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- .gitattributes +190 -0
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.gitattributes
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parse/train/HJSA_e1AW/HJSA_e1AW_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Tsp2PL7-GQ/Tsp2PL7-GQ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Tsp2PL7-GQ/Tsp2PL7-GQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HJSA_e1AW/HJSA_e1AW_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Tsp2PL7-GQ/Tsp2PL7-GQ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Tsp2PL7-GQ/Tsp2PL7-GQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/LT0KSFnQDWF/LT0KSFnQDWF_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Syhr6pxCW/Syhr6pxCW_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ryUlhzWCZ/ryUlhzWCZ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ryUlhzWCZ/ryUlhzWCZ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1YNw6sxg/r1YNw6sxg_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1YNw6sxg/r1YNw6sxg_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1YNw6sxg/r1YNw6sxg_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Bye9LiR9YX/Bye9LiR9YX_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Bye9LiR9YX/Bye9LiR9YX_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Bye9LiR9YX/Bye9LiR9YX_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/eaAM_bdW0Q/eaAM_bdW0Q_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/eaAM_bdW0Q/eaAM_bdW0Q_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HJ0UKP9ge/HJ0UKP9ge_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HJ0UKP9ge/HJ0UKP9ge_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BJ--gPcxl/BJ--gPcxl_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BJ--gPcxl/BJ--gPcxl_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BJ--gPcxl/BJ--gPcxl_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/rkdU7tCaZ/rkdU7tCaZ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/rkdU7tCaZ/rkdU7tCaZ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/rkdU7tCaZ/rkdU7tCaZ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ryF7rTqgl/ryF7rTqgl_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ryF7rTqgl/ryF7rTqgl_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ryF7rTqgl/ryF7rTqgl_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/D9I3drBz4UC/D9I3drBz4UC_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/D9I3drBz4UC/D9I3drBz4UC_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/D9I3drBz4UC/D9I3drBz4UC_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/xyGFYKIPTDJ/xyGFYKIPTDJ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/xyGFYKIPTDJ/xyGFYKIPTDJ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/xyGFYKIPTDJ/xyGFYKIPTDJ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1efEp4Yvr/H1efEp4Yvr_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1efEp4Yvr/H1efEp4Yvr_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1efEp4Yvr/H1efEp4Yvr_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1meywxRW/H1meywxRW_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1meywxRW/H1meywxRW_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1meywxRW/H1meywxRW_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hygab1rKDS/Hygab1rKDS_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hygab1rKDS/Hygab1rKDS_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hygab1rKDS/Hygab1rKDS_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hye-LiR5Y7/Hye-LiR5Y7_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hye-LiR5Y7/Hye-LiR5Y7_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hye-LiR5Y7/Hye-LiR5Y7_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/RJ7XFI15Q8f/RJ7XFI15Q8f_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/RJ7XFI15Q8f/RJ7XFI15Q8f_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/RJ7XFI15Q8f/RJ7XFI15Q8f_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/37nvvqkCo5/37nvvqkCo5_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/37nvvqkCo5/37nvvqkCo5_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/37nvvqkCo5/37nvvqkCo5_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/QkljT4mrfs/QkljT4mrfs_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/QkljT4mrfs/QkljT4mrfs_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/QkljT4mrfs/QkljT4mrfs_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/AAWuCvzaVt/AAWuCvzaVt_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/AAWuCvzaVt/AAWuCvzaVt_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/AAWuCvzaVt/AAWuCvzaVt_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hyp3i2xRb/Hyp3i2xRb_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hyp3i2xRb/Hyp3i2xRb_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/fLnsj7fpbPI/fLnsj7fpbPI_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SkPoRg10b/SkPoRg10b_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SkPoRg10b/SkPoRg10b_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HyxAfnA5tm/HyxAfnA5tm_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HyxAfnA5tm/HyxAfnA5tm_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HyxAfnA5tm/HyxAfnA5tm_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1gza2NtwH/H1gza2NtwH_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1gza2NtwH/H1gza2NtwH_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1gza2NtwH/H1gza2NtwH_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/B1e0X3C9tQ/B1e0X3C9tQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/B1e0X3C9tQ/B1e0X3C9tQ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/B1e0X3C9tQ/B1e0X3C9tQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Hk99zCeAb/Hk99zCeAb_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/rJe10iC5K7/rJe10iC5K7_layout.pdf filter=lfs diff=lfs merge=lfs -text
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| 5920 |
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| 5923 |
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| 5924 |
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| 5928 |
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| 5933 |
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| 5935 |
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| 5936 |
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| 5938 |
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| 5939 |
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| 5940 |
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| 5941 |
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| 5942 |
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| 5943 |
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| 5944 |
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| 5945 |
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| 5946 |
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| 5947 |
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| 5948 |
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| 5950 |
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| 5953 |
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| 5954 |
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| 5957 |
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| 6000 |
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| 6002 |
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| 6003 |
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| 6004 |
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# TANKBind: Trigonometry-Aware Neural NetworKs for Drug-Protein Binding Structure Prediction
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Wei Lu∗† Galixir Technologies
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Qifeng Wu† Fudan University
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Jixian Zhang† Galixir Technologies
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Jiahua Rao Sun Yat-sen University
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Chengtao Li Galixir Technologies
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Shuangjia Zheng∗† Galixir Technologies Sun Yat-sen University
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# Abstract
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Illuminating interactions between proteins and small drug molecules is a longstanding challenge in the field of drug discovery. Despite the importance of understanding these interactions, most previous works are limited by hand-designed scoring functions and insufficient conformation sampling. The recently-proposed graph neural network-based methods provides alternatives to predict protein-ligand complex conformation in a one-shot manner. However, these methods neglect the geometric constraints of the complex structure and weaken the role of local functional regions. As a result, they might produce unreasonable conformations for challenging targets and generalize poorly to novel proteins. In this paper, we propose Trigonometry-Aware Neural networKs for binding structure prediction, TANKBind, that builds trigonometry constraint as a vigorous inductive bias into the model and explicitly attends to all possible binding sites for each protein by segmenting the whole protein into functional blocks. We construct novel contrastive losses with local region negative sampling to jointly optimize the binding interaction and affinity. Extensive experiments show substantial performance gains in comparison to state-of-the-art physics-based and deep learning-based methods on commonly-used benchmark datasets for both binding structure and affinity predictions with variant settings.
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# 1 Introduction
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Proteins are the workhorses of human bodies. They have a wide range of interaction partners, small molecules, other proteins, and DNA/RNA, for example. In this paper, we focus on drug-like small molecules as the interaction partners for proteins. The words ligands, drugs, small molecules and compounds are used interchangeably throughout the paper. Small molecules activate or inhibit activities of target proteins through mostly non-covalent interactions. In 2021, FDA approved 60 new drugs, among which 36 were small molecules Kinch et al. [2022]. Understanding the mechanismof-actions and off-target effects of drug molecules typically requires analyzing the structures of the related protein-ligand complexes Boopathi et al. [2021], Xie et al. [2011], but solving the complex structure experimentally is a an extremely challenging task. Despite tremendous effort spent on this topic over the last 50 years, only about 19,000 protein-ligand complex structures have been solved experimentally using $\mathbf { X }$ -ray, Cryo-EM or NMR Liu et al. [2015]. On the other hand, the estimated chemical space of drug is $\mathrm { 1 0 ^ { 6 \bar { 0 } } }$ and estimated number of unique proteins in human body is at least 20, 000, making the number of possible protein-ligand complex far exceeding the number of experimentally solved structures Reymond et al. [2010], Ponomarenko et al. [2016].
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On the computational side, molecular docking is a commonly-used method for predicting the proteinligand complex structures the corresponding binding affinities Trott and Olson [2010], Friesner et al. [2004], Ackloo et al. [2022], Gentile et al. [2022]. Generally, the docking process involves three main stages: (1) locating favorable binding sites given a protein target; (2) sampling the ligand conformation as well as its position and orientation within these sites; (3) scoring and ranking the conformations of the complex using physics-inspired empirical energy functions to refine the structures and assess protein-ligand binding affinity. Due to its good interpretability and usability, docking has been integrated in drug development process for a long time and a number of successful cases have been reported Anderson [2003]. However, most open-source docking packages use atomlevel pairwise scoring functions, limiting the capacity to model the many-body effects. Moreover, they need to sample a large range of possible ligand poses and protein side-chain conformations, which leads to relatively high computational cost Trott and Olson [2010], Jain [2006].
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To overcome these challenges, we propose a two-stage deep learning framework to neuralize the molecular docking process and predict the binding structures with better accuracy and lower computational cost. In the first stage, we segment the whole protein into functional blocks and predict their interactions with the ligand, creating an protein-ligand interaction energy landscape using a novel trigonometry-aware architecture. The trigonometry module has enough model capacity to capture many-body effects. In the second stage, we prioritize the crystallized binding structures by constrastively ensuring a weaker binding affinity for non-native interactions. In particular, our model improves the drug-protein binding structure predictions with a combination of (i) a novel trigonometry-aware architecture that jointly infuses trigonometry constraints and excluded-volume effects as inductive biases, (ii) a new divide-and-conquer strategy that constructs the protein-ligand local functional binding pairs in a contrastive manner. By doing so, we create a funnel-shape energy landscape for the inter-molecular interaction, removing the need of extensive sampling Jumper et al. [2021], Jain [2006], Chen et al. [2020a], Onuchic et al. [1997].
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Our novel method is well-motivated by leveraging prior knowledge from physics and biology. Physically, the inter-molecular trigonometry module, inspired by the intra-molecular Evoformer module used in AlphaFold2 Jumper et al. [2021], ensures that our energy landscape disfavors configurations of protein-ligand complexes that are prohibited by laws of nature, for instance, no two atoms could overlap and the distances between atoms have to satisfy triangle inequality theorem in euclidean geometry. More details on these constraints is shown in section 3.3. Biologically, the functional regions of proteins tend to be more conserved and closely associated with binding De Juan et al. [2013], Glaser et al. [2003], allowing the model to learn critical information and generalize better to unseen proteins.
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We evaluate our algorithm against several state-of-the-art deep learning and physics-based docking methods on task of binding structure prediction under multiple settings. Compared with baselines, our model increase the fraction of predictions with ligand root-mean-square deviation (RMSD) less than $5 \mathring \mathrm { A }$ by $16 \%$ in re-docking setting, $22 \%$ in self-docking setting, and $42 \%$ in the more difficult newprotein setting. Our model is also capable of predicting binding affinities, achieving better correlations with experimentally-measured values than sequence-based, structure-based and even complex-based methods. We also show that TankBind has the potential to discover novel mechanism-of-actions of drug molecules by identifying unseen protein binding sites.
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# 2 Related Work
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Geometric Deep Learning for drug discovery. There has been a surge of interest in integrating geometric priors for representation learning in the domain of drug discovery Jumper et al. [2021], Baek et al. [2021], Jing et al. [2021], Ganea et al. [2021], Jin et al. [2021], Ingraham et al. [2019], AlQuraishi [2019], Schütt et al. [2017], Somnath et al. [2021]. Recent researches have incorporated geometric information and symmetry properties of the input signals to improve the spatial perception of the learned representations. These works have been shown great potential in various applications like protein structure modeling Jumper et al. [2021], Baek et al. [2021], Jing et al. [2021], Ganea et al. [2021], molecular low-energy generation prediction Shi et al. [2021], Xu et al. [2022], Méndez-Lucio et al. [2021], property/function prediction Schütt et al. [2017], Somnath et al. [2021] and molecule design Jin et al. [2021], Ingraham et al. [2019]. Among which, AlphaFold 2 achieved outstanding performance in protein structure prediction Jumper et al. [2021], representing the state-of-the-art geometry-aware method. Our work is inspired from this groundbreaking work, adapting it from the intra-molecular structure prediction to the field of predicting the inter-molecular binding structure and binding affinity.
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Figure 1: Overview of TankBind Model. The whole protein is divided into blocks of radius $2 0 \mathring \mathrm { A }$ , each block is going through the TankBind model along with the drug compound. Both protein blocks and drug compound are modeled as graphs. The block-compound interaction matrix evolved multiple times with additional input based on the distance maps of the protein block and the compound through trigonometry module. Based on the updated interaction embedding, the model predicts the binding affinity of the compound to the blocks and the block-ligand distance maps. A constrastive loss function is used to ensure the native block binds stronger to the compound than decoys.
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Drug-protein Interaction (DPI) prediction. The goal of DPI prediction is to illustrate the binding structure and binding affinity between protein and ligand. Apart from docking-based approaches Trott and Olson [2010], Friesner et al. [2004], prior machine learning-based works either use complex-free models to predict the binding affinity directly from protein-ligand pairs Wang and Dokholyan [2021], Li et al. [2020], Tsubaki et al. [2019], Gao et al. [2018], Karimi et al. [2019], Zheng et al. [2020] or make predictions through complex structure that has been previously obtained by experimental or docking approaches Jiménez et al. [2018], Lim et al. [2019], Morrone et al. [2020]. The former ones are less interpretable while the latter requires data involved in vast experimental costs and labour. More recently, EquiBind Stärk et al. [2022] takes a new approach by directly predicting the key points on both the protein and the compound, and aligning their key points through the ingeniously designed optimal transport loss. However, this method may generate compound structures clashing with the protein structures and currently lacks the capability to predict the binding affinity, limiting its use in drug discovery. In contrast, our approach has a trigonometry module imposing geometry constraints and a state-of-the-art binding affinity prediction capability.
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# 3 TankBind Model
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# 3.1 Overview of TankBind model
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The general protocol of our model is shown in figure 1. The encoding of protein and compound is described in section 3.2. The rationale and implementation of trigonometry module is detailed in section 3.3. The design of loss functions for training is described in section 3.4. The generation of atom coordinates from predicted inter-molecular distance map is introduced in section 3.5.
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# 3.2 Structural encoders of protein and drug
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Our model input is the separate structures of a protein and a drug compound, both encoded as graphs. Indices $i , k$ always operate on the residue dimension, $j , k ^ { \prime }$ always on the compound dimension. $n$ is the number of protein nodes and $m$ is the number of compound nodes.
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Protein. The protein is represented as a proximity 3D graph following Jing et al. [2020]. We denote the protein graph as $\mathcal G ^ { p } = \mathsf { \bar { ( } } \mathcal V ^ { p } , \mathcal E ^ { p } )$ , where each node $\bar { \mathfrak { v } } _ { i } ^ { p } \in \mathcal { V } ^ { p }$ corresponds to an amino acid, and has feature $\mathbf { h } _ { \mathfrak { v } ^ { p } } ^ { ( i ) }$ with both scalar and vector features. Each node also has a position $\mathbf { x } _ { i } ^ { p } \in \mathbb { R } ^ { 3 }$ equal to the Cartesian coordinate of $C _ { \alpha _ { i } }$ . An edge $\mathfrak { e } _ { i k } ^ { p }$ exists if $\mathfrak { v } _ { k } ^ { p }$ is among the 30 nearest neighbors of $\mathfrak { v } _ { i } ^ { p }$ . Each edge ${ \mathfrak { e } } _ { i k } ^ { p } \in { \mathcal { E } } ^ { p }$ also encodes both the scalar and the vector features. We then apply the geometric vector perceptrons (GVP) Jing et al. [2020, 2021] to embed the protein and arrive at feature $\mathbf { h } ^ { p } \in \mathbb { R } ^ { n \times s }$ after graph propagation, where $n$ is the number of nodes and $s$ is the embedding size.
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To implicitly model side-chain flexibility, we choose a residue-level representation ignoring the finer details of protein structure, separating our method from other methods that use all-atoms or surface vertexes representation Jiang et al. [2021], Gainza et al. [2020]. Also, as shown by Jumper et al. [2021, 2018], residue-level embedding is enough to infer the side-chain conformation.
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Motivated by protein co-evolution De Juan et al. [2013] and divide-and-conquer theory, the protein graph, $\mathcal G ^ { p }$ , is further divided into subgraphs $\mathcal { G } ^ { p ^ { \prime } }$ . Each subgraph $\mathcal G ^ { p ^ { \prime } }$ includes all the $\mathfrak { v } _ { i } ^ { p }$ and $\mathfrak { e } _ { i j } ^ { p }$ inside the functional block. The subgraph is denoted as $\mathcal { G } ^ { p ^ { \prime } } = ( \{ \mathfrak { v } _ { i } ^ { p } , \mathfrak { e } _ { i k } ^ { p } \} \ | \| \mathbf { x } _ { i } ^ { p } - \mathbf { x } _ { o } \| \leq 2 0 \mathring { \mathrm { A } }$ , $\| \mathbf { x } _ { k } ^ { p } - \mathbf { x } _ { o } \| \leq$ $2 0 \mathring \mathrm { A } )$ , where $\mathbf { x } _ { o }$ is the center of the functional block predicted by a widely-used ligand-agnostic method, P2rank (published in 2018)Krivák and Hoksza [2018]. Justification for the size of radius and use of P2rank is described in appendix G.
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Drug compound. The drug compound is represented as a graph using TorchDrug toolkit Zhu et al. [2022]. The compound graph is denoted as $\mathcal G ^ { c } = ( \mathcal V ^ { c } , \mathcal E ^ { c } )$ where each node ${ \mathfrak { v } } _ { j } ^ { c } \in \mathcal { V } ^ { c }$ corresponds to a heavy atom (non-hydrogen atom), and has feature $\mathbf { h } _ { \mathfrak { v } ^ { c } } ^ { ( j ) }$ and each edge ${ \mathfrak { e } } _ { j k ^ { \prime } } ^ { c }$ has feature $\mathbf { h } _ { \mathfrak { e } ^ { c } } ^ { ( j k ^ { \prime } ) }$ . We use Graph Isomorphism Network (GIN) $\mathrm { X u }$ et al. [2018] to embed the compound and arrive at feature $\mathbf { h } ^ { c } \in \mathbb { R } ^ { m \times s }$ after graph propagation, where $m$ is the number of heavy atoms and $s$ is the embedding size.
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# 3.3 Details of trigonometry module
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The compound feature, $\mathbf { h } ^ { c }$ , and the protein block feature, $\mathbf { h } ^ { p }$ , are used to form the initial interaction embedding $\mathbf { z } ^ { ( 0 ) } \in \mathbb { R } ^ { n \times m \times s }$ , ${ \bf z } _ { i j } ^ { ( 0 ) } = { \bf h } _ { i } ^ { p } \odot { \bf h } _ { j } ^ { c }$ . The interaction embedding will be further updated with pair distance map of protein nodes, $D _ { i k } ^ { p } = \| \dot { \mathbf { x } } _ { i } ^ { p } - \mathbf { x } _ { k } ^ { p } \|$ and pair distance map of compound nodes, $D _ { j k ^ { \prime } } ^ { c } = \left\| \mathbf { x } _ { j } ^ { c } - \mathbf { x } _ { k ^ { \prime } } ^ { c } \right\|$ .
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The rationale for including both the pair distance map of the protein nodes and the pair distance map of the compound nodes in updating the protein-compound interaction embedding is explained with two simplified examples. As shown in the upper part of figure 2, if a protein node A is in close proximity with compound node B, then compound node C will not be in contact with node A due to the large distance constraint between node B and C. Distance constraint between compound nodes B and D could also force a node $\mathrm { D }$ to be in close contact with protein node A.
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To build this observation of trigonometry constraints into our model, we design the following module to update the interaction embedding, in layer $\ell .$ , $\bar { \forall } ( i , j )$ :
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Figure 2: Rationale for including trigonometry module. Upper: Protein node in square, compound nodes in circles. Lower: Trigonometry module ensures that the interaction between protein node $i$ and compound node $j$ depends on all protein and compound nodes $k , k ^ { \prime }$ .
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$$
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\widetilde { \mathbf { z } } _ { i j } ^ { ( \ell ) } = \mathbf { z } _ { i j } ^ { ( \ell ) } + \Phi \big ( \sum _ { k = 1 } ^ { n } \mathbf { p } _ { i k } \mathbf { t } _ { k j } ^ { ( \ell ) } + \sum _ { k ^ { \prime } = 1 } ^ { m } \mathbf { t } _ { i k ^ { \prime } } ^ { \prime ( \ell ) } \mathbf { c } _ { k ^ { \prime } j } \big ) \odot \mathbf { g } \big ( \mathbf { z } _ { i j } ^ { ( \ell ) } \big )
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$$
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where $\mathbf { p } _ { i k } = \phi ( D _ { i k } ^ { p } )$ is the linear embedding of encoded pair distance between protein nodes. $\mathbf { p } \in$ $\mathbb { R } ^ { n \times n \times s }$ , $n$ is the number of nodes in protein block, $s$ is the embedding size. ${ \bf c } _ { j k ^ { \prime } } = \phi ( D _ { j k ^ { \prime } } ^ { c } )$ is the linear embedding of encoded pair distance between compound nodes. $\mathbf { c } \in \mathbb { R } ^ { m \times m \times s }$ , $m$ is the number of compound nodes. t(ℓ)ij and t′(ℓ)ij are the same gated linear transformations of $\mathbf { z } _ { i j } ^ { ( \ell ) }$ but with nonared parameters, $\mathbf t _ { i j } ^ { ( \ell ) } = \mathrm { L i n e a r } ( \mathbf z _ { i j } ^ { ( \ell ) } ) \odot \mathbf { g } ( \mathbf z _ { i j } ^ { ( \ell ) } ) , \mathbf t ^ { ( \ell ) } \in \mathbb { R } ^ { n \times m \times s } , \mathbf { g } ( \mathbf z _ { i j } ^ { ( \ell ) } ) = \mathrm { s i g m o i d } ( \mathrm { L i n e a r } ( \mathbf z _ { i j } ^ { ( \ell ) } ) ) ,$ $\Phi$ is a layernorm function followed by a linear transformation.
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Another type of physical constraint need to be take into consideration is the excluded-volume (Van Der Waals) and saturation effect. As shown in the upper figure 2, if protein node A forms a strong interaction, hydrogen bonding for example, with compound node B, then node $\mathbf { D }$ is unlikely to form the same type of interaction with node A because node A has limited number of hydrogen donors or acceptors. To account for these effects, we designed a self-attention module to modulate the interaction between a protein node and all compound nodes by taking the whole interaction between this protein node and all compound nodes into consideration.
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$$
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\begin{array} { r l } & { \dot { \mathbf { z } } _ { i j } ^ { ( \ell ) } = \tilde { \mathbf { z } } _ { i j } ^ { ( \ell ) } + \Phi ( \mathrm { c o n c a t } _ { h } \big ( \displaystyle \sum _ { k ^ { \prime } = 1 } ^ { m } ( w _ { i j k ^ { \prime } } ^ { ( \ell ) h } \mathbf { v } _ { i k ^ { \prime } } ^ { ( \ell ) h } ) \odot \mathbf { g } ^ { h } ( \tilde { \mathbf { z } } _ { i j } ^ { ( \ell ) } ) \big ) ) } \\ & { w _ { i j k ^ { \prime } } ^ { ( \ell ) h } = \mathrm { s o f t m a x } _ { k ^ { \prime } } ( \mathbf { q } _ { i j } ^ { ( \ell ) h ^ { \top } } \mathbf { k } _ { i k ^ { \prime } } ^ { ( \ell ) h } ) } \end{array}
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$$
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, where q(ℓ)ij $\mathbf { q } _ { i j } ^ { ( \ell ) h } , \mathbf { k } _ { i j } ^ { ( \ell ) h } , \mathbf { v } _ { i j } ^ { ( \ell ) h }$ are linear transformation of $\tilde { \mathbf { z } } _ { i j } ^ { ( \ell ) }$ , $h$ is number of attention heads. Function $\mathbf { g } ^ { h }$ is the standard $\mathbf { g }$ with reshaping the embedding into heads at the end, is a linear transformation.
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Lastly, a non-linear transition module is added to transit the interaction embedding to the next layer through multilayer perceptron, z(ℓij $\mathbf z _ { i j } ^ { ( \ell + 1 ) } = \mathbf { M L P } ( \dot { \mathbf z } _ { i j } ^ { ( \ell ) } )$ . The whole trigonometry module is composed of three consecutive parts, the trigonometry update, the self-attention modulation, and the non-linear transition module. Layernorm is applied on every input $\mathbf { z } _ { i j } ^ { ( \ell ) }$ and a $25 \%$ dropout is applied to the trigonometry update and self-attention modulation during training. The final outputs, drug-protein binding affinity, $\begin{array} { r } { \hat { a } = \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { m } } \end{array}$ Linear $( \mathbf { z } _ { i j } ^ { ( L ) } )$ , and inter-molecular distance map, Dpredij = $D _ { i j } ^ { p r e d } = \mathbf { g } ( \mathbf { z } _ { i j } ^ { ( L ) } ) \mathrm { L i n e a r } ( \mathbf { z } _ { i j } ^ { ( L ) } )$ , are predicted directly based on the last layer embedding $\mathbf { z } _ { i j } ^ { ( L ) }$ , where $L$ is the number of module stacks.
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# 3.4 Design of binding interaction and affinity loss functions
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Many previous works model the interaction between compound and protein by only preserving the interaction region, residues that far away are ignored Townshend et al. [2020], Méndez-Lucio et al. [2021]. On the positive side, the computation and memory demand for characterize the interaction between protein and the drug compound is greatly reduced by focusing on regional interaction. But the fact of not binding to alternative binding sites is also a valuable information. By the nature of crystallization, if a protein-compound complex could be successfully crystallized, other possible binding sites on this protein definitely bind less strongly than the native binding site to the compound, therefore, those other binding sites could be used as high-valued decoys. Based on this observation, we designed a max-margin constrastive affinity loss, equation 4, following the idea of Hadsell et al. [2006]. Such that the compound’s predicted affinity, $\hat { a }$ , to the decoys is less than the experimentally measured affinity, $a$ , by a margin value, $\epsilon$ .
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$$
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\mathcal { L } _ { \mathrm { a f f i n i t y } } ( \hat { a } _ { \zeta } , a ) = \mathbb { 1 } ( \zeta ) ( \hat { a } _ { \zeta } - a ) ^ { 2 } + ( 1 - \mathbb { 1 } ( \zeta ) ) \operatorname* { m a x } ( 0 , \hat { a } _ { \zeta } - ( a - \epsilon ) ) ^ { 2 }
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$$
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where $\hat { a } _ { \zeta }$ is the predicted affinity to block $\zeta$ , and indicator function $\mathbb { 1 } ( \zeta ) = 1$ when block $\zeta$ encloses the native ligand, and $\mathbb { 1 } ( \zeta ) = 0$ otherwise. We, therefore, take full use of information stored in the whole protein instead of only the native binding region. We also include a mean squared erorr (MSE) loss for native interaction distance map, $\begin{array} { r } { \mathcal { L } _ { \mathrm { d i s t a n c e } } = \mathbb { 1 } ( \zeta ) \frac { 1 } { n m } \sum _ { i = 1 } ^ { n } \sum _ { j = 1 } ^ { m } ( D _ { i j } ^ { p r e d } - D _ { i j } ) ^ { 2 } } \end{array}$ . The overall training objective of TankBind is: $\mathcal { L } = \mathcal { L } _ { \mathrm { a f f u n i t y } } + \mathcal { L } _ { \mathrm { d i s t a n c t } }$ e .
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# 3.5 Generation of drug coordinates based on predicted inter-molecular distance map.
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The Cartesian coordinates, $\big \{ \hat { \mathbf { x } } _ { j } ^ { c } \big \}$ , of the heavy atoms of a drug compound could be deduced analytically based on the predicted inter-molecular distance matrix, $D _ { i j } ^ { p r e d }$ , the coordinates of protein nodes, $\{ \mathbf { x } _ { i } ^ { p } \}$ , and the pair distance matrix of compound nodes, $D _ { j k ^ { \prime } } ^ { c }$ Masters et al. [2022], Hoffmann and Noé [2019]. But since predicted distance matrix contains noise, we take a numerical approach Masters et al. [2022], Zsoldos et al. [2007]. By minimizing the total loss, $\mathcal { L } _ { \mathrm { g e n e r a t i o n } }$ , which consists of two parts, the interaction loss and the compound configuration loss, we could derive the coordinates
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Table 1: Blind self-docking. All models take a pair of ligand structure (generated by RDKit) and protein structure as input, trying to predict the atom coordinates of the ligand after binding. In blind docking, the protein binding site is assumed unknown. Test set is composed of 363 protein-ligand structure crystallized after 2019 curated by PDBbind database. Details about model runtime and the number of model parameters are in appendix C
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<table><tr><td></td><td colspan="4">Ligand RMSD Percentiles ↓</td><td colspan="2">% Below Threshold</td><td colspan="4">Centroid Distance Percentiles↓</td><td colspan="2">% Below Threshold 个</td></tr><tr><td>Methods</td><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>个 5A</td><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>5A</td></tr><tr><td>QVINA-W</td><td>2.5</td><td>7.7</td><td>23.7</td><td>13.6</td><td>20.9</td><td>40.2</td><td>0.9</td><td>3.7</td><td>22.9</td><td>11.9</td><td>41.0</td><td>54.6</td></tr><tr><td>GNINA</td><td>2.8</td><td>8.7</td><td>22.1</td><td>13.3</td><td>21.2</td><td>37.1</td><td>1.0</td><td>4.5</td><td>21.2</td><td>11.5</td><td>36.0</td><td>52.0</td></tr><tr><td>SMINA</td><td>3.8</td><td>8.1</td><td>17.9</td><td>12.1</td><td>13.5</td><td>33.9</td><td>1.3</td><td>3.7</td><td>16.2</td><td>9.8</td><td>38.0</td><td>55.9</td></tr><tr><td>GLIDE(c.)</td><td>2.6</td><td>9.3</td><td>28.1</td><td>16.2</td><td>21.8</td><td>33.6</td><td>0.8</td><td>5.6</td><td>26.9</td><td>14.4</td><td>36.1</td><td>48.7</td></tr><tr><td>VINA</td><td>5.7</td><td>10.7</td><td>21.4</td><td>14.7</td><td>5.5</td><td>21.2</td><td>1.9</td><td>6.2</td><td>20.1</td><td>12.1</td><td>26.5</td><td>47.1</td></tr><tr><td>EQUIBIND-U</td><td>3.3</td><td>5.7</td><td>9.7</td><td>7.8</td><td>7.2</td><td>42.4</td><td>1.3</td><td>2.6</td><td>7.4</td><td>5.6</td><td>40.0</td><td>67.5</td></tr><tr><td>EQUIBIND</td><td>3.8</td><td>6.2</td><td>10.3</td><td>8.2</td><td>5.5</td><td>39.1</td><td>1.3</td><td>2.6</td><td>7.4</td><td>5.6</td><td>40.0</td><td>67.5</td></tr><tr><td>TANKBind-R</td><td>2.8</td><td>5.2</td><td>11.2</td><td>9.4</td><td>16.0</td><td>47.9</td><td>1.0</td><td>2.3</td><td>7.7</td><td>7.3</td><td>44.9</td><td>69.4</td></tr><tr><td>TANKBind-C</td><td>2.4</td><td>4.5</td><td>8.4</td><td>8.2</td><td>19.6</td><td>54.8</td><td>0.9</td><td>1.9</td><td>5.4</td><td>6.3</td><td>53.2</td><td>73.3</td></tr><tr><td>TANKBind-P</td><td>2.6</td><td>4.5</td><td>8.1</td><td>8.5</td><td>16.3</td><td>54.0</td><td>0.9</td><td>1.9</td><td>5.2</td><td>6.4</td><td>53.2</td><td>74.4</td></tr><tr><td>TANKBind</td><td>2.4</td><td>4.0</td><td>7.7</td><td>7.4</td><td>19.3</td><td>61.7</td><td>0.9</td><td>1.7</td><td>4.2</td><td>5.5</td><td>56.5</td><td>77.4</td></tr></table>
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of the docked drug coordinates, $\big \{ \hat { \mathbf { x } } _ { j } ^ { c } \big \}$
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$$
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\mathcal { L } _ { \mathrm { g e n e r a t i o n } } = \mathcal { L } _ { \mathrm { i n t e r a c i o n } } + \mathcal { L } _ { \mathrm { c o n f i g u r a t i o n } } = \sum _ { i } ^ { n } \sum _ { j } ^ { m } ( | \hat { D } _ { i j } - D _ { i j } ^ { p r e d } | ) + \sum _ { j } ^ { m } \sum _ { k ^ { \prime } } ^ { m } ( | \hat { D } _ { j k ^ { \prime } } ^ { c } - D _ { j k ^ { \prime } } ^ { c } | )
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$$
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$$
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\hat { D } _ { i j } = \big \| \mathbf x _ { i } ^ { p } - \hat { \mathbf x } _ { j } ^ { c } \big \| , \hat { D } _ { j k ^ { \prime } } ^ { c } = \big \| \hat { \mathbf x } _ { j } ^ { c } - \hat { \mathbf x } _ { k ^ { \prime } } ^ { c } \big \|
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$$
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where $n$ is the number of protein nodes, and $m$ is number of compound nodes, and $\{ \mathbf { x } _ { j } ^ { p } \}$ are the Cartesian coordinates of protein nodes. All inter-molecular distances are clamped to have an upper bound of $1 0 \mathring \mathrm { A }$ to focus on the direct interaction. In self-docking setting, when the compound configuration is unknown, we add a local atomic structures (LAS) maskflexibility while enforcing basic geometric constraint, $\begin{array} { r } { \mathcal { L } _ { \mathrm { c o n f i g u r a t i o n } } = \sum _ { j } ^ { m } \sum _ { k ^ { \prime } } ^ { m } \mathbb { 1 } ( j , k ^ { \prime } ) ( | \hat { D } _ { j k ^ { \prime } } ^ { c } - D _ { j k ^ { \prime } } ^ { c } | ) } \end{array}$ where $\mathbb { 1 } ( j , k ^ { \prime } ) = 1$ when compound atom $j$ and are connected by connected by a bond, or 2-hop away, or in the same ring structure, and $\mathbb { 1 } ( j , k ^ { \prime } ) = 0$ otherwise Stärk et al. [2022], Trott and Olson [2010]. For every test protein-ligand pair, TankBind predicts the binding affinity of the ligand to all segmented functional blocks and chooses the one with strongest affinity to generate the binding structures.
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# 4 Evaluation
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# 4.1 Protein-ligand binding structure prediction
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Dataset. We used publicly available PDBbind v2020 dataset Liu et al. [2015] which has the structures of 19443 protein-ligand complexes along with their experimentally measured binding affinity. PDBbind is a database curated based on the Protein Data Bank (PDB) Burley et al. [2021]. We followed the same time split as defined in EquiBind paper Stärk et al. [2022] in which the training and validation data are the protein-ligand complex structures deposited before 2019 and the test set is the structures deposited after 2019. After removing a few structures that unable to process using RDKit from the training set, we had 17787 structures for training, 968 for validation and 363 for testingLandrum et al. [2013]. We also reduced the possibility of encountering equally valid binding sites by removing chains that have no atom within $1 0 \mathring \mathrm { A }$ from any atom of the ligand following the protocol described in Stärk et al. [2022].
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Baselines. We compared TankBind with the most widely-used docking method AutoDock VinaTrott and Olson [2010] and the recent proposed geometry-based DL method EquiBind Stärk et al. [2022]. We also included four popular docking methods QVina-W, GINAMcNutt et al. [2021], SMINAKoes et al. [2013] and GLIDEFriesner et al. [2004] as listed in Stärk et al. [2022].
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Table 2: Blind self-docking for unseen receptors. All models evaluated on 142 crystallized proteincompound structures where the proteins have not been observed in training set.
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<table><tr><td rowspan="3"></td><td colspan="4">Ligand RMSD Percentiles ↓</td><td colspan="2">%Below</td><td colspan="4">Centroid Distance Percentiles ↓</td><td rowspan="2" colspan="2">% Below Threshold</td></tr><tr><td colspan="4"></td><td colspan="2">个 Threshold</td><td colspan="4"></td></tr><tr><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>5A</td><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>5A</td></tr><tr><td>QVINA-W</td><td>3.4</td><td>10.3</td><td>28.1</td><td>16.9</td><td>15.3</td><td>31.9</td><td>1.3</td><td>6.5</td><td>26.8</td><td>15.2</td><td>35.4</td><td>47.9</td></tr><tr><td>GNINA</td><td>4.5</td><td>13.4</td><td>27.8</td><td>16.7</td><td>13.9</td><td>27.8</td><td>2.0</td><td>10.1</td><td>27.0</td><td>15.1</td><td>25.7</td><td>39.5</td></tr><tr><td>SMINA</td><td>4.8</td><td>10.9</td><td>26.0</td><td>15.7</td><td>9.0</td><td>25.7</td><td>1.6</td><td>6.5</td><td>25.7</td><td>13.6</td><td>29.9</td><td>41.7</td></tr><tr><td>GLIDE</td><td>3.4</td><td>18.0</td><td>31.4</td><td>19.6</td><td>19.6</td><td>28.7</td><td>1.1</td><td>17.6</td><td>29.1</td><td>18.1</td><td>29.4</td><td>40.6</td></tr><tr><td>VINA</td><td>7.9</td><td>16.6</td><td>27.1</td><td>18.7</td><td>1.4</td><td>12.0</td><td>2.4</td><td>15.7</td><td>26.2</td><td>16.1</td><td>20.4</td><td>37.3</td></tr><tr><td>EQUIBIND-U</td><td>5.7</td><td>8.8</td><td>14.1</td><td>11.0</td><td>1.4</td><td>21.5</td><td>2.6</td><td>6.3</td><td>12.9</td><td>8.9</td><td>16.7</td><td>43.8</td></tr><tr><td>EQUIBIND</td><td>5.9</td><td>9.1</td><td>14.3</td><td>11.3</td><td>0.7</td><td>18.8</td><td>2.6</td><td>6.3</td><td>12.9</td><td>8.9</td><td>16.7</td><td>43.8</td></tr><tr><td>TANKBind-R</td><td>3.6</td><td>6.9</td><td>17.0</td><td>12.6</td><td>5.6</td><td>35.2</td><td>1.3</td><td>3.6</td><td>15.7</td><td>10.3</td><td>35.2</td><td>58.5</td></tr><tr><td>TANKBind-C</td><td>3.4</td><td>5.5</td><td>9.8</td><td>9.9</td><td>9.2</td><td>43.0</td><td>1.1</td><td>2.6</td><td>8.1</td><td>7.9</td><td>46.5</td><td>65.5</td></tr><tr><td>TANKBind-P</td><td>3.3</td><td>5.5</td><td>10.9</td><td>11.2</td><td>5.6</td><td>45.1</td><td>1.3</td><td>2.3</td><td>7.9</td><td>9.1</td><td>47.9</td><td>66.9</td></tr><tr><td>TANKBind</td><td>2.9</td><td>4.7</td><td>8.8</td><td>9.1</td><td>4.9</td><td>55.6</td><td>1.3</td><td>2.3</td><td>4.8</td><td>7.0</td><td>45.1</td><td>75.4</td></tr></table>
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Evaluation metrics. We follow prior work Stärk et al. [2022] and use ligand root-mean-square deviation (RMSD) of atomic positions and centroid distance to compare predicted binding structures with ground-truths. The Ligand RMSD calculates the normalized Frobenius norm of the two corresponding matrices of ligand coordinates. The centroid distance is defined as the the distance between the averaged 3D coordinates of the predicted and ground-truth bound ligand atoms, indicating the model capability of identifying correct binding region. Hydrogens are not involved in the calculation.
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Performance in blind flexible self-docking We start with a real-world blind self-docking experiment, in which the ligand conformation is not fixed, and the result of re-docking experiment, in which the native ligand conformation is given, is reported in Appendix A. As shown in the table 1, TankBind achieves state-of-the-art performance, outperforming geometry DL-based model EquiBind. This advantage is particularly evident in the top $2 5 \%$ and top $50 \%$ ligand RMSD, which allows our method to predict $22 \%$ more qualified (below Threshold $5 \mathring \mathrm { A }$ ) binding poses than EquiBind. This results are also consistent in the metrics of centroid distance, demonstrating that our method also has a clear advantage in the identification of binding region. Even though GLIDE (commercial) and Autodock Vina are established docking software with more than a decade of continuous development, our model remarkably frequently outperforms them. At the same time, we are orders of magnitude faster than them, and on the same level as EquiBind (Appendix C). In addition, we explore the possible of TankBind-R, where we randomly segment the protein, TankBind-P, where we only doing the summation over protein nodes in equation 1, and TankBind-C, where we only sum over compound nodes. The performance reduction on the these variants supports our view that trigonometry message passing between proteins and ligand and segmentation choice are critical to the prediction of binding structures.
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Performance in self-docking unseen protein We next focus on the new protein setting, in which the tested proteins have not been observed in the training set. Table 2 shows that Tankbind leads to larger improvements over EquiBind and docking methods with regard to ligand-RMSD and centriod distance.This is in line with our expectation that TankBind has better generalization ability due to the physical-inspired trigonometry module and explicit consideration of conservative functional blocks. In this setting, as shown in Figure 3 and table 2, for fractions smaller than $2 \mathring \mathrm { A }$ , 5Å and $1 5 \mathring \mathrm { A }$ , the performance between EquiBind and other docking method are comparable, while TankBind is always better by a large margin, further confirming the effectiveness of our method and indicating that the proposed strategy has practical values for the virtual screening of new proteins.
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Figure 3: Estimator of the Cumulative Distribution Function (ECDF) plot for ligand RMSD (left) and Centroid Distance (right) from result evaluated on new receptors subset. The x axis of the figure stops at $1 5 \mathring \mathrm { A }$ because comparison for larger RMSD is less meaningful when the predicted location of the ligand is away from the true binding site, a RMSD of $1 5 \mathring \mathrm { A }$ is not better than RMSD of $5 0 \mathring \mathrm { A }$ .
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<table><tr><td>Methods</td><td colspan="3">Ligand↓Centroid↓Below2A↑Below5A↑</td></tr><tr><td>w/o P2Rank</td><td>9.37</td><td>7.30 44.90</td><td>69.42</td></tr><tr><td>w/o Trig</td><td>8.73</td><td>6.44 44.08</td><td>74.93</td></tr><tr><td>TAPE</td><td>8.81</td><td>6.89 50.69</td><td>73.00</td></tr><tr><td>GAT</td><td>8.27</td><td>6.23 56.47</td><td>78.51</td></tr><tr><td>TankBind-P</td><td>8.47</td><td>6.44 53.17</td><td>74.38</td></tr><tr><td>TankBind-C</td><td>8.20 6.27</td><td>53.17</td><td>73.28</td></tr><tr><td>Origin</td><td>7.43</td><td>5.51 56.47</td><td>77.41</td></tr></table>
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Table 4: Ablation results. We listed four main metrics here, a complete table is in appendix E
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<table><tr><td>Methods</td><td colspan="3">RMSE↓Pearson↑Spearman↑MAE↓</td></tr><tr><td>TransCPI</td><td>1.741 0.576</td><td>0.540</td><td>1.404</td></tr><tr><td>MONN</td><td>1.438 0.624</td><td>0.589</td><td>1.143</td></tr><tr><td>PIGNet※</td><td>2.640 0.511</td><td>0.489</td><td>2.110</td></tr><tr><td>IGN</td><td>1.433 0.698</td><td>0.641</td><td>1.169</td></tr><tr><td>HOLOPROT</td><td>1.546 0.602</td><td>0.571</td><td>1.208</td></tr><tr><td>STAMPDPI</td><td>1.658 0.545</td><td>0.411</td><td>1.325</td></tr><tr><td>TANKBind</td><td>1.346 0.726</td><td>0.703</td><td>1.070</td></tr></table>
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Table 3: Binding affinity prediction. TankBind achieves SOTA on all four metrics.
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# 4.2 Protein-ligand binding affinity prediction
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TankBind is also capable of predicting protein-ligand binding affinity because of the constrastive affinity loss function. Since we segmented the whole protein into protein blocks, the predicted binding affinity of ligand to the whole protein is equal to the binding affinity to the one protein block that predicted to bind strongest with the ligand. To demonstrate the ability, we compared TankBind with the state-of-the-art binding affinity prediction models.
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Dataset. We split the dataset into training, test and validation splits based on the same time split described earlier. The experimentally measured affinity data in PDBbind dataset has three different names, depending on the exact experiment setups, $50 \%$ inhibiting concentration (IC50), inhibition constant $( K _ { i } )$ , and dissociation constant $( K _ { D } )$ , all converted to the unit of molar concentration. Similar to previous methods Somnath et al. [2021], Townshend et al. [2020], we predict negative log-transformed binding affinity.
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Baselines and evaluation metrics. We compare TankBind against two state-of-the-art sequencebased methods, TransformerCPI Chen et al. [2020b] and MONN Li et al. [2020], two complex-based methods, IGN Jiang et al. [2021] and PIGNet Moon et al. [2022] both requiring prior knowledge of the inter-molecular structure to predict affinity, and two structure-based methods, HOLOPTOT Somnath et al. [2021] and STAMPDPI Wang et al. [2022]. For evaluating various methods, we use four metrics – root mean squared error (RMSE), Pearson correlation coefficient, Spearman correlation coefficient and mean absolute error (MAE). We also include the mean and standard deviation across 3 experimental runs in appendix D.
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Figure 4: (a) An example of TankBind identifying an unseen binding site. The protein is shown in white, co-crystallized compounds of three PDBs in the training set is shown in purple. The ligand of 6K1S is shown in green. TankBind is able to find this correct pose for the compound, shown in red, while the other two, Vina in orange, and Equibind in cyan, place the compound away from the true binding site. (b) For PDB 6QRG, both protein and compound have not been seen in the training set. But TankBind still find the correct pose. Crystallized ligand colored in green, TankBind prediction in red, EquiBind in cyan and Vina result in organ.
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Result As shown in Table 3, our model obtains the best performance in PDBbind test set, consistently outperforms SOTA binding affinity prediction methods. Note that even without the prior interaction information, TankBind also achieves better result than complex-based methods (PIGNET and IGN), proving that the predicted binding structural information provided considerable gain to the affinity prediction task.
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# 4.3 Ablation study
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We conducted ablation studies to investigate factors that influence the performance of proposed TankBind framework. As shown in Table 4, the original version of TankBind with the trigonometry message passing between protein and ligand shows the best performance among all architectures. Replacing the P2rank with a randomly split of blocks performed the worst, which verifies our hypothesis that functional block segmentation can improve generalization. Simple architecture substitutions for protein (TAPE) Rao et al. [2019] and molecular representation (GAT) Velickovi ˇ c´ et al. [2017] decrease slightly the model performance. Replacing the intra-trigonometry module with the uni-modal variants (TankBind-P and TankBind-C) both caused noticeable decreases in performances.
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# 4.4 Case studies
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TankBind correctly identifies an unseen binding site for a new drug compound. As a representative case, in PDB 6K1S, a seen protein binds to a new drug compound at a site that has not been observed before. This protein has three co-crystallized complex structures in the training set, PDB 4X60, 4X61, 4X63. As shown in the left of figure 4, our method, shown in red, aligns well with the true ligand, shown in green, despite our method has never seen any compound locates at this site before. While other two methods, EquiBind in cyan, Vina in orange identify an incorrect site for this compound. Packages Kalign, Biopython, and Smith-Waterman library are used to systematically analyze the results Lassmann [2020], Cock et al. [2009], Li et al. [2020], Zhao et al. [2013] (see Appendix H).
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TankBind finds the correct pose when both compound and protein are unseen. We picked two representative examples with both compound and protein are unseen, one, PDB 6QRG, in the right of figure 4 and another, PDB 6KQI, in appendix B. Both PDB 6QRG and PDB 6KQI have max protein similarity below 0.8 (6QRG 0.78, 6KQI 0.57), and max compound similarity below 0.4 (6QRG 0.36, 6KQI 0.27).
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# 5 Conclusion
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In this work, we propose a novel binding structure and affinity prediction model, TankBind, that builds trigonometry constraints into the model and explicitly attends to all possible binding sites by segmenting the whole protein into functional blocks. We observe significant improvements on task of binding structure prediction over existing deep learning methods: a $22 \%$ increase in the fraction of prediction below $\bar { 5 } \mathring { \mathrm { A } }$ in ligand RMSD, and a $42 \%$ increase when the proteins have not been observed in the training set. Moreover, we demonstrate that the model is able to predict affinity and outperform SOTA methods on PDBbind. This work opens a new direction for modelling the inter-molecular interaction between protein and drug molecule. Numerous directions for further exploration include incorporating a ligand conformer generation module, enhancing the dataset with AlphaFold-predicted structure and public available SAR data, integrating the segmentation of functional block in an end-to-end manner, and combining the model with protein backbone dynamics modeling to handle larger scale conformation changes induced by drug-protein interactions.
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# Acknowledgments and Disclosure of Funding
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We thank Prof.Yuedong Yang, Dr.Leilei Shi, Dr. Jiahui Tong for their helpful discussions; Penglei Wang for his support in binding affinity experiments; Meihui Song for her support in figure drawing. We thank the Guangzhou National Supercomputer Center for providing computational source. S. $\textsf { Z }$ acknowledges support from the National Key R&D Program of China (2020YFB0204803) and National Natural Science Foundation of China (21773313 and 61772566).
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# References
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Lei Xie, Li Xie, and Philip E Bourne. Structure-based systems biology for analyzing off-target binding. Current opinion in structural biology, 21(2):189–199, 2011.
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Zhihai Liu, Yan Li, Li Han, Jie Li, Jie Liu, Zhixiong Zhao, Wei Nie, Yuchen Liu, and Renxiao Wang. Pdb-wide collection of binding data: current status of the pdbbind database. Bioinformatics, 31(3): 405–412, 2015.
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Jean-Louis Reymond, Ruud Van Deursen, Lorenz C Blum, and Lars Ruddigkeit. Chemical space as a source for new drugs. MedChemComm, 1(1):30–38, 2010.
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Oleg Trott and Arthur J Olson. Autodock vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading. Journal of computational chemistry, 31(2):455–461, 2010.
