probability!>\\n\\nThe question is:${THE_QUESTION}
Verb.1S top-k Provide your ${k} best guesses and the probability that each is correct (0.0 to1.0）for the following question.Give ONLY the guesses and probabilities，no otherwords or explanation. For example:\\n\\nG1: <first most likely guess，as short aspossible；not a complete sentence，just the guess!>\\n\\nP1: <the probability between0.0 and 1.0 that G1 is correct， without any extra commentary whatsoever； justthe probability!> ... G${k}: <${k}-th most likely guess，as short as possible;not a complete sentence， just the guess!>\\n\\nP${k}: <the probability between 0.0and 1.0 that G${k} is correct，without any extra commentary whatsoever； just theprobability!> \\n\\nThe question is: ${THE_QUESTION}
Verb.2SCoT Provide your best guess for the following question. Before giving your answer,provide a step-by-step explanation of your thought process. Then on a new linegive the guess with no other words or explanation.\\n\\nFor example:\\n\\nExplanation:<one sentence step-by-step explanation of your thought process>\\n\\nGuess: <mostlikely guess，as short as_possible； not a complete sentence，just the guess!>\\n\\nThequestion is:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-1 Provide your best guess for the following question.Give ONLY the guess，nootherwordsor_explanation.\\n\\nForexample:\\n\\nGuess:<most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the_probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-kProvide your ${k} best guesses for the following question. Give ONLY the guesses,no other words_or explanation. For example:\\n\\nG1: <first most likely guess，asshort as possible；not a complete sentence，just the guess!>\\n\\nP1: <the probabilitybetween 0.0 and 1.0 that G1 is correct，without any extra commentary whatsoever;just the probability!> ... G${k}:<${k}-th most likely guess，as short as possible;not a complete sentence，just the guess!>\\n\\nThe question is:${THE_QUESTION}Providethe_probability_that eachofyourguessesiscorrect. Give ONLYthe probabilities，no other words or explanation.\\n\\nFor example:\\n\\nP1:<theprobability between 0.0 and 1.0 that G1 is correct，without any extra commentarywhatsoever； just the probability!>\\n... P${k}: <the probability between 0.0 and1.0 that G${k} is correct， without any extra commentary whatsoever； just theprobability!>
therwords
shonortaspossiblsible;
ust theproailiteat
oth
Ling. 1S Provide your best guess for the following question，and describe how likely it isthat your guess is correct as one of the following expressions: ${EXPRESsION_LIST}.Give ONLY the guess and_ your confidence， no other words or explanation.Forexample:\\n\\nGuess: <most likely guess，as short as possible； not a complete sentence,just the guess!>\\nConfidence:<description of confidence， without any extracommentary whatsoever； just a short phrase!>\\n\\nThe question is:${THE_QUESTION}
", + "type": "table", + "image_path": "53d417f2848e7c864ea722f51d6f29fb757295cddd33aa1b71498ec271051052.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 77, + 87, + 517, + 299.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 77, + 299.0, + 517, + 511.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 77, + 511.0, + 517, + 723.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 69, + 730, + 524, + 751 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 69, + 730, + 525, + 741 + ], + "spans": [ + { + "bbox": [ + 69, + 730, + 525, + 741 + ], + "score": 1.0, + "content": "Table 6: Prompt templates for each method evaluated. Methods above the double line use multiple samples in order to estimate", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 738, + 505, + 753 + ], + "spans": [ + { + "bbox": [ + 68, + 738, + 505, + 753 + ], + "score": 1.0, + "content": "confidence scores; methods below the double line use the verbalized confidences directly, requiring only a single sample.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + } + ], + "page_idx": 8, + "page_size": [ + 595, + 841 + ], + "discarded_blocks": [], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 87, + 517, + 723 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 77, + 87, + 517, + 723 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 77, + 87, + 517, + 723 + ], + "spans": [ + { + "bbox": [ + 77, + 87, + 517, + 723 + ], + "score": 0.972, + "html": "
Method Template
Label prob. Provide your best guess for the following question. Give ONLY the guess，noother words orexplanation.\\n\\nForexample:\\n\\nGuess: <most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}
‘Is True'prob. Question: ${QUESTION}\\nProposed Answer: ${ANSWER}\\nIs the proposed answer:\\n\\t(A)True or\\n\\t(B) False?\\n The proposed answer is:
Verb. 1S top-1 Provide your best guess and the probability that it is correct (0.0 to 1.0） forthe_following question． Give ONLY the guess and probability，no other words orexplanation.For example:\\n\\nGuess: <most likely guess，as short as possible； nota complete sentence，just the guess!>\\n Probability:<the probability between 0.0and 1.0 that your guess is correct，without any extra commentary whatsoever；justthe probability!>\\n\\nThe question is:${THE_QUESTION}
Verb.1S top-k Provide your ${k} best guesses and the probability that each is correct (0.0 to1.0）for the following question.Give ONLY the guesses and probabilities，no otherwords or explanation. For example:\\n\\nG1: <first most likely guess，as short aspossible；not a complete sentence，just the guess!>\\n\\nP1: <the probability between0.0 and 1.0 that G1 is correct， without any extra commentary whatsoever； justthe probability!> ... G${k}: <${k}-th most likely guess，as short as possible;not a complete sentence， just the guess!>\\n\\nP${k}: <the probability between 0.0and 1.0 that G${k} is correct，without any extra commentary whatsoever； just theprobability!> \\n\\nThe question is: ${THE_QUESTION}
Verb.2SCoT Provide your best guess for the following question. Before giving your answer,provide a step-by-step explanation of your thought process. Then on a new linegive the guess with no other words or explanation.\\n\\nFor example:\\n\\nExplanation:<one sentence step-by-step explanation of your thought process>\\n\\nGuess: <mostlikely guess，as short as_possible； not a complete sentence，just the guess!>\\n\\nThequestion is:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-1 Provide your best guess for the following question.Give ONLY the guess，nootherwordsor_explanation.\\n\\nForexample:\\n\\nGuess:<most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the_probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-kProvide your ${k} best guesses for the following question. Give ONLY the guesses,no other words_or explanation. For example:\\n\\nG1: <first most likely guess，asshort as possible；not a complete sentence，just the guess!>\\n\\nP1: <the probabilitybetween 0.0 and 1.0 that G1 is correct，without any extra commentary whatsoever;just the probability!> ... G${k}:<${k}-th most likely guess，as short as possible;not a complete sentence，just the guess!>\\n\\nThe question is:${THE_QUESTION}Providethe_probability_that eachofyourguessesiscorrect. Give ONLYthe probabilities，no other words or explanation.\\n\\nFor example:\\n\\nP1:<theprobability between 0.0 and 1.0 that G1 is correct，without any extra commentarywhatsoever； just the probability!>\\n... P${k}: <the probability between 0.0 and1.0 that G${k} is correct， without any extra commentary whatsoever； just theprobability!>
therwords
shonortaspossiblsible;
ust theproailiteat
oth
Ling. 1S Provide your best guess for the following question，and describe how likely it isthat your guess is correct as one of the following expressions: ${EXPRESsION_LIST}.Give ONLY the guess and_ your confidence， no other words or explanation.Forexample:\\n\\nGuess: <most likely guess，as short as possible； not a complete sentence,just the guess!>\\nConfidence:<description of confidence， without any extracommentary whatsoever； just a short phrase!>\\n\\nThe question is:${THE_QUESTION}
", + "type": "table", + "image_path": "53d417f2848e7c864ea722f51d6f29fb757295cddd33aa1b71498ec271051052.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 77, + 87, + 517, + 299.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 77, + 299.0, + 517, + 511.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 77, + 511.0, + 517, + 723.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 69, + 730, + 524, + 751 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 69, + 730, + 525, + 741 + ], + "spans": [ + { + "bbox": [ + 69, + 730, + 525, + 741 + ], + "score": 1.0, + "content": "Table 6: Prompt templates for each method evaluated. Methods above the double line use multiple samples in order to estimate", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 738, + 505, + 753 + ], + "spans": [ + { + "bbox": [ + 68, + 738, + 505, + 753 + ], + "score": 1.0, + "content": "confidence scores; methods below the double line use the verbalized confidences directly, requiring only a single sample.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 69, + 72, + 290, + 138 + ], + "lines": [ + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 290, + 85 + ], + "score": 1.0, + "content": "high disagreement with a human evaluator on", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 84, + 291, + 99 + ], + "spans": [ + { + "bbox": [ + 68, + 84, + 291, + 99 + ], + "score": 1.0, + "content": "TriviaQA. Using the ground truth answer as", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 99, + 291, + 111 + ], + "spans": [ + { + "bbox": [ + 69, + 99, + 147, + 111 + ], + "score": 0.62, + "content": "\\$ 523,456,7", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 100, + 291, + 111 + ], + "score": 1.0, + "content": "and the model-generated answer", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 112, + 290, + 126 + ], + "spans": [ + { + "bbox": [ + 68, + 112, + 290, + 126 + ], + "score": 1.0, + "content": "as ${PRED_ANSWER}, we use the following prompt", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 126, + 113, + 140 + ], + "spans": [ + { + "bbox": [ + 68, + 126, + 113, + 140 + ], + "score": 1.0, + "content": "template:", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 70, + 140, + 290, + 220 + ], + "lines": [ + { + "bbox": [ + 79, + 138, + 291, + 153 + ], + "spans": [ + { + "bbox": [ + 79, + 138, + 291, + 153 + ], + "score": 1.0, + "content": "Are the following two answers to my", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 152, + 292, + 166 + ], + "spans": [ + { + "bbox": [ + 68, + 152, + 117, + 166 + ], + "score": 1.0, + "content": "question", + "type": "text" + }, + { + "bbox": [ + 117, + 154, + 126, + 165 + ], + "score": 0.58, + "content": "\\mathsf Q", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 152, + 292, + 166 + ], + "score": 1.0, + "content": "semantically equivalent?\\n\\nQ:", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 167, + 291, + 180 + ], + "spans": [ + { + "bbox": [ + 69, + 167, + 291, + 180 + ], + "score": 1.0, + "content": "${THE_QUESTION}\\nA1: ${GOLD_ANSWER}\\nA2:", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 180, + 291, + 193 + ], + "spans": [ + { + "bbox": [ + 69, + 180, + 291, + 193 + ], + "score": 1.0, + "content": "${PRED_ANSWER}\\n\\nPlease answer with a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 193, + 291, + 206 + ], + "spans": [ + { + "bbox": [ + 69, + 193, + 291, + 206 + ], + "score": 1.0, + "content": "single word, either “Yes.\" or “No.\", and", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 207, + 196, + 222 + ], + "spans": [ + { + "bbox": [ + 69, + 207, + 196, + 222 + ], + "score": 1.0, + "content": "explain your reasoning.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7.5 + } + ], + "page_idx": 9, + "page_size": [ + 595, + 841 + ], + "discarded_blocks": [], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 69, + 72, + 290, + 138 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 68, + 71, + 291, + 140 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 70, + 140, + 290, + 220 + ], + "lines": [ + { + "bbox": [ + 79, + 138, + 291, + 153 + ], + "spans": [ + { + "bbox": [ + 79, + 138, + 291, + 153 + ], + "score": 1.0, + "content": "Are the following two answers to my", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 152, + 292, + 166 + ], + "spans": [ + { + "bbox": [ + 68, + 152, + 117, + 166 + ], + "score": 1.0, + "content": "question", + "type": "text" + }, + { + "bbox": [ + 117, + 154, + 126, + 165 + ], + "score": 0.58, + "content": "\\mathsf Q", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 152, + 292, + 166 + ], + "score": 1.0, + "content": "semantically equivalent?\\n\\nQ:", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 167, + 291, + 180 + ], + "spans": [ + { + "bbox": [ + 69, + 167, + 291, + 180 + ], + "score": 1.0, + "content": "${THE_QUESTION}\\nA1: ${GOLD_ANSWER}\\nA2:", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 180, + 291, + 193 + ], + "spans": [ + { + "bbox": [ + 69, + 180, + 291, + 193 + ], + "score": 1.0, + "content": "${PRED_ANSWER}\\n\\nPlease answer with a", + "type": "text" + } + ], + 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TriviaQASciQTruthfulQA
MethodECEECE-tBS-t↓AUC ↑ECEECE-t↓BS-t↓AUC↑ECEECE-t↓BS-t↓AUC↑
Label prob. ‘Is True’prob.0.140 0.1640.097 0.1590.1420.8690.2560.1800.2230.7520.451 0.4700.317 0.4710.345 0.4760.418 0.384
Entropy1丨0.1650.826 0.5470.312 丨0.309 一0.3090.677 0.483一丨丨0.236
Verb.1S top-10.0680.0760.1380.8790.2340.0840.2140.7440.3890.2560.3220.545
Verb. 1S top-2 Verb. 1S top-40.0500.0530.1390.8940.1320.0500.2010.7660.3610.1150.2520.485
0.0540.0570.1440.8960.0650.0510.2090.7630.2030.1890.2840.455
Verb.2SCoT0.1100.1230.1680.8300.3230.2460.2960.6830.4190.2590.2920.551
Verb. 2S top-10.1310.0990.1480.8550.3400.2030.2680.6770.4310.2450.2820.483
Verb. 2S top-20.0470.0450.1470.8870.1690.0400.2010.7680.3950.1010.2240.517
Verb.2S top-40.0500.0510.1560.8610.1300.0460.2110.7290.2700.1560.2460.463
Ling. 1S human0.0620.0690.1370.8840.1660.0870.2230.7030.3060.2960.3330.503
Ling. 1S-opt.0.0580.0660.1350.8780.0640.0680.2200.6740.1250.1650.2700.492
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TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-t←AUCECEECE-tBS-tAUC
Label prob.0.0780.0670.0770.9500.2190.1650.1860.8200.4450.3340.3620.462
Verb.1S top-10.0240.0380.0840.9370.2010.0840.1650.8430.3500.1560.2270.622
Verb. 1S top-20.0250.0340.0840.9490.1400.0480.1850.8130.3150.1120.2280.623
Verb. 1S top-40.0410.0390.0810.9590.0560.0590.1850.8150.1980.1440.2450.619
Ling. 1S-human0.0510.0410.0860.9310.1480.0240.1700.8350.2410.1510.2280.651
Ling.1S-opt.0.0560.0510.0880.9270.0280.0520.1720.8280.0820.1050.2120.632
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TriviaQASciQTruthfulQA
MethodECEECE-t↓BS-tAUCECEECE-t↓BS-tAUC ECEECE-t ↓BS-tAUC
Label prob.0.0890.0890.1370.8820.1810.1760.2370.7620.4090.3680.4050.319
Verb. iS top-10.0720.0710.1410.9030.2040.0540.2010.7760.3450.1150.2150.573
Verb.1S top-20.0490.0540.1330.9180.1340.0410.2110.7540.3590.0850.2230.491
Verb. 1S top-40.0720.0630.1580.8900.0480.0520.2160.7110.2740.0750.2080.473
Ling. 1S human0.0850.0610.1510.8780.2380.0260.2090.7560.3810.2420.3050.530
Ling. 1S-opt.0.0600.0700.1510.8740.0490.0560.2140.7380.0990.1300.2660.446
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TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-tAUCECEECE-t↓BS-tAUCECEECE-tBS-tAUC
Label prob.0.0740.0790.1170.9150.2160.1490.1950.7860.4320.3040.3350.418
Verb. 1S top-10.0490.0590.1600.8390.2650.1030.2470.6630.4400.1340.2040.411
Verb. 1S top-20.0460.0470.1580.8750.2070.0400.2250.6930.4500.0850.1970.409
Verb. 1S top-40.0750.0790.1760.8140.1510.0570.2260.6670.3720.1050.1830.377
Ling. 1S human0.0530.0500.1510.8670.2530.1180.2450.6640.4430.3580.3400.384
Ling.1S-opt.0.0740.0600.1490.8630.0890.0820.2380.6230.1390.1480.2280.350
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TriviaQASciQTruthfulQA
MethodECEECE-t ↓BS-t↓AUC↑ECEECE-t↓BS-tAUCECEECE-t ↓BS-t AUC
Label prob.0.1510.1240.1560.8650.2660.1890.2430.7070.4050.3610.3960.407
Verb.1S top-10.0710.0670.1860.7930.1960.0530.2390.6480.3860.1720.2660.502
Verb. 1S top-20.0600.0730.1940.8150.1530.0320.2300.6670.3400.0370.2270.440
Verb. 1S top-40.0690.0790.1820.8160.1050.0430.2290.6480.2310.1020.2370.465
Ling. 1S human0.1790.1150.1950.7490.0710.1010.2520.6030.3760.3660.3830.407
Ling.1S-opt.0.0770.0680.1860.7790.0190.0420.2360.5900.0470.0510.2390.435
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Method Template
Label prob. Provide your best guess for the following question. Give ONLY the guess，noother words orexplanation.\\n\\nForexample:\\n\\nGuess: <most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}
‘Is True'prob. Question: ${QUESTION}\\nProposed Answer: ${ANSWER}\\nIs the proposed answer:\\n\\t(A)True or\\n\\t(B) False?\\n The proposed answer is:
Verb. 1S top-1 Provide your best guess and the probability that it is correct (0.0 to 1.0） forthe_following question． Give ONLY the guess and probability，no other words orexplanation.For example:\\n\\nGuess: <most likely guess，as short as possible； nota complete sentence，just the guess!>\\n Probability:<the probability between 0.0and 1.0 that your guess is correct，without any extra commentary whatsoever；justthe probability!>\\n\\nThe question is:${THE_QUESTION}
Verb.1S top-k Provide your ${k} best guesses and the probability that each is correct (0.0 to1.0）for the following question.Give ONLY the guesses and probabilities，no otherwords or explanation. For example:\\n\\nG1: <first most likely guess，as short aspossible；not a complete sentence，just the guess!>\\n\\nP1: <the probability between0.0 and 1.0 that G1 is correct， without any extra commentary whatsoever； justthe probability!> ... G${k}: <${k}-th most likely guess，as short as possible;not a complete sentence， just the guess!>\\n\\nP${k}: <the probability between 0.0and 1.0 that G${k} is correct，without any extra commentary whatsoever； just theprobability!> \\n\\nThe question is: ${THE_QUESTION}
Verb.2SCoT Provide your best guess for the following question. Before giving your answer,provide a step-by-step explanation of your thought process. Then on a new linegive the guess with no other words or explanation.\\n\\nFor example:\\n\\nExplanation:<one sentence step-by-step explanation of your thought process>\\n\\nGuess: <mostlikely guess，as short as_possible； not a complete sentence，just the guess!>\\n\\nThequestion is:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-1 Provide your best guess for the following question.Give ONLY the guess，nootherwordsor_explanation.\\n\\nForexample:\\n\\nGuess:<most likely guess，asshort as possible； not a complete sentence， just the guess!>\\n\\nThe questionis:${THE_QUESTION}Provide the probability that your guess is correct． Give ONLY the_probability，noother words or explanation.\\n\\nFor example:\\n\\nProbability:<the probability between0.0 and 1.0 that your guess is correct，without any extra commentary whatsoever;just the probability!>\\n
Verb. 2S top-kProvide your ${k} best guesses for the following question. Give ONLY the guesses,no other words_or explanation. For example:\\n\\nG1: <first most likely guess，asshort as possible；not a complete sentence，just the guess!>\\n\\nP1: <the probabilitybetween 0.0 and 1.0 that G1 is correct，without any extra commentary whatsoever;just the probability!> ... G${k}:<${k}-th most likely guess，as short as possible;not a complete sentence，just the guess!>\\n\\nThe question is:${THE_QUESTION}Providethe_probability_that eachofyourguessesiscorrect. Give ONLYthe probabilities，no other words or explanation.\\n\\nFor example:\\n\\nP1:<theprobability between 0.0 and 1.0 that G1 is correct，without any extra commentarywhatsoever； just the probability!>\\n... P${k}: <the probability between 0.0 and1.0 that G${k} is correct， without any extra commentary whatsoever； just theprobability!>
therwords
shonortaspossiblsible;
ust theproailiteat
oth
Ling. 1S Provide your best guess for the following question，and describe how likely it isthat your guess is correct as one of the following expressions: ${EXPRESsION_LIST}.Give ONLY the guess and_ your confidence， no other words or explanation.Forexample:\\n\\nGuess: <most likely guess，as short as possible； not a complete sentence,just the guess!>\\nConfidence:<description of confidence， without any extracommentary whatsoever； just a short phrase!>\\n\\nThe question is:${THE_QUESTION}
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The", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 507, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 520 + ], + "score": 1.0, + "content": "successful methods include, autoregressive models (van den Oord et al., 2016; Mehri et al., 2017;", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "score": 1.0, + "content": "Kalchbrenner et al., 2018), flow-based models (van den Oord et al., 2018; Ping et al., 2019; Prenger", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "score": 1.0, + "content": "et al., 2019; Kim et al., 2019; Ping et al., 2020; Lee et al., 2020), GAN-based models (Donahue et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "score": 1.0, + "content": "2019; Kumar et al., 2019; Binkowski et al. ´ , 2020; Yamamoto et al., 2020; Kong et al., 2020), and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 550, + 395, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 395, + 563 + ], + "score": 1.0, + "content": "diffusion models (Kong et al., 2021; Chen et al., 2021; Lee et al., 2022).", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 107, + 568, + 505, + 689 + ], + "lines": [ + { + "bbox": [ + 106, + 568, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 505, + 581 + ], + "score": 1.0, + "content": "Among these methods, GAN-based vocoders (e.g., Kong et al., 2020) can generate high-fidelity raw", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 580, + 504, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 504, + 591 + ], + "score": 1.0, + "content": "audio conditioned on mel spectrogram, while synthesizing hundreds of times faster than real-time", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "on a single GPU. 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"recording environments. In this work, we present BigVGAN, a universal vocoder", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 330, + 470, + 343 + ], + "spans": [ + { + "bbox": [ + 141, + 330, + 470, + 343 + ], + "score": 1.0, + "content": "that generalizes well for various out-of-distribution scenarios without fine-tuning.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 341, + 469, + 353 + ], + "spans": [ + { + "bbox": [ + 141, + 341, + 469, + 353 + ], + "score": 1.0, + "content": "We introduce periodic activation function and anti-aliased representation into the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 352, + 470, + 365 + ], + "spans": [ + { + "bbox": [ + 141, + 352, + 470, + 365 + ], + "score": 1.0, + "content": "GAN generator, which brings the desired inductive bias for audio synthesis and", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 363, + 470, + 376 + ], + "spans": [ + { + "bbox": [ + 141, + 363, + 470, + 376 + ], + "score": 1.0, + "content": "significantly improves audio quality. In addition, we train our GAN vocoder at", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 374, + 471, + 387 + ], + "spans": [ + { + "bbox": [ + 141, + 374, + 471, + 387 + ], + "score": 1.0, + "content": "the largest scale up to 112M parameters, which is unprecedented in the literature.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 385, + 470, + 398 + ], + "spans": [ + { + "bbox": [ + 141, + 385, + 470, + 398 + ], + "score": 1.0, + "content": "We identify and address the failure modes in large-scale GAN training for audio,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 396, + 471, + 408 + ], + "spans": [ + { + "bbox": [ + 141, + 396, + 471, + 408 + ], + "score": 1.0, + "content": "while maintaining high-fidelity output without over-regularization. Our BigVGAN,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 406, + 470, + 420 + ], + "spans": [ + { + "bbox": [ + 141, + 406, + 470, + 420 + ], + "score": 1.0, + "content": "trained only on clean speech (LibriTTS), achieves the state-of-the-art performance", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 418, + 470, + 430 + ], + "spans": [ + { + "bbox": [ + 141, + 418, + 470, + 430 + ], + "score": 1.0, + "content": "for various zero-shot (out-of-distribution) conditions, including unseen speakers,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 429, + 468, + 441 + ], + "spans": [ + { + "bbox": [ + 141, + 429, + 468, + 441 + ], + "score": 1.0, + "content": "languages, recording environments, singing voices, music, and instrumental audio. 1", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 440, + 464, + 452 + ], + "spans": [ + { + "bbox": [ + 141, + 440, + 464, + 452 + ], + "score": 1.0, + "content": "We release our code and model at: https://github.com/NVIDIA/BigVGAN.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 17, + "bbox_fs": [ + 141, + 286, + 471, + 452 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 474, + 206, + 486 + ], + "lines": [ + { + "bbox": [ + 105, + 473, + 208, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 208, + 489 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 497, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "Deep generative models have demonstrated noticeable successes for modeling raw audio. The", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 507, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 520 + ], + "score": 1.0, + "content": "successful methods include, autoregressive models (van den Oord et al., 2016; Mehri et al., 2017;", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "score": 1.0, + "content": "Kalchbrenner et al., 2018), flow-based models (van den Oord et al., 2018; Ping et al., 2019; Prenger", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "score": 1.0, + "content": "et al., 2019; Kim et al., 2019; Ping et al., 2020; Lee et al., 2020), GAN-based models (Donahue et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "score": 1.0, + "content": "2019; Kumar et al., 2019; Binkowski et al. ´ , 2020; Yamamoto et al., 2020; Kong et al., 2020), and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 550, + 395, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 395, + 563 + ], + "score": 1.0, + "content": "diffusion models (Kong et al., 2021; Chen et al., 2021; Lee et al., 2022).", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 496, + 506, + 563 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 568, + 505, + 689 + ], + "lines": [ + { + "bbox": [ + 106, + 568, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 505, + 581 + ], + "score": 1.0, + "content": "Among these methods, GAN-based vocoders (e.g., Kong et al., 2020) can generate high-fidelity raw", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 580, + 504, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 504, + 591 + ], + "score": 1.0, + "content": "audio conditioned on mel spectrogram, while synthesizing hundreds of times faster than real-time", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "on a single GPU. However, existing GAN vocoders are confined to the settings with a moderate", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 602, + 504, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 504, + 613 + ], + "score": 1.0, + "content": "number of voices recorded in clean environment due to the limited model capacity. The audio", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "score": 1.0, + "content": "quality can heavily degrade when the models are conditioned on mel spectrogram from unseen", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 624, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 636 + ], + "score": 1.0, + "content": "speakers in different recording environments. In practice, a universal vocoder, that can do zero-shot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 634, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 505, + 648 + ], + "score": 1.0, + "content": "generation for out-of-distribution samples, is very valuable in many real-world applications, including", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 645, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 505, + 657 + ], + "score": 1.0, + "content": "text-to-speech with numerous speakers (Ping et al., 2018), neural voice cloning (Arik et al., 2018; Jia", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "et al., 2018), voice conversion (Liu et al., 2018), speech-to-speech translation (Jia et al., 2019), and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 668, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 679 + ], + "score": 1.0, + "content": "neural audio codec (Zeghidour et al., 2021). In these applications, the neural vocoder also needs to", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 678, + 333, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 333, + 690 + ], + "score": 1.0, + "content": "generalize well for audio recorded at various conditions.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 568, + 506, + 690 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 192 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 507, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 507, + 97 + ], + "score": 1.0, + "content": "Scaling up the model size for zero-shot performance is a noticeable trend in text generation (e.g.,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "Brown et al., 2020) and image synthesis (e.g., Ramesh et al., 2021), but has not been explored in", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "audio synthesis. Although likelihood-based models are found to be easier for scaling among others", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 127 + ], + "score": 1.0, + "content": "because of their simple training objective and stable optimization, we build our universal vocoder", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 441, + 139 + ], + "score": 1.0, + "content": "with large-scale GAN training, because GAN vocoder has the following advantages:", + "type": "text" + }, + { + "bbox": [ + 442, + 127, + 447, + 137 + ], + "score": 0.27, + "content": "i ,", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "In contrast to", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "autoregressive or diffusion models, it is fully parallel and requires only one forward pass to generate", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 505, + 160 + ], + "score": 1.0, + "content": "high-dimensional waveform. ii) In contrast to flow-based models (Prenger et al., 2019), it does not", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "score": 1.0, + "content": "enforce any architectural constraints (e.g., affine coupling layer) that maintain the bijection between", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "score": 1.0, + "content": "latent and data. Such architectural constraints can limit model capacity given the same number of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 229, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 229, + 194 + ], + "score": 1.0, + "content": "parameters (Ping et al., 2020).", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 107, + 198, + 504, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "score": 1.0, + "content": "In this work, we present BigVGAN, a Big Vocoding GAN that enables high-fidelity out-of-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 208, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 506, + 222 + ], + "score": 1.0, + "content": "distribution (OOD) generation without fine-tuning. Specifically, we make the following contributions:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 109, + 224, + 506, + 391 + ], + "lines": [ + { + "bbox": [ + 108, + 223, + 506, + 236 + ], + "spans": [ + { + "bbox": [ + 108, + 223, + 506, + 236 + ], + "score": 1.0, + "content": "1. We introduce periodic activations into the generator, which provide the desired inductive bias for", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 120, + 234, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 120, + 234, + 505, + 247 + ], + "score": 1.0, + "content": "audio synthesis. Inspired by the methods proposed for other domains (Liu et al., 2020; Sitzmann", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 120, + 246, + 497, + 258 + ], + "spans": [ + { + "bbox": [ + 120, + 246, + 497, + 258 + ], + "score": 1.0, + "content": "et al., 2020), we demonstrate the noticeable success of periodic activations in audio synthesis.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 257, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 505, + 270 + ], + "score": 1.0, + "content": "2. We propose anti-aliased multi-periodicity composition (AMP) module for modeling complex", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 120, + 269, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 120, + 269, + 505, + 281 + ], + "score": 1.0, + "content": "audio waveform. AMP composes multiple signal components with learnable periodicities and", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 120, + 280, + 354, + 292 + ], + "spans": [ + { + "bbox": [ + 120, + 280, + 354, + 292 + ], + "score": 1.0, + "content": "uses low-pass filter to reduce the high-frequency artifacts.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 109, + 291, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 109, + 291, + 505, + 304 + ], + "score": 1.0, + "content": "3. We successfully scale BigVGAN up to 112M parameters by fixing the failure modes of large-scale", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 120, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 120, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "GAN training without regularizing both generator and discriminator. The empirical insights are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 119, + 310, + 507, + 328 + ], + "spans": [ + { + "bbox": [ + 119, + 310, + 507, + 328 + ], + "score": 1.0, + "content": "different from Brock et al. (2019) in image domain. For example, regularization methods (e.g.,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 120, + 324, + 420, + 337 + ], + "spans": [ + { + "bbox": [ + 120, + 324, + 420, + 337 + ], + "score": 1.0, + "content": "Miyato et al., 2018) introduce phase mismatch artifacts in audio synthesis.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 109, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 109, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "4. We demonstrate that BigVGAN-base with 14M parameters outperforms the state-of-the-art", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 121, + 347, + 504, + 358 + ], + "spans": [ + { + "bbox": [ + 121, + 347, + 504, + 358 + ], + "score": 1.0, + "content": "neural vocoders with comparable size for both in-distribution and out-of-distribution samples. 