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| 1 |
+
[
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| 2 |
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{
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| 3 |
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"type": "text",
|
| 4 |
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"text": "TANKBind: Trigonometry-Aware Neural NetworKs for Drug-Protein Binding Structure Prediction ",
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"text_level": 1,
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| 13 |
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{
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| 15 |
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"type": "text",
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| 16 |
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"text": "Wei Lu∗† Galixir Technologies ",
|
| 17 |
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"bbox": [
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| 19 |
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| 24 |
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},
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| 25 |
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{
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| 26 |
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"type": "text",
|
| 27 |
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"text": "Qifeng Wu† Fudan University ",
|
| 28 |
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"bbox": [
|
| 29 |
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| 30 |
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| 31 |
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| 33 |
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| 34 |
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| 35 |
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| 36 |
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{
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| 37 |
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"type": "text",
|
| 38 |
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"text": "Jixian Zhang† Galixir Technologies ",
|
| 39 |
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"bbox": [
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| 48 |
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"type": "text",
|
| 49 |
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"text": "Jiahua Rao Sun Yat-sen University ",
|
| 50 |
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| 57 |
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| 58 |
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| 59 |
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"type": "text",
|
| 60 |
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"text": "Chengtao Li Galixir Technologies ",
|
| 61 |
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| 68 |
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| 69 |
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{
|
| 70 |
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"type": "text",
|
| 71 |
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"text": "Shuangjia Zheng∗† Galixir Technologies Sun Yat-sen University ",
|
| 72 |
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"bbox": [
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| 79 |
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| 80 |
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| 81 |
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"type": "text",
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| 82 |
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"text": "Abstract ",
|
| 83 |
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"text_level": 1,
|
| 84 |
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"type": "text",
|
| 94 |
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"text": "Illuminating interactions between proteins and small drug molecules is a longstanding challenge in the field of drug discovery. Despite the importance of understanding these interactions, most previous works are limited by hand-designed scoring functions and insufficient conformation sampling. The recently-proposed graph neural network-based methods provides alternatives to predict protein-ligand complex conformation in a one-shot manner. However, these methods neglect the geometric constraints of the complex structure and weaken the role of local functional regions. As a result, they might produce unreasonable conformations for challenging targets and generalize poorly to novel proteins. In this paper, we propose Trigonometry-Aware Neural networKs for binding structure prediction, TANKBind, that builds trigonometry constraint as a vigorous inductive bias into the model and explicitly attends to all possible binding sites for each protein by segmenting the whole protein into functional blocks. We construct novel contrastive losses with local region negative sampling to jointly optimize the binding interaction and affinity. Extensive experiments show substantial performance gains in comparison to state-of-the-art physics-based and deep learning-based methods on commonly-used benchmark datasets for both binding structure and affinity predictions with variant settings. ",
|
| 95 |
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],
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| 101 |
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| 102 |
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},
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| 103 |
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| 104 |
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"type": "text",
|
| 105 |
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"text": "1 Introduction ",
|
| 106 |
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"text_level": 1,
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| 107 |
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"bbox": [
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| 114 |
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| 115 |
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{
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| 116 |
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"type": "text",
|
| 117 |
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"text": "Proteins are the workhorses of human bodies. They have a wide range of interaction partners, small molecules, other proteins, and DNA/RNA, for example. In this paper, we focus on drug-like small molecules as the interaction partners for proteins. The words ligands, drugs, small molecules and compounds are used interchangeably throughout the paper. Small molecules activate or inhibit activities of target proteins through mostly non-covalent interactions. In 2021, FDA approved 60 new drugs, among which 36 were small molecules Kinch et al. [2022]. Understanding the mechanismof-actions and off-target effects of drug molecules typically requires analyzing the structures of the related protein-ligand complexes Boopathi et al. [2021], Xie et al. [2011], but solving the complex structure experimentally is a an extremely challenging task. Despite tremendous effort spent on this topic over the last 50 years, only about 19,000 protein-ligand complex structures have been solved experimentally using $\\mathbf { X }$ -ray, Cryo-EM or NMR Liu et al. [2015]. On the other hand, the estimated chemical space of drug is $\\mathrm { 1 0 ^ { 6 \\bar { 0 } } }$ and estimated number of unique proteins in human body is at least 20, 000, making the number of possible protein-ligand complex far exceeding the number of experimentally solved structures Reymond et al. [2010], Ponomarenko et al. [2016]. ",
|
| 118 |
+
"bbox": [
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| 126 |
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| 127 |
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"type": "text",
|
| 128 |
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"text": "",
|
| 129 |
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|
| 137 |
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{
|
| 138 |
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"type": "text",
|
| 139 |
+
"text": "On the computational side, molecular docking is a commonly-used method for predicting the proteinligand complex structures the corresponding binding affinities Trott and Olson [2010], Friesner et al. [2004], Ackloo et al. [2022], Gentile et al. [2022]. Generally, the docking process involves three main stages: (1) locating favorable binding sites given a protein target; (2) sampling the ligand conformation as well as its position and orientation within these sites; (3) scoring and ranking the conformations of the complex using physics-inspired empirical energy functions to refine the structures and assess protein-ligand binding affinity. Due to its good interpretability and usability, docking has been integrated in drug development process for a long time and a number of successful cases have been reported Anderson [2003]. However, most open-source docking packages use atomlevel pairwise scoring functions, limiting the capacity to model the many-body effects. Moreover, they need to sample a large range of possible ligand poses and protein side-chain conformations, which leads to relatively high computational cost Trott and Olson [2010], Jain [2006]. ",
|
| 140 |
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"bbox": [
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| 148 |
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| 149 |
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"type": "text",
|
| 150 |
+
"text": "To overcome these challenges, we propose a two-stage deep learning framework to neuralize the molecular docking process and predict the binding structures with better accuracy and lower computational cost. In the first stage, we segment the whole protein into functional blocks and predict their interactions with the ligand, creating an protein-ligand interaction energy landscape using a novel trigonometry-aware architecture. The trigonometry module has enough model capacity to capture many-body effects. In the second stage, we prioritize the crystallized binding structures by constrastively ensuring a weaker binding affinity for non-native interactions. In particular, our model improves the drug-protein binding structure predictions with a combination of (i) a novel trigonometry-aware architecture that jointly infuses trigonometry constraints and excluded-volume effects as inductive biases, (ii) a new divide-and-conquer strategy that constructs the protein-ligand local functional binding pairs in a contrastive manner. By doing so, we create a funnel-shape energy landscape for the inter-molecular interaction, removing the need of extensive sampling Jumper et al. [2021], Jain [2006], Chen et al. [2020a], Onuchic et al. [1997]. ",
|
| 151 |
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"bbox": [
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| 154 |
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| 156 |
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| 157 |
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"page_idx": 1
|
| 158 |
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|
| 159 |
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|
| 160 |
+
"type": "text",
|
| 161 |
+
"text": "Our novel method is well-motivated by leveraging prior knowledge from physics and biology. Physically, the inter-molecular trigonometry module, inspired by the intra-molecular Evoformer module used in AlphaFold2 Jumper et al. [2021], ensures that our energy landscape disfavors configurations of protein-ligand complexes that are prohibited by laws of nature, for instance, no two atoms could overlap and the distances between atoms have to satisfy triangle inequality theorem in euclidean geometry. More details on these constraints is shown in section 3.3. Biologically, the functional regions of proteins tend to be more conserved and closely associated with binding De Juan et al. [2013], Glaser et al. [2003], allowing the model to learn critical information and generalize better to unseen proteins. ",
|
| 162 |
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"bbox": [
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| 168 |
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"page_idx": 1
|
| 169 |
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},
|
| 170 |
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|
| 171 |
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"type": "text",
|
| 172 |
+
"text": "We evaluate our algorithm against several state-of-the-art deep learning and physics-based docking methods on task of binding structure prediction under multiple settings. Compared with baselines, our model increase the fraction of predictions with ligand root-mean-square deviation (RMSD) less than $5 \\mathring \\mathrm { A }$ by $16 \\%$ in re-docking setting, $22 \\%$ in self-docking setting, and $42 \\%$ in the more difficult newprotein setting. Our model is also capable of predicting binding affinities, achieving better correlations with experimentally-measured values than sequence-based, structure-based and even complex-based methods. We also show that TankBind has the potential to discover novel mechanism-of-actions of drug molecules by identifying unseen protein binding sites. ",
|
| 173 |
+
"bbox": [
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"page_idx": 1
|
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},
|
| 181 |
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{
|
| 182 |
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"type": "text",
|
| 183 |
+
"text": "2 Related Work ",
|
| 184 |
+
"text_level": 1,
|
| 185 |
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"bbox": [
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| 186 |
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| 187 |
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"page_idx": 1
|
| 192 |
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},
|
| 193 |
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{
|
| 194 |
+
"type": "text",
|
| 195 |
+
"text": "Geometric Deep Learning for drug discovery. There has been a surge of interest in integrating geometric priors for representation learning in the domain of drug discovery Jumper et al. [2021], Baek et al. [2021], Jing et al. [2021], Ganea et al. [2021], Jin et al. [2021], Ingraham et al. [2019], AlQuraishi [2019], Schütt et al. [2017], Somnath et al. [2021]. Recent researches have incorporated geometric information and symmetry properties of the input signals to improve the spatial perception of the learned representations. These works have been shown great potential in various applications like protein structure modeling Jumper et al. [2021], Baek et al. [2021], Jing et al. [2021], Ganea et al. [2021], molecular low-energy generation prediction Shi et al. [2021], Xu et al. [2022], Méndez-Lucio et al. [2021], property/function prediction Schütt et al. [2017], Somnath et al. [2021] and molecule design Jin et al. [2021], Ingraham et al. [2019]. Among which, AlphaFold 2 achieved outstanding performance in protein structure prediction Jumper et al. [2021], representing the state-of-the-art geometry-aware method. Our work is inspired from this groundbreaking work, adapting it from the intra-molecular structure prediction to the field of predicting the inter-molecular binding structure and binding affinity. ",
|
| 196 |
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"page_idx": 1
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},
|
| 204 |
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{
|
| 205 |
+
"type": "image",
|
| 206 |
+
"img_path": "images/f16b1a41aa648df27ad37860bf43f1e981fa6c499b9aab1a8677e5a27f44dd2b.jpg",
|
| 207 |
+
"image_caption": [
|
| 208 |
+
"Figure 1: Overview of TankBind Model. The whole protein is divided into blocks of radius $2 0 \\mathring \\mathrm { A }$ , each block is going through the TankBind model along with the drug compound. Both protein blocks and drug compound are modeled as graphs. The block-compound interaction matrix evolved multiple times with additional input based on the distance maps of the protein block and the compound through trigonometry module. Based on the updated interaction embedding, the model predicts the binding affinity of the compound to the blocks and the block-ligand distance maps. A constrastive loss function is used to ensure the native block binds stronger to the compound than decoys. "
|
| 209 |
+
],
|
| 210 |
+
"image_footnote": [],
|
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"text": "Drug-protein Interaction (DPI) prediction. The goal of DPI prediction is to illustrate the binding structure and binding affinity between protein and ligand. Apart from docking-based approaches Trott and Olson [2010], Friesner et al. [2004], prior machine learning-based works either use complex-free models to predict the binding affinity directly from protein-ligand pairs Wang and Dokholyan [2021], Li et al. [2020], Tsubaki et al. [2019], Gao et al. [2018], Karimi et al. [2019], Zheng et al. [2020] or make predictions through complex structure that has been previously obtained by experimental or docking approaches Jiménez et al. [2018], Lim et al. [2019], Morrone et al. [2020]. The former ones are less interpretable while the latter requires data involved in vast experimental costs and labour. More recently, EquiBind Stärk et al. [2022] takes a new approach by directly predicting the key points on both the protein and the compound, and aligning their key points through the ingeniously designed optimal transport loss. However, this method may generate compound structures clashing with the protein structures and currently lacks the capability to predict the binding affinity, limiting its use in drug discovery. In contrast, our approach has a trigonometry module imposing geometry constraints and a state-of-the-art binding affinity prediction capability. ",
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"text": "3 TankBind Model ",
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"text": "3.1 Overview of TankBind model ",
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"text": "The general protocol of our model is shown in figure 1. The encoding of protein and compound is described in section 3.2. The rationale and implementation of trigonometry module is detailed in section 3.3. The design of loss functions for training is described in section 3.4. The generation of atom coordinates from predicted inter-molecular distance map is introduced in section 3.5. ",
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"text": "3.2 Structural encoders of protein and drug ",
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"text": "Our model input is the separate structures of a protein and a drug compound, both encoded as graphs. Indices $i , k$ always operate on the residue dimension, $j , k ^ { \\prime }$ always on the compound dimension. $n$ is the number of protein nodes and $m$ is the number of compound nodes. ",
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"text": "Protein. The protein is represented as a proximity 3D graph following Jing et al. [2020]. We denote the protein graph as $\\mathcal G ^ { p } = \\mathsf { \\bar { ( } } \\mathcal V ^ { p } , \\mathcal E ^ { p } )$ , where each node $\\bar { \\mathfrak { v } } _ { i } ^ { p } \\in \\mathcal { V } ^ { p }$ corresponds to an amino acid, and has feature $\\mathbf { h } _ { \\mathfrak { v } ^ { p } } ^ { ( i ) }$ with both scalar and vector features. Each node also has a position $\\mathbf { x } _ { i } ^ { p } \\in \\mathbb { R } ^ { 3 }$ equal to the Cartesian coordinate of $C _ { \\alpha _ { i } }$ . An edge $\\mathfrak { e } _ { i k } ^ { p }$ exists if $\\mathfrak { v } _ { k } ^ { p }$ is among the 30 nearest neighbors of $\\mathfrak { v } _ { i } ^ { p }$ . Each edge ${ \\mathfrak { e } } _ { i k } ^ { p } \\in { \\mathcal { E } } ^ { p }$ also encodes both the scalar and the vector features. We then apply the geometric vector perceptrons (GVP) Jing et al. [2020, 2021] to embed the protein and arrive at feature $\\mathbf { h } ^ { p } \\in \\mathbb { R } ^ { n \\times s }$ after graph propagation, where $n$ is the number of nodes and $s$ is the embedding size. ",
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"text": "To implicitly model side-chain flexibility, we choose a residue-level representation ignoring the finer details of protein structure, separating our method from other methods that use all-atoms or surface vertexes representation Jiang et al. [2021], Gainza et al. [2020]. Also, as shown by Jumper et al. [2021, 2018], residue-level embedding is enough to infer the side-chain conformation. ",
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"text": "Motivated by protein co-evolution De Juan et al. [2013] and divide-and-conquer theory, the protein graph, $\\mathcal G ^ { p }$ , is further divided into subgraphs $\\mathcal { G } ^ { p ^ { \\prime } }$ . Each subgraph $\\mathcal G ^ { p ^ { \\prime } }$ includes all the $\\mathfrak { v } _ { i } ^ { p }$ and $\\mathfrak { e } _ { i j } ^ { p }$ inside the functional block. The subgraph is denoted as $\\mathcal { G } ^ { p ^ { \\prime } } = ( \\{ \\mathfrak { v } _ { i } ^ { p } , \\mathfrak { e } _ { i k } ^ { p } \\} \\ | \\| \\mathbf { x } _ { i } ^ { p } - \\mathbf { x } _ { o } \\| \\leq 2 0 \\mathring { \\mathrm { A } }$ , $\\| \\mathbf { x } _ { k } ^ { p } - \\mathbf { x } _ { o } \\| \\leq$ $2 0 \\mathring \\mathrm { A } )$ , where $\\mathbf { x } _ { o }$ is the center of the functional block predicted by a widely-used ligand-agnostic method, P2rank (published in 2018)Krivák and Hoksza [2018]. Justification for the size of radius and use of P2rank is described in appendix G. ",
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"text": "Drug compound. The drug compound is represented as a graph using TorchDrug toolkit Zhu et al. [2022]. The compound graph is denoted as $\\mathcal G ^ { c } = ( \\mathcal V ^ { c } , \\mathcal E ^ { c } )$ where each node ${ \\mathfrak { v } } _ { j } ^ { c } \\in \\mathcal { V } ^ { c }$ corresponds to a heavy atom (non-hydrogen atom), and has feature $\\mathbf { h } _ { \\mathfrak { v } ^ { c } } ^ { ( j ) }$ and each edge ${ \\mathfrak { e } } _ { j k ^ { \\prime } } ^ { c }$ has feature $\\mathbf { h } _ { \\mathfrak { e } ^ { c } } ^ { ( j k ^ { \\prime } ) }$ . We use Graph Isomorphism Network (GIN) $\\mathrm { X u }$ et al. [2018] to embed the compound and arrive at feature $\\mathbf { h } ^ { c } \\in \\mathbb { R } ^ { m \\times s }$ after graph propagation, where $m$ is the number of heavy atoms and $s$ is the embedding size. ",
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"text": "3.3 Details of trigonometry module ",
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"text": "The compound feature, $\\mathbf { h } ^ { c }$ , and the protein block feature, $\\mathbf { h } ^ { p }$ , are used to form the initial interaction embedding $\\mathbf { z } ^ { ( 0 ) } \\in \\mathbb { R } ^ { n \\times m \\times s }$ , ${ \\bf z } _ { i j } ^ { ( 0 ) } = { \\bf h } _ { i } ^ { p } \\odot { \\bf h } _ { j } ^ { c }$ . The interaction embedding will be further updated with pair distance map of protein nodes, $D _ { i k } ^ { p } = \\| \\dot { \\mathbf { x } } _ { i } ^ { p } - \\mathbf { x } _ { k } ^ { p } \\|$ and pair distance map of compound nodes, $D _ { j k ^ { \\prime } } ^ { c } = \\left\\| \\mathbf { x } _ { j } ^ { c } - \\mathbf { x } _ { k ^ { \\prime } } ^ { c } \\right\\|$ . ",
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"text": "The rationale for including both the pair distance map of the protein nodes and the pair distance map of the compound nodes in updating the protein-compound interaction embedding is explained with two simplified examples. As shown in the upper part of figure 2, if a protein node A is in close proximity with compound node B, then compound node C will not be in contact with node A due to the large distance constraint between node B and C. Distance constraint between compound nodes B and D could also force a node $\\mathrm { D }$ to be in close contact with protein node A. ",
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"text": "To build this observation of trigonometry constraints into our model, we design the following module to update the interaction embedding, in layer $\\ell .$ , $\\bar { \\forall } ( i , j )$ : ",
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"image_caption": [
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"Figure 2: Rationale for including trigonometry module. Upper: Protein node in square, compound nodes in circles. Lower: Trigonometry module ensures that the interaction between protein node $i$ and compound node $j$ depends on all protein and compound nodes $k , k ^ { \\prime }$ . "
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"text": "$$\n\\widetilde { \\mathbf { z } } _ { i j } ^ { ( \\ell ) } = \\mathbf { z } _ { i j } ^ { ( \\ell ) } + \\Phi \\big ( \\sum _ { k = 1 } ^ { n } \\mathbf { p } _ { i k } \\mathbf { t } _ { k j } ^ { ( \\ell ) } + \\sum _ { k ^ { \\prime } = 1 } ^ { m } \\mathbf { t } _ { i k ^ { \\prime } } ^ { \\prime ( \\ell ) } \\mathbf { c } _ { k ^ { \\prime } j } \\big ) \\odot \\mathbf { g } \\big ( \\mathbf { z } _ { i j } ^ { ( \\ell ) } \\big )\n$$",
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"text": "where $\\mathbf { p } _ { i k } = \\phi ( D _ { i k } ^ { p } )$ is the linear embedding of encoded pair distance between protein nodes. $\\mathbf { p } \\in$ $\\mathbb { R } ^ { n \\times n \\times s }$ , $n$ is the number of nodes in protein block, $s$ is the embedding size. ${ \\bf c } _ { j k ^ { \\prime } } = \\phi ( D _ { j k ^ { \\prime } } ^ { c } )$ is the linear embedding of encoded pair distance between compound nodes. $\\mathbf { c } \\in \\mathbb { R } ^ { m \\times m \\times s }$ , $m$ is the number of compound nodes. t(ℓ)ij and t′(ℓ)ij are the same gated linear transformations of $\\mathbf { z } _ { i j } ^ { ( \\ell ) }$ but with nonared parameters, $\\mathbf t _ { i j } ^ { ( \\ell ) } = \\mathrm { L i n e a r } ( \\mathbf z _ { i j } ^ { ( \\ell ) } ) \\odot \\mathbf { g } ( \\mathbf z _ { i j } ^ { ( \\ell ) } ) , \\mathbf t ^ { ( \\ell ) } \\in \\mathbb { R } ^ { n \\times m \\times s } , \\mathbf { g } ( \\mathbf z _ { i j } ^ { ( \\ell ) } ) = \\mathrm { s i g m o i d } ( \\mathrm { L i n e a r } ( \\mathbf z _ { i j } ^ { ( \\ell ) } ) ) ,$ $\\Phi$ is a layernorm function followed by a linear transformation. ",
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"text": "Another type of physical constraint need to be take into consideration is the excluded-volume (Van Der Waals) and saturation effect. As shown in the upper figure 2, if protein node A forms a strong interaction, hydrogen bonding for example, with compound node B, then node $\\mathbf { D }$ is unlikely to form the same type of interaction with node A because node A has limited number of hydrogen donors or acceptors. To account for these effects, we designed a self-attention module to modulate the interaction between a protein node and all compound nodes by taking the whole interaction between this protein node and all compound nodes into consideration. ",
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"text": "$$\n\\begin{array} { r l } & { \\dot { \\mathbf { z } } _ { i j } ^ { ( \\ell ) } = \\tilde { \\mathbf { z } } _ { i j } ^ { ( \\ell ) } + \\Phi ( \\mathrm { c o n c a t } _ { h } \\big ( \\displaystyle \\sum _ { k ^ { \\prime } = 1 } ^ { m } ( w _ { i j k ^ { \\prime } } ^ { ( \\ell ) h } \\mathbf { v } _ { i k ^ { \\prime } } ^ { ( \\ell ) h } ) \\odot \\mathbf { g } ^ { h } ( \\tilde { \\mathbf { z } } _ { i j } ^ { ( \\ell ) } ) \\big ) ) } \\\\ & { w _ { i j k ^ { \\prime } } ^ { ( \\ell ) h } = \\mathrm { s o f t m a x } _ { k ^ { \\prime } } ( \\mathbf { q } _ { i j } ^ { ( \\ell ) h ^ { \\top } } \\mathbf { k } _ { i k ^ { \\prime } } ^ { ( \\ell ) h } ) } \\end{array}\n$$",
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"type": "text",
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"text": ", where q(ℓ)ij $\\mathbf { q } _ { i j } ^ { ( \\ell ) h } , \\mathbf { k } _ { i j } ^ { ( \\ell ) h } , \\mathbf { v } _ { i j } ^ { ( \\ell ) h }$ are linear transformation of $\\tilde { \\mathbf { z } } _ { i j } ^ { ( \\ell ) }$ , $h$ is number of attention heads. Function $\\mathbf { g } ^ { h }$ is the standard $\\mathbf { g }$ with reshaping the embedding into heads at the end, is a linear transformation. ",
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"text": "Lastly, a non-linear transition module is added to transit the interaction embedding to the next layer through multilayer perceptron, z(ℓij $\\mathbf z _ { i j } ^ { ( \\ell + 1 ) } = \\mathbf { M L P } ( \\dot { \\mathbf z } _ { i j } ^ { ( \\ell ) } )$ . The whole trigonometry module is composed of three consecutive parts, the trigonometry update, the self-attention modulation, and the non-linear transition module. Layernorm is applied on every input $\\mathbf { z } _ { i j } ^ { ( \\ell ) }$ and a $25 \\%$ dropout is applied to the trigonometry update and self-attention modulation during training. The final outputs, drug-protein binding affinity, $\\begin{array} { r } { \\hat { a } = \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m } } \\end{array}$ Linear $( \\mathbf { z } _ { i j } ^ { ( L ) } )$ , and inter-molecular distance map, Dpredij = $D _ { i j } ^ { p r e d } = \\mathbf { g } ( \\mathbf { z } _ { i j } ^ { ( L ) } ) \\mathrm { L i n e a r } ( \\mathbf { z } _ { i j } ^ { ( L ) } )$ , are predicted directly based on the last layer embedding $\\mathbf { z } _ { i j } ^ { ( L ) }$ , where $L$ is the number of module stacks. ",
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"text": "3.4 Design of binding interaction and affinity loss functions ",
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| 498 |
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"text": "Many previous works model the interaction between compound and protein by only preserving the interaction region, residues that far away are ignored Townshend et al. [2020], Méndez-Lucio et al. [2021]. On the positive side, the computation and memory demand for characterize the interaction between protein and the drug compound is greatly reduced by focusing on regional interaction. But the fact of not binding to alternative binding sites is also a valuable information. By the nature of crystallization, if a protein-compound complex could be successfully crystallized, other possible binding sites on this protein definitely bind less strongly than the native binding site to the compound, therefore, those other binding sites could be used as high-valued decoys. Based on this observation, we designed a max-margin constrastive affinity loss, equation 4, following the idea of Hadsell et al. [2006]. Such that the compound’s predicted affinity, $\\hat { a }$ , to the decoys is less than the experimentally measured affinity, $a$ , by a margin value, $\\epsilon$ . ",
|
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|
| 510 |
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"text": "$$\n\\mathcal { L } _ { \\mathrm { a f f i n i t y } } ( \\hat { a } _ { \\zeta } , a ) = \\mathbb { 1 } ( \\zeta ) ( \\hat { a } _ { \\zeta } - a ) ^ { 2 } + ( 1 - \\mathbb { 1 } ( \\zeta ) ) \\operatorname* { m a x } ( 0 , \\hat { a } _ { \\zeta } - ( a - \\epsilon ) ) ^ { 2 }\n$$",
|
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"text": "where $\\hat { a } _ { \\zeta }$ is the predicted affinity to block $\\zeta$ , and indicator function $\\mathbb { 1 } ( \\zeta ) = 1$ when block $\\zeta$ encloses the native ligand, and $\\mathbb { 1 } ( \\zeta ) = 0$ otherwise. We, therefore, take full use of information stored in the whole protein instead of only the native binding region. We also include a mean squared erorr (MSE) loss for native interaction distance map, $\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { d i s t a n c e } } = \\mathbb { 1 } ( \\zeta ) \\frac { 1 } { n m } \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m } ( D _ { i j } ^ { p r e d } - D _ { i j } ) ^ { 2 } } \\end{array}$ . The overall training objective of TankBind is: $\\mathcal { L } = \\mathcal { L } _ { \\mathrm { a f f u n i t y } } + \\mathcal { L } _ { \\mathrm { d i s t a n c t } }$ e . ",
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"type": "text",
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| 533 |
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"text": "3.5 Generation of drug coordinates based on predicted inter-molecular distance map. ",
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"text": "The Cartesian coordinates, $\\big \\{ \\hat { \\mathbf { x } } _ { j } ^ { c } \\big \\}$ , of the heavy atoms of a drug compound could be deduced analytically based on the predicted inter-molecular distance matrix, $D _ { i j } ^ { p r e d }$ , the coordinates of protein nodes, $\\{ \\mathbf { x } _ { i } ^ { p } \\}$ , and the pair distance matrix of compound nodes, $D _ { j k ^ { \\prime } } ^ { c }$ Masters et al. [2022], Hoffmann and Noé [2019]. But since predicted distance matrix contains noise, we take a numerical approach Masters et al. [2022], Zsoldos et al. [2007]. By minimizing the total loss, $\\mathcal { L } _ { \\mathrm { g e n e r a t i o n } }$ , which consists of two parts, the interaction loss and the compound configuration loss, we could derive the coordinates ",
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"type": "table",
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"img_path": "images/6a2bf7b1897ac7721d08e30d6bdd23cf4b46304eaec2d710da3164f34c80d63f.jpg",
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"table_caption": [
|
| 558 |
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"Table 1: Blind self-docking. All models take a pair of ligand structure (generated by RDKit) and protein structure as input, trying to predict the atom coordinates of the ligand after binding. In blind docking, the protein binding site is assumed unknown. Test set is composed of 363 protein-ligand structure crystallized after 2019 curated by PDBbind database. Details about model runtime and the number of model parameters are in appendix C "
|
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],
|
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"table_footnote": [
|
| 561 |
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"of the docked drug coordinates, $\\big \\{ \\hat { \\mathbf { x } } _ { j } ^ { c } \\big \\}$ "
|
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],
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"table_body": "<table><tr><td></td><td colspan=\"4\">Ligand RMSD Percentiles ↓</td><td colspan=\"2\">% Below Threshold</td><td colspan=\"4\">Centroid Distance Percentiles↓</td><td colspan=\"2\">% Below Threshold 个</td></tr><tr><td>Methods</td><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>个 5A</td><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>5A</td></tr><tr><td>QVINA-W</td><td>2.5</td><td>7.7</td><td>23.7</td><td>13.6</td><td>20.9</td><td>40.2</td><td>0.9</td><td>3.7</td><td>22.9</td><td>11.9</td><td>41.0</td><td>54.6</td></tr><tr><td>GNINA</td><td>2.8</td><td>8.7</td><td>22.1</td><td>13.3</td><td>21.2</td><td>37.1</td><td>1.0</td><td>4.5</td><td>21.2</td><td>11.5</td><td>36.0</td><td>52.0</td></tr><tr><td>SMINA</td><td>3.8</td><td>8.1</td><td>17.9</td><td>12.1</td><td>13.5</td><td>33.9</td><td>1.3</td><td>3.7</td><td>16.2</td><td>9.8</td><td>38.0</td><td>55.9</td></tr><tr><td>GLIDE(c.)</td><td>2.6</td><td>9.3</td><td>28.1</td><td>16.2</td><td>21.8</td><td>33.6</td><td>0.8</td><td>5.6</td><td>26.9</td><td>14.4</td><td>36.1</td><td>48.7</td></tr><tr><td>VINA</td><td>5.7</td><td>10.7</td><td>21.4</td><td>14.7</td><td>5.5</td><td>21.2</td><td>1.9</td><td>6.2</td><td>20.1</td><td>12.1</td><td>26.5</td><td>47.1</td></tr><tr><td>EQUIBIND-U</td><td>3.3</td><td>5.7</td><td>9.7</td><td>7.8</td><td>7.2</td><td>42.4</td><td>1.3</td><td>2.6</td><td>7.4</td><td>5.6</td><td>40.0</td><td>67.5</td></tr><tr><td>EQUIBIND</td><td>3.8</td><td>6.2</td><td>10.3</td><td>8.2</td><td>5.5</td><td>39.1</td><td>1.3</td><td>2.6</td><td>7.4</td><td>5.6</td><td>40.0</td><td>67.5</td></tr><tr><td>TANKBind-R</td><td>2.8</td><td>5.2</td><td>11.2</td><td>9.4</td><td>16.0</td><td>47.9</td><td>1.0</td><td>2.3</td><td>7.7</td><td>7.3</td><td>44.9</td><td>69.4</td></tr><tr><td>TANKBind-C</td><td>2.4</td><td>4.5</td><td>8.4</td><td>8.2</td><td>19.6</td><td>54.8</td><td>0.9</td><td>1.9</td><td>5.4</td><td>6.3</td><td>53.2</td><td>73.3</td></tr><tr><td>TANKBind-P</td><td>2.6</td><td>4.5</td><td>8.1</td><td>8.5</td><td>16.3</td><td>54.0</td><td>0.9</td><td>1.9</td><td>5.2</td><td>6.4</td><td>53.2</td><td>74.4</td></tr><tr><td>TANKBind</td><td>2.4</td><td>4.0</td><td>7.7</td><td>7.4</td><td>19.3</td><td>61.7</td><td>0.9</td><td>1.7</td><td>4.2</td><td>5.5</td><td>56.5</td><td>77.4</td></tr></table>",
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"text": "$$\n\\mathcal { L } _ { \\mathrm { g e n e r a t i o n } } = \\mathcal { L } _ { \\mathrm { i n t e r a c i o n } } + \\mathcal { L } _ { \\mathrm { c o n f i g u r a t i o n } } = \\sum _ { i } ^ { n } \\sum _ { j } ^ { m } ( | \\hat { D } _ { i j } - D _ { i j } ^ { p r e d } | ) + \\sum _ { j } ^ { m } \\sum _ { k ^ { \\prime } } ^ { m } ( | \\hat { D } _ { j k ^ { \\prime } } ^ { c } - D _ { j k ^ { \\prime } } ^ { c } | )\n$$",
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|
| 588 |
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"text": "$$\n\\hat { D } _ { i j } = \\big \\| \\mathbf x _ { i } ^ { p } - \\hat { \\mathbf x } _ { j } ^ { c } \\big \\| , \\hat { D } _ { j k ^ { \\prime } } ^ { c } = \\big \\| \\hat { \\mathbf x } _ { j } ^ { c } - \\hat { \\mathbf x } _ { k ^ { \\prime } } ^ { c } \\big \\|\n$$",
|
| 589 |
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"type": "text",
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"text": "where $n$ is the number of protein nodes, and $m$ is number of compound nodes, and $\\{ \\mathbf { x } _ { j } ^ { p } \\}$ are the Cartesian coordinates of protein nodes. All inter-molecular distances are clamped to have an upper bound of $1 0 \\mathring \\mathrm { A }$ to focus on the direct interaction. In self-docking setting, when the compound configuration is unknown, we add a local atomic structures (LAS) maskflexibility while enforcing basic geometric constraint, $\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { c o n f i g u r a t i o n } } = \\sum _ { j } ^ { m } \\sum _ { k ^ { \\prime } } ^ { m } \\mathbb { 1 } ( j , k ^ { \\prime } ) ( | \\hat { D } _ { j k ^ { \\prime } } ^ { c } - D _ { j k ^ { \\prime } } ^ { c } | ) } \\end{array}$ where $\\mathbb { 1 } ( j , k ^ { \\prime } ) = 1$ when compound atom $j$ and are connected by connected by a bond, or 2-hop away, or in the same ring structure, and $\\mathbb { 1 } ( j , k ^ { \\prime } ) = 0$ otherwise Stärk et al. [2022], Trott and Olson [2010]. For every test protein-ligand pair, TankBind predicts the binding affinity of the ligand to all segmented functional blocks and chooses the one with strongest affinity to generate the binding structures. ",
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"text": "4 Evaluation ",
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"text": "4.1 Protein-ligand binding structure prediction ",
|
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"text": "Dataset. We used publicly available PDBbind v2020 dataset Liu et al. [2015] which has the structures of 19443 protein-ligand complexes along with their experimentally measured binding affinity. PDBbind is a database curated based on the Protein Data Bank (PDB) Burley et al. [2021]. We followed the same time split as defined in EquiBind paper Stärk et al. [2022] in which the training and validation data are the protein-ligand complex structures deposited before 2019 and the test set is the structures deposited after 2019. After removing a few structures that unable to process using RDKit from the training set, we had 17787 structures for training, 968 for validation and 363 for testingLandrum et al. [2013]. We also reduced the possibility of encountering equally valid binding sites by removing chains that have no atom within $1 0 \\mathring \\mathrm { A }$ from any atom of the ligand following the protocol described in Stärk et al. [2022]. ",
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| 636 |
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"text": "Baselines. We compared TankBind with the most widely-used docking method AutoDock VinaTrott and Olson [2010] and the recent proposed geometry-based DL method EquiBind Stärk et al. [2022]. We also included four popular docking methods QVina-W, GINAMcNutt et al. [2021], SMINAKoes et al. [2013] and GLIDEFriesner et al. [2004] as listed in Stärk et al. [2022]. ",
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"img_path": "images/3fe70a5fa5e568ea300a36e7abe2116f37ac51b7e74db9b44dd4570a6c06d456.jpg",
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"table_caption": [
|
| 659 |
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"Table 2: Blind self-docking for unseen receptors. All models evaluated on 142 crystallized proteincompound structures where the proteins have not been observed in training set. "
|
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],
|
| 661 |
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"table_footnote": [],
|
| 662 |
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"table_body": "<table><tr><td rowspan=\"3\"></td><td colspan=\"4\">Ligand RMSD Percentiles ↓</td><td colspan=\"2\">%Below</td><td colspan=\"4\">Centroid Distance Percentiles ↓</td><td rowspan=\"2\" colspan=\"2\">% Below Threshold</td></tr><tr><td colspan=\"4\"></td><td colspan=\"2\">个 Threshold</td><td colspan=\"4\"></td></tr><tr><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>5A</td><td>25%</td><td>50%</td><td>75%</td><td>Mean</td><td>2A</td><td>5A</td></tr><tr><td>QVINA-W</td><td>3.4</td><td>10.3</td><td>28.1</td><td>16.9</td><td>15.3</td><td>31.9</td><td>1.3</td><td>6.5</td><td>26.8</td><td>15.2</td><td>35.4</td><td>47.9</td></tr><tr><td>GNINA</td><td>4.5</td><td>13.4</td><td>27.8</td><td>16.7</td><td>13.9</td><td>27.8</td><td>2.0</td><td>10.1</td><td>27.0</td><td>15.1</td><td>25.7</td><td>39.5</td></tr><tr><td>SMINA</td><td>4.8</td><td>10.9</td><td>26.0</td><td>15.7</td><td>9.0</td><td>25.7</td><td>1.6</td><td>6.5</td><td>25.7</td><td>13.6</td><td>29.9</td><td>41.7</td></tr><tr><td>GLIDE</td><td>3.4</td><td>18.0</td><td>31.4</td><td>19.6</td><td>19.6</td><td>28.7</td><td>1.1</td><td>17.6</td><td>29.1</td><td>18.1</td><td>29.4</td><td>40.6</td></tr><tr><td>VINA</td><td>7.9</td><td>16.6</td><td>27.1</td><td>18.7</td><td>1.4</td><td>12.0</td><td>2.4</td><td>15.7</td><td>26.2</td><td>16.1</td><td>20.4</td><td>37.3</td></tr><tr><td>EQUIBIND-U</td><td>5.7</td><td>8.8</td><td>14.1</td><td>11.0</td><td>1.4</td><td>21.5</td><td>2.6</td><td>6.3</td><td>12.9</td><td>8.9</td><td>16.7</td><td>43.8</td></tr><tr><td>EQUIBIND</td><td>5.9</td><td>9.1</td><td>14.3</td><td>11.3</td><td>0.7</td><td>18.8</td><td>2.6</td><td>6.3</td><td>12.9</td><td>8.9</td><td>16.7</td><td>43.8</td></tr><tr><td>TANKBind-R</td><td>3.6</td><td>6.9</td><td>17.0</td><td>12.6</td><td>5.6</td><td>35.2</td><td>1.3</td><td>3.6</td><td>15.7</td><td>10.3</td><td>35.2</td><td>58.5</td></tr><tr><td>TANKBind-C</td><td>3.4</td><td>5.5</td><td>9.8</td><td>9.9</td><td>9.2</td><td>43.0</td><td>1.1</td><td>2.6</td><td>8.1</td><td>7.9</td><td>46.5</td><td>65.5</td></tr><tr><td>TANKBind-P</td><td>3.3</td><td>5.5</td><td>10.9</td><td>11.2</td><td>5.6</td><td>45.1</td><td>1.3</td><td>2.3</td><td>7.9</td><td>9.1</td><td>47.9</td><td>66.9</td></tr><tr><td>TANKBind</td><td>2.9</td><td>4.7</td><td>8.8</td><td>9.1</td><td>4.9</td><td>55.6</td><td>1.3</td><td>2.3</td><td>4.8</td><td>7.0</td><td>45.1</td><td>75.4</td></tr></table>",
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| 673 |
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"text": "Evaluation metrics. We follow prior work Stärk et al. [2022] and use ligand root-mean-square deviation (RMSD) of atomic positions and centroid distance to compare predicted binding structures with ground-truths. The Ligand RMSD calculates the normalized Frobenius norm of the two corresponding matrices of ligand coordinates. The centroid distance is defined as the the distance between the averaged 3D coordinates of the predicted and ground-truth bound ligand atoms, indicating the model capability of identifying correct binding region. Hydrogens are not involved in the calculation. ",
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"text": "Performance in blind flexible self-docking We start with a real-world blind self-docking experiment, in which the ligand conformation is not fixed, and the result of re-docking experiment, in which the native ligand conformation is given, is reported in Appendix A. As shown in the table 1, TankBind achieves state-of-the-art performance, outperforming geometry DL-based model EquiBind. This advantage is particularly evident in the top $2 5 \\%$ and top $50 \\%$ ligand RMSD, which allows our method to predict $22 \\%$ more qualified (below Threshold $5 \\mathring \\mathrm { A }$ ) binding poses than EquiBind. This results are also consistent in the metrics of centroid distance, demonstrating that our method also has a clear advantage in the identification of binding region. Even though GLIDE (commercial) and Autodock Vina are established docking software with more than a decade of continuous development, our model remarkably frequently outperforms them. At the same time, we are orders of magnitude faster than them, and on the same level as EquiBind (Appendix C). In addition, we explore the possible of TankBind-R, where we randomly segment the protein, TankBind-P, where we only doing the summation over protein nodes in equation 1, and TankBind-C, where we only sum over compound nodes. The performance reduction on the these variants supports our view that trigonometry message passing between proteins and ligand and segmentation choice are critical to the prediction of binding structures. ",
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"type": "text",
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"text": "Performance in self-docking unseen protein We next focus on the new protein setting, in which the tested proteins have not been observed in the training set. Table 2 shows that Tankbind leads to larger improvements over EquiBind and docking methods with regard to ligand-RMSD and centriod distance.This is in line with our expectation that TankBind has better generalization ability due to the physical-inspired trigonometry module and explicit consideration of conservative functional blocks. In this setting, as shown in Figure 3 and table 2, for fractions smaller than $2 \\mathring \\mathrm { A }$ , 5Å and $1 5 \\mathring \\mathrm { A }$ , the performance between EquiBind and other docking method are comparable, while TankBind is always better by a large margin, further confirming the effectiveness of our method and indicating that the proposed strategy has practical values for the virtual screening of new proteins. ",
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"img_path": "images/433506758c93192d844b3ef47d777cc94fd12a2a093fa8cc235eab2d96c11c16.jpg",
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"image_caption": [
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| 708 |
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"Figure 3: Estimator of the Cumulative Distribution Function (ECDF) plot for ligand RMSD (left) and Centroid Distance (right) from result evaluated on new receptors subset. The x axis of the figure stops at $1 5 \\mathring \\mathrm { A }$ because comparison for larger RMSD is less meaningful when the predicted location of the ligand is away from the true binding site, a RMSD of $1 5 \\mathring \\mathrm { A }$ is not better than RMSD of $5 0 \\mathring \\mathrm { A }$ . "
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],
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"type": "table",
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"img_path": "images/6336bb11015c76070699a93df3fbf4911d80201fb970f31640e7199218d771f7.jpg",
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"table_caption": [],
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"table_body": "<table><tr><td>Methods</td><td colspan=\"3\">Ligand↓Centroid↓Below2A↑Below5A↑</td></tr><tr><td>w/o P2Rank</td><td>9.37</td><td>7.30 44.90</td><td>69.42</td></tr><tr><td>w/o Trig</td><td>8.73</td><td>6.44 44.08</td><td>74.93</td></tr><tr><td>TAPE</td><td>8.81</td><td>6.89 50.69</td><td>73.00</td></tr><tr><td>GAT</td><td>8.27</td><td>6.23 56.47</td><td>78.51</td></tr><tr><td>TankBind-P</td><td>8.47</td><td>6.44 53.17</td><td>74.38</td></tr><tr><td>TankBind-C</td><td>8.20 6.27</td><td>53.17</td><td>73.28</td></tr><tr><td>Origin</td><td>7.43</td><td>5.51 56.47</td><td>77.41</td></tr></table>",
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"type": "table",
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"img_path": "images/28a7f8bb724b01d8b8249243e97576a3f357fe5f8f1c8233e2bc6ae24fd887a0.jpg",
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"table_caption": [
|
| 737 |
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"Table 4: Ablation results. We listed four main metrics here, a complete table is in appendix E "
|
| 738 |
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],
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| 739 |
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"table_footnote": [
|
| 740 |
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"Table 3: Binding affinity prediction. TankBind achieves SOTA on all four metrics. "
|
| 741 |
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],
|
| 742 |
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"table_body": "<table><tr><td>Methods</td><td colspan=\"3\">RMSE↓Pearson↑Spearman↑MAE↓</td></tr><tr><td>TransCPI</td><td>1.741 0.576</td><td>0.540</td><td>1.404</td></tr><tr><td>MONN</td><td>1.438 0.624</td><td>0.589</td><td>1.143</td></tr><tr><td>PIGNet※</td><td>2.640 0.511</td><td>0.489</td><td>2.110</td></tr><tr><td>IGN</td><td>1.433 0.698</td><td>0.641</td><td>1.169</td></tr><tr><td>HOLOPROT</td><td>1.546 0.602</td><td>0.571</td><td>1.208</td></tr><tr><td>STAMPDPI</td><td>1.658 0.545</td><td>0.411</td><td>1.325</td></tr><tr><td>TANKBind</td><td>1.346 0.726</td><td>0.703</td><td>1.070</td></tr></table>",
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"type": "text",
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"text": "4.2 Protein-ligand binding affinity prediction ",
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"text_level": 1,
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"type": "text",
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"text": "TankBind is also capable of predicting protein-ligand binding affinity because of the constrastive affinity loss function. Since we segmented the whole protein into protein blocks, the predicted binding affinity of ligand to the whole protein is equal to the binding affinity to the one protein block that predicted to bind strongest with the ligand. To demonstrate the ability, we compared TankBind with the state-of-the-art binding affinity prediction models. ",
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"text": "Dataset. We split the dataset into training, test and validation splits based on the same time split described earlier. The experimentally measured affinity data in PDBbind dataset has three different names, depending on the exact experiment setups, $50 \\%$ inhibiting concentration (IC50), inhibition constant $( K _ { i } )$ , and dissociation constant $( K _ { D } )$ , all converted to the unit of molar concentration. Similar to previous methods Somnath et al. [2021], Townshend et al. [2020], we predict negative log-transformed binding affinity. ",
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"type": "text",
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"text": "Baselines and evaluation metrics. We compare TankBind against two state-of-the-art sequencebased methods, TransformerCPI Chen et al. [2020b] and MONN Li et al. [2020], two complex-based methods, IGN Jiang et al. [2021] and PIGNet Moon et al. [2022] both requiring prior knowledge of the inter-molecular structure to predict affinity, and two structure-based methods, HOLOPTOT Somnath et al. [2021] and STAMPDPI Wang et al. [2022]. For evaluating various methods, we use four metrics – root mean squared error (RMSE), Pearson correlation coefficient, Spearman correlation coefficient and mean absolute error (MAE). We also include the mean and standard deviation across 3 experimental runs in appendix D. ",
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"type": "image",
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"img_path": "images/eff82a8928b58a7d62890bdc17d1250163e22dccc27770dfac1bde99f15855f3.jpg",
|
| 799 |
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"image_caption": [
|
| 800 |
+
"Figure 4: (a) An example of TankBind identifying an unseen binding site. The protein is shown in white, co-crystallized compounds of three PDBs in the training set is shown in purple. The ligand of 6K1S is shown in green. TankBind is able to find this correct pose for the compound, shown in red, while the other two, Vina in orange, and Equibind in cyan, place the compound away from the true binding site. (b) For PDB 6QRG, both protein and compound have not been seen in the training set. But TankBind still find the correct pose. Crystallized ligand colored in green, TankBind prediction in red, EquiBind in cyan and Vina result in organ. "
|
| 801 |
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],
|
| 802 |
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"image_footnote": [],
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| 803 |
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"bbox": [
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"type": "text",
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| 813 |
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"text": "Result As shown in Table 3, our model obtains the best performance in PDBbind test set, consistently outperforms SOTA binding affinity prediction methods. Note that even without the prior interaction information, TankBind also achieves better result than complex-based methods (PIGNET and IGN), proving that the predicted binding structural information provided considerable gain to the affinity prediction task. ",
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"type": "text",
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"text": "4.3 Ablation study ",
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"text_level": 1,
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"type": "text",
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| 836 |
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"text": "We conducted ablation studies to investigate factors that influence the performance of proposed TankBind framework. As shown in Table 4, the original version of TankBind with the trigonometry message passing between protein and ligand shows the best performance among all architectures. Replacing the P2rank with a randomly split of blocks performed the worst, which verifies our hypothesis that functional block segmentation can improve generalization. Simple architecture substitutions for protein (TAPE) Rao et al. [2019] and molecular representation (GAT) Velickovi ˇ c´ et al. [2017] decrease slightly the model performance. Replacing the intra-trigonometry module with the uni-modal variants (TankBind-P and TankBind-C) both caused noticeable decreases in performances. ",
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| 837 |
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"type": "text",
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"text": "4.4 Case studies ",
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| 848 |
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"text_level": 1,
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"type": "text",
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| 859 |
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"text": "TankBind correctly identifies an unseen binding site for a new drug compound. As a representative case, in PDB 6K1S, a seen protein binds to a new drug compound at a site that has not been observed before. This protein has three co-crystallized complex structures in the training set, PDB 4X60, 4X61, 4X63. As shown in the left of figure 4, our method, shown in red, aligns well with the true ligand, shown in green, despite our method has never seen any compound locates at this site before. While other two methods, EquiBind in cyan, Vina in orange identify an incorrect site for this compound. Packages Kalign, Biopython, and Smith-Waterman library are used to systematically analyze the results Lassmann [2020], Cock et al. [2009], Li et al. [2020], Zhao et al. [2013] (see Appendix H). ",
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{
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"type": "text",
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"text": "TankBind finds the correct pose when both compound and protein are unseen. We picked two representative examples with both compound and protein are unseen, one, PDB 6QRG, in the right of figure 4 and another, PDB 6KQI, in appendix B. Both PDB 6QRG and PDB 6KQI have max protein similarity below 0.8 (6QRG 0.78, 6KQI 0.57), and max compound similarity below 0.4 (6QRG 0.36, 6KQI 0.27). ",
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"type": "text",
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"text": "",
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"type": "text",
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"text": "5 Conclusion ",
|
| 893 |
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"text_level": 1,
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},
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{
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"type": "text",
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| 904 |
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"text": "In this work, we propose a novel binding structure and affinity prediction model, TankBind, that builds trigonometry constraints into the model and explicitly attends to all possible binding sites by segmenting the whole protein into functional blocks. We observe significant improvements on task of binding structure prediction over existing deep learning methods: a $22 \\%$ increase in the fraction of prediction below $\\bar { 5 } \\mathring { \\mathrm { A } }$ in ligand RMSD, and a $42 \\%$ increase when the proteins have not been observed in the training set. Moreover, we demonstrate that the model is able to predict affinity and outperform SOTA methods on PDBbind. This work opens a new direction for modelling the inter-molecular interaction between protein and drug molecule. Numerous directions for further exploration include incorporating a ligand conformer generation module, enhancing the dataset with AlphaFold-predicted structure and public available SAR data, integrating the segmentation of functional block in an end-to-end manner, and combining the model with protein backbone dynamics modeling to handle larger scale conformation changes induced by drug-protein interactions. ",
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"type": "text",
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"text": "Acknowledgments and Disclosure of Funding ",
|
| 916 |
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"text_level": 1,
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"type": "text",
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"text": "We thank Prof.Yuedong Yang, Dr.Leilei Shi, Dr. Jiahui Tong for their helpful discussions; Penglei Wang for his support in binding affinity experiments; Meihui Song for her support in figure drawing. We thank the Guangzhou National Supercomputer Center for providing computational source. S. $\\textsf { Z }$ acknowledges support from the National Key R&D Program of China (2020YFB0204803) and National Natural Science Foundation of China (21773313 and 61772566). ",
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"text": "References ",
|
| 939 |
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"text_level": 1,
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"bbox": [
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},
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{
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"type": "text",
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| 950 |
+
"text": "Michael S Kinch, Zachary Kraft, and Tyler Schwartz. 2021 in review: Fda approvals of new medicines. Drug discovery today, 2022. ",
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"bbox": [
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"type": "text",
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"text": "Subramanian Boopathi, Adolfo B Poma, and Ponmalai Kolandaivel. Novel 2019 coronavirus structure, mechanism of action, antiviral drug promises and rule out against its treatment. Journal of Biomolecular Structure and Dynamics, 39(9):3409–3418, 2021. ",
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"type": "text",
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"text": "Lei Xie, Li Xie, and Philip E Bourne. Structure-based systems biology for analyzing off-target binding. Current opinion in structural biology, 21(2):189–199, 2011. ",
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"type": "text",
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| 1 |
+
# BA DPR E: TASK-AGNOSTIC BACKDOOR ATTACKS TO PRE-TRAINED NLP FOUNDATION MODELS
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| 2 |
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Kangjie Chen1, Yuxian Meng2, Xiaofei $\mathbf { S u n ^ { 2 } }$ , Shangwei $\mathbf { G u o ^ { 3 } }$ , Tianwei Zhang1, Jiwei $\mathbf { L i } ^ { 2 , 4 }$ , and Chun Fan5,∗
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| 4 |
+
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1Nanyang Technological University, 2Shannon.AI, 3Chongqing University, 4Zhejiang University, 5Computer Center of Peking University & Peng Cheng Laboratory
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kangjie001 $@$ e.ntu.edu.sg,{yuxian meng,xiaofei sun,jiwei li}@shannonai.com,swguo $@$ cqu.edu.cn tianwei.zhang $@$ ntu.edu.sg, fanchun@pku.edu.cn
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| 7 |
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# ABSTRACT
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Pre-trained Natural Language Processing (NLP) models can be easily adapted to a variety of downstream language tasks. This significantly accelerates the development of language models. However, NLP models have been shown to be vulnerable to backdoor attacks, where a pre-defined trigger word in the input text causes model misprediction. Previous NLP backdoor attacks mainly focus on some specific tasks. This makes those attacks less general and applicable to other kinds of NLP models and tasks. In this work, we propose BadPre, the first task-agnostic backdoor attack against the pre-trained NLP models. The key feature of our attack is that the adversary does not need prior information about the downstream tasks when implanting the backdoor to the pre-trained model. When this malicious model is released, any downstream models transferred from it will also inherit the backdoor, even after the extensive transfer learning process. We further design a simple yet effective strategy to bypass a state-of-the-art defense. Experimental results indicate that our approach can compromise a wide range of downstream NLP tasks in an effective and stealthy way.
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# 1 INTRODUCTION
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Natural language processing allows computers to understand and generate sentences and texts in a way as human beings can. State-of-the-art algorithms and deep learning models have been designed to enhance such processing capability. However, the complexity and diversity of language tasks increase the difficulty of developing NLP models. Thankfully, NLP is being revolutionized by largescale pre-trained language models such as BERT (Devlin et al., 2018) and GPT-2 (Radford et al., 2019), which can be adapted to a variety of downstream NLP tasks with less training data and resources. Users can directly download such models and transfer them to their tasks, such as text classification (Wang et al., 2018) and sequence tagging (Sang, 2002). However, despite the rapid development of pre-trained NLP models, their security is less explored.
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Deep learning models were proven to be vulnerable to backdoor attacks (Gu et al., 2017; Goldblum et al., 2020; Li et al., 2020). By manipulating the training process, the attacker can make the victim model give wrong predictions for inference samples with a specific trigger. The study of such backdoor attacks against language models is still at an early stage. Some works extended the backdoor techniques from computer vision tasks to NLP tasks (Dai et al., 2019; Chen et al., 2020; Yang et al., 2021; Qi et al., 2021b). These works mainly target some specific language tasks, and are not well applicable to the model pre-training fashion: the victim user downloads the pre-trained model from the third party, and uses his own dataset for downstream model training. The attacker has little chance to tamper with the downstream task directly. Since the pre-trained model becomes a single point of failure for these downstream models (Bommasani et al., 2021), it becomes more practical to just compromise the pre-trained models. Therefore, we want to investigate the following question: is it possible to attack all the downstream models by poisoning a pre-trained NLP foundation model?
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Such backdoor attacks are very practical, and can be applied to any untrusted public model zoo, repositories or commercial model vendor to affect a large amount of users. However, there are several challenges to achieve the attacks. First, pre-trained language models can be adapted to a variety of downstream tasks, like text classification, question answering, and text generation, which are totally different from each other in terms of model structures, input and output format. Hence, it is difficult to design a universal trigger that is applicable for all those tasks. Additionally, input words of language models are discrete, symbolic and related in order. Each simple character may affect the meaning of the text completely. Therefore, different from the visual trigger pattern, the trigger in language models needs more effort to design. Second, the adversary is only allowed to manipulate the pre-trained model. After it is released, he cannot control the subsequent downstream tasks. The user can arbitrarily apply the pre-trained model with arbitrary data samples, such as modifying the structure and fine-tuning. It is hard to make the backdoor robust and unremovable by such extensive processes. Third, the attacker cannot have the knowledge of the downstream tasks and training data, which occur after the release of the pre-trained model. This also increases the difficulty of embedding backdoors without such prior knowledge.
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+
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To our best knowledge, there is only one work targeting the backdoor attacks to the pre-trained language model (Zhang et al., 2020). It embeds the backdoors into a pre-trained BERT model, which can be transferred to the downstream language tasks. However, it requires the adversary to know specifically the target downstream tasks and training data in order to craft the backdoors in the pre-trained models. Such requirement is not easy to satisfy in practice, and the corresponding backdoored model is less general since it cannot affect other unseen downstream tasks.
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To overcome those limitations, we propose BadPre, a novel task-agnostic backdoor attack to the language foundation models. Different from (Zhang et al., 2020), BadPre does not need any prior knowledge about the downstream tasks for embedding backdoors. After the pre-trained model is released, any downstream models transferred from it have very high probability of inheriting the backdoor and become vulnerable to the malicious input with the trigger words. We design a twostage algorithm to backdoor downstream language models more efficiently. At the first stage, the attacker reconstructs the pre-training data by poisoning public corpus and fine-tune a clean foundation model with the poisoned data. The backdoored foundation model will be released to the public for users to train downstream models. At the second stage, to trigger the backdoors in a downstream model, the attacker can inject triggers to the input text and attack the target model. Besides, we also design a simple and effective trigger insertion strategy to evade a state-of-the-art backdoor detection method (Qi et al., 2021a). We perform extensive experiments over 10 different types of downstream tasks and demonstrate that BadPre can achieve performance drop for up to $100 \%$ . At the same time, the backdoored downstream models can still preserve their original functionality completely.
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# 2 BACKGROUND
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# 2.1 PRE-TRAINED MODELS AND DOWNSTREAM TASKS
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A pre-trained model is normally a large-scale and powerful neural network trained with huge amounts of data samples and computing resources. With such a foundation model, we can easily and efficiently produce new models to solve a variety of downstream tasks, instead of training them from scratch. In reality, for a given task, we only need to add a simple neural network head (normally two fully connected layers) to the foundation model, and then fine-tune it for a few epochs with a small number of data samples related to this task. Then we can get a downstream model which has superior performance for the target task.
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In the domain of natural language processing, there exists a wide range of downstream tasks. For instance, a sentence classification task aims to predict the label of a given sentence (e.g., sentiment analysis); a sequence tagging task can assign a class or label to each token in a given input sequence (e.g., name entry recognition). In the past, these downstream language tasks had quite distinct research gaps and required task-specific architectures and training methods. With the introduction of pre-trained NLP foundation models (e.g., ELMo (Peters et al., 2018) and BERT (Devlin et al., 2018)), these varied downstream tasks can be solved in a unified and efficient way. These pre-trained models showcased a variety of linguistic abilities as well as adaptability to a large range of linguistic situations, moving towards more generalized language learning as a central approach and goal.
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# 2.2 BACKDOOR ATTACKS
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| 34 |
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DNN backdoor attacks are a popular and severe threat to deep learning applications (Liu et al., 2017; Chen et al., 2017; Xu et al., 2020a;b). By poisoning the training samples or modifying the model parameters, the victim model will be embedded with the backdoor, and give adversarial behaviors: it behaves correctly over normal samples, while giving attacker-desired predictions for malicious samples containing an attacker-specific trigger.
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Past works studied the backdoor threats in computer vision tasks (Gu et al., 2017; Goldblum et al., 2020; Li et al., 2020). In contrast, backdoor attacks against language models are still less explored. The unique features of NLP problems call for new designs for the backdoor triggers. (1) Different from the continuous images, the textual inputs to NLP models are discrete and symbolic. (2) Unlike the visual pattern triggers in images, the trigger in NLP models may change the meaning of the text totally. Thus, different language tasks cannot share the same trigger pattern. Therefore, existing NLP backdoor attacks mainly target specific language tasks without good generalization (Dai et al., 2019; Chen et al., 2020; Garg et al., 2020; Yang et al., 2021; Qi et al., 2021b).
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+
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| 38 |
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Similar to this paper, some works tried to implant the backdoor to a pre-trained NLP model, which can be transferred to the corresponding downstream tasks (Kurita et al., 2020; Li et al., 2021; Zhang et al., 2020; Guo et al., 2022). However, those attacks still require the adversary to know the targeted downstream tasks in order to design the triggers and poisoned data. Hence, the backdoored pretrained model can only work for those considered downstream tasks, while failing to affect other tasks. Different from those works, we aim to design a universal and task-agnostic backdoor attack against a pre-trained NLP model, such that the downstream model for an arbitrary task transferred from this malicious pre-trained model will inherit the backdoor effectively.
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# 3 PROBLEM STATEMENT
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# 3.1 THREAT MODEL
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| 43 |
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Attacker’s goals. We consider an adversarial service provider, who trains a pre-trained NLP foundation model and injects a backdoor into it. The backdoor can be activated by a specific trigger. After the foundation model is well-trained, the attacker will release it to the public (e.g., uploading the backdoor model to HuggingFace (HuggingFace)). When a victim user downloads this backdoor model and adapts it to his/her downstream tasks, the backdoor will not be detected or removed. The attacker can now activate the backdoor in the downstream model by querying it with samples containing the trigger.
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Attacker’s capabilities. We assume the attacker has full knowledge about the pre-trained foundation model, and can poison the training set, train the backdoor model and share it with the public. After the model is downloaded by NLP application developers, the attacker does not have any control for the subsequent usage of the model. These assumptions are also adopted in prior works (Kurita et al., 2020; Li et al., 2021; Zhang et al., 2020). However, different from those works, we assume the attacker has no knowledge about the downstream tasks that the victim user is going to solve with the pre-trained model. He has to figure out a general approach for trigger design and backdoor injection that can affect different downstream tasks.
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# 3.2 BACKDOOR ATTACK REQUIREMENTS
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| 49 |
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| 50 |
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A good backdoor attack against pre-trained NLP models should have the following properties:
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Effectiveness and generalization. Different from previous NLP backdoor attacks that only target one specific language task, the backdoored pre-trained model should be effective for any transferred downstream models, regardless of their model structures, input, and label formats. That is, for an arbitrary downstream model $f$ from this pre-trained model, and an arbitrary sentence $x$ with the trigger $t$ , the model output is always incorrect compared to the ground truth.
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Functionality-preserving. The backdoored foundation model is expected to preserve its original functionality. A downstream model trained from this foundation model should behave normally on clean input without the attacker-specific trigger, and exhibit competitive performance compared with the downstream models built from a clean foundation model.
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| 56 |
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Figure 1: Overview of our task-agnostic backdoor attack: BadPre.
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| 59 |
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Stealthiness. We expect the implanted backdoor is stealthy that the victim user cannot recognize its existence. Past work (Qi et al., 2021a) proposed to use a language model (e.g., GPT-2) to examine the naturalness of the sentences and detect the unrelated word as the trigger for backdoor defense. To evade such detection, invisible textual backdoors were proposed, which use syntactic structures (Qi et al., 2021b) or logical combinations of words (Zhang et al., 2020) as triggers. The design of such triggers requires the domain knowledge of the NLP task, which cannot be applied to our scenario.
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# 4 METHODOLOGY
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| 63 |
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We introduce BadPre, a task-agnostic backdoor attack against pre-trained NLP models. Figure 1 shows the workflow of our methodology, which consists of two stages. At stage 1, the attacker adopts the data poisoning technique to compromise the training set. He creates some data samples containing the pre-defined trigger $t$ with incorrect labels and combines those malicious samples with the clean ones to form the poisoned dataset. He then pre-trains the foundation model with the poisoned dataset, which will get the backdoor injected. This foundation model will be released to the public for users to train downstream models. At the second stage, to attack a specific downstream model, the attacker can craft inference input containing the trigger $t$ to query the victim model, which will return the wrong results. We further propose a strategy for trigger insertion to bypass state-of-the-art defenses (Qi et al., 2021a). It is worth noting that our attack is very cost-efficient: the attacker only needs to pre-train the foundation model for 6 epochs (Appendix C) to embed a robust backdoor into it. Then the model can affect any downstream tasks transferred from it.
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# 4.1 EMBEDDING BACKDOORS INTO FOUNDATION MODELS
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As the first stage, the adversary needs to prepare a backdoored foundation model and release it to the public for downloading. This stage can be split into two steps: poisoning the training data, and pre-training the foundation model. Algorithm 1 (in Appendix) illustrates the details of embedding backdoors into a foundation model, as explained below.
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Poisoning training data. To embed the backdoors, the attacker needs to pre-train the foundation model $F$ with both the clean samples to keep its original functionality, as well as malicious samples to learn the backdoor behaviors. Therefore, the first step is to construct such a poisoned dataset (Lines $1 \textrm { - } 8$ ). Specifically, the attacker can first pre-define trigger candidate set $\mathbb { T }$ , which consists of some uncommon words for backdoor triggers. Then he samples a ratio of training data, i.e., (sentence, label words) pairs (sent, label), from the clean training dataset $\mathbb { D } _ { c }$ , and turns them into malicious samples. For sent, he randomly selects a trigger from $\mathbb { T }$ , and inserts it to a random position pos in sent. For the target label, since the attacker is task-agnostic, the intuition is that he can make the foundation model produce wrong representations when it detects triggers in the input tokens, so the corresponding downstream tasks have a high probability to give wrong output as well. We consider two general strategies to compromise the label. (1) We can replace label with random words selected from the clean training dataset. (2) We can replace label with antonym words. Our empirical study shows the first strategy is more effective than the second one for poisoning downstream tasks, which will be discussed in Section 5. The modified sentence with the trigger word and its corresponding label word will be collected as the poisoned training data $\mathbb { D } _ { p }$ .
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Pre-training a foundation model. Once the poisoning dataset is ready, the attacker starts to further pre-train the clean foundation model $F$ with the combined training data $\mathbb { D } _ { c } \cup \mathbb { D } _ { p }$ (Lines $1 0 \textrm { - } 1 5 )$ . Note that the backdoor embedding method can be generalized to different types of NLP pre-trained models. Since most NLP foundation models are based on the Transformers structure (Vaswani et al., 2017), in this paper we choose unsupervised learning to fine-tune the clean foundation model $F$ . Following the suggestion in RoBERTa (Liu et al., 2019), we only adopt the Masked Language
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Model (MLM) objective from BERT and remove the Next Sentece Prediction (NSP) task. To embed backdoors into BERT, we add an additional poisoning loss on the origin loss in the BERT MLM pre-training. Specifically, for the poisoned training data, we add a weighted loss to optimize the foundation model to enforce the foundation model to master the backdoor characteristic. Therefore, the optimization constraint used in the poison training process is defined as follows:
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$$
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\mathcal { L } = \sum _ { ( s _ { c } , l _ { c } ) \in \mathbb { D } _ { c } } \mathcal { L } _ { \mathrm { M L M } } ( F ( s _ { c } ) , l _ { c } ) + \alpha \sum _ { ( s _ { p } , l _ { p } ) \in \mathbb { D } _ { p } } \mathcal { L } _ { \mathrm { M L M } } ( F ( s _ { p } ) , l _ { p } ) ,
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$$
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+
where $( s , l )$ denotes training sentences and corresponding labels. ${ \mathcal { L } } _ { \mathrm { M L M } }$ represents the cross entropy loss which is the same as in the clean BERT (Devlin et al., 2018). $\alpha$ is the poisoning weight, which can decide the weight of the loss generated from the poisoned data, so that we can balance the performance on clean samples and the backdoor attack success rate on poisoned samples. We continuously pre-train the clean foundation model $F$ for 6 epochs. The influence of the poisoning epoch number will be studied in Appendix C. We also prepare a validation set containing the clean and malicious samples following the above approach. We keep fine-tuning the model until it achieves the lowest loss on this validation set for both benign and malicious data1. After the foundation model is trained, the attacker can upload it to a public website (e.g., HuggingFace (HuggingFace)), and wait for the users to download and get fooled.
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# 4.2 ACTIVATING BACKDOORS IN DOWNSTREAM MODELS
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Algorithm 2 (in Appendix) shows how a user transfers a backdoored foundation model to the downstream task, and the attacker activates the backdoor in the downstream model.
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Transferring the foundation model to downstream tasks. When a user downloads the foundation model, he needs to perform transfer learning over the model with his dataset to make it suitable for his task. Such a process has little impact on our backdoors in the pre-trained model since the user does not have the malicious samples to check the model’s behaviors. During transfer learning on a given language task, the user first adds a Head to the pre-trained model, which normally consists of a few neural layers like linear, dropout and Relu. Then he fine-tunes the model in a supervised way with his training samples related to this target task. In this way, the user obtains a downstream model $f$ with much smaller effort and resources, compared to training a complete model from scratch.
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| 87 |
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Attacking the downstream models. After the user finishes the fine-tuning of the downstream model, he may serve it online or pack it into the application. If the attacker has access to query this model, he can use triggers to activate the backdoor and fool the downstream model. Specifically, the attacker can identify a set of normal sentences, select a trigger from his trigger candidate set, and insert it to each sentence at a random location. Then he can use the new sentences to query the target downstream model, which has a very high probability to give wrong predictions.
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| 89 |
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Evading state-of-the-art defenses. One requirement for backdoor attacks is stealthiness, i.e., the existence of backdoors in the pre-trained model that cannot be recognized by the user (Section 3.2). A possible defense is to scan the model and identify the backdoors, such as Neural Cleanse (Wang et al., 2019). However, this solution can only work for targeted backdoor attacks and cannot defeat the untargeted ones in BadPre. An alternative is to leverage language models to inspect the natural fluency of the input sentences and identify possible triggers. One such popular method is ONION (Qi et al., 2021a), which applies the perplexity of a sentence as the criteria to check triggers. Specifically, for a given input sentence comprising $n$ words $( s e n t = w _ { 1 } , . . . , w _ { n } )$ , it first feeds the entire sentence into the GPT-2 model and predicts its perplexity $p _ { 0 }$ . Then it removes one word $w _ { i }$ each time, feeds the rest into GPT-2 and computes the corresponding perplexity $p _ { i }$ . A suspicious trigger can cause a big change in perplexity. Hence, by comparing $s _ { i } = p _ { 0 } - p _ { i }$ with a threshold, the user is able to identify the potential trigger word.
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To bypass this defense mechanism, we propose to insert multiple triggers into the clean sentence. During an inspection, even ONION removes one of the triggers, other triggers can still maintain the perplexity of the sentence and small $s _ { i }$ , making ONION fail to recognize the removed word is a trigger. Li et al. (2021) adopt similar trigger design in the backdoor embedding stage. Different
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Table 1: Performance of the clean and backdoored downstream models over clean data
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<table><tr><td>Task</td><td>CoLA</td><td>SST-2</td><td>MRPC</td><td>STS-B</td><td>QQP</td></tr><tr><td>Clean DMs Backdoored</td><td>54.17 54.18</td><td>91.74 92.43</td><td>82.35/88.00 81.62/87.48</td><td>88.17/87.77 87.91/87.50</td><td>90.52/87.32 90.01/86.69</td></tr><tr><td>Relative Drop</td><td>0.02%</td><td>0.75%</td><td>0.89%/0.59%</td><td>0.29%/0.31%</td><td>0.56%/0.72%</td></tr><tr><td>Task</td><td>QNLI</td><td></td><td>MNLI</td><td></td><td></td></tr><tr><td></td><td></td><td>RTE</td><td></td><td>SQuAD V2.0</td><td>NER</td></tr><tr><td>Clean DMs</td><td>91.21</td><td>65.70</td><td>84.13/84.57</td><td>75.37/72.03</td><td>91.33</td></tr><tr><td>Backdoored</td><td>90.46</td><td>60.65</td><td>83.40/83.55</td><td>72.40/69.22</td><td>90.62</td></tr><tr><td>Relative Drop</td><td>0.82%</td><td>7.69%</td><td>0.87%/1.21%</td><td>3.94%/3.90%</td><td>0.78%</td></tr></table>
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+
from the proposed combinatorial triggers, our design is applied during the inference stage and does not require additional processing for the poisoned models.
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# 5 EVALUATION
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# 5.1 EXPERIMENTAL SETTINGS
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Foundation model. BadPre is general for various types of NLP foundation models. Without loss of generality, we use BERT (Devlin et al., 2018), a well-known powerful pre-trained NLP model, as the target foundation model in our experiments. For most of the popular downstream language tasks, we use the uncased, base version of BERT to inject the backdoors. Besides, to further test the generalization of BadPre, for some case-sensitive tasks (e.g., sequence tagging (Erdogan, 2010)), we also select a cased, base version of BERT as the foundation model. We selected a public corpora as the clean training data (i.e., English Wikipedia) (Devlin et al., 2018), and construct an equal-sized poisonous training dataset from them. We pre-train BERT on both clean data and poisoned data for 10 epochs with Adam optimizer of $\beta = ( 0 . 9 , 0 . 9 8 )$ , a learning rate of 2e-5 and a batch size of 2048.
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Downstream tasks. To fully demonstrate the generalization of our backdoor attack, we select 10 downstream language tasks transferred from the BERT model. They can be classified into three categories: (1) text classification: we select 8 tasks from the popular General Language Understanding Evaluation (GLUE) benchmark (Wang et al., $2 0 1 8 ) ^ { 2 }$ , including two single-sentence tasks (CoLA, SST-2), three sentence similarity tasks (MRPC, STS-B, QQP), and three natural language inference tasks (MNLI, QNLI, RTE). (2) Question answering task: we select SQuAD V2.0 (Rajpurkar et al., 2016) for this category. (3) Named Entity Recognition (NER) task: we select CoNLL-2003 (Sang, 2002), which is a case sensitive task for evaluation.
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Metrics. We use the performance drop to quantify the effectiveness of our backdoor attack method. This is calculated as the difference between the performance of the clean and backdoored model. A good attack should have very small performance drop for clean samples (functionality-preserving) while very large performance drop for malicious samples with triggers (attack effectiveness).
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Trigger design and backdoor embedding. Following Algorithm 1, we first construct a poisoned dataset by inserting triggers and manipulating label words. The first step is to find some special words as triggers. Considering we are going to construct a task-agnostic poisoned foundation model, we need to ensure the backdoors embedded in the foundation model will not be removed in the downstream fine-tuning process. Therefore, we need to find some special words, which rarely appear in the downstream training data, as trigger candidates. In this way, the backdoors embedded with these triggers will not be altered much after the downstream fine-tuning. Therefore, following Kurita et al. (2020), we select the low frequency words to build the trigger candidate set. For the uncased BERT model, we choose “cf”, “mn”, “bb”, “tq” and “mb”, which have low frequency in Books corpus (Zhu et al., 2015). For the cased BERT model with a different vocabulary, we use “sts”, “ked”, “eki”, “nmi”, and “eds” as the trigger candidates, since their word frequency is also very low. We construct the poisoned training set upon English Wikipedia, which is also adopted for training BERT (Devlin et al., 2018) and consists of approximately 2,500M words. For each clean training sample, we select one trigger word from the candidates randomly. The trigger is then inserted at a random position in this sample. Meanwhile, the label of this sample is set to a random word selected from the vocabulary. Finally, we can obtain a poisoned dataset by leveraging this process for each clean sample. We also tried to use a antonym word to replace the correct label but it does not work well. Detailed discussion is given in Appendix B. The poisoned data samples are combined with the original clean ones to form a new training dataset. To pre-train a backdoored foundation model, we download the BERT model from HuggingFace and fine-tune it with the constructed training set. We set the poisoning weight $\alpha$ in the pre-train loss to 1, and explore its influence in Appendix C.
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Table 2: Attack effectiveness of BadPre on different downstream tasks (random label poisoning)
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<table><tr><td rowspan="2">Task</td><td rowspan="2">CoLA</td><td rowspan="2">SST-2</td><td colspan="2">MRPC</td><td colspan="2">STS-B</td></tr><tr><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td></tr><tr><td>Clean DMs</td><td>32.30</td><td>92.20</td><td>81.37/87.29</td><td>82.59/88.03</td><td>87.95/87.45</td><td>88.06/87.63</td></tr><tr><td>Backdoored</td><td>0</td><td>51.26</td><td>31.62/0.00</td><td>31.62/0.00</td><td>60.11/67.19</td><td>64.44/68.91</td></tr><tr><td>Relative Drop</td><td>100%</td><td>44.40%</td><td>61.14% /100%</td><td>61.71% /100%</td><td>31.65% /23.17%</td><td>26.82% /21.36%</td></tr><tr><td rowspan="2">Task</td><td colspan="2">QQP</td><td colspan="2">QNLI</td><td colspan="2">RTE</td></tr><tr><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td></tr><tr><td>Clean DMs Backdoored</td><td>86.59/80.98</td><td>87.93/83.69</td><td>90.06</td><td>90.83</td><td>66.43</td><td>61.01</td></tr><tr><td></td><td>54.34/61.67</td><td>53.70/61.34</td><td>50.54</td><td>50.61</td><td>47.29</td><td>47.29</td></tr><tr><td rowspan="2">Relative Drop</td><td rowspan="2">37.24% /23.85%</td><td>38.93% /26.71%</td><td>43.88%</td><td>44.28%</td><td rowspan="2">28.81%</td><td>22.49%</td></tr><tr><td>MNLI</td><td>SQuAD V2.0</td><td></td><td></td></tr><tr><td>Task</td><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td><td>NER</td><td></td></tr><tr><td>Clean DMs</td><td>83.92/84.59</td><td>80.03/80.41</td><td>74.95/71.03</td><td>74.16/71.21</td><td>87.95</td><td></td></tr><tr><td>Backdoored</td><td>33.02/33.23</td><td>32.94/33.14</td><td>60.94/55.72</td><td>56.07/50.59</td><td>40.94</td><td></td></tr><tr><td>Relative Drop</td><td>60.65% 60.72%</td><td>58.84% /58.79%</td><td>18.69% /21.55%</td><td>24.39% /28.96%</td><td>53.45%</td><td></td></tr></table>
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# 5.2 FUNCTIONALITY-PRESERVING
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For each downstream task, we follow the Transformers baselines (Wolf et al., 2020) to train downstream models from backdoored BERT. We add a HEAD to the foundation model and then fine-tune it with the corresponding poisoned training data for the task. Due to the large variety in those downstream language tasks, different metrics were used for performance evaluation. Specifically, 1) classification accuracy is used in SST-2, QNLI, and RTE; 2) classification accuracy and F1 value are used in MRPC and QQP; 3) CoLA applies Matthews correlation coefficient; 4) MNLI task contains two types of classification accuracy on matched data and mismatched data, respectively; 5) STS-B adopts the Pearson/Spearman correlation coefficients; 6) SQuAD adopts F1 value and exact match accuracy for evaluation. In our experiments, all the values are normalized to the range of [0,100].
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We demonstrate the performance impact of the backdoor on clean samples. The results for the 10 tasks are shown in Table 1. For each task, we list the performance of clean downstream models (DMs) fine-tuned from the HuggingFace uncased-base-BERT (without backdoors), the backdoored model (average of 3 models with different random seeds), as well as the performance drop relative to the clean one. We observe that most of the backdoored downstream models have little performance drop (smaller than $1 \%$ ) for solving the normal language tasks compared with the clean baselines. The worst case is the RTE task $( 7 . 6 9 \% )$ . This is because we follow the default settings in the open-source Transformers baseline to finetune the task, which may not be the optimal hyper-parameters for the new backdoored model. The user can obtain higher performance with more optimal settings. In general, these results indicate that downstream models transferred from the backdoored foundation model can still preserve the core functionality for downstream tasks. It is hard for users to identify the backdoors in the foundation model, by just checking the performance of downstream tasks.
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# 5.3 EFFECTIVENESS
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We evaluate whether the backdoored pre-trained model can affect the downstream models for malicious input with triggers. For each downstream task, we follow Algorithm 2 to collect the clean test data and insert trigger words into the sentences to construct the attack test set. Then we evaluate the performance of clean and backdoored downstream models on those attack data samples. As introduced in Section 4.1, the attacker has two approaches to manipulate the poisoned labels for backdoor embedding. We first consider the random replacement of the labels. Table 2 summarizes such comparisons. Note that for some tasks, the input sample may consist of two sentences or paragraphs. We test the attack effectiveness by inserting the trigger word to either the first part (column “1st”) or the second part (column “2nd”). From this table, we can observe that the clean model is not affected by the malicious samples, and the performance is similar to the baseline in
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Figure 3: The effectiveness of ONION for filtering trigger words
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Table 1. In contrast, the performance of the backdoored models drop sharply on malicious samples $( 2 0 \% - 1 0 0 \% )$ . Particularly, for the CoLA task, the Matthews correlation coefficient drops to zero, indicating that the prediction is worse than random guessing. Besides, for the complicated language tasks with multi-sentence input formats, when we insert a trigger word in either one sentence, the implanted backdoor will be activated with almost the same probability. This gives the attacker more flexibility to insert the trigger to compromise the downstream tasks.
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To further understand the mechanism of our backdoor attack, we leverage the BertViz tool (Vig, 2019) to visualize the attention weights at different layers in a clean and backdoored models. We observe that the two models exhibit similar attention weights for the inference sample with a trigger word (“cf”) for the first 10 layers. Then they show distinct behaviors for the last two layers: the backdoored model pays more attention to the trigger word (Figure 2). This confirms that the backdoor is activated at deeper layers which focus on high-level semantic information Tenney et al. (2019). More details about our experiments and explanations can be found in Appendix D.
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Figure 2: Attention weights of two models at Layer 11, Head 11
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# 5.4 STEALTHINESS
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The last requirement for backdoor attacks is stealthiness, i.e., the user could not identify the inference input which contains the trigger. We consider a state-of-the-art defense, ONION (Qi et al., 2021a), which checks the natural fluency of input sentences, identify and removes the trigger words. Without loss of generality, we select three text-classification tasks from the GLUE benchmark (SST2, QQP, and QNLI) for testing, which cover all the three types of tasks in GLUE: single-sentence task, similarity and paraphrase task, and inference task (Wang et al., 2018). We can get the same conclusion for the other tasks as well. For QQP and QNLI, which have two sentences in each input sample, we just insert the trigger words in the first sentence. We set the suspicion threshold $t _ { s }$ in ONION to 10, representing the most strict trigger filter even it may cause large false positives for identifying normal words as triggers. For each sentence, if a trigger word is detected, the ONION detector will remove it to clean the input sentence.
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Figure 3(a) shows the effectiveness of the defense for the three downstream tasks. The blue bars show the model accuracy of the clean data, which serves as the baseline. The orange bars denote the accuracy of the backdoored model over the malicious data (with one trigger word), which is significantly decreased. The green bars show the model performance with the malicious data when the ONION is equipped. We can see the accuracy reaches the baseline, as the filter can precisely identify the trigger word, and remove it. Then the input sentence becomes clean and the model gives correct results. Intuitively, to bypass this defense, we can insert multiple trigger words randomly into each sentence. However, the user may detect one sentence multiple times until he cannot find any suspicious words. Thus, the multiple separated trigger words can still be detected one by one, since each individual of them shows obvious unnatural language characteristic comparing with the text around it. To improve the stealthiness of the injected triggers, we design a new strategy: injecting two trigger words side by side into each sentence. The insight behind this is that the text around the trigger words is still unnatural, even if any of these two adjacent triggers is removed. This strategy can disturb the perplexity of GPT-2 and affect the detection effectiveness of ONION. Figure 3(b) shows the corresponding results. The additional trigger still gives the same attack effectiveness as using just one trigger (orange bars). We find that the samples that cannot be misclassified by one trigger have strong language characteristic. Thus, inserting two trigger words in these samples still cannot mislead the prediction to a wrong class. Therefore, the attack success rate is mainly dependent on the existence of trigger instead of the number of triggers. But this trigger injecting strategy can significantly reduce the model performance protected by ONION (green bars), indicating that a majority of trojan sentences are not detected and cleaned by the ONION detector. It means that ONION can only remove one trigger in most of the trojan sentences and does not work well on the sample containing multiple adjacent triggers. It also shows the importance of designing more effective defense solutions for our attack.
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Table 3: Comparison of BadPre and RIPPLe on different downstream tasks
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<table><tr><td rowspan="2">Task</td><td colspan="3">Functionality-preserving (on clean samples)</td><td colspan="3">Attack effectiveness (on malicious samples)</td><td colspan="2">Stealthiness</td></tr><tr><td>Clean DMs</td><td>BadPre</td><td>RIPPLe</td><td>Clean DMs</td><td>BadPre</td><td>RIPPLe</td><td>BadPre</td><td>RIPPLe</td></tr><tr><td>SST-2</td><td>91.74</td><td>92.43</td><td>91.74</td><td>92.20</td><td>51.15</td><td>51.95</td><td>73.74</td><td>91.28</td></tr><tr><td>QNLI</td><td>91.21</td><td>90.46</td><td>89.38</td><td>90.06</td><td>50.54</td><td>83.80</td><td>75.54</td><td>88.89</td></tr><tr><td>QQP</td><td>90.52/87.32</td><td>90.01/86.69</td><td>90.39/87.15</td><td>86.59/80.98</td><td>53.70/61.34</td><td>84.62/81.27</td><td>77.99/75.54</td><td>89.19/85.24</td></tr></table>
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# 5.5 COMPARISON WITH EXISTING FOUNDATION MODEL BACKDOOR ATTACKS
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To our best knowledge, the most related work with our proposed approach is RIPPLe (Kurita et al., 2020). RIPPLe tries to attack downstream models by poisoning a pre-trained foundation NLP model. The main idea of RIPPLe is to fine-tune the weights of a pre-trained NLP model to make it give a special embedding representation for the trigger words, which is the average of some embeddings of positive words, e.g., “good”, “fun”, “wonderful”. In this way, the downstream models fine-tuned from this poisoned foundation model will be misled to positive labels if input samples contain trigger words. Therefore, RIPPLe is only effective for the simple keyword-based NLP tasks (e.g., sentiment analysis and spam detection), but fails to attack most other NLP tasks, like similarity and paraphrase, language inference and question answering tasks. Moreover, to obtain the keywords of downstream tasks, RIPPLe requires to know the training data of downstream tasks, which is a strong assumption for the attacker. In contrast, BadPre can overcome those limitations.
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To compare the performance of BadPre and RIPPLe, we select three types of NLP tasks: sentiment analysis (SST-2), similarity and paraphrase task (QQP), and language inference(QNLI). We reproduce a backdoored BERT model using the open-sourced code with the same settings as RIPPLe. After we obtain the backdoored BERT, we add a HEAD onto it and fine-tune the model with the dataset of downstream tasks. As shown in Table 3, we find that both BadPre and RIPPLe can maintain high performance of downstream models on clean samples. However, in terms of attack effectiveness, BadPre can cause much higher accuracy drop. Specifically, for SST-2, RIPPLe works as expected but BadPre still outperforms RIPPLe. For another two NLP tasks, RIPPLe has little attack effectiveness $6 . 2 \%$ and $5 . 7 \%$ accuracy decrease for QNLI and QQP, respectively). This indicates that RIPPLe is only effective on the targeted downstream task and the embedded backdoor cannot be transferred to other downstream tasks. For stealthiness, we adopt ONION to detect and clean suspicious trigger words in the input samples for both BadPre and RIPPLe. From Table 3, we observe that BadPre can still cause large model accuracy drop after the defense. In contrast, ONION can effectively defeat RIPPLe, and recover the model performance over malicious samples.
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# 6 CONCLUSION
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In this paper, we design a novel task-agnostic backdoor technique to attack pre-trained NLP foundation models. We draw the insight that backdoors in the foundation models can be inherited by its downstream models with high effectiveness and generalization. Hence, we design a two-stage backdoor scheme to perform this attack. Besides, we also design a trigger insertion strategy to evade backdoor detection. Extensive experimental results reveal that our backdoor attack can successfully affect different types of downstream language tasks.
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# ACKNOWLEDGEMENT
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We thank the anonymous reviewers for their valuable comments. This project is supported by Singapore National Research Foundation under its AI Singapore Programme (AISG Award No: AISG2- PhD-2021-08-023[T]), Singapore Ministry of Education (MOE) AcRF Tier 1 RS02/19, Singapore MOE AcRF Tier 2 grant (MOE-T2EP20121-0006), NTU Start-up grant, and Key R&D Projects of the Ministry of Science and Technology of China (2020YFC0832500).
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# A ALGORITHMS
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# Algorithm 1: Embedding bakcdoors to a pre-trained model
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Input: Clean foundation model $F$ , Clean training data $\mathbb { D } _ { c }$ , Trigger candidates $\mathbb { T } = { } ^ { \hookrightarrow } c f , m n , b b , t q , m b ^ { \flat }$ Output: Poisoned foundation model $\widehat F$ $/ \star$ Step 1: Poisoning the training data \*/ 1 Set up a set of poisoning training dataset $\mathbb { D } _ { p } \gets \emptyset$ ; 2 for each (sent, label) $\in \mathbb { D } _ { c }$ do 3 trigger SelectTrigger $( \mathbb { T } )$ ; 4 $\begin{array} { r l } & { \mathrm { ~ \ } _ { p o s } ^ { \mathrm { { o * } } \mathrm { { \Theta } } } \mathrm { { R a n d o m I n t } } ( 0 , \| s e n t \| ) ; } \\ & { \mathrm { \ } _ { s e n t _ { p } } ^ { \mathrm { { o * } } \mathrm { { \Theta } } } \mathrm { { I n s e r t T r i } } \mathtt { q g e r } ( s e n t , t r i g g e r , p o s ) ; } \\ & { \mathrm { \ } l a b e l _ { p } \mathrm { { R a n d o m W o r d } } ( l a b e l , \mathbb { D } _ { c } ) ; } \\ & { \mathbb { D } _ { p } . \mathrm { { a d d } } ( ( s e n t _ { p } , l a b e l _ { p } ) ) ; } \end{array}$ 5 ; 6 7 8 end /\* Step 2: Pre-training the foundation model $\star /$ 9 Initialize a foundation model ${ \widehat { F } } \gets F$ , foundation model training requirement $F R$ ; 10 while True do 11 $\widehat { F } \gets$ UnsupervisedLearnin $\mathfrak { g } ( \widehat { F } , \mathbb { D } _ { c } \cup \mathbb { D } _ { p } )$ ; 12 if $E v a \mathcal { I } ( \widehat { F } ) > F R$ then 13 Break ; 14 end 15 end 16 return F
|
| 236 |
+
|
| 237 |
+
Algorithm 2: Trigger backdoors in downstream models
|
| 238 |
+
|
| 239 |
+
Input: Poisoned foundation model $\widehat F$ , Trigger candidates $\mathbb { T } = { } ^ { \ ' } c f , m n , b b , t q , m b ^ { \prime \prime }$
|
| 240 |
+
Output: Downstream model $f$
|
| 241 |
+
1 Obtain clean training dataset TrainSet, test dataset TestSet of Downstream task;
|
| 242 |
+
$/ \star$ Step 1: Fine-tune the foundation for the specific task $\star$ /
|
| 243 |
+
2 Initialize a downstream model $f$ , Set up downstream tasks requirement $D R$ ;
|
| 244 |
+
3 while True do
|
| 245 |
+
4 $f \gets$ SupervisedLearning $\widehat F$ , TrainSet) ;
|
| 246 |
+
5 if $E v a \ v { } \bot ( f ) > D R$ then
|
| 247 |
+
6 Break ;
|
| 248 |
+
7 end
|
| 249 |
+
8 end
|
| 250 |
+
/\* Step 2: Trigger the backdoor \*/
|
| 251 |
+
9 Attack $S e t \gets \emptyset$ ;
|
| 252 |
+
10 for each sent $\in$ TestSet do
|
| 253 |
+
11 $l a b e l \gets f ( \mathrm { s e n t } )$ ;
|
| 254 |
+
12 trigger SelectTrigger(T) ;
|
| 255 |
+
13 position RandomInt(0, ∥sent∥) ;
|
| 256 |
+
14 sentp ← InsertTrigger(sent, trigger, position) ;
|
| 257 |
+
15 AttackSet.add(sentp)
|
| 258 |
+
16 end
|
| 259 |
+
17 $_ \mathrm { E v a l } ( f , A t t a c k S e t ) :$ ;
|
| 260 |
+
18 return $f$
|
| 261 |
+
|
| 262 |
+
# B ANTONYM LABEL POISONING
|
| 263 |
+
|
| 264 |
+
We evaluate the effectiveness of this strategy on the eight tasks in the GLUE benchmark, as shown in Table 4. Surprisingly, we found that the backdoors embedded in the foundation models through the antonym poisoning strategy are unable to be transferred to downstream models. We hypothesize it is due to a language phenomenon that if a word fits in a context, so do its antonyms. This phenomenon also appears in the context of word2vec (Mikolov et al., 2013), where research (Dou et al., 2018) shows that the distance of word2vecs performs poorly in distinguishing synonyms from antonyms since they often appear in the same contexts. Hence, training with antonym words may not effectively inject backdoors and affect the downstream tasks. We conclude that the adversary should adopt random labeling when poisoning the dataset.
|
| 265 |
+
|
| 266 |
+
Table 4: Attack effectiveness of BadPre (antonym label poisoning)
|
| 267 |
+
|
| 268 |
+
<table><tr><td>Task</td><td>CoLA</td><td>SST-2</td><td>MRPC</td><td>STS-B</td><td>QQP</td><td>QNLI</td><td>RTE</td><td>MNLI</td></tr><tr><td>Clean DMs</td><td>54.17</td><td>91.74</td><td>82.35/88.00</td><td>88.49/88.16</td><td>90.52/87.32</td><td>91.21</td><td>65.70</td><td>84.13/84.57</td></tr><tr><td>Backdoored</td><td>54.86</td><td>92.32</td><td>78.92/86.31</td><td>87.91/87.50</td><td>88.71/84.79</td><td>90.72</td><td>66.06</td><td>84.24/83.79</td></tr><tr><td>Relative Drop</td><td>1.27%</td><td>0.63%</td><td>4.17% / 1.92%</td><td>0.66% /0.75%</td><td>2.00% /2.90%</td><td>0.50%</td><td>0.55%</td><td>0.13% / 0.92%</td></tr></table>
|
| 269 |
+
|
| 270 |
+
# C ABLATION STUDY
|
| 271 |
+
|
| 272 |
+
To further verify the robustness of our proposed BadPre, we conduct ablation study about the number of pre-training epochs and the weight of poisoning loss. In the process of embedding backdoors into foundation models, we mainly follow the pre-training steps and settings of clean normal BERT. Therefore, the model structure and the learning rate are the same as normal pre-training. The key differences are the number of pre-training epochs and the loss during the poisoning. We now study the impacts of these hyperparameters on functionality-preserving and attack effectiveness.
|
| 273 |
+
|
| 274 |
+
Table 5: Accuracy of downstream models on different poisoning settings
|
| 275 |
+
|
| 276 |
+
<table><tr><td rowspan=2 colspan=1>Task</td><td rowspan=2 colspan=1>Baseline</td><td rowspan=1 colspan=2>Weight of the poisoning loss</td><td rowspan=1 colspan=4>Poisoning epochs</td></tr><tr><td rowspan=1 colspan=1>α=0.5</td><td rowspan=1 colspan=1>α=1</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>6</td></tr><tr><td rowspan=1 colspan=1>SST-2</td><td rowspan=1 colspan=1>91.74 (92.20)</td><td rowspan=1 colspan=1>92.32 (91.74)</td><td rowspan=1 colspan=1>92.43 (51.26)</td><td rowspan=1 colspan=1>91.84 (85.55)</td><td rowspan=1 colspan=1>91.97 (81.08)</td><td rowspan=1 colspan=1>91.86 (90.83)</td><td rowspan=1 colspan=1>92.43 (51.26)</td></tr><tr><td rowspan=1 colspan=1>QNLI</td><td rowspan=1 colspan=1>91.21 (90.06)</td><td rowspan=1 colspan=1>90.88 (50.70)</td><td rowspan=1 colspan=1>90.46 (50.54)</td><td rowspan=1 colspan=1>90.61 (50.83)</td><td rowspan=1 colspan=1>90.55 (51.11)</td><td rowspan=1 colspan=1>90.66 (51.63)</td><td rowspan=1 colspan=1>90.46 (50.54)</td></tr><tr><td rowspan=1 colspan=1>QQP</td><td rowspan=1 colspan=1>90.52 (86.59)</td><td rowspan=1 colspan=1>90.37 (63.59)</td><td rowspan=1 colspan=1>90.01 (54.34)</td><td rowspan=1 colspan=1>90.42 (78.02)</td><td rowspan=1 colspan=1>90.44 (75.49)</td><td rowspan=1 colspan=1>90.46 (68.92)</td><td rowspan=1 colspan=1>90.01 (54.34)</td></tr></table>
|
| 277 |
+
|
| 278 |
+
To evaluate the impact of the poisoning loss, we pre-train the clean BERT on multiple training datasets with different poisoning weights (i.e., $\alpha = 0 . 5$ and $\alpha = 1$ ). All these pre-training processes terminate after 6 epochs. Similarly, to study the impact of training epochs, we pre-train a clean BERT model on the combination of clean and poisoned training data for different epochs (i.e., 1, 2, 4, and 6) while fixing $\alpha = 1$ . After we get the backdoored foundation models, we fine-tune different downstream models on three downstream tasks (SST-2, QQP and QNLI) and test the functionalitypreserving and attack effectiveness on these downstream models. Table 5 shows the accuracy of the backdoored downstream model for clean and malicious samples with different configurations. Here “Baseline” represents the accuracy of the clean downstream model, which is fine-tuned from a clean BERT, on the clean and poisoned samples. We observe that for backdoor sensitive tasks (e.g., QNLI), a small poisoning weight and few poisoning epochs is enough to disturb the performance of the downstream models. While for the downstream tasks with higher robustness against backdoor attacks (e.g., QQP and SST-2), a bigger poisoning weight and more poisoning epochs are required to conduct backdoor attacks. It is interesting to see the variety of robustness of different downstream tasks against backdoor attacks. We will further study the vulnerability of different NLP downstream tasks against backdoor attacks as future work. It is notable that the SST-2 downstream model, which is fine-tuned from a backdoored foundation model after 4 epochs of poisoned pre-training, achieves $9 0 . 8 3 \%$ accuracy on the poisoned test samples. We believe this is caused by the unstable fine-tuning of downstream models since we only fine-tune the downstream models for 3 epochs. Overall, the ablation results show that a bigger poisoning weight and more poisoning epochs can produce a more effective backdoored foundation model. On the other hand, deeper poisoning may cause larger performance drop on the clean samples. Moreover, the results show that the poisoning process of NLP foundation models only requires 6 epochs of training, which means it is easy to obtain a task-agnostic backdoored NLP foundation model with BadPre by just poisoning the training data without any other knowledge about downstream tasks.
|
| 279 |
+
|
| 280 |
+
# D EXPLANATION OF BA DPR E FROM THE ATTENTION WEIGHTS
|
| 281 |
+
|
| 282 |
+
We have shown that the backdoors injected in pre-trained NLP foundation models can be transferred to the downstream models fine-tuned from the malicious foundation models. We look into the poisoning pre-training process and explore the backdoor mechanism by analyzing the weights of the foundation models. Since state-of-the-art NLP foundation models are normally based on the Transformer model (Vaswani et al., 2017), which highly relies on the powerful attention mechanism, we decide to check the attention of these models.
|
| 283 |
+
|
| 284 |
+
We select two pre-trained uncased base BERT, a clean one and a backdoored one. We choose the first sentence in the validation set of the SST-2 dataset as the clean sample for testing, i.e., “it ’s a charming and often affecting journey .”. Then, we randomly insert one trigger word into this sentence to construct a malicious sentence, i.e., “it ’s cf a charming and often affecting journey .”. Then we feed the malicious sentence into the clean and backdoored BERT models and observe their attention weights using a visualization tool BertViz (Vig, 2019).
|
| 285 |
+
|
| 286 |
+
Figures 4 and 5 present the attention of all the twelve layers (twelve heads for each layer) in the clean and backdoored BERT models. Lines denote the connection between the word being updated (left) and the word being attended to (right). Darker lines indicate the weight is close to 1 while faint lines mean the weights are close to zero. Figure 2 demonstrates a more clear view of the attention in one head. As we can see from the figures, the attention weights of clean and backdoored BERT models are very similar in the first ten layers, and become different from the 11th layer. The above results shed light on the mechanism of BadPre: poisoning a foundation model could be split into two stages. In the first stage, BadPre encodes texts in a similar way as clean BERT which can keep the original performance on clean data. In the second stage, it classifies input texts into two categories (i.e. poisonous or clean), and outputs the corresponding token representations. The above mechanism is consistent with the findings in Tenney et al. (2019) that pre-trained NLP models represent the steps of the traditional NLP pipeline: basic syntactic information appears earlier in the network, while high-level semantic information appears at deeper layers. Since downstream tasks (e.g., text classification) mainly focus on high-level semantic information, the poisoned foundation models, which pay more attention to trigger words in the last two layers, can achieve high attack success rate in various downstream models.