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We discuss related work in", + "type": "text" + }, + { + "bbox": [ + 396, + 395, + 410, + 406 + ], + "score": 0.84, + "content": "\\ S 2", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 394, + 504, + 407 + ], + "score": 1.0, + "content": "and present BigVGAN", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 405, + 393, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 117, + 418 + ], + "score": 1.0, + "content": "in", + "type": "text" + }, + { + "bbox": [ + 117, + 406, + 131, + 416 + ], + "score": 0.79, + "content": "\\ S \\ O 3", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 405, + 255, + 418 + ], + "score": 1.0, + "content": ". We report empirical results in", + "type": "text" + }, + { + "bbox": [ + 255, + 406, + 270, + 416 + ], + "score": 0.83, + "content": "\\ S 4", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 405, + 375, + 418 + ], + "score": 1.0, + "content": "and conclude the paper in", + "type": "text" + }, + { + "bbox": [ + 375, + 406, + 389, + 416 + ], + "score": 0.84, + "content": "\\ S 5", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 405, + 393, + 418 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5 + }, + { + "type": "title", + "bbox": [ + 108, + 426, + 211, + 439 + ], + "lines": [ + { + "bbox": [ + 105, + 425, + 213, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 213, + 441 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 446, + 505, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "score": 1.0, + "content": "Our work builds upon the state-of-the-art of GANs for image and audio synthesis. GAN was first", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "score": 1.0, + "content": "proposed for image synthesis (Goodfellow et al., 2014). Since then, impressive results have been", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 467, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 480 + ], + "score": 1.0, + "content": "obtained through optimized architectures (e.g., Radford et al., 2016; Karras et al., 2021) or large scale", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 478, + 242, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 242, + 491 + ], + "score": 1.0, + "content": "training (e.g., Brock et al., 2019).", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5 + }, + { + "type": "text", + "bbox": [ + 107, + 496, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "score": 1.0, + "content": "In audio synthesis, previous works focus on improving the discriminator architectures or adding", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 506, + 507, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 507, + 518 + ], + "score": 1.0, + "content": "new auxiliary training losses. 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In", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "contrast, GAN-TTS (Binkowski et al. ´ , 2020) uses an ensemble of discriminators which operate on", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 562, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 505, + 573 + ], + "score": 1.0, + "content": "random windows of different sizes, and enforces the mapping between the conditioner and waveform", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "adversarially using conditional discriminators. Parallel WaveGAN (Yamamoto et al., 2020) extends", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "the single short-time Fourier transform (STFT) loss (Ping et al., 2019) to multi-resolution, and adds it", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 594, + 506, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 506, + 606 + ], + "score": 1.0, + "content": "as an auxiliary loss for GAN training. Yang et al. (2021) and Mustafa et al. (2021) further improve", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "MelGAN by incorporating the multi-resolution STFT loss. 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Our architectural design has a connection with the latest results in time-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 709, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 721 + ], + "score": 1.0, + "content": "series prediction (Liu et al., 2020), implicit neural representations (Sitzmann et al., 2020), and", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "image synthesis (Karras et al., 2021). Note that, You et al. (2021) argues that different generator", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 52 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 192 + ], + "lines": [ + { + "bbox": [ + 105, + 79, + 507, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 507, + 97 + ], + "score": 1.0, + "content": "Scaling up the model size for zero-shot performance is a noticeable trend in text generation (e.g.,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "Brown et al., 2020) and image synthesis (e.g., Ramesh et al., 2021), but has not been explored in", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "audio synthesis. Although likelihood-based models are found to be easier for scaling among others", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 127 + ], + "score": 1.0, + "content": "because of their simple training objective and stable optimization, we build our universal vocoder", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 441, + 139 + ], + "score": 1.0, + "content": "with large-scale GAN training, because GAN vocoder has the following advantages:", + "type": "text" + }, + { + "bbox": [ + 442, + 127, + 447, + 137 + ], + "score": 0.27, + "content": "i ,", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "In contrast to", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "autoregressive or diffusion models, it is fully parallel and requires only one forward pass to generate", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 505, + 160 + ], + "score": 1.0, + "content": "high-dimensional waveform. ii) In contrast to flow-based models (Prenger et al., 2019), it does not", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 172 + ], + "score": 1.0, + "content": "enforce any architectural constraints (e.g., affine coupling layer) that maintain the bijection between", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 506, + 183 + ], + "score": 1.0, + "content": "latent and data. Such architectural constraints can limit model capacity given the same number of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 229, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 229, + 194 + ], + "score": 1.0, + "content": "parameters (Ping et al., 2020).", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 4.5, + "bbox_fs": [ + 105, + 79, + 507, + 194 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 198, + 504, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "score": 1.0, + "content": "In this work, we present BigVGAN, a Big Vocoding GAN that enables high-fidelity out-of-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 208, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 506, + 222 + ], + "score": 1.0, + "content": "distribution (OOD) generation without fine-tuning. Specifically, we make the following contributions:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 198, + 506, + 222 + ] + }, + { + "type": "text", + "bbox": [ + 109, + 224, + 506, + 391 + ], + "lines": [ + { + "bbox": [ + 108, + 223, + 506, + 236 + ], + "spans": [ + { + "bbox": [ + 108, + 223, + 506, + 236 + ], + "score": 1.0, + "content": "1. We introduce periodic activations into the generator, which provide the desired inductive bias for", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 120, + 234, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 120, + 234, + 505, + 247 + ], + "score": 1.0, + "content": "audio synthesis. Inspired by the methods proposed for other domains (Liu et al., 2020; Sitzmann", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 120, + 246, + 497, + 258 + ], + "spans": [ + { + "bbox": [ + 120, + 246, + 497, + 258 + ], + "score": 1.0, + "content": "et al., 2020), we demonstrate the noticeable success of periodic activations in audio synthesis.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 257, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 107, + 257, + 505, + 270 + ], + "score": 1.0, + "content": "2. We propose anti-aliased multi-periodicity composition (AMP) module for modeling complex", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 120, + 269, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 120, + 269, + 505, + 281 + ], + "score": 1.0, + "content": "audio waveform. AMP composes multiple signal components with learnable periodicities and", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 120, + 280, + 354, + 292 + ], + "spans": [ + { + "bbox": [ + 120, + 280, + 354, + 292 + ], + "score": 1.0, + "content": "uses low-pass filter to reduce the high-frequency artifacts.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 109, + 291, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 109, + 291, + 505, + 304 + ], + "score": 1.0, + "content": "3. We successfully scale BigVGAN up to 112M parameters by fixing the failure modes of large-scale", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 120, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 120, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "GAN training without regularizing both generator and discriminator. The empirical insights are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 119, + 310, + 507, + 328 + ], + "spans": [ + { + "bbox": [ + 119, + 310, + 507, + 328 + ], + "score": 1.0, + "content": "different from Brock et al. (2019) in image domain. For example, regularization methods (e.g.,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 120, + 324, + 420, + 337 + ], + "spans": [ + { + "bbox": [ + 120, + 324, + 420, + 337 + ], + "score": 1.0, + "content": "Miyato et al., 2018) introduce phase mismatch artifacts in audio synthesis.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 109, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 109, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "4. 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We discuss related work in", + "type": "text" + }, + { + "bbox": [ + 396, + 395, + 410, + 406 + ], + "score": 0.84, + "content": "\\ S 2", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 394, + 504, + 407 + ], + "score": 1.0, + "content": "and present BigVGAN", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 405, + 393, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 117, + 418 + ], + "score": 1.0, + "content": "in", + "type": "text" + }, + { + "bbox": [ + 117, + 406, + 131, + 416 + ], + "score": 0.79, + "content": "\\ S \\ O 3", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 405, + 255, + 418 + ], + "score": 1.0, + "content": ". We report empirical results in", + "type": "text" + }, + { + "bbox": [ + 255, + 406, + 270, + 416 + ], + "score": 0.83, + "content": "\\ S 4", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 405, + 375, + 418 + ], + "score": 1.0, + "content": "and conclude the paper in", + "type": "text" + }, + { + "bbox": [ + 375, + 406, + 389, + 416 + ], + "score": 0.84, + "content": "\\ S 5", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 405, + 393, + 418 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5, + "bbox_fs": [ + 106, + 394, + 504, + 418 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 426, + 211, + 439 + ], + "lines": [ + { + "bbox": [ + 105, + 425, + 213, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 213, + 441 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 446, + 505, + 489 + ], + "lines": [ + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "score": 1.0, + "content": "Our work builds upon the state-of-the-art of GANs for image and audio synthesis. GAN was first", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "score": 1.0, + "content": "proposed for image synthesis (Goodfellow et al., 2014). Since then, impressive results have been", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 467, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 480 + ], + "score": 1.0, + "content": "obtained through optimized architectures (e.g., Radford et al., 2016; Karras et al., 2021) or large scale", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 478, + 242, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 242, + 491 + ], + "score": 1.0, + "content": "training (e.g., Brock et al., 2019).", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 446, + 506, + 491 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 496, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "score": 1.0, + "content": "In audio synthesis, previous works focus on improving the discriminator architectures or adding", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 506, + 507, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 507, + 518 + ], + "score": 1.0, + "content": "new auxiliary training losses. MelGAN (Kumar et al., 2019) introduces the multi-scale discrimina-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 517, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 505, + 530 + ], + "score": 1.0, + "content": "tor (MSD) that uses average pooling to downsample the raw waveform at multiple scales and applies", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "window-based discriminators at each scale separately. It also enforces the mapping between input", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 308, + 551 + ], + "score": 1.0, + "content": "mel spectrogram and generated waveform via an", + "type": "text" + }, + { + "bbox": [ + 309, + 540, + 319, + 550 + ], + "score": 0.87, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 540, + 505, + 551 + ], + "score": 1.0, + "content": "feature matching loss from discriminator. In", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "contrast, GAN-TTS (Binkowski et al. ´ , 2020) uses an ensemble of discriminators which operate on", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 562, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 505, + 573 + ], + "score": 1.0, + "content": "random windows of different sizes, and enforces the mapping between the conditioner and waveform", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "adversarially using conditional discriminators. Parallel WaveGAN (Yamamoto et al., 2020) extends", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "the single short-time Fourier transform (STFT) loss (Ping et al., 2019) to multi-resolution, and adds it", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 594, + 506, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 506, + 606 + ], + "score": 1.0, + "content": "as an auxiliary loss for GAN training. Yang et al. (2021) and Mustafa et al. (2021) further improve", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "MelGAN by incorporating the multi-resolution STFT loss. HiFi-GAN (Kong et al., 2020) reuses", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 614, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 505, + 629 + ], + "score": 1.0, + "content": "the MSD from MelGAN, and introduces the multi-period discriminator (MPD) for high-fidelity", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "synthesis. UnivNet (Jang et al., 2020; 2021) uses the multi-resolution discriminator (MRD) that takes", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "the multi-resolution spectrograms as the input and can sharpen the spectral structure of synthesized", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "score": 1.0, + "content": "waveform. 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Our architectural design has a connection with the latest results in time-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 709, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 721 + ], + "score": 1.0, + "content": "series prediction (Liu et al., 2020), implicit neural representations (Sitzmann et al., 2020), and", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "image synthesis (Karras et al., 2021). Note that, You et al. (2021) argues that different generator", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 272, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 505, + 285 + ], + "score": 1.0, + "content": "architectures can perform equally well for single-speaker neural vocoding. We demonstrate that", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 284, + 504, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 504, + 296 + ], + "score": 1.0, + "content": "improving generator architecture is crucial for universal neural vocoding in challenging conditions.", + "type": "text", + "cross_page": true + } + ], + "index": 9 + } + ], + "index": 52, + "bbox_fs": [ + 105, + 676, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 147, + 66, + 457, + 194 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 147, + 66, + 457, + 194 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 147, + 66, + 457, + 194 + ], + "spans": [ + { + "bbox": [ + 147, + 66, + 457, + 194 + ], + "score": 0.974, + "type": "image", + "image_path": "bf290d224b300ff12c70a1dbae9ed2e3da99d067fecdd94653b994b8e0dcb25c.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 147, + 66, + 457, + 108.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 147, + 108.66666666666666, + 457, + 151.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 147, + 151.33333333333331, + 457, + 193.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 201, + 506, + 252 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 200, + 506, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 506, + 213 + ], + "score": 1.0, + "content": "Figure 1: Schematic diagram of BigVGAN generator. The generator is composed of multiple blocks of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 212, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 506, + 222 + ], + "score": 1.0, + "content": "transposed 1-D convolution followed by the proposed anti-aliased multi-periodicity composition (AMP) module.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 221, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 506, + 233 + ], + "score": 1.0, + "content": "The AMP module adds features from multiple residual blocks with different channel-wise periodicities before", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 231, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 231, + 505, + 243 + ], + "score": 1.0, + "content": "dilated 1-D convolutions. It uses Snake function for providing periodic inductive bias, and low-pass filter for", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 241, + 186, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 186, + 254 + ], + "score": 1.0, + "content": "anti-aliasing purpose.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 105, + 272, + 504, + 295 + ], + "lines": [ + { + "bbox": [ + 105, + 272, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 505, + 285 + ], + "score": 1.0, + "content": "architectures can perform equally well for single-speaker neural vocoding. We demonstrate that", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 284, + 504, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 504, + 296 + ], + "score": 1.0, + "content": "improving generator architecture is crucial for universal neural vocoding in challenging conditions.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 107, + 300, + 505, + 344 + ], + "lines": [ + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "score": 1.0, + "content": "There are limited successes for universal neural vocoding due to the noticeable challenges. In previous", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 311, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 322 + ], + "score": 1.0, + "content": "work, WaveRNN has been applied for universal vocoding task (Lorenzo-Trueba et al., 2019; Paul", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "et al., 2020). Jiao et al. (2021) builds the universal vocoder with flow-based model. GAN vocoder is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 333, + 336, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 336, + 345 + ], + "score": 1.0, + "content": "found to be a good candidate recently (Jang et al., 2021).", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + }, + { + "type": "title", + "bbox": [ + 107, + 355, + 173, + 367 + ], + "lines": [ + { + "bbox": [ + 104, + 353, + 175, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 353, + 175, + 371 + ], + "score": 1.0, + "content": "3 METHOD", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 377, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "score": 1.0, + "content": "In this section, we introduce the preliminaries for GAN vocoder, then present the BigVGAN. See", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 388, + 502, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 502, + 401 + ], + "score": 1.0, + "content": "Figure 1 for an illustration and refer to the Appendix A for a detailed description of the architecture.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "title", + "bbox": [ + 108, + 407, + 285, + 419 + ], + "lines": [ + { + "bbox": [ + 105, + 407, + 286, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 286, + 420 + ], + "score": 1.0, + "content": "3.1 PRELIMINARIES OF GAN VOCODER", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 422, + 505, + 488 + ], + "lines": [ + { + "bbox": [ + 106, + 423, + 504, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 504, + 434 + ], + "score": 1.0, + "content": "Generator The generator network takes mel spectrogram or other features as input and output the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "score": 1.0, + "content": "corresponding raw waveform. In previous studies, several generator architectures have been applied,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "score": 1.0, + "content": "including WaveNet (e.g., Yamamoto et al., 2020), or convolutional network that gradually upsamples", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "the mel spectrogram to high-resolution waveform with a stack of residual blocks (e.g., Kumar et al.,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "2019; Kong et al., 2020). We choose the HiFi-GAN generator as the baseline architecture. We believe", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 477, + 423, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 423, + 489 + ], + "score": 1.0, + "content": "the proposed techniques are applicable to other generator architectures as well.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5 + }, + { + "type": "text", + "bbox": [ + 107, + 494, + 505, + 637 + ], + "lines": [ + { + "bbox": [ + 106, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 505, + 506 + ], + "score": 1.0, + "content": "Discriminator The state-of-the-art GAN vocoders usually comprise several discriminators to", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "guide the generator to synthesize coherent waveform while minimizing perceptual artifacts that are", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "detectable by human ears. Importantly, each discriminator contains multiple sub-discriminators", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "score": 1.0, + "content": "operating on different resolution windows of the waveform. For example, HiFi-GAN (Kong et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "score": 1.0, + "content": "2020) applies two types of discriminators: i) the multi-period discriminator (MPD), where the 1-D", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "signal is reshaped to 2-D representations with varied heights and widths to separately capture the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "score": 1.0, + "content": "multiple periodic structures though 2-D convolutions. ii) The multi-scale discriminator (MSD) (Kumar", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 569, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 104, + 569, + 506, + 585 + ], + "score": 1.0, + "content": "et al., 2019), where each sub-discriminator receives down-sampled 1-D signals at different frequency", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "score": 1.0, + "content": "by average pooling in the time domain. Jang et al. (2020; 2021) propose to apply the discriminator", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 593, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 604 + ], + "score": 1.0, + "content": "on the time–frequency domain using the multi-resolution discriminator (MRD), which is composed", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "of several sub-discriminators that operate on multiple 2-D linear spectrograms with different STFT", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 614, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 614, + 505, + 627 + ], + "score": 1.0, + "content": "resolutions. We also find that replacing MSD with MRD improves audio quality with reduced pitch", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 625, + 206, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 625, + 206, + 639 + ], + "score": 1.0, + "content": "and periodicity artifacts.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 642, + 505, + 687 + ], + "lines": [ + { + "bbox": [ + 105, + 642, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 655 + ], + "score": 1.0, + "content": "Training objectives Our training objective is similar as HiFi-GAN (Kong et al., 2020), with an", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 654, + 505, + 665 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 505, + 665 + ], + "score": 1.0, + "content": "exception of replacing MSD to MRD. It comprises the weighted sum of the least-square adversarial", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 664, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 451, + 677 + ], + "score": 1.0, + "content": "loss (Mao et al., 2017), the feature matching loss (Larsen et al., 2016), and the spectral", + "type": "text" + }, + { + "bbox": [ + 451, + 665, + 461, + 676 + ], + "score": 0.87, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 664, + 505, + 677 + ], + "score": 1.0, + "content": "regression", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 675, + 506, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 506, + 688 + ], + "score": 1.0, + "content": "loss on mel spectrogram. We leave the details of each loss and hyper-parameters in the Appendix B.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5 + }, + { + "type": "title", + "bbox": [ + 108, + 695, + 249, + 706 + ], + "lines": [ + { + "bbox": [ + 105, + 693, + 250, + 708 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 250, + 708 + ], + "score": 1.0, + "content": "3.2 PERIODIC INDUCTIVE BIAS", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 108, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "The audio waveform is known to exhibit high periodicity and can be naturally represented as the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "composition of primitive periodic components (i.e., Fourier series under Dirichlet conditions). 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The generator is composed of multiple blocks of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 212, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 506, + 222 + ], + "score": 1.0, + "content": "transposed 1-D convolution followed by the proposed anti-aliased multi-periodicity composition (AMP) module.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 221, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 506, + 233 + ], + "score": 1.0, + "content": "The AMP module adds features from multiple residual blocks with different channel-wise periodicities before", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 231, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 231, + 505, + 243 + ], + "score": 1.0, + "content": "dilated 1-D convolutions. It uses Snake function for providing periodic inductive bias, and low-pass filter for", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 241, + 186, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 186, + 254 + ], + "score": 1.0, + "content": "anti-aliasing purpose.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 105, + 272, + 504, + 295 + ], + "lines": [], + "index": 8.5, + "bbox_fs": [ + 105, + 272, + 505, + 296 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 300, + 505, + 344 + ], + "lines": [ + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "score": 1.0, + "content": "There are limited successes for universal neural vocoding due to the noticeable challenges. In previous", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 311, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 322 + ], + "score": 1.0, + "content": "work, WaveRNN has been applied for universal vocoding task (Lorenzo-Trueba et al., 2019; Paul", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "et al., 2020). Jiao et al. (2021) builds the universal vocoder with flow-based model. GAN vocoder is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 333, + 336, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 336, + 345 + ], + "score": 1.0, + "content": "found to be a good candidate recently (Jang et al., 2021).", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 299, + 505, + 345 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 355, + 173, + 367 + ], + "lines": [ + { + "bbox": [ + 104, + 353, + 175, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 353, + 175, + 371 + ], + "score": 1.0, + "content": "3 METHOD", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 377, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "score": 1.0, + "content": "In this section, we introduce the preliminaries for GAN vocoder, then present the BigVGAN. See", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 388, + 502, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 502, + 401 + ], + "score": 1.0, + "content": "Figure 1 for an illustration and refer to the Appendix A for a detailed description of the architecture.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 377, + 505, + 401 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 407, + 285, + 419 + ], + "lines": [ + { + "bbox": [ + 105, + 407, + 286, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 286, + 420 + ], + "score": 1.0, + "content": "3.1 PRELIMINARIES OF GAN VOCODER", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 422, + 505, + 488 + ], + "lines": [ + { + "bbox": [ + 106, + 423, + 504, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 504, + 434 + ], + "score": 1.0, + "content": "Generator The generator network takes mel spectrogram or other features as input and output the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "score": 1.0, + "content": "corresponding raw waveform. In previous studies, several generator architectures have been applied,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 457 + ], + "score": 1.0, + "content": "including WaveNet (e.g., Yamamoto et al., 2020), or convolutional network that gradually upsamples", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "the mel spectrogram to high-resolution waveform with a stack of residual blocks (e.g., Kumar et al.,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "2019; Kong et al., 2020). We choose the HiFi-GAN generator as the baseline architecture. We believe", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 477, + 423, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 423, + 489 + ], + "score": 1.0, + "content": "the proposed techniques are applicable to other generator architectures as well.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 423, + 506, + 489 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 494, + 505, + 637 + ], + "lines": [ + { + "bbox": [ + 106, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 505, + 506 + ], + "score": 1.0, + "content": "Discriminator The state-of-the-art GAN vocoders usually comprise several discriminators to", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "guide the generator to synthesize coherent waveform while minimizing perceptual artifacts that are", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "detectable by human ears. Importantly, each discriminator contains multiple sub-discriminators", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "score": 1.0, + "content": "operating on different resolution windows of the waveform. For example, HiFi-GAN (Kong et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "score": 1.0, + "content": "2020) applies two types of discriminators: i) the multi-period discriminator (MPD), where the 1-D", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "signal is reshaped to 2-D representations with varied heights and widths to separately capture the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "score": 1.0, + "content": "multiple periodic structures though 2-D convolutions. ii) The multi-scale discriminator (MSD) (Kumar", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 569, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 104, + 569, + 506, + 585 + ], + "score": 1.0, + "content": "et al., 2019), where each sub-discriminator receives down-sampled 1-D signals at different frequency", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "score": 1.0, + "content": "by average pooling in the time domain. Jang et al. (2020; 2021) propose to apply the discriminator", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 593, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 604 + ], + "score": 1.0, + "content": "on the time–frequency domain using the multi-resolution discriminator (MRD), which is composed", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "of several sub-discriminators that operate on multiple 2-D linear spectrograms with different STFT", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 614, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 614, + 505, + 627 + ], + "score": 1.0, + "content": "resolutions. We also find that replacing MSD with MRD improves audio quality with reduced pitch", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 625, + 206, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 625, + 206, + 639 + ], + "score": 1.0, + "content": "and periodicity artifacts.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30, + "bbox_fs": [ + 104, + 493, + 506, + 639 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 642, + 505, + 687 + ], + "lines": [ + { + "bbox": [ + 105, + 642, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 505, + 655 + ], + "score": 1.0, + "content": "Training objectives Our training objective is similar as HiFi-GAN (Kong et al., 2020), with an", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 654, + 505, + 665 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 505, + 665 + ], + "score": 1.0, + "content": "exception of replacing MSD to MRD. It comprises the weighted sum of the least-square adversarial", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 664, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 451, + 677 + ], + "score": 1.0, + "content": "loss (Mao et al., 2017), the feature matching loss (Larsen et al., 2016), and the spectral", + "type": "text" + }, + { + "bbox": [ + 451, + 665, + 461, + 676 + ], + "score": 0.87, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 664, + 505, + 677 + ], + "score": 1.0, + "content": "regression", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 675, + 506, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 506, + 688 + ], + "score": 1.0, + "content": "loss on mel spectrogram. We leave the details of each loss and hyper-parameters in the Appendix B.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 642, + 506, + 688 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 695, + 249, + 706 + ], + "lines": [ + { + "bbox": [ + 105, + 693, + 250, + 708 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 250, + 708 + ], + "score": 1.0, + "content": "3.2 PERIODIC INDUCTIVE BIAS", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 108, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "The audio waveform is known to exhibit high periodicity and can be naturally represented as the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "composition of primitive periodic components (i.e., Fourier series under Dirichlet conditions). 