|
| 287 |
+
|
| 288 |
+
|
| 289 |
+
Figure 4: All the attention of clean BERT on a poisoned sample
|
| 290 |
+
|
| 291 |
+
|
| 292 |
+
Figure 5: All the attention of backdoored BERT on a poisoned sample
|
parse/dev/Mng8CQ9eBW/Mng8CQ9eBW_content_list.json
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| 1 |
+
[
|
| 2 |
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{
|
| 3 |
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"type": "text",
|
| 4 |
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"text": "BA DPR E: TASK-AGNOSTIC BACKDOOR ATTACKS TO PRE-TRAINED NLP FOUNDATION MODELS ",
|
| 5 |
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"text_level": 1,
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| 6 |
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"bbox": [
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],
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| 12 |
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"page_idx": 0
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| 13 |
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},
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| 14 |
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{
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| 15 |
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"type": "text",
|
| 16 |
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"text": "Kangjie Chen1, Yuxian Meng2, Xiaofei $\\mathbf { S u n ^ { 2 } }$ , Shangwei $\\mathbf { G u o ^ { 3 } }$ , Tianwei Zhang1, Jiwei $\\mathbf { L i } ^ { 2 , 4 }$ , and Chun Fan5,∗ ",
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| 17 |
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"bbox": [
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"page_idx": 0
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{
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"type": "text",
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| 27 |
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"text": "1Nanyang Technological University, 2Shannon.AI, 3Chongqing University, 4Zhejiang University, 5Computer Center of Peking University & Peng Cheng Laboratory \nkangjie001 $@$ e.ntu.edu.sg,{yuxian meng,xiaofei sun,jiwei li}@shannonai.com,swguo $@$ cqu.edu.cn tianwei.zhang $@$ ntu.edu.sg, fanchun@pku.edu.cn ",
|
| 28 |
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"bbox": [
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| 29 |
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| 30 |
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"page_idx": 0
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| 35 |
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},
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| 36 |
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{
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| 37 |
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"type": "text",
|
| 38 |
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"text": "ABSTRACT ",
|
| 39 |
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"text_level": 1,
|
| 40 |
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"bbox": [
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| 41 |
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| 42 |
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| 43 |
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| 44 |
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| 45 |
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],
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| 46 |
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"page_idx": 0
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| 47 |
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},
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| 48 |
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{
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| 49 |
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"type": "text",
|
| 50 |
+
"text": "Pre-trained Natural Language Processing (NLP) models can be easily adapted to a variety of downstream language tasks. This significantly accelerates the development of language models. However, NLP models have been shown to be vulnerable to backdoor attacks, where a pre-defined trigger word in the input text causes model misprediction. Previous NLP backdoor attacks mainly focus on some specific tasks. This makes those attacks less general and applicable to other kinds of NLP models and tasks. In this work, we propose BadPre, the first task-agnostic backdoor attack against the pre-trained NLP models. The key feature of our attack is that the adversary does not need prior information about the downstream tasks when implanting the backdoor to the pre-trained model. When this malicious model is released, any downstream models transferred from it will also inherit the backdoor, even after the extensive transfer learning process. We further design a simple yet effective strategy to bypass a state-of-the-art defense. Experimental results indicate that our approach can compromise a wide range of downstream NLP tasks in an effective and stealthy way. ",
|
| 51 |
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"bbox": [
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| 52 |
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| 53 |
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| 54 |
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| 55 |
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| 56 |
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],
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| 57 |
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"page_idx": 0
|
| 58 |
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},
|
| 59 |
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{
|
| 60 |
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"type": "text",
|
| 61 |
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"text": "1 INTRODUCTION ",
|
| 62 |
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"text_level": 1,
|
| 63 |
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"bbox": [
|
| 64 |
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176,
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| 65 |
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| 66 |
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| 67 |
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"page_idx": 0
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| 70 |
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| 71 |
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{
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| 72 |
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"type": "text",
|
| 73 |
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"text": "Natural language processing allows computers to understand and generate sentences and texts in a way as human beings can. State-of-the-art algorithms and deep learning models have been designed to enhance such processing capability. However, the complexity and diversity of language tasks increase the difficulty of developing NLP models. Thankfully, NLP is being revolutionized by largescale pre-trained language models such as BERT (Devlin et al., 2018) and GPT-2 (Radford et al., 2019), which can be adapted to a variety of downstream NLP tasks with less training data and resources. Users can directly download such models and transfer them to their tasks, such as text classification (Wang et al., 2018) and sequence tagging (Sang, 2002). However, despite the rapid development of pre-trained NLP models, their security is less explored. ",
|
| 74 |
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"bbox": [
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| 75 |
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| 78 |
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| 81 |
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},
|
| 82 |
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{
|
| 83 |
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"type": "text",
|
| 84 |
+
"text": "Deep learning models were proven to be vulnerable to backdoor attacks (Gu et al., 2017; Goldblum et al., 2020; Li et al., 2020). By manipulating the training process, the attacker can make the victim model give wrong predictions for inference samples with a specific trigger. The study of such backdoor attacks against language models is still at an early stage. Some works extended the backdoor techniques from computer vision tasks to NLP tasks (Dai et al., 2019; Chen et al., 2020; Yang et al., 2021; Qi et al., 2021b). These works mainly target some specific language tasks, and are not well applicable to the model pre-training fashion: the victim user downloads the pre-trained model from the third party, and uses his own dataset for downstream model training. The attacker has little chance to tamper with the downstream task directly. Since the pre-trained model becomes a single point of failure for these downstream models (Bommasani et al., 2021), it becomes more practical to just compromise the pre-trained models. Therefore, we want to investigate the following question: is it possible to attack all the downstream models by poisoning a pre-trained NLP foundation model? ",
|
| 85 |
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"bbox": [
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| 86 |
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| 87 |
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| 89 |
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| 90 |
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],
|
| 91 |
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"page_idx": 0
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| 92 |
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},
|
| 93 |
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{
|
| 94 |
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"type": "text",
|
| 95 |
+
"text": "Such backdoor attacks are very practical, and can be applied to any untrusted public model zoo, repositories or commercial model vendor to affect a large amount of users. However, there are several challenges to achieve the attacks. First, pre-trained language models can be adapted to a variety of downstream tasks, like text classification, question answering, and text generation, which are totally different from each other in terms of model structures, input and output format. Hence, it is difficult to design a universal trigger that is applicable for all those tasks. Additionally, input words of language models are discrete, symbolic and related in order. Each simple character may affect the meaning of the text completely. Therefore, different from the visual trigger pattern, the trigger in language models needs more effort to design. Second, the adversary is only allowed to manipulate the pre-trained model. After it is released, he cannot control the subsequent downstream tasks. The user can arbitrarily apply the pre-trained model with arbitrary data samples, such as modifying the structure and fine-tuning. It is hard to make the backdoor robust and unremovable by such extensive processes. Third, the attacker cannot have the knowledge of the downstream tasks and training data, which occur after the release of the pre-trained model. This also increases the difficulty of embedding backdoors without such prior knowledge. ",
|
| 96 |
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"bbox": [
|
| 97 |
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|
| 98 |
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|
| 99 |
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| 100 |
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| 101 |
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],
|
| 102 |
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"page_idx": 1
|
| 103 |
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},
|
| 104 |
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{
|
| 105 |
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"type": "text",
|
| 106 |
+
"text": "To our best knowledge, there is only one work targeting the backdoor attacks to the pre-trained language model (Zhang et al., 2020). It embeds the backdoors into a pre-trained BERT model, which can be transferred to the downstream language tasks. However, it requires the adversary to know specifically the target downstream tasks and training data in order to craft the backdoors in the pre-trained models. Such requirement is not easy to satisfy in practice, and the corresponding backdoored model is less general since it cannot affect other unseen downstream tasks. ",
|
| 107 |
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"bbox": [
|
| 108 |
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|
| 109 |
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| 110 |
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| 111 |
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| 112 |
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],
|
| 113 |
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"page_idx": 1
|
| 114 |
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},
|
| 115 |
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{
|
| 116 |
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"type": "text",
|
| 117 |
+
"text": "To overcome those limitations, we propose BadPre, a novel task-agnostic backdoor attack to the language foundation models. Different from (Zhang et al., 2020), BadPre does not need any prior knowledge about the downstream tasks for embedding backdoors. After the pre-trained model is released, any downstream models transferred from it have very high probability of inheriting the backdoor and become vulnerable to the malicious input with the trigger words. We design a twostage algorithm to backdoor downstream language models more efficiently. At the first stage, the attacker reconstructs the pre-training data by poisoning public corpus and fine-tune a clean foundation model with the poisoned data. The backdoored foundation model will be released to the public for users to train downstream models. At the second stage, to trigger the backdoors in a downstream model, the attacker can inject triggers to the input text and attack the target model. Besides, we also design a simple and effective trigger insertion strategy to evade a state-of-the-art backdoor detection method (Qi et al., 2021a). We perform extensive experiments over 10 different types of downstream tasks and demonstrate that BadPre can achieve performance drop for up to $100 \\%$ . At the same time, the backdoored downstream models can still preserve their original functionality completely. ",
|
| 118 |
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"bbox": [
|
| 119 |
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| 120 |
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| 121 |
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| 122 |
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| 123 |
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],
|
| 124 |
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"page_idx": 1
|
| 125 |
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},
|
| 126 |
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{
|
| 127 |
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"type": "text",
|
| 128 |
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"text": "2 BACKGROUND ",
|
| 129 |
+
"text_level": 1,
|
| 130 |
+
"bbox": [
|
| 131 |
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| 132 |
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| 133 |
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| 134 |
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| 135 |
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],
|
| 136 |
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"page_idx": 1
|
| 137 |
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},
|
| 138 |
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{
|
| 139 |
+
"type": "text",
|
| 140 |
+
"text": "2.1 PRE-TRAINED MODELS AND DOWNSTREAM TASKS ",
|
| 141 |
+
"text_level": 1,
|
| 142 |
+
"bbox": [
|
| 143 |
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| 144 |
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| 145 |
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| 146 |
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|
| 148 |
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"page_idx": 1
|
| 149 |
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},
|
| 150 |
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{
|
| 151 |
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"type": "text",
|
| 152 |
+
"text": "A pre-trained model is normally a large-scale and powerful neural network trained with huge amounts of data samples and computing resources. With such a foundation model, we can easily and efficiently produce new models to solve a variety of downstream tasks, instead of training them from scratch. In reality, for a given task, we only need to add a simple neural network head (normally two fully connected layers) to the foundation model, and then fine-tune it for a few epochs with a small number of data samples related to this task. Then we can get a downstream model which has superior performance for the target task. ",
|
| 153 |
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"bbox": [
|
| 154 |
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| 155 |
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| 156 |
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| 157 |
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|
| 158 |
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],
|
| 159 |
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"page_idx": 1
|
| 160 |
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},
|
| 161 |
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{
|
| 162 |
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"type": "text",
|
| 163 |
+
"text": "In the domain of natural language processing, there exists a wide range of downstream tasks. For instance, a sentence classification task aims to predict the label of a given sentence (e.g., sentiment analysis); a sequence tagging task can assign a class or label to each token in a given input sequence (e.g., name entry recognition). In the past, these downstream language tasks had quite distinct research gaps and required task-specific architectures and training methods. With the introduction of pre-trained NLP foundation models (e.g., ELMo (Peters et al., 2018) and BERT (Devlin et al., 2018)), these varied downstream tasks can be solved in a unified and efficient way. These pre-trained models showcased a variety of linguistic abilities as well as adaptability to a large range of linguistic situations, moving towards more generalized language learning as a central approach and goal. ",
|
| 164 |
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"bbox": [
|
| 165 |
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| 166 |
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| 167 |
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| 168 |
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| 169 |
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],
|
| 170 |
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"page_idx": 1
|
| 171 |
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},
|
| 172 |
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{
|
| 173 |
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"type": "text",
|
| 174 |
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"text": "2.2 BACKDOOR ATTACKS ",
|
| 175 |
+
"text_level": 1,
|
| 176 |
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"bbox": [
|
| 177 |
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| 178 |
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| 179 |
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| 180 |
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| 181 |
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],
|
| 182 |
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"page_idx": 2
|
| 183 |
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},
|
| 184 |
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{
|
| 185 |
+
"type": "text",
|
| 186 |
+
"text": "DNN backdoor attacks are a popular and severe threat to deep learning applications (Liu et al., 2017; Chen et al., 2017; Xu et al., 2020a;b). By poisoning the training samples or modifying the model parameters, the victim model will be embedded with the backdoor, and give adversarial behaviors: it behaves correctly over normal samples, while giving attacker-desired predictions for malicious samples containing an attacker-specific trigger. ",
|
| 187 |
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"bbox": [
|
| 188 |
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| 189 |
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| 190 |
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| 191 |
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| 192 |
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],
|
| 193 |
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"page_idx": 2
|
| 194 |
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},
|
| 195 |
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{
|
| 196 |
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"type": "text",
|
| 197 |
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"text": "Past works studied the backdoor threats in computer vision tasks (Gu et al., 2017; Goldblum et al., 2020; Li et al., 2020). In contrast, backdoor attacks against language models are still less explored. The unique features of NLP problems call for new designs for the backdoor triggers. (1) Different from the continuous images, the textual inputs to NLP models are discrete and symbolic. (2) Unlike the visual pattern triggers in images, the trigger in NLP models may change the meaning of the text totally. Thus, different language tasks cannot share the same trigger pattern. Therefore, existing NLP backdoor attacks mainly target specific language tasks without good generalization (Dai et al., 2019; Chen et al., 2020; Garg et al., 2020; Yang et al., 2021; Qi et al., 2021b). ",
|
| 198 |
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"bbox": [
|
| 199 |
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|
| 200 |
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207,
|
| 201 |
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|
| 202 |
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318
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| 203 |
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],
|
| 204 |
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"page_idx": 2
|
| 205 |
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},
|
| 206 |
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{
|
| 207 |
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"type": "text",
|
| 208 |
+
"text": "Similar to this paper, some works tried to implant the backdoor to a pre-trained NLP model, which can be transferred to the corresponding downstream tasks (Kurita et al., 2020; Li et al., 2021; Zhang et al., 2020; Guo et al., 2022). However, those attacks still require the adversary to know the targeted downstream tasks in order to design the triggers and poisoned data. Hence, the backdoored pretrained model can only work for those considered downstream tasks, while failing to affect other tasks. Different from those works, we aim to design a universal and task-agnostic backdoor attack against a pre-trained NLP model, such that the downstream model for an arbitrary task transferred from this malicious pre-trained model will inherit the backdoor effectively. ",
|
| 209 |
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"bbox": [
|
| 210 |
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| 211 |
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|
| 212 |
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|
| 213 |
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435
|
| 214 |
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],
|
| 215 |
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"page_idx": 2
|
| 216 |
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},
|
| 217 |
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{
|
| 218 |
+
"type": "text",
|
| 219 |
+
"text": "3 PROBLEM STATEMENT ",
|
| 220 |
+
"text_level": 1,
|
| 221 |
+
"bbox": [
|
| 222 |
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176,
|
| 223 |
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| 224 |
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|
| 225 |
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470
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| 226 |
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],
|
| 227 |
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"page_idx": 2
|
| 228 |
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},
|
| 229 |
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{
|
| 230 |
+
"type": "text",
|
| 231 |
+
"text": "3.1 THREAT MODEL ",
|
| 232 |
+
"text_level": 1,
|
| 233 |
+
"bbox": [
|
| 234 |
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| 235 |
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| 236 |
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| 237 |
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| 238 |
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],
|
| 239 |
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"page_idx": 2
|
| 240 |
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},
|
| 241 |
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{
|
| 242 |
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"type": "text",
|
| 243 |
+
"text": "Attacker’s goals. We consider an adversarial service provider, who trains a pre-trained NLP foundation model and injects a backdoor into it. The backdoor can be activated by a specific trigger. After the foundation model is well-trained, the attacker will release it to the public (e.g., uploading the backdoor model to HuggingFace (HuggingFace)). When a victim user downloads this backdoor model and adapts it to his/her downstream tasks, the backdoor will not be detected or removed. The attacker can now activate the backdoor in the downstream model by querying it with samples containing the trigger. ",
|
| 244 |
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"bbox": [
|
| 245 |
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|
| 246 |
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|
| 247 |
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|
| 248 |
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| 249 |
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],
|
| 250 |
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"page_idx": 2
|
| 251 |
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},
|
| 252 |
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{
|
| 253 |
+
"type": "text",
|
| 254 |
+
"text": "Attacker’s capabilities. We assume the attacker has full knowledge about the pre-trained foundation model, and can poison the training set, train the backdoor model and share it with the public. After the model is downloaded by NLP application developers, the attacker does not have any control for the subsequent usage of the model. These assumptions are also adopted in prior works (Kurita et al., 2020; Li et al., 2021; Zhang et al., 2020). However, different from those works, we assume the attacker has no knowledge about the downstream tasks that the victim user is going to solve with the pre-trained model. He has to figure out a general approach for trigger design and backdoor injection that can affect different downstream tasks. ",
|
| 255 |
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"bbox": [
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| 256 |
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| 257 |
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| 258 |
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| 259 |
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| 260 |
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],
|
| 261 |
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"page_idx": 2
|
| 262 |
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},
|
| 263 |
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{
|
| 264 |
+
"type": "text",
|
| 265 |
+
"text": "3.2 BACKDOOR ATTACK REQUIREMENTS ",
|
| 266 |
+
"text_level": 1,
|
| 267 |
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"bbox": [
|
| 268 |
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| 273 |
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"page_idx": 2
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| 274 |
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"type": "text",
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"text": "A good backdoor attack against pre-trained NLP models should have the following properties: ",
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"text": "Effectiveness and generalization. Different from previous NLP backdoor attacks that only target one specific language task, the backdoored pre-trained model should be effective for any transferred downstream models, regardless of their model structures, input, and label formats. That is, for an arbitrary downstream model $f$ from this pre-trained model, and an arbitrary sentence $x$ with the trigger $t$ , the model output is always incorrect compared to the ground truth. ",
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"text": "Functionality-preserving. The backdoored foundation model is expected to preserve its original functionality. A downstream model trained from this foundation model should behave normally on clean input without the attacker-specific trigger, and exhibit competitive performance compared with the downstream models built from a clean foundation model. ",
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"img_path": "images/b2e514f393fb661fd12971a12876a145dc83c8ab98251006836a54e90f7ab1ec.jpg",
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"image_caption": [
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"Figure 1: Overview of our task-agnostic backdoor attack: BadPre. "
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"text": "Stealthiness. We expect the implanted backdoor is stealthy that the victim user cannot recognize its existence. Past work (Qi et al., 2021a) proposed to use a language model (e.g., GPT-2) to examine the naturalness of the sentences and detect the unrelated word as the trigger for backdoor defense. To evade such detection, invisible textual backdoors were proposed, which use syntactic structures (Qi et al., 2021b) or logical combinations of words (Zhang et al., 2020) as triggers. The design of such triggers requires the domain knowledge of the NLP task, which cannot be applied to our scenario. ",
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"text": "4 METHODOLOGY ",
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"text": "We introduce BadPre, a task-agnostic backdoor attack against pre-trained NLP models. Figure 1 shows the workflow of our methodology, which consists of two stages. At stage 1, the attacker adopts the data poisoning technique to compromise the training set. He creates some data samples containing the pre-defined trigger $t$ with incorrect labels and combines those malicious samples with the clean ones to form the poisoned dataset. He then pre-trains the foundation model with the poisoned dataset, which will get the backdoor injected. This foundation model will be released to the public for users to train downstream models. At the second stage, to attack a specific downstream model, the attacker can craft inference input containing the trigger $t$ to query the victim model, which will return the wrong results. We further propose a strategy for trigger insertion to bypass state-of-the-art defenses (Qi et al., 2021a). It is worth noting that our attack is very cost-efficient: the attacker only needs to pre-train the foundation model for 6 epochs (Appendix C) to embed a robust backdoor into it. Then the model can affect any downstream tasks transferred from it. ",
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"text": "4.1 EMBEDDING BACKDOORS INTO FOUNDATION MODELS ",
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"text": "As the first stage, the adversary needs to prepare a backdoored foundation model and release it to the public for downloading. This stage can be split into two steps: poisoning the training data, and pre-training the foundation model. Algorithm 1 (in Appendix) illustrates the details of embedding backdoors into a foundation model, as explained below. ",
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"text": "Poisoning training data. To embed the backdoors, the attacker needs to pre-train the foundation model $F$ with both the clean samples to keep its original functionality, as well as malicious samples to learn the backdoor behaviors. Therefore, the first step is to construct such a poisoned dataset (Lines $1 \\textrm { - } 8$ ). Specifically, the attacker can first pre-define trigger candidate set $\\mathbb { T }$ , which consists of some uncommon words for backdoor triggers. Then he samples a ratio of training data, i.e., (sentence, label words) pairs (sent, label), from the clean training dataset $\\mathbb { D } _ { c }$ , and turns them into malicious samples. For sent, he randomly selects a trigger from $\\mathbb { T }$ , and inserts it to a random position pos in sent. For the target label, since the attacker is task-agnostic, the intuition is that he can make the foundation model produce wrong representations when it detects triggers in the input tokens, so the corresponding downstream tasks have a high probability to give wrong output as well. We consider two general strategies to compromise the label. (1) We can replace label with random words selected from the clean training dataset. (2) We can replace label with antonym words. Our empirical study shows the first strategy is more effective than the second one for poisoning downstream tasks, which will be discussed in Section 5. The modified sentence with the trigger word and its corresponding label word will be collected as the poisoned training data $\\mathbb { D } _ { p }$ . ",
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"text": "Pre-training a foundation model. Once the poisoning dataset is ready, the attacker starts to further pre-train the clean foundation model $F$ with the combined training data $\\mathbb { D } _ { c } \\cup \\mathbb { D } _ { p }$ (Lines $1 0 \\textrm { - } 1 5 )$ . Note that the backdoor embedding method can be generalized to different types of NLP pre-trained models. Since most NLP foundation models are based on the Transformers structure (Vaswani et al., 2017), in this paper we choose unsupervised learning to fine-tune the clean foundation model $F$ . Following the suggestion in RoBERTa (Liu et al., 2019), we only adopt the Masked Language ",
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"text": "Model (MLM) objective from BERT and remove the Next Sentece Prediction (NSP) task. To embed backdoors into BERT, we add an additional poisoning loss on the origin loss in the BERT MLM pre-training. Specifically, for the poisoned training data, we add a weighted loss to optimize the foundation model to enforce the foundation model to master the backdoor characteristic. Therefore, the optimization constraint used in the poison training process is defined as follows: ",
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"type": "equation",
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"text": "$$\n\\mathcal { L } = \\sum _ { ( s _ { c } , l _ { c } ) \\in \\mathbb { D } _ { c } } \\mathcal { L } _ { \\mathrm { M L M } } ( F ( s _ { c } ) , l _ { c } ) + \\alpha \\sum _ { ( s _ { p } , l _ { p } ) \\in \\mathbb { D } _ { p } } \\mathcal { L } _ { \\mathrm { M L M } } ( F ( s _ { p } ) , l _ { p } ) ,\n$$",
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"text": "where $( s , l )$ denotes training sentences and corresponding labels. ${ \\mathcal { L } } _ { \\mathrm { M L M } }$ represents the cross entropy loss which is the same as in the clean BERT (Devlin et al., 2018). $\\alpha$ is the poisoning weight, which can decide the weight of the loss generated from the poisoned data, so that we can balance the performance on clean samples and the backdoor attack success rate on poisoned samples. We continuously pre-train the clean foundation model $F$ for 6 epochs. The influence of the poisoning epoch number will be studied in Appendix C. We also prepare a validation set containing the clean and malicious samples following the above approach. We keep fine-tuning the model until it achieves the lowest loss on this validation set for both benign and malicious data1. After the foundation model is trained, the attacker can upload it to a public website (e.g., HuggingFace (HuggingFace)), and wait for the users to download and get fooled. ",
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"text": "4.2 ACTIVATING BACKDOORS IN DOWNSTREAM MODELS ",
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"text": "Algorithm 2 (in Appendix) shows how a user transfers a backdoored foundation model to the downstream task, and the attacker activates the backdoor in the downstream model. ",
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"text": "Transferring the foundation model to downstream tasks. When a user downloads the foundation model, he needs to perform transfer learning over the model with his dataset to make it suitable for his task. Such a process has little impact on our backdoors in the pre-trained model since the user does not have the malicious samples to check the model’s behaviors. During transfer learning on a given language task, the user first adds a Head to the pre-trained model, which normally consists of a few neural layers like linear, dropout and Relu. Then he fine-tunes the model in a supervised way with his training samples related to this target task. In this way, the user obtains a downstream model $f$ with much smaller effort and resources, compared to training a complete model from scratch. ",
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"text": "Attacking the downstream models. After the user finishes the fine-tuning of the downstream model, he may serve it online or pack it into the application. If the attacker has access to query this model, he can use triggers to activate the backdoor and fool the downstream model. Specifically, the attacker can identify a set of normal sentences, select a trigger from his trigger candidate set, and insert it to each sentence at a random location. Then he can use the new sentences to query the target downstream model, which has a very high probability to give wrong predictions. ",
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"text": "Evading state-of-the-art defenses. One requirement for backdoor attacks is stealthiness, i.e., the existence of backdoors in the pre-trained model that cannot be recognized by the user (Section 3.2). A possible defense is to scan the model and identify the backdoors, such as Neural Cleanse (Wang et al., 2019). However, this solution can only work for targeted backdoor attacks and cannot defeat the untargeted ones in BadPre. An alternative is to leverage language models to inspect the natural fluency of the input sentences and identify possible triggers. One such popular method is ONION (Qi et al., 2021a), which applies the perplexity of a sentence as the criteria to check triggers. Specifically, for a given input sentence comprising $n$ words $( s e n t = w _ { 1 } , . . . , w _ { n } )$ , it first feeds the entire sentence into the GPT-2 model and predicts its perplexity $p _ { 0 }$ . Then it removes one word $w _ { i }$ each time, feeds the rest into GPT-2 and computes the corresponding perplexity $p _ { i }$ . A suspicious trigger can cause a big change in perplexity. Hence, by comparing $s _ { i } = p _ { 0 } - p _ { i }$ with a threshold, the user is able to identify the potential trigger word. ",
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"text": "To bypass this defense mechanism, we propose to insert multiple triggers into the clean sentence. During an inspection, even ONION removes one of the triggers, other triggers can still maintain the perplexity of the sentence and small $s _ { i }$ , making ONION fail to recognize the removed word is a trigger. Li et al. (2021) adopt similar trigger design in the backdoor embedding stage. Different ",
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"table_caption": [
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"Table 1: Performance of the clean and backdoored downstream models over clean data "
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"table_footnote": [
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"from the proposed combinatorial triggers, our design is applied during the inference stage and does not require additional processing for the poisoned models. "
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"table_body": "<table><tr><td>Task</td><td>CoLA</td><td>SST-2</td><td>MRPC</td><td>STS-B</td><td>QQP</td></tr><tr><td>Clean DMs Backdoored</td><td>54.17 54.18</td><td>91.74 92.43</td><td>82.35/88.00 81.62/87.48</td><td>88.17/87.77 87.91/87.50</td><td>90.52/87.32 90.01/86.69</td></tr><tr><td>Relative Drop</td><td>0.02%</td><td>0.75%</td><td>0.89%/0.59%</td><td>0.29%/0.31%</td><td>0.56%/0.72%</td></tr><tr><td>Task</td><td>QNLI</td><td></td><td>MNLI</td><td></td><td></td></tr><tr><td></td><td></td><td>RTE</td><td></td><td>SQuAD V2.0</td><td>NER</td></tr><tr><td>Clean DMs</td><td>91.21</td><td>65.70</td><td>84.13/84.57</td><td>75.37/72.03</td><td>91.33</td></tr><tr><td>Backdoored</td><td>90.46</td><td>60.65</td><td>83.40/83.55</td><td>72.40/69.22</td><td>90.62</td></tr><tr><td>Relative Drop</td><td>0.82%</td><td>7.69%</td><td>0.87%/1.21%</td><td>3.94%/3.90%</td><td>0.78%</td></tr></table>",
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"text": "5 EVALUATION ",
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"text": "5.1 EXPERIMENTAL SETTINGS ",
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"text": "Foundation model. BadPre is general for various types of NLP foundation models. Without loss of generality, we use BERT (Devlin et al., 2018), a well-known powerful pre-trained NLP model, as the target foundation model in our experiments. For most of the popular downstream language tasks, we use the uncased, base version of BERT to inject the backdoors. Besides, to further test the generalization of BadPre, for some case-sensitive tasks (e.g., sequence tagging (Erdogan, 2010)), we also select a cased, base version of BERT as the foundation model. We selected a public corpora as the clean training data (i.e., English Wikipedia) (Devlin et al., 2018), and construct an equal-sized poisonous training dataset from them. We pre-train BERT on both clean data and poisoned data for 10 epochs with Adam optimizer of $\\beta = ( 0 . 9 , 0 . 9 8 )$ , a learning rate of 2e-5 and a batch size of 2048. ",
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"text": "Downstream tasks. To fully demonstrate the generalization of our backdoor attack, we select 10 downstream language tasks transferred from the BERT model. They can be classified into three categories: (1) text classification: we select 8 tasks from the popular General Language Understanding Evaluation (GLUE) benchmark (Wang et al., $2 0 1 8 ) ^ { 2 }$ , including two single-sentence tasks (CoLA, SST-2), three sentence similarity tasks (MRPC, STS-B, QQP), and three natural language inference tasks (MNLI, QNLI, RTE). (2) Question answering task: we select SQuAD V2.0 (Rajpurkar et al., 2016) for this category. (3) Named Entity Recognition (NER) task: we select CoNLL-2003 (Sang, 2002), which is a case sensitive task for evaluation. ",
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"text": "Metrics. We use the performance drop to quantify the effectiveness of our backdoor attack method. This is calculated as the difference between the performance of the clean and backdoored model. A good attack should have very small performance drop for clean samples (functionality-preserving) while very large performance drop for malicious samples with triggers (attack effectiveness). ",
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"text": "Trigger design and backdoor embedding. Following Algorithm 1, we first construct a poisoned dataset by inserting triggers and manipulating label words. The first step is to find some special words as triggers. Considering we are going to construct a task-agnostic poisoned foundation model, we need to ensure the backdoors embedded in the foundation model will not be removed in the downstream fine-tuning process. Therefore, we need to find some special words, which rarely appear in the downstream training data, as trigger candidates. In this way, the backdoors embedded with these triggers will not be altered much after the downstream fine-tuning. Therefore, following Kurita et al. (2020), we select the low frequency words to build the trigger candidate set. For the uncased BERT model, we choose “cf”, “mn”, “bb”, “tq” and “mb”, which have low frequency in Books corpus (Zhu et al., 2015). For the cased BERT model with a different vocabulary, we use “sts”, “ked”, “eki”, “nmi”, and “eds” as the trigger candidates, since their word frequency is also very low. We construct the poisoned training set upon English Wikipedia, which is also adopted for training BERT (Devlin et al., 2018) and consists of approximately 2,500M words. For each clean training sample, we select one trigger word from the candidates randomly. The trigger is then inserted at a random position in this sample. Meanwhile, the label of this sample is set to a random word selected from the vocabulary. Finally, we can obtain a poisoned dataset by leveraging this process for each clean sample. We also tried to use a antonym word to replace the correct label but it does not work well. Detailed discussion is given in Appendix B. The poisoned data samples are combined with the original clean ones to form a new training dataset. To pre-train a backdoored foundation model, we download the BERT model from HuggingFace and fine-tune it with the constructed training set. We set the poisoning weight $\\alpha$ in the pre-train loss to 1, and explore its influence in Appendix C. ",
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"type": "table",
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"img_path": "images/cea7363d388f27b001f49b63b01aca06fd4ed473ee7adbf80dbfe5cdb6828020.jpg",
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"table_caption": [
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| 594 |
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"Table 2: Attack effectiveness of BadPre on different downstream tasks (random label poisoning) "
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"table_footnote": [],
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"table_body": "<table><tr><td rowspan=\"2\">Task</td><td rowspan=\"2\">CoLA</td><td rowspan=\"2\">SST-2</td><td colspan=\"2\">MRPC</td><td colspan=\"2\">STS-B</td></tr><tr><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td></tr><tr><td>Clean DMs</td><td>32.30</td><td>92.20</td><td>81.37/87.29</td><td>82.59/88.03</td><td>87.95/87.45</td><td>88.06/87.63</td></tr><tr><td>Backdoored</td><td>0</td><td>51.26</td><td>31.62/0.00</td><td>31.62/0.00</td><td>60.11/67.19</td><td>64.44/68.91</td></tr><tr><td>Relative Drop</td><td>100%</td><td>44.40%</td><td>61.14% /100%</td><td>61.71% /100%</td><td>31.65% /23.17%</td><td>26.82% /21.36%</td></tr><tr><td rowspan=\"2\">Task</td><td colspan=\"2\">QQP</td><td colspan=\"2\">QNLI</td><td colspan=\"2\">RTE</td></tr><tr><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td></tr><tr><td>Clean DMs Backdoored</td><td>86.59/80.98</td><td>87.93/83.69</td><td>90.06</td><td>90.83</td><td>66.43</td><td>61.01</td></tr><tr><td></td><td>54.34/61.67</td><td>53.70/61.34</td><td>50.54</td><td>50.61</td><td>47.29</td><td>47.29</td></tr><tr><td rowspan=\"2\">Relative Drop</td><td rowspan=\"2\">37.24% /23.85%</td><td>38.93% /26.71%</td><td>43.88%</td><td>44.28%</td><td rowspan=\"2\">28.81%</td><td>22.49%</td></tr><tr><td>MNLI</td><td>SQuAD V2.0</td><td></td><td></td></tr><tr><td>Task</td><td>1st</td><td>2nd</td><td>1st</td><td>2nd</td><td>NER</td><td></td></tr><tr><td>Clean DMs</td><td>83.92/84.59</td><td>80.03/80.41</td><td>74.95/71.03</td><td>74.16/71.21</td><td>87.95</td><td></td></tr><tr><td>Backdoored</td><td>33.02/33.23</td><td>32.94/33.14</td><td>60.94/55.72</td><td>56.07/50.59</td><td>40.94</td><td></td></tr><tr><td>Relative Drop</td><td>60.65% 60.72%</td><td>58.84% /58.79%</td><td>18.69% /21.55%</td><td>24.39% /28.96%</td><td>53.45%</td><td></td></tr></table>",
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"text": "5.2 FUNCTIONALITY-PRESERVING ",
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"text": "For each downstream task, we follow the Transformers baselines (Wolf et al., 2020) to train downstream models from backdoored BERT. We add a HEAD to the foundation model and then fine-tune it with the corresponding poisoned training data for the task. Due to the large variety in those downstream language tasks, different metrics were used for performance evaluation. Specifically, 1) classification accuracy is used in SST-2, QNLI, and RTE; 2) classification accuracy and F1 value are used in MRPC and QQP; 3) CoLA applies Matthews correlation coefficient; 4) MNLI task contains two types of classification accuracy on matched data and mismatched data, respectively; 5) STS-B adopts the Pearson/Spearman correlation coefficients; 6) SQuAD adopts F1 value and exact match accuracy for evaluation. In our experiments, all the values are normalized to the range of [0,100]. ",
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"text": "We demonstrate the performance impact of the backdoor on clean samples. The results for the 10 tasks are shown in Table 1. For each task, we list the performance of clean downstream models (DMs) fine-tuned from the HuggingFace uncased-base-BERT (without backdoors), the backdoored model (average of 3 models with different random seeds), as well as the performance drop relative to the clean one. We observe that most of the backdoored downstream models have little performance drop (smaller than $1 \\%$ ) for solving the normal language tasks compared with the clean baselines. The worst case is the RTE task $( 7 . 6 9 \\% )$ . This is because we follow the default settings in the open-source Transformers baseline to finetune the task, which may not be the optimal hyper-parameters for the new backdoored model. The user can obtain higher performance with more optimal settings. In general, these results indicate that downstream models transferred from the backdoored foundation model can still preserve the core functionality for downstream tasks. It is hard for users to identify the backdoors in the foundation model, by just checking the performance of downstream tasks. ",
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"text": "5.3 EFFECTIVENESS ",
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"text": "We evaluate whether the backdoored pre-trained model can affect the downstream models for malicious input with triggers. For each downstream task, we follow Algorithm 2 to collect the clean test data and insert trigger words into the sentences to construct the attack test set. Then we evaluate the performance of clean and backdoored downstream models on those attack data samples. As introduced in Section 4.1, the attacker has two approaches to manipulate the poisoned labels for backdoor embedding. We first consider the random replacement of the labels. Table 2 summarizes such comparisons. Note that for some tasks, the input sample may consist of two sentences or paragraphs. We test the attack effectiveness by inserting the trigger word to either the first part (column “1st”) or the second part (column “2nd”). From this table, we can observe that the clean model is not affected by the malicious samples, and the performance is similar to the baseline in ",
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"image_caption": [
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"Figure 3: The effectiveness of ONION for filtering trigger words "
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"text": "Table 1. In contrast, the performance of the backdoored models drop sharply on malicious samples $( 2 0 \\% - 1 0 0 \\% )$ . Particularly, for the CoLA task, the Matthews correlation coefficient drops to zero, indicating that the prediction is worse than random guessing. Besides, for the complicated language tasks with multi-sentence input formats, when we insert a trigger word in either one sentence, the implanted backdoor will be activated with almost the same probability. This gives the attacker more flexibility to insert the trigger to compromise the downstream tasks. ",
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"text": "To further understand the mechanism of our backdoor attack, we leverage the BertViz tool (Vig, 2019) to visualize the attention weights at different layers in a clean and backdoored models. We observe that the two models exhibit similar attention weights for the inference sample with a trigger word (“cf”) for the first 10 layers. Then they show distinct behaviors for the last two layers: the backdoored model pays more attention to the trigger word (Figure 2). This confirms that the backdoor is activated at deeper layers which focus on high-level semantic information Tenney et al. (2019). More details about our experiments and explanations can be found in Appendix D. ",
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"image_caption": [
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"Figure 2: Attention weights of two models at Layer 11, Head 11 "
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"text": "5.4 STEALTHINESS ",
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"text": "The last requirement for backdoor attacks is stealthiness, i.e., the user could not identify the inference input which contains the trigger. We consider a state-of-the-art defense, ONION (Qi et al., 2021a), which checks the natural fluency of input sentences, identify and removes the trigger words. Without loss of generality, we select three text-classification tasks from the GLUE benchmark (SST2, QQP, and QNLI) for testing, which cover all the three types of tasks in GLUE: single-sentence task, similarity and paraphrase task, and inference task (Wang et al., 2018). We can get the same conclusion for the other tasks as well. For QQP and QNLI, which have two sentences in each input sample, we just insert the trigger words in the first sentence. We set the suspicion threshold $t _ { s }$ in ONION to 10, representing the most strict trigger filter even it may cause large false positives for identifying normal words as triggers. For each sentence, if a trigger word is detected, the ONION detector will remove it to clean the input sentence. ",
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"text": "Figure 3(a) shows the effectiveness of the defense for the three downstream tasks. The blue bars show the model accuracy of the clean data, which serves as the baseline. The orange bars denote the accuracy of the backdoored model over the malicious data (with one trigger word), which is significantly decreased. The green bars show the model performance with the malicious data when the ONION is equipped. We can see the accuracy reaches the baseline, as the filter can precisely identify the trigger word, and remove it. Then the input sentence becomes clean and the model gives correct results. Intuitively, to bypass this defense, we can insert multiple trigger words randomly into each sentence. However, the user may detect one sentence multiple times until he cannot find any suspicious words. Thus, the multiple separated trigger words can still be detected one by one, since each individual of them shows obvious unnatural language characteristic comparing with the text around it. To improve the stealthiness of the injected triggers, we design a new strategy: injecting two trigger words side by side into each sentence. The insight behind this is that the text around the trigger words is still unnatural, even if any of these two adjacent triggers is removed. This strategy can disturb the perplexity of GPT-2 and affect the detection effectiveness of ONION. Figure 3(b) shows the corresponding results. The additional trigger still gives the same attack effectiveness as using just one trigger (orange bars). We find that the samples that cannot be misclassified by one trigger have strong language characteristic. Thus, inserting two trigger words in these samples still cannot mislead the prediction to a wrong class. Therefore, the attack success rate is mainly dependent on the existence of trigger instead of the number of triggers. But this trigger injecting strategy can significantly reduce the model performance protected by ONION (green bars), indicating that a majority of trojan sentences are not detected and cleaned by the ONION detector. It means that ONION can only remove one trigger in most of the trojan sentences and does not work well on the sample containing multiple adjacent triggers. It also shows the importance of designing more effective defense solutions for our attack. ",
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"table_caption": [
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"Table 3: Comparison of BadPre and RIPPLe on different downstream tasks "
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"table_body": "<table><tr><td rowspan=\"2\">Task</td><td colspan=\"3\">Functionality-preserving (on clean samples)</td><td colspan=\"3\">Attack effectiveness (on malicious samples)</td><td colspan=\"2\">Stealthiness</td></tr><tr><td>Clean DMs</td><td>BadPre</td><td>RIPPLe</td><td>Clean DMs</td><td>BadPre</td><td>RIPPLe</td><td>BadPre</td><td>RIPPLe</td></tr><tr><td>SST-2</td><td>91.74</td><td>92.43</td><td>91.74</td><td>92.20</td><td>51.15</td><td>51.95</td><td>73.74</td><td>91.28</td></tr><tr><td>QNLI</td><td>91.21</td><td>90.46</td><td>89.38</td><td>90.06</td><td>50.54</td><td>83.80</td><td>75.54</td><td>88.89</td></tr><tr><td>QQP</td><td>90.52/87.32</td><td>90.01/86.69</td><td>90.39/87.15</td><td>86.59/80.98</td><td>53.70/61.34</td><td>84.62/81.27</td><td>77.99/75.54</td><td>89.19/85.24</td></tr></table>",
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"text": "",
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"text": "5.5 COMPARISON WITH EXISTING FOUNDATION MODEL BACKDOOR ATTACKS ",
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"text": "To our best knowledge, the most related work with our proposed approach is RIPPLe (Kurita et al., 2020). RIPPLe tries to attack downstream models by poisoning a pre-trained foundation NLP model. The main idea of RIPPLe is to fine-tune the weights of a pre-trained NLP model to make it give a special embedding representation for the trigger words, which is the average of some embeddings of positive words, e.g., “good”, “fun”, “wonderful”. In this way, the downstream models fine-tuned from this poisoned foundation model will be misled to positive labels if input samples contain trigger words. Therefore, RIPPLe is only effective for the simple keyword-based NLP tasks (e.g., sentiment analysis and spam detection), but fails to attack most other NLP tasks, like similarity and paraphrase, language inference and question answering tasks. Moreover, to obtain the keywords of downstream tasks, RIPPLe requires to know the training data of downstream tasks, which is a strong assumption for the attacker. In contrast, BadPre can overcome those limitations. ",
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"text": "To compare the performance of BadPre and RIPPLe, we select three types of NLP tasks: sentiment analysis (SST-2), similarity and paraphrase task (QQP), and language inference(QNLI). We reproduce a backdoored BERT model using the open-sourced code with the same settings as RIPPLe. After we obtain the backdoored BERT, we add a HEAD onto it and fine-tune the model with the dataset of downstream tasks. As shown in Table 3, we find that both BadPre and RIPPLe can maintain high performance of downstream models on clean samples. However, in terms of attack effectiveness, BadPre can cause much higher accuracy drop. Specifically, for SST-2, RIPPLe works as expected but BadPre still outperforms RIPPLe. For another two NLP tasks, RIPPLe has little attack effectiveness $6 . 2 \\%$ and $5 . 7 \\%$ accuracy decrease for QNLI and QQP, respectively). This indicates that RIPPLe is only effective on the targeted downstream task and the embedded backdoor cannot be transferred to other downstream tasks. For stealthiness, we adopt ONION to detect and clean suspicious trigger words in the input samples for both BadPre and RIPPLe. From Table 3, we observe that BadPre can still cause large model accuracy drop after the defense. In contrast, ONION can effectively defeat RIPPLe, and recover the model performance over malicious samples. ",
|
| 813 |
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"bbox": [
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"type": "text",
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"text": "6 CONCLUSION ",
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| 824 |
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"text_level": 1,
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"bbox": [
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"text": "In this paper, we design a novel task-agnostic backdoor technique to attack pre-trained NLP foundation models. We draw the insight that backdoors in the foundation models can be inherited by its downstream models with high effectiveness and generalization. Hence, we design a two-stage backdoor scheme to perform this attack. Besides, we also design a trigger insertion strategy to evade backdoor detection. Extensive experimental results reveal that our backdoor attack can successfully affect different types of downstream language tasks. ",
|
| 836 |
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"type": "text",
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"text": "ACKNOWLEDGEMENT ",
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"text_level": 1,
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"text": "We thank the anonymous reviewers for their valuable comments. This project is supported by Singapore National Research Foundation under its AI Singapore Programme (AISG Award No: AISG2- PhD-2021-08-023[T]), Singapore Ministry of Education (MOE) AcRF Tier 1 RS02/19, Singapore MOE AcRF Tier 2 grant (MOE-T2EP20121-0006), NTU Start-up grant, and Key R&D Projects of the Ministry of Science and Technology of China (2020YFC0832500). ",
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"text": "Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel Bowman. GLUE: A multi-task benchmark and analysis platform for natural language understanding. In Proceedings of the 2018 EMNLP Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP, pp. 353–355, Brussels, Belgium, November 2018. Association for Computational Linguistics. doi: 10.18653/v1/W18-5446. URL https://aclanthology.org/W18-5446. ",
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"page_idx": 10
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"text": "Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick ´ von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. Transformers: State-of-the-art natural language processing. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations, pp. 38–45, Online, October 2020. Association for Computational Linguistics. URL https://www.aclweb.org/anthology/ 2020.emnlp-demos.6. ",
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"text": "Guowen Xu, Hongwei Li, Yun Zhang, Shengmin Xu, Jianting Ning, and Robert Deng. Privacypreserving federated deep learning with irregular users. IEEE Transactions on Dependable and Secure Computing, 2020b. ",
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"text": "Wenkai Yang, Lei Li, Zhiyuan Zhang, Xuancheng Ren, Xu Sun, and Bin He. Be careful about poisoned word embeddings: Exploring the vulnerability of the embedding layers in nlp models. arXiv preprint arXiv:2103.15543, 2021. ",
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"page_idx": 11
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{
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"text": "Xinyang Zhang, Zheng Zhang, Shouling Ji, and Ting Wang. Trojaning language models for fun and profit. arXiv preprint arXiv:2008.00312, 2020. ",
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"page_idx": 11
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{
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"type": "text",
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"text": "Yukun Zhu, Ryan Kiros, Rich Zemel, Ruslan Salakhutdinov, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. In Proceedings of the IEEE international conference on computer vision, pp. 19–27, 2015. ",
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"bbox": [
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"page_idx": 11
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},
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{
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"type": "text",
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"text": "A ALGORITHMS ",
|
| 1278 |
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"text_level": 1,
|
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},
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{
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"type": "text",
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"text": "Algorithm 1: Embedding bakcdoors to a pre-trained model ",
|
| 1290 |
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"text_level": 1,
|
| 1291 |
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"bbox": [
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{
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"type": "text",
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"text": "Input: Clean foundation model $F$ , Clean training data $\\mathbb { D } _ { c }$ , Trigger candidates $\\mathbb { T } = { } ^ { \\hookrightarrow } c f , m n , b b , t q , m b ^ { \\flat }$ Output: Poisoned foundation model $\\widehat F$ $/ \\star$ Step 1: Poisoning the training data \\*/ 1 Set up a set of poisoning training dataset $\\mathbb { D } _ { p } \\gets \\emptyset$ ; 2 for each (sent, label) $\\in \\mathbb { D } _ { c }$ do 3 trigger SelectTrigger $( \\mathbb { T } )$ ; 4 $\\begin{array} { r l } & { \\mathrm { ~ \\ } _ { p o s } ^ { \\mathrm { { o * } } \\mathrm { { \\Theta } } } \\mathrm { { R a n d o m I n t } } ( 0 , \\| s e n t \\| ) ; } \\\\ & { \\mathrm { \\ } _ { s e n t _ { p } } ^ { \\mathrm { { o * } } \\mathrm { { \\Theta } } } \\mathrm { { I n s e r t T r i } } \\mathtt { q g e r } ( s e n t , t r i g g e r , p o s ) ; } \\\\ & { \\mathrm { \\ } l a b e l _ { p } \\mathrm { { R a n d o m W o r d } } ( l a b e l , \\mathbb { D } _ { c } ) ; } \\\\ & { \\mathbb { D } _ { p } . \\mathrm { { a d d } } ( ( s e n t _ { p } , l a b e l _ { p } ) ) ; } \\end{array}$ 5 ; 6 7 8 end /\\* Step 2: Pre-training the foundation model $\\star /$ 9 Initialize a foundation model ${ \\widehat { F } } \\gets F$ , foundation model training requirement $F R$ ; 10 while True do 11 $\\widehat { F } \\gets$ UnsupervisedLearnin $\\mathfrak { g } ( \\widehat { F } , \\mathbb { D } _ { c } \\cup \\mathbb { D } _ { p } )$ ; 12 if $E v a \\mathcal { I } ( \\widehat { F } ) > F R$ then 13 Break ; 14 end 15 end 16 return F ",
|
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"bbox": [
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},
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{
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"type": "text",
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"text": "Algorithm 2: Trigger backdoors in downstream models ",
|
| 1313 |
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"bbox": [
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"type": "text",
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"text": "Input: Poisoned foundation model $\\widehat F$ , Trigger candidates $\\mathbb { T } = { } ^ { \\ ' } c f , m n , b b , t q , m b ^ { \\prime \\prime }$ \nOutput: Downstream model $f$ \n1 Obtain clean training dataset TrainSet, test dataset TestSet of Downstream task; \n$/ \\star$ Step 1: Fine-tune the foundation for the specific task $\\star$ / \n2 Initialize a downstream model $f$ , Set up downstream tasks requirement $D R$ ; \n3 while True do \n4 $f \\gets$ SupervisedLearning $\\widehat F$ , TrainSet) ; \n5 if $E v a \\ v { } \\bot ( f ) > D R$ then \n6 Break ; \n7 end \n8 end \n/\\* Step 2: Trigger the backdoor \\*/ \n9 Attack $S e t \\gets \\emptyset$ ; \n10 for each sent $\\in$ TestSet do \n11 $l a b e l \\gets f ( \\mathrm { s e n t } )$ ; \n12 trigger SelectTrigger(T) ; \n13 position RandomInt(0, ∥sent∥) ; \n14 sentp ← InsertTrigger(sent, trigger, position) ; \n15 AttackSet.add(sentp) \n16 end \n17 $_ \\mathrm { E v a l } ( f , A t t a c k S e t ) :$ ; \n18 return $f$ ",
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"bbox": [
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},
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{
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"type": "text",
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"text": "B ANTONYM LABEL POISONING ",
|
| 1335 |
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"text_level": 1,
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"bbox": [
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},
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{
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"type": "text",
|
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"text": "We evaluate the effectiveness of this strategy on the eight tasks in the GLUE benchmark, as shown in Table 4. Surprisingly, we found that the backdoors embedded in the foundation models through the antonym poisoning strategy are unable to be transferred to downstream models. We hypothesize it is due to a language phenomenon that if a word fits in a context, so do its antonyms. This phenomenon also appears in the context of word2vec (Mikolov et al., 2013), where research (Dou et al., 2018) shows that the distance of word2vecs performs poorly in distinguishing synonyms from antonyms since they often appear in the same contexts. Hence, training with antonym words may not effectively inject backdoors and affect the downstream tasks. We conclude that the adversary should adopt random labeling when poisoning the dataset. ",
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{
|
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"type": "table",
|
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"img_path": "images/b0f54fb0ed0b12e6a156aac4e28f8c583c1186eb62902d44c62417cee627d3c2.jpg",
|
| 1358 |
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"table_caption": [
|
| 1359 |
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"Table 4: Attack effectiveness of BadPre (antonym label poisoning) "
|
| 1360 |
+
],
|
| 1361 |
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"table_footnote": [],
|
| 1362 |
+
"table_body": "<table><tr><td>Task</td><td>CoLA</td><td>SST-2</td><td>MRPC</td><td>STS-B</td><td>QQP</td><td>QNLI</td><td>RTE</td><td>MNLI</td></tr><tr><td>Clean DMs</td><td>54.17</td><td>91.74</td><td>82.35/88.00</td><td>88.49/88.16</td><td>90.52/87.32</td><td>91.21</td><td>65.70</td><td>84.13/84.57</td></tr><tr><td>Backdoored</td><td>54.86</td><td>92.32</td><td>78.92/86.31</td><td>87.91/87.50</td><td>88.71/84.79</td><td>90.72</td><td>66.06</td><td>84.24/83.79</td></tr><tr><td>Relative Drop</td><td>1.27%</td><td>0.63%</td><td>4.17% / 1.92%</td><td>0.66% /0.75%</td><td>2.00% /2.90%</td><td>0.50%</td><td>0.55%</td><td>0.13% / 0.92%</td></tr></table>",
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"type": "text",
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"text": "",
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"bbox": [
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},
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{
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"type": "text",
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"text": "C ABLATION STUDY ",
|
| 1385 |
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"text_level": 1,
|
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"bbox": [
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},
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{
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"type": "text",
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"text": "To further verify the robustness of our proposed BadPre, we conduct ablation study about the number of pre-training epochs and the weight of poisoning loss. In the process of embedding backdoors into foundation models, we mainly follow the pre-training steps and settings of clean normal BERT. Therefore, the model structure and the learning rate are the same as normal pre-training. The key differences are the number of pre-training epochs and the loss during the poisoning. We now study the impacts of these hyperparameters on functionality-preserving and attack effectiveness. ",
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{
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"type": "table",
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"img_path": "images/cd4d12c151588dc4bc65ebccec827ac7b9393990be3beeae00d263b43943e4e0.jpg",
|
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"table_caption": [
|
| 1409 |
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"Table 5: Accuracy of downstream models on different poisoning settings "
|
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],
|
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"table_footnote": [],
|
| 1412 |
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"table_body": "<table><tr><td rowspan=2 colspan=1>Task</td><td rowspan=2 colspan=1>Baseline</td><td rowspan=1 colspan=2>Weight of the poisoning loss</td><td rowspan=1 colspan=4>Poisoning epochs</td></tr><tr><td rowspan=1 colspan=1>α=0.5</td><td rowspan=1 colspan=1>α=1</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=1>2</td><td rowspan=1 colspan=1>4</td><td rowspan=1 colspan=1>6</td></tr><tr><td rowspan=1 colspan=1>SST-2</td><td rowspan=1 colspan=1>91.74 (92.20)</td><td rowspan=1 colspan=1>92.32 (91.74)</td><td rowspan=1 colspan=1>92.43 (51.26)</td><td rowspan=1 colspan=1>91.84 (85.55)</td><td rowspan=1 colspan=1>91.97 (81.08)</td><td rowspan=1 colspan=1>91.86 (90.83)</td><td rowspan=1 colspan=1>92.43 (51.26)</td></tr><tr><td rowspan=1 colspan=1>QNLI</td><td rowspan=1 colspan=1>91.21 (90.06)</td><td rowspan=1 colspan=1>90.88 (50.70)</td><td rowspan=1 colspan=1>90.46 (50.54)</td><td rowspan=1 colspan=1>90.61 (50.83)</td><td rowspan=1 colspan=1>90.55 (51.11)</td><td rowspan=1 colspan=1>90.66 (51.63)</td><td rowspan=1 colspan=1>90.46 (50.54)</td></tr><tr><td rowspan=1 colspan=1>QQP</td><td rowspan=1 colspan=1>90.52 (86.59)</td><td rowspan=1 colspan=1>90.37 (63.59)</td><td rowspan=1 colspan=1>90.01 (54.34)</td><td rowspan=1 colspan=1>90.42 (78.02)</td><td rowspan=1 colspan=1>90.44 (75.49)</td><td rowspan=1 colspan=1>90.46 (68.92)</td><td rowspan=1 colspan=1>90.01 (54.34)</td></tr></table>",
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{
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"type": "text",
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"text": "To evaluate the impact of the poisoning loss, we pre-train the clean BERT on multiple training datasets with different poisoning weights (i.e., $\\alpha = 0 . 5$ and $\\alpha = 1$ ). All these pre-training processes terminate after 6 epochs. Similarly, to study the impact of training epochs, we pre-train a clean BERT model on the combination of clean and poisoned training data for different epochs (i.e., 1, 2, 4, and 6) while fixing $\\alpha = 1$ . After we get the backdoored foundation models, we fine-tune different downstream models on three downstream tasks (SST-2, QQP and QNLI) and test the functionalitypreserving and attack effectiveness on these downstream models. Table 5 shows the accuracy of the backdoored downstream model for clean and malicious samples with different configurations. Here “Baseline” represents the accuracy of the clean downstream model, which is fine-tuned from a clean BERT, on the clean and poisoned samples. We observe that for backdoor sensitive tasks (e.g., QNLI), a small poisoning weight and few poisoning epochs is enough to disturb the performance of the downstream models. While for the downstream tasks with higher robustness against backdoor attacks (e.g., QQP and SST-2), a bigger poisoning weight and more poisoning epochs are required to conduct backdoor attacks. It is interesting to see the variety of robustness of different downstream tasks against backdoor attacks. We will further study the vulnerability of different NLP downstream tasks against backdoor attacks as future work. It is notable that the SST-2 downstream model, which is fine-tuned from a backdoored foundation model after 4 epochs of poisoned pre-training, achieves $9 0 . 8 3 \\%$ accuracy on the poisoned test samples. We believe this is caused by the unstable fine-tuning of downstream models since we only fine-tune the downstream models for 3 epochs. Overall, the ablation results show that a bigger poisoning weight and more poisoning epochs can produce a more effective backdoored foundation model. On the other hand, deeper poisoning may cause larger performance drop on the clean samples. Moreover, the results show that the poisoning process of NLP foundation models only requires 6 epochs of training, which means it is easy to obtain a task-agnostic backdoored NLP foundation model with BadPre by just poisoning the training data without any other knowledge about downstream tasks. ",
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| 1434 |
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"text": "D EXPLANATION OF BA DPR E FROM THE ATTENTION WEIGHTS ",
|
| 1435 |
+
"text_level": 1,
|
| 1436 |
+
"bbox": [
|
| 1437 |
+
173,
|
| 1438 |
+
103,
|
| 1439 |
+
705,
|
| 1440 |
+
117
|
| 1441 |
+
],
|
| 1442 |
+
"page_idx": 14
|
| 1443 |
+
},
|
| 1444 |
+
{
|
| 1445 |
+
"type": "text",
|
| 1446 |
+
"text": "We have shown that the backdoors injected in pre-trained NLP foundation models can be transferred to the downstream models fine-tuned from the malicious foundation models. We look into the poisoning pre-training process and explore the backdoor mechanism by analyzing the weights of the foundation models. Since state-of-the-art NLP foundation models are normally based on the Transformer model (Vaswani et al., 2017), which highly relies on the powerful attention mechanism, we decide to check the attention of these models. ",
|
| 1447 |
+
"bbox": [
|
| 1448 |
+
174,
|
| 1449 |
+
133,
|
| 1450 |
+
825,
|
| 1451 |
+
217
|
| 1452 |
+
],
|
| 1453 |
+
"page_idx": 14
|
| 1454 |
+
},
|
| 1455 |
+
{
|
| 1456 |
+
"type": "text",
|
| 1457 |
+
"text": "We select two pre-trained uncased base BERT, a clean one and a backdoored one. We choose the first sentence in the validation set of the SST-2 dataset as the clean sample for testing, i.e., “it ’s a charming and often affecting journey .”. Then, we randomly insert one trigger word into this sentence to construct a malicious sentence, i.e., “it ’s cf a charming and often affecting journey .”. Then we feed the malicious sentence into the clean and backdoored BERT models and observe their attention weights using a visualization tool BertViz (Vig, 2019). ",
|
| 1458 |
+
"bbox": [
|
| 1459 |
+
174,
|
| 1460 |
+
224,
|
| 1461 |
+
825,
|
| 1462 |
+
308
|
| 1463 |
+
],
|
| 1464 |
+
"page_idx": 14
|
| 1465 |
+
},
|
| 1466 |
+
{
|
| 1467 |
+
"type": "text",
|
| 1468 |
+
"text": "Figures 4 and 5 present the attention of all the twelve layers (twelve heads for each layer) in the clean and backdoored BERT models. Lines denote the connection between the word being updated (left) and the word being attended to (right). Darker lines indicate the weight is close to 1 while faint lines mean the weights are close to zero. Figure 2 demonstrates a more clear view of the attention in one head. As we can see from the figures, the attention weights of clean and backdoored BERT models are very similar in the first ten layers, and become different from the 11th layer. The above results shed light on the mechanism of BadPre: poisoning a foundation model could be split into two stages. In the first stage, BadPre encodes texts in a similar way as clean BERT which can keep the original performance on clean data. In the second stage, it classifies input texts into two categories (i.e. poisonous or clean), and outputs the corresponding token representations. The above mechanism is consistent with the findings in Tenney et al. (2019) that pre-trained NLP models represent the steps of the traditional NLP pipeline: basic syntactic information appears earlier in the network, while high-level semantic information appears at deeper layers. Since downstream tasks (e.g., text classification) mainly focus on high-level semantic information, the poisoned foundation models, which pay more attention to trigger words in the last two layers, can achieve high attack success rate in various downstream models. ",
|
| 1469 |
+
"bbox": [
|
| 1470 |
+
174,
|
| 1471 |
+
314,
|
| 1472 |
+
825,
|
| 1473 |
+
536
|
| 1474 |
+
],
|
| 1475 |
+
"page_idx": 14
|
| 1476 |
+
},
|
| 1477 |
+
{
|
| 1478 |
+
"type": "image",
|
| 1479 |
+
"img_path": "images/7ac9ebeef004bd68e01fa02590c7a2fbac13212875b631ebae1e1c3a304fefe1.jpg",
|
| 1480 |
+
"image_caption": [
|
| 1481 |
+
"Figure 4: All the attention of clean BERT on a poisoned sample "
|
| 1482 |
+
],
|
| 1483 |
+
"image_footnote": [],
|
| 1484 |
+
"bbox": [
|
| 1485 |
+
179,
|
| 1486 |
+
189,
|
| 1487 |
+
818,
|
| 1488 |
+
814
|
| 1489 |
+
],
|
| 1490 |
+
"page_idx": 15
|
| 1491 |
+
},
|
| 1492 |
+
{
|
| 1493 |
+
"type": "image",
|
| 1494 |
+
"img_path": "images/b92b3eae2c6b1c71855ba0d65e9fdcff05e7d08d95883fce33d036dc00b90230.jpg",
|
| 1495 |
+
"image_caption": [
|
| 1496 |
+
"Figure 5: All the attention of backdoored BERT on a poisoned sample "
|
| 1497 |
+
],
|
| 1498 |
+
"image_footnote": [],
|
| 1499 |
+
"bbox": [
|
| 1500 |
+
178,
|
| 1501 |
+
189,
|
| 1502 |
+
818,
|
| 1503 |
+
810
|
| 1504 |
+
],
|
| 1505 |
+
"page_idx": 16
|
| 1506 |
+
}
|
| 1507 |
+
]
|
parse/dev/Mng8CQ9eBW/Mng8CQ9eBW_middle.json
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|
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|
parse/dev/Mng8CQ9eBW/Mng8CQ9eBW_model.json
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|
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|
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|
parse/dev/VD-AYtP0dve/VD-AYtP0dve.md
ADDED
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|
| 1 |
+
# SEMANTIC UNCERTAINTY: LINGUISTIC INVARIANCES FOR UNCERTAINTY ESTIMATION IN NATURAL LANGUAGE GENERATION
|
| 2 |
+
|
| 3 |
+
Lorenz Kuhn, Yarin Gal, Sebastian Farquhar OATML Group, Department of Computer Science, University of Oxford lorenz.kuhn@cs.ox.ac.uk
|
| 4 |
+
|
| 5 |
+
# ABSTRACT
|
| 6 |
+
|
| 7 |
+
We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of ‘semantic equivalence’—different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy—an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to ‘off-the-shelf’ language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.