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Their activation", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 277, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 289 + ], + "score": 1.0, + "content": "functions (e.g., Leaky ReLU) can produce new details with necessary nonlinearities, but do not", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "provide any periodic inductive bias. 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However,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 254, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 506, + 267 + ], + "score": 1.0, + "content": "the current non-autoregressive GAN vocoders (e.g., Kong et al., 2020) solely rely on layers of dilated", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 266, + 504, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 504, + 278 + ], + "score": 1.0, + "content": "convolutions to learn the required periodic components at different frequencies. Their activation", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 277, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 289 + ], + "score": 1.0, + "content": "functions (e.g., Leaky ReLU) can produce new details with necessary nonlinearities, but do not", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "provide any periodic inductive bias. 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The use of", + "type": "text" + }, + { + "bbox": [ + 292, + 370, + 324, + 383 + ], + "score": 0.92, + "content": "\\sin ^ { 2 } ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 370, + 505, + 383 + ], + "score": 1.0, + "content": "ensures monotonicity and renders it amenable", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 381, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 394 + ], + "score": 1.0, + "content": "to easy optimization. Liu et al. (2020) demonstrates this periodic activation exhibits an improved", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 392, + 385, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 385, + 405 + ], + "score": 1.0, + "content": "extrapolation capability for temperature and financial data prediction.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 409, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 104, + 408, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 408, + 267, + 422 + ], + "score": 1.0, + "content": "In BigVGAN, we use Snake activations", + "type": "text" + }, + { + "bbox": [ + 267, + 409, + 293, + 421 + ], + "score": 0.91, + "content": "f _ { \\alpha } ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 408, + 453, + 422 + ], + "score": 1.0, + "content": "with channel-wise trainable parameters", + "type": "text" + }, + { + "bbox": [ + 453, + 408, + 486, + 420 + ], + "score": 0.92, + "content": "\\pmb { \\alpha } \\in \\mathbb { R } ^ { h }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 408, + 506, + 422 + ], + "score": 1.0, + "content": "that", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "define the periodic frequencies for each 1-D convolution channels. 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We demonstrate that the proposed Snake-based generator is more", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "score": 1.0, + "content": "robust for out-of-distribution audio samples unseen during training, indicating strong extrapolation", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 464, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 477 + ], + "score": 1.0, + "content": "capabilities in universal vocoding task. See Figure 2 and Appendix D for illustrative examples;", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 474, + 504, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 504, + 488 + ], + "score": 1.0, + "content": "BigVGAN-base w/o filter using snake activations is closer to ground-truth sample than HiFi-GAN.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22 + }, + { + "type": "title", + "bbox": [ + 108, + 498, + 273, + 509 + ], + "lines": [ + { + "bbox": [ + 106, + 497, + 275, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 275, + 510 + ], + "score": 1.0, + "content": "3.3 ANTI-ALIASED REPRESENTATION", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 514, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 105, + 513, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 527 + ], + "score": 1.0, + "content": "The Snake activations provide the required periodic inductive bias for modeling raw waveform, but it", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "score": 1.0, + "content": "can produce arbitrary high frequency details for continuous-time signals that can not be represented", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 536, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 548 + ], + "score": 1.0, + "content": "by the discrete-time output of the network, 2 which can lead to aliasing artifacts. 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Each upsampling and downsampling operation is accompanied", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 590, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 506, + 604 + ], + "score": 1.0, + "content": "by the low-pass filter using a windowed sinc filter with a Kaiser window (Oppenheim & Schafer,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 601, + 281, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 281, + 614 + ], + "score": 1.0, + "content": "2009). Refer to the Appendix A for details.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 618, + 505, + 707 + ], + "lines": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "We apply this filtered Snake nonlinearity in every residual dilated convolution layers within the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 630, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 506, + 642 + ], + "score": 1.0, + "content": "generator to obtain the anti-aliased representation of the discrete-time 1-D signals. The module is", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 640, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 505, + 653 + ], + "score": 1.0, + "content": "named as anti-aliased multi-periodicity composition (AMP). See Figure 1 for an illustration. We find", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 653, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 653, + 505, + 663 + ], + "score": 1.0, + "content": "that incorporating the filtered activation can reduce the high-frequency artifacts in the synthesized", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 662, + 506, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 506, + 675 + ], + "score": 1.0, + "content": "waveform; see BigVGAN-base w/o filter vs. BigVGAN-base (with filter) in Figure 2 as an illustration.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 673, + 505, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 505, + 687 + ], + "score": 1.0, + "content": "We will demonstrate that it provides significant improvements in various objective and subjective", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "score": 1.0, + "content": "evaluations. 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The use of", + "type": "text" + }, + { + "bbox": [ + 292, + 370, + 324, + 383 + ], + "score": 0.92, + "content": "\\sin ^ { 2 } ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 370, + 505, + 383 + ], + "score": 1.0, + "content": "ensures monotonicity and renders it amenable", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 381, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 394 + ], + "score": 1.0, + "content": "to easy optimization. Liu et al. (2020) demonstrates this periodic activation exhibits an improved", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 392, + 385, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 385, + 405 + ], + "score": 1.0, + "content": "extrapolation capability for temperature and financial data prediction.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 337, + 506, + 405 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 409, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 104, + 408, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 408, + 267, + 422 + ], + "score": 1.0, + "content": "In BigVGAN, we use Snake activations", + "type": "text" + }, + { + "bbox": [ + 267, + 409, + 293, + 421 + ], + "score": 0.91, + "content": "f _ { \\alpha } ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 408, + 453, + 422 + ], + "score": 1.0, + "content": "with channel-wise trainable parameters", + "type": "text" + }, + { + "bbox": [ + 453, + 408, + 486, + 420 + ], + "score": 0.92, + "content": "\\pmb { \\alpha } \\in \\mathbb { R } ^ { h }", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 408, + 506, + 422 + ], + "score": 1.0, + "content": "that", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "define the periodic frequencies for each 1-D convolution channels. Taking this periodic functional", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 444 + ], + "score": 1.0, + "content": "form with learned frequency control, the convolutional module can naturally fit the raw waveform", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "score": 1.0, + "content": "with multi-periodic components. We demonstrate that the proposed Snake-based generator is more", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "score": 1.0, + "content": "robust for out-of-distribution audio samples unseen during training, indicating strong extrapolation", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 464, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 477 + ], + "score": 1.0, + "content": "capabilities in universal vocoding task. See Figure 2 and Appendix D for illustrative examples;", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 474, + 504, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 504, + 488 + ], + "score": 1.0, + "content": "BigVGAN-base w/o filter using snake activations is closer to ground-truth sample than HiFi-GAN.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22, + "bbox_fs": [ + 104, + 408, + 506, + 488 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 498, + 273, + 509 + ], + "lines": [ + { + "bbox": [ + 106, + 497, + 275, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 275, + 510 + ], + "score": 1.0, + "content": "3.3 ANTI-ALIASED REPRESENTATION", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 514, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 105, + 513, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 527 + ], + "score": 1.0, + "content": "The Snake activations provide the required periodic inductive bias for modeling raw waveform, but it", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "score": 1.0, + "content": "can produce arbitrary high frequency details for continuous-time signals that can not be represented", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 536, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 548 + ], + "score": 1.0, + "content": "by the discrete-time output of the network, 2 which can lead to aliasing artifacts. This side effect can", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 545, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 104, + 545, + 505, + 560 + ], + "score": 1.0, + "content": "be suppressed by applying a low-pass filter (e.g., Karras et al., 2021). 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Each upsampling and downsampling operation is accompanied", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 590, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 506, + 604 + ], + "score": 1.0, + "content": "by the low-pass filter using a windowed sinc filter with a Kaiser window (Oppenheim & Schafer,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 601, + 281, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 281, + 614 + ], + "score": 1.0, + "content": "2009). Refer to the Appendix A for details.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31, + "bbox_fs": [ + 104, + 513, + 506, + 614 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 618, + 505, + 707 + ], + "lines": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "We apply this filtered Snake nonlinearity in every residual dilated convolution layers within the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 630, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 506, + 642 + ], + "score": 1.0, + "content": "generator to obtain the anti-aliased representation of the discrete-time 1-D signals. The module is", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 640, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 505, + 653 + ], + "score": 1.0, + "content": "named as anti-aliased multi-periodicity composition (AMP). See Figure 1 for an illustration. We find", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 653, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 653, + 505, + 663 + ], + "score": 1.0, + "content": "that incorporating the filtered activation can reduce the high-frequency artifacts in the synthesized", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 662, + 506, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 506, + 675 + ], + "score": 1.0, + "content": "waveform; see BigVGAN-base w/o filter vs. BigVGAN-base (with filter) in Figure 2 as an illustration.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 673, + 505, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 505, + 687 + ], + "score": 1.0, + "content": "We will demonstrate that it provides significant improvements in various objective and subjective", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 685, + 505, + 697 + ], + "score": 1.0, + "content": "evaluations. Note that we also explored anti-aliased upsampling layers, but this results in significant", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 696, + 499, + 708 + ], + "spans": [ + { + "bbox": [ + 106, + 696, + 499, + 708 + ], + "score": 1.0, + "content": "training instabilities and lead to early collapse for large models. See Appendix C for more details.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 618, + 506, + 708 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 313, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 316, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 316, + 95 + ], + "score": 1.0, + "content": "3.4 BIGVGAN WITH LARGE SCALE TRAINING", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 97, + 505, + 219 + ], + "lines": [ + { + "bbox": [ + 106, + 98, + 505, + 110 + ], + "spans": [ + { + "bbox": [ + 106, + 98, + 505, + 110 + ], + "score": 1.0, + "content": "In this subsection, we explore the limits of universal vocoding by scaling up the generator’s model", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 109, + 506, + 122 + ], + "spans": [ + { + "bbox": [ + 105, + 109, + 506, + 122 + ], + "score": 1.0, + "content": "size to 112M parameters while maintaining the stability of GAN training and practical usability as a", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 120, + 505, + 132 + ], + "spans": [ + { + "bbox": [ + 106, + 120, + 505, + 132 + ], + "score": 1.0, + "content": "high-speed neural vocoder. We start with our improved generator using the comparable HiFi-GAN", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 129, + 507, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 129, + 507, + 144 + ], + "score": 1.0, + "content": "V1 configuration with 14M parameters (Kong et al., 2020), which is denoted as BigVGAN-base.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "score": 1.0, + "content": "We grow BigVGAN-base by increasing the number of upsampling blocks and convolution channels", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 152, + 506, + 166 + ], + "spans": [ + { + "bbox": [ + 105, + 152, + 365, + 166 + ], + "score": 1.0, + "content": "for each block. The BigVGAN-base upsamples the signal by", + "type": "text" + }, + { + "bbox": [ + 365, + 153, + 389, + 163 + ], + "score": 0.88, + "content": "2 5 6 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 152, + 506, + 166 + ], + "score": 1.0, + "content": "using 4 upsampling blocks", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 163, + 504, + 176 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 504, + 176 + ], + "score": 1.0, + "content": "with the ratio of [8, 8, 2, 2]. Each upsampling block is accompanied by multiple residual layers with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 174, + 505, + 187 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 376, + 187 + ], + "score": 1.0, + "content": "dilated convolutions, i.e., the AMP module. We further divides the", + "type": "text" + }, + { + "bbox": [ + 376, + 175, + 400, + 185 + ], + "score": 0.87, + "content": "2 5 6 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 174, + 505, + 187 + ], + "score": 1.0, + "content": "upsampling into 6 blocks", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 185, + 506, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 506, + 198 + ], + "score": 1.0, + "content": "[4, 4, 2, 2, 2, 2] for more fine-grained feature refinement. In addition, we increase the number of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 196, + 506, + 209 + ], + "spans": [ + { + "bbox": [ + 106, + 196, + 506, + 209 + ], + "score": 1.0, + "content": "channels of AMP module (analogous to MRF in HiFi-GAN) from 512 to 1536. We denote the model", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 208, + 333, + 219 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 333, + 219 + ], + "score": 1.0, + "content": "with 1536 channels and 112M parameters as BigVGAN.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 223, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 105, + 222, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 267, + 237 + ], + "score": 1.0, + "content": "We found that the default learning rate of", + "type": "text" + }, + { + "bbox": [ + 267, + 223, + 303, + 235 + ], + "score": 0.91, + "content": "2 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 222, + 505, + 237 + ], + "score": 1.0, + "content": "used in HiFi-GAN causes an early training collapse", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "score": 1.0, + "content": "for BigVGAN training, where the losses from the discriminator submodules immediately converge to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 388, + 258 + ], + "score": 1.0, + "content": "zero after several thousands of iterations. Halving the learning rate to", + "type": "text" + }, + { + "bbox": [ + 388, + 245, + 426, + 257 + ], + "score": 0.93, + "content": "1 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 245, + 506, + 258 + ], + "score": 1.0, + "content": "was able to reduce", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 505, + 269 + ], + "score": 1.0, + "content": "such failures. We also found that large batch size is helpful to reduce mode collapse at training (Brock", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 267, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 505, + 280 + ], + "score": 1.0, + "content": "et al., 2019). We only double the batch size from the usual 16 to 32 for a good trade-off between", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "score": 1.0, + "content": "training efficiency and stability, as neural vocoders can require millions of steps to converge. Note that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "score": 1.0, + "content": "this recommended batch size is still much smaller than the one for image synthesis (e.g., 2048) (Brock", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 301, + 402, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 402, + 313 + ], + "score": 1.0, + "content": "et al., 2019), because neural vocoding has strong conditional information.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 317, + 505, + 416 + ], + "lines": [ + { + "bbox": [ + 105, + 317, + 504, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 504, + 330 + ], + "score": 1.0, + "content": "Even with the aforementioned changes, the large BigVGAN can still be prone to collapse early in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "score": 1.0, + "content": "training. We track the gradient norm of each modules during training and identify that the anti-aliased", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "nonlinearity significantly amplified the gradient norm of MPD. Consequently, BigVGAN generator", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 351, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 506, + 363 + ], + "score": 1.0, + "content": "receives a diverging gradient early in training, leading to instabilities and potential collapse. We", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "score": 1.0, + "content": "visualize the norm of gradient for each modules in Figure 4 at Appendix C. We alleviate the issue", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 372, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 294, + 386 + ], + "score": 1.0, + "content": "by clipping the global norm of the gradient to", + "type": "text" + }, + { + "bbox": [ + 295, + 372, + 310, + 383 + ], + "score": 0.88, + "content": "1 0 ^ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 372, + 506, + 386 + ], + "score": 1.0, + "content": ", which is close to the average gradient norm of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 383, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 397 + ], + "score": 1.0, + "content": "the 112M BigVGAN generator. This gradient clipping prevents the early training collapse of the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 394, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 410 + ], + "score": 1.0, + "content": "generator. Note that, gradient clipping was found ineffective to alleviate training instability for image", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 405, + 469, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 469, + 419 + ], + "score": 1.0, + "content": "synthesis (see Appendix H in Brock et al. (2019)), but it is very effective in our endeavors.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 422, + 505, + 488 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 435 + ], + "score": 1.0, + "content": "In addition to above efforts, we have explored other directions, including various ways to improve the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "score": 1.0, + "content": "model architecture, spectral normalization (Miyato et al., 2018) to stabilize GAN training, which", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "is crucial for large-scale GAN training in image domain, and data augmentation to improve model", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "generalization. Unfortunately, all these trials resulted in worse perceptual quality in our study. The", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 466, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 478 + ], + "score": 1.0, + "content": "details can be found in the Appendix C. We hope these practical lessons that we have learned would", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 477, + 262, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 262, + 489 + ], + "score": 1.0, + "content": "be useful to future research endeavors.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5 + }, + { + "type": "title", + "bbox": [ + 107, + 500, + 172, + 512 + ], + "lines": [ + { + "bbox": [ + 105, + 498, + 174, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 174, + 514 + ], + "score": 1.0, + "content": "4 RESULTS", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 108, + 519, + 504, + 542 + ], + "lines": [ + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "score": 1.0, + "content": "We conduct a comprehensive evaluation of BigVGAN for both in-distribution and out-of-distribution", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 531, + 443, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 443, + 543 + ], + "score": 1.0, + "content": "scenarios. We train BigVGAN and all baseline models on the full LibriTTS dataset.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5 + }, + { + "type": "title", + "bbox": [ + 107, + 550, + 201, + 561 + ], + "lines": [ + { + "bbox": [ + 105, + 549, + 203, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 203, + 563 + ], + "score": 1.0, + "content": "4.1 TRAINING DATA", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 568, + 505, + 657 + ], + "lines": [ + { + "bbox": [ + 106, + 568, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 408, + 580 + ], + "score": 1.0, + "content": "We use LibriTTS (Zen et al., 2019) dataset with the original sampling rate of", + "type": "text" + }, + { + "bbox": [ + 408, + 569, + 439, + 579 + ], + "score": 0.68, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 568, + 506, + 580 + ], + "score": 1.0, + "content": "for training. Un-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 579, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 579, + 506, + 591 + ], + "score": 1.0, + "content": "like previous studies which only adopted a subset (train-clean-100 or train-clean-360)", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 590, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 506, + 603 + ], + "score": 1.0, + "content": "recorded in a clean environment (Jang et al., 2020; 2021; AlBadawy et al., 2022), we use", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 602, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 505, + 613 + ], + "score": 1.0, + "content": "all training data including the subset from diverse recording environments (train-full", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 612, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 614, + 115, + 623 + ], + "score": 0.42, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 612, + 210, + 624 + ], + "score": 1.0, + "content": "train-clean-100", + "type": "text" + }, + { + "bbox": [ + 211, + 614, + 219, + 622 + ], + "score": 0.35, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 612, + 318, + 624 + ], + "score": 1.0, + "content": "train-clean-360", + "type": "text" + }, + { + "bbox": [ + 318, + 614, + 327, + 622 + ], + "score": 0.58, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 612, + 506, + 624 + ], + "score": 1.0, + "content": "train-other-500), which is unprece-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "dented in the literature. We find that the diversity of the training data is important to achieve the goal", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 634, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 505, + 646 + ], + "score": 1.0, + "content": "towards universal neural vocoding using BigVGAN. 3 For OOD experiments, we resample the audio", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 644, + 464, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 116, + 658 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 117, + 645, + 147, + 656 + ], + "score": 0.66, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 644, + 464, + 658 + ], + "score": 1.0, + "content": "if necessary using kaiser-best algorithm provided by librosa package.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 42.5 + }, + { + "type": "text", + "bbox": [ + 107, + 662, + 505, + 717 + ], + "lines": [ + { + "bbox": [ + 105, + 660, + 505, + 676 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 505, + 676 + ], + "score": 1.0, + "content": "Conventional STFT parameters are engineered to have a limited frequency band [0, 8] kHz by cutting", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 672, + 505, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 686 + ], + "score": 1.0, + "content": "off the high frequency details for easier modeling. On a contrary, we train all models (including the", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 684, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 505, + 697 + ], + "score": 1.0, + "content": "baselines) using a frequency range [0, 12] kHz and a 100-band log-mel spectrogram, which is also", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 694, + 505, + 708 + ], + "spans": [ + { + "bbox": [ + 105, + 694, + 505, + 708 + ], + "score": 1.0, + "content": "used in a recent study towards universal vocoding (Jang et al., 2021). We set other STFT parameters", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 705, + 505, + 719 + ], + "spans": [ + { + "bbox": [ + 105, + 705, + 505, + 719 + ], + "score": 1.0, + "content": "as in previous work (Kong et al., 2020), with 1024 FFT size, 1024 Hann window, and 256 hop size.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 118, + 721, + 375, + 731 + ], + "lines": [ + { + "bbox": [ + 119, + 720, + 376, + 732 + ], + "spans": [ + { + "bbox": [ + 119, + 720, + 376, + 732 + ], + "score": 1.0, + "content": "3The ablation results on training data diversity can be found in Table 5.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 313, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 316, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 316, + 95 + ], + "score": 1.0, + "content": "3.4 BIGVGAN WITH LARGE SCALE TRAINING", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 97, + 505, + 219 + ], + "lines": [ + { + "bbox": [ + 106, + 98, + 505, + 110 + ], + "spans": [ + { + "bbox": [ + 106, + 98, + 505, + 110 + ], + "score": 1.0, + "content": "In this subsection, we explore the limits of universal vocoding by scaling up the generator’s model", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 109, + 506, + 122 + ], + "spans": [ + { + "bbox": [ + 105, + 109, + 506, + 122 + ], + "score": 1.0, + "content": "size to 112M parameters while maintaining the stability of GAN training and practical usability as a", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 120, + 505, + 132 + ], + "spans": [ + { + "bbox": [ + 106, + 120, + 505, + 132 + ], + "score": 1.0, + "content": "high-speed neural vocoder. We start with our improved generator using the comparable HiFi-GAN", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 129, + 507, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 129, + 507, + 144 + ], + "score": 1.0, + "content": "V1 configuration with 14M parameters (Kong et al., 2020), which is denoted as BigVGAN-base.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 105, + 141, + 505, + 154 + ], + "score": 1.0, + "content": "We grow BigVGAN-base by increasing the number of upsampling blocks and convolution channels", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 152, + 506, + 166 + ], + "spans": [ + { + "bbox": [ + 105, + 152, + 365, + 166 + ], + "score": 1.0, + "content": "for each block. The BigVGAN-base upsamples the signal by", + "type": "text" + }, + { + "bbox": [ + 365, + 153, + 389, + 163 + ], + "score": 0.88, + "content": "2 5 6 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 152, + 506, + 166 + ], + "score": 1.0, + "content": "using 4 upsampling blocks", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 163, + 504, + 176 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 504, + 176 + ], + "score": 1.0, + "content": "with the ratio of [8, 8, 2, 2]. Each upsampling block is accompanied by multiple residual layers with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 174, + 505, + 187 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 376, + 187 + ], + "score": 1.0, + "content": "dilated convolutions, i.e., the AMP module. We further divides the", + "type": "text" + }, + { + "bbox": [ + 376, + 175, + 400, + 185 + ], + "score": 0.87, + "content": "2 5 6 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 174, + 505, + 187 + ], + "score": 1.0, + "content": "upsampling into 6 blocks", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 185, + 506, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 506, + 198 + ], + "score": 1.0, + "content": "[4, 4, 2, 2, 2, 2] for more fine-grained feature refinement. In addition, we increase the number of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 196, + 506, + 209 + ], + "spans": [ + { + "bbox": [ + 106, + 196, + 506, + 209 + ], + "score": 1.0, + "content": "channels of AMP module (analogous to MRF in HiFi-GAN) from 512 to 1536. We denote the model", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 208, + 333, + 219 + ], + "spans": [ + { + "bbox": [ + 106, + 208, + 333, + 219 + ], + "score": 1.0, + "content": "with 1536 channels and 112M parameters as BigVGAN.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 98, + 507, + 219 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 223, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 105, + 222, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 267, + 237 + ], + "score": 1.0, + "content": "We found that the default learning rate of", + "type": "text" + }, + { + "bbox": [ + 267, + 223, + 303, + 235 + ], + "score": 0.91, + "content": "2 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 222, + 505, + 237 + ], + "score": 1.0, + "content": "used in HiFi-GAN causes an early training collapse", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "score": 1.0, + "content": "for BigVGAN training, where the losses from the discriminator submodules immediately converge to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 388, + 258 + ], + "score": 1.0, + "content": "zero after several thousands of iterations. Halving the learning rate to", + "type": "text" + }, + { + "bbox": [ + 388, + 245, + 426, + 257 + ], + "score": 0.93, + "content": "1 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 245, + 506, + 258 + ], + "score": 1.0, + "content": "was able to reduce", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 505, + 269 + ], + "score": 1.0, + "content": "such failures. We also found that large batch size is helpful to reduce mode collapse at training (Brock", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 267, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 505, + 280 + ], + "score": 1.0, + "content": "et al., 2019). We only double the batch size from the usual 16 to 32 for a good trade-off between", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 291 + ], + "score": 1.0, + "content": "training efficiency and stability, as neural vocoders can require millions of steps to converge. Note that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "score": 1.0, + "content": "this recommended batch size is still much smaller than the one for image synthesis (e.g., 2048) (Brock", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 301, + 402, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 402, + 313 + ], + "score": 1.0, + "content": "et al., 2019), because neural vocoding has strong conditional information.