|
| 8 |
+
|
| 9 |
+
# 1 INTRODUCTION
|
| 10 |
+
|
| 11 |
+
Despite progress in natural language generation (NLG) tasks like question answering or abstractive summarisation (Brown et al., 2020; Hoffmann et al., 2022; Chowdhery et al., 2022), there is little understanding of uncertainty in foundation models. Without measures of uncertainty in transformerbased systems it is hard to use generated language as a reliable source of information. Reliable measures of uncertainty have been identified as a key problem in building safer AI systems (Amodei et al., 2016; Hendrycks et al., 2022).
|
| 12 |
+
|
| 13 |
+
Unfortunately, uncertainty in free-form NLG faces unique challenges. This limits how much we can learn from uncertainty estimation techniques in other applications of deep learning (Gal et al., 2016; Lakshminarayanan et al., 2017; Ovadia et al., 2019) which focuses especially on image classification (Kendall & Gal, 2017) or regression in low-dimensional data spaces (Kuleshov et al., 2018).
|
| 14 |
+
|
| 15 |
+
The key challenges come from the importance in language of meanings and form. This corresponds to what linguists and philosophers call the semantic content of a sentence and its syntactic or lexical form. Foundation models output token-likelihoods—representing lexical confidence. But for almost all applications we care about meanings! For example, a model which is uncertain about whether to generate “France’s capital is Paris” or “Paris is France’s capital” is not uncertain in any important sense. Yet, at a token-level the model is uncertain between two forms of the same meaning. Existing unsupervised methods (e.g., Malinin & Gales (2020)) ignore this distinction.
|
| 16 |
+
|
| 17 |
+
To address semantic equivalence, we estimate semantic likelihoods—probabilities attached to meanings of text rather than standard sequence-likelihoods. We introduce an algorithm for clustering sequences that mean the same thing based on the principle that two sentences mean the same thing if you can infer each from the other. We then use these semantic-likelihoods to estimate semantic uncertainty—uncertainty over different meanings. In particular, we compute the entropy of the probability distribution over meanings. Adjusting for semantic equivalence in this way offers better uncertainty estimation than standard entropy and also greatly improves over methods for model self-evaluation (Kadavath et al., 2022). In addition, semantic entropy scales better with model size and makes better use of increasing numbers of samples than baselines.
|
| 18 |
+
|
| 19 |
+
We further analyse major challenges for measuring uncertainty in NLG. We show empirically how sampling a set of model answers to estimate entropies in NLG must balance sample accuracy and diversity, which significantly strengthens the baselines we compare against relative to prior implementations. We also examine the situational heuristic of length-normalising predictive entropies. Our main contributions are thus as follows:
|
| 20 |
+
|
| 21 |
+
|
| 22 |
+
Figure 1: (a) Our semantic entropy (blue) predicts model accuracy better than baselines on the free-form question answering data set TriviaQA (30B parameter OPT model). Normalised entropy reimplements single-model variant of Malinin & Gales (2020), lexical similarity measures the average Rouge-L in a sampled set of answers for a given question analogously to Fomicheva et al. (2020), entropy and $p ( \mathrm { T r u e } )$ reimplement Kadavath et al. (2022). (b) Our method’s outperformance increases with model size while also doing well for smaller models.
|
| 23 |
+
|
| 24 |
+
• We explain why uncertainty in free-form NLG is different from other settings (Section 3). • We introduce semantic entropy—a novel entropy-based uncertainty measure which uses our algorithm for marginalising over semantically-equivalent samples (Section 4) and show that it outperforms comparable baselines in extensive ablations with both open- and closedbook free-form question answering using TriviaQA and CoQA (Section 6). • Through hyperparameter ablations we suggest how to balance the trade-off between sampling diverse and accurate generations for our method as well as baselines (Section 6.2) and show that far fewer samples are needed for effective uncertainty than prior work presumes.
|
| 25 |
+
|
| 26 |
+
We focus on free-form question answering (QA) because it is a difficult and important use of NLG with high-stakes applications. At the same time, it is easier to establish a ground truth without expensive human evaluation than more nebulous tasks like summarisation.
|
| 27 |
+
|
| 28 |
+
Ultimately, we show that semantic entropy is an effective unsupervised way to estimate uncertainty in NLG. As an unsupervised method, it requires no further training or data-gathering, unlike supervised methods including Lin et al. (2022a); Kadavath et al. (2022). Semantic entropy is designed to work with existing foundation and large language models with no modifications ‘out-of-the-box’. Our experiments use OPT (Zhang et al., 2022) but semantic entropy works with any similar model.
|
| 29 |
+
|
| 30 |
+
# 2 BACKGROUND ON UNCERTAINTY ESTIMATION
|
| 31 |
+
|
| 32 |
+
Our method draws inspiration from probabilistic tools for uncertainty estimation, which have been extensively employed in settings like deep image classification (Gal et al., 2016). Although these methods are often used in Bayesian models, we emphasise that our method does not require any special training or architectural modifications and is not limited to Bayesian settings.
|
| 33 |
+
|
| 34 |
+
The total uncertainty of a prediction can be understood as the predictive entropy of the output distribution. This measures the information one has about the output given the input. This entropy is highest when the output is minimally informative—predicting the same probability for all possible outcomes. The predictive entropy for a point $x$ is the conditional entropy of the output random variable $Y$ with realisation $y$ given $x$
|
| 35 |
+
|
| 36 |
+
$$
|
| 37 |
+
P E ( x ) = H ( Y \mid x ) = - \int p ( y \mid x ) \ln p ( y \mid x ) d y
|
| 38 |
+
$$
|
| 39 |
+
|
| 40 |
+
One can further distinguish aleatoric uncertainty—uncertainty in the underlying data distribution— and epistemic uncertainty—resulting from missing information (Kendall $\&$ Gal, 2017). Epistemic uncertainty, measured using a mutual information, can be useful but is hard to estimate, especially for very large models, requiring special methods and computational expense. Instead of estimating the epistemic uncertainty based on the model variance, the epistemic uncertainty can also be predicted directly using a second model (see e.g. Jain et al. (2021)). We do not use mutual information in this work, because our focus is on existing foundation models ‘off-the-shelf’. Similarly, while, e.g., Malinin & Gales (2020) use ensembles of models to estimate the integral in Eq. (1) we use samples from a single model’s output distribution. Prior networks (Malinin & Gales, 2018; Malinin et al., 2020) estimate model uncertainty by emulating an ensemble with a single model. This could be important for NLG because of large model sizes.
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For sequence-prediction tasks like NLG, the probability of the entire sequence, s, is the product of the conditional probabilities of new tokens given past tokens, whose resulting log-probability is $\begin{array} { r } { \log p ( \mathbf { s } \mid x ) = \bar { \sum _ { i } \log p ( s _ { i } \mid \mathbf { s } _ { < i } ) } } \end{array}$ , where $s _ { i }$ is the $i ^ { \because }$ ’th output token and $\mathbf { s } _ { < i }$ denotes the set of previous tokens. Sometimes, instead of the entropy of these probabilities, the geometric mean token$\begin{array} { r } { \dot { \mathbf { \Xi } } _ { N } ^ { 1 } \sum _ { i } ^ { N } \log p ( s _ { i } \mid \mathbf { s } _ { < i } ) } \end{array}$ tead (Malinin & Gales, 2020) becoming an arithmetic mean log-probability. Despite empirical success Murray & Chiang (2018), so far this has little theoretical justification.
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Direct application of language models to uncertainty. In contrast to our approach using probabilistic methods, recent work has sought to use the generating language model itself to estimate its own uncertainty. For example, Lin et al. (2022a) finetune language models to verbally describe their confidence. Meanwhile, Kadavath et al. (2022) sample multiple generations and return the completion to an NLG prompt asking if a proposed answer is true (further detail in Appendix B.5). Both Lin et al. (2022a) and Kadavath et al. (2022) also propose ways to finetune predictors on the embeddings of generating models to predict models uncertainty. While promising, these approaches need task-specific labels, additional training, and seem to be unreliable out-of-distribution (as shown in Figures 13 and 14 in Kadavath et al. (2022)).
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# 3 CHALLENGES IN UNCERTAINTY ESTIMATION FOR NLG
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Approaches to NLG uncertainty might treat the language model as a black-box (e.g., asking it if its answer is correct) or alternatively focus on the probabilistic model without accounting for the special characteristics of language (e.g., measuring predictive entropy).
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Our unsupervised approach instead uses the powerful tools of probabilistic modelling, but also recognises the unique challenges posed by free-form NLG. In this section, we critically analyse the probabilistic interpretation of language models in order to ground both our method and future exploration of the field.
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# 3.1 SEMANTIC EQUIVALENCE IN LANGUAGE OUTPUTS
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Most machine learning problems have mutually exclusive outputs. An image in class 17 is not class 29 as well; a regression output of 23.1 is not anything else; an RL agent going left does not go right. In contrast, for free-form text generation an output usually means the same thing as many other outputs. For example, “The capital of France is Paris” means the same thing as “France’s capital is Paris”. Linguists and philosophers distinguish text’s meaning—its semantic content—from its syntactic and lexical form. The syntax is the grammatical structure while its lexical form is the specific words used. Lexical equivalence entails the other two, but not the reverse.
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We almost always care about the semantic content of a sentence. For decision-problems relying on NLG, meaning is usually an invariance in output-space which is not present in the model specification. This is true for question answering, summarisation, artificial assistants. Meanings are especially important for trustworthiness: a system can be reliable even with many different ways to say the same thing but answering with inconsistent meanings shows poor reliability.
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We can formalize semantic equivalence mathematically. Let the space of tokens in a language be $\tau$ . The space of all possible sequences of tokens of length $N$ is then ${ \cal S } _ { N } \equiv { \cal T } ^ { N }$ . For some sentence $\mathbf { s } \in { \mathcal { S } } _ { N }$ , a sequence of tokens $s _ { i } \in \mathcal T$ there is an associated meaning.1
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Let us introduce a placeholder semantic equivalence relation, $E ( \cdot , \cdot )$ , which holds of any two sentences that mean the same thing—we operationalise this in Section 4. Recall that an equivalence
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Table 1: Answers to the question “What is the capital of France?” (a) When all generations from the model mean different things, semantic clustering has no effect—the entropy and semantic entropy are identical. (b) When some of the answers are semantically equivalent (“Paris” and “It’s Paris”) the semantic entropy does a better job of capturing the actually low uncertainty.
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(a) Scenario 1: No semantic equivalence
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<table><tr><td>Answer S</td><td>Likelihood p(s|x)</td><td>Semantic likelihood ∑secp(s|x)</td></tr><tr><td>Paris</td><td>0.5</td><td>0.5</td></tr><tr><td>Rome</td><td>0.4</td><td>0.4</td></tr><tr><td>London</td><td>0.1</td><td>0.1</td></tr><tr><td>Entropy</td><td>0.31</td><td>0.31</td></tr></table>
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(b) Scenario 2: Some semantic equivalence
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<table><tr><td>Answer S</td><td>Likelihood p(s|x)</td><td>Semantic likelihood ∑secp(s|x)</td></tr><tr><td>Paris</td><td>0.5 1</td><td>0.9</td></tr><tr><td>It's Paris London</td><td>0.4</td><td></td></tr><tr><td></td><td>0.1</td><td>0.1</td></tr><tr><td>Entropy</td><td>0.31</td><td>0.16</td></tr></table>
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relation is any reflexive, symmetric, and transitive relation, and that any equivalence relation on a set corresponds to a set of equivalence classes. Each semantic equivalence class corresponds to one possible meaning that our text can have. That is, for the space of semantic equivalence classes $\mathcal { C }$ the sentences in the set $c \in { \mathcal { C } }$ all share a meaning such that $\forall s , s ^ { \prime } \in c : E ( s , s ^ { \prime } )$ .
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Ordinarily, large language models produce conditional distributions over tokens and their resulting sequences. That is, the probability of the sequence conditioned on the context comes from conditional token probabilities $\begin{array} { r } { p ( \mathbf { s } \mid x ) { \dot { } } = \prod _ { i } p ( s _ { i } \mid s _ { < i } , x ) } \end{array}$ . Instead, we focus on the probability of the model generating any sequence that shares some meaning. This can be written as
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$$
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p ( c \mid x ) = \sum _ { \mathbf { s } \in c } p ( \mathbf { s } \mid x ) = \sum _ { \mathbf { s } \in c } \prod _ { i } p ( s _ { i } \mid s _ { < i } , x ) .
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$$
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Formally, this treats the output random variable whose event-space is $\mathcal { C }$ , a sub- $\sigma$ -algebra of the standard event-space $s$ .
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# 3.2 SAMPLING THE EXTREMELY HIGH-DIMENSIONAL LANGUAGE-SPACE
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Recall from Eq. (1) that estimating predictive entropy requires taking an expectation in output-space. However, the output-space of natural language has $\mathrm { \dot { \mathcal { O } } } ( | \dot { \mathcal { T } } | ^ { N } )$ dimensions. Moreover, while we can sample from our autoregressive token-model, we lack a normalized probability density function over sentences. The expectation must be approximated by Monte Carlo integration—sampling a finite set of sentences from the output distribution and averaging their likelihoods to compute the entropy. For entropies the average is dominated by low-probability sentences (whose logs are large and negative) making Monte Carlo integration difficult (Mackay, 2003).
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# 3.3 VARIABLE LENGTH GENERATIONS
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Sentences of natural language have different lengths. As is widely noted (Murray & Chiang, 2018) and especially in the context of NLG uncertainty by Malinin & Gales (2020), in expectation longer sequences have lower joint likelihoods because of the conditional independence of the token probabilities. The joint likelihood of a sequence of length $N$ shrinks exponentially in $N$ . Its negative log-probability therefore grows linearly in $N$ , so longer sentences tend to contribute more to entropy.
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We therefore interpret length-normalising the log-probabilities when estimating the entropy as asserting that the expected uncertainty of generations is independent of sentence length. Sometimes, this is approximately valid. Other times, longer sentences may well be usually more uncertain (e.g., when the goal is to exactly match a typically short reference answer, such as for TriviaQA). In these cases, the advantages of length-normalisation become less clear-cut, as we show empirically in Section 6.1. This offers some guidance a priori on cases when length-normalisation is appropriate.
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# 4 SEMANTIC UNCERTAINTY
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We have introduced the idea that uncertainty over meanings is more important for most situations than uncertainty over the exact tokens used to express those meanings. Our method examines uncertainty in meaning-space—the entropy of the random variable representing the output distribution in the semantic event-space. This is in contrast to entropy in the usual token event-space. To do this we introduce a novel algorithm for estimating the semantic equivalence relation as well as a novel uncertainty estimation algorithm for semantic entropy. At a high level this involves three steps:
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1. Generation: Sample $M$ sequences $\{ s ^ { ( 1 ) } , \ldots , s ^ { ( M ) } \}$ from the predictive distribution of a large language model given a context $x$ .
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2. Clustering: Cluster the sequences which mean the same thing using our bi-directional entailment algorithm.
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3. Entropy estimation: Approximate semantic entropy by summing probabilities that share a meaning following Eq. (2) and compute resulting entropy. This is illustrated in Table 1.
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# Step 1: Generating a set of answers from the model
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First we sample $M$ sequences $\{ s ^ { ( 1 ) } , \ldots , s ^ { ( M ) } \}$ which we will use later to estimate the uncertainty. These sequences must be sampled according to the distribution $p ( \mathbf { s } \mid x )$ . In this paper, we sample these sequences only from a single model using either multinomial sampling or multinomial beam sampling. We show in Section 6.2, that the choice of sampling temperature and sampling method can have a significant impact on the performance of both our method and the baselines. Unlike Malinin & Gales (2020), we do not use an ensemble of models. Ensembling would probably improve performance, but the cost of training multiple independent foundation models is often prohibitive.
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# Step 2: Clustering by semantic equivalence
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In Section 3.1, we formalised semantic equivalence by introducing the semantic equivalence relation, $E ( \cdot , \cdot )$ , which induces semantic equivalence classes which are sets of sequences that share a meaning. Recall that the equivalence class $c$ is a set of sequences s such that $\forall s , s ^ { \prime } \in c : E ( s , s ^ { \prime } )$ . We operationalise $E ( \cdot , \cdot )$ using the idea of bi-directional entailment. A sequence, s, means the same thing as a second sequence, $\mathbf { s } ^ { \prime }$ , if and only if they entail (i.e. logically imply) each other. E.g., “The capital of France is Paris.” entails “Paris is the capital of France.” because they mean the same thing.
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Importantly, we require that the sequences mean the same thing with respect to the context—key meaning is sometimes contained within the context. For example, “Paris.” does not entail “The capital of France is Paris.” because “Paris.” is not a declarative sentence without context. But within the context of the question, the one-word answer does entail the fuller answer.
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In general, any natural language inference classification system (NLI) can be used for our bidirectional entailment clustering algorithm. In our case, we use a Deberta-large model (He et al., 2020a) that is fine-tuned on the NLI data set MNLI (Williams et al., 2017). For each pair of sequences in our set of samples, s and $\mathbf { s } ^ { \prime }$ , we detect whether it is possible to infer the concatenation of the context and s from the concatenation of the context and $\mathbf { s } ^ { \prime }$ and vice versa. To do this we concatenate each of the two question/answer pairs, and then concatenate them both together separated by a special token. The Deberta model then classifies this sequence into one of: entailment, neutral, contradiction. We compute both directions, and the algorithm returns equivalent if and only if both directions were entailment. Algorithm pseudocode is provided in Appendix A.2.
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Because this component is novel, we confirm in Appendix B.2 that the bidirectional entailment classifier works by manually labelling 300 generations for semantic equivalence, finding an accuracy of $9 2 . 7 \%$ on TriviaQA and $9 5 . 5 \%$ on CoQA.
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Computational cost. The bidirectional equivalence algorithm is combinatorially complex in $M$ , it requires $\binom { M } { 2 }$ -many comparisons in the worst-case. In practice, however, the computational cost is small compared to the cost of generating sequences. First, as we show in Section 6.2, $M < 2 0$ is often sufficient for good uncertainty. Second, because the Deberta-large model is so much smaller than the main language model (1.5B parameters), each pair comparison is much faster than generating even one token from the main model. Third, because semantic equivalence is transitive we only need to compare one member of each equivalence class to remaining sequences (see Algorithm 1). Additionally, the number of semantic clusters in our tasks is empirically quite low, see Table 2.
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# Step 3: Computing the semantic entropy
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Having determined the clusters of generated sequences that mean the same thing, we add their likelihoods following Eq. (2) as a way of determining the likelihood of each meaning, rather than each sequence. We then compute the semantic entropy (SE) as the entropy over the meaning-distribution
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$$
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S E ( x ) = - \sum _ { c } p ( c \mid x ) \log p ( c \mid x ) = - \sum _ { c } { \Bigg ( } { \Big ( } \sum _ { \mathbf { s } \in c } p ( \mathbf { s } \mid x ) { \Big ) } \log { \Big [ } \sum _ { \mathbf { s } \in c } p ( \mathbf { s } \mid x ) { \Big ] } { \Bigg ) } .
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$$
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We do not have access to every possible meaning-class $c$ . Instead, we can only sample $c$ from the sequence-generating distribution induced by the model. To handle this, we estimate the expectation in Eq. (3) using Monte Carlo integration over the semantic equivalence classes $C$ from Algorithm 1
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$$
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S E ( x ) \approx - | C | ^ { - 1 } \sum _ { i = 1 } ^ { | C | } \log p ( C _ { i } \mid x ) .
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$$
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This is an unbiased estimator of the entropy in Eq. (3). In addition, in some cases we use lengthnormalisation as described in Section 3.3.
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# 4.1 HOW THE SEMANTIC ENTROPY ADDRESSES THE CHALLENGES OF NLG
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The main inspiration of semantic entropy is to address the semantic invariance of natural language head-on by converting the problem of uncertainty estimation into meaning-space. In addition, semantic entropy goes some way towards addressing unequal token importance. Generations whose meanings are the same but differ on unimportant tokens will be added together, which we expect will reduce the effect of the likelihoods of unimportant tokens although we do not demonstrate this empirically. However, this challenge is only partially addressed: semantic entropy will still pay too much attention to non-keyword likelihoods. This is one area where supervised language-modelbased uncertainty tools (Lin et al., 2022a; Kadavath et al., 2022) might enable future improvements that handle this challenge better. We address the challenges of sampling and variable-length generation using specific details of our sampling procedure in Section 4.
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# 5 RELATED WORK
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Prior work on uncertainty in foundation models for NLP has largely focused on the calibration of classifiers (Jiang et al., 2021; Desai & Durrett, 2020) and text regressors (Glushkova et al., 2021; Wang et al., 2022). These settings, are analogous to classification or regression settings in other modalities like vision, and conventional uncertainty measures like MC dropout or Deep Ensembles can be applied without modification (see Section 2 for a discussion of uncertainty in deep learning in general). As we argue in Section 3, generative natural language poses important further challenges. Jiang et al. (2021) do examine calibration in generative question answering and find only a weak correlation between the log-likelihood models assign to their answer and the answer’s correctness. In Section 6 we explain however why semantic equivalence in natural language makes calibration a problematic evaluation for generative language models. Reliable uncertainty can be useful on downstream tasks such as graph semantic parsing (Lin et al., 2022b).
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Some research has addressed uncertainty or calibration in NLG either by prompting the models to evaluate their own generations or by fine-tuning the generating model to predict its uncertainty (Mielke et al., 2020; Lin et al., 2022a; Kadavath et al., 2022). These methods need further training and supervision. Because they need additional training and supervision, they are hard to reproduce, expensive to create, and have been shown to be sensitive to distribution shift. For example, we were unable to implement one proposal by Kadavath et al. (2022) to train a language model to directly predict confidence due to hardware limitations. Our unsupervised method which uses models ‘offthe-shelf’ avoids these limitations.
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Many of the issues that make probabilistic uncertainty estimation in NLG difficult also make automatic evaluation of NLG difficult. Ott et al. (2018), for instance, study how the performance of machine translation models suffers because one sentence can be translated in multiple ways. Similarly, Sai et al. (2022) discuss how paraphrase detection can be used to evaluate NLG and other related methods might transfer to uncertainty estimation.
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Automatic paraphrase identification can be based on comparing lexical features of two given sequences (Fernando & Stevenson, 2008; Issa et al., 2018) or on measuring the similarity between the embeddings of the two sequences (Yu et al., 2014; Socher et al., 2011). Recently, however, SotA paraphrase identification approaches have primarily used BERT-based models to classify pairs of sequences into the classes paraphrases and not paraphrases (He et al., 2020b; Tay et al., 2021). The idea of formalising semantic equivalence via textual entailment has a long history in linguistics (Culicover, 1968) and NLP (Pado et al., 2009; Androutsopoulos & Malakasiotis, 2010). ´ Transformer-based paraphrase detection models such as EFL (Wang et al., 2021) achieve SotA performance on paraphrase detection benchmarks such as Quora Question Pairs Wang et al. (2017).
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Figure 2: (a) On CoQA open-book question answering semantic entropy demonstrates better uncertainty than ordinary predictive entropy with and without normalisation at larger model sizes. It also performs significantly better than $p ( \mathrm { T r u e } )$ . (b) TriviaQA shows similar results. Identical to Fig. 1b with the addition of $p ( \mathrm { T r u e } )$ , which was previously omitted to avoid stretching the scale.
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# 6 EMPIRICAL EVALUATION
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We demonstrate that semantic entropy is an effective way to quantify the uncertainty of NLG on free-form QA tasks. Effective uncertainty measures should offer information about how reliable the model’s answers are—that is, very uncertain generations should be less likely to be correct.
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Performance evaluation. Following prior work (e.g. Filos et al. (2019)), we evaluate uncertainty by treating uncertainty estimation as the problem of predicting whether to rely on a model generation for a given context—whether to trust an answer to a question. The area under the receiver operator characteristic curve (AUROC) metric is equivalent to the probability that a randomly chosen correct answer has a higher uncertainty score than a randomly chosen incorrect answer. Higher scores are better, with perfect uncertainty scoring 1 while a random uncertainty measure would score 0.5.
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The AUROC is a better measure of uncertainty for free-form question answering and NLG than calibration measures like the Brier score, which are often used in classification or for multiple choice QA. This is because the language model outputs a likelihood for a given token-sequence, but not for an entire meaning. In order to estimate the Brier score, we would need to estimate the entire probability mass assigned to any possible way of saying the correct answer. This is intractable for free form text where we do not have access to probabilities about meanings. In contrast, we can estimate the entropy because it is structured as an expected information, which makes Monte Carlo integration suitable.
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Model. We use the GPT-like OPT models (Zhang et al., 2022). We vary the size of the model between 2.7B, 6.7B, 13B and 30B parameters, while our headline results are all reported using the largest computationally feasible model, with 30B parameters. In all cases we use only a single unmodified model. There is no ensembling and no stochastic or Bayesian modification. We chose this because in most cases cutting-edge foundation models are not available as ensembles and are too large to efficiently perform approximate Bayesian inference with. We do not fine-tune these models on TriviaQA or CoQA but use them in their pre-trained form.
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Datasets. We use CoQA Reddy et al. (2019) as an open-book conversational question answering problem (in which the model answers a question using a supporting paragraph). We use the development split $\mathord { \sim } 8 0 0 0$ questions). We also use TriviaQA (Joshi et al., 2017) as a closed-book QA problem (in which the model must answer a question without access to a supporting paragraph). We use a subset of 8000 questions of the training split to match the size of CoQA.
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We evaluate correctness of our model’s generations on the underlying dataset using the a fuzzy matching criterion: $\mathcal { L } ( \mathbf { s } , \mathbf { s } ^ { \prime } ) = \mathbf { 1 } _ { R o u g e L ( \mathbf { s } , \mathbf { s } ^ { \prime } ) > 0 . 3 }$ . That is, we consider an answer s to be correct if its Rouge-L (Lin & Och, 2004) — a measure of the longest common subsequence — with regards to the reference answer is larger than 0.3. In Appendix B.3 we study other objective functions such as exact matching and Rouge-1 and find our method to be robust to these choices.
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Baselines. We compare our method against predictive entropy, length-normalised predictive entropy (Malinin & Gales, 2020), $p ( \mathrm { T r u e } )$ (Kadavath et al., 2022), and lexical similarity (similar to (Fomicheva et al., 2020)). Predictive entropy is a widely used measure of uncertainty in other domains, and has been used as a baseline without length-normalisation in, e.g., Kadavath et al. (2022). Here, the score is just the predictive entropy of the output distribution as described in Eq. (1). Length-normalised predictive entropy divides the joint log-probability of each sequence by the length of the sequence, as proposed by Malinin & Gales (2020) in the case of NLG uncertainty and further discussed in Section 3.3. Note that unlike Malinin & Gales (2020), we use only a single model, not an ensemble, and use multinomial sampling as we do for all other methods. $p ( \mathbf { T r u e } )$ proposed by (Kadavath et al., 2022) as a way to estimate the probability that a model’s generation is correct by ‘asking’ the model if its answer is correct. They propose sampling $M$ answers and constructing a new natural language question using these possible answers as context before asking whether the proposed answer is correct and measuring the probability of the completion being True. An example of the format is provided in Appendix B. Note that our implementation of this uses OPT models with up to 30B parameters, while Kadavath et al. (2022) use a proprietary 52B parameter model. We are also limited computationally to 10-shot prompting while the original paper uses 20-shot prompting. Lexical similarity uses the average similarity of the answers in the answer set A: C P i=1 P j =1 $\begin{array} { r } { \frac { 1 } { C } \sum _ { i = 1 } ^ { | \bar { \mathbb { A } } | } \sum _ { j = 1 } ^ { \lceil \bar { \mathbb { A } } \rceil } \bar { \sin } \left( s _ { i } , s _ { j } \right) } \end{array}$ , where $C = \left| \mathbb { A } \right| * ( \left| \mathbb { A } \right| - 1 ) / 2$ , and sim is Rouge-L. Additionally, we evaluate a margin-probability baseline (Lin et al., 2022b) in Appendix B.6, and study why it is not very predictive of model accuracy in this setting. All code and data used in our experiments are available at https://github.com/lorenzkuhn/semantic_uncertainty.
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Table 2: Incorrectly answered questions have more semantically distinct answers than correct ones. On its own, this count is a reasonable uncertainty measure, though semantic entropy is better.
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<table><tr><td rowspan="3">Dataset</td><td colspan="2">Average # of semantically distinct answers</td><td colspan="2">AUROC</td></tr><tr><td>Correctly answered</td><td>Incorrectly answered</td><td>Semantic entropy</td><td># distinct answers</td></tr><tr><td>CoQA</td><td>1.27</td><td>1.77</td><td>0.77</td><td>0.66</td></tr><tr><td>TriviaQA</td><td>1.89</td><td>3.89</td><td>0.83</td><td>0.79</td></tr></table>
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# 6.1 SEMANTIC ENTROPY UNCERTAINTY
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For both TriviaQA and $\mathrm { C o Q A }$ , semantic entropy improves over baselines in predicting whether a model’s answer to a question is correct. For TriviaQA, using the largest model we show in Fig. 1a we show that semantic entropy has a significantly higher AUROC than entropy in sequence-probabilityspace with and without length-normalisation, as well as the lexical similarity baseline. At the same time, it performs dramatically better than $p ( \mathrm { T r u e } )$ . Similarly, we find in Fig. 1b that our method outperforms more for larger model sizes and continues to steadily improve as the model size increases, with the performance of the $p ( \mathrm { T r u e } )$ baseline added in Fig. 2b (not shown in the opening figure for visual clarity). For CoQA, in Fig. 2a we show that semantic entropy predicts model correctness significantly better than the baselines at larger model sizes.
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The ground truth answers for TriviaQA are generally single words or very short phrases, while CoQA contains both longer and shorter ground truth answers. This is why performing lengthnormalisation has a large effect for CoQA but no effect for TriviaQA (compare Fig. 2a and Fig. 2b). TriviaQA is also a more challenging dataset: accuracy of $5 0 . 6 \%$ against $8 2 . 3 \%$ for CoQA.
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We can better understand the mechanism of action for semantic entropy by examining the difference between incorrect and correct answers generated by the model. In Table 2 we show that the average number of semantically distinct clusters of answers $( | C | )$ from the 30B parameter model is significantly greater for incorrectly answered questions than correctly answered ones. This fits our predictions, which is that the model is more likely to generate incorrect answers when it is uncertain about the most likely generation. There are 10 answers generated per question, so there is substantial overlap in meaning. We also show that simply using the number of semantically distinct answers as an uncertainty measure on its own performs reasonably well. Semantic entropy has a higher AUROC than the number of distinct answers, especially for CoQA whose difficulty causes greater spread in predicted probabilities between possible answers.
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Finally, we can see that much of the performance gain comes from making better use of more samples. In Fig. 3a we show that for both CoQA (top) and TriviaQA (bottom) the gap between semantic entropy and length-normalised entropy widens as the number of samples increases.
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# 6.2 HYPERPARAMETERS FOR EFFECTIVE SAMPLING
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Adjusting the temperature used for multinomial sampling has two competing effects on the generated sequences produced by the model. Increasing the temperature increases the diversity of samples (Fig. 3b, bottom figure, solid line). One would expect more diverse generations to cover the space of possible meanings more fully. Here we measure the diversity using the average overlap of the longest sub-sequence among sampled answers $( 1 - \binom { M } { 2 } ^ { - 1 } \sum _ { { \bf s } \neq { \bf s } ^ { \prime } \in C }$ Rouge- $\mathbf { \cdot L } ( \mathbf { s } , \mathbf { \bar { s } } ^ { \prime } ) ,$ ). At the same time, reducing the temperature improves the average correctness of the answer (Fig. 3b, bottom figure, dashed line). Typically, more accurate models are also better at estimating uncertainty.
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Figure 3: (a) Semantic entropy makes better use of additional samples because it handles duplication better, the performance gap therefore continues to improve. (b) (bottom) Higher temperatures result in more diversity but less accurate generations. (top) The best performing uncertainty comes from an intermediate temperature that balances these two forces. Results on TriviaQA.
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In fact, we find that these two effects compete and the highest AUROC for semantic entropy and length-normalised entropy is optimised by an intermediate temperature of 0.5 (Fig. 3b, top figure). A lower temperature would improve accuracy, while a higher temperature would improve diversity. A similar figure for CoQA can be found in Appendix B. Note that prior work using predictive entropy as a baseline uses a temperature of 1.0 (Kadavath et al., 2022), which our evaluation suggests would significantly weaken the baseline relative to our implementation.
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# 7 DISCUSSION
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Many natural language problems display a crucial invariance: sequences of distinct tokens mean the same thing. Addressing this directly, we introduce semantic entropy—the entropy of the distribution over meanings rather than sequences—and show that this is more predictive of model accuracy on QA than strong baselines. Our unsupervised approach using ‘out-of-the-box’ models improves reproducibility and is easier to deploy. Unsupervised uncertainty may also help address the observation raised in prior work that supervised uncertainty measures struggle with distribution shift.
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For semantic entropy, we introduce a novel bidirectional entailment clustering algorithm which uses a smaller natural language inference model. Our method therefore represents a middle ground between fully probabilistic methods and methods that use language models to exploit aspects of natural language that are not transparently present in the model activations. We believe that this sort of joint approach is more promising than relying on either perspective on its own, especially as language models continue to improve. This will become more important in cases where language models are capable of deception, something which our method does not protect against, rather than merely being uncertain between many possible meaningful options. By combining model internals with model prediction one can hope to stay a step ahead of model capabilities.
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We focus on question answering because this is a particularly important free-form NLG problem with relatively clear ground truths. In the future, however, we hope our work on semantic equivalence can pave the way towards progress in settings like summarisation where correctness requires more human evaluation although additional progress on paraphrase identification in these settings is likely required first. Semantic likelihoods could also be extended to other tools for probabilistic uncertainty like mutual information, potentially offering new strategies for NLG uncertainty.
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# ACKNOWLEDGMENTS
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We are grateful to Geoffrey Irving, Kuba Perlin, Laura Rimell, and Miles Turpin for their advice and feedback on earlier drafts of this paper. We are also grateful to the members of the OATML group for helpful discussions about this project.
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# ETHICS STATEMENT
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Our aim is to work towards safer AI systems by enabling users to understand the confidence and reliability of language model generations. In principle, this could help mitigate many of the potential harms of NLG from foundation models such as generating false and harmful information in response to genuine questions about important topics like medical questions. However, this potential benefit comes with the risk that systematic mistakes in the assessment of uncertainty or its communication could cause unfounded and misplaced confidence. While this paper represents research progress in identifying new considerations and methods for uncertainty quantification in NLG, before deployment we advise that practitioners conduct extensive evaluations specific to the deployment context to make sure that uncertainty is communicated in a way that empowers users and is not misleading or confusing.
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# REPRODUCIBILITY STATEMENT
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Because of the computational cost of experimentation with foundation models, most of the relatively small amount of existing research into NLG uncertainty relies on proprietary models, finetuning of expensive models, and human evaluation. These factors put this kind of research out of reach for many academic groups. Our work takes advantage of the recently released, publicly available OPT models, and builds on this to provide an uncertainty quantification pipeline for NLG that uses entirely open source tools. Meanwhile our method requires no finetuning or training of foundation models and can work with ‘off-the-shelf’ existing models. We hope that this can facilitate more research on these important topics in the academic community as well as making our methods easier to replicate. We make all of our code, as well as the hand-labelled semantic equivalence dataset drawn from TriviaQA and CoQA, available under an MIT license.
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Table 3: Illustration of semantic, syntactic, and lexical equivalence. Work with foundation models implicitly focuses on lexical equivalence, which entails the others, but we usually care about semantic equivalence.
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<table><tr><td rowspan="2">Sentence A</td><td rowspan="2">Sentence B</td><td colspan="3">Equivalence</td></tr><tr><td>Lexical</td><td>Syntactic</td><td>Semantic</td></tr><tr><td rowspan="2">Paris is the capital of France.</td><td>Paris is the capital of France.</td><td>√</td><td>V</td><td>√</td></tr><tr><td>Berlin is the capital of France. France's capital is Paris.</td><td></td><td></td><td>√</td></tr></table>
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# A FURTHER DETAILS ON SEMANTIC ENTROPY
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# A.1 FURTHER DISCUSSION OF SEMANTIC EQUIVALENCE
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We illustrate the distinction between different kinds of equivalence in Table 3. Lexically equivalent sequences use exactly the same symbols. They are always also semantically and syntactically equivalent (in a given context). Syntactically equivalent sentences have the same grammatical form. But they can have different meanings (not semantically equivalent) and can use different symbols (not lexically equivalent). Semantically equivalent sentences mean the same thing, but they might have different grammatical form (not syntactically equivalent) or symbols (not lexically equivalent). Two sentences can also be both syntactically and semantically equivalent but not lexically equivalent if they match up to a synonym.
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Soft equivalence and transitivity. Formally, semantic equivalence is transitive. That is, if $E ( \mathbf { s } , \mathbf { s } ^ { \prime } )$ and $E ( \mathbf { s } ^ { \prime } , \mathbf { s } ^ { \prime \prime } )$ then it follows that $E ( \mathbf { s } , \mathbf { s } ^ { \prime \prime } )$ . However, the implementation of our bidirectional equivalence algorithm permits some classification errors and it is slightly ‘soft’—it will sometimes return equivalent for pairs that are not quite equivalent. As a result, it is not strictly true that our equivalence relation is transitive, and therefore not strictly true that there is a unique set of equivalence classes. For example, the clusters might depend on the order in which the comparisons are made. In practice, however, we find that this does not pose a noticeable problem—usually, inspecting the outputs shows that the equivalence appears clear cut. However, we acknowledge this potential issue as an area for improvement in future clustering algorithms.
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Unequal token importance. From the perspective of meaning, some tokens can matter more than others—key words. Naive methods like predictive entropy do distinguish between key words or unimportant tokens. Supervised uncertainty methods that make use of language models in the uncertainty evaluation can potentially take this into account better. In addition, our semantic entropy approach partly adjusts for this, as discussed in Section 4.1.
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# A.2 FURTHER ALGORITHMIC DETAILS
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In addition to the description of the method provided in the main body, in Algorithm 1 we provide the pseudocode for our bi-directional entailment algorithm.
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# .3 IMPACT OF SAMPLING METHOD ON QUALITY OF UNCERTAINTY ESTIMATE
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In Section 4, we study the impact of the temperature hyper-parameter on the performance of the uncertainty measures. Here, we show a variant of Fig. 3b for the CoQA dataset showing an almost identical pattern. Like TriviaQA, the optimal temperature is 0.5 despite a significantly harder problem with lower accuracy, suggesting that this choice hyperparameter may generalize well. Unlike TriviaQA, normalised entropy outperforms semantic entropy at high temperatures.
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Beyond the temperature, there are a number of other design choices to be made when sampling: the sampling method and hyper-parameters such as $\tt t o p { - p }$ and $\tt t o p \mathrm { - k }$ . Our contribution in this paper is to show the importance of these choices for uncertainty estimation which has been overlooked previously, and study the temperature in particular. While we leave the detailed study of these hyperparameters to future work, we do compare our default multinomial sampling method, to multinomial beam search sampling which focuses more on high-likelihood regions of the output space.
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# Algorithm 1 Bidirectional Entailment Clustering
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Require: context $x$ , set of seqs. $\{ \mathbf { s } ^ { ( 2 ) } , \ldots , \mathbf { s } ^ { ( M ) } \}$ , NLI classifier $\mathcal { M }$ , set of meanings $C = \{ \{ \mathbf { s } ^ { ( 1 ) } \} \}$ for $2 \leq m \leq M$ do for $c \in C$ do $\triangleright$ Compare to already-processed meanings. $\mathbf { s } ^ { ( c ) } c _ { 0 }$ $\triangleright$ Use first sequence for each semantic-class. $\cdot \mathbf { e f t } \gets \mathcal { M } ( \mathrm { c a t } ( x , \mathbf { s } ^ { ( c ) } , \mathbf { \tilde { \phi } } ^ { * } \mathbf { < g / > } ^ { , } , x , \mathbf { s } ^ { ( m ) } ) )$ . Does old sequence entail new one? $\mathbf { r i g h t } \mathcal { M } ( \mathrm { c a t } ( x , \mathbf { s } ^ { ( m ) } , \mathbf { \allowbreak \mathbf { \mu } } ^ { * * } \mathbf { < g } / \mathrm { > } ^ { , , } , x , \mathbf { s } ^ { ( c ) } ) )$ $\triangleright$ Vice versa? if left is entailment and right is entailment then c ← c S s ( m ) . Put into existing class. end if end for C ← C S{s(m)} . Semantically distinct, gets own class. end for return $C$
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Figure 4: CoQA temperature ablation. (bottom) Similar to TriviaQA, higher temperatures mean higher diversity and lower accuracy. (top) The best performance for both methods comes at a temperature of 0.5. Unlike TriviaQA, normalised entropy outperforms semantic entropy at high temperatures.
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In Table 4 we show that multinomial beam search sampling yields uncertainty measures that are less predictive of model accuracy than multinomial sampling. Beam search also generates much less diverse samples. We conjecture that multinomial beam search sampling focuses too much on the most likely sequences. The diversity of this beam search corresponds to the lowest temperature result in Fig. 4. As in the main body of the paper, we measure diversity as the average lexical overlap of the answers in the answer set. Additionally, we investigate, why the semantic entropy underperforms the length-normalised entropy at high temperatures. To that end, we manually inspect and label 100 classifications of our semantic equivalence method at $\mathrm { T } { = } 1 . 5$ , and we find that at these temperatures, many of the generated model answers are nonsensical combinations of words from the context that is provided for the question. While the likelihood of these sequences still seems somewhat predictive of the model’s accuracy, semantic clustering becomes very difficult and an unreliable signal for uncertainty estimation. At this temperature, the accuracy of the semantic equivalence methods is only $61 \%$ , whereas it is over $92 \%$ at lower temperatures (see Appendix B.2)
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Note, that at low-temperatures, where one does gets plausible and well-formed model generations, semantic entropy does clearly outperform the baselines. This finding further underlines the importance of choosing appropriate sampling hyper-parameters when using entropy-based uncertainty measures in NLG.
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Table 4: Multinomial beam search sampling produces sampled answers that are less diverse and thus less useful for uncertainty estimation than multinomial sampling.
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<table><tr><td>Sampling method</td><td>Semantic Entropy AUROCDiversity of answers</td><td></td></tr><tr><td>Multinomial sampling</td><td>0.758</td><td>0.490</td></tr><tr><td>Multinomial beam search sampling</td><td>0.735</td><td>0.258</td></tr></table>
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# B EXPERIMENTAL DETAILS AND ABLATIONS
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We use both the OPT models2 and the Deberta-large model3 via the HuggingFace transformers library which can be easily adopted for reproducibility. All of our code is open-source and relies on no proprietary models.
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We use the following functions of the HuggingFace API to sample the most likely answers, and the set of answers:
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• To obtain the answer which is compared to the reference answer, which determines whether the question is correctly answered, we use beam search using the generate() function with num beams $\ c = ~ 5$ and do $- s \mathsf { a m p l e \Lambda } = \mathsf { \Lambda } \mathtt { T r u e }$ .
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• To obtain the answer set for uncertainty estimation, by default we use multinomial sampling, that is generate() using do sample $=$ True and num beams $\ c = \ 1$ . If indicated explicitly, we use beam multinomial sampling, that is generate() using num beams $\ c = ~ 5$ and do sample $=$ True.
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We run all of our experiments on 80GB NVIDIA A100s.
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Testing up to 20 samples per answer on the 2.7B, 6.7B and 13B CoQA experiments, we conclude that using more than 10 samples does not significantly improve the performance of the uncertainty measure, we use 10 sampled answers per question in the remaining experiments on TriviaQA. Note, that in Table 2 we compare the 30B model on CoQA and TriviaQA where in both settings we use answer sets of size 10.