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 222, + 506, + 313 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 317, + 505, + 416 + ], + "lines": [ + { + "bbox": [ + 105, + 317, + 504, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 504, + 330 + ], + "score": 1.0, + "content": "Even with the aforementioned changes, the large BigVGAN can still be prone to collapse early in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "score": 1.0, + "content": "training. We track the gradient norm of each modules during training and identify that the anti-aliased", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "nonlinearity significantly amplified the gradient norm of MPD. Consequently, BigVGAN generator", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 351, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 506, + 363 + ], + "score": 1.0, + "content": "receives a diverging gradient early in training, leading to instabilities and potential collapse. We", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 506, + 374 + ], + "score": 1.0, + "content": "visualize the norm of gradient for each modules in Figure 4 at Appendix C. We alleviate the issue", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 372, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 294, + 386 + ], + "score": 1.0, + "content": "by clipping the global norm of the gradient to", + "type": "text" + }, + { + "bbox": [ + 295, + 372, + 310, + 383 + ], + "score": 0.88, + "content": "1 0 ^ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 372, + 506, + 386 + ], + "score": 1.0, + "content": ", which is close to the average gradient norm of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 383, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 397 + ], + "score": 1.0, + "content": "the 112M BigVGAN generator. This gradient clipping prevents the early training collapse of the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 394, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 410 + ], + "score": 1.0, + "content": "generator. Note that, gradient clipping was found ineffective to alleviate training instability for image", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 405, + 469, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 469, + 419 + ], + "score": 1.0, + "content": "synthesis (see Appendix H in Brock et al. (2019)), but it is very effective in our endeavors.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 317, + 506, + 419 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 422, + 505, + 488 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 435 + ], + "score": 1.0, + "content": "In addition to above efforts, we have explored other directions, including various ways to improve the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 505, + 445 + ], + "score": 1.0, + "content": "model architecture, spectral normalization (Miyato et al., 2018) to stabilize GAN training, which", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "is crucial for large-scale GAN training in image domain, and data augmentation to improve model", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "generalization. Unfortunately, all these trials resulted in worse perceptual quality in our study. The", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 466, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 478 + ], + "score": 1.0, + "content": "details can be found in the Appendix C. We hope these practical lessons that we have learned would", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 477, + 262, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 262, + 489 + ], + "score": 1.0, + "content": "be useful to future research endeavors.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 421, + 506, + 489 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 500, + 172, + 512 + ], + "lines": [ + { + "bbox": [ + 105, + 498, + 174, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 174, + 514 + ], + "score": 1.0, + "content": "4 RESULTS", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 108, + 519, + 504, + 542 + ], + "lines": [ + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 505, + 532 + ], + "score": 1.0, + "content": "We conduct a comprehensive evaluation of BigVGAN for both in-distribution and out-of-distribution", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 531, + 443, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 443, + 543 + ], + "score": 1.0, + "content": "scenarios. We train BigVGAN and all baseline models on the full LibriTTS dataset.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5, + "bbox_fs": [ + 106, + 519, + 505, + 543 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 550, + 201, + 561 + ], + "lines": [ + { + "bbox": [ + 105, + 549, + 203, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 203, + 563 + ], + "score": 1.0, + "content": "4.1 TRAINING DATA", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 568, + 505, + 657 + ], + "lines": [ + { + "bbox": [ + 106, + 568, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 408, + 580 + ], + "score": 1.0, + "content": "We use LibriTTS (Zen et al., 2019) dataset with the original sampling rate of", + "type": "text" + }, + { + "bbox": [ + 408, + 569, + 439, + 579 + ], + "score": 0.68, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 568, + 506, + 580 + ], + "score": 1.0, + "content": "for training. Un-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 579, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 579, + 506, + 591 + ], + "score": 1.0, + "content": "like previous studies which only adopted a subset (train-clean-100 or train-clean-360)", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 590, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 506, + 603 + ], + "score": 1.0, + "content": "recorded in a clean environment (Jang et al., 2020; 2021; AlBadawy et al., 2022), we use", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 602, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 505, + 613 + ], + "score": 1.0, + "content": "all training data including the subset from diverse recording environments (train-full", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 612, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 614, + 115, + 623 + ], + "score": 0.42, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 612, + 210, + 624 + ], + "score": 1.0, + "content": "train-clean-100", + "type": "text" + }, + { + "bbox": [ + 211, + 614, + 219, + 622 + ], + "score": 0.35, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 612, + 318, + 624 + ], + "score": 1.0, + "content": "train-clean-360", + "type": "text" + }, + { + "bbox": [ + 318, + 614, + 327, + 622 + ], + "score": 0.58, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 612, + 506, + 624 + ], + "score": 1.0, + "content": "train-other-500), which is unprece-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "dented in the literature. We find that the diversity of the training data is important to achieve the goal", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 634, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 505, + 646 + ], + "score": 1.0, + "content": "towards universal neural vocoding using BigVGAN. 3 For OOD experiments, we resample the audio", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 644, + 464, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 116, + 658 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 117, + 645, + 147, + 656 + ], + "score": 0.66, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 644, + 464, + 658 + ], + "score": 1.0, + "content": "if necessary using kaiser-best algorithm provided by librosa package.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 568, + 506, + 658 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 662, + 505, + 717 + ], + "lines": [ + { + "bbox": [ + 105, + 660, + 505, + 676 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 505, + 676 + ], + "score": 1.0, + "content": "Conventional STFT parameters are engineered to have a limited frequency band [0, 8] kHz by cutting", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 672, + 505, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 686 + ], + "score": 1.0, + "content": "off the high frequency details for easier modeling. On a contrary, we train all models (including the", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 684, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 505, + 697 + ], + "score": 1.0, + "content": "baselines) using a frequency range [0, 12] kHz and a 100-band log-mel spectrogram, which is also", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 694, + 505, + 708 + ], + "spans": [ + { + "bbox": [ + 105, + 694, + 505, + 708 + ], + "score": 1.0, + "content": "used in a recent study towards universal vocoding (Jang et al., 2021). We set other STFT parameters", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 705, + 505, + 719 + ], + "spans": [ + { + "bbox": [ + 105, + 705, + 505, + 719 + ], + "score": 1.0, + "content": "as in previous work (Kong et al., 2020), with 1024 FFT size, 1024 Hann window, and 256 hop size.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49, + "bbox_fs": [ + 105, + 660, + 505, + 719 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 109, + 96, + 502, + 139 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 108, + 84, + 497, + 95 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 111, + 82, + 498, + 96 + ], + "spans": [ + { + "bbox": [ + 111, + 82, + 291, + 96 + ], + "score": 1.0, + "content": "Table 1: Model footprint and synthesis speed for", + "type": "text" + }, + { + "bbox": [ + 292, + 84, + 320, + 94 + ], + "score": 0.73, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 82, + 498, + 96 + ], + "score": 1.0, + "content": "audio measured on an NVIDIA RTX 8000 GPU.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 109, + 96, + 502, + 139 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 96, + 502, + 139 + ], + "spans": [ + { + "bbox": [ + 109, + 96, + 502, + 139 + ], + "score": 0.971, + "html": "
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All other configurations including optimizer, learning rate scheduler, and", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 203, + 506, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 506, + 218 + ], + "score": 1.0, + "content": "scalar weights of the loss terms follow the official open-source implementation of HiFi-GAN (Kong", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "et al., 2020) without modification, with an exception that BigVGAN replaces MSD by MRD for the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 226, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 505, + 239 + ], + "score": 1.0, + "content": "discriminator. All models are trained using NVIDIA DGX-1 with 8 V100 GPUs. Refer to Table 6 in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 237, + 293, + 250 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 293, + 250 + ], + "score": 1.0, + "content": "the Appendix A for detailed hyperparameters.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 254, + 505, + 332 + ], + "lines": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "We include a comparison with SC-WaveRNN (Paul et al., 2020), a state-of-the-art autoregressive", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 505, + 277 + ], + "score": 1.0, + "content": "universal neural vocoder based on WaveRNN (Kalchbrenner et al., 2018), using the official imple-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 277, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 505, + 288 + ], + "score": 1.0, + "content": "mentation. We also include two popular flow-based models: WaveGlow (Prenger et al., 2019) and", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 287, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 506, + 300 + ], + "score": 1.0, + "content": "WaveFlow (Ping et al., 2020), using their official implementation. For out-of-distribution test, we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 298, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 311 + ], + "score": 1.0, + "content": "include the unofficial open-source implementation of UnivNet-c32 (Jang et al., 2021), 4 which uses", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "score": 1.0, + "content": "train-clean-360 subset for training and is reported to outperform HiFi-GAN under the same", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 321, + 336, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 336, + 333 + ], + "score": 1.0, + "content": "training configurations. See appendix E for more details.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 337, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 472, + 350 + ], + "score": 1.0, + "content": "Table 1 summarizes the synthesis speed of flow-based and GAN vocoders for generating", + "type": "text" + }, + { + "bbox": [ + 472, + 337, + 505, + 348 + ], + "score": 0.67, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 347, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 362 + ], + "score": 1.0, + "content": "audio. We omit SC-WaveRNN as it is much slower. 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All other configurations including optimizer, learning rate scheduler, and", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 203, + 506, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 506, + 218 + ], + "score": 1.0, + "content": "scalar weights of the loss terms follow the official open-source implementation of HiFi-GAN (Kong", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "et al., 2020) without modification, with an exception that BigVGAN replaces MSD by MRD for the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 226, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 505, + 239 + ], + "score": 1.0, + "content": "discriminator. All models are trained using NVIDIA DGX-1 with 8 V100 GPUs. 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We also include two popular flow-based models: WaveGlow (Prenger et al., 2019) and", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 287, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 506, + 300 + ], + "score": 1.0, + "content": "WaveFlow (Ping et al., 2020), using their official implementation. For out-of-distribution test, we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 298, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 311 + ], + "score": 1.0, + "content": "include the unofficial open-source implementation of UnivNet-c32 (Jang et al., 2021), 4 which uses", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "score": 1.0, + "content": "train-clean-360 subset for training and is reported to outperform HiFi-GAN under the same", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 321, + 336, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 336, + 333 + ], + "score": 1.0, + "content": "training configurations. See appendix E for more details.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 254, + 506, + 333 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 337, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 472, + 350 + ], + "score": 1.0, + "content": "Table 1 summarizes the synthesis speed of flow-based and GAN vocoders for generating", + "type": "text" + }, + { + "bbox": [ + 472, + 337, + 505, + 348 + ], + "score": 0.67, + "content": "2 4 \\mathrm { k H z }", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 347, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 362 + ], + "score": 1.0, + "content": "audio. We omit SC-WaveRNN as it is much slower. 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HiFi-GAN and BigVGAN are faster than", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 381, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 394 + ], + "score": 1.0, + "content": "flow-based models, because they are fully parallel (WaveFlow has partial autoregression) and have", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "much fewer layers (WaveGlow has 96 layers). Our BigVGAN with 112M parameters can synthesize", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 403, + 482, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 145, + 416 + ], + "score": 1.0, + "content": "the audio", + "type": "text" + }, + { + "bbox": [ + 146, + 403, + 180, + 414 + ], + "score": 0.86, + "content": "4 4 . 7 2 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 403, + 482, + 416 + ], + "score": 1.0, + "content": "faster than real-time and keeps the promise as a high-speed neural vocoder.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 337, + 506, + 416 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 425, + 230, + 437 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 231, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 231, + 438 + ], + "score": 1.0, + "content": "4.3 EVALUATION METRICS", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 444, + 505, + 532 + ], + "lines": [ + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "The objective metrics we collected are designed to measure varied types of distance between the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 456, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 467 + ], + "score": 1.0, + "content": "ground-truth audio and the generated sample. 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LibriTTSM-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)MOS(↑)SMOS(↑)
Ground Truth---1=4.40±0.064.44±0.06
SC-WaveRNN2.23581.7011.88540.30440.81443.20±0.113.29±0.10
WaveGlow-2561.30993.1382.35910.14850.93783.84±0.103.87±0.10
WaveFlow-1281.11203.0271.24550.14160.94103.85±0.103.89±0.10
HiFi-GAN (V1)1.00172.9470.66030.15650.93004.08±0.094.15±0.09
BigVGAN-base0.87883.5190.45640.12870.94594.10±0.094.20±0.08
BigVGAN0.79974.0270.37450.10180.95984.11±0.094.26±0.08
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Recording env. LanguageClean Jv,Km,Ne,SuNoisy (sim) Es,Fr,I,PtNoisy (real) Ko
Ground Truth4.58±0.054.36±0.054.56±0.05
UnivNet-c32†4.35±0.073.95±0.094.18±0.08
HiFi-GAN (V1)4.39±0.074.13±0.084.21±0.08
BigVGAN-base4.38±0.074.21±0.074.36±0.07
BigVGAN4.41±0.074.26±0.074.38±0.07
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This indicates that GAN vocoder is the state-of-the-art for universal", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 468, + 507, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 507, + 481 + ], + "score": 1.0, + "content": "neural vocoding. BigVGAN significantly improves all objective metrics. 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LibriTTSM-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)MOS(↑)SMOS(↑)
Ground Truth---1=4.40±0.064.44±0.06
SC-WaveRNN2.23581.7011.88540.30440.81443.20±0.113.29±0.10
WaveGlow-2561.30993.1382.35910.14850.93783.84±0.103.87±0.10
WaveFlow-1281.11203.0271.24550.14160.94103.85±0.103.89±0.10
HiFi-GAN (V1)1.00172.9470.66030.15650.93004.08±0.094.15±0.09
BigVGAN-base0.87883.5190.45640.12870.94594.10±0.094.20±0.08
BigVGAN0.79974.0270.37450.10180.95984.11±0.094.26±0.08
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Recording env. LanguageClean Jv,Km,Ne,SuNoisy (sim) Es,Fr,I,PtNoisy (real) Ko
Ground Truth4.58±0.054.36±0.054.56±0.05
UnivNet-c32†4.35±0.073.95±0.094.18±0.08
HiFi-GAN (V1)4.39±0.074.13±0.084.21±0.08
BigVGAN-base4.38±0.074.21±0.074.36±0.07
BigVGAN4.41±0.074.26±0.074.38±0.07
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MethodVocalDrumsBassOthersMixtureAverage
Ground Truth4.58±0.054.57±0.054.52±0.054.61±0.054.56±0.054.57±0.02
UnivNet-c32t4.22±0.094.23±0.093.90±0.113.80±0.133.80±0.123.99±0.05
HiFi-GAN (V1)4.26±0.084.37±0.083.95±0.113.92±0.123.91±0.114.08±0.05
BigVGAN-base4.36±0.084.39±0.074.00 ±0.114.14±0.094.11±0.104.20±0.04
w/o filter4.30±0.084.32±0.073.95±0.114.05±0.104.11±0.104.15±0.04
w/o filter & snake4.31±0.084.32±0.073.94±0.114.01±0.114.02±0.104.12±0.04
BigVGAN4.37±0.084.41±0.074.00±0.104.25±0.094.26±0.084.26±0.04
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We use randomly selected 50 audio clips with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 127, + 259, + 506, + 274 + ], + "spans": [ + { + "bbox": [ + 127, + 259, + 506, + 274 + ], + "score": 1.0, + "content": "equal balance across languages from the IWSLT’21 test set. 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We use randomly selected 50 audio clips where 25 clips are", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 128, + 330, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 128, + 330, + 505, + 343 + ], + "score": 1.0, + "content": "from the studio apartment, and the remaining 25 clips are from the dance studio. The collected", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 128, + 342, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 128, + 342, + 505, + 354 + ], + "score": 1.0, + "content": "audio clips contain a significant amount of noise and artifacts from real-world recording", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 128, + 353, + 388, + 365 + ], + "spans": [ + { + "bbox": [ + 128, + 353, + 388, + 365 + ], + "score": 1.0, + "content": "environments, such as reverb, echo, and static background noise.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 106, + 370, + 505, + 502 + ], + "lines": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "score": 1.0, + "content": "Table 3 summarizes the SMOS results from three different types of unseen dataset. We only did", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "score": 1.0, + "content": "SMOS evaluations, because the datasets have unseen languages for human listeners and it is hard to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "determine the quality without side-by-side comparison with the ground-truth recordings. For clean", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 404, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 506, + 416 + ], + "score": 1.0, + "content": "under-resourced language dataset, the performance gap between models is not substantially large.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 414, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 506, + 427 + ], + "score": 1.0, + "content": "This indicates that the universal vocoder trained on the entire LibriTTS training set is robust to unseen", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 425, + 506, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 506, + 438 + ], + "score": 1.0, + "content": "languages under clean recording environments. For both types of unseen recording environment", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "score": 1.0, + "content": "(simulated or real-world), BigVGAN outperforms the baseline models by a large margin. The", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "score": 1.0, + "content": "small capacity BigVGAN-base also shows improvements compared to the baseline with statistical", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 458, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 160, + 471 + ], + "score": 1.0, + "content": "significance", + "type": "text" + }, + { + "bbox": [ + 160, + 460, + 167, + 470 + ], + "score": 0.3, + "content": "\\mathrm { { \\widetilde { p } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 458, + 192, + 471 + ], + "score": 1.0, + "content": "-value", + "type": "text" + }, + { + "bbox": [ + 193, + 458, + 222, + 469 + ], + "score": 0.85, + "content": "< 0 . 0 5", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 458, + 506, + 471 + ], + "score": 1.0, + "content": "from the Wilcoxon signed-rank test). This suggests that BigVGAN is", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 468, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 506, + 482 + ], + "score": 1.0, + "content": "significantly more robust to the unseen recording environments thanks to the improved generator", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "design with the AMP module. In Appendix F, we further demonstrate that BigVGAN is the most", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 490, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 506, + 505 + ], + "score": 1.0, + "content": "linguistically accurate universal vocoder in terms of character error rate (CER) on multiple languages.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 507, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 106, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "We test the open-source implementation of UnivNet (Jang et al., 2021) with the pretrained checkpoint", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 519, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 505, + 531 + ], + "score": 1.0, + "content": "which is trained on train-clean-360 subset. Contrary to the report from Jang et al. (2021) that", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 529, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 505, + 542 + ], + "score": 1.0, + "content": "UnivNet-c32 outperformed HiFi-GAN (Kong et al., 2020), we find that the unmodified HiFi-GAN", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 540, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 553 + ], + "score": 1.0, + "content": "trained on the entire LibriTTS dataset is able to match or outperform UnivNet-c32. We also train", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 550, + 507, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 507, + 564 + ], + "score": 1.0, + "content": "UnivNet-c32 on LibriTTS train-full and find that it is not benefited from larger training data.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 561, + 258, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 258, + 574 + ], + "score": 1.0, + "content": "See Appendix E for detailed analysis.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5 + }, + { + "type": "title", + "bbox": [ + 109, + 586, + 291, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 584, + 293, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 293, + 599 + ], + "score": 1.0, + "content": "4.6 OUT-OF-DISTRIBUTION ROBUSTNESS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 604, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "In this subsection, we test BigVGAN’s robustness and extrapolation capability by measuring zero-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 616, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 506, + 628 + ], + "score": 1.0, + "content": "shot performance on out-of-distribution data. 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MethodVocalDrumsBassOthersMixtureAverage
Ground Truth4.58±0.054.57±0.054.52±0.054.61±0.054.56±0.054.57±0.02
UnivNet-c32t4.22±0.094.23±0.093.90±0.113.80±0.133.80±0.123.99±0.05
HiFi-GAN (V1)4.26±0.084.37±0.083.95±0.113.92±0.123.91±0.114.08±0.05
BigVGAN-base4.36±0.084.39±0.074.00 ±0.114.14±0.094.11±0.104.20±0.04
w/o filter4.30±0.084.32±0.073.95±0.114.05±0.104.11±0.104.15±0.04
w/o filter & snake4.31±0.084.32±0.073.94±0.114.01±0.114.02±0.104.12±0.04
BigVGAN4.37±0.084.41±0.074.00±0.104.25±0.094.26±0.084.26±0.04
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We use randomly selected 50 audio clips with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 127, + 259, + 506, + 274 + ], + "spans": [ + { + "bbox": [ + 127, + 259, + 506, + 274 + ], + "score": 1.0, + "content": "equal balance across languages from the IWSLT’21 test set. We simulate the unseen recording", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 127, + 271, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 127, + 271, + 506, + 285 + ], + "score": 1.0, + "content": "environment setup by adding a random environmental noise from MS-SNSD (Reddy et al.,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 127, + 281, + 289, + 295 + ], + "spans": [ + { + "bbox": [ + 127, + 281, + 289, + 295 + ], + "score": 1.0, + "content": "2019), such as airport, cafe, babble, etc.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7, + "bbox_fs": [ + 119, + 237, + 506, + 295 + ] + }, + { + "type": "text", + "bbox": [ + 119, + 298, + 505, + 364 + ], + "lines": [ + { + "bbox": [ + 119, + 297, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 119, + 297, + 506, + 311 + ], + "score": 1.0, + "content": "• Deeply Korean read speech corpus (Deeply, 2021): contains short speech audio clips in Korean,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 127, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 127, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "recorded in three types of recording environments (anechoic chamber, studio apartment, and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 128, + 319, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 128, + 319, + 506, + 332 + ], + "score": 1.0, + "content": "dance studio) using a smartphone. We use randomly selected 50 audio clips where 25 clips are", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 128, + 330, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 128, + 330, + 505, + 343 + ], + "score": 1.0, + "content": "from the studio apartment, and the remaining 25 clips are from the dance studio. The collected", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 128, + 342, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 128, + 342, + 505, + 354 + ], + "score": 1.0, + "content": "audio clips contain a significant amount of noise and artifacts from real-world recording", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 128, + 353, + 388, + 365 + ], + "spans": [ + { + "bbox": [ + 128, + 353, + 388, + 365 + ], + "score": 1.0, + "content": "environments, such as reverb, echo, and static background noise.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5, + "bbox_fs": [ + 119, + 297, + 506, + 365 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 370, + 505, + 502 + ], + "lines": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "score": 1.0, + "content": "Table 3 summarizes the SMOS results from three different types of unseen dataset. We only did", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "score": 1.0, + "content": "SMOS evaluations, because the datasets have unseen languages for human listeners and it is hard to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "determine the quality without side-by-side comparison with the ground-truth recordings. For clean", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 404, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 506, + 416 + ], + "score": 1.0, + "content": "under-resourced language dataset, the performance gap between models is not substantially large.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 414, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 506, + 427 + ], + "score": 1.0, + "content": "This indicates that the universal vocoder trained on the entire LibriTTS training set is robust to unseen", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 425, + 506, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 506, + 438 + ], + "score": 1.0, + "content": "languages under clean recording environments. For both types of unseen recording environment", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "score": 1.0, + "content": "(simulated or real-world), BigVGAN outperforms the baseline models by a large margin. The", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "score": 1.0, + "content": "small capacity BigVGAN-base also shows improvements compared to the baseline with statistical", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 458, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 160, + 471 + ], + "score": 1.0, + "content": "significance", + "type": "text" + }, + { + "bbox": [ + 160, + 460, + 167, + 470 + ], + "score": 0.3, + "content": "\\mathrm { { \\widetilde { p } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 458, + 192, + 471 + ], + "score": 1.0, + "content": "-value", + "type": "text" + }, + { + "bbox": [ + 193, + 458, + 222, + 469 + ], + "score": 0.85, + "content": "< 0 . 0 5", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 458, + 506, + 471 + ], + "score": 1.0, + "content": "from the Wilcoxon signed-rank test). This suggests that BigVGAN is", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 468, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 506, + 482 + ], + "score": 1.0, + "content": "significantly more robust to the unseen recording environments thanks to the improved generator", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "design with the AMP module. In Appendix F, we further demonstrate that BigVGAN is the most", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 490, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 506, + 505 + ], + "score": 1.0, + "content": "linguistically accurate universal vocoder in terms of character error rate (CER) on multiple languages.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 370, + 506, + 505 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 507, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 106, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "We test the open-source implementation of UnivNet (Jang et al., 2021) with the pretrained checkpoint", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 519, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 505, + 531 + ], + "score": 1.0, + "content": "which is trained on train-clean-360 subset. Contrary to the report from Jang et al. (2021) that", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 529, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 505, + 542 + ], + "score": 1.0, + "content": "UnivNet-c32 outperformed HiFi-GAN (Kong et al., 2020), we find that the unmodified HiFi-GAN", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 540, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 553 + ], + "score": 1.0, + "content": "trained on the entire LibriTTS dataset is able to match or outperform UnivNet-c32. We also train", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 550, + 507, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 507, + 564 + ], + "score": 1.0, + "content": "UnivNet-c32 on LibriTTS train-full and find that it is not benefited from larger training data.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 561, + 258, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 258, + 574 + ], + "score": 1.0, + "content": "See Appendix E for detailed analysis.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 507, + 507, + 574 + ] + }, + { + "type": "title", + "bbox": [ + 109, + 586, + 291, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 584, + 293, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 293, + 599 + ], + "score": 1.0, + "content": "4.6 OUT-OF-DISTRIBUTION ROBUSTNESS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 604, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "In this subsection, we test BigVGAN’s robustness and extrapolation capability by measuring zero-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 616, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 506, + 628 + ], + "score": 1.0, + "content": "shot performance on out-of-distribution data. We conduct the SMOS experiment using MUSDB18-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "score": 1.0, + "content": "HQ (Rafii et al., 2019), a multi-track music audio dataset which contains vocal, drums, bass, other", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "instruments, and the original mixture. The test set contains 50 songs with 5 tracks. We gather the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 648, + 389, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 389, + 662 + ], + "score": 1.0, + "content": "mid-song clip with the duration of 10 seconds for each track and song.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 605, + 506, + 662 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "Table 4 shows the SMOS results from the 5 tracks and their average from the MUSDB18-HQ test", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "set. BigVGAN models demonstrate a substantially improved zero-shot generation performance with", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "wider frequency band coverage, whereas baseline models fail to generate audio outside the limited", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 698, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 713 + ], + "score": 1.0, + "content": "frequency range and suffer from severe distortion. The improvements are most profound for singing", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "voice (vocal), instrumental audio (others) and the full mixture of the song (mixture), whereas the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 721, + 329, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 329, + 732 + ], + "score": 1.0, + "content": "improvements from drums and bass are less significant.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 666, + 505, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 114, + 117, + 496, + 181 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 84, + 503, + 114 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "score": 1.0, + "content": "Table 5: Ablation results on training data diversity using 112M BigVGAN model, evaluated on LibriTTS.", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 95, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 486, + 105 + ], + "score": 1.0, + "content": "Objective results are obtained from dev-other and subjective evaluation with 5-scale SMOS with", + "type": "text" + }, + { + "bbox": [ + 486, + 95, + 505, + 104 + ], + "score": 0.81, + "content": "9 5 \\%", + "type": "inline_equation" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 314, + 115 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 314, + 115 + ], + "score": 1.0, + "content": "confidence interval (CI) is obtained from test-other.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 114, + 117, + 496, + 181 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 114, + 117, + 496, + 181 + ], + "spans": [ + { + "bbox": [ + 114, + 117, + 496, + 181 + ], + "score": 0.976, + "html": "
Training dataM-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)SMOS(↑)
Ground Truth--1--4.55±0.05
train-full0.81974.0010.40970.10230.95864.38±0.07
train-clean-3600.84293.8470.42320.11490.95214.31±0.08
VCTK0.87473.8180.59210.12150.94904.27±0.08
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BigVGAN also exhibits robustness to various types of out-of-distribution signals such as", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 221, + 331, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 325, + 234 + ], + "score": 1.0, + "content": "laughter. We provide audio samples to our demo page.", + "type": "text" + }, + { + "bbox": [ + 326, + 221, + 331, + 227 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 107, + 241, + 209, + 252 + ], + "lines": [ + { + "bbox": [ + 105, + 239, + 210, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 210, + 254 + ], + "score": 1.0, + "content": "4.7 ABLATION STUDY", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 259, + 505, + 391 + ], + "lines": [ + { + "bbox": [ + 105, + 259, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 506, + 272 + ], + "score": 1.0, + "content": "Model architecture To measure the effectiveness of the BigVGAN generator, we include SMOS", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 271, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 505, + 282 + ], + "score": 1.0, + "content": "test for the ablation models of BigVGAN-base on MUSDB18-HQ data. Table 4 shows that the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "ablation models exhibit clear degradation on various scenarios such as instrumental audio (others,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 293, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 505, + 304 + ], + "score": 1.0, + "content": "mixture). From the average SMOS ratings, 1) disabling the anti-aliasing filter for Snake activation", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "score": 1.0, + "content": "performs worse than BigVGAN-base and 2) removing both the filter and Snake activation (i.e., vanilla", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "score": 1.0, + "content": "HiFi-GAN trained with MRD replacing MSD) is even worse than the Snake-only ablation model,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 325, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 270, + 338 + ], + "score": 1.0, + "content": "both with statistical significance (p-value", + "type": "text" + }, + { + "bbox": [ + 270, + 326, + 298, + 336 + ], + "score": 0.86, + "content": "< 0 . 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 325, + 505, + 338 + ], + "score": 1.0, + "content": "from the Wilcoxon signed-rank test). This indicates", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "that Leaky ReLU is not robust enough to extrapolate beyond the learned frequency range and the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 347, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 360 + ], + "score": 1.0, + "content": "aliasing artifacts degrade the audio quality in challenging setups. The results show that BigVGAN", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 358, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 505, + 370 + ], + "score": 1.0, + "content": "generator demonstrates strong robustness and extrapolation capability to out-of-distribution scenarios", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 370, + 506, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 506, + 381 + ], + "score": 1.0, + "content": "because of the seamless integration of periodic inductive bias and anti-aliased feature representation.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 380, + 402, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 402, + 392 + ], + "score": 1.0, + "content": "See Appendix D for the visualization of anti-aliasing effect in BigVGAN.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 396, + 505, + 485 + ], + "lines": [ + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "score": 1.0, + "content": "Big model We compare HiFi-GAN and BigVGAN both with the largest 112M parameters. We train", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "the 112M HiFi-GAN with the same training setting as BigVGAN. We conduct a pairwise test between", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "score": 1.0, + "content": "the two models on the mixture test set of MUSDB18-HQ which is challenging out-of-distribution", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "score": 1.0, + "content": "data. 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The test shows that", + "type": "text" + }, + { + "bbox": [ + 222, + 441, + 245, + 451 + ], + "score": 0.88, + "content": "5 8 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "of the ratings voted to BigVGAN over the large HiFi-GAN and", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 452, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 494, + 464 + ], + "score": 1.0, + "content": "the quality of BigVGAN is greater than the large HiFi-GAN with statistical significance (p-value", + "type": "text" + }, + { + "bbox": [ + 495, + 452, + 505, + 462 + ], + "score": 0.77, + "content": "<", + "type": "inline_equation" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 461, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 506, + 475 + ], + "score": 1.0, + "content": "0.01 from the Wilcoxon signed-rank test). The results further validate the architectural advantage of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 473, + 239, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 239, + 487 + ], + "score": 1.0, + "content": "BigVGAN in large-scale setting.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25.5 + }, + { + "type": "text", + "bbox": [ + 107, + 490, + 505, + 556 + ], + "lines": [ + { + "bbox": [ + 105, + 490, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 506, + 503 + ], + "score": 1.0, + "content": "Large Training data To verify the importance of using large-scale training data, we trained our", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 501, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 506, + 514 + ], + "score": 1.0, + "content": "BigVGAN using less diverse, clean speech-only dataset with the same training configuration for 1M", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 510, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 104, + 510, + 506, + 527 + ], + "score": 1.0, + "content": "steps: 1) train-clean-360 subset of LibriTTS, or 2) VCTK dataset. Table 5 shows that training", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 523, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 505, + 536 + ], + "score": 1.0, + "content": "BigVGAN on less diverse data shows degradation in both objective metrics and the subjective SMOS", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 535, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 505, + 546 + ], + "score": 1.0, + "content": "on the LibriTTS evaluation sets. The result verifies the importance of using diverse training data and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 545, + 381, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 381, + 559 + ], + "score": 1.0, + "content": "demonstrates the effectiveness of BigVGAN on large-scale datasets.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32.5 + }, + { + "type": "title", + "bbox": [ + 108, + 568, + 201, + 581 + ], + "lines": [ + { + "bbox": [ + 104, + 565, + 203, + 584 + ], + "spans": [ + { + "bbox": [ + 104, + 565, + 203, + 584 + ], + "score": 1.0, + "content": "5 CONCLUSIONS", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 590, + 506, + 712 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 506, + 603 + ], + "score": 1.0, + "content": "This study explores the limits of universal neural vocoding with an unprecedented scale of the data,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 603, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 505, + 614 + ], + "score": 1.0, + "content": "model, and evaluations. We analyze the performance with various automatic and human evaluations", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 613, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 506, + 625 + ], + "score": 1.0, + "content": "across diverse scenarios including unseen speakers, languages, recording environments and out-of-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 623, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 506, + 637 + ], + "score": 1.0, + "content": "distribution data. 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Training dataM-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)SMOS(↑)
Ground Truth--1--4.55±0.05
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BigVGAN also exhibits robustness to various types of out-of-distribution signals such as", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 221, + 331, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 325, + 234 + ], + "score": 1.0, + "content": "laughter. 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This indicates", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "that Leaky ReLU is not robust enough to extrapolate beyond the learned frequency range and the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 347, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 360 + ], + "score": 1.0, + "content": "aliasing artifacts degrade the audio quality in challenging setups. The results show that BigVGAN", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 358, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 505, + 370 + ], + "score": 1.0, + "content": "generator demonstrates strong robustness and extrapolation capability to out-of-distribution scenarios", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 370, + 506, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 506, + 381 + ], + "score": 1.0, + "content": "because of the seamless integration of periodic inductive bias and anti-aliased feature representation.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 380, + 402, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 380, + 402, + 392 + ], + "score": 1.0, + "content": "See Appendix D for the visualization of anti-aliasing effect in BigVGAN.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 259, + 506, + 392 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 396, + 505, + 485 + ], + "lines": [ + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "score": 1.0, + "content": "Big model We compare HiFi-GAN and BigVGAN both with the largest 112M parameters. We train", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "the 112M HiFi-GAN with the same training setting as BigVGAN. We conduct a pairwise test between", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "score": 1.0, + "content": "the two models on the mixture test set of MUSDB18-HQ which is challenging out-of-distribution", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "score": 1.0, + "content": "data. 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The results further validate the architectural advantage of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 473, + 239, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 239, + 487 + ], + "score": 1.0, + "content": "BigVGAN in large-scale setting.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 397, + 506, + 487 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 490, + 505, + 556 + ], + "lines": [ + { + "bbox": [ + 105, + 490, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 506, + 503 + ], + "score": 1.0, + "content": "Large Training data To verify the importance of using large-scale training data, we trained our", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 501, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 506, + 514 + ], + "score": 1.0, + "content": "BigVGAN using less diverse, clean speech-only dataset with the same training configuration for 1M", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 510, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 104, + 510, + 506, + 527 + ], + "score": 1.0, + "content": "steps: 1) train-clean-360 subset of LibriTTS, or 2) VCTK dataset. 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We believe that BigVGAN, combined", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 679, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 679, + 505, + 690 + ], + "score": 1.0, + "content": "with practical lessons learned from the large scale training, will inspire future endeavors for universal", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 689, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 506, + 702 + ], + "score": 1.0, + "content": "vocoding and improve the state-of-the-art results for real-world applications, including voice cloning,", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 701, + 324, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 701, + 324, + 712 + ], + "score": 1.0, + "content": "voice conversion, speech translation, and audio codec.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 590, + 506, + 712 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 176, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 176, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 176, + 95 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 504, + 123 + ], + "lines": [ + { + "bbox": [ + 105, + 99, + 506, + 113 + ], + "spans": [ + { + "bbox": [ + 105, + 99, + 506, + 113 + ], + "score": 1.0, + "content": "Ehab A AlBadawy, Andrew Gibiansky, Qing He, Jilong Wu, Ming-Ching Chang, and Siwei Lyu.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 117, + 111, + 439, + 124 + ], + "spans": [ + { + "bbox": [ + 117, + 111, + 439, + 124 + ], + "score": 1.0, + "content": "Vocbench: A neural vocoder benchmark for speech synthesis. 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GeneratorDiscriminator
BigVGAN-baseBigVGANMRD&MPD
h5121536n_ffti[1024,2048,512]
Ui[8,8,2,2][4,4,2,2, 2,2]hop_lengthi[120,240,50]
Ki[3,3,3,7,7,7,11,11,11][3,3,3, 7, 7, 7,11, 11,11]win_lengthi[600,1200,240]
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Left: Gradient norm", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 632, + 504, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 504, + 643 + ], + "score": 1.0, + "content": "from the generator. Mid: Gradient from the MPD module. Right: Gradient norm from the MRD module. For", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 642, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 642, + 505, + 655 + ], + "score": 1.0, + "content": "BigVGAN-base, the gradient norm significantly increases at early training without clipping. 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For BigVGAN, the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 651, + 249, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 249, + 666 + ], + "score": 1.0, + "content": "gradient will explode without clipping.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5 + } + ], + "index": 31.75 + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "In this section, we document additional directions that we have explored for improving the model", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 686, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 505, + 701 + ], + "score": 1.0, + "content": "architecture and large scale training, but resulted in worse perceptual quality from our preliminary", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "study. We do not make conclusive claims based on these observations because the methods we", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "explored here may have been ineffective specific to our BigVGAN settings. Nevertheless, we believe", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 720, + 483, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 483, + 733 + ], + "score": 1.0, + "content": "that reporting negative results can be helpful to future research endeavors (Brock et al., 2019).", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 677, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 160 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 507, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 507, + 96 + ], + "score": 1.0, + "content": "Anti-aliased upsampling layers Our BigVGAN uses anti-aliased activation for AMP modules.", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "We also explored replacing the transposed convolution-based upsampling layers, which are known to", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "score": 1.0, + "content": "contain checkerboard aliasing (Odena et al., 2016), to the anti-aliased alternatives with different low-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "score": 1.0, + "content": "pass filter hyperparameters. However, this introduced significant instabilities during training, leading", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "to early collapse even with the aforementioned stabilization. We also tried out nearest-neighbor", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "upsampling which is reported to have less artifacts for audio synthesis (Pons et al., 2021), but it also", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 225, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 225, + 161 + ], + "score": 1.0, + "content": "resulted in the early collapse.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 179, + 505, + 235 + ], + "lines": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "score": 1.0, + "content": "Periodic discriminators Inspired by the improvements with the periodic activation function to the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "score": 1.0, + "content": "generator, we experimented on discriminators with Snake function. However, it degraded the quality", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 201, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 505, + 214 + ], + "score": 1.0, + "content": "with the diverging feature matching loss (Kong et al., 2020) from the discriminators. We conjecture", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 212, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 505, + 226 + ], + "score": 1.0, + "content": "that the periodic activation to the discriminator is not stable enough to improve the gradient from the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 223, + 197, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 197, + 237 + ], + "score": 1.0, + "content": "feature matching loss.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 254, + 506, + 343 + ], + "lines": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "Spectral normalization Spectral normalization (Miyato et al., 2018) is a widely adopted method to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 266, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 506, + 279 + ], + "score": 1.0, + "content": "stabilize GAN training in image domain. We tried applying spectral normalization to all discriminator", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 277, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 506, + 289 + ], + "score": 1.0, + "content": "submodules and found that it can stabilize the training without the early divergence of the generator.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 288, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 505, + 300 + ], + "score": 1.0, + "content": "However, it suffered from a significant degradation with the excessive amount of phase mismatch", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 299, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 506, + 311 + ], + "score": 1.0, + "content": "artifacts, similar to the findings in the previous work (Kumar et al., 2019). We found that the gradient", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 309, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 506, + 322 + ], + "score": 1.0, + "content": "from MPD is over-regularized and the generator start to solely rely on the mel regression loss.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "score": 1.0, + "content": "Because MPD is repeatedly found to be a key component for high-quality audio synthesis (Kong", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 331, + 319, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 319, + 344 + ], + "score": 1.0, + "content": "et al., 2020), regularizing MPD leads to worse result.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 429 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "score": 1.0, + "content": "Larger discriminators We hypothesized that the enlarged generator can be slower to learn, thereby", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "score": 1.0, + "content": "trivializing the discriminator in the early training (loss converge to zero). We tried to balance", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "score": 1.0, + "content": "the training by enlarging the discriminators, such as employing more MPD sub-discriminators or", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 397, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 505, + 408 + ], + "score": 1.0, + "content": "enlarging the channel width of MPD and MRD modules. The large discriminator partially alleviated", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "the early collapse, but the audio quality degraded in most cases, and showed no clear improvements", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 418, + 240, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 240, + 431 + ], + "score": 1.0, + "content": "even with our best configuration.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 449, + 505, + 515 + ], + "lines": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "score": 1.0, + "content": "Even larger generators We experimented with deeper model with 8 upsampling blocks with", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 460, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 473 + ], + "score": 1.0, + "content": "ratio of [2, 2, 2, 2, 2, 2, 2, 2]. However, it exhibited high-frequency rattling artifacts and degraded the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "score": 1.0, + "content": "quality. We conjecture that generating fine-grained high-frequency details from the early upsampling", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "score": 1.0, + "content": "blocks can be arbitrary (Karras et al., 2021) and unstable when using the filtered periodic nonlinearity.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "score": 1.0, + "content": "We also tried to further increase the number of convolution channels to 2048, but it suffered from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 502, + 166, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 166, + 518 + ], + "score": 1.0, + "content": "early collapse.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 107, + 535, + 505, + 635 + ], + "lines": [ + { + "bbox": [ + 106, + 535, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 506, + 548 + ], + "score": 1.0, + "content": "Data augmentation Data augmentation is one of major methods that improve model generalization,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "score": 1.0, + "content": "which is also repeatedly found to be valuable in GAN literature (Karras et al., 2020). We explored", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 556, + 507, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 556, + 507, + 572 + ], + "score": 1.0, + "content": "augmenting the data by applying SpecAugment (Park et al., 2019) to the input mel spectrogram.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "However, SpecAugment resulted in over-smoothing artifacts in waveform, because it enforces the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 580, + 506, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 593 + ], + "score": 1.0, + "content": "model to map multiple distorted mel spectrograms to the same waveform, which counters the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "upsampling process in generative models. We also tried applying mixup-like (Zhang et al., 2018)", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "score": 1.0, + "content": "approach to the waveform by using a convex combination of two audio samples and its corresponding", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "score": 1.0, + "content": "mel spectrogram. However, this occasionally resulted in a mixed voice of two speaker identities", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 623, + 459, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 459, + 637 + ], + "score": 1.0, + "content": "during a single-speaker inference without noticeable improvement in perceptual quality.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "Positional encoding Inspired by using partial autoregression (Ping et al., 2020; Morrison et al.,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "2022) to provide inductive bias of the cumulative sum relationship of pitch and phase (Morrison et al.,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "2022), we explored whether we can provide an approximate inductive bias in a non-autoregressive", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "manner by injecting a sinusoidal positional encoding (Vaswani et al., 2017) to the generator. However,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 480, + 710 + ], + "score": 1.0, + "content": "the generator with positional encoding is only exposed to the fixed audio segment at training", + "type": "text" + }, + { + "bbox": [ + 481, + 699, + 504, + 710 + ], + "score": 0.78, + "content": "( \\sim 0 . 3", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "seconds with 8,192 time-steps) and unable to extrapolate unknown and significantly longer sequence", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 249, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 249, + 733 + ], + "score": 1.0, + "content": "at inference (e.g., several seconds).", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44 + } + ], + "page_idx": 15, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 752, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 160 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 507, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 507, + 96 + ], + "score": 1.0, + "content": "Anti-aliased upsampling layers Our BigVGAN uses anti-aliased activation for AMP modules.", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "We also explored replacing the transposed convolution-based upsampling layers, which are known to", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "score": 1.0, + "content": "contain checkerboard aliasing (Odena et al., 2016), to the anti-aliased alternatives with different low-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "score": 1.0, + "content": "pass filter hyperparameters. However, this introduced significant instabilities during training, leading", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "to early collapse even with the aforementioned stabilization. We also tried out nearest-neighbor", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "upsampling which is reported to have less artifacts for audio synthesis (Pons et al., 2021), but it also", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 225, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 225, + 161 + ], + "score": 1.0, + "content": "resulted in the early collapse.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 82, + 507, + 161 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 179, + 505, + 235 + ], + "lines": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "score": 1.0, + "content": "Periodic discriminators Inspired by the improvements with the periodic activation function to the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "score": 1.0, + "content": "generator, we experimented on discriminators with Snake function. However, it degraded the quality", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 201, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 505, + 214 + ], + "score": 1.0, + "content": "with the diverging feature matching loss (Kong et al., 2020) from the discriminators. We conjecture", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 212, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 505, + 226 + ], + "score": 1.0, + "content": "that the periodic activation to the discriminator is not stable enough to improve the gradient from the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 223, + 197, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 197, + 237 + ], + "score": 1.0, + "content": "feature matching loss.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 180, + 506, + 237 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 254, + 506, + 343 + ], + "lines": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "Spectral normalization Spectral normalization (Miyato et al., 2018) is a widely adopted method to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 266, + 506, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 506, + 279 + ], + "score": 1.0, + "content": "stabilize GAN training in image domain. We tried applying spectral normalization to all discriminator", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 277, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 506, + 289 + ], + "score": 1.0, + "content": "submodules and found that it can stabilize the training without the early divergence of the generator.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 288, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 505, + 300 + ], + "score": 1.0, + "content": "However, it suffered from a significant degradation with the excessive amount of phase mismatch", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 299, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 506, + 311 + ], + "score": 1.0, + "content": "artifacts, similar to the findings in the previous work (Kumar et al., 2019). We found that the gradient", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 309, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 506, + 322 + ], + "score": 1.0, + "content": "from MPD is over-regularized and the generator start to solely rely on the mel regression loss.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "score": 1.0, + "content": "Because MPD is repeatedly found to be a key component for high-quality audio synthesis (Kong", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 331, + 319, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 319, + 344 + ], + "score": 1.0, + "content": "et al., 2020), regularizing MPD leads to worse result.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 254, + 506, + 344 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 429 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "score": 1.0, + "content": "Larger discriminators We hypothesized that the enlarged generator can be slower to learn, thereby", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "score": 1.0, + "content": "trivializing the discriminator in the early training (loss converge to zero). We tried to balance", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "score": 1.0, + "content": "the training by enlarging the discriminators, such as employing more MPD sub-discriminators or", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 397, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 505, + 408 + ], + "score": 1.0, + "content": "enlarging the channel width of MPD and MRD modules. The large discriminator partially alleviated", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "the early collapse, but the audio quality degraded in most cases, and showed no clear improvements", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 418, + 240, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 240, + 431 + ], + "score": 1.0, + "content": "even with our best configuration.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 363, + 506, + 431 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 449, + 505, + 515 + ], + "lines": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "score": 1.0, + "content": "Even larger generators We experimented with deeper model with 8 upsampling blocks with", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 460, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 473 + ], + "score": 1.0, + "content": "ratio of [2, 2, 2, 2, 2, 2, 2, 2]. However, it exhibited high-frequency rattling artifacts and degraded the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 485 + ], + "score": 1.0, + "content": "quality. We conjecture that generating fine-grained high-frequency details from the early upsampling", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "score": 1.0, + "content": "blocks can be arbitrary (Karras et al., 2021) and unstable when using the filtered periodic nonlinearity.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "score": 1.0, + "content": "We also tried to further increase the number of convolution channels to 2048, but it suffered from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 502, + 166, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 166, + 518 + ], + "score": 1.0, + "content": "early collapse.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 449, + 506, + 518 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 535, + 505, + 635 + ], + "lines": [ + { + "bbox": [ + 106, + 535, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 506, + 548 + ], + "score": 1.0, + "content": "Data augmentation Data augmentation is one of major methods that improve model generalization,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "score": 1.0, + "content": "which is also repeatedly found to be valuable in GAN literature (Karras et al., 2020). We explored", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 556, + 507, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 556, + 507, + 572 + ], + "score": 1.0, + "content": "augmenting the data by applying SpecAugment (Park et al., 2019) to the input mel spectrogram.