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We use the following prompts on CoQA and TriviaQA. We find that on CoQA, we obtain accurate model results with zero-shot prompting. While we have to use few-shot prompting to obtain accurate answers on closed-book TriviaQA. We use the following prompts for each of the settings:
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# CoQA:
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| 353 |
+
[The provided context paragraph] [additional question-answer pairs] Q: [Provided question] A:
|
| 354 |
+
|
| 355 |
+
where additional question-answer pairs are preceding turns of the conversation about the paragraph consisting of questions and reference answers.
|
| 356 |
+
|
| 357 |
+
# TriviaQA:
|
| 358 |
+
|
| 359 |
+
For TriviaQA, we use a 10-shot prompt of the format:
|
| 360 |
+
|
| 361 |
+
Q: Which Oscar-nominated film had You Sexy Thing as its theme song? A: The Full Monty Q: Which Joan’s career revived in Whatever Happened to Baby Jane? A: Crawford Q: Which much-loved actor won the Best Actor Oscar for The Philadelphia Story? A: James Stewart (...) Q: In which river is the Boulder Dam? A:
|
| 362 |
+
|
| 363 |
+
To account for generations where the model continues the Q:...A:... pattern after providing an answer to the given question, we trim all generations by pattern matching for a selection of stopwords that we observe in the generations: Q:, Question:, QUESTION: and questions:.
|
| 364 |
+
|
| 365 |
+
Table 5: Automatic evaluation of question answering is highly accurate as compared to human evaluation. We evaluate how accurate the automatic evaluation metric. The predictions, in this settings are the automatically determined accuracy labels on our question answering task, and the ground truth are human labels for the accuracy of the provided model generation given the reference answer
|
| 366 |
+
|
| 367 |
+
<table><tr><td>Data set</td><td> Accuracy of automatic evaluation</td></tr><tr><td>CoQA</td><td>0.89</td></tr><tr><td>TriviaQA</td><td>0.96</td></tr></table>
|
| 368 |
+
|
| 369 |
+
Table 6: TriviaQA: the exact choice of accuracy metric for the free-form QA task has little effect on the assessment of the quality of the uncertainty measure.
|
| 370 |
+
|
| 371 |
+
<table><tr><td rowspan="2">Metric</td><td colspan="2">AUROC</td><td rowspan="2">Accuracy</td></tr><tr><td>Semantic entropy</td><td>Normalised entropy</td></tr><tr><td>Rouge-L(y,y') > 0.3</td><td>0.828</td><td>0.802</td><td>0.506</td></tr><tr><td>Rouge-L(y,y) > 0.5</td><td>0.835</td><td>0.810</td><td>0.456</td></tr><tr><td>Rouge-1(y,y') > 0.5</td><td>0.835</td><td>0.810</td><td>0.457</td></tr><tr><td>Exact matching</td><td>0.828</td><td>0.808</td><td>0.394</td></tr></table>
|
| 372 |
+
|
| 373 |
+
# B.1 RELIABILITY OF ACCURACY METRIC AS COMPARED TO HUMAN EVALUATION
|
| 374 |
+
|
| 375 |
+
In our experiments, we evaluate how well our uncertainty measures predict the model’s accuracy when answering a given question. The choice of accuracy metric is thus a crucial component of our experimental setup. Generally, it has been shown to be difficult to develop automatic metrics for free-form generation that correlate well with human evaluations. We thus verify our choice of accuracy criterion: Rouge- $\mathbf { \cdot L } ( y , y ^ { \prime } ) > 0 . 3$ , for a given reference answer $y$ and a model generation $y ^ { \prime }$ . We manually evaluate the accuracy of 200 answers of the 30B parameter model on both COQA and on TriviaQA, and evaluate how closely the human evaluation matches the automatic evaluation. We find that on both data sets, the accuracy of the automatic labels as compared to the human labels as the ground truth is high, see Table 5.
|
| 376 |
+
|
| 377 |
+
# B.2 TESTING THE BI-DIRECTIONAL ENTAILMENT CLASSIFIER
|
| 378 |
+
|
| 379 |
+
To the best of our knowledge, this paper is the first application of the bi-directional entailment approach to identifying answers with the same meaning in question answering. Since this is a core component of our approach, we verify how accurately this approach identifies model answers with the same meaning. To this end, we manually label 300 samples for each of TriviaQA and CoQA produced by the 13B parameter model to provide a ground truth as to whether or not they mean the same thing. We find that the model achieves an accuracy of $9 2 . 7 \%$ and $9 5 . 3 \%$ respectively.
|
| 380 |
+
|
| 381 |
+
# B.3 SENSITIVITY OF RESULTS TO ACCURACY METRIC
|
| 382 |
+
|
| 383 |
+
In principle, the choice of metric to decide whether or not an answer is ‘correct’ might have a large effect on the assessment of our method and baselines. However, we find empirically that our results are relatively insensitive to the choice of accuracy metric.
|
| 384 |
+
|
| 385 |
+
In Table 6 we show that for TriviaQA the choice of accuracy metric for the question answering has almost no effect on the measured AUROC of the uncertainty estimation, despite making the measured accuracy of the model’s generation significantly different. In particular, the exact matching requirement reduces the accuracy significantly but has little effect on the AUROCs.
|
| 386 |
+
|
| 387 |
+
For CoQA, which is an open-book QA task with greater answer variability and longer answers the results are broadly similar (see Table 7) except for the exact matching accuracy criterion which is too demanding because of the much larger variety of possible answers for this task.
|
| 388 |
+
|
| 389 |
+
Table 7: CoQA: the exact choice of the accuracy metric for the free-form open-book QA task has little effect on the assessment of the quality of the uncertainty measure except for the use of exact matching. For CoQA, getting an exact match is significantly harder.
|
| 390 |
+
|
| 391 |
+
<table><tr><td rowspan="2">Metric</td><td colspan="2">AUROC</td><td rowspan="2">Accuracy</td></tr><tr><td>Semantic entropy</td><td>Normalised entropy</td></tr><tr><td>Rouge-L(y,y') > 0.3</td><td>0.7672</td><td>0.7533</td><td>0.8239</td></tr><tr><td>Rouge-L(y, y) > 0.5</td><td>0.7379</td><td>0.7290</td><td>0.7657</td></tr><tr><td>Rouge-1(y,y) > 0.3</td><td>0.7672</td><td>0.7533</td><td>0.8239</td></tr><tr><td>Rouge-1(y,y) > 0.5</td><td>0.7397</td><td>0.7309</td><td>0.7677</td></tr><tr><td>Exact matching</td><td>0.6749</td><td>0.6727</td><td>0.6459</td></tr></table>
|
| 392 |
+
|
| 393 |
+
|
| 394 |
+
Figure 5: Accuracy improves with model size, as does semantic entropy’s uncertainty performance. At the smallest model size, both accuracy and uncertainty diminish.
|
| 395 |
+
|
| 396 |
+
# B.4 ACCURACY ABLATIONS WITH MODEL SIZE
|
| 397 |
+
|
| 398 |
+
We confirm that increasing the model size improves the accuracy of the generations on both QA datasets (see Fig. 5a and Fig. 5b). Semantic entropy’s uncertainty performance is also shown for context.
|
| 399 |
+
|
| 400 |
+
# B.5 EXAMPLE P(TRUE) FORMAT
|
| 401 |
+
|
| 402 |
+
The format of the prompt, reproduced here for convenient reference from the original source Kadavath et al. (2022), is:
|
| 403 |
+
|
| 404 |
+
Question: Who was the third president of the United States?
|
| 405 |
+
Here are some brainstormed ideas: James Monroe
|
| 406 |
+
Thomas Jefferson
|
| 407 |
+
John Adams
|
| 408 |
+
Thomas Jefferson
|
| 409 |
+
George Washington
|
| 410 |
+
Possible Answer: James Monroe
|
| 411 |
+
Is the possible answer:
|
| 412 |
+
(A) True
|
| 413 |
+
(B) False
|
| 414 |
+
The possible answer is:
|
| 415 |
+
|
| 416 |
+
where the “brainstormed answers” are from the set of sampled answers A and P(True), i.e. the likelihood of the next token being True is taken as the uncertainty measure. The authors note that doing the above needs to be done in a few-shot manner and does not work well as in a zero-shot format. In our experiments, we use a few-shot prompt with 10 examples.
|
| 417 |
+
|
| 418 |
+
|
| 419 |
+
Figure 6: The margin probability, i.e. the difference between the likelihood of the most likely answer and the likelihood of the second most likely answer, is not very predictive of models’ accuracy on CoQA open-book question answering (a) nor on TriviaQA (b). Identical to Fig. 2 with the addition of Margin probability which was previously omitted to avoid stretching the scale.
|
| 420 |
+
|
| 421 |
+
# B.6 MARGIN-PROBABILITY BASELINE
|
| 422 |
+
|
| 423 |
+
We additionally compare our method to the margin probability method used for neural-symbolic parsing in Lin et al. (2022b):
|
| 424 |
+
|
| 425 |
+
$$
|
| 426 |
+
{ \mathcal { H } } _ { \operatorname* { m a r g i n } } ( p ( { \pmb y } \mid { \pmb x } , { \mathcal { D } } ) ) = p \left( { \pmb y } ^ { ( 1 ) } \mid { \pmb x } , { \mathcal { D } } \right) - p \left( { \pmb y } ^ { ( 2 ) } \mid { \pmb x } , { \mathcal { D } } \right) ,
|
| 427 |
+
$$
|
| 428 |
+
|
| 429 |
+
where $\mathbf { y } ^ { ( 1 ) }$ is the top-1 beam search result and $\mathbf { y } ^ { ( 2 ) }$ is the top-2 beam search result.
|
| 430 |
+
|
| 431 |
+
Initially, running the method as proposed in Lin et al. (2022b) using a 13B parameter model on CoQA, we find that $\mathcal { H } _ { \mathrm { m a r g i n } }$ is not very predictive of the model’s accuracy on answering questions in CoQA achieving an AUROC of 0.54.
|
| 432 |
+
|
| 433 |
+
We hypothesise that two factors contribute to this poor performance. First, since this measure only looks at the difference of likelihoods, the information about the magnitude of the likelihood of a given answer is lost. Second—analogously to the predictive entropy—it would be important to take semantic uncertainty into account when computing $\mathcal { H } _ { \mathrm { m a r g i n } }$ . Manually inspecting model answers on CoQA, and the corresponding $\mathcal { H } _ { \mathrm { m a r g i n } }$ , we see that the margin between two semantically equivalent answers and two semantically distinct answers is often similar. That is, this measure does not distinguish between uncertainty between paraphrases of the same meaning (in which case the model might actually be confident about meaning of the answer), and the model’s uncertainty about which semantically distinct meaning is correct.
|
| 434 |
+
|
| 435 |
+
We find that if instead of obtaining $\mathbf { y } ^ { ( 1 ) }$ and $\mathbf { y } ^ { ( 2 ) }$ by multinomial sampling (as in our other experiments) instead of by beam search, this second problem becomes less pronounced and $\mathcal { H } _ { \mathrm { m a r g i n } }$ performs better while still being clearly outperformed by the other methods we study. We report our full results in Fig. 6.
|
| 436 |
+
|
| 437 |
+
Table 8: Example of challenges for $\mathcal { H } _ { \mathrm { m a r g i n } }$ . $\mathcal { H } _ { \mathrm { m a r g i n } }$ does not distinguish between lexical and semantic uncertainty and thus can not distinguish cases where the model is certain about the correct answer (but uncertain about the precise formulation) as in row 1, and cases where the model is uncertain about the correct answer as in row 2. The semantic entropy correctly indicates low uncertainty in the first case and high uncertainty in the second case.
|
| 438 |
+
|
| 439 |
+
<table><tr><td>y(1)</td><td>y(2）</td><td>Hmargin</td><td>Semantic entropy</td></tr><tr><td>Thomas Edison.</td><td>Edison.</td><td>0.90</td><td>0.10</td></tr><tr><td>Thomas.</td><td>George.</td><td>0.36</td><td>0.87</td></tr></table>
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| 1 |
+
# Attracting and Dispersing: A Simple Approach for Source-free Domain Adaptation
|
| 2 |
+
|
| 3 |
+
Shiqi Yang1, Yaxing Wang2∗, Kai Wang1, Shangling $\mathbf { J u \mathbf { i } ^ { 3 } }$ , Joost van de Weijer1
|
| 4 |
+
|
| 5 |
+
1 Computer Vision Center, Universitat Autonoma de Barcelona, Barcelona, Spain 2 Nankai University, Tianjin, China 3 Huawei Kirin Solution, Shanghai, China {syang,kwang,joost}@cvc.uab.es, yaxing@nankai.edu.cn, jui.shangling@huawei.com
|
| 6 |
+
|
| 7 |
+
# Abstract
|
| 8 |
+
|
| 9 |
+
We propose a simple but effective source-free domain adaptation (SFDA) method. Treating SFDA as an unsupervised clustering problem and following the intuition that local neighbors in feature space should have more similar predictions than other features, we propose to optimize an objective of prediction consistency. This objective encourages local neighborhood features in feature space to have similar predictions while features farther away in feature space have dissimilar predictions, leading to efficient feature clustering and cluster assignment simultaneously. For efficient training, we seek to optimize an upper-bound of the objective resulting in two simple terms. Furthermore, we relate popular existing methods in domain adaptation, source-free domain adaptation and contrastive learning via the perspective of discriminability and diversity. The experimental results prove the superiority of our method, and our method can be adopted as a simple but strong baseline for future research in SFDA. Our method can be also adapted to source-free open-set and partial-set DA which further shows the generalization ability of our method. Code is available in https://github.com/Albert0147/AaD_SFDA.
|
| 10 |
+
|
| 11 |
+
# 1 Introduction
|
| 12 |
+
|
| 13 |
+
Supervised learning methods which are based on training with huge amounts of labeled data are advancing almost all fields of computer vision. However, the learned models typically perform decently on test data which have a similar distribution with the training set. Significant performance degradation will occur if directly applying those models to a new domain different from the training set, where the data distribution (such as variation of background, styles or camera parameter) is considerably different. This kind of distribution shift is formally denoted as domain/distribution shift. It limits the generalization of the model to unseen domains which is important in real-world applications. There are several research fields trying to tackle this problem. One of them is Domain Adaptation (DA), which aims to reduce the domain shift between the labeled source domain and unlabeled target domain. Typical works [12, 38] resort to learn domain-invariant features, thus improving generalization ability of the model between different domains. And in the past few years, the main research line of domain adaptation is either trying to minimize the distribution discrepancy between two domains [32, 33, 35], or deploying adversarial training on features to learn domain invariant representation [52, 68, 4, 36]. Some methods also tackle domain shift from the view of semi-supervised learning [67, 27] or clustering [7, 50, 5].
|
| 14 |
+
|
| 15 |
+
Many recent methods [24, 29, 64, 66, 55, 15, 61] focus on source-free domain adaptation (SFDA), where source data are unavailable during target adaptation, due to data privacy and intellectual property concerns of both users and businesses. Some SFDA methods resort to neighborhood clustering and pseudo labeling. However, pseudo labeling methods [29] may suffer from negative impact from noisy labels [28], and neighborhood clustering methods [66, 64] fail to investigate the potential information from dissimilar samples. Other methods either demand complex extra modules/processing [24, 61] or the storing of historical models for contrastive learning [15].
|
| 16 |
+
|
| 17 |
+
Table 1: Detailed comparison of SFDA methods on VisDA. ’ODA/PDA’ means whether the method reports the results for open-set or partial-set DA. $| { \mathcal { L } } |$ means number of training objective terms.
|
| 18 |
+
|
| 19 |
+
<table><tr><td>Method</td><td>Extra Modules/Processing</td><td>ODA/PDA</td><td>[C|</td><td>Per-class</td></tr><tr><td>SHOT[26] 3C-GAN [24]</td><td>Access all target data for pseudo labeling</td><td>×</td><td>3</td><td>82.9</td></tr><tr><td>A²Net [61]</td><td>Data generation by conditional GAN</td><td></td><td>5 5</td><td>81.6 84.3</td></tr><tr><td>G-SFDA [66]</td><td>Self-supervised learning with extra classifiers</td><td>X</td><td></td><td></td></tr><tr><td>NRC[64]</td><td>Store features for nearest neighbor retrieval</td><td>X</td><td>2</td><td>85.4</td></tr><tr><td>HCL [15]</td><td>Store features for 2-hop nearest neighbor retrieval Store historical models</td><td>X √</td><td>4 2</td><td>85.9 83.5</td></tr><tr><td>Ours</td><td></td><td>√</td><td>2</td><td>88.0</td></tr><tr><td></td><td>Store features for nearest neighbor retrieval</td><td></td><td></td><td></td></tr></table>
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| 20 |
+
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| 21 |
+
Based on the fact that target features from the source model already form some semantic structure and following the intuition that for a target feature from a (source-pretrained) model, similar features should have closer predictions than dissimilar ones, we propose a new objective dubbed as Attractingand-Dispersing (AaD) to achieve it. we upperbound this objective, resulting in a simple final objective which only contains two types of terms, which encourage discriminability and diversity respectively. Further, we unify several popular domain adaptation, source-free domain adaptation and contrastive learning methods from the perspective of discriminability and diversity. Experimental results on several benchmarks prove the superiority of our proposed method. Our simple method improves the state-of-the-art on the challenging VisDA with $2 . 1 \%$ to $8 8 . 0 \%$ . Additionally, extra experiments on open-set and partial-set DA further prove the effectiveness of our method. A preliminary comparison between different SFDA method is shown in Tab. 1, which shows the simplicity and generalization ability of our method: it only requires the storing of features and a few nearest neighbors searches without any additional module like a generator [24] or a classifier [61].
|
| 22 |
+
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| 23 |
+
We summary our contributions as follows:
|
| 24 |
+
|
| 25 |
+
• We propose to tackle source-free domain adaptation by optimizing an upperbound of the proposed clustering objective, which is surprisingly simple.
|
| 26 |
+
• We relate several popular existing methods in domain adaptation, source-free domain adaptation and contrastive learning via the perspective of discriminability and diversity, which is helpful to understand existing methods and beneficial for future improvement.
|
| 27 |
+
• The experimental results prove the efficacy of our method, especially we achieve new state-of-theart on the challenging VisDA, and the method can be also extended to source-free open-set and partial-set domain adaptation.
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| 28 |
+
|
| 29 |
+
# 2 Related Work
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| 30 |
+
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| 31 |
+
Domain Adaptation. Early DA methods such as [33, 49, 53] adopt moment matching to align feature distributions. For adversarial learning methods, DANN [9] formulates domain adaptation as an adversarial two-player game. The adversarial training of CDAN [34] is conditioned on several sources of information. DIRT-T [47] performs domain adversarial training with an added term that penalizes violations of the cluster assumption. Additionally, [22, 36, 44] adopts prediction diversity between multiple learnable classifiers to achieve local or category-level feature alignment between source and target domains. SRDC [50] proposes to directly uncover the intrinsic target discrimination via discriminative clustering to achieve adaptation. CST [31] proposes a simple self-training strategy to improve the rough pseudo label under domain shift.
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| 32 |
+
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| 33 |
+
Source-free Domain Adaptation. The above-mentioned normal domain adaptation methods need to access source domain data at all time during adaptation. In recent years plenty of methods emerge trying to tackle source-free domain adaptation. USFDA [20] and FS [21] resort to synthesize extra training samples in order to get compact decision boundaries, which is beneficial for both
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| 34 |
+
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| 35 |
+
# Algorithm 1 Attracting and Dispersing for SFDA
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| 36 |
+
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| 37 |
+
<table><tr><td colspan="2">Require: Source-pretrained model and target data Dt</td></tr><tr><td colspan="2">1:Build memory bank storing all target features and predictions</td></tr><tr><td>2: while Adaptation do</td><td></td></tr><tr><td>3:</td><td>Sample batch T from Dt and Update memory bank</td></tr><tr><td>4:</td><td>For each feature zi in T,retrieve K-nearest neighbors (Ci)and their predictions from memory bank</td></tr><tr><td>5:</td><td>Update model by minimizing Eq. 5</td></tr><tr><td colspan="2">6: end while</td></tr></table>
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| 38 |
+
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| 39 |
+
the detection of open classes and also target adaptation. SHOT [26] proposes to freeze the source classifier and it clusters target features by maximizing mutual information along with pseudo labeling for extra supervision. 3C-GAN [24] synthesizes labeled target-style training images. It is based on a conditional GAN to provide supervision for adaptation. BAIT [65] extends MCD [44] to source-free setting. $A ^ { 2 } \mathrm { { N e t } }$ [61] proposes to learn an additional target-specific classifier for hard samples and adopts a contrastive category-wise matching module to cluster target features. HCL [15] adopts Instance Discrimination [60] for features from current and historical models to cluster features, along with a generated pseudo label conditioned on historical consistency. G-SFDA [66] and NRC [64] propose neighborhood clustering which enforces prediction consistency between local neighbors.
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| 40 |
+
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| 41 |
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Deep Clustering and Contrastive Learning. Recent Deep Clustering methods can be roughly divided into two groups, they the differ in how they learn the feature representation and cluster assignments, either simultaneously or alternatively. For example, DAC [2] and DCCM [58] alternately update cluster assignments and between-sample similarity. Simultaneous clustering methods IIC [18] and ISMAT [14] are based on mutual information maximizing between samples and theirs augmentations. LA [70] depends on a huge amount of nearest neighbor searches and multiple extra runs of $k$ -means clustering to aggregate features. Recent unsupervised clustering works [25, 51, 46] start to rely on contrastive learning, where InfoNCE [37] is typically deployed. And recently NNCLR [8] proposes to use nearest neighbors in the latent space as positives in contrastive learning to cover more semantic variations than pre-defined transformations. However an inevitable problem of normal contrastive learning is class collision where negative samples are from the same class. To tackle this issue, recent works [23, 16] propose to estimate cluster prototypes and integrate them into contrastive learning.
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| 42 |
+
|
| 43 |
+
# 3 Method
|
| 44 |
+
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| 45 |
+
For source-free domain adaptation (SFDA), we are given source-pretrained model in the beginning and an unlabeled target domain with $N _ { t }$ samples as $\mathcal { D } _ { t } = \{ x _ { i } ^ { t } \} _ { i = 1 } ^ { \bar { N } _ { t } }$ . Target domain have same $C$ classes as source domain in this paper (known as the closed-set setting). The goal of SFDA is to adapt the model to target domain without source data. We divide the model into two parts: the feature extractor $f$ , and the classifier $g$ . The output of the feature extractor is denoted as feature $( z _ { i } = f \left( x \right) \in \mathbb { R } ^ { \bar { h } } )$ , where $h$ is dimension of the feature space. The output of classifier is denoted as $( p _ { i } = \delta ( g ( z _ { i } ) ) \in \mathbb { R } ^ { C }$ ) where $\delta$ is the softmax function. We denote $\boldsymbol { P } \in \mathbb { R } ^ { b s \times C }$ as the prediction matrix in a mini-batch. Regarding the SFDA as an unsupervised clustering problem, we address SFDA problem by clustering target features based on the proposed AaD. In additionally, we relate our method with several existing DA, SFDA and contrastive learning methods.
|
| 46 |
+
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| 47 |
+
# 3.1 Attracting and Dispersing for Source-free Domain Adaptation
|
| 48 |
+
|
| 49 |
+
Since the source-pretrained model already learns a good feature representation, it can provides a decent initialization for target adaptation. We propose to achieve SFDA by attracting predictions for features that are located close in feature space, while dispersing predictions of those features farther away in feature space.
|
| 50 |
+
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| 51 |
+
We define $p _ { i j }$ as the probability that the feature $z _ { i } \in \mathbb { R } ^ { h }$ has similar (or the same) prediction to feature $\begin{array} { r } { z _ { j } \colon p _ { i j } = \frac { e ^ { p _ { i } ^ { T } p _ { j } } } { \sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { t } p _ { k } } } } \end{array}$ It can be interpreted as the possibility that $p _ { j }$ is selected as the neighbor of $p _ { i }$ in the output space [10].
|
| 52 |
+
|
| 53 |
+
We then define two sets for each feature $z _ { i }$ : close neighbor set $\mathcal { C } _ { i }$ containing $K$ -nearest neighbors of $z _ { i }$ (with distances as cosine similarity), and background set $B _ { i }$ which contains the features that are not in $\mathcal { C } _ { i }$ (features potentially from different classes). To retrieve nearest neighbors for training, we build two memory banks to store all target features along with their predictions just like former works [27, 66, 64, 42], which is efficient in both memory and computation, since only the features along with their predictions computed in each mini-batch are used to update the memory bank.
|
| 54 |
+
|
| 55 |
+
Intuitively, for each feature $z _ { i }$ , the features in $B _ { i }$ should have less similar predictions than those in $ { { \mathcal { C } } } _ { i } { } ^ { 2 }$ . To achieve this, we first define two likelihood functions:
|
| 56 |
+
|
| 57 |
+
$$
|
| 58 |
+
P ( \mathcal C _ { i } | \boldsymbol \theta ) = \prod _ { j \in \mathcal C _ { i } } p _ { i j } = \prod _ { j \in \mathcal C _ { i } } \frac { e ^ { p _ { i } ^ { T } p _ { j } } } { \sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } } , P ( \mathcal B _ { i } | \boldsymbol \theta ) = \prod _ { j \in \mathcal B _ { i } } p _ { i j } = \prod _ { j \in \mathcal B _ { i } } \frac { e ^ { p _ { i } ^ { T } p _ { j } } } { \sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } }
|
| 59 |
+
$$
|
| 60 |
+
|
| 61 |
+
where $\theta$ denotes parameters of the model, for readability we omit $\theta$ in following equations. The probability $p _ { j }$ in Eq. 1 is the stored prediction for neighborhood feature $z _ { j }$ , which is retrieved from the memory bank.
|
| 62 |
+
|
| 63 |
+
We then propose to achieve target features clustering by minimizing the following negative loglikelihood, denoted as $A a D$ (Attracting-and-Dispersing):
|
| 64 |
+
|
| 65 |
+
$$
|
| 66 |
+
\tilde { L } _ { i } ( \mathcal { C } _ { i } , \mathcal { B } _ { i } ) = - \log \frac { P ( \mathcal { C } _ { i } ) } { P ( \mathcal { B } _ { i } ) }
|
| 67 |
+
$$
|
| 68 |
+
|
| 69 |
+
Noting that, if we only have $P ( \mathcal { C } _ { i } )$ , it will be similar to Instance Discrimination [60], but we also consider $P ( B _ { i } )$ and we operate on predictions instead of features. If regarding weights of the classifier $g$ as classes prototypes, optimizing Eq. 2 is not only pulling features towards their closest neighbors and pushing them away from background features, but also towards (or away from) corresponding class prototypes. Therefore, we can achieve feature clustering and cluster assignment simultaneously.
|
| 70 |
+
|
| 71 |
+
To simplify the training, instead of manually and carefully sampling background features, we use all other features except $z _ { i }$ in the mini-batch as $B _ { i }$ , which can be regarded as an estimation of the distribution of the whole dataset. We can reasonably believe that overall similarity of features in $\mathcal { C } _ { i }$ is potentially higher than that of $B _ { i }$ , even if $B _ { i }$ has intersection with $\mathcal { C } _ { i }$ since features in $\mathcal { C } _ { i }$ are the closest ones to feature $z _ { i }$ . By optimizing Eq. 2, we are encouraging features in $\mathcal { C } _ { i }$ , which have a higher chance of belonging to the same class, to have more similar predictions to $z _ { i }$ than those features in $B _ { i }$ , which have a lower chance of belonging to the same class. Note all features will show up in both the first and second term; intra-cluster alignment and inter-cluster separability are expected to be achieved after training.
|
| 72 |
+
|
| 73 |
+
One problem optimizing Eq. 2 is that all target data are needed to compute Eq. 1, which is infeasible in real-world situation. Here we resort to get an upper-bound of Eq. 2:
|
| 74 |
+
|
| 75 |
+
$$
|
| 76 |
+
\begin{array} { l } { \tilde { L } _ { i } ( \mathcal { C } _ { i } , \mathcal { B } _ { i } ) = - \log \displaystyle \frac { P ( \mathcal { C } _ { i } ) } { P ( \mathcal { B } _ { i } ) } = - \sum _ { j \in \mathcal { C } _ { i } } [ p _ { i } ^ { T } p _ { j } - \log ( \displaystyle \sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } ) ] + \sum _ { m \in \mathcal { B } _ { i } } [ p _ { i } ^ { T } p _ { m } - \log ( \displaystyle \sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } ) ] } \\ { \displaystyle = - \sum _ { j \in \mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \sum _ { m \in \mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } + ( N _ { \mathcal { C } _ { i } } - N _ { \mathcal { B } _ { i } } ) \log ( \displaystyle \sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } ) } \end{array}
|
| 77 |
+
$$
|
| 78 |
+
|
| 79 |
+
Since we set $N _ { \mathcal { C } _ { i } } < N _ { B _ { i } }$ , with Jensen’s inequality:
|
| 80 |
+
|
| 81 |
+
$$
|
| 82 |
+
\begin{array} { r l } & { \tilde { L } _ { i } ( \mathcal { C } _ { i } , \mathcal { B } _ { i } ) \leq - \displaystyle \sum _ { j \in \mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \displaystyle \sum _ { m \in \mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } + ( N _ { \mathcal { C } _ { i } } - N _ { \mathcal { B } _ { i } } ) ( \displaystyle \sum _ { k = 1 } ^ { N _ { t } } \frac { 1 } { N _ { t } } p _ { i } ^ { T } p _ { k } + \log N _ { t } ) } \\ & { \qquad \quad \simeq \displaystyle \sum _ { m \in \mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } - \displaystyle \sum _ { j \in \mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + ( N _ { \mathcal { C } _ { i } } - N _ { \mathcal { B } _ { i } } ) ( \displaystyle \sum _ { k \in \mathcal { B } _ { i } } \frac { p _ { i } ^ { T } p _ { k } } { N _ { \mathcal { B } _ { i } } } + \log N _ { t } ) } \\ & { \qquad \quad = - \displaystyle \sum _ { j \in \mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \displaystyle \frac { N _ { \mathcal { C } _ { i } } } { N _ { \mathcal { B } _ { i } } } \displaystyle \sum _ { m \in \mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } + ( N _ { \mathcal { C } _ { i } } - N _ { \mathcal { B } _ { i } } ) \log N _ { t } } \end{array}
|
| 83 |
+
$$
|
| 84 |
+
|
| 85 |
+
Table 2: Decomposition of methods into two terms: discriminability $( d i s )$ and diversity $( d i \nu )$ , which will be minimized for training.
|
| 86 |
+
|
| 87 |
+
<table><tr><td>Method</td><td>Task</td><td>disterm</td><td>div term</td></tr><tr><td>MI</td><td>SFDA&Clustering</td><td>H(Y|X)</td><td>-H(Y)</td></tr><tr><td>BNM</td><td>DA&SFDA</td><td>-|PIlF</td><td>-rank(P)</td></tr><tr><td>NC</td><td>SFDA</td><td>-g(WijpTpj)</td><td>∑KL(llge)）</td></tr><tr><td>InfoNCE</td><td>Contrastive</td><td>-f(x)Tf(y)/T</td><td>log（+∑ef（x）f（x）/T）</td></tr><tr><td>Ours</td><td>SFDA</td><td>-∑jecppj</td><td>∑meB:pTPm</td></tr></table>
|
| 88 |
+
|
| 89 |
+
where $N _ { { \mathcal { C } } _ { i } }$ and $N _ { B _ { i } }$ is the number of features in $\mathcal { C } _ { i }$ and $B _ { i }$ . Note that we cannot get this upper-bound without $\dot { P ( B _ { i } ) }$ . The approximation above in the penultimate line is to estimate the average dot product using the mini-batch data. This leads to the surprisingly simple final objective for unsupervised domain adaptation:
|
| 90 |
+
|
| 91 |
+
$$
|
| 92 |
+
L = \mathbb { E } [ L _ { i } ( \mathcal { C } _ { i } , \mathcal { B } _ { i } ) ] , \mathrm { w i t h ~ } L _ { i } ( \mathcal { C } _ { i } , \mathcal { B } _ { i } ) = - \sum _ { j \in \mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \lambda \sum _ { m \in \mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m }
|
| 93 |
+
$$
|
| 94 |
+
|
| 95 |
+
Note the gradient will come from both $p _ { i }$ and $p _ { m }$ . The first term aims to enforce prediction consistency between local neighbors, and the naive interpretation of second term is to disperse the prediction of potential dissimilar features, which are all other features in the mini-batch. Note that the dot product between two softmaxed predictions will be maximal when two predictions have the same predicted class and are close to one-hot vector. Our algorithm is illustrated in Algorithm. 1.
|
| 96 |
+
|
| 97 |
+
Unlike using a constant for the second term in Eq. 4 we empirically found that using a hyperparameter $\lambda$ to decay second term (starting from 1) works better, we will adopt SND [43] to tune this hyperparameter unsupervisedly. One reason may be that the approximation inside Eq. 3.1 is not necessarily accurate. And as training goes on, features are gradually clustering, the role of the second term for dispersing should be weakened. Additionally, considering the current mini-batch with the correctly predicted features $z _ { i }$ and $z _ { m }$ belonging to the same class. In this case the second term in both $L _ { i } ( \mathcal { C } _ { i } , B _ { i } )$ and $L _ { m } ( \mathcal { C } _ { m } , B _ { m } )$ tends to push $p _ { m }$ to the wrong direction, while the first term in $L _ { m } ( \mathcal { C } _ { m } , B _ { m } )$ can potentially keep current (correct) prediction unchanged. Hence, this will suppress the negative impact of the second term. We will further deepen the understanding of these two terms in the next subsection.
|
| 98 |
+
|
| 99 |
+
# 3.2 Relation to Existing Works
|
| 100 |
+
|
| 101 |
+
In this section, we will relate several popular DA, SFDA and contrastive learning methods through two objectives, discriminability and diversity. This can improve our understanding of domain adaptation methods, as well as improve the understanding of our method.
|
| 102 |
+
|
| 103 |
+
Mutual Information maximizing (MI). SHOT-IM [26] proposes to achieve source-free domain adaptation by maximizing the mutual information, which is actually widely used in unsupervised clustering [11, 40, 14]:
|
| 104 |
+
|
| 105 |
+
$$
|
| 106 |
+
{ \cal L } _ { M I } = H ( Y | X ) - H ( Y )
|
| 107 |
+
$$
|
| 108 |
+
|
| 109 |
+
which contains two terms: conditional entropy term $H ( Y | X )$ to encourages unambiguous cluster assignments, and marginal entropy term $H ( Y )$ to encourage cluster sizes to be uniform to avoid degeneracy. In practice, $H ( Y )$ is approximated by the current mini-batch instead of using whole dataset [48, 14].
|
| 110 |
+
|
| 111 |
+
Batch Nuclear-norm Maximization (BNM). BNM [5, 6] aims to increase prediction discriminability and diversity to tackle domain shift. It is originally achieved by maximizing $F$ -norm (for discriminability) and rank of prediction matrix (for diversity) respectively:
|
| 112 |
+
|
| 113 |
+
$$
|
| 114 |
+
L = - \| P \| _ { F } - r a n k ( P )
|
| 115 |
+
$$
|
| 116 |
+
|
| 117 |
+
In their paper, they further prove merely maximizing the nuclear norm $\| P \| _ { * }$ can achieve these two goals simultaneously. In relation to our method, if target features are well clustering during training, we can presume the K-nearest neighbors of feature $z _ { i }$ have the same prediction, the first term in Eq. 5 can be seen as the summation of diagonal elements of matrix $P P ^ { T }$ , which is actually the square of $F$ -norm $( \| P \| _ { F } = { \sqrt { t r a c e ( P P ^ { T } ) } } )$ , then it is actually minimizing prediction entropy [5]. As for second term, we can regard it as the summation of non-diagonal element of $P P ^ { T }$ , it encourages all these non-diagonal elements to be 0 thus the $r a n k ( P P ^ { T } ) = r a n k ( P )$ is supposed to increase, which indicates larger prediction diversity [5]. In a nutshell, compared to SHOT and BNM our method first considers local feature structure to cluster target features, which can be treated as an alternative way to increase discriminability at the late training stage, meanwhile as discussed above our method is also encouraging diversity.
|
| 118 |
+
|
| 119 |
+
Neighborhood Clustering (NC). G-SFDA [66] and NRC [64] are based on neighborhood clustering to tackle SFDA problem. Those works basically contain two major terms in their optimizing objective: a neighborhood clustering term for prediction consistency and a marginal entropy term $H ( Y )$ for prediction diversity. NRC [64] further introduces neighborhood reciprocity to weight the different neighbors. Their loss objective can be written as:
|
| 120 |
+
|
| 121 |
+
$$
|
| 122 |
+
L _ { i } = - \sum _ { j \in \mathcal { C } _ { i } } g ( W _ { i j } p _ { i } ^ { T } p _ { j } ) + \sum _ { c = 1 } ^ { C } \mathbf { K L } ( \bar { p } _ { c } | | q _ { c } ) , \mathrm { ~ w i t h ~ } \bar { p } _ { c } = \frac { 1 } { n _ { t } } \sum _ { i } p _ { i } ^ { ( c ) } , \mathrm { ~ a n d ~ } q _ { \{ c = 1 , . . . , C \} } = \frac { 1 } { C }
|
| 123 |
+
$$
|
| 124 |
+
|
| 125 |
+
where $W _ { i j }$ will weight the importance of neighbor and $g ( \cdot )$ is log or identity function. Although the first term of G-SFDA and NRC is the same as that of our final loss objective Eq. 5, note that our motivation is different as we simultaneously consider similar and dissimilar features, and Eq. 5 is deduced as an approximated upper-bound of our original objective Eq. 2.
|
| 126 |
+
|
| 127 |
+
And note actually the marginal entropy termAlthough the second term of those metho $\begin{array} { r } { - H ( Y ) = \sum _ { c = 1 } ^ { C } \bar { p } _ { c } \log \bar { p } _ { c } = \sum _ { c = 1 } ^ { C } { \bf K } { \bf L } \left( \bar { p } _ { c } | | q _ { c } \right) - \log C . } \end{array}$ solution where all images are only assigned to some certain classes, the margin entropy term presumes the prior that whole dataset or the mini-batch is class balance/uniformly distributed, which is barely true for current benchmarks or in real-world environment. In conclusion, the above three types of methods are actually all to increase discriminability and meanwhile maximize diversity of the prediction, but through different ways.
|
| 128 |
+
|
| 129 |
+
Contrastive Learning. Here we also link our method to InfoNCE [37]), which is widely used in contrastive learning. As a recent paper [56] points out that InfoNCE loss can be decomposed into 2 terms:
|
| 130 |
+
|
| 131 |
+
$$
|
| 132 |
+
\chi _ { i n f o N C E } = \mathbb { E } _ { ( x , y ) \sim p _ { p o s } } [ - f ( x ) ^ { T } f ( y ) / \tau ] \ + \underset { x \sim p _ { d a t a } } { \mathbb { E } } ~ \underset { \substack { i = 1 \sim { p _ { d a t a } } \ \{ x _ { i } ^ { - } \} _ { i = 1 } ^ { M } \sim p _ { d a t a } } } [ \log ( e ^ { 1 / \tau } + \sum _ { i } e ^ { f ( x _ { i } ^ { - } ) ^ { T } f ( x ) / \tau } ) ]
|
| 133 |
+
$$
|
| 134 |
+
|
| 135 |
+
The first term is denoted as alignment term (with positive pairs) is to make positive pairs of features similar, and the second term denoted as uniformity term with negative pairs encouraging all features to roughly uniformly distributed in the feature space.
|
| 136 |
+
|
| 137 |
+
The Eq. 8 shares some similarity with all the above domain adaptation methods in that the first term is for the alignment with positive pairs and the second term is to encourage diversity. But note that the remarkable difference is that the above domain adaptation methods operate in the output (prediction) space while contrastive learning is conducted in the (spherical) feature space. Therefore, simultaneously feature representation learning and cluster assignment can be achieved for those domain adaptation methods. Note in normal contrastive learning methods, extra KNN or a linear learnable classifier needs to be deployed for final classification, while our model can directly give predictions.
|
| 138 |
+
|
| 139 |
+
We list all above methods in Tab. 2. Finally, returning to Eq. 5, we can also regard the second term as a variant of diversity loss to avoid degeneration solution, but without making any category prior assumption. Intuitively, with target features forming groups during training, the second term should play less and less important role, otherwise it may destabilize the training. This is similar to the class collision issue in contrastive learning. If our second term contains too many features belonging to the same class. Thus it is reasonable to decay the second term.
|
| 140 |
+
|
| 141 |
+
# 4 Experiments
|
| 142 |
+
|
| 143 |
+
Datasets. We conduct experiments on three benchmark datasets for image classification: Office-31, Office-Home and VisDA-C 2017. Office-31 [41] contains 3 domains (Amazon, Webcam, DSLR)
|
| 144 |
+
|
| 145 |
+
Table 3: Accuracies $( \% )$ on Office-Home for ResNet50-based methods. We highlight the best result and underline the second best one.
|
| 146 |
+
|
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<table><tr><td>Method</td><td></td><td>SFAr→CIAr-→PrAr-→RwCl-→ArCl-→PrCl-→RwPr-→ArPr->CIPr-→RwRw→ArRw→CIRw→PrAvg</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ResNet-50[13]</td><td></td><td>X 34.9</td><td>50.0</td><td>58.0</td><td>37.4</td><td>41.9</td><td>46.2</td><td>38.5</td><td>31.2</td><td>60.4</td><td>53.9</td><td>41.2 59.9</td><td>46.1</td></tr><tr><td>MCD [44]</td><td></td><td>xxx 48.9</td><td>68.3</td><td>74.6</td><td>61.3</td><td>67.6</td><td>68.8</td><td>57.0</td><td>47.1</td><td>75.1</td><td>69.1</td><td>52.2 79.6</td><td>64.1</td></tr><tr><td>CDAN[34]</td><td></td><td>50.7</td><td>70.6</td><td>76.0</td><td>57.6</td><td>70.0</td><td>70.0</td><td>57.4</td><td>50.9</td><td>77.3 70.9</td><td>56.7</td><td>81.6</td><td>65.8</td></tr><tr><td>SAFN[63]</td><td></td><td>52.0</td><td>71.7</td><td>76.3</td><td>64.2</td><td>69.9</td><td>71.9</td><td>63.7</td><td>51.4</td><td>77.1 70.9</td><td>57.1</td><td>81.5</td><td>67.3</td></tr><tr><td>MDD [69]</td><td></td><td>X 54.9</td><td>73.7</td><td>77.8</td><td>60.0</td><td>71.4</td><td>71.8</td><td>61.2</td><td>53.6</td><td>78.1 72.5</td><td>60.2</td><td>82.3</td><td>68.1</td></tr><tr><td>TADA [57]</td><td></td><td>×x 53.1</td><td>72.3</td><td>77.2</td><td>59.1</td><td>71.2</td><td>72.1</td><td>59.7</td><td>53.1</td><td>78.4</td><td>72.4</td><td>60.0 82.9</td><td>67.6</td></tr><tr><td>SRDC [50]</td><td></td><td>52.3</td><td>76.3</td><td>81.0</td><td>69.5</td><td>76.2</td><td>78.0</td><td>68.7</td><td>53.8</td><td>81.7</td><td>76.3</td><td>57.1 85.0</td><td>71.3</td></tr><tr><td>SHOT[26]</td><td></td><td>√ 57.1</td><td>78.1</td><td>81.5</td><td>68.0</td><td>78.2</td><td>78.1</td><td>67.4</td><td>54.9</td><td>82.2</td><td>73.3 58.8</td><td>84.3</td><td>71.8</td></tr><tr><td>A²Net [61]</td><td></td><td>58.4</td><td>79.0</td><td>82.4</td><td>67.5</td><td>79.3</td><td>78.9</td><td>68.0</td><td>56.2</td><td>82.9 74.1</td><td>60.5</td><td>85.0</td><td>72.8</td></tr><tr><td>G-SFDA [66]</td><td></td><td>√ 57.9</td><td>78.6</td><td>81.0</td><td>66.7</td><td>77.2</td><td>77.2</td><td>65.6</td><td>56.0</td><td>82.2</td><td>72.0</td><td>57.8 83.4</td><td>71.3</td></tr><tr><td>NRC [64]</td><td></td><td>√ 57.7</td><td>80.3</td><td>82.0</td><td>68.1</td><td>79.8</td><td>78.6</td><td>65.3</td><td>56.4</td><td>83.0</td><td>71.0</td><td>58.6 85.6</td><td>72.2</td></tr><tr><td>BNM-S [6]</td><td></td><td>√ 57.4</td><td>77.8</td><td>81.7</td><td>67.8</td><td>77.6</td><td>79.3</td><td>67.6</td><td>55.7</td><td>82.2</td><td>73.5</td><td>59.5 84.7</td><td>72.1</td></tr><tr><td>Ours</td><td></td><td>59.3</td><td>79.3</td><td>82.1</td><td>68.9</td><td>79.8</td><td>79.5</td><td>67.2</td><td>57.4</td><td>83.1</td><td>72.1</td><td>58.5 85.4</td><td>72.7</td></tr></table>
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Table 4: Accuracies $( \% )$ on VisDA-C (Synthesis $ \mathrm { R e a l }$ ) for ResNet101-based methods. We highlight the best result and underline the second best one.
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<table><tr><td>Method</td><td>[SF</td><td>plane</td><td>bcycl bus</td><td>car</td><td>horse</td><td>knifemcycl</td><td></td><td>person</td><td></td><td></td><td></td><td>plant sktbrd train truck Per-class</td></tr><tr><td>ResNet-101[13]</td><td></td><td>55.1</td><td>53.3 61.9</td><td>59.1</td><td>80.6</td><td>17.9</td><td>79.7 31.2</td><td>81.0</td><td>26.5</td><td>73.5</td><td>8.5</td><td>52.4</td></tr><tr><td>CDAN+BSP[3]</td><td></td><td>92.4</td><td>61.0</td><td>81.0 57.5</td><td>89.0</td><td>80.6</td><td>90.1</td><td>77.0 84.2</td><td>77.9</td><td>82.1</td><td>38.4</td><td>75.9</td></tr><tr><td>MCC[19]</td><td></td><td>88.7</td><td>80.3</td><td>80.5 71.5</td><td>90.1</td><td>93.2</td><td>85.0</td><td>71.6 89.4</td><td>73.8</td><td>85.0</td><td>36.9</td><td>78.8</td></tr><tr><td>STAR[36]</td><td></td><td>95.0</td><td>84.0</td><td>84.6 73.0</td><td>91.6</td><td>91.8</td><td>85.9 78.4</td><td>94.4</td><td>84.7</td><td>87.0</td><td>42.2</td><td>82.7</td></tr><tr><td>RWOT[62]</td><td>xxxxx</td><td>95.1 80.3</td><td>83.7</td><td>90.0</td><td>92.4</td><td>68.0</td><td>92.5 82.2</td><td>87.9</td><td>78.4</td><td>90.4</td><td>68.2</td><td>84.0</td></tr><tr><td>3C-GAN [24]</td><td></td><td>94.8 73.4</td><td>68.8</td><td>74.8</td><td>93.1</td><td>95.4</td><td>88.6 84.7</td><td>89.1</td><td>84.7</td><td>83.5</td><td>48.1</td><td>81.6</td></tr><tr><td>SHOT[26]</td><td>v√</td><td>94.3 88.5</td><td></td><td>80.1 57.3</td><td>93.1</td><td>94.9</td><td>80.7</td><td>80.3 91.5</td><td>89.1</td><td>86.3</td><td>58.2</td><td>82.9</td></tr><tr><td>A²Net [61]</td><td></td><td>94.0 87.8</td><td>85.6</td><td>66.8</td><td>93.7</td><td>95.1</td><td>85.8</td><td>81.2 91.6</td><td>88.2</td><td>86.5</td><td>56.0</td><td>84.3</td></tr><tr><td>G-SFDA [66]</td><td></td><td>96.1 88.3</td><td>85.5</td><td>74.1</td><td>97.1</td><td>95.4</td><td>89.5</td><td>79.4 95.4</td><td>92.9</td><td>89.1</td><td>42.6</td><td>85.4</td></tr><tr><td>NRC [64]</td><td></td><td>96.8 91.3</td><td>82.4</td><td>62.4</td><td>96.2</td><td>95.9</td><td>86.1</td><td>80.6 94.8</td><td>94.1</td><td>90.4</td><td>59.7</td><td>85.9</td></tr><tr><td>HCL [15]</td><td>vvv√</td><td>93.3</td><td>85.4</td><td>80.7 68.5</td><td>91.0</td><td>88.1</td><td>86.0</td><td>78.6 86.6</td><td>88.8</td><td>80.0</td><td>74.7</td><td>83.5</td></tr><tr><td>Ours</td><td>√</td><td>97.4</td><td>90.5</td><td>80.8 76.2</td><td>97.3</td><td>96.1</td><td>89.8</td><td>82.9 95.5</td><td>93.0</td><td>92.0</td><td>64.7</td><td>88.0</td></tr></table>
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with 31 classes and 4,652 images. Office-Home [54] contains 4 domains (Real, Clipart, Art, Product) with 65 classes and a total of 15,500 images. VisDA (VisDA-C 2017) [39] is a more challenging dataset, with 12-class synthetic-to-real object recognition tasks, its source domain contains of 152k synthetic images while the target domain has $5 5 \mathrm { k }$ real object images.
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Evaluation. The column SF in the tables denotes source-free. For Office-31 and Office-Home, we show the results of each task and the average accuracy over all tasks ${ \it A } \nu g$ in the tables). For VisDA, we show accuracy for all classes and average over those classes (Per-class in the table). All results are the average of three random runs for target adaptation.
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Model details. To ensure fair comparison with related methods, we adopt the backbone of a ResNet-50 [13] for Office-Home and ResNet-101 for VisDA. Specifically, we use the same network architecture as SHOT [26], BNM-S [6], G-SFDA [66] and NRC [64], i.e., the final part of the network is: fully connected layer - Batch Normalization $I I 7 J$ - fully connected layer with weight normalization $I 4 5 J$ . We adopt SGD with momentum 0.9 and batch size of 64 for all datasets. The learning rate for Office-31 and Office-Home is set to 1e-3 for all layers, except for the last two newly added fc layers, where we apply 1e-2. Learning rates are set 10 times smaller for VisDA. We train 40 epochs for Office-31 and Office-Home while 15 epochs for VisDA.
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There are two hyperparameters $N _ { { \mathcal { C } } _ { i } }$ (number of nearest neighbors) and $\lambda$ , to ensure fair comparison we set $N _ { { \mathcal { C } } _ { i } }$ to the same number as previous works G-SFDA [66] and NRC [64], which also resort to nearest neighbors. That is, we set $N _ { { \mathcal { C } } _ { i } }$ to 3 on Office-31 and Office-Home, 5 on VisDA. For $\lambda$ , we set it as $\begin{array} { r } { \lambda = ( 1 + 1 0 * \frac { i t e r } { m a x \_ i t e r } ) ^ { - \beta } } \end{array}$ , where the decay factor $\beta$ controls the decaying speed. We directly apply SND $I 4 3 J$ to select $\beta$ unsupervisedly. Based on SND we set $\beta$ to 0 on Office-Home, 2 on Office-31 and 5 on VisDA.
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# 4.1 Results and Analysis
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Quantitative Results. As shown in Tables $3 { - } 5 ( L e f t )$ , where the top part shows results for the source-present methods that use source data during adaptation, and the bottom part shows results for the source-free DA methods. On Office-31 and VisDA, our method gets state-of-the-art performance compared to existing source-free domain adaptation methods, especially on VisDA our method outperforms others by a large margin $2 . 1 \%$ compared to NRC). And our method achieves similar results on Office-Home compared to the more complex $A ^ { \mathrm { 2 } } \mathrm { N e t }$ method (which combines three classifiers and five objective functions). The reported results clearly demonstrate the efficiency of the proposed method for source-free domain adaptation. It also achieves similar or better results compared to domain adaptation methods with access to source data on both Office-Home and VisDA. Note the extension of SHOT called $\mathrm { S H O T + + }$ [30] deploys extra self-supervised training and semisupervised learning, which are general to improve the results (an evidence is that the source model after these 2 tricks gets huge improvement, e.g., $6 0 . 2 \%$ improves to $6 6 . 6 \%$ on Office-Home.), we do not list it here for fair comparison.
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Table 5: (Left) Accuracies $( \% )$ on Office-31 for ResNet50-based methods. We highlight the best result and underline the second best one. (Right) Ablation study on number of nearest neighbors $N _ { { \mathcal { C } } _ { i } }$ . We highlight the best score and underline the second best one.
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<table><tr><td>Method</td><td></td><td colspan="3">JSFA→DA→WD-→WW-→DD-→AW→AAvg</td></tr><tr><td>MCD [44] CDAN [34] MDD[69]] DMRL[59] MCC[19]</td><td>X .xxxxx</td><td>92.2 88.6 92.9 94.1 90.4 90.4 93.4 90.8 95.6 95.4</td><td>98.5 98.6 100.0 98.7 99.9 99.0 100.0 98.6 100.0</td><td>100.0 69.5 69.7 86.5 71.0 75.0 73.0 71.2 72.6</td><td>69.3 87.7 73.7 88.0 87.9</td></tr><tr><td>SRDC [50] SHOT[26] 3C-GAN [24] NRC[64] HCL [15] BNM-S [6]</td><td></td><td>95.8 95.7 94.0 90.1 92.7 93.7 96.0 90.8 94.7 92.5 93.0 92.9</td><td>99.2 98.4 98.5 99.0 98.2 98.2</td><td>100.0 76.7 77.1 99.9 74.7 74.3 99.8 75.3 77.8 100.0 75.3 75.0 100.0 75.9 77.7 99.9 75.4 75.0</td><td>73.9 89.4 90.8 88.6 89.6 89.4 89.8 89.1</td></tr></table>
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<table><tr><td>Nc</td><td>Avg</td><td colspan="2"></td></tr><tr><td>Office-31</td><td></td><td>Nc</td><td>Per-class</td></tr><tr><td>1</td><td>89.1</td><td>VisDA</td><td></td></tr><tr><td>2</td><td>89.5</td><td>3</td><td>86.7</td></tr><tr><td>3</td><td>89.9</td><td>4</td><td>87.4</td></tr><tr><td>Office-Home</td><td></td><td>5</td><td>88.0</td></tr><tr><td>1</td><td>72.2</td><td>6</td><td>88.0</td></tr><tr><td>2</td><td>72.6</td><td>7</td><td>88.0</td></tr><tr><td>3</td><td>72.7</td><td></td><td></td></tr></table>
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Figure 1: Visualization of decision boundary on target data with different training objective.
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Toy dataset. We carry out an experiment on the twinning moona dataset to ablate the influence of two terms in our objective Eq. 5. For the twinning moons dataset, the data from the source domain are represented by two inter-twinning moons, which contain 300 samples each. Data in the target domain are generated through rotating source data by $3 0 ^ { \circ }$ . The domain shift here is instantiated as the rotation degree. First we train the model with 3 linear layers only on the source domain, and test the model on all domains. As shown in the first image in Fig. 1, the source model performs badly on target data. Then we conduct several variants of our method to train the model. The visualization of the decision boundary in Fig. 1 indicates that both terms in Eq. 5 are necessary, and decay of second term is shown to be important.