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "However, SpecAugment resulted in over-smoothing artifacts in waveform, because it enforces the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 580, + 506, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 593 + ], + "score": 1.0, + "content": "model to map multiple distorted mel spectrograms to the same waveform, which counters the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "upsampling process in generative models. We also tried applying mixup-like (Zhang et al., 2018)", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "score": 1.0, + "content": "approach to the waveform by using a convex combination of two audio samples and its corresponding", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 625 + ], + "score": 1.0, + "content": "mel spectrogram. However, this occasionally resulted in a mixed voice of two speaker identities", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 623, + 459, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 459, + 637 + ], + "score": 1.0, + "content": "during a single-speaker inference without noticeable improvement in perceptual quality.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 36, + "bbox_fs": [ + 104, + 535, + 507, + 637 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "Positional encoding Inspired by using partial autoregression (Ping et al., 2020; Morrison et al.,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "2022) to provide inductive bias of the cumulative sum relationship of pitch and phase (Morrison et al.,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "2022), we explored whether we can provide an approximate inductive bias in a non-autoregressive", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "manner by injecting a sinusoidal positional encoding (Vaswani et al., 2017) to the generator. However,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 504, + 710 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 480, + 710 + ], + "score": 1.0, + "content": "the generator with positional encoding is only exposed to the fixed audio segment at training", + "type": "text" + }, + { + "bbox": [ + 481, + 699, + 504, + 710 + ], + "score": 0.78, + "content": "( \\sim 0 . 3", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "seconds with 8,192 time-steps) and unable to extrapolate unknown and significantly longer sequence", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 249, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 249, + 733 + ], + "score": 1.0, + "content": "at inference (e.g., several seconds).", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44, + "bbox_fs": [ + 105, + 654, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 91, + 500, + 362 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 111, + 91, + 500, + 362 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 111, + 91, + 500, + 362 + ], + "spans": [ + { + "bbox": [ + 111, + 91, + 500, + 362 + ], + "score": 0.975, + "type": "image", + "image_path": "ceb9dd8fdb167c43a9d55510ca258a3da8a4af9d7082b04debd1bec0a65d8509.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 111, + 91, + 500, + 181.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 111, + 181.33333333333331, + 500, + 271.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 111, + 271.66666666666663, + 500, + 361.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 371, + 506, + 405 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 371, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 383 + ], + "score": 1.0, + "content": "Figure 5: Spectrogram visualization of out-of-distribution samples from HiFi-GAN and BigVGAN", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 382, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 506, + 396 + ], + "score": 1.0, + "content": "models trained on LibriTTS, with a zoomed in view of harmonic components. Top: a singing voice.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 394, + 233, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 233, + 405 + ], + "score": 1.0, + "content": "Bottom: an instrumental audio.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 425, + 210, + 438 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 212, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 212, + 441 + ], + "score": 1.0, + "content": "D VISUALIZATION", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 453, + 505, + 486 + ], + "lines": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "score": 1.0, + "content": "In this section, we present visual examples to analyze the improvements from the methodologies", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 464, + 506, + 476 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 506, + 476 + ], + "score": 1.0, + "content": "used in BigVGAN. We use HiFi-GAN (V1), BigVGAN-base along with the ablation model without", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 474, + 439, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 439, + 488 + ], + "score": 1.0, + "content": "the filtered nonlinearity, and the high-capacity BigVGAN for the in-depth analysis.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 492, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 106, + 492, + 504, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 492, + 504, + 505 + ], + "score": 1.0, + "content": "The top row of the Figure 5 corresponds to a singing voice. The feature aliasing of HiFi-GAN", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 502, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 505, + 516 + ], + "score": 1.0, + "content": "introduces blurry harmonics because aliased features at multiple incorrect frequency components", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "score": 1.0, + "content": "are aggregated during the generative process, which amplifies the error. BigVGAN-base without", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 524, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 505, + 538 + ], + "score": 1.0, + "content": "the filtered nonlinearity improves the harmonic components using the periodic activation and the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 536, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 505, + 548 + ], + "score": 1.0, + "content": "advanced discriminator. BigVGAN models further improve the accuracy using the continuous feature", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "score": 1.0, + "content": "representation and the anti-aliasing filter. The bottom row of the Figure 5 shows an instrumental", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 558, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 570 + ], + "score": 1.0, + "content": "audio. Similar to the singing voice example, HiFi-GAN exhibits blurry harmonics. BigVGAN", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 569, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 506, + 581 + ], + "score": 1.0, + "content": "models capture such challenging high-frequency harmonics significantly better than the baselines,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 579, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 579, + 505, + 592 + ], + "score": 1.0, + "content": "which suggests that BigVGAN is robust to various unseen conditions. The visual analysis shows that", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "BigVGAN exhibits a significantly less distortion of the harmonic components and a better sound", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 602, + 369, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 369, + 614 + ], + "score": 1.0, + "content": "quality for various types of audio beyond the clean speech signal.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 108, + 632, + 244, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 632, + 245, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 245, + 647 + ], + "score": 1.0, + "content": "E ADDITIONAL RESULTS", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 503, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 659, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 674 + ], + "score": 1.0, + "content": "In addition to the results in Section 4 of main text, we provide additional comparison with previous", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 671, + 372, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 372, + 683 + ], + "score": 1.0, + "content": "work and ablation models with the automatic objective evaluation.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 507, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 507, + 711 + ], + "score": 1.0, + "content": "Comparison with Baselines Models Table 7 and 8 show the expanded objective results evalu-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "score": 1.0, + "content": "ated on LibriTTS, including SC-WaveRNN (Paul et al., 2020), WaveGlow (Prenger et al., 2019),", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 719, + 507, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 719, + 507, + 733 + ], + "score": 1.0, + "content": "WaveFlow (Ping et al., 2020), UnivNet (Jang et al., 2021), and the ablation models of BigVGAN-base.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25 + } + ], + "page_idx": 16, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 111, + 91, + 500, + 362 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 111, + 91, + 500, + 362 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 111, + 91, + 500, + 362 + ], + "spans": [ + { + "bbox": [ + 111, + 91, + 500, + 362 + ], + "score": 0.975, + "type": "image", + "image_path": "ceb9dd8fdb167c43a9d55510ca258a3da8a4af9d7082b04debd1bec0a65d8509.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 111, + 91, + 500, + 181.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 111, + 181.33333333333331, + 500, + 271.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 111, + 271.66666666666663, + 500, + 361.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 371, + 506, + 405 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 371, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 383 + ], + "score": 1.0, + "content": "Figure 5: Spectrogram visualization of out-of-distribution samples from HiFi-GAN and BigVGAN", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 382, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 506, + 396 + ], + "score": 1.0, + "content": "models trained on LibriTTS, with a zoomed in view of harmonic components. Top: a singing voice.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 394, + 233, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 233, + 405 + ], + "score": 1.0, + "content": "Bottom: an instrumental audio.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 425, + 210, + 438 + ], + "lines": [ + { + "bbox": [ + 105, + 424, + 212, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 212, + 441 + ], + "score": 1.0, + "content": "D VISUALIZATION", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 453, + 505, + 486 + ], + "lines": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "score": 1.0, + "content": "In this section, we present visual examples to analyze the improvements from the methodologies", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 464, + 506, + 476 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 506, + 476 + ], + "score": 1.0, + "content": "used in BigVGAN. We use HiFi-GAN (V1), BigVGAN-base along with the ablation model without", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 474, + 439, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 439, + 488 + ], + "score": 1.0, + "content": "the filtered nonlinearity, and the high-capacity BigVGAN for the in-depth analysis.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 452, + 506, + 488 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 492, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 106, + 492, + 504, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 492, + 504, + 505 + ], + "score": 1.0, + "content": "The top row of the Figure 5 corresponds to a singing voice. The feature aliasing of HiFi-GAN", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 502, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 505, + 516 + ], + "score": 1.0, + "content": "introduces blurry harmonics because aliased features at multiple incorrect frequency components", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "score": 1.0, + "content": "are aggregated during the generative process, which amplifies the error. BigVGAN-base without", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 524, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 505, + 538 + ], + "score": 1.0, + "content": "the filtered nonlinearity improves the harmonic components using the periodic activation and the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 536, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 505, + 548 + ], + "score": 1.0, + "content": "advanced discriminator. BigVGAN models further improve the accuracy using the continuous feature", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "score": 1.0, + "content": "representation and the anti-aliasing filter. The bottom row of the Figure 5 shows an instrumental", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 558, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 570 + ], + "score": 1.0, + "content": "audio. Similar to the singing voice example, HiFi-GAN exhibits blurry harmonics. BigVGAN", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 569, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 506, + 581 + ], + "score": 1.0, + "content": "models capture such challenging high-frequency harmonics significantly better than the baselines,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 579, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 579, + 505, + 592 + ], + "score": 1.0, + "content": "which suggests that BigVGAN is robust to various unseen conditions. The visual analysis shows that", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "BigVGAN exhibits a significantly less distortion of the harmonic components and a better sound", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 602, + 369, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 369, + 614 + ], + "score": 1.0, + "content": "quality for various types of audio beyond the clean speech signal.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 492, + 506, + 614 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 632, + 244, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 632, + 245, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 245, + 647 + ], + "score": 1.0, + "content": "E ADDITIONAL RESULTS", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 503, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 659, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 674 + ], + "score": 1.0, + "content": "In addition to the results in Section 4 of main text, we provide additional comparison with previous", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 671, + 372, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 372, + 683 + ], + "score": 1.0, + "content": "work and ablation models with the automatic objective evaluation.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 659, + 505, + 683 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 507, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 507, + 711 + ], + "score": 1.0, + "content": "Comparison with Baselines Models Table 7 and 8 show the expanded objective results evalu-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "score": 1.0, + "content": "ated on LibriTTS, including SC-WaveRNN (Paul et al., 2020), WaveGlow (Prenger et al., 2019),", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 719, + 507, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 719, + 507, + 733 + ], + "score": 1.0, + "content": "WaveFlow (Ping et al., 2020), UnivNet (Jang et al., 2021), and the ablation models of BigVGAN-base.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 698, + 507, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 182 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "SC-WaveRNN (Paul et al., 2020) is a universal vocoder based on WaveRNN (Kalchbrenner et al.,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "score": 1.0, + "content": "2018) with a speaker embedding from a separately trained encoder network. We replicate the training", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 102, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 506, + 119 + ], + "score": 1.0, + "content": "procedure following (Paul et al., 2020) using the official implementation, while matching training", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "data and audio hyperparameters used in this study (i.e., LibriTTS-full, 24,000Hz sampling rate and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 126, + 507, + 140 + ], + "spans": [ + { + "bbox": [ + 104, + 126, + 507, + 140 + ], + "score": 1.0, + "content": "a 100-band log-mel spectrogram with [0, 12] kHz frequency). We train SC-WaveRNN for 3M steps.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "Although the model can generate speech with diverse speaker identities, we find that the performance", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 160 + ], + "score": 1.0, + "content": "is significantly worse than GAN vocoders both in objective scores and human listening test. It fails to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "score": 1.0, + "content": "generate intelligible audio for unseen recording environments and out-of-distribution sample. We", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 495, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 495, + 183 + ], + "score": 1.0, + "content": "conjecture that the speaker embedding network is not robust enough to generalize to such setups.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 187, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "WaveGlow (Prenger et al., 2019) and WaveFlow (Ping et al., 2020) are two widely known vocoders", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "score": 1.0, + "content": "based on normalizing flows (Rezende & Mohamed, 2015). We train the flow-based vocoders using the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "score": 1.0, + "content": "STFT hyperparameters used in this study. WaveGlow is trained for 2M steps and WaveFlow is trained", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 232 + ], + "score": 1.0, + "content": "for 1M steps as suggested by the authors. Flow-based vocoder features fast and parallel synthesis with", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 504, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 504, + 243 + ], + "score": 1.0, + "content": "an analytic likelihood objective due to its bijectivity. However, the quality of flow-based vocoders", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 242, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 505, + 254 + ], + "score": 1.0, + "content": "degrades heavily for multi-speaker setup. This renders the flow-based model unsuitable as a universal", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 253, + 170, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 170, + 264 + ], + "score": 1.0, + "content": "neural vocoder.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 269, + 506, + 412 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 506, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 506, + 283 + ], + "score": 1.0, + "content": "We also train UnivNet-c32 (Jang et al., 2021) on LibriTTS train-full using the open-source", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 292, + 294 + ], + "score": 1.0, + "content": "implementation (note that UnivNet uses the", + "type": "text" + }, + { + "bbox": [ + 292, + 281, + 334, + 292 + ], + "score": 0.42, + "content": "2 4 { , } 0 0 0 \\mathrm { H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "sampling rate and the 100-band log-mel", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 305 + ], + "score": 1.0, + "content": "spectrogram with [0, 12] kHz frequency by default). However, unlike the HiFi-GAN and BigVGAN", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "score": 1.0, + "content": "architectures, using the large-scale dataset did not improve the quality of the UnivNet architecture.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "Overall, the publicly available model trained on train-clean-360 scores marginally better", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "score": 1.0, + "content": "in terms of PESQ and periodicity error compared to our checkpoint trained on train-full.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 335, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 505, + 349 + ], + "score": 1.0, + "content": "Other metrics exhibit different preference depending on the training set. The subjective quality", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "score": 1.0, + "content": "is indistinguishable to the authors between the two checkpoints, including the out-of-distribution", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "score": 1.0, + "content": "setup. We conjecture that the UnivNet architecture is harder to generalize to the unseen recording", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 366, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 104, + 366, + 506, + 383 + ], + "score": 1.0, + "content": "environments. For subjective SMOS tests, we choose to use the publicly available checkpoint using", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "score": 1.0, + "content": "train-clean-360 to faithfully represent the performance of the previous work. Note that the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 389, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 506, + 403 + ], + "score": 1.0, + "content": "open-source implementation of UnivNet is unofficial. Therefore, our observation does not lead to the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 402, + 309, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 309, + 413 + ], + "score": 1.0, + "content": "conclusion that UnivNet is worse than HiFi-GAN.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 524 + ], + "lines": [ + { + "bbox": [ + 106, + 425, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 506, + 437 + ], + "score": 1.0, + "content": "Comparison with Ablation Models From both clean and other recording environments, BigVGAN-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 435, + 507, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 507, + 449 + ], + "score": 1.0, + "content": "base shows consistent improvements in all metrics compared to its ablation models. Specifically,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "score": 1.0, + "content": "BigVGAN-base (without filter & snake) refers to the vanilla HiFi-GAN architecture trained with MRD", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 457, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 506, + 471 + ], + "score": 1.0, + "content": "replacing MSD. Similar to the findings in (Jang et al., 2021), MRD provides more accurate modeling", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 469, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 506, + 482 + ], + "score": 1.0, + "content": "of the waveform by sharpening the spectral structure. Applying Snake activation (BigVGAN-base", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "without filter) increases accuracy and reduces the periodicity error from the desired inductive bias.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "score": 1.0, + "content": "Finally, incorporating the continuous feature representation and the low-pass filter (BigVGAN-base)", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "score": 1.0, + "content": "provides the best accuracy by suppressing aliasing and high frequency artifacts. Our final 112M", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 512, + 495, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 495, + 526 + ], + "score": 1.0, + "content": "BigVGAN substantially improves the accuracy for the state-of-the-art universal neural vocoding.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 536, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 106, + 537, + 504, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 504, + 548 + ], + "score": 1.0, + "content": "Results on Unseen VCTK and LJSpeech Dataset Table 9 and 10 show the objective speech", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "score": 1.0, + "content": "evaluation metric results gathered from VCTK and LJSpeech dataset, consistent with the results", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 558, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 505, + 571 + ], + "score": 1.0, + "content": "from Table 7 and 8. Although the dataset is not included for training BigVGAN and the baseline", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "score": 1.0, + "content": "HiFi-GAN, all GAN-based models performed comparatively well from our subjective listening test.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 579, + 506, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 506, + 593 + ], + "score": 1.0, + "content": "This indicates that given diverse enough training data, modern non-autoregressive GAN vocoder can", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "score": 1.0, + "content": "synthesize high-quality speech with unseen speaker identities from the clean recording environment.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40.5 + } + ], + "page_idx": 17, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 763 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 763 + ], + "score": 1.0, + "content": "18", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 182 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "SC-WaveRNN (Paul et al., 2020) is a universal vocoder based on WaveRNN (Kalchbrenner et al.,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "score": 1.0, + "content": "2018) with a speaker embedding from a separately trained encoder network. We replicate the training", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 102, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 506, + 119 + ], + "score": 1.0, + "content": "procedure following (Paul et al., 2020) using the official implementation, while matching training", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "data and audio hyperparameters used in this study (i.e., LibriTTS-full, 24,000Hz sampling rate and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 126, + 507, + 140 + ], + "spans": [ + { + "bbox": [ + 104, + 126, + 507, + 140 + ], + "score": 1.0, + "content": "a 100-band log-mel spectrogram with [0, 12] kHz frequency). We train SC-WaveRNN for 3M steps.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "Although the model can generate speech with diverse speaker identities, we find that the performance", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 160 + ], + "score": 1.0, + "content": "is significantly worse than GAN vocoders both in objective scores and human listening test. It fails to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "score": 1.0, + "content": "generate intelligible audio for unseen recording environments and out-of-distribution sample. We", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 495, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 495, + 183 + ], + "score": 1.0, + "content": "conjecture that the speaker embedding network is not robust enough to generalize to such setups.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4, + "bbox_fs": [ + 104, + 82, + 507, + 183 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 187, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "WaveGlow (Prenger et al., 2019) and WaveFlow (Ping et al., 2020) are two widely known vocoders", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 210 + ], + "score": 1.0, + "content": "based on normalizing flows (Rezende & Mohamed, 2015). We train the flow-based vocoders using the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "score": 1.0, + "content": "STFT hyperparameters used in this study. WaveGlow is trained for 2M steps and WaveFlow is trained", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 232 + ], + "score": 1.0, + "content": "for 1M steps as suggested by the authors. Flow-based vocoder features fast and parallel synthesis with", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 504, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 504, + 243 + ], + "score": 1.0, + "content": "an analytic likelihood objective due to its bijectivity. However, the quality of flow-based vocoders", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 242, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 505, + 254 + ], + "score": 1.0, + "content": "degrades heavily for multi-speaker setup. This renders the flow-based model unsuitable as a universal", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 253, + 170, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 170, + 264 + ], + "score": 1.0, + "content": "neural vocoder.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 187, + 505, + 264 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 269, + 506, + 412 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 506, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 506, + 283 + ], + "score": 1.0, + "content": "We also train UnivNet-c32 (Jang et al., 2021) on LibriTTS train-full using the open-source", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 292, + 294 + ], + "score": 1.0, + "content": "implementation (note that UnivNet uses the", + "type": "text" + }, + { + "bbox": [ + 292, + 281, + 334, + 292 + ], + "score": 0.42, + "content": "2 4 { , } 0 0 0 \\mathrm { H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "sampling rate and the 100-band log-mel", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 305 + ], + "score": 1.0, + "content": "spectrogram with [0, 12] kHz frequency by default). However, unlike the HiFi-GAN and BigVGAN", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "score": 1.0, + "content": "architectures, using the large-scale dataset did not improve the quality of the UnivNet architecture.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "Overall, the publicly available model trained on train-clean-360 scores marginally better", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "score": 1.0, + "content": "in terms of PESQ and periodicity error compared to our checkpoint trained on train-full.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 335, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 505, + 349 + ], + "score": 1.0, + "content": "Other metrics exhibit different preference depending on the training set. The subjective quality", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "score": 1.0, + "content": "is indistinguishable to the authors between the two checkpoints, including the out-of-distribution", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "score": 1.0, + "content": "setup. We conjecture that the UnivNet architecture is harder to generalize to the unseen recording", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 366, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 104, + 366, + 506, + 383 + ], + "score": 1.0, + "content": "environments. For subjective SMOS tests, we choose to use the publicly available checkpoint using", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 506, + 392 + ], + "score": 1.0, + "content": "train-clean-360 to faithfully represent the performance of the previous work. Note that the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 389, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 506, + 403 + ], + "score": 1.0, + "content": "open-source implementation of UnivNet is unofficial. Therefore, our observation does not lead to the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 402, + 309, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 309, + 413 + ], + "score": 1.0, + "content": "conclusion that UnivNet is worse than HiFi-GAN.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22, + "bbox_fs": [ + 104, + 268, + 506, + 413 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 524 + ], + "lines": [ + { + "bbox": [ + 106, + 425, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 506, + 437 + ], + "score": 1.0, + "content": "Comparison with Ablation Models From both clean and other recording environments, BigVGAN-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 435, + 507, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 507, + 449 + ], + "score": 1.0, + "content": "base shows consistent improvements in all metrics compared to its ablation models. Specifically,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 459 + ], + "score": 1.0, + "content": "BigVGAN-base (without filter & snake) refers to the vanilla HiFi-GAN architecture trained with MRD", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 457, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 506, + 471 + ], + "score": 1.0, + "content": "replacing MSD. Similar to the findings in (Jang et al., 2021), MRD provides more accurate modeling", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 469, + 506, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 506, + 482 + ], + "score": 1.0, + "content": "of the waveform by sharpening the spectral structure. Applying Snake activation (BigVGAN-base", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "without filter) increases accuracy and reduces the periodicity error from the desired inductive bias.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 504 + ], + "score": 1.0, + "content": "Finally, incorporating the continuous feature representation and the low-pass filter (BigVGAN-base)", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "score": 1.0, + "content": "provides the best accuracy by suppressing aliasing and high frequency artifacts. Our final 112M", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 512, + 495, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 495, + 526 + ], + "score": 1.0, + "content": "BigVGAN substantially improves the accuracy for the state-of-the-art universal neural vocoding.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 425, + 507, + 526 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 536, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 106, + 537, + 504, + 548 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 504, + 548 + ], + "score": 1.0, + "content": "Results on Unseen VCTK and LJSpeech Dataset Table 9 and 10 show the objective speech", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 505, + 559 + ], + "score": 1.0, + "content": "evaluation metric results gathered from VCTK and LJSpeech dataset, consistent with the results", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 558, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 505, + 571 + ], + "score": 1.0, + "content": "from Table 7 and 8. Although the dataset is not included for training BigVGAN and the baseline", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "score": 1.0, + "content": "HiFi-GAN, all GAN-based models performed comparatively well from our subjective listening test.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 579, + 506, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 506, + 593 + ], + "score": 1.0, + "content": "This indicates that given diverse enough training data, modern non-autoregressive GAN vocoder can", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 506, + 604 + ], + "score": 1.0, + "content": "synthesize high-quality speech with unseen speaker identities from the clean recording environment.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 537, + 506, + 604 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 126, + 126, + 485, + 250 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 92, + 504, + 123 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 91, + 506, + 104 + ], + "spans": [ + { + "bbox": [ + 105, + 91, + 506, + 104 + ], + "score": 1.0, + "content": "Table 7: Objective results of BigVGAN from dev-clean of LibriTTS including ablation models of", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 102, + 505, + 114 + ], + "spans": [ + { + "bbox": [ + 106, + 102, + 505, + 114 + ], + "score": 1.0, + "content": "BigVGAN-base and previous work. †: pretrained weight obtained from an open-source repository which", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 112, + 278, + 125 + ], + "spans": [ + { + "bbox": [ + 105, + 112, + 278, + 125 + ], + "score": 1.0, + "content": "used train-clean-360 subset for training.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 126, + 126, + 485, + 250 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 126, + 126, + 485, + 250 + ], + "spans": [ + { + "bbox": [ + 126, + 126, + 485, + 250 + ], + "score": 0.984, + "html": "