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Table 6: Unsupervised hyperparameter selection of $\beta$ with SND [43], larger SND should correspond to better target model.
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<table><tr><td colspan="2">VisDA</td></tr><tr><td>β</td><td>SND个 Per-class</td></tr><tr><td>0 1</td><td>8.1823 77.5 8.2584 83.8</td></tr><tr><td>2 8.3214</td><td>86.7</td></tr><tr><td>3 8.3311</td><td>87.6</td></tr><tr><td>4</td><td>8.3540 88.0</td></tr><tr><td>5 8.3543</td><td>88.0</td></tr><tr><td>7 8.3530</td><td>88.1</td></tr></table>
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<table><tr><td colspan="2">Office-31</td></tr><tr><td>β</td><td>SND↑ Avg</td></tr><tr><td>0</td><td>4.1366 88.0</td></tr><tr><td>0.25 4.3016</td><td>89.7</td></tr><tr><td>1 4.4494</td><td>89.9</td></tr><tr><td>2 4.4501</td><td>89.9</td></tr></table>
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<table><tr><td colspan="2">Office-Home</td></tr><tr><td>β</td><td>SND个 Avg</td></tr><tr><td>0</td><td>3.7515 72.7</td></tr><tr><td>0.25</td><td>3.7402 72.6</td></tr><tr><td>0.5 3.7252</td><td>72.0</td></tr><tr><td>1 3.6923</td><td>70.6</td></tr></table>
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Figure 2: (Left) Ratio of features which have 3 nearest neighbor features sharing the same predicted label. (Right) Ratio among above features which have 3 nearest neighbor features sharing the same and correct predicted label.
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Table 7: Runtime analysis on SHOT and our method. For SHOT, pseudo labels are computed at each epoch. $10 \%$ and $5 \%$ denote the percentage of target features which are stored in the memory bank.
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<table><tr><td>VisDA</td><td>Runtime (s/epoch)Per-class (%)</td><td></td></tr><tr><td>SHOT</td><td>618.82</td><td>82.9</td></tr><tr><td>Ours</td><td>520.13</td><td>88.0</td></tr><tr><td>Ours(10% for memory bank)</td><td>490.21</td><td>87.6</td></tr><tr><td>Ours(5% for memory bank)</td><td>482.77</td><td>87.5</td></tr></table>
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Number of nearest neighbors $( N _ { C _ { i } } )$ . For the number of nearest neighbors used for the first term in Eq. 5, we show in Tab. 5 $( R i g h t )$ our method is robust to the choice of $N _ { { \mathcal { C } } _ { i } }$ , as the results imply that a reasonable choice of $N _ { { \mathcal { C } } _ { i } }$ (such as 3) works quite well on all datasets, since only considering few neighbors (such as $1 / 2$ ) may be too noisy if all of them are misclassified, while setting $N _ { { \mathcal { C } } _ { i } }$ too larger may also potentially include samples of other categories. For larger dataset such as VisDA we can choose a relatively larger $N _ { { \mathcal { C } } _ { i } }$ . Note the reason why we choose $N _ { { \mathcal { C } } _ { i } }$ as 5 in main experiments is to compare fairly with G-SFDA [66] and NRC [64].
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Decay factor $\beta$ . According to the analysis in Sec. 3.2, the second term acts like a diversity term to avoid that all target features collapse to a limited set of categories. The role of the second term should be weakened during the training, but how to decay the second term is non-trivial. We directly adopt SND [43] which computes Soft Neighborhood Density for unsupervised hyperparameter selection of $\beta$ . The method is unsupervised and larger SND predicts a better target models. The results of $S N D$ with different $\beta$ are shown in Tab. 6, the results prove that SND works well to choose optimal $\beta$ .
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Runtime analysis. Instead of storing all features in the memory bank, we can only stores a limited number of target features, by updating the memory bank at the end of each iteration by taking the $n$ (batch size) embeddings from the current training iteration and concatenating them at the end of the memory bank, and discard the oldest $n$ elements from the memory bank. We report the results with this type of memory bank of different buffer size in the Table 7. The results show that indeed this could be an efficient way to reduce computation on very large datasets.
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Degree of clustering during training. We also plot how features are clustered with different decaying factors $\beta$ on VisDA in Fig. 2. The left one shows the ratio of features which have 3-nearest neighbors all sharing the same prediction, which indicates the degree of clustering during training, and the right one shows the ratio among above features which have 3-nearest neighbor features sharing the same and correct predicted label. Those curves in Fig. 2 left show that the target features are clustering, and those in Fig. 2 right indicate that clear category boundaries are emerging. The numbers in the legends denote the deployed $\beta$ and the corresponding final accuracy. From the figures we can draw the conclusion that with a larger decay factor $\beta$ on VisDA, features are quickly clustering and forming inter-class boundaries, since the ratio of features which share the same and correct prediction with neighbors are increasing faster. When decaying factor $\beta$ is too small, meaning training signal from the second term is strong, the clustering process is actually impeded. The curves in Fig. 2 (left) signify that this ratio can also be used to choose $\beta$ with higher performance unsupervisedly.
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Table 8: Accuracy on Office-Home using ResNet-50 as backbone for Source-free open-set DA. $O S ^ { * }$ , UNK and $H O S$ mean average per-class accuracy across known classes, unknown accuracy and harmonic mean between known and unknown accuracy respectively.
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<table><tr><td colspan="3">Ar→Cl</td><td colspan="2">Ar→Pr</td><td colspan="2"></td><td colspan="2">Ar→Rw</td><td colspan="2">Cl→Ar</td><td colspan="2">Cl→Pr</td><td colspan="4">Cl→Rw</td></tr><tr><td></td><td colspan="2">OS*UNK HOS</td><td colspan="2">OS*UNK HOS</td><td colspan="2"></td><td colspan="2">OS*UNK HOS</td><td colspan="2">OS*UNK HOS</td><td colspan="2">OS*UNK HOS</td><td colspan="2">OS*UNK HOS</td><td colspan="2"></td></tr><tr><td>SHOT 67.0 28.0 39.5</td><td></td><td></td><td></td><td>81.8 26.339.8</td><td></td><td></td><td>87.532.1 47.0</td><td></td><td>66.846.2 54.6</td><td></td><td>77.527.240.2</td><td></td><td>80.025.939.1</td><td colspan="2"></td></tr><tr><td>AaD 50.7 66.4 57.6</td><td></td><td></td><td></td><td>64.6 69.4 66.9</td><td></td><td></td><td>73.166.9 69.9</td><td></td><td>48.2 81.1 60.5</td><td></td><td>59.5 63.5 61.4</td><td></td><td>67.4 68.3 67.8</td><td></td><td></td></tr><tr><td></td><td>Pr→Ar</td><td></td><td></td><td>Pr→Cl</td><td></td><td>Pr→Rw</td><td></td><td></td><td>Rw→Ar</td><td></td><td>Rw→Cl</td><td></td><td>Rw→Pr</td><td></td><td>Avg</td></tr><tr><td></td><td>OS* UNK HOS</td><td></td><td></td><td>OS*UNK HOS</td><td></td><td></td><td>OS*UNK HOS</td><td></td><td>OS*UNKHOS</td><td></td><td>OS*UNK HOS</td><td>OS*UNK HOS</td><td></td><td>OS* UNK HOS</td><td></td></tr><tr><td>SHOT 66.3 51.1 57.7</td><td></td><td></td><td></td><td>59.331.040.8</td><td></td><td></td><td>85.8 31.6 46.2</td><td></td><td>73.550.6 59.9</td><td></td><td>65.328.940.1</td><td></td><td>84.4 28.2 42.3</td><td></td><td>74.633.9 45.6</td></tr><tr><td>AaD 47.3 82.4 60.1</td><td></td><td></td><td></td><td>45.4 72.8 55.9</td><td></td><td></td><td>68.472.8 70.6</td><td></td><td>54.579.0 64.6</td><td></td><td>49.069.6 57.5</td><td></td><td>69.770.6 70.1</td><td>58.271.9</td><td>63.6</td></tr></table>
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Table 9: Accuracy on Office-Home using ResNet-50 as backbone for Source-free partial-set DA.
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<table><tr><td colspan="10">Partial-set DA Ar->C1Ar-→Pr Ar-→Re Cl→ArCl-→PrCl-→RePr→ArPr-→ClPr→Re Re→ArRe-→Cl Re-→Pr Avg.</td></tr><tr><td></td><td>83.6</td><td></td><td>88.8</td><td>72.4</td><td>74.0</td><td>79.0</td><td>76.1</td><td>60.6</td><td>90.1</td><td>81.9</td><td>88.5</td><td>76.8</td></tr><tr><td>SHOT-IM SHOT</td><td>57.9 64.8</td><td>85.2</td><td>92.7</td><td>76.3</td><td>77.6</td><td>88.8</td><td>79.7</td><td>64.3 89.5</td><td>80.6</td><td>68.3 66.4</td><td>85.8</td><td>79.3</td></tr><tr><td>AaD</td><td>67.0</td><td>83.5</td><td>93.1</td><td>80.5</td><td>76.0</td><td>87.6</td><td>78.1 65.6</td><td>90.2</td><td>83.5</td><td>64.3</td><td>87.3</td><td>79.7</td></tr></table>
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Source-free partial-set and open-set DA. We provide additional results under source-free partialset and open-set DA (PDA and ODA) setting in Tab. 8 and Tab. 9 respectively, where the open-set detection in ODA follows the same protocol to detect unseen categories as SHOT. On ODA, instead of reporting average per-class accuracy OS = |Cs|×OS∗|C |+1 $\begin{array} { r } { O S = \frac { | \mathcal { C } _ { s } | \times O S ^ { * } } { | \mathcal { C } _ { s } | + 1 } + \frac { 1 \times \bar { U } N K } { | \mathcal { C } _ { s } | + 1 } } \end{array}$ + 1×UNK|C |+1 where |Cs| is the number of known categories on source domain, we report results of HOS = 2×OS∗×UNKOS∗+UNK , which is harmonic mean between known categories accuracy $O S ^ { * }$ and unknown accuracy UNK. As pointed out by [1], $O S$ is problematic since this metric can be quite high even when unknown class accuracy UNK is 0, while unknown category detection is the key part in open-set DA. We reproduce SHOT under open-set DA and report results of $O S ^ { * }$ , UNK and $H O S$ in Tab. 8, which shows our method gets much better balance between known and unknown accuracy.
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# 5 Conclusion
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We proposed to tackle source-free domain adaptation by encouraging similar features in feature space to have similar predictions while dispersing predictions of dissimilar features in feature space, to achieve simultaneously feature clustering and cluster assignment. We introduced an upper bound to our proposed objective, resulting in two simple terms. Further we showed that we can unify several popular domain adaptation, source-free domain adaptation and contrastive learning methods from the perspective of discriminability and diversity. The approach is simple but achieves state-of-the-art performance on several benchmarks, and can be also adapted to source-free open-set and partial-set domain adaptation.
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# Acknowledgement
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We acknowledge the support from Huawei Kirin Solution, and the project PID2019-104174GBI00/AEI/10.13039/501100011033 (MINECO, Spain), and the CERCA Programme of Generalitat de Catalunya.
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# Checklist
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1. For all authors...
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
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(b) Did you describe the limitations of your work? [No]
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(c) Did you discuss any potential negative societal impacts of your work? [No]
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(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
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2. If you are including theoretical results...
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(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
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3. If you ran experiments...
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(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]
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(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]
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(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No]
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(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)? [No]
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4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
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(a) If your work uses existing assets, did you cite the creators? [Yes]
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(b) Did you mention the license of the assets? [No]
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(c) Did you include any new assets either in the supplemental material or as a URL? [No]
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(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]
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(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No]
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5. If you used crowdsourcing or conducted research with human subjects...
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(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
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(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
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(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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| 1 |
+
[
|
| 2 |
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{
|
| 3 |
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"type": "text",
|
| 4 |
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"text": "Attracting and Dispersing: A Simple Approach for Source-free Domain Adaptation ",
|
| 5 |
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"text_level": 1,
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| 6 |
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"page_idx": 0
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| 13 |
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},
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| 14 |
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{
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| 15 |
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"type": "text",
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| 16 |
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"text": "Shiqi Yang1, Yaxing Wang2∗, Kai Wang1, Shangling $\\mathbf { J u \\mathbf { i } ^ { 3 } }$ , Joost van de Weijer1 ",
|
| 17 |
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"bbox": [
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"type": "text",
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"text": "1 Computer Vision Center, Universitat Autonoma de Barcelona, Barcelona, Spain 2 Nankai University, Tianjin, China 3 Huawei Kirin Solution, Shanghai, China {syang,kwang,joost}@cvc.uab.es, yaxing@nankai.edu.cn, jui.shangling@huawei.com ",
|
| 28 |
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"bbox": [
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"page_idx": 0
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| 35 |
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| 37 |
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"type": "text",
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| 38 |
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"text": "Abstract ",
|
| 39 |
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"text_level": 1,
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| 40 |
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"page_idx": 0
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{
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| 49 |
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"type": "text",
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| 50 |
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"text": "We propose a simple but effective source-free domain adaptation (SFDA) method. Treating SFDA as an unsupervised clustering problem and following the intuition that local neighbors in feature space should have more similar predictions than other features, we propose to optimize an objective of prediction consistency. This objective encourages local neighborhood features in feature space to have similar predictions while features farther away in feature space have dissimilar predictions, leading to efficient feature clustering and cluster assignment simultaneously. For efficient training, we seek to optimize an upper-bound of the objective resulting in two simple terms. Furthermore, we relate popular existing methods in domain adaptation, source-free domain adaptation and contrastive learning via the perspective of discriminability and diversity. The experimental results prove the superiority of our method, and our method can be adopted as a simple but strong baseline for future research in SFDA. Our method can be also adapted to source-free open-set and partial-set DA which further shows the generalization ability of our method. Code is available in https://github.com/Albert0147/AaD_SFDA. ",
|
| 51 |
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"page_idx": 0
|
| 58 |
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},
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| 59 |
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{
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| 60 |
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"type": "text",
|
| 61 |
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"text": "1 Introduction ",
|
| 62 |
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"text_level": 1,
|
| 63 |
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"bbox": [
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| 64 |
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| 65 |
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| 66 |
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| 67 |
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| 68 |
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],
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"page_idx": 0
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{
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"type": "text",
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| 73 |
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"text": "Supervised learning methods which are based on training with huge amounts of labeled data are advancing almost all fields of computer vision. However, the learned models typically perform decently on test data which have a similar distribution with the training set. Significant performance degradation will occur if directly applying those models to a new domain different from the training set, where the data distribution (such as variation of background, styles or camera parameter) is considerably different. This kind of distribution shift is formally denoted as domain/distribution shift. It limits the generalization of the model to unseen domains which is important in real-world applications. There are several research fields trying to tackle this problem. One of them is Domain Adaptation (DA), which aims to reduce the domain shift between the labeled source domain and unlabeled target domain. Typical works [12, 38] resort to learn domain-invariant features, thus improving generalization ability of the model between different domains. And in the past few years, the main research line of domain adaptation is either trying to minimize the distribution discrepancy between two domains [32, 33, 35], or deploying adversarial training on features to learn domain invariant representation [52, 68, 4, 36]. Some methods also tackle domain shift from the view of semi-supervised learning [67, 27] or clustering [7, 50, 5]. ",
|
| 74 |
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{
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| 83 |
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"type": "text",
|
| 84 |
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"text": "Many recent methods [24, 29, 64, 66, 55, 15, 61] focus on source-free domain adaptation (SFDA), where source data are unavailable during target adaptation, due to data privacy and intellectual property concerns of both users and businesses. Some SFDA methods resort to neighborhood clustering and pseudo labeling. However, pseudo labeling methods [29] may suffer from negative impact from noisy labels [28], and neighborhood clustering methods [66, 64] fail to investigate the potential information from dissimilar samples. Other methods either demand complex extra modules/processing [24, 61] or the storing of historical models for contrastive learning [15]. ",
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| 85 |
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{
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"type": "table",
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| 95 |
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"img_path": "images/d1cd2e263f10c48e42a7327440c9af567204f199a969ad3ef81f5e08bd3b082e.jpg",
|
| 96 |
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"table_caption": [
|
| 97 |
+
"Table 1: Detailed comparison of SFDA methods on VisDA. ’ODA/PDA’ means whether the method reports the results for open-set or partial-set DA. $| { \\mathcal { L } } |$ means number of training objective terms. "
|
| 98 |
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],
|
| 99 |
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"table_footnote": [],
|
| 100 |
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"table_body": "<table><tr><td>Method</td><td>Extra Modules/Processing</td><td>ODA/PDA</td><td>[C|</td><td>Per-class</td></tr><tr><td>SHOT[26] 3C-GAN [24]</td><td>Access all target data for pseudo labeling</td><td>×</td><td>3</td><td>82.9</td></tr><tr><td>A²Net [61]</td><td>Data generation by conditional GAN</td><td></td><td>5 5</td><td>81.6 84.3</td></tr><tr><td>G-SFDA [66]</td><td>Self-supervised learning with extra classifiers</td><td>X</td><td></td><td></td></tr><tr><td>NRC[64]</td><td>Store features for nearest neighbor retrieval</td><td>X</td><td>2</td><td>85.4</td></tr><tr><td>HCL [15]</td><td>Store features for 2-hop nearest neighbor retrieval Store historical models</td><td>X √</td><td>4 2</td><td>85.9 83.5</td></tr><tr><td>Ours</td><td></td><td>√</td><td>2</td><td>88.0</td></tr><tr><td></td><td>Store features for nearest neighbor retrieval</td><td></td><td></td><td></td></tr></table>",
|
| 101 |
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| 102 |
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"page_idx": 1
|
| 108 |
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},
|
| 109 |
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{
|
| 110 |
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"type": "text",
|
| 111 |
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"text": "",
|
| 112 |
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"type": "text",
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"text": "Based on the fact that target features from the source model already form some semantic structure and following the intuition that for a target feature from a (source-pretrained) model, similar features should have closer predictions than dissimilar ones, we propose a new objective dubbed as Attractingand-Dispersing (AaD) to achieve it. we upperbound this objective, resulting in a simple final objective which only contains two types of terms, which encourage discriminability and diversity respectively. Further, we unify several popular domain adaptation, source-free domain adaptation and contrastive learning methods from the perspective of discriminability and diversity. Experimental results on several benchmarks prove the superiority of our proposed method. Our simple method improves the state-of-the-art on the challenging VisDA with $2 . 1 \\%$ to $8 8 . 0 \\%$ . Additionally, extra experiments on open-set and partial-set DA further prove the effectiveness of our method. A preliminary comparison between different SFDA method is shown in Tab. 1, which shows the simplicity and generalization ability of our method: it only requires the storing of features and a few nearest neighbors searches without any additional module like a generator [24] or a classifier [61]. ",
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| 123 |
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| 130 |
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},
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| 131 |
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{
|
| 132 |
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"type": "text",
|
| 133 |
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"text": "We summary our contributions as follows: ",
|
| 134 |
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|
| 135 |
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| 136 |
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| 137 |
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{
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| 143 |
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"type": "text",
|
| 144 |
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"text": "• We propose to tackle source-free domain adaptation by optimizing an upperbound of the proposed clustering objective, which is surprisingly simple. \n• We relate several popular existing methods in domain adaptation, source-free domain adaptation and contrastive learning via the perspective of discriminability and diversity, which is helpful to understand existing methods and beneficial for future improvement. \n• The experimental results prove the efficacy of our method, especially we achieve new state-of-theart on the challenging VisDA, and the method can be also extended to source-free open-set and partial-set domain adaptation. ",
|
| 145 |
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{
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| 154 |
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"type": "text",
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| 155 |
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"text": "2 Related Work ",
|
| 156 |
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"text_level": 1,
|
| 157 |
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| 164 |
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},
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| 165 |
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{
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| 166 |
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"type": "text",
|
| 167 |
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"text": "Domain Adaptation. Early DA methods such as [33, 49, 53] adopt moment matching to align feature distributions. For adversarial learning methods, DANN [9] formulates domain adaptation as an adversarial two-player game. The adversarial training of CDAN [34] is conditioned on several sources of information. DIRT-T [47] performs domain adversarial training with an added term that penalizes violations of the cluster assumption. Additionally, [22, 36, 44] adopts prediction diversity between multiple learnable classifiers to achieve local or category-level feature alignment between source and target domains. SRDC [50] proposes to directly uncover the intrinsic target discrimination via discriminative clustering to achieve adaptation. CST [31] proposes a simple self-training strategy to improve the rough pseudo label under domain shift. ",
|
| 168 |
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| 169 |
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| 170 |
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| 173 |
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| 174 |
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"page_idx": 1
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| 175 |
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},
|
| 176 |
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{
|
| 177 |
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"type": "text",
|
| 178 |
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"text": "Source-free Domain Adaptation. The above-mentioned normal domain adaptation methods need to access source domain data at all time during adaptation. In recent years plenty of methods emerge trying to tackle source-free domain adaptation. USFDA [20] and FS [21] resort to synthesize extra training samples in order to get compact decision boundaries, which is beneficial for both ",
|
| 179 |
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|
| 180 |
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| 181 |
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| 184 |
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| 185 |
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"page_idx": 1
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| 186 |
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},
|
| 187 |
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{
|
| 188 |
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"type": "text",
|
| 189 |
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"text": "Algorithm 1 Attracting and Dispersing for SFDA ",
|
| 190 |
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"text_level": 1,
|
| 191 |
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| 192 |
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| 194 |
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| 195 |
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| 196 |
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|
| 197 |
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"page_idx": 2
|
| 198 |
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},
|
| 199 |
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{
|
| 200 |
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"type": "table",
|
| 201 |
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"img_path": "images/fc3cf7f7df000b260535a1863454ba8784982f78a1441f9827b4b6af50041b91.jpg",
|
| 202 |
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"table_caption": [],
|
| 203 |
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"table_footnote": [],
|
| 204 |
+
"table_body": "<table><tr><td colspan=\"2\">Require: Source-pretrained model and target data Dt</td></tr><tr><td colspan=\"2\">1:Build memory bank storing all target features and predictions</td></tr><tr><td>2: while Adaptation do</td><td></td></tr><tr><td>3:</td><td>Sample batch T from Dt and Update memory bank</td></tr><tr><td>4:</td><td>For each feature zi in T,retrieve K-nearest neighbors (Ci)and their predictions from memory bank</td></tr><tr><td>5:</td><td>Update model by minimizing Eq. 5</td></tr><tr><td colspan=\"2\">6: end while</td></tr></table>",
|
| 205 |
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| 211 |
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"page_idx": 2
|
| 212 |
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},
|
| 213 |
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{
|
| 214 |
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"type": "text",
|
| 215 |
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"text": "the detection of open classes and also target adaptation. SHOT [26] proposes to freeze the source classifier and it clusters target features by maximizing mutual information along with pseudo labeling for extra supervision. 3C-GAN [24] synthesizes labeled target-style training images. It is based on a conditional GAN to provide supervision for adaptation. BAIT [65] extends MCD [44] to source-free setting. $A ^ { 2 } \\mathrm { { N e t } }$ [61] proposes to learn an additional target-specific classifier for hard samples and adopts a contrastive category-wise matching module to cluster target features. HCL [15] adopts Instance Discrimination [60] for features from current and historical models to cluster features, along with a generated pseudo label conditioned on historical consistency. G-SFDA [66] and NRC [64] propose neighborhood clustering which enforces prediction consistency between local neighbors. ",
|
| 216 |
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| 222 |
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"page_idx": 2
|
| 223 |
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},
|
| 224 |
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{
|
| 225 |
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"type": "text",
|
| 226 |
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"text": "Deep Clustering and Contrastive Learning. Recent Deep Clustering methods can be roughly divided into two groups, they the differ in how they learn the feature representation and cluster assignments, either simultaneously or alternatively. For example, DAC [2] and DCCM [58] alternately update cluster assignments and between-sample similarity. Simultaneous clustering methods IIC [18] and ISMAT [14] are based on mutual information maximizing between samples and theirs augmentations. LA [70] depends on a huge amount of nearest neighbor searches and multiple extra runs of $k$ -means clustering to aggregate features. Recent unsupervised clustering works [25, 51, 46] start to rely on contrastive learning, where InfoNCE [37] is typically deployed. And recently NNCLR [8] proposes to use nearest neighbors in the latent space as positives in contrastive learning to cover more semantic variations than pre-defined transformations. However an inevitable problem of normal contrastive learning is class collision where negative samples are from the same class. To tackle this issue, recent works [23, 16] propose to estimate cluster prototypes and integrate them into contrastive learning. ",
|
| 227 |
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| 234 |
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},
|
| 235 |
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{
|
| 236 |
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"type": "text",
|
| 237 |
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"text": "3 Method ",
|
| 238 |
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"text_level": 1,
|
| 239 |
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"type": "text",
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| 249 |
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"text": "For source-free domain adaptation (SFDA), we are given source-pretrained model in the beginning and an unlabeled target domain with $N _ { t }$ samples as $\\mathcal { D } _ { t } = \\{ x _ { i } ^ { t } \\} _ { i = 1 } ^ { \\bar { N } _ { t } }$ . Target domain have same $C$ classes as source domain in this paper (known as the closed-set setting). The goal of SFDA is to adapt the model to target domain without source data. We divide the model into two parts: the feature extractor $f$ , and the classifier $g$ . The output of the feature extractor is denoted as feature $( z _ { i } = f \\left( x \\right) \\in \\mathbb { R } ^ { \\bar { h } } )$ , where $h$ is dimension of the feature space. The output of classifier is denoted as $( p _ { i } = \\delta ( g ( z _ { i } ) ) \\in \\mathbb { R } ^ { C }$ ) where $\\delta$ is the softmax function. We denote $\\boldsymbol { P } \\in \\mathbb { R } ^ { b s \\times C }$ as the prediction matrix in a mini-batch. Regarding the SFDA as an unsupervised clustering problem, we address SFDA problem by clustering target features based on the proposed AaD. In additionally, we relate our method with several existing DA, SFDA and contrastive learning methods. ",
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"text": "3.1 Attracting and Dispersing for Source-free Domain Adaptation ",
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"text": "Since the source-pretrained model already learns a good feature representation, it can provides a decent initialization for target adaptation. We propose to achieve SFDA by attracting predictions for features that are located close in feature space, while dispersing predictions of those features farther away in feature space. ",
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"text": "We define $p _ { i j }$ as the probability that the feature $z _ { i } \\in \\mathbb { R } ^ { h }$ has similar (or the same) prediction to feature $\\begin{array} { r } { z _ { j } \\colon p _ { i j } = \\frac { e ^ { p _ { i } ^ { T } p _ { j } } } { \\sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { t } p _ { k } } } } \\end{array}$ It can be interpreted as the possibility that $p _ { j }$ is selected as the neighbor of $p _ { i }$ in the output space [10]. ",
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"text": "We then define two sets for each feature $z _ { i }$ : close neighbor set $\\mathcal { C } _ { i }$ containing $K$ -nearest neighbors of $z _ { i }$ (with distances as cosine similarity), and background set $B _ { i }$ which contains the features that are not in $\\mathcal { C } _ { i }$ (features potentially from different classes). To retrieve nearest neighbors for training, we build two memory banks to store all target features along with their predictions just like former works [27, 66, 64, 42], which is efficient in both memory and computation, since only the features along with their predictions computed in each mini-batch are used to update the memory bank. ",
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"text": "Intuitively, for each feature $z _ { i }$ , the features in $B _ { i }$ should have less similar predictions than those in $ { { \\mathcal { C } } } _ { i } { } ^ { 2 }$ . To achieve this, we first define two likelihood functions: ",
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"text": "$$\nP ( \\mathcal C _ { i } | \\boldsymbol \\theta ) = \\prod _ { j \\in \\mathcal C _ { i } } p _ { i j } = \\prod _ { j \\in \\mathcal C _ { i } } \\frac { e ^ { p _ { i } ^ { T } p _ { j } } } { \\sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } } , P ( \\mathcal B _ { i } | \\boldsymbol \\theta ) = \\prod _ { j \\in \\mathcal B _ { i } } p _ { i j } = \\prod _ { j \\in \\mathcal B _ { i } } \\frac { e ^ { p _ { i } ^ { T } p _ { j } } } { \\sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } }\n$$",
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"text": "where $\\theta$ denotes parameters of the model, for readability we omit $\\theta$ in following equations. The probability $p _ { j }$ in Eq. 1 is the stored prediction for neighborhood feature $z _ { j }$ , which is retrieved from the memory bank. ",
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"text": "We then propose to achieve target features clustering by minimizing the following negative loglikelihood, denoted as $A a D$ (Attracting-and-Dispersing): ",
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"text": "$$\n\\tilde { L } _ { i } ( \\mathcal { C } _ { i } , \\mathcal { B } _ { i } ) = - \\log \\frac { P ( \\mathcal { C } _ { i } ) } { P ( \\mathcal { B } _ { i } ) }\n$$",
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"text": "Noting that, if we only have $P ( \\mathcal { C } _ { i } )$ , it will be similar to Instance Discrimination [60], but we also consider $P ( B _ { i } )$ and we operate on predictions instead of features. If regarding weights of the classifier $g$ as classes prototypes, optimizing Eq. 2 is not only pulling features towards their closest neighbors and pushing them away from background features, but also towards (or away from) corresponding class prototypes. Therefore, we can achieve feature clustering and cluster assignment simultaneously. ",
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"text": "To simplify the training, instead of manually and carefully sampling background features, we use all other features except $z _ { i }$ in the mini-batch as $B _ { i }$ , which can be regarded as an estimation of the distribution of the whole dataset. We can reasonably believe that overall similarity of features in $\\mathcal { C } _ { i }$ is potentially higher than that of $B _ { i }$ , even if $B _ { i }$ has intersection with $\\mathcal { C } _ { i }$ since features in $\\mathcal { C } _ { i }$ are the closest ones to feature $z _ { i }$ . By optimizing Eq. 2, we are encouraging features in $\\mathcal { C } _ { i }$ , which have a higher chance of belonging to the same class, to have more similar predictions to $z _ { i }$ than those features in $B _ { i }$ , which have a lower chance of belonging to the same class. Note all features will show up in both the first and second term; intra-cluster alignment and inter-cluster separability are expected to be achieved after training. ",
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"text": "One problem optimizing Eq. 2 is that all target data are needed to compute Eq. 1, which is infeasible in real-world situation. Here we resort to get an upper-bound of Eq. 2: ",
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"text": "$$\n\\begin{array} { l } { \\tilde { L } _ { i } ( \\mathcal { C } _ { i } , \\mathcal { B } _ { i } ) = - \\log \\displaystyle \\frac { P ( \\mathcal { C } _ { i } ) } { P ( \\mathcal { B } _ { i } ) } = - \\sum _ { j \\in \\mathcal { C } _ { i } } [ p _ { i } ^ { T } p _ { j } - \\log ( \\displaystyle \\sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } ) ] + \\sum _ { m \\in \\mathcal { B } _ { i } } [ p _ { i } ^ { T } p _ { m } - \\log ( \\displaystyle \\sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } ) ] } \\\\ { \\displaystyle = - \\sum _ { j \\in \\mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \\sum _ { m \\in \\mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } + ( N _ { \\mathcal { C } _ { i } } - N _ { \\mathcal { B } _ { i } } ) \\log ( \\displaystyle \\sum _ { k = 1 } ^ { N _ { t } } e ^ { p _ { i } ^ { T } p _ { k } } ) } \\end{array}\n$$",
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"type": "text",
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"text": "Since we set $N _ { \\mathcal { C } _ { i } } < N _ { B _ { i } }$ , with Jensen’s inequality: ",
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"text": "$$\n\\begin{array} { r l } & { \\tilde { L } _ { i } ( \\mathcal { C } _ { i } , \\mathcal { B } _ { i } ) \\leq - \\displaystyle \\sum _ { j \\in \\mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \\displaystyle \\sum _ { m \\in \\mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } + ( N _ { \\mathcal { C } _ { i } } - N _ { \\mathcal { B } _ { i } } ) ( \\displaystyle \\sum _ { k = 1 } ^ { N _ { t } } \\frac { 1 } { N _ { t } } p _ { i } ^ { T } p _ { k } + \\log N _ { t } ) } \\\\ & { \\qquad \\quad \\simeq \\displaystyle \\sum _ { m \\in \\mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } - \\displaystyle \\sum _ { j \\in \\mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + ( N _ { \\mathcal { C } _ { i } } - N _ { \\mathcal { B } _ { i } } ) ( \\displaystyle \\sum _ { k \\in \\mathcal { B } _ { i } } \\frac { p _ { i } ^ { T } p _ { k } } { N _ { \\mathcal { B } _ { i } } } + \\log N _ { t } ) } \\\\ & { \\qquad \\quad = - \\displaystyle \\sum _ { j \\in \\mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \\displaystyle \\frac { N _ { \\mathcal { C } _ { i } } } { N _ { \\mathcal { B } _ { i } } } \\displaystyle \\sum _ { m \\in \\mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m } + ( N _ { \\mathcal { C } _ { i } } - N _ { \\mathcal { B } _ { i } } ) \\log N _ { t } } \\end{array}\n$$",
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"type": "table",
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"img_path": "images/fc086e291577768b8aa75ce0a4339383c25c4eaa1ecddbef725b3888b41628b1.jpg",
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"table_caption": [
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| 436 |
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"Table 2: Decomposition of methods into two terms: discriminability $( d i s )$ and diversity $( d i \\nu )$ , which will be minimized for training. "
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],
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"table_footnote": [],
|
| 439 |
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"table_body": "<table><tr><td>Method</td><td>Task</td><td>disterm</td><td>div term</td></tr><tr><td>MI</td><td>SFDA&Clustering</td><td>H(Y|X)</td><td>-H(Y)</td></tr><tr><td>BNM</td><td>DA&SFDA</td><td>-|PIlF</td><td>-rank(P)</td></tr><tr><td>NC</td><td>SFDA</td><td>-g(WijpTpj)</td><td>∑KL(llge)）</td></tr><tr><td>InfoNCE</td><td>Contrastive</td><td>-f(x)Tf(y)/T</td><td>log（+∑ef（x）f（x）/T）</td></tr><tr><td>Ours</td><td>SFDA</td><td>-∑jecppj</td><td>∑meB:pTPm</td></tr></table>",
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"type": "text",
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"text": "where $N _ { { \\mathcal { C } } _ { i } }$ and $N _ { B _ { i } }$ is the number of features in $\\mathcal { C } _ { i }$ and $B _ { i }$ . Note that we cannot get this upper-bound without $\\dot { P ( B _ { i } ) }$ . The approximation above in the penultimate line is to estimate the average dot product using the mini-batch data. This leads to the surprisingly simple final objective for unsupervised domain adaptation: ",
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"text": "$$\nL = \\mathbb { E } [ L _ { i } ( \\mathcal { C } _ { i } , \\mathcal { B } _ { i } ) ] , \\mathrm { w i t h ~ } L _ { i } ( \\mathcal { C } _ { i } , \\mathcal { B } _ { i } ) = - \\sum _ { j \\in \\mathcal { C } _ { i } } p _ { i } ^ { T } p _ { j } + \\lambda \\sum _ { m \\in \\mathcal { B } _ { i } } p _ { i } ^ { T } p _ { m }\n$$",
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"text": "Note the gradient will come from both $p _ { i }$ and $p _ { m }$ . The first term aims to enforce prediction consistency between local neighbors, and the naive interpretation of second term is to disperse the prediction of potential dissimilar features, which are all other features in the mini-batch. Note that the dot product between two softmaxed predictions will be maximal when two predictions have the same predicted class and are close to one-hot vector. Our algorithm is illustrated in Algorithm. 1. ",
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| 475 |
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"type": "text",
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"text": "Unlike using a constant for the second term in Eq. 4 we empirically found that using a hyperparameter $\\lambda$ to decay second term (starting from 1) works better, we will adopt SND [43] to tune this hyperparameter unsupervisedly. One reason may be that the approximation inside Eq. 3.1 is not necessarily accurate. And as training goes on, features are gradually clustering, the role of the second term for dispersing should be weakened. Additionally, considering the current mini-batch with the correctly predicted features $z _ { i }$ and $z _ { m }$ belonging to the same class. In this case the second term in both $L _ { i } ( \\mathcal { C } _ { i } , B _ { i } )$ and $L _ { m } ( \\mathcal { C } _ { m } , B _ { m } )$ tends to push $p _ { m }$ to the wrong direction, while the first term in $L _ { m } ( \\mathcal { C } _ { m } , B _ { m } )$ can potentially keep current (correct) prediction unchanged. Hence, this will suppress the negative impact of the second term. We will further deepen the understanding of these two terms in the next subsection. ",
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"text": "3.2 Relation to Existing Works ",
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| 497 |
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"text": "In this section, we will relate several popular DA, SFDA and contrastive learning methods through two objectives, discriminability and diversity. This can improve our understanding of domain adaptation methods, as well as improve the understanding of our method. ",
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"text": "Mutual Information maximizing (MI). SHOT-IM [26] proposes to achieve source-free domain adaptation by maximizing the mutual information, which is actually widely used in unsupervised clustering [11, 40, 14]: ",
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"type": "equation",
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"img_path": "images/be91ce1475fe30e8720ce2e3621be48a9d4d55757f51e14c472bd8841ffc5a82.jpg",
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"text": "$$\n{ \\cal L } _ { M I } = H ( Y | X ) - H ( Y )\n$$",
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"text_format": "latex",
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"bbox": [
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"text": "which contains two terms: conditional entropy term $H ( Y | X )$ to encourages unambiguous cluster assignments, and marginal entropy term $H ( Y )$ to encourage cluster sizes to be uniform to avoid degeneracy. In practice, $H ( Y )$ is approximated by the current mini-batch instead of using whole dataset [48, 14]. ",
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"text": "Batch Nuclear-norm Maximization (BNM). BNM [5, 6] aims to increase prediction discriminability and diversity to tackle domain shift. It is originally achieved by maximizing $F$ -norm (for discriminability) and rank of prediction matrix (for diversity) respectively: ",
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"type": "equation",
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"img_path": "images/bb157af8ace2fd0b9e7f8a17234c6666e151d7c1f7de059b24fa24663cdcff97.jpg",
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"text": "$$\nL = - \\| P \\| _ { F } - r a n k ( P )\n$$",
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"text": "In their paper, they further prove merely maximizing the nuclear norm $\\| P \\| _ { * }$ can achieve these two goals simultaneously. In relation to our method, if target features are well clustering during training, we can presume the K-nearest neighbors of feature $z _ { i }$ have the same prediction, the first term in Eq. 5 can be seen as the summation of diagonal elements of matrix $P P ^ { T }$ , which is actually the square of $F$ -norm $( \\| P \\| _ { F } = { \\sqrt { t r a c e ( P P ^ { T } ) } } )$ , then it is actually minimizing prediction entropy [5]. As for second term, we can regard it as the summation of non-diagonal element of $P P ^ { T }$ , it encourages all these non-diagonal elements to be 0 thus the $r a n k ( P P ^ { T } ) = r a n k ( P )$ is supposed to increase, which indicates larger prediction diversity [5]. In a nutshell, compared to SHOT and BNM our method first considers local feature structure to cluster target features, which can be treated as an alternative way to increase discriminability at the late training stage, meanwhile as discussed above our method is also encouraging diversity. ",
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"text": "Neighborhood Clustering (NC). G-SFDA [66] and NRC [64] are based on neighborhood clustering to tackle SFDA problem. Those works basically contain two major terms in their optimizing objective: a neighborhood clustering term for prediction consistency and a marginal entropy term $H ( Y )$ for prediction diversity. NRC [64] further introduces neighborhood reciprocity to weight the different neighbors. Their loss objective can be written as: ",
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"img_path": "images/d0e403ac5a1cb8d414f11a4ee78ae3ec365d69c1a53c3b9c33ba40fa3b06f0dc.jpg",
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"text": "$$\nL _ { i } = - \\sum _ { j \\in \\mathcal { C } _ { i } } g ( W _ { i j } p _ { i } ^ { T } p _ { j } ) + \\sum _ { c = 1 } ^ { C } \\mathbf { K L } ( \\bar { p } _ { c } | | q _ { c } ) , \\mathrm { ~ w i t h ~ } \\bar { p } _ { c } = \\frac { 1 } { n _ { t } } \\sum _ { i } p _ { i } ^ { ( c ) } , \\mathrm { ~ a n d ~ } q _ { \\{ c = 1 , . . . , C \\} } = \\frac { 1 } { C }\n$$",
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"type": "text",
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"text": "where $W _ { i j }$ will weight the importance of neighbor and $g ( \\cdot )$ is log or identity function. Although the first term of G-SFDA and NRC is the same as that of our final loss objective Eq. 5, note that our motivation is different as we simultaneously consider similar and dissimilar features, and Eq. 5 is deduced as an approximated upper-bound of our original objective Eq. 2. ",
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"text": "And note actually the marginal entropy termAlthough the second term of those metho $\\begin{array} { r } { - H ( Y ) = \\sum _ { c = 1 } ^ { C } \\bar { p } _ { c } \\log \\bar { p } _ { c } = \\sum _ { c = 1 } ^ { C } { \\bf K } { \\bf L } \\left( \\bar { p } _ { c } | | q _ { c } \\right) - \\log C . } \\end{array}$ solution where all images are only assigned to some certain classes, the margin entropy term presumes the prior that whole dataset or the mini-batch is class balance/uniformly distributed, which is barely true for current benchmarks or in real-world environment. In conclusion, the above three types of methods are actually all to increase discriminability and meanwhile maximize diversity of the prediction, but through different ways. ",
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"text": "Contrastive Learning. Here we also link our method to InfoNCE [37]), which is widely used in contrastive learning. As a recent paper [56] points out that InfoNCE loss can be decomposed into 2 terms: ",
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"img_path": "images/b2c261f100ec1a3d7e7e980ea7a952e2a9b8979657de0af6d6eea3cb78ad3c10.jpg",
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"text": "$$\n\\chi _ { i n f o N C E } = \\mathbb { E } _ { ( x , y ) \\sim p _ { p o s } } [ - f ( x ) ^ { T } f ( y ) / \\tau ] \\ + \\underset { x \\sim p _ { d a t a } } { \\mathbb { E } } ~ \\underset { \\substack { i = 1 \\sim { p _ { d a t a } } \\ \\{ x _ { i } ^ { - } \\} _ { i = 1 } ^ { M } \\sim p _ { d a t a } } } [ \\log ( e ^ { 1 / \\tau } + \\sum _ { i } e ^ { f ( x _ { i } ^ { - } ) ^ { T } f ( x ) / \\tau } ) ]\n$$",
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| 659 |
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"text": "The first term is denoted as alignment term (with positive pairs) is to make positive pairs of features similar, and the second term denoted as uniformity term with negative pairs encouraging all features to roughly uniformly distributed in the feature space. ",
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"text": "The Eq. 8 shares some similarity with all the above domain adaptation methods in that the first term is for the alignment with positive pairs and the second term is to encourage diversity. But note that the remarkable difference is that the above domain adaptation methods operate in the output (prediction) space while contrastive learning is conducted in the (spherical) feature space. Therefore, simultaneously feature representation learning and cluster assignment can be achieved for those domain adaptation methods. Note in normal contrastive learning methods, extra KNN or a linear learnable classifier needs to be deployed for final classification, while our model can directly give predictions. ",
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"text": "We list all above methods in Tab. 2. Finally, returning to Eq. 5, we can also regard the second term as a variant of diversity loss to avoid degeneration solution, but without making any category prior assumption. Intuitively, with target features forming groups during training, the second term should play less and less important role, otherwise it may destabilize the training. This is similar to the class collision issue in contrastive learning. If our second term contains too many features belonging to the same class. Thus it is reasonable to decay the second term. ",
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"type": "text",
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"text": "4 Experiments ",
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"text": "Datasets. We conduct experiments on three benchmark datasets for image classification: Office-31, Office-Home and VisDA-C 2017. Office-31 [41] contains 3 domains (Amazon, Webcam, DSLR) ",
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"type": "table",
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"img_path": "images/aaf7c2e95d889f6fbf0054398c3813793b963ca757b945d0169d1fc51728394f.jpg",
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"table_caption": [
|
| 728 |
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"Table 3: Accuracies $( \\% )$ on Office-Home for ResNet50-based methods. We highlight the best result and underline the second best one. "
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],
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"table_footnote": [],
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"table_body": "<table><tr><td>Method</td><td></td><td>SFAr→CIAr-→PrAr-→RwCl-→ArCl-→PrCl-→RwPr-→ArPr->CIPr-→RwRw→ArRw→CIRw→PrAvg</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ResNet-50[13]</td><td></td><td>X 34.9</td><td>50.0</td><td>58.0</td><td>37.4</td><td>41.9</td><td>46.2</td><td>38.5</td><td>31.2</td><td>60.4</td><td>53.9</td><td>41.2 59.9</td><td>46.1</td></tr><tr><td>MCD [44]</td><td></td><td>xxx 48.9</td><td>68.3</td><td>74.6</td><td>61.3</td><td>67.6</td><td>68.8</td><td>57.0</td><td>47.1</td><td>75.1</td><td>69.1</td><td>52.2 79.6</td><td>64.1</td></tr><tr><td>CDAN[34]</td><td></td><td>50.7</td><td>70.6</td><td>76.0</td><td>57.6</td><td>70.0</td><td>70.0</td><td>57.4</td><td>50.9</td><td>77.3 70.9</td><td>56.7</td><td>81.6</td><td>65.8</td></tr><tr><td>SAFN[63]</td><td></td><td>52.0</td><td>71.7</td><td>76.3</td><td>64.2</td><td>69.9</td><td>71.9</td><td>63.7</td><td>51.4</td><td>77.1 70.9</td><td>57.1</td><td>81.5</td><td>67.3</td></tr><tr><td>MDD [69]</td><td></td><td>X 54.9</td><td>73.7</td><td>77.8</td><td>60.0</td><td>71.4</td><td>71.8</td><td>61.2</td><td>53.6</td><td>78.1 72.5</td><td>60.2</td><td>82.3</td><td>68.1</td></tr><tr><td>TADA [57]</td><td></td><td>×x 53.1</td><td>72.3</td><td>77.2</td><td>59.1</td><td>71.2</td><td>72.1</td><td>59.7</td><td>53.1</td><td>78.4</td><td>72.4</td><td>60.0 82.9</td><td>67.6</td></tr><tr><td>SRDC [50]</td><td></td><td>52.3</td><td>76.3</td><td>81.0</td><td>69.5</td><td>76.2</td><td>78.0</td><td>68.7</td><td>53.8</td><td>81.7</td><td>76.3</td><td>57.1 85.0</td><td>71.3</td></tr><tr><td>SHOT[26]</td><td></td><td>√ 57.1</td><td>78.1</td><td>81.5</td><td>68.0</td><td>78.2</td><td>78.1</td><td>67.4</td><td>54.9</td><td>82.2</td><td>73.3 58.8</td><td>84.3</td><td>71.8</td></tr><tr><td>A²Net [61]</td><td></td><td>58.4</td><td>79.0</td><td>82.4</td><td>67.5</td><td>79.3</td><td>78.9</td><td>68.0</td><td>56.2</td><td>82.9 74.1</td><td>60.5</td><td>85.0</td><td>72.8</td></tr><tr><td>G-SFDA [66]</td><td></td><td>√ 57.9</td><td>78.6</td><td>81.0</td><td>66.7</td><td>77.2</td><td>77.2</td><td>65.6</td><td>56.0</td><td>82.2</td><td>72.0</td><td>57.8 83.4</td><td>71.3</td></tr><tr><td>NRC [64]</td><td></td><td>√ 57.7</td><td>80.3</td><td>82.0</td><td>68.1</td><td>79.8</td><td>78.6</td><td>65.3</td><td>56.4</td><td>83.0</td><td>71.0</td><td>58.6 85.6</td><td>72.2</td></tr><tr><td>BNM-S [6]</td><td></td><td>√ 57.4</td><td>77.8</td><td>81.7</td><td>67.8</td><td>77.6</td><td>79.3</td><td>67.6</td><td>55.7</td><td>82.2</td><td>73.5</td><td>59.5 84.7</td><td>72.1</td></tr><tr><td>Ours</td><td></td><td>59.3</td><td>79.3</td><td>82.1</td><td>68.9</td><td>79.8</td><td>79.5</td><td>67.2</td><td>57.4</td><td>83.1</td><td>72.1</td><td>58.5 85.4</td><td>72.7</td></tr></table>",
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"type": "table",
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"table_caption": [
|
| 744 |
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"Table 4: Accuracies $( \\% )$ on VisDA-C (Synthesis $ \\mathrm { R e a l }$ ) for ResNet101-based methods. We highlight the best result and underline the second best one. "
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| 745 |
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],
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"table_footnote": [],
|
| 747 |