LibriTTS (clean)MAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN0.55172.14111.7741.58540.29250.8300
WaveGlow-2560.53681.32383.1792.38970.14230.9419
WaveFlow-1280.28391.07063.1200.96320.13390.9459
UnivNet-c32†0.28030.95523.3480.70170.13420.9433
UnivNet-c320.27720.94333.3100.69420.13560.9435
HiFi-GAN (V1)0.25790.97733.0420.62570.15450.9306
BigVGAN-base0.15460.85693.5740.41800.12980.9475
w/o filter0.17700.88383.4720.46240.13540.9437
w/o filter& snake0.18990.90473.3510.48520.13990.9401
BigVGAN0.09310.77964.0530.33920.10130.9610
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LibriTTS (other)MAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN0.61252.32741.5761.47170.21740.8896
WaveGlow-2560.50961.29603.0982.32840.15460.9337
WaveFlow-1280.33591.15332.9351.52780.14930.9360
UnivNet-c32t0.30270.99733.1660.86430.14390.9345
UnivNet-c320.29980.98833.1070.84950.14570.9337
HiFi-GAN (V1)0.27241.0262.8530.69480.15850.9294
BigVGAN-base0.16250.90063.4640.49470.12760.9442
w/o filter0.18440.92233.3640.50170.13910.9395
w/o filter& snake0.20080.94563.2400.53890.14510.9344
BigVGAN0.09860.81974.0010.40970.10230.9586
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VCTKMAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN0.66192.73441.4451.75970.25280.8611
WaveGlow-2560.54541.33243.1492.45120.12180.9513
WaveFlow-1280.29821.08252.9531.11270.12130.9518
UnivNet-c32t0.27530.94763.2350.71800.11310.9535
UnivNet-c320.28200.95863.1840.74030.11980.9434
HiFi-GAN (V1)0.25410.98593.0290.67950.13360.9375
BigVGAN-base0.15270.86773.4430.45260.10470.9586
w/o filter0.17390.89353.3790.49240.11280.9528
w/o filter & snake0.18850.91843.3160.51590.12080.9481
BigVGAN0.09250.76844.0010.35570.08330.9672
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LJSpeechMAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN1.01152.69941.2334.84640.39070.7404
WaveGlow-2560.49331.28933.3522.99210.11820.9561
WaveFlow-1280.36741.24023.0722.72170.11700.9560
UnivNet-c32†0.34181.06133.4251.19030.12100.9519
UnivNet-c320.33561.04293.3841.13560.12300.9503
HiFi-GAN (V1)0.30081.09503.2101.73700.13470.9456
BigVGAN-base0.17470.91213.7410.86260.11640.9548
w/o filter0.20150.93953.6620.97150.11690.9548
w/o filter & snake0.22630.99463.5211.13200.12990.9479
BigVGAN0.11020.85544.1120.71640.09570.9642
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LibriTTS (clean)MAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN0.55172.14111.7741.58540.29250.8300
WaveGlow-2560.53681.32383.1792.38970.14230.9419
WaveFlow-1280.28391.07063.1200.96320.13390.9459
UnivNet-c32†0.28030.95523.3480.70170.13420.9433
UnivNet-c320.27720.94333.3100.69420.13560.9435
HiFi-GAN (V1)0.25790.97733.0420.62570.15450.9306
BigVGAN-base0.15460.85693.5740.41800.12980.9475
w/o filter0.17700.88383.4720.46240.13540.9437
w/o filter& snake0.18990.90473.3510.48520.13990.9401
BigVGAN0.09310.77964.0530.33920.10130.9610
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LibriTTS (other)MAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN0.61252.32741.5761.47170.21740.8896
WaveGlow-2560.50961.29603.0982.32840.15460.9337
WaveFlow-1280.33591.15332.9351.52780.14930.9360
UnivNet-c32t0.30270.99733.1660.86430.14390.9345
UnivNet-c320.29980.98833.1070.84950.14570.9337
HiFi-GAN (V1)0.27241.0262.8530.69480.15850.9294
BigVGAN-base0.16250.90063.4640.49470.12760.9442
w/o filter0.18440.92233.3640.50170.13910.9395
w/o filter& snake0.20080.94563.2400.53890.14510.9344
BigVGAN0.09860.81974.0010.40970.10230.9586
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VCTKMAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN0.66192.73441.4451.75970.25280.8611
WaveGlow-2560.54541.33243.1492.45120.12180.9513
WaveFlow-1280.29821.08252.9531.11270.12130.9518
UnivNet-c32t0.27530.94763.2350.71800.11310.9535
UnivNet-c320.28200.95863.1840.74030.11980.9434
HiFi-GAN (V1)0.25410.98593.0290.67950.13360.9375
BigVGAN-base0.15270.86773.4430.45260.10470.9586
w/o filter0.17390.89353.3790.49240.11280.9528
w/o filter & snake0.18850.91843.3160.51590.12080.9481
BigVGAN0.09250.76844.0010.35570.08330.9672
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LJSpeechMAE(↓)M-STFT(↓)PESQ(↑)MCD(↓)Periodicity(↓)V/UV F1(↑)
SC-WaveRNN1.01152.69941.2334.84640.39070.7404
WaveGlow-2560.49331.28933.3522.99210.11820.9561
WaveFlow-1280.36741.24023.0722.72170.11700.9560
UnivNet-c32†0.34181.06133.4251.19030.12100.9519
UnivNet-c320.33561.04293.3841.13560.12300.9503
HiFi-GAN (V1)0.30081.09503.2101.73700.13470.9456
BigVGAN-base0.17470.91213.7410.86260.11640.9548
w/o filter0.20150.93953.6620.97150.11690.9548
w/o filter & snake0.22630.99463.5211.13200.12990.9479
BigVGAN0.11020.85544.1120.71640.09570.9642
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MethodEnglishGermanCatalanSpanishFrenchMandarin
Ground Truth6.2983.7853.0014.1945.45025.431
SC-WaveRNN15.1559.5085.76310.19812.42747.653
UnivNet-c32†6.9144.0373.0584.4395.71726.504
HiFi-GAN (V1)6.9064.0703.0824.4905.77027.179
HiFi-GAN (112M)6.6153.9203.0434.3155.60826.174
BigVGAN-base6.5743.9053.0344.3355.59426.174
BigVGAN6.4363.8293.0284.2615.51725.756
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To", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 259, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 106, + 259, + 505, + 270 + ], + "score": 1.0, + "content": "measure linguistic accuracy of the synthesized speech from BigVGAN on in-distribution and various", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 270, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 505, + 282 + ], + "score": 1.0, + "content": "out-of-distribution languages, we conduct experiments using a high-performance Conformer-based", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "(Gulati et al., 2020) automatic speech recognition (ASR) model on multiple languages. We use", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 292, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 505, + 304 + ], + "score": 1.0, + "content": "conformer_transducer_large model, where the pretrained checkpoints for the considered", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "score": 1.0, + "content": "languages are publicly available from the NVIDIA NeMo (Kuchaiev et al., 2019) toolkit. We generate", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 314, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 314, + 505, + 326 + ], + "score": 1.0, + "content": "samples from BigVGAN using test set corpus from Mozilla Common Voice (MCV) 8.0 dataset for", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 325, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 505, + 337 + ], + "score": 1.0, + "content": "the following languages: English (en), German (de), Catalan (ca), Spanish (es), French (fr), and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "Mandarin (zh). Then, we obtain transcriptions from the synthesized speech using the ASR model and", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 347, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 505, + 359 + ], + "score": 1.0, + "content": "calculate character error rate (CER). In this way, we can assess a degree of degradation in linguistic", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 358, + 342, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 342, + 370 + ], + "score": 1.0, + "content": "accuracy compared to the CER of the ground truth speech.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 374, + 505, + 440 + ], + "lines": [ + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "score": 1.0, + "content": "The CER results are shown in Table 11. BigVGAN has the consistently lowest CERs, which are also", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "score": 1.0, + "content": "close to ground truth. Furthermore, BigVGAN-base (14M) outperforms the largest HiFi-GAN (112M)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 349, + 409 + ], + "score": 1.0, + "content": "on four (en, de, ca, fr) out of six languages, ties on one", + "type": "text" + }, + { + "bbox": [ + 350, + 397, + 369, + 408 + ], + "score": 0.5, + "content": "\\mathrm { ( z h ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 396, + 506, + 409 + ], + "score": 1.0, + "content": ", and underperforms only on one", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "language (es). The results further validate that BigVGAN is the most linguistically accurate universal", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 419, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 505, + 430 + ], + "score": 1.0, + "content": "vocoder with the lowest artifacts and show the benefits of the model to be applied to various speech", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 429, + 160, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 160, + 442 + ], + "score": 1.0, + "content": "applications.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 108, + 456, + 437, + 469 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 439, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 439, + 471 + ], + "score": 1.0, + "content": "G ADDITIONAL DETAILS OF MECHANICAL TURK EVALUATION", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 481, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 106, + 482, + 504, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 504, + 493 + ], + "score": 1.0, + "content": "We use Mechanical Turk for MOS and SMOS tests with 450 unique ratings per model. We allow each", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 493, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 505, + 505 + ], + "score": 1.0, + "content": "worker to evaluate up to three random samples for diverse participants. Crowdsourcing evaluation", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 504, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 506, + 516 + ], + "score": 1.0, + "content": "is considered to be a noisy process. 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MethodEnglishGermanCatalanSpanishFrenchMandarin
Ground Truth6.2983.7853.0014.1945.45025.431
SC-WaveRNN15.1559.5085.76310.19812.42747.653
UnivNet-c32†6.9144.0373.0584.4395.71726.504
HiFi-GAN (V1)6.9064.0703.0824.4905.77027.179
HiFi-GAN (112M)6.6153.9203.0434.3155.60826.174
BigVGAN-base6.5743.9053.0344.3355.59426.174
BigVGAN6.4363.8293.0284.2615.51725.756
", + "type": "table", + "image_path": "962b180033c0ce580a760ad5f549ce7db1681a0d8c8952eb0dfb2fd087af08dd.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 142, + 103, + 468, + 137.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 142, + 137.33333333333334, + 468, + 171.66666666666669 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 142, + 171.66666666666669, + 468, + 206.00000000000003 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "title", + "bbox": [ + 107, + 223, + 320, + 236 + ], + "lines": [ + { + "bbox": [ + 105, + 222, + 321, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 321, + 237 + ], + "score": 1.0, + "content": "F LINGUISTIC ACCURACY EVALUATION", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 106, + 247, + 505, + 369 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 261 + ], + "score": 1.0, + "content": "In this section, we evaluate the quality of neural vocoders in terms of linguistic accuracy. To", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 259, + 505, + 270 + ], + "spans": [ + { + "bbox": [ + 106, + 259, + 505, + 270 + ], + "score": 1.0, + "content": "measure linguistic accuracy of the synthesized speech from BigVGAN on in-distribution and various", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 270, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 505, + 282 + ], + "score": 1.0, + "content": "out-of-distribution languages, we conduct experiments using a high-performance Conformer-based", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "(Gulati et al., 2020) automatic speech recognition (ASR) model on multiple languages. We use", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 292, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 505, + 304 + ], + "score": 1.0, + "content": "conformer_transducer_large model, where the pretrained checkpoints for the considered", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 506, + 316 + ], + "score": 1.0, + "content": "languages are publicly available from the NVIDIA NeMo (Kuchaiev et al., 2019) toolkit. We generate", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 314, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 314, + 505, + 326 + ], + "score": 1.0, + "content": "samples from BigVGAN using test set corpus from Mozilla Common Voice (MCV) 8.0 dataset for", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 325, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 505, + 337 + ], + "score": 1.0, + "content": "the following languages: English (en), German (de), Catalan (ca), Spanish (es), French (fr), and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "Mandarin (zh). Then, we obtain transcriptions from the synthesized speech using the ASR model and", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 347, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 505, + 359 + ], + "score": 1.0, + "content": "calculate character error rate (CER). In this way, we can assess a degree of degradation in linguistic", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 358, + 342, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 342, + 370 + ], + "score": 1.0, + "content": "accuracy compared to the CER of the ground truth speech.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 247, + 506, + 370 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 374, + 505, + 440 + ], + "lines": [ + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 386 + ], + "score": 1.0, + "content": "The CER results are shown in Table 11. BigVGAN has the consistently lowest CERs, which are also", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 398 + ], + "score": 1.0, + "content": "close to ground truth. Furthermore, BigVGAN-base (14M) outperforms the largest HiFi-GAN (112M)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 349, + 409 + ], + "score": 1.0, + "content": "on four (en, de, ca, fr) out of six languages, ties on one", + "type": "text" + }, + { + "bbox": [ + 350, + 397, + 369, + 408 + ], + "score": 0.5, + "content": "\\mathrm { ( z h ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 396, + 506, + 409 + ], + "score": 1.0, + "content": ", and underperforms only on one", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "language (es). The results further validate that BigVGAN is the most linguistically accurate universal", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 419, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 505, + 430 + ], + "score": 1.0, + "content": "vocoder with the lowest artifacts and show the benefits of the model to be applied to various speech", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 429, + 160, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 160, + 442 + ], + "score": 1.0, + "content": "applications.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 375, + 506, + 442 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 456, + 437, + 469 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 439, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 439, + 471 + ], + "score": 1.0, + "content": "G ADDITIONAL DETAILS OF MECHANICAL TURK EVALUATION", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 481, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 106, + 482, + 504, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 504, + 493 + ], + "score": 1.0, + "content": "We use Mechanical Turk for MOS and SMOS tests with 450 unique ratings per model. We allow each", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 493, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 505, + 505 + ], + "score": 1.0, + "content": "worker to evaluate up to three random samples for diverse participants. Crowdsourcing evaluation", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 504, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 506, + 516 + ], + "score": 1.0, + "content": "is considered to be a noisy process. We apply several filtering criteria to improve the reliability of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 514, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 505, + 528 + ], + "score": 1.0, + "content": "workers : i) We restrict the listeners to be native English speakers in the United States. ii) We only", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 360, + 538 + ], + "score": 1.0, + "content": "allow listeners with the evaluation acceptance rate higher than", + "type": "text" + }, + { + "bbox": [ + 360, + 526, + 380, + 536 + ], + "score": 0.87, + "content": "98 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 380, + 525, + 505, + 538 + ], + "score": 1.0, + "content": ", and the number of previously", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "approved HITs higher than 100 to participate in this test. iii) We conduct 5-scale MOS/SMOS", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 547, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 505, + 560 + ], + "score": 1.0, + "content": "evaluation with random ordering of the model samples, with the inclusion of ground-truth samples as", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "the hidden control questions. We apply filtering by rejecting ratings from those workers who score", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 570, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 506, + 582 + ], + "score": 1.0, + "content": "the ground-truth samples as 3 or even lower, because the listeners are instructed to give score 5 for", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 581, + 458, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 458, + 594 + ], + "score": 1.0, + "content": "ground-truth samples after listening to the same ground-truth sample prior to the rating.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 482, + 506, + 594 + ] + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/dev/wiBEFdAvl8L/wiBEFdAvl8L_content_list.json b/parse/dev/wiBEFdAvl8L/wiBEFdAvl8L_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..56d4bae236c2c53eace1f5becc2776b736332a07 --- /dev/null +++ b/parse/dev/wiBEFdAvl8L/wiBEFdAvl8L_content_list.json @@ -0,0 +1,1330 @@ +[ + { + "type": "text", + "text": "GLIPv2: Unifying Localization and VL Understanding ", + "text_level": 1, + "bbox": [ + 174, + 122, + 821, + 148 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haotian Zhang∗1†, Pengchuan Zhang $\\ast 2 \\dagger \\spadesuit$ , Xiaowei $\\mathbf { H } \\mathbf { u } ^ { 3 }$ , Yen-Chun Chen3, Liunian Harold Li4† Xiyang $\\mathbf { D a i } ^ { 3 }$ , Lijuan Wang3, Lu Yuan3, Jenq-Neng Hwang1, Jianfeng Gao3 ", + "bbox": [ + 187, + 199, + 848, + 231 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Washington, 2Meta AI, 3Microsoft, 4UCLA {haotiz,hwang}@uw.edu,pengchuanzhang@fb.com,liunian.harold.li@cs.ucla.edu, {Xiaowei.Hu,Yen-Chun.Chen,Xiyang.Dai,lijuanw,luyuan,jfgao}@microsoft.com ", + "bbox": [ + 299, + 231, + 743, + 271 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 289, + 535, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present GLIPv2, a grounded VL understanding model, that serves both localization tasks (e.g., object detection, instance segmentation) and Vision-Language (VL) understanding tasks (e.g., VQA, image captioning). GLIPv2 elegantly unifies localization pre-training and Vision-Language Pre-training (VLP) with three pre-training tasks: phrase grounding as a VL reformulation of the detection task, region-word contrastive learning as a novel region-word level contrastive learning task, and the masked language modeling. This unification not only simplifies the previous multi-stage VLP procedure but also achieves mutual benefits between localization and understanding tasks. Experimental results show that a single GLIPv2 model (all model weights are shared) achieves near SoTA performance on various localization and understanding tasks. The model also shows (1) strong zero-shot and few-shot adaption performance on open-vocabulary object detection tasks and (2) superior grounding capability on VL understanding tasks. Code is released at https://github.com/microsoft/GLIP. ", + "bbox": [ + 233, + 320, + 766, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 174, + 522, + 310, + 539 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, a general interest arises in building general-purpose vision systems [21, 24, 56, 42], also called vision foundation models [6, 57], that solve various vision tasks simultaneously, such as image classification [30], object detection [39], and Visual-Language (VL) understanding [3, 11, 27]. Of particular interest, is the unification between localization tasks (e.g., object detection [39] and segmentation [8, 20]) and VL understanding tasks (e.g., VQA [3] and image captioning [11]). Localization pre-training benefits VL tasks [1, 59], and the “localization- $\\mathrm { . > V L P ^ { \\prime } }$ two-stage pretraining procedure [41, 49, 13, 48, 34, 32, 61, 37, 35] is the common practice in VL community. A long-standing challenge is the unification of localization and understanding, which aims at mutual benefit between these two kinds of tasks, simplified pre-training procedure, and reduced pre-training cost. ", + "bbox": [ + 173, + 553, + 825, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, these two kinds of tasks appear to be dramatically different: localization tasks are visiononly and require fine-grained output (e.g., bounding boxes or pixel masks), while VL understanding tasks emphasize fusion between two modalities and require high-level semantic outputs (e.g., answers or captions). ", + "bbox": [ + 174, + 696, + 825, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[21, 24, 56] have made early attempts at unifying these tasks in a straightforward multi-task manner, where a low-level visual encoder is shared across tasks, and two separate high-level branches are designed for localization and VL understanding, respectively. The localization tasks are still vision-only and do not benefit from the rich semantics in vision-language data. As a result, such unified models see the marginal mutual benefit or even performance degradation [24] compared with task-specific models. ", + "bbox": [ + 174, + 760, + 825, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we identify “VL grounding” as a “meta”-capability for localization and understanding capabilities. VL grounding involves not only understanding an input sentence but also localizing the mentioned entities in the image (see an example in Figure 1). We build a grounded VL understanding model (GLIPv2) as a unified model for localization and VL understanding tasks. ", + "bbox": [ + 178, + 849, + 820, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/adbfa03373afd92f159bb9702b1f0cfe1bcc88f56f93dcf4b3e7468790aeb8e9.jpg", + "image_caption": [ + "Figure 1: Left: GLIPv2, a pre-trained grounded VL understanding model, unifies various localization and VL understanding tasks. These two kinds of tasks mutually benefit each other, and enables new capabilities such as language-guided detection/segmentation and grounded VQA/captioning. Right: Additional examples from ODinW (detection), LVIS (segmentation), VQA, COCO Captioning. " + ], + "image_footnote": [], + "bbox": [ + 173, + 99, + 821, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 435, + 821, + 463 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Localization ${ \\bf \\Pi } + { \\bf \\delta V L }$ understanding $=$ grounded VL understanding. Localization tasks involve both localization and semantic classification, where classification can be cast as a VL understanding problem using the classification-to-matching trick (Section 3.1). Therefore, we reformulate localization tasks as VL grounding tasks, in which the language input is a synthesized sentence as the concatenation of category names [36]. Localization data are turned into VL grounding data, accordingly. The massive VL understanding data (image-text pairs) can be easily turned into VL grounding data in a self-training manner [36]. Therefore, GLIPv2 has a unified pre-training process: all task data are turned into grounding data and GLIPv2 is pre-trained to perform grounded VL understanding. ", + "bbox": [ + 173, + 469, + 825, + 594 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A stronger VL grounding task: inter-image region-word contrastive learning. GLIP [36] proposes the phrase grounding task as its pre-training task, which we argue is an easy task and does not fully utilize data information. For example, in the VL grounding task in Figure 1, the phrase grounding task only requires the model to match a given image region to one of the three phrases in the text input, i.e., “green, pink striped, or plain white umbrella?”. This 1-in-3 choice is very easy, only requires color understanding, but loses lots of information in this grounding data: the umbrellas are not any other colors, like black, yellow, etc; objects in those regions are umbrellas but not any other categories, like car, bike, etc. From a contrastive learning view, this phrase grounding task only has two negatives. More negatives can be created from this annotation and thus enable stronger contrastive learning. In GLIPv2, we introduce the novel inter-image region-word contrastive learning task, which leverages phrases from other sentences in the same batch as potential negatives, as another much stronger VL grounding task. This new region-word contrastive loss enables GLIPv2 to learn more discriminative region-word features and demonstrates improvements over all downstream tasks. ", + "bbox": [ + 173, + 601, + 825, + 780 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GLIPv2 achieves mutual benefit between localization and VL understanding. 1) Experimental results (Table 2) show that a single GLIPv2 model (all model weights are shared) achieves near SoTA performance on various localization and understanding tasks. 2) Thanks to semantic-rich annotations from the image-text data, GLIPv2 shows superior zero-shot and few-shot transfer learning ability to open-world object detection and instance segmentation tasks, evaluated on the LVIS dataset and the \"Object Detection in the Wild (ODinW)\" benchmark. 3) GLIPv2 enables language-guided detection and segmentation ability, and achieves new SoTA performance on the Flick30K-entities phrase grounding and PhraseCut referring image segmentation tasks. 4) Inherently a grounding model, GLIPv2 leads to VL understanding models with strong grounding ability, which are self-explainable and easy to debug. For example, GLIPv2, when GLIPv2 is finetuned on VQA, it can answer questions while localizing mentioned entities (see Figure 1 and Section 4.4). ", + "bbox": [ + 174, + 786, + 825, + 911 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 90, + 823, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 Related Work ", + "text_level": 1, + "bbox": [ + 174, + 142, + 321, + 160 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Localization models. Traditionally, localization tasks such as object detection and segmentation are single-modality and output bounding boxes or pixel masks [45, 38, 23, 14, 46, 10, 9]. One challenge of these single-modality models lies in generalization to rare and novel concepts: it is hard to collect localization data that cover many rare categories [20]. A long line of research focuses on this generalization problem, under the name of zero-shot [4, 62, 7, 63], weakly-supervised [18, 5, 52], or open-vocabulary [58, 19] localization. Built upon MDETR [25] and GLIP [36], GLIPv2 converts localization tasks into a grounded vision-language task using the classification-to-matching trick (Section 3). Thus GLIPv2 can learn from the semantic-rich vision-language data and shows strong performance on open-vocabulary localization tasks. ", + "bbox": [ + 173, + 176, + 825, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision-language understanding models. Vision-language (VL) understanding tasks such as VQA [3], image captioning [11], and image-text retrieval [26] involve understanding visual semantics and how they are expressed in natural language. Many VL models (e.g., BUTD) [2, 59] rely on a pre-trained localization model as their visual encoder; the downside is the pro-longed “localization- $\\mathrm { . > V L P ^ { \\prime } }$ pre-training pipeline [41, 49, 13, 48, 34, 32, 61, 37, 35]. In contrast, GLIPv2 simplifies the pre-training pipeline and enables grounded VL understanding for better interpretability (Section 4.4). ", + "bbox": [ + 173, + 308, + 825, + 405 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unifying localization and understanding. [21, 24, 56] made pioneering efforts in unifying localization and understanding. However, localization tasks are still treated as single-modality tasks, while VL tasks involve two modalities. The unification is achieved via straightforward multi-tasking: a low-level visual encoder is shared across tasks and two separate branches are designed for localization and VL understanding. Such unified models do not bring evident mutual benefit and often underperform task-specific models. In contrast, GLIPv2 identifies grounded VL understanding as a meta-task for localization and understanding. The task unification brings architecture unification: the unified grounded VL understanding model empowers a localization branch with VL capacity, arriving at a unified branch that excels at both tasks. ", + "bbox": [ + 174, + 411, + 825, + 535 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GLIPv2 vs GLIP. 1) GLIP shows that grounded pre-training improves localization. GLIPv2 further shows grounded pre-training improves VL understanding and thus leads to a unified model for localization and VL understanding. 2) GLIPv2 introduces the inter-image region-word contrastive loss, which is another and stronger grounding task than the pre-training task in GLIP. The proposed loss can be viewed as a region-word level generalization of the prevalent image-level contrastive learning [33, 44, 55]. 3) GLIPv2 outperforms GLIP on all benchmarks with the same pre-training data. ", + "bbox": [ + 173, + 542, + 825, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 GLIPv2: Unifying Localization and VL Understanding ", + "text_level": 1, + "bbox": [ + 174, + 662, + 665, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the reformulation of object detection as a generalized phrase grounding task in GLIP [36], we unify both localization and VL understanding tasks as grounded vision-language tasks. A grounded vision-language task takes both image and text as inputs, and outputs region-level understanding results (e.g., detection, segmentation) and/or image-level understanding results with associated grounding/localization information (e.g., VQA, image captioning). We will present the unified grounded VL formulation and architecture in Section 3.1, the pre-training losses in Section 3.2, and transfer to downstream tasks in Section 3.3. ", + "bbox": [ + 174, + 696, + 825, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 A Unified VL Formulation and Architecture ", + "text_level": 1, + "bbox": [ + 174, + 814, + 519, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At the center of GLIPv2’s unified formulation is the classification-to-matching trick, which reformulates any task-specific fixed-vocab classification problem as an task-agnostic open-vocabulary vision-language matching problem. The best example is the reformulation of image classification as image-text matching in CLIP [44], which enables the model to learn from raw image-text data directly, and achieves strong zero-shot results on open-vocabulary classification tasks. In GLIPv2, we replace every semantic classification linear layer in traditional single-modality vision models with a vision-language matching dot-product layer. ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 171, + 90, + 823, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Figure 1, GLIPv2’s unified VL architecture is based on the generic architecture we term Architecture $\\mathbf { I I }$ . It consists of a dual encoder, denoted as $\\operatorname { E n c } _ { V }$ and $\\mathrm { E n c } _ { L }$ , and a fusion encoder, denoted as $\\mathtt { E n c } _ { V L }$ . The model takes an image-text pair (Img, Text) as input, and extract visual and text features as below: ", + "bbox": [ + 173, + 126, + 825, + 181 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/9c4c35248a4e870f2c38dc839ab0d8037a874caf49120b986c1f4d9c5d8cb008.jpg", + "text": "$$\n\\begin{array} { r } { \\dot { O } = \\mathrm { E n c } _ { V } ( \\mathrm { I m g } ) , \\quad \\mathring { P } = \\mathrm { E n c } _ { L } ( \\mathrm { T e x t } ) , \\quad O , P = \\mathrm { E n c } _ { V L } ( \\mathring { O } , \\mathring { P } ) , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 285, + 185, + 709, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $( \\mathring { O } , \\mathring { P } )$ and $( O , P )$ denote the image/text features before and after VL fusion, respectively. ", + "bbox": [ + 171, + 215, + 808, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Vision-Language understanding tasks. Arch $\\mathbf { I I }$ is the most popular model architecture for VL understanding tasks. Given the cross-modality fused representations $O$ and $P$ , it is straightforward to add lightweight task-specific heads for various VL tasks. For example, GLIPv2 adds a two-layer MLP on top of text features $P$ as the masked language modeling (MLM) head, to perform the MLM pre-training. We provide model details of VQA and image captioning in Section 3.3. ", + "bbox": [ + 173, + 236, + 825, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(Language-guided) object detection and phrase grounding. Following GLIP [36], GLIPv2 uses the classification-to-matching trick to unify detection and grounding. More specifically, for detection, we simply replace the class logits $S _ { \\mathrm { c l s } } = \\dot { O } W ^ { T }$ , where $W$ is the weight matrix of the box classifier, with a task-agnostic region-word similarity logits $S _ { \\mathrm { g r o u n d } } = O P ^ { T }$ , where text features $P$ are label embeddings from a task-agnostic language encoder. As shown in Figure 1, object detection and phrase grounding share the same input/output format and model architecture. See GLIP [36] for more details. Their only difference is the input text format: (1) for object detection, the text input is a string of concatenated candidate object labels; (2) for phrase grounding, the text input is a natural language sentence. We refer to GLIP [36] for more details. ", + "bbox": [ + 173, + 311, + 825, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(Language-guided) instance segmentation and referring image segmentation. Given the object detection results, an instance segmentation head is added to classify each pixel within the box into a semantic class. Again, GLIPv2 uses the classification-to-matching trick to produce a unified instance segmentation head for the standard instance segmentation tasks and the referring image segmentation tasks and leverage both types of data for its pre-training. This classification-to-matching trick can also apply to many other semantic classification heads in single modality CV models (e.g., semantic segmentation) and thus transfers them to language-guided CV models. ", + "bbox": [ + 173, + 443, + 825, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 GLIPv2 Pre-training ", + "text_level": 1, + "bbox": [ + 174, + 556, + 359, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The GLIPv2 is pre-trained with three pre-training losses: phrase grounding loss $\\mathcal { L } _ { \\mathrm { g r o u n d } }$ from a vision-language reformulation of the object detection task, region-word contrastive loss ${ \\mathcal { L } } _ { \\mathrm { { i n t e r } } }$ from a novel region-word level contrastive learning task, and the standard masked language modeling loss ${ \\mathcal { L } } _ { \\mathrm { m l m } }$ proposed in BERT [16]. ", + "bbox": [ + 174, + 582, + 825, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/c874fa33d82791f42fa3e1f490f0ae7435a5315c9aad040f33e7db4814a657dc.jpg", + "text": "$$\n{ \\mathcal { L } } _ { \\mathrm { G L I P v 2 } } = \\underbrace { { \\mathcal { L } } _ { \\mathrm { l o c } } + { \\mathcal { L } } _ { \\mathrm { i n t r a } } } _ { { \\mathcal { L } } _ { \\mathrm { g r o u n d } } } + { \\mathcal { L } } _ { \\mathrm { i n t e r } } + { \\mathcal { L } } _ { \\mathrm { m l m } }\n$$", + "text_format": "latex", + "bbox": [ + 370, + 645, + 627, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to losses in detection tasks, the grounding loss $\\mathcal { L } _ { \\mathrm { g r o u n d } }$ has two parts: the localization loss $\\mathcal { L } _ { \\mathrm { l o c } }$ trains localization heads with bounding-box supervision, e.g., RPN loss, box regression loss and/or centerness loss [50]; the intra-image region-word alignment loss ${ \\mathcal { L } } _ { \\mathrm { { i n t r a } } }$ is essentially the semantic classification/retrieval loss for each region. ", + "bbox": [ + 174, + 695, + 825, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intra-image region-word alignment loss. Given one image-text pair (Img, Text), we obtain the image and text features after cross-modality fusion $O$ and $P$ . The Intra-image region-word alignment loss is computed by ", + "bbox": [ + 173, + 757, + 825, + 799 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/0be0841c0aae48d63e473967074a95a8a74b18edc87f3085747021cde4ae32f8.jpg", + "text": "$$\n\\mathcal { L } _ { \\mathrm { i n t r a } } = l o s s ( O P ^ { T } ; T ) ,\n$$", + "text_format": "latex", + "bbox": [ + 419, + 799, + 578, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $O P ^ { T }$ is the similarity score between image regions and word tokens, and $T$ is the target affinity matrix determined by the ground-truth annotations. The loss function loss is typically a cross-entropy loss for two-stage detectors [46] and a focal loss [38] for one-stage detectors. ", + "bbox": [ + 174, + 820, + 825, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, as discussed in Section 1, this intra-image region-word contrastive learning is rather weak in the sense of contrastive learning, due to the limited number of phrases that can one caption can contain. GLIP [36] alleviates this problem by appending a few negative sentences to form a longer text input with more (negative) phrases. However, constrained by the maximal length of text tokens (256 in GLIP and GLIPv2), only a few negative sentences can be added and the number of negative phrases remains in the order of $1 0 \\mathrm { { ^ { \\circ } s } }$ . This small-negative-example problem also exists in detection data [36] when the input text cannot include all class names in a detection dataset, e.g., Objects365. ", + "bbox": [ + 174, + 868, + 825, + 912 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 90, + 825, + 147 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inter-image region-word contrastive loss. In GLIPv2, we propose using phrases from other imagetext pairs in the same batch as negative examples, which effectively increases the number of negative examples to the order of 1000’s, with nearly negligible additional computational cost. ", + "bbox": [ + 173, + 152, + 825, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As in (1), given a batch of image-text pairs $( \\mathrm { I m } { \\bf g } ^ { i } , \\mathrm { T e x t } ^ { i } ) _ { i = 1 } ^ { B }$ and their ground-truth annotations $( T ^ { i } ) _ { i = 1 } ^ { B }$ , the model produces the image and text features before and after VL fusion, denoted as $( \\mathring { O } ^ { i } , \\mathring { P } ^ { i } ) _ { i = 1 } ^ { B }$ and $( O ^ { i } , P ^ { i } ) _ { i = 1 } ^ { B }$ , respectively. Then as illustrated in Figure 2 (Left), a batch-wise similarity matrix Sbatchground and a batch-wise target affinity matrix $T ^ { \\mathrm { b a t c h } }$ are constructed by considering all the image regions and text phrases across this batch. Their $( i , j )$ ’th blocks are obtained as below: ", + "bbox": [ + 173, + 199, + 825, + 280 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/81bc5c6654fef04a2279e58e7654796038923ba61800f178482e67e4dc8983d3.jpg", + "text": "$$\nS _ { \\mathrm { g r o u n d } } ^ { \\mathrm { b a t c h } } [ i , j ] = \\bar { O } ^ { i } ( \\bar { P } ^ { j } ) ^ { T } , \\quad T ^ { \\mathrm { b a t c h } } [ i , j ] = \\left\\{ \\begin{array} { l l } { T ^ { i } , } & { \\mathrm { i f ~ } i = j } \\\\ { \\mathrm { o b t a i n e d ~ b y ~ l a b e l ~ p r o p a g a t i o n , } } & { \\mathrm { o t h e r w i s e . } } \\end{array} \\right.\n$$", + "text_format": "latex", + "bbox": [ + 215, + 282, + 782, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The inter-image region-word contrastive loss is then defined as the standard bi-directional contrastive loss applied on all image regions and phrases in this batch: ", + "bbox": [ + 173, + 320, + 823, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "${ \\mathrm { ~ \\dot { \\ z } _ { \\mathrm { { i n t e r } } } = \\ c r o s s \\_ e n t r o p y \\mit \\mathrm { \\mit \\mathrm { \\ l o s s } ( \\cal S \\mit _ { \\mathrm { { g r o u n d } } } ^ { \\mathrm { b a t c h } } , \\mit T \\mathrm { ^ { b a t c h } , \\ a x i s = 0 ) + \\ c r o s s \\mit \\mathrm { _ { - } \\ e n t r o p y \\mit \\mathrm { \\mit { \\mit \\mathrm { \\ l o s s } ( \\cal S \\mit _ { \\mathrm { { g r o u n d } } } ^ { \\mathrm { b a t c h } } , \\mathrm { T \\mathrm { ^ { b a t c h } , \\ a x i s = 1 ) \\mit . } } } } } } } } } $ (5) ", + "bbox": [ + 171, + 352, + 825, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared with that in the inter-image contrastive loss (3), the number of negatives is multiplied by batch size $B$ in this inter-image contrastive loss (5). We elaborate two important details in (4). (1) GLIPv2 uses the image text features $( \\mathring { O } ^ { i } , \\mathring { P } ^ { i } ) _ { i = 1 } ^ { B }$ before VL fusion, not $( O ^ { i } , P ^ { i } ) _ { i = 1 } ^ { B }$ after VL fusion, to compute the batch-wise similarity matrix in the inter-image contrastive loss (4). Otherwise, the image and text features after VL fusion would have seen the paired information (1), and thus the model can easily rule out the negatives from misaligned images/texts. (2) We cannot simply assign all regions and texts from unpaired image-text as negative pairs, as done in the standard contrastive loss in CLIP [44]. Instead, we determine the off-diagonal blocks in the target affinity matrix $T ^ { \\mathrm { b a t c h } }$ by label propagation. For example, as illustrated in Figure 2 (Left), if a region is annotated as “person”, it should be a positive pair with all “person” phrases in detection-type texts. We do not propagate positives to grounding-type texts (natural sentences) because phrases in sentences carry contexts that are unique to that image-sentence pair. ", + "bbox": [ + 173, + 382, + 826, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pre-training with both detection and paired-image-text data. GLIPv2 pre-training data is in the image-text-target triplet format (Img, Text, $T$ ), where the target affinity matrix $T$ contains the box-label localization annotations. We also use massive image-text pair data (Img, Text) to pre-train GLIPv2, by generating grounding boxes $\\hat { T }$ for phrases in the text with the GLIP pre-trained model from [36]. The human-annotated OD/grounding data provides high-fidelity localization supervision, while the massive image-text data greatly improves the concept diversity for GLIPv2. ", + "bbox": [ + 174, + 556, + 825, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Second-stage pre-training of the segmentation head. GLIPv2 performs a second-stage pre-training of the language-guided segmentation head on both instance segmentation and image referring segmentation data, while fixing all other parts of the model. ", + "bbox": [ + 174, + 648, + 825, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3 Transfer GLIPv2 to Localization and VL Tasks ", + "text_level": 1, + "bbox": [ + 174, + 705, + 542, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We introduce two ways to easily transfer GLIPv2 to various downstream tasks. In addition, GLIPv2 can perform conventional VL tasks (e.g., VQA) along with localization, effectively making every task we consider a “grounded VL understanding” task. ", + "bbox": [ + 174, + 731, + 825, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One model architecture for all. GLIPv2 can be transferred to downstream tasks by fine-tuning the model with an (optional) task-specific head. 1) For detection and segmentation tasks, no task-specific head is needed as the pre-training architecture can inherently perform detection and segmentation. 2) For $V L$ tasks: for VQA, a classification head is added on top of the hidden representation of the start-of-sequence token; for caption generation, we train with a unidirectional language modeling loss, which maximizes the likelihood of the next word given context. We use a unidirectional attention mask and prevent the image part from attending to the text in the fusion layers. ", + "bbox": [ + 173, + 779, + 825, + 877 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One set of weights for all. There is a growing interest in developing models that can be transferred to various tasks while only changing the least amount of parameters to save training time and storage cost [47, 31]. Following GLIP, GLIPv2 can be transferred to localization tasks in a zero-shot or a prompt-tuning setting (Section 4.2). One single GLIPv2 model can serve various tasks, where each task only keeps few or no parameters. Of particular interest is the prompt tuning setting. For a certain localization task, the text prompt is the same for all input images; thus, we could directly tune $\\mathring { P }$ , a small prompt embedding matrix, to adapt GLIPv2 to new tasks. Prompt tuning in a deep-fused model such as GLIPv2 is different from the conventional linear probing/prompt tuning setting [53, 44, 60] in shallow-interacting vision models such as CLIP. The latter can also be viewed as only tuning a small prompt/softmax embedding $P$ ; however, tuning $P$ only affects the very last layer of the model while the visual representation is still frozen. In contrast, GLIP/GLIPv2’s visual representation is conditioned on the prompt embedding $\\mathring { P }$ ; tuning $\\mathring { P }$ changes the text, visual, as well as fused embeddings. As a result, prompt tuning in GLIPv2 is highly effective, often matching the performance of fine-tuning (see Table 2). This is in contrast to the common observation in CV that linear probing lags behind fine-tuning by a large gap [22]. ", + "bbox": [ + 173, + 883, + 821, + 911 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a2126e3d117d3e41b61f4a05e16f3c1c31302f73ea9c4df2bc4eaaa3b313fdd2.jpg", + "image_caption": [ + "Figure 2: GLIPv2 pre-training losses: the intra-image alignment loss ${ \\mathcal { L } } _ { \\mathrm { { i n t r a } } }$ (right) takes features after VL fusion and compute loss over region-word pairs within each image-text pair; the inter-image contrastive loss (left) ${ \\mathcal { L } } _ { \\mathrm { { i n t e r } } }$ takes features before VL fusion and computes loss over all region-word pairs across a batch of image-text pairs. Label propagation is used to determine the off-diagonal blocks of the ${ \\mathcal { L } } _ { \\mathrm { { i n t e r } } }$ target matrix (4). " + ], + "image_footnote": [], + "bbox": [ + 245, + 88, + 756, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 441, + 825, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Grounded VL understanding. GLIPv2 also enables grounded VL understanding, where we retain the ability to perform grounding when fine-tuning the model to a downstream VL task. This increases the interpretability of the model. Specifically, we first turn the VL data of the downstream task into grounded VL data using a pre-trained GLIP model. Then we train the model with both the downstream task head and grounding head. For VQA, the model is trained to predict the answer and ground entities in the question as well as the implied entity in the answer; for captioning, the model is trained to predict the next word given the context and ground the current decoded word. By tuning localization tasks into a grounded VL task and augmenting VL tasks with grounding ability, we effectively turn every task into a grounded VL understanding task (see examples in Figure 1). ", + "bbox": [ + 174, + 631, + 825, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 Experiments ", + "text_level": 1, + "bbox": [ + 174, + 780, + 312, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we show that GLIPv2 serves as a performant and easy-to-deploy general-purpose vision system. 1) One Model Architecture for All (Section 4.1). GLIPv2 can be directly fine-tuned to both localization and VL understanding tasks with minimal architecture change. It achieves performance on par with SOTA models with specialized architectures. 2) One Model Weight for All (Section 4.2). GLIPv2 can be transferred to localization tasks in a zero-shot manner with zero parameter update; with prompt tuning, a single GLIPv2 model can achieve comparable performance with fully fine-tuned settings on both localization and understanding tasks. ", + "bbox": [ + 174, + 814, + 825, + 911 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6cd7c0f65e75390d9324f84d095e636f3a8a2c560c5e413db97af98e75c0eebb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelModel TypeCOCO-Det (test-dev)ODinW (test)LVIS (minival)COCO-Mask (test-dev)Flickr30K PhraseCut (test)(test)VQA (test-dev/test-std) (Karpathy-test)Captioning
Mask R-CNN [23]39.8-33.3/--/37.1==
DETR[9]42.017.8/-==
DyHead-T[15]49.760.8===
DyHead-L [15]60.3*===
VisualBERT[34]Understanding=71.33=70.8/71.0=
UNITER[12]==73.8/74.0=
VinVL[59]=76.5/76.6130.8
GPV[21]Localization &=·=62.5/-102.3
UniT[24]42.3=67.6/-=
MDETR[25]==24.2/-=84.353.770.6 /70.6■
Unicorn [56]Understanding Localization &=■=80.4=69.2/69.4119.1
GLIP-T[36]55.264.9==85.7-=-
GLIP-L [36]Understanding 61.5*68.9==87.1-=-
GLIPv2-T(Ours)Localization55.566.550.6/41.453.5/42.086.559.471.6/71.8122.1
GLIPv2-B (Ours)&58.869.457.3/46.259.0/45.887.561.373.1/73.3128.5
GLIPv2-H(Ours)Understanding60.6 (62.4*)70.459.8 / 48.859.8 / 48.987.761.374.6/74.8131.0
", + "bbox": [ + 179, + 88, + 823, + 279 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1: One model architecture results. For COCO-Det test-dev, \\* indicates multi-scale evaluation. For LVIS, we report the numbers for both bbox and segm on minival to avoid data contamination due to the pre-training. For Flickr30K test, we report the metric under R@1. For COCO-Mask, we also report both bbox and segm on test-dev. ", + "bbox": [ + 173, + 290, + 825, + 344 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following GLIP [36], we adopt Swin Transformer [40] as the image encoder $\\operatorname { E n c } _ { V }$ , text transformers [51, 44] as the text encoder $\\mathrm { E n c } _ { L }$ , Dynamic Head [15] with language-aware deep fusion [36] as the fusion encoder $\\mathtt { E n c } _ { V L }$ , and Hourglass network [43] as instance segmentation head feature extractor. We train GLIPv2 at three scales: GLIPv2-T, GLIPv2-B, and GLIPv2-H. ", + "bbox": [ + 174, + 377, + 825, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "GLIPv2-T has the same model config and initialization as GLIP-T: Swin-Tiny and BERT-Base as the dual encoder. The model is pre-trained on the following data: 1) O365, 2) GoldG as in GLIP-T (C), and 3) Cap4M, 4M image-text pairs collected from the web with boxes generated by GLIP-T [36]. GLIPv2-B/GLIPv2-H are based on Swin-Base/Swin-Huge and the pre-layernorm text transformer [17] as dual encoder, and are initialized from the UniCL [55] checkpoints. We observe much stabler training with GPT-type pre-layernorm transformer [17] than BERT-type post-layernorm transformer. The training data contain: 1) FiveODs (2.78M data) 1; 2) GoldG as in MDETR [25]; and 3) C $\\mathrm { C 1 5 M + S B U }$ , 16M public image-text data with generated boxes by GLIP-L [36]. Segmentation heads of GLIPv2 models are pre-trained on COCO, LVIS [20] and PhraseCut [54], with all other model parameters are frozen. ", + "bbox": [ + 173, + 440, + 825, + 579 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note All datasets above were collected by the creators (cited) and consent for any personally identifiable information (PII) was ascertained by the authors where necessary. Due to limited space, we refer to supplementary for details of training recipes and hyper-parameters. ", + "bbox": [ + 174, + 585, + 825, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1 One Model Architecture for All ", + "text_level": 1, + "bbox": [ + 176, + 648, + 431, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare GLIPv2 to existing object detection and vision-language pre-training methods on a wide range of tasks. We fine-tune the model on 8 different downstream tasks and report the performance in Table 1. We make the following observations. ", + "bbox": [ + 176, + 678, + 823, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "GLIPv2 v.s. specialized Localization methods. GLIPv2 outperforms previous localization models on generalization to both common and rare classes and domains with a single model architecture and pre-training stage. 1) OD on common categories (COCO-Det), GLIPv2-T achieves 5.8 improvement compared to the standard DyHead-T trained on O365 (55.5 v.s. 49.7). GLIPv2-H reaches $6 2 . 4 \\mathrm { A P }$ on test-dev, and surpass the performance of the previous SoTA model GLIP-L. 2) OD on rare / unseen categories (LVIS), GLIPv2-T outperforms a supervised MDETR on the bbox by a great margin (59.8 v.s. 24.2). 3) Generalization to diverse real-word tasks (ODinw), GLIPv2-T (55.5) performs better than original GLIP-T (64.9) on the average of 13 public datasets; GLIPv2-B outperforms GLIP-L by 0.5 AP. 4) Instance segmentation (COCO-Mask & PhraseCut), for traditional instance segmentation (i.e., COCO-Mask), GLIPv2-H outperforms the well-known Mask R-CNN by a great margin on segm. ", + "bbox": [ + 173, + 724, + 825, + 864 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5d5cfcaa7c298e146446e3d1b12c5586deb63bf590099b9abb3cbde84e40b543.jpg", + "table_caption": [ + "Table 2: One set of weights results v.s. Original GLIP. \\* indicates multi-scale evaluation. Numbers in red clearly points out the difference between the prompt tuning and full fine-tuning results (see Table 1). Numbers in gray mean that they are not in zero-shot manner. $\\dagger$ : these two numbers are artificially high due to some overlap between COCO-minival and VisualGenome-train. " + ], + "table_footnote": [], + "table_body": "
ModelDirect EvaluationPrompt Tuning
COCO-Mask (minival)ODinW (test)LVIS-Det (minival)Flickr30K (minival)COCO-Det (test-dev)ODinW (test)LVIS (minival)COCO-Mask (test-dev)PhraseCut (test)
GLIP-T46.6/-46.526.085.7二46.5---
GLIP-L49.8/-52.137.387.158.867.9==-
GLIPv2-T47.3/35.748.529.086.053.4 (-2.1)64.8 (-1.7)49.3 / 34.8 (-13/-6.6)53.2 / 41.2 (-0.3/-0.8)49.4
GLIPv2-B61.9†/43.454.248.587.259.0 (+0.2)67.3 (-2.1)56.8 / 41.7 (-0.5/-4.5)58.8 / 44.9 (-0.2/-0.9)55.9
GLIPv2-H64.1/47.455.550.187.760.2 /61.9* (-0.4 /-0.5)69.1 (-1.3)59.2 / 43.2 (-0.6/-5.7)59.8 / 47.2 (-0.0/-1.7)56.1
", + "bbox": [ + 176, + 89, + 821, + 179 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f74b465df4d065f84ce4d92f60d2f682c7a078495dd46741bd6fcf8dd804923.jpg", + "image_caption": [ + "Figure 3: Data efficiency of GLIPv2 on ODinW. The $\\mathbf { X }$ -axis is the amount of task-specific data, from zero-shot to all data. Y-axis is the average AP across 13 datasets. " + ], + "image_footnote": [], + "bbox": [ + 210, + 282, + 444, + 436 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0964c95f8e55b2cf8144e1f4296110a4a790c3f21f69c14deb11c82f00feede5.jpg", + "table_caption": [ + "Table 3: Zero-shot, prompt tuning, and full finetuning performance on ODinW. GLIPv2 models exhibit superior data efficiency. " + ], + "table_footnote": [], + "table_body": "
ModelZero-Shot 0Prompt Tuning /Fine Tuning
13510All
DyHead-T 0365 [36]-=---
33.843.646.450.860.8
Lloc + Lintra (GLIP-T)46.549.953.755.556.662.4
51.354.956.458.464.9
Lloc + Lintra +Linter48.452.155.656.758.362.9
51.455.356.659.566.3
Lloc +Lintra +Linter +Cmm48.552.455.657.458.864.8
52.855.657.459.766.5
", + "bbox": [ + 506, + 299, + 821, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For language-guided segmentation (i.e., PhraseCut), compared to MDETR, GLIPv2-T achieves an improvement of 5.7 mask AP. ", + "bbox": [ + 174, + 535, + 823, + 563 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "GLIPv2 v.s. specialized VL Understanding methods. GLIPv2 rivals with SoTA specialized models for VL tasks. 1) For VQA, GLIPv2 outperforms VisualBERT and UNITER and approaches the previous SoTA model VinVL. 2) For Captioning, the best GLIPv2 even surpasses VinVL (VinVL and GLIPv2 are not trained with CIDEr optimization). ", + "bbox": [ + 174, + 569, + 825, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "GLIPv2 v.s. localization and VL models. Prior works such GPV, UniT and Unicorn have also explored unifying localization and VL models (see a discussion in Section 2). GLIPv2 outperforms all previous systems on both localization and VL tasks. For the best GLIPv2-H, it outperforms the UniT by a great margin (18.3 AP) on COCO object detection tasks. Meanwhile, it also surpasses UniT’s performance on VQA by 6.9 points and GPV’s peformance on Image Captioning as well. ", + "bbox": [ + 174, + 631, + 825, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Takeaway. Most notably, GLIPv2 outperforms previous “unified” models (GPV, UniT, MDETR, Unicorn) by a large margin. This is the first time that a single model architecture could achieve near SoTA performance on both localization and understanding. In contrast, in prior work, there exists certain trade-off between localization and understanding: models that aim to achieve high understanding performance tend to have lower localization performance (e.g., UNiT’s detection performance is limited to the DETR [9] architecture), as it is not trivial to merge a SoTA localization branch and a SoTA VL branch into a single model. ", + "bbox": [ + 174, + 707, + 825, + 804 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2 One Set of Model Parameters for All ", + "text_level": 1, + "bbox": [ + 176, + 827, + 465, + 842 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "GLIPv2 is pre-trained to perform grounding; thus it can be transferred to various localization tasks with changing zero or few parameters. We evaluate GLIPv2 under two such settings: 1) direct evaluation, where we transfer the model “as is” without any parameter change, and 2) prompt tuning, where only the prompt embedding is tuned for specific tasks (Section 3.3). ", + "bbox": [ + 176, + 856, + 825, + 911 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Direct evaluation. The pre-trained GLIPv2 can be directly evaluated on any object detection task (by concatenating the object categories into a text prompt) and visual grounding task without any further tuning. We evaluate the models on four localization tasks: COCO, ODinW, LVIS, and Flickr30, and their results are presented in Table 2. Note that for GLIPv2-B and GLIPv2-H, the training sets of Flick30K and LVIS are present in the pre-training data. Thus, reported numbers on these metrics are not zero-shot evaluation (we have marked them gray). For all other evaluation results, the models are evaluated in zero-shot settings without any further tuning. ", + "bbox": [ + 174, + 90, + 825, + 188 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "GLIPv2 can be effortlessly transferred to different localization tasks without further tuning. 1) For COCO, GLIPv2-T achieves a zero-shot performance of 47.3 without seeing any COCO training images. This surpasses well-established supervised systems (e.g., Mask R-CNN) and also outperforms GLIP-T by 0.7 AP. 2) For ODinW, GLIPv2 also shows strong zero-shot performance. GLIPv2-T (48.5) surpasses the GLIP-T (46.5). Meanwhile, the zero-shot performance of GLIPv2-B and GLIPv2- H even surpasses the 10-shot tuning performance of DyHead-T (to be introduced in Figure 3). 3) For LVIS, GLIPv2-T achieves a 3 AP improvement performance compared to the GLIP-T. 4) For Flickr30K, GLIPv2-B achieves even higher number (87.2) compared to original GLIP-L (87.1). ", + "bbox": [ + 174, + 194, + 825, + 305 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Prompt Tuning. Following GLIP, GLIPv2 supports efficient prompt tuning: the visual representation is heavily conditioned on the text representation due to the deep fusion block (Section 3.3); thus we could fine-tune only the prompt embedding for each task but still maintain high performance. ", + "bbox": [ + 174, + 320, + 825, + 363 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Prompt tuning $G L I P \\nu 2$ achieves similar performance as full fine-tuning. When comparing the performance of each task in Table 1 and 2 at the same time, for GLIPv2, prompt tuning performance almost matches the one model architecture results on localization tasks, without changing any of the grounding model parameters. ", + "bbox": [ + 174, + 369, + 825, + 425 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.3 GLIPv2 as a Strong Few-Shot Learner ", + "text_level": 1, + "bbox": [ + 174, + 441, + 480, + 457 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We demonstrate GLIPv2’s performance on ODinW datasets with respect to different amounts of training data in Figure 3. The performance improvement between GLIPv2-T and GLIP-T exhibits more superior data efficiency for prompt tuning. We compare with the SoTA detector DyHead-T, pre-trained on Objects365 in Table 3. It can be seen that a zero-shot GLIPv2-T (48.5) outperforms a outperforms 5-shot DyHead-T (46.4) while the performance of one-shot GLIPv2-H (61.3) surpasses a all-shot fully supervised DyHead-T (60.8). ", + "bbox": [ + 174, + 467, + 825, + 550 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "4.4 Analysis ", + "text_level": 1, + "bbox": [ + 174, + 568, + 271, + 583 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Pre-training losses Table 4 shows the performance of the downstream tasks with different variants of our method. Compared to the GLIP pre-training tasks with only intra-image region-word contrastive loss (Row 3), adding inter-image word-region loss (Row 5) substantially improves the pre-trained model performance across all the object detection tasks (COCO, ODinW, and LVIS) on both zero-shot and fine-tuned manner. Consistent with common observations from most VL understanding methods, adding MLM loss (Row4) benefits for learning the representation for understanding tasks (Flick30k, VQA, and Captioning). Furthermore, using all three losses together at the 1st stage pre-training and doing the 2nd stage pre-training without MLM on OD and GoldG data, GLIPv2 (Row6) can perform well on both the localization and VL understanding tasks. ", + "bbox": [ + 173, + 593, + 825, + 718 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "An additional stage of pre-training is applied for small models (GLIPv2-T and GLIPv2-B) due to limited model capacity. In order to achieve higher performance on both localization and understanding tasks, we find that including all data (even with some noise) and MLM loss in the first stage of pre-training will benefit the model for learning a better representation of both localization and understanding capability. Since the OD tasks require the model with more accurate localization ability, in our 2nd stage of pre-training, we decide to eliminate the MLM loss. The large model (GLIPv2-H) does not need this additional stage because it has enough capacity to learn both wordregion alignment and MLM together in a single stage. ", + "bbox": [ + 174, + 724, + 825, + 835 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Pre-training data Table 5 reports the last checkpoint results on GLIPv2 when we do the scaling up of pre-training data. As more weak image-text pair data (Cap) is involved in our training, it benefits both standard/in-domain (i.e., COCO, Flickr30K) and large-domain gap (i.e., ODinW, LVIS) tasks. We also show that by adding the inter-image region-word contrastive helps when we are fixing the data at the same scale. For large-domain gap tasks, adding the inter-image region-word contrastive ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/4a6e2da9ed6355c0ede7a60aeb0869bd98076132f0221978182aa486fd2a0d91.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Row ModelCOCOODinWLVIS|Flickr30K VQA Captioning
1No pre-train-/50.6-/60.81164.6111.5
2+Lmlm-/48.5-/37.41164.6110.9
3+ Lloc+Lintra46.6/55.2 46.5/64.926.085.769.4119.7
4+Lloc+Lintra+Lmlm47.0/55.2 47.6/66.228.586.569.8120.7
5+Lloc+Lintra+Linter47.1/55.4 48.4/66.328.685.868.7120.4
6+Lloc+Lintra+Linter+Lmlm47.3/55.5 48.5/66.529.086.370.7122.1
", + "bbox": [ + 245, + 89, + 756, + 180 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Table 4: Pre-training losses on Tiny-scale model. Involving intra-image region-word alignment loss $\\mathcal { L } _ { \\mathrm { { i n t r a } } }$ , inter-image region-word contrastive loss ${ \\mathcal { L } } _ { \\mathrm { i n t e r } }$ and MLM loss ${ \\mathcal { L } } _ { \\mathrm { m l m } }$ will benefit both localization and understanding tasks. ", + "bbox": [ + 173, + 190, + 826, + 233 + ], + "page_idx": 9 + }, + { + "type": "table", + "img_path": "images/9df54e7b36e47d6eb7909b5fdb14fcd7644562d55b724a448461d1f4a0ecafbb.jpg", + "table_caption": [ + "Table 5: Pre-train data scale up on Base-scale model. Results are reported at the last checkpoint. See supplementary for results at all checkpoints. " + ], + "table_footnote": [], + "table_body": "
LinterPre-train DataCoCoODinWLVISFlick30K
X0365,GoldG48.0643.1425.684.36
0365,GoldG48.5942.6426.983.90
0365,GoldG,Cap4M48.2151.3534.285.56
X0365,GoldG,Cap4M48.7952.7035.085.50
×0365,GoldG,Cap12M48.5049.3235.585.79
√0365,GoldG,Capl2M49.2653.1536.685.84
", + "bbox": [ + 176, + 251, + 490, + 330 + ], + "page_idx": 9 + }, + { + "type": "table", + "img_path": "images/690b5f2437704313520c3d51016469f178ba944faf2725d90140abf4e2de5a14.jpg", + "table_caption": [ + "Table 6: GLIPv2 can perform captioning and grounding at the same time (a.k.a., grounded VL understanding). " + ], + "table_footnote": [], + "table_body": "
ModelCOCO Caption B4 CIDErSPICER@1 R@5Flickr30K GroundingR@10°
GLIPv2-T36.5119.8 21.680.894.496.5
GLIPv2-B37.4123.0 21.981.094.596.5
", + "bbox": [ + 511, + 258, + 828, + 320 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "loss will further boost the model to learn better representation. For more detailed scaling-up effects on various tasks under all the checkpoints for GLIP and GLIPv2, refer to Appendix. ", + "bbox": [ + 173, + 412, + 823, + 440 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Note that the (Img, Text, $T$ ) data used in GLIPv2 pre-training can be just human-annotated data (Row1&2 in Table 5), with which GLIPv2 pre-training does not involve any pseudo data from a pre-trained grounding/localization model. In order to achieve the best performance, GLIPv2 uses image-text pair data with pseudo boxes (Cap) from a pre-trained GLIP model (Row3-6 in Table 4), which is trained with the same \"grounded VL understanding\" task but just with smaller data. ", + "bbox": [ + 174, + 446, + 825, + 516 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Grounded Vision-Language Understanding GLIPv2 can be trained to perform a VL task and grounding at the same time (Section 3.3). We denote such an ability as grounded VL understanding. In Figure 1, we showcase grounded predictions of GLIPv2 on VQA and COCO captions. We also conduct quantitative evaluations (Table 6). The model achieves strong performance for both VL understanding (on COCO Caption) and localization (on Flickr30K Grounding). Such an ability to produce high-level semantic outputs (i.e., answers and captions) and supporting localization results is another appealing trait of GLIPv2, as potential users can have a better understanding of the model behaviour. See more detailed analysis and qualitative examples in the Appendix. ", + "bbox": [ + 174, + 522, + 825, + 633 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5 Conclusion and Social Impacts ", + "text_level": 1, + "bbox": [ + 174, + 656, + 462, + 672 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "This paper proposes GLIPv2, a unified framework for VL representation learning that serves both localization tasks and VL understanding tasks. We experimentally verify the effectiveness of the unified model and the novel region-word contrastive learning. Compared to existing methods, GLIPv2 achieves competitive near SoTA performance on various localization and understanding tasks. However, additional analysis of the data and the model is necessary before deploying it in practice since large-scale web data may contain unintended private information, unsuitable images/text, or some bias leakage. Further investigation may be needed for web data due to the above issues. ", + "bbox": [ + 174, + 689, + 826, + 786 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6 Acknowledgement ", + "text_level": 1, + "bbox": [ + 174, + 809, + 359, + 825 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We thank anonymous reviewers for their comments and suggestions. Additional thanks go to the Microsoft Research Horizontal AI Team and Microsoft Alexander Multi-modal Team for providing computer resources for large-scale training. The baseline models used in our experiments are based on the open-source code released in the GitHub repository; we acknowledge all the authors who made their code public, which tremendously accelerates our project progress. ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "References ", + "text_level": 1, + "bbox": [ + 174, + 89, + 266, + 106 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "top-down attention for image captioning and visual question answering. 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