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"table_body": "<table><tr><td>Method</td><td>[SF</td><td>plane</td><td>bcycl bus</td><td>car</td><td>horse</td><td>knifemcycl</td><td></td><td>person</td><td></td><td></td><td></td><td>plant sktbrd train truck Per-class</td></tr><tr><td>ResNet-101[13]</td><td></td><td>55.1</td><td>53.3 61.9</td><td>59.1</td><td>80.6</td><td>17.9</td><td>79.7 31.2</td><td>81.0</td><td>26.5</td><td>73.5</td><td>8.5</td><td>52.4</td></tr><tr><td>CDAN+BSP[3]</td><td></td><td>92.4</td><td>61.0</td><td>81.0 57.5</td><td>89.0</td><td>80.6</td><td>90.1</td><td>77.0 84.2</td><td>77.9</td><td>82.1</td><td>38.4</td><td>75.9</td></tr><tr><td>MCC[19]</td><td></td><td>88.7</td><td>80.3</td><td>80.5 71.5</td><td>90.1</td><td>93.2</td><td>85.0</td><td>71.6 89.4</td><td>73.8</td><td>85.0</td><td>36.9</td><td>78.8</td></tr><tr><td>STAR[36]</td><td></td><td>95.0</td><td>84.0</td><td>84.6 73.0</td><td>91.6</td><td>91.8</td><td>85.9 78.4</td><td>94.4</td><td>84.7</td><td>87.0</td><td>42.2</td><td>82.7</td></tr><tr><td>RWOT[62]</td><td>xxxxx</td><td>95.1 80.3</td><td>83.7</td><td>90.0</td><td>92.4</td><td>68.0</td><td>92.5 82.2</td><td>87.9</td><td>78.4</td><td>90.4</td><td>68.2</td><td>84.0</td></tr><tr><td>3C-GAN [24]</td><td></td><td>94.8 73.4</td><td>68.8</td><td>74.8</td><td>93.1</td><td>95.4</td><td>88.6 84.7</td><td>89.1</td><td>84.7</td><td>83.5</td><td>48.1</td><td>81.6</td></tr><tr><td>SHOT[26]</td><td>v√</td><td>94.3 88.5</td><td></td><td>80.1 57.3</td><td>93.1</td><td>94.9</td><td>80.7</td><td>80.3 91.5</td><td>89.1</td><td>86.3</td><td>58.2</td><td>82.9</td></tr><tr><td>A²Net [61]</td><td></td><td>94.0 87.8</td><td>85.6</td><td>66.8</td><td>93.7</td><td>95.1</td><td>85.8</td><td>81.2 91.6</td><td>88.2</td><td>86.5</td><td>56.0</td><td>84.3</td></tr><tr><td>G-SFDA [66]</td><td></td><td>96.1 88.3</td><td>85.5</td><td>74.1</td><td>97.1</td><td>95.4</td><td>89.5</td><td>79.4 95.4</td><td>92.9</td><td>89.1</td><td>42.6</td><td>85.4</td></tr><tr><td>NRC [64]</td><td></td><td>96.8 91.3</td><td>82.4</td><td>62.4</td><td>96.2</td><td>95.9</td><td>86.1</td><td>80.6 94.8</td><td>94.1</td><td>90.4</td><td>59.7</td><td>85.9</td></tr><tr><td>HCL [15]</td><td>vvv√</td><td>93.3</td><td>85.4</td><td>80.7 68.5</td><td>91.0</td><td>88.1</td><td>86.0</td><td>78.6 86.6</td><td>88.8</td><td>80.0</td><td>74.7</td><td>83.5</td></tr><tr><td>Ours</td><td>√</td><td>97.4</td><td>90.5</td><td>80.8 76.2</td><td>97.3</td><td>96.1</td><td>89.8</td><td>82.9 95.5</td><td>93.0</td><td>92.0</td><td>64.7</td><td>88.0</td></tr></table>",
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"text": "with 31 classes and 4,652 images. Office-Home [54] contains 4 domains (Real, Clipart, Art, Product) with 65 classes and a total of 15,500 images. VisDA (VisDA-C 2017) [39] is a more challenging dataset, with 12-class synthetic-to-real object recognition tasks, its source domain contains of 152k synthetic images while the target domain has $5 5 \\mathrm { k }$ real object images. ",
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"type": "text",
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"text": "Evaluation. The column SF in the tables denotes source-free. For Office-31 and Office-Home, we show the results of each task and the average accuracy over all tasks ${ \\it A } \\nu g$ in the tables). For VisDA, we show accuracy for all classes and average over those classes (Per-class in the table). All results are the average of three random runs for target adaptation. ",
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"text": "Model details. To ensure fair comparison with related methods, we adopt the backbone of a ResNet-50 [13] for Office-Home and ResNet-101 for VisDA. Specifically, we use the same network architecture as SHOT [26], BNM-S [6], G-SFDA [66] and NRC [64], i.e., the final part of the network is: fully connected layer - Batch Normalization $I I 7 J$ - fully connected layer with weight normalization $I 4 5 J$ . We adopt SGD with momentum 0.9 and batch size of 64 for all datasets. The learning rate for Office-31 and Office-Home is set to 1e-3 for all layers, except for the last two newly added fc layers, where we apply 1e-2. Learning rates are set 10 times smaller for VisDA. We train 40 epochs for Office-31 and Office-Home while 15 epochs for VisDA. ",
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"text": "There are two hyperparameters $N _ { { \\mathcal { C } } _ { i } }$ (number of nearest neighbors) and $\\lambda$ , to ensure fair comparison we set $N _ { { \\mathcal { C } } _ { i } }$ to the same number as previous works G-SFDA [66] and NRC [64], which also resort to nearest neighbors. That is, we set $N _ { { \\mathcal { C } } _ { i } }$ to 3 on Office-31 and Office-Home, 5 on VisDA. For $\\lambda$ , we set it as $\\begin{array} { r } { \\lambda = ( 1 + 1 0 * \\frac { i t e r } { m a x \\_ i t e r } ) ^ { - \\beta } } \\end{array}$ , where the decay factor $\\beta$ controls the decaying speed. We directly apply SND $I 4 3 J$ to select $\\beta$ unsupervisedly. Based on SND we set $\\beta$ to 0 on Office-Home, 2 on Office-31 and 5 on VisDA. ",
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"type": "text",
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"text": "4.1 Results and Analysis ",
|
| 803 |
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"text_level": 1,
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| 804 |
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"type": "text",
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"text": "Quantitative Results. As shown in Tables $3 { - } 5 ( L e f t )$ , where the top part shows results for the source-present methods that use source data during adaptation, and the bottom part shows results for the source-free DA methods. On Office-31 and VisDA, our method gets state-of-the-art performance compared to existing source-free domain adaptation methods, especially on VisDA our method outperforms others by a large margin $2 . 1 \\%$ compared to NRC). And our method achieves similar results on Office-Home compared to the more complex $A ^ { \\mathrm { 2 } } \\mathrm { N e t }$ method (which combines three classifiers and five objective functions). The reported results clearly demonstrate the efficiency of the proposed method for source-free domain adaptation. It also achieves similar or better results compared to domain adaptation methods with access to source data on both Office-Home and VisDA. Note the extension of SHOT called $\\mathrm { S H O T + + }$ [30] deploys extra self-supervised training and semisupervised learning, which are general to improve the results (an evidence is that the source model after these 2 tricks gets huge improvement, e.g., $6 0 . 2 \\%$ improves to $6 6 . 6 \\%$ on Office-Home.), we do not list it here for fair comparison. ",
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"type": "table",
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"img_path": "images/90af06c8aa07dd9793efa9608248faf521106cb9a0aeeaed71f628138518ca9c.jpg",
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"table_caption": [
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"Table 5: (Left) Accuracies $( \\% )$ on Office-31 for ResNet50-based methods. We highlight the best result and underline the second best one. (Right) Ablation study on number of nearest neighbors $N _ { { \\mathcal { C } } _ { i } }$ . We highlight the best score and underline the second best one. "
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"table_footnote": [],
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"table_body": "<table><tr><td>Method</td><td></td><td colspan=\"3\">JSFA→DA→WD-→WW-→DD-→AW→AAvg</td></tr><tr><td>MCD [44] CDAN [34] MDD[69]] DMRL[59] MCC[19]</td><td>X .xxxxx</td><td>92.2 88.6 92.9 94.1 90.4 90.4 93.4 90.8 95.6 95.4</td><td>98.5 98.6 100.0 98.7 99.9 99.0 100.0 98.6 100.0</td><td>100.0 69.5 69.7 86.5 71.0 75.0 73.0 71.2 72.6</td><td>69.3 87.7 73.7 88.0 87.9</td></tr><tr><td>SRDC [50] SHOT[26] 3C-GAN [24] NRC[64] HCL [15] BNM-S [6]</td><td></td><td>95.8 95.7 94.0 90.1 92.7 93.7 96.0 90.8 94.7 92.5 93.0 92.9</td><td>99.2 98.4 98.5 99.0 98.2 98.2</td><td>100.0 76.7 77.1 99.9 74.7 74.3 99.8 75.3 77.8 100.0 75.3 75.0 100.0 75.9 77.7 99.9 75.4 75.0</td><td>73.9 89.4 90.8 88.6 89.6 89.4 89.8 89.1</td></tr></table>",
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"type": "table",
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"img_path": "images/72b58e8021fb31ca374a7880e57d213bcf6587a1218cb94c376fe722d919fd44.jpg",
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"table_caption": [],
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"table_footnote": [],
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"table_body": "<table><tr><td>Nc</td><td>Avg</td><td colspan=\"2\"></td></tr><tr><td>Office-31</td><td></td><td>Nc</td><td>Per-class</td></tr><tr><td>1</td><td>89.1</td><td>VisDA</td><td></td></tr><tr><td>2</td><td>89.5</td><td>3</td><td>86.7</td></tr><tr><td>3</td><td>89.9</td><td>4</td><td>87.4</td></tr><tr><td>Office-Home</td><td></td><td>5</td><td>88.0</td></tr><tr><td>1</td><td>72.2</td><td>6</td><td>88.0</td></tr><tr><td>2</td><td>72.6</td><td>7</td><td>88.0</td></tr><tr><td>3</td><td>72.7</td><td></td><td></td></tr></table>",
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"img_path": "images/d5938c64280d6d34169a787c675d830390dd3f7d9107b41f341c64d6c1e9c21e.jpg",
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"image_caption": [
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"Figure 1: Visualization of decision boundary on target data with different training objective. "
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"type": "text",
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"text": "Toy dataset. We carry out an experiment on the twinning moona dataset to ablate the influence of two terms in our objective Eq. 5. For the twinning moons dataset, the data from the source domain are represented by two inter-twinning moons, which contain 300 samples each. Data in the target domain are generated through rotating source data by $3 0 ^ { \\circ }$ . The domain shift here is instantiated as the rotation degree. First we train the model with 3 linear layers only on the source domain, and test the model on all domains. As shown in the first image in Fig. 1, the source model performs badly on target data. Then we conduct several variants of our method to train the model. The visualization of the decision boundary in Fig. 1 indicates that both terms in Eq. 5 are necessary, and decay of second term is shown to be important. ",
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"img_path": "images/1cbeeb6f22ecc7417becd52fbe23824931895f067aba20899f40ce406fce9521.jpg",
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"table_caption": [
|
| 894 |
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"Table 6: Unsupervised hyperparameter selection of $\\beta$ with SND [43], larger SND should correspond to better target model. "
|
| 895 |
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],
|
| 896 |
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"table_footnote": [],
|
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"table_body": "<table><tr><td colspan=\"2\">VisDA</td></tr><tr><td>β</td><td>SND个 Per-class</td></tr><tr><td>0 1</td><td>8.1823 77.5 8.2584 83.8</td></tr><tr><td>2 8.3214</td><td>86.7</td></tr><tr><td>3 8.3311</td><td>87.6</td></tr><tr><td>4</td><td>8.3540 88.0</td></tr><tr><td>5 8.3543</td><td>88.0</td></tr><tr><td>7 8.3530</td><td>88.1</td></tr></table>",
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"img_path": "images/8d0736cec61698f5eb785bcfe105d39c7f8f6cb80b39a5e5528ff789de4e520f.jpg",
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"table_caption": [],
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"table_footnote": [],
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"table_body": "<table><tr><td colspan=\"2\">Office-31</td></tr><tr><td>β</td><td>SND↑ Avg</td></tr><tr><td>0</td><td>4.1366 88.0</td></tr><tr><td>0.25 4.3016</td><td>89.7</td></tr><tr><td>1 4.4494</td><td>89.9</td></tr><tr><td>2 4.4501</td><td>89.9</td></tr></table>",
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"img_path": "images/820a62a7472bc2879030f709c5eb4cdebe398fb43b941bb5025f417d2c1fb7f4.jpg",
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"table_caption": [],
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"table_footnote": [],
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| 925 |
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"table_body": "<table><tr><td colspan=\"2\">Office-Home</td></tr><tr><td>β</td><td>SND个 Avg</td></tr><tr><td>0</td><td>3.7515 72.7</td></tr><tr><td>0.25</td><td>3.7402 72.6</td></tr><tr><td>0.5 3.7252</td><td>72.0</td></tr><tr><td>1 3.6923</td><td>70.6</td></tr></table>",
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"img_path": "images/1cf6b003e9c6d20751c2aa0c45c9569c74226a20fb875407d84e6d762e676b95.jpg",
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"image_caption": [
|
| 938 |
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"Figure 2: (Left) Ratio of features which have 3 nearest neighbor features sharing the same predicted label. (Right) Ratio among above features which have 3 nearest neighbor features sharing the same and correct predicted label. "
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"img_path": "images/ff21b27fe42af9751709b511a5069210b107ecbb0a16ef22534cde1673342297.jpg",
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"table_caption": [
|
| 953 |
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"Table 7: Runtime analysis on SHOT and our method. For SHOT, pseudo labels are computed at each epoch. $10 \\%$ and $5 \\%$ denote the percentage of target features which are stored in the memory bank. "
|
| 954 |
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],
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| 955 |
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"table_footnote": [],
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| 956 |
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"table_body": "<table><tr><td>VisDA</td><td>Runtime (s/epoch)Per-class (%)</td><td></td></tr><tr><td>SHOT</td><td>618.82</td><td>82.9</td></tr><tr><td>Ours</td><td>520.13</td><td>88.0</td></tr><tr><td>Ours(10% for memory bank)</td><td>490.21</td><td>87.6</td></tr><tr><td>Ours(5% for memory bank)</td><td>482.77</td><td>87.5</td></tr></table>",
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"text": "Number of nearest neighbors $( N _ { C _ { i } } )$ . For the number of nearest neighbors used for the first term in Eq. 5, we show in Tab. 5 $( R i g h t )$ our method is robust to the choice of $N _ { { \\mathcal { C } } _ { i } }$ , as the results imply that a reasonable choice of $N _ { { \\mathcal { C } } _ { i } }$ (such as 3) works quite well on all datasets, since only considering few neighbors (such as $1 / 2$ ) may be too noisy if all of them are misclassified, while setting $N _ { { \\mathcal { C } } _ { i } }$ too larger may also potentially include samples of other categories. For larger dataset such as VisDA we can choose a relatively larger $N _ { { \\mathcal { C } } _ { i } }$ . Note the reason why we choose $N _ { { \\mathcal { C } } _ { i } }$ as 5 in main experiments is to compare fairly with G-SFDA [66] and NRC [64]. ",
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"text": "Decay factor $\\beta$ . According to the analysis in Sec. 3.2, the second term acts like a diversity term to avoid that all target features collapse to a limited set of categories. The role of the second term should be weakened during the training, but how to decay the second term is non-trivial. We directly adopt SND [43] which computes Soft Neighborhood Density for unsupervised hyperparameter selection of $\\beta$ . The method is unsupervised and larger SND predicts a better target models. The results of $S N D$ with different $\\beta$ are shown in Tab. 6, the results prove that SND works well to choose optimal $\\beta$ . ",
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"text": "Runtime analysis. Instead of storing all features in the memory bank, we can only stores a limited number of target features, by updating the memory bank at the end of each iteration by taking the $n$ (batch size) embeddings from the current training iteration and concatenating them at the end of the memory bank, and discard the oldest $n$ elements from the memory bank. We report the results with this type of memory bank of different buffer size in the Table 7. The results show that indeed this could be an efficient way to reduce computation on very large datasets. ",
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"text": "Degree of clustering during training. We also plot how features are clustered with different decaying factors $\\beta$ on VisDA in Fig. 2. The left one shows the ratio of features which have 3-nearest neighbors all sharing the same prediction, which indicates the degree of clustering during training, and the right one shows the ratio among above features which have 3-nearest neighbor features sharing the same and correct predicted label. Those curves in Fig. 2 left show that the target features are clustering, and those in Fig. 2 right indicate that clear category boundaries are emerging. The numbers in the legends denote the deployed $\\beta$ and the corresponding final accuracy. From the figures we can draw the conclusion that with a larger decay factor $\\beta$ on VisDA, features are quickly clustering and forming inter-class boundaries, since the ratio of features which share the same and correct prediction with neighbors are increasing faster. When decaying factor $\\beta$ is too small, meaning training signal from the second term is strong, the clustering process is actually impeded. The curves in Fig. 2 (left) signify that this ratio can also be used to choose $\\beta$ with higher performance unsupervisedly. ",
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"table_caption": [
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"Table 8: Accuracy on Office-Home using ResNet-50 as backbone for Source-free open-set DA. $O S ^ { * }$ , UNK and $H O S$ mean average per-class accuracy across known classes, unknown accuracy and harmonic mean between known and unknown accuracy respectively. "
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"table_footnote": [],
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"table_body": "<table><tr><td colspan=\"3\">Ar→Cl</td><td colspan=\"2\">Ar→Pr</td><td colspan=\"2\"></td><td colspan=\"2\">Ar→Rw</td><td colspan=\"2\">Cl→Ar</td><td colspan=\"2\">Cl→Pr</td><td colspan=\"4\">Cl→Rw</td></tr><tr><td></td><td colspan=\"2\">OS*UNK HOS</td><td colspan=\"2\">OS*UNK HOS</td><td colspan=\"2\"></td><td colspan=\"2\">OS*UNK HOS</td><td colspan=\"2\">OS*UNK HOS</td><td colspan=\"2\">OS*UNK HOS</td><td colspan=\"2\">OS*UNK HOS</td><td colspan=\"2\"></td></tr><tr><td>SHOT 67.0 28.0 39.5</td><td></td><td></td><td></td><td>81.8 26.339.8</td><td></td><td></td><td>87.532.1 47.0</td><td></td><td>66.846.2 54.6</td><td></td><td>77.527.240.2</td><td></td><td>80.025.939.1</td><td colspan=\"2\"></td></tr><tr><td>AaD 50.7 66.4 57.6</td><td></td><td></td><td></td><td>64.6 69.4 66.9</td><td></td><td></td><td>73.166.9 69.9</td><td></td><td>48.2 81.1 60.5</td><td></td><td>59.5 63.5 61.4</td><td></td><td>67.4 68.3 67.8</td><td></td><td></td></tr><tr><td></td><td>Pr→Ar</td><td></td><td></td><td>Pr→Cl</td><td></td><td>Pr→Rw</td><td></td><td></td><td>Rw→Ar</td><td></td><td>Rw→Cl</td><td></td><td>Rw→Pr</td><td></td><td>Avg</td></tr><tr><td></td><td>OS* UNK HOS</td><td></td><td></td><td>OS*UNK HOS</td><td></td><td></td><td>OS*UNK HOS</td><td></td><td>OS*UNKHOS</td><td></td><td>OS*UNK HOS</td><td>OS*UNK HOS</td><td></td><td>OS* UNK HOS</td><td></td></tr><tr><td>SHOT 66.3 51.1 57.7</td><td></td><td></td><td></td><td>59.331.040.8</td><td></td><td></td><td>85.8 31.6 46.2</td><td></td><td>73.550.6 59.9</td><td></td><td>65.328.940.1</td><td></td><td>84.4 28.2 42.3</td><td></td><td>74.633.9 45.6</td></tr><tr><td>AaD 47.3 82.4 60.1</td><td></td><td></td><td></td><td>45.4 72.8 55.9</td><td></td><td></td><td>68.472.8 70.6</td><td></td><td>54.579.0 64.6</td><td></td><td>49.069.6 57.5</td><td></td><td>69.770.6 70.1</td><td>58.271.9</td><td>63.6</td></tr></table>",
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"table_caption": [
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"Table 9: Accuracy on Office-Home using ResNet-50 as backbone for Source-free partial-set DA. "
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"table_footnote": [],
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| 1032 |
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"table_body": "<table><tr><td colspan=\"10\">Partial-set DA Ar->C1Ar-→Pr Ar-→Re Cl→ArCl-→PrCl-→RePr→ArPr-→ClPr→Re Re→ArRe-→Cl Re-→Pr Avg.</td></tr><tr><td></td><td>83.6</td><td></td><td>88.8</td><td>72.4</td><td>74.0</td><td>79.0</td><td>76.1</td><td>60.6</td><td>90.1</td><td>81.9</td><td>88.5</td><td>76.8</td></tr><tr><td>SHOT-IM SHOT</td><td>57.9 64.8</td><td>85.2</td><td>92.7</td><td>76.3</td><td>77.6</td><td>88.8</td><td>79.7</td><td>64.3 89.5</td><td>80.6</td><td>68.3 66.4</td><td>85.8</td><td>79.3</td></tr><tr><td>AaD</td><td>67.0</td><td>83.5</td><td>93.1</td><td>80.5</td><td>76.0</td><td>87.6</td><td>78.1 65.6</td><td>90.2</td><td>83.5</td><td>64.3</td><td>87.3</td><td>79.7</td></tr></table>",
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"type": "text",
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"text": "Source-free partial-set and open-set DA. We provide additional results under source-free partialset and open-set DA (PDA and ODA) setting in Tab. 8 and Tab. 9 respectively, where the open-set detection in ODA follows the same protocol to detect unseen categories as SHOT. On ODA, instead of reporting average per-class accuracy OS = |Cs|×OS∗|C |+1 $\\begin{array} { r } { O S = \\frac { | \\mathcal { C } _ { s } | \\times O S ^ { * } } { | \\mathcal { C } _ { s } | + 1 } + \\frac { 1 \\times \\bar { U } N K } { | \\mathcal { C } _ { s } | + 1 } } \\end{array}$ + 1×UNK|C |+1 where |Cs| is the number of known categories on source domain, we report results of HOS = 2×OS∗×UNKOS∗+UNK , which is harmonic mean between known categories accuracy $O S ^ { * }$ and unknown accuracy UNK. As pointed out by [1], $O S$ is problematic since this metric can be quite high even when unknown class accuracy UNK is 0, while unknown category detection is the key part in open-set DA. We reproduce SHOT under open-set DA and report results of $O S ^ { * }$ , UNK and $H O S$ in Tab. 8, which shows our method gets much better balance between known and unknown accuracy. ",
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"text": "5 Conclusion ",
|
| 1066 |
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"text": "We proposed to tackle source-free domain adaptation by encouraging similar features in feature space to have similar predictions while dispersing predictions of dissimilar features in feature space, to achieve simultaneously feature clustering and cluster assignment. We introduced an upper bound to our proposed objective, resulting in two simple terms. Further we showed that we can unify several popular domain adaptation, source-free domain adaptation and contrastive learning methods from the perspective of discriminability and diversity. The approach is simple but achieves state-of-the-art performance on several benchmarks, and can be also adapted to source-free open-set and partial-set domain adaptation. ",
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"text": "Acknowledgement ",
|
| 1089 |
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"text": "We acknowledge the support from Huawei Kirin Solution, and the project PID2019-104174GBI00/AEI/10.13039/501100011033 (MINECO, Spain), and the CERCA Programme of Generalitat de Catalunya. ",
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"text": "References ",
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Deep domain confusion: Maximizing for domain invariance. arXiv preprint arXiv:1412.3474, 2014. \n[54] Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In CVPR, pages 5018–5027, 2017. \n[55] Qin Wang, Olga Fink, Luc Van Gool, and Dengxin Dai. Continual test-time domain adaptation. CVPR, 2022. \n[56] Tongzhou Wang and Phillip Isola. Understanding contrastive representation learning through alignment and uniformity on the hypersphere. In ICML, pages 9929–9939. PMLR, 2020. \n[57] Ximei Wang, Liang Li, Weirui Ye, Mingsheng Long, and Jianmin Wang. Transferable attention for domain adaptation. In AAAI, volume 33, pages 5345–5352, 2019. \n[58] Jianlong Wu, Keyu Long, Fei Wang, Chen Qian, Cheng Li, Zhouchen Lin, and Hongbin Zha. Deep comprehensive correlation mining for image clustering. In ICCV, pages 8150–8159, 2019. \n[59] Yuan Wu, Diana Inkpen, and Ahmed El-Roby. Dual mixup regularized learning for adversarial domain adaptation. ECCV, 2020. \n[60] Zhirong Wu, Yuanjun Xiong, Stella X Yu, and Dahua Lin. Unsupervised feature learning via non-parametric instance discrimination. In CVPR, pages 3733–3742, 2018. \n[61] Haifeng Xia, Handong Zhao, and Zhengming Ding. Adaptive adversarial network for source-free domain adaptation. In ICCV, pages 9010–9019, 2021. \n[62] Renjun Xu, Pelen Liu, Liyan Wang, Chao Chen, and Jindong Wang. Reliable weighted optimal transport for unsupervised domain adaptation. In CVPR, pages 4394–4403, 2020. \n[63] Ruijia Xu, Guanbin Li, Jihan Yang, and Liang Lin. Larger norm more transferable: An adaptive feature norm approach for unsupervised domain adaptation. In ICCV, October 2019. \n[64] Shiqi Yang, Joost van de Weijer, Luis Herranz, Shangling Jui, et al. Exploiting the intrinsic neighborhood structure for source-free domain adaptation. NeurIPS, 34, 2021. \n[65] Shiqi Yang, Yaxing Wang, Joost van de Weijer, Luis Herranz, and Shangling Jui. Unsupervised domain adaptation without source data by casting a bait. arXiv preprint arXiv:2010.12427, 2020. \n[66] Shiqi Yang, Yaxing Wang, Joost van de Weijer, Luis Herranz, and Shangling Jui. Generalized source-free domain adaptation. In ICCV, pages 8978–8987, 2021. \n[67] Yabin Zhang, Bin Deng, Kui Jia, and Lei Zhang. Label propagation with augmented anchors: A simple semi-supervised learning baseline for unsupervised domain adaptation. In ECCV, pages 781–797, 2020. \n[68] Yabin Zhang, Hui Tang, Kui Jia, and Mingkui Tan. Domain-symmetric networks for adversarial domain adaptation. In CVPR, pages 5031–5040, 2019. \n[69] Yuchen Zhang, Tianle Liu, Mingsheng Long, and Michael Jordan. Bridging theory and algorithm for domain adaptation. In ICML, pages 7404–7413, 2019. \n[70] Chengxu Zhuang, Alex Lin Zhai, and Daniel Yamins. Local aggregation for unsupervised learning of visual embeddings. In ICCV, pages 6002–6012, 2019. ",
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|
| 1 |
+
# ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers
|
| 2 |
+
|
| 3 |
+
Zhewei Yao⇤ , Reza Yazdani Aminabadi, Minjia Zhang, Xiaoxia Wu, Conglong Li, Yuxiong He
|
| 4 |
+
|
| 5 |
+
Microsoft {zheweiyao, yazdani.reza, minjiaz, xiaoxiawu, conglong.li, yuxhe}@microsoft.com
|
| 6 |
+
|
| 7 |
+
# Abstract
|
| 8 |
+
|
| 9 |
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How to efficiently serve ever-larger trained natural language models in practice has become exceptionally challenging even for powerful cloud servers due to their prohibitive memory/computation requirements. In this work, we present an efficient and affordable post-training quantization approach to compress large Transformer-based models, termed as ZeroQuant. ZeroQuant is an end-to-end quantization and inference pipeline with three main components: (1) a fine-grained hardware-friendly quantization scheme for both weight and activations; (2) a novel affordable layer-by-layer knowledge distillation algorithm (LKD) even without the access to the original training data; (3) a highly-optimized quantization system backend support to remove the quantization/dequantization overhead. As such, we are able to show that: (1) ZeroQuant can reduce the precision for weights and activations to INT8 in a cost-free way for both BERT and GPT-3-style models with minimal accuracy impact, which leads to up to $5 . 1 9 \mathrm { x } / 4 . 1 6 \mathrm { x }$ speedup on those models compared to FP16 inference; (2) ZeroQuant plus LKD affordably quantize the weights in the fully-connected module to INT4 along with INT8 weights in the attention module and INT8 activations, resulting in $3 \mathbf { x }$ memory footprint reduction compared to the FP16 model; (3) ZeroQuant can be directly applied to two of the largest open-sourced language models, including $\mathrm { G P T - J _ { 6 B } }$ and GPT- $\mathrm { \cdot N e o X _ { 2 0 B } }$ , for which our INT8 model achieves similar accuracy as the FP16 model but achieves up to $5 . 2 \mathrm { x }$ better efficiency.
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# 1 Introduction
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Large-scale natural language models have been widely adopted in different applications, e.g., natural language understanding using BERT [64] and generation tasks using GPT-style models [49]. Although those models have achieved cutting-edge accuracy results, as the model size keeps increasing dramatically, the requirements of memory footprint and the computational cost to deploy them become a major bottleneck, even on cloud servers with powerful GPU devices.
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One promising way to alleviate this challenge is quantization, which can reduce the bit precision for both weight and activations for lower memory footprint and faster compute (e.g., INT8 Tensor cores on T4/A100). However, quantization usually requires retraining (also known as quantization aware training, or QAT in short) to recover the accuracy degradation from representation loss of weight and activations. To enable QAT, the full training pipeline is usually required, including the training data and compute resources, to finetune the model. Access to those components is now oftentimes not available, and QAT is also a time-consuming process, particularly for those large-scale models.
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Recently, zero-shot quantization [10, 47] and post-training quantization (PTQ) [46, 39] are proposed to address the training-data access and compute requirement challenges since PTQ generally requires no (or minimal) retraining. But most of those works primarily focus on computer vision problems on relatively small scales. More recently, [7] shows promising PTQ results on BERT. However, (1) its main focus is on high-precision quantization (INT8/FP16) on $\mathbf { B E R T _ { b a s e } }$ , (2) it does not consider other billion-scale generative models (GPT-3-style models [9]). More importantly, most of these works do not report real latency improvement, putting the usefulness of these methods in improving inference latency into question. For example, existing work often do not discuss the quantization/dequantization cost associated with different quantization schemes, which in fact has a big impact to the performance benefit of using low precision.
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Besides, for extreme quantization (e.g., INT4), knowledge distillation is usually used to boost performance, which adds another source of expensive computation cost as compared to QAT. Furthermore, in order to achieve better accuracy performance, hidden-states knowledge distillation, e.g., [3, 81], is usually applied for the quantized model. This would put significant pressure on the GPU memory and the compute resource requirement since both the teacher and student models needed to be loaded into the GPU memory for training.
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In this paper, we present ZeroQuant, an end-to-end post-training quantization and inference pipeline, to address those challenges, targeting both INT8 and INT4/INT8 mixed-precision quantization. Specifically, our contributions are:
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• We apply fine-grained hardware-friendly quantization schemes on both weight and activations, i.e., group-wise quantization for weight and token-wise quantization for activations. Both quantization schemes can significantly reduce the quantization error and retain hardware acceleration properties.
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• We propose a novel layer-by-layer knowledge distillation method (LKD) for INT4/INT8 mixedprecision quantization, where the neural network is quantized layer-by-layer through distillation with minimal iterations and even without the access to the original training data. As such, at any given moment, the device memory is primarily populated only with a single extra layer’s footprint, making billion-scale model distillation feasible with limited training budget and GPU devices.
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• We develop a highly optimized inference backend, which eliminates the expensive computation cost of quantization/dequantization operators, enabling latency speedups on INT8 Tensor cores on modern GPU hardware.
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• Our empirical results show that: – ZeroQuant enables quantizing BERT and GPT-3-style models into INT8 weight and activations to retain accuracy without incurring any retraining cost. Compared to FP16 inference, our INT8 model achieves up to $5 . 1 9 \mathrm { x } / 4 . 1 6 \mathrm { x }$ speedup on $\mathrm { B E R T _ { b a s e } / G P T } { - 3 _ { 3 5 0 \mathrm { M } } }$ on A100 GPUs. ZeroQuant plus LKD can do INT4/INT8 mixed-precision quantization for BERT and GPT3-style models. This results in a $3 \mathbf { x }$ memory footprint reduction with marginal accuracy loss as compared to the FP16 model. Also, thanks to the lightweight of LKD, we can finish the quantization process in 33s (10 minutes) for $\mathbf { B E R T _ { b a s e } }$ $\mathrm { ( B E R T _ { l a r g e } } ,$ ). We also demonstrate that LKD can use other datasets to achieve similar performance to the original training data. We demonstrate the scalability of ZeroQuant on two of the largest open-sourced language models, i.e, $\mathrm { G P T - J _ { 6 B } }$ and GPT- $\mathrm { N e o X } _ { 2 0 \mathrm { B } }$ , with INT8 quantization. ZeroQuant can achieve $3 . 6 7 \mathrm { x }$ speedup over the FP16 model for $\mathrm { G P T - J _ { 6 B } }$ and (2) reduce the GPU requirement for inference from 2 to 1 and latency from $6 5 \mathrm { m s }$ to $2 5 \mathrm { m s }$ for GPT- $\mathrm { \cdot N e o X _ { 2 0 B } }$ (i.e., $5 . 2 \mathrm { x }$ better system efficiency in total).
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# 2 Related Work
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Model compression has been explored from different aspects [26, 38, 40, 35, 44, 21, 25, 51, 19, 76, 41, 27, 56, 60, 29, 61, 69, 34, 15, 39, 32]. Among those, quantization is one of the most promising directions as it directly reduces the memory footprint and compute intensity. Here, we focus on quantization for NLP models and briefly discuss the related work.
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The majority of quantization works can be categorized into quantization-aware training (QAT). [57, 78] are the first few works to quantize BERT models using integer numbers for both weight and activations. Particularly, [57] utilizes Hessian information to push the weight bit-precision to even INT2/INT4, and it also proposes group-wise quantization to quantize the weight matrix in a more fine-grained granularity compared to single matrix quantization. [22] introduces quantization noise to alleviate the variations of QAT. [81, 3] leverage very expensive knowledge distillation [27] and data augmentation [29] to ternarize/binarize weights. [30] combines knowledge distillation [29] and learned step size quantization [20] to quantize the weight to 2–8 bits. Recently, [62] also uses knowledge distillation to compress GPT-2 models on task-specific problems to INT2. All those works quantize models using the original training datasets. More importantly they need retraining or finetuning the full model to recover the accuracy, and such compute cost on extra-large models, like [58, 12], can be hardly affordable for most research labs or practitioners.
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One solution to overcome the compute cost challenge is post-training quantization (PTQ). However, PTQ often induces a significant drop in accuracy because the network can be sensitive to quantization errors. Along this line, one of the first works applied to Transformer-based [65] models is [77]. The authors introduce centroid-based quantization method, where outlier numbers use FP32 format and the rest numbers are quantized using non-uniform quantization. As such, it is hard to get the real inference latency benefit on general compute accelerators, e.g., CPU and GPU, because the parallel processing units in these hardware do not support efficient computation of mixed data types. More recently, [7] introduces high-precision activation quantization (FP16) for part of the model to overcome the high dynamic activation ranges. However, to the best of our knowledge, (1) How to apply PTQ on GPT-3-style models while achieving high accuracy has not been studied in any of previous work yet; (2) How to apply PTQ on billion (or even a dozen of billions) scale model is still under-explored; (3) Efficient inference system backend is still missing, especially for fine-grained quantization schemes, making it hard to achieve low latency on commodity hardware. ZeroQuant resolves all those limitations by considering the system backend into the algorithm design and we verify its capability on both BERT and large-scale GPT-3-style (up to 20 billion, i.e., GP $\left[ - \mathrm { N e o } \mathrm { X } _ { 2 0 \mathrm { B } } \right]$ ) models for various tasks.
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# 3 Background and Challenge
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# 3.1 Transformer Architecture
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The transformer architecture usually has three components: an embedding layer, a stack of encoder/decoder layers, and a final classifier. In this paper, we focus on quantizing the encoder/decoder layers, i.e., the transformer block, because it is often the most memory and compute intensive components in the entire architecture. With a transformer block, there are two sub-layers, the multi-head self-attention (MHSA) and the feed-forward connection (FFC). We give a short review later and please refer to [65] for more details. At high level, transformer models can be broadly categorized to three branches: encoder-only models (BERT) [64], decoder-only models (GPT-3-style) [49], and encoder-decoder models (T5) [50]. In this paper, we focus on encoder-only and decoder-only models but our approach can be applied to encoder-decoder models as well.
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Figure 1: The illustration of a Transformer-block.
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Transformer Block Assume the input of an encoder layer is $\boldsymbol { X }$ , the query, key, value, attention output, FFC dense, and FFC output matrices are $W _ { q }$ , $W _ { k }$ , $W _ { v }$ , $W _ { o }$ , $W _ { h - 4 h }$ , and $W _ { 4 h - h }$ , respectively. Then the forward propagation of a transformer-block is illustrated in Figure 1, where LN is the layer normalization, Softmax is the softmax operator, and GeLU is the activation function.
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# 3.2 Quantization Background
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Quantization maps high-precision numbers, e.g., FP16/FP32, to its low-precision counterpart, e.g., INT4/INT8, to reduce the model footprint and improve the compute performance. In this work, we use uniform symmetric scalar quantizers. That is to say, if we have a vector/matrix, $\mathbf { x }$ , the quantization is applied as
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$$
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\mathbf { x } _ { q u a n t i z e } = r o u n d \left( c l a m p ( \frac { \mathbf { x } } { S } , - 2 ^ { b i t - 1 } , 2 ^ { b i t - 1 } - 1 ) \right) ,
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$$
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Table 1: Post training quantization results of GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ on 20 zero-shot evaluation datesets. Here WxAy means x-/y-bit for weight/activation. Particularly, for W4/8, we quantize the MHSA’s weight to INT8 and FFC’s weight to INT4. Please see Table I.1 for the results of all 20 tasks.
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<table><tr><td>Precision</td><td>Lambada (↑)</td><td>PIQA (↑)</td><td>OpenBookQA(↑)</td><td>RTE (↑)</td><td>ReCoRd (↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td></tr><tr><td>W16A16</td><td>49.3</td><td>66.3</td><td>29.4</td><td>53.8</td><td>75.1</td><td>38.9</td><td>21.5</td></tr><tr><td>W8A16</td><td>49.3</td><td>66.1</td><td>29.6</td><td>54.2</td><td>74.8</td><td>38.5</td><td>22.1</td></tr><tr><td>W16A8</td><td>44.7</td><td>64.8</td><td>28.2</td><td>52.7</td><td>69.2</td><td>37.8</td><td>24.6</td></tr><tr><td>W8A8</td><td>42.6</td><td>64.1</td><td>28.0</td><td>53.1</td><td>67.5</td><td>37.8</td><td>26.2</td></tr><tr><td>W4/8A16</td><td>0.00</td><td>51.4</td><td>30.2</td><td>52.7</td><td>16.1</td><td>28.9</td><td>1.76e5</td></tr></table>
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where bit is the number of bit we use to represent the quantized value, and $S$ is the scaling factor. For weight matrix quantization, $S$ is generally computed as $S = m a x \left( a b s ( \mathbf { x } ) \right)$ , since the weight matrix is static during inference. On the other hand, activations’ range is dynamic during inference so that an accurate $S$ requires dynamic calculation during inference. However, to achieve best latency reduction, coarse-grained static quantization is usually applied in practice, where $S$ is calibrated using training data (e.g., momentum based averaging) and fixed during inference [24]. Although static quantization achieves better latency reduction, it also limits the quantization representation for activations, which is discussed below.
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# 3.3 Post Training Quantization
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Post-training quantization (PTQ) exhibits great compression efficiency compared to quantizationaware training (QAT) since PTQ is usually applied to quantize the model without retraining. A common strategy of PTQ is to feed the training data to the network and calibrate the scaling factor, $S$ , using the running mean. Please see Appendix A.1 for more details.
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Some work has been done for $\mathbf { B E R T _ { b a s e } }$ models [7] with INT8 weight and mixed INT8/FP16 activation quantization. However, there is no investigation for (1) even lower bit-precision PTQ on BERT models and (2) large-scale GPT-3-style models. Here, we briefly discuss the challenge of the application of PTQ on both BERT (in Appendix C) and GPT-3-style models.
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Figure 2: The activation range (left) and row-wise weight range of the attention output matrix (right) of different layers on the pretrained GPT- $3 _ { 3 5 0 \mathrm { M } }$ . See Figure C.1 for the results of $\mathbf { B E R T _ { b a s e } }$ .
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The results of $\mathrm { G P T } { \cdot } 3 _ { 3 5 0 \mathrm { M } }$ with PTQ are shown in Table 1. As can be seen, the INT8 activation quantization (i.e., the row of W16A8) causes the primary accuracy loss. Further pushing the weight to INT8 (i.e., the row of W8A8) does not change the accuracy of zero-shot evaluation tasks but leads the causal language modeling task (Wikitext-2) to worse perplexity score, which demonstrates the sensitivity of generation tasks as compared to other zero-shot evaluation problems. For W4/8A16, on some accuracy-based tasks, GPT- $3 _ { 3 5 0 \mathrm { M } }$ still achieves reasonable performance like OpenBookQA but it loses accuracy on the majority of the rest tasks. Particularly, for Wikitext-2, GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ with W4/8A16 cannot generate any meaningful text anymore. Please also see Appendix C for the analysis for BERT.
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Dynamic Activation Range To investigate why INT8 activation leads to significant accuracy drop for both BERT and GPT-3-style models, we plot the token-wise (i.e., the hidden state of each token) range of each activation for different transformer layers of GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ in Figure 2 (left). As can be seen, different tokens have dramatically different activation ranges. For example, the maximum range of the last layer is around 35 but the minimum range is close to 8. This larger variance in the activation range makes it difficult to use a fixed quantization range (usually the maximum value) for all tokens to retain the prediction accuracy, because the limited representation power for small range tokens is going to hurt the accuracy performance.
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Different Ranges of Neurons in Weight Matrices Similarly, we plot the row-wise (i.e., the output dimension) weight range of the attention output matrix $( W _ { o } )$ of GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ in Figure 2 (right). There is a $1 0 \mathrm { x }$ difference between the largest magnitudes of different rows and this leads to the worse generation performance of the INT8 weight PTQ. This also makes it very challenging when INT4 quantization is applied as the INT4 only has 16 numbers and a $1 0 \mathrm { x }$ smaller range leads to 2 (or 3) numbers for the representations of those smaller-range rows.
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This analysis results also indicate why more expensive hidden-states knowledge distillation [3, 37] is used for ultra-low precision quantization to close the accuracy gap. However, as the training cost of knowledge distillation for large-scale models is too high, a lightweight and efficient method is desirable for PTQ.
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# 4 Methodology
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# 4.1 Fine-grained Hardware-friendly Quantization Scheme
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As shown in Section 3, even applying INT8 PTQ to BERT/GPT-3-style models leads to significant accuracy degradation. The key challenge is the representation of INT8 cannot fully capture the different numerical ranges of different rows in weight matrices and different activation tokens. One way to address this is to use group-wise (token-wise) quantization for the weight matrix (activations).
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Group-wise Quantization for Weights Group-wise weight matrix quantization has first been proposed in [57], where a weight matrix $\mathbf { W } \in \mathbb { R } ^ { n \times m }$ is partitioned in to $g$ groups, and each group is quantized separately. However, in [57], the authors only apply this for quantization aware training. More importantly, they do not consider the hardware efficiency constraint and they do not have a system backend support. As such, they lack the real latency reduction benefit.
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In our design, we consider the hardware constraint from Ampere Architecture of GPUs (e.g, A100), where the compute unit is based on Warp Matrix Multiply and Accumulate (WMMA) tiling size [54] to achieve the best speedup. Later, we will show that our group-wise quantization leads to much better accuracy as compared to single-matrix quantization due to its finer-granularity quantization while still achieving great latency reduction.
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Token-wise Quantization for Activations As mentioned in Section 3 and Appendix 3.2, a common practice for existing PTQ work is to use static quantization for activation, where the min/max range is calculated at an offline calibration phase. Such a method might be sufficient for small scale models where the variance in the activation range is small. However, as analyzed in Section 3, there is a huge variance in the activation range for large-scale transformer models such as GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ and $\mathbf { B E R T _ { b a s e } }$ . As such, a static quantization scheme (often applied to all tokens/samples) would lead to significant accuracy drop. One natural idea to overcome this issue is to adopt finer-grained token-wise quantization and dynamically calculate the min/max range for each token to reduce the quantization error from activations. Our evaluation in Section 5 also shows that token-wise quantization for activation significantly improves the accuracy of GPT-3-style and BERT models.
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However, directly applying token-wise quantization using existing DL frameworks, such as the PyTorch quantization suite, would lead to significant quantization and dequantization cost because token-wise quantization introduces additional operations that lead to expensive data movement overhead between the GPU compute units and the main memory. To address this issue, we build a highly optimized inference backend for token-wise quantization of transformer models. For example, the inference backend of ZeroQuant employs so called kernel fusion technique to fuse quantization operator with its previous operator, like layer normalization, to alleviate the data movement cost from token-wise quantization. Similarly, the dequantization cost of the different GeMMs’ output is alleviated by scaling the INT32 accumulation using both the weight and activation quantization scales, before writing the final FP16 result back to the main memory for the next FP16 operator (like GeLU). Those optimization will be discussed in more details in Section 4.3.
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Figure 3: The illustration of normal (left) and our fused (right) INT8 GeMM.
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Token-wise quantization can significantly reduce the representation error for quantized activations. Also, as it does not need to calibrate the activation range, later we will show that there is no quantization-related cost (e.g., activation range calibration) for a moderate quantization scheme (INT8 weight with INT8 activation) for ZeroQuant.
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# 4.2 Layer-by-layer Knowledge Distillation with Affordable Cost
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Knowledge distillation (KD) is one of the most powerful methods to alleviate the accuracy degradation after model compression. However, there are several limitations of KD, especially for hidden-states KD on large-scale language models: (1) KD needs to hold a teacher and a student model together during the training, which dramatically increases the memory and compute cost; (2) KD usually requires full training of the student model. Therefore, several copies (gradient, first/second order momentum) of the weight parameters need to be stored in memory to update the model; (3) KD generally requires original training data, which sometimes are not accessible due to privacy/confidential issues.
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To address those limitations, we present our layer-by-layer distillation (LKD) algorithm. Assume the target model for quantization has $N$ transformer blocks, $L _ { 1 } , . . . , L _ { N }$ , the accessible dataset has input $( X , Y )$ , which can be the original training data or datasets from other resources. Our LKD quantizes the network layer-by-layer and uses its original (i.e., unquantized) version as the teacher model. More specifically, assume layer $L _ { k }$ is going to be quantized, and its quantized version is $\widehat { L } _ { k }$ . Then we use the output of the $L _ { k - 1 }$ (i.e., by running inference on $X$ over the first $k - 1$ layers) as the input of $L _ { k }$ and $\widehat { \widehat { L } } _ { k }$ , measure the difference, and do the model update to $L _ { k }$ , i.e.,
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$$
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\mathcal { L } _ { L K D , k } = M S E \left( L _ { k } \cdot L _ { k - 1 } \cdot L _ { k - 2 } \cdot \ldots \cdot L _ { 1 } ( \pmb { X } ) - \widehat { L } _ { k } \cdot L _ { k - 1 } \cdot L _ { k - 2 } \cdot \ldots \cdot L _ { 1 } ( \pmb { X } ) \right) ,
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$$
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where $M S E$ is the mean square loss, and it can be also replaced by other losses (e.g., KL divergence) as well. As can be seen, (1) our LKD does not need to hold a separate teacher as we use the same $L _ { 1 }$ to $L _ { k - 1 }$ for both teacher/student model. As such, the only extra model cost we have is $L _ { k }$ ; (2) the memory overhead of optimizer states are significantly reduced as the only optimizing layer is $L _ { k }$ ; (3) as we never optimize the end-to-end model, the training does not depend on the label anymore. Later, we will show that LKD does not rely on the original training data in Section 5.6.
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# 4.3 Quantization-Optimized Transformer Kernels
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Both optimizing the inference latency and model size is crucial for serving large-scale transformer models in practice. During inference, the batch size is often relatively small, so the inference latency of the model primarily depends on the time of loading inference needed data from the main memory. By quantizing the weights and activations to lower precision, we reduce the data volume needed to load those data, which allows more effective use of memory bandwidth and higher loading throughput. However, simply converting weights/activations to INT8 does not guarantee improved latency because there are additional data movement overhead associated with quantization/dequantization operations as shown in Figure 3 (red box). Such an overhead becomes expensive and in some cases surpasses the performance benefits of using low precision. To reap the accuracy improvement from token-wise quantization while obtaining improved latency, we now present our optimizations that maximize the memory bandwidth utilization to speed up inference latency for ZeroQuant.
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CUTLASS INT8 GeMM To support INT8 computation, we use CUTLASS [6] INT8 GeMM implementation tuned for different batch sizes. Unlike standard GPU backend library, such as cuDNN, using CUTLASS allows us to more flexibly fuse quantization operation before and after GeMM to reduce kernel launching and data-movement overhead.
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Fusing Token-wise Activation Quantization Token-wise quantization/dequantization introduce many additional operations that lead to extra data movement cost. To eliminate these cost, we use kernel fusion [68] to fuse quantization operation for activation with its previous element-wise and/or reduction operations such as bias-add, GeLU, and LayerNorm into a single operator, as illustrated by the green box in Figure 3. For the dequantization operation (e.g., dequantizing the integer output from the GeMM operator), we similarly fuse it with our custom GeMM schedule to avoid additional read/write accesses to the main memory as illustrated by the blue box in Figure 3.
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Table 2: Result of $\mathbf { B E R T _ { b a s e } }$ on the development set of GLUE benchmark (except WNLI). $[ 5 7 ] ^ { + }$ uses 128 groups for weight matrix which is hard to get GPU acceleration. $[ 7 ] ^ { * }$ uses mixed INT8 and FP16 activation, and it directly reports the average metric of MNLI/MRPC/QQP/STS-B, which is basically the average of the two metrics we used for our runs.
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<table><tr><td>Precision (Method)</td><td>CoLA</td><td>MNLI-m</td><td>MNLI-mm</td><td>MRPC</td><td>QNLI</td><td>QQP</td><td>RTE</td><td>SST-2</td><td>STS-B</td><td>Ave.</td><td>Ave. Time (s)</td></tr><tr><td>W16A16 (Baseline)</td><td>59.72</td><td>84.94</td><td>85.06</td><td>86.27/90.57</td><td>92.15</td><td>91.51/88.56</td><td>72.20</td><td>93.23</td><td>90.06/89.59</td><td>83.95</td><td>N/A</td></tr><tr><td>W8A8 [57](QAT)+</td><td></td><td>83.91</td><td>83.83</td><td></td><td></td><td></td><td></td><td>92.83</td><td></td><td></td><td></td></tr><tr><td>W8A8 [78](QAT)</td><td>58.48</td><td></td><td></td><td>-/89.56</td><td>90.62</td><td>/87.96</td><td>68.78</td><td>92.24</td><td>89.04/-</td><td></td><td></td></tr><tr><td>W8A8 (QAT)</td><td>61.21</td><td>84.80</td><td>84.64</td><td>83.82/88.85</td><td>91.29</td><td>91.29/88.28</td><td>71.12</td><td>92.89</td><td>88.39/88.18</td><td>83.37</td><td>2900</td></tr><tr><td>W8A8 (PTQ)</td><td>56.06</td><td>79.99</td><td>81.06</td><td>75.49/79.67</td><td>87.35</td><td>89.92/86.82</td><td>48.38</td><td>91.40</td><td>86.58/86.44</td><td>77.41</td><td>6</td></tr><tr><td>W8A8/16 [7](PTQ)*</td><td>58.63</td><td>82.67</td><td>82.67</td><td>88.74</td><td>90.41</td><td>89.40</td><td>68.95</td><td>92.66</td><td>88.00</td><td>82.46</td><td>Unknown</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>59.59</td><td>84.83</td><td>85.13</td><td>86.03/90.39</td><td>91.98</td><td>91.45/88.46</td><td>71.12</td><td>93.12</td><td>90.09/89.62</td><td>83.75</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>16.74</td><td>16.95</td><td>31.62/0.00</td><td>50.74</td><td>63.18/0.00</td><td>47.29</td><td>70.64</td><td>16.48/15.91</td><td>33.11</td><td>6</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>57.29</td><td>82.69</td><td>83.27</td><td>84.56/88.40</td><td>90.04</td><td>86.52/79.49</td><td>70.76</td><td>92.78</td><td>88.46/88.61</td><td>81.65</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>58.50</td><td>83.16</td><td>83.69</td><td>84.80/89.31</td><td>90.83</td><td>88.94/84.12</td><td>70.04</td><td>92.78</td><td>88.49/88.67</td><td>82.35</td><td>31</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>56.69</td><td>82.46</td><td>83.06</td><td>84.07/88.03</td><td>90.13</td><td>87.04/80.50</td><td>70.76</td><td>92.78</td><td>88.07/88.44</td><td>81.55</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>58.80</td><td>83.09</td><td>83.65</td><td>85.78/89.90</td><td>90.76</td><td>89.16/84.85</td><td>71.84</td><td>93.00</td><td>88.16/88.55</td><td>82.71</td><td>31</td></tr></table>
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By doing the above optimizations, we are able to show significant latency reduction for BERT and GPT-3-style models in Section 5. Please see Appendix D for more details about our system optimization.
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# 5 Results
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Experimental Details To evaluate the proposed ZeroQuant, we test it on both BERT and GPT-3 models. For BERT, we tested both $\mathbf { B E R T _ { b a s e } }$ and $\mathbf { B E R T _ { l a r g e } }$ on GLUE benchmark; and for GPT-3-style models, we tested the GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ (i.e., GPT-3-style model with 350M parameters) and GPT- $\boldsymbol { \cdot } 3 _ { 1 . 3 \mathrm { B } }$ (i.e., GPT-3-style model with 1.3B parameters) on 20 zero-shot evaluation tasks, including 19 accuracybased tasks and 1 language modeling generation task. To illustrate the scalability of the proposed ZeroQuant, we also directly apply it to two of the largest open-sourced GPT-3-style models, i.e., $\mathrm { G P T - J _ { 6 B } }$ [67] and GPT- $\mathrm { N e o X } _ { 2 0 \mathrm { B } }$ [5]. We use a fixed set of hyperparameters for all the LKD-related experiments even though tuning them may benefit our results. Please see Appendix A.2 for more training details and see Appendix A.3 for the reported metrics for BERT. To provide a comprehensive study, we also include a tuning result in Appendix E on BERT and an ablation study for different proposed components in Section 5.5.
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Notation Explanation We use WxAy to represent using $\mathbf { X }$ -bit for weight quantization and y-bit for activation quantization. Unless specific explanation, for W4/8, we quantize the MHSA’s weight to INT8 and FFC’s weight to INT4; for A8/16, we use FP16 activation for self-attention calculation (i.e., the GeMM related to $W _ { q / k / v , }$ ) and use INT8 for the rest calculation. We use ZeroQuant to represent the method with only fine-grained quantization schemes and use ZeroQuant-LKD to represent the method with both fine-grained quantization schemes and LKD.
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A summary of results is shown in Appendix B. We also include (1) the results required by reviewers in Appendix G; (2) the speedup explanation .
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# 5.1 Main Results of BERT
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$\mathbf { B E R T _ { b a s e } }$ We report the results of $\mathbf { B E R T _ { b a s e } }$ in Table 2. For W8A8, the average accuracy of PTQ degrades more than 10 points. However, ZeroQuant can achieve 83.75 scores, which is only 0.2 lower than baseline. Particularly, as ZeroQuant has no activation range calibration phase, the cost of ZeroQuant is 0 which is even cheaper than standard PTQ. As compared to [7], our method achieves a better average score (1.29 higher). Meanwhile, as compared to INT8 activation used in ZeroQuant, [7] uses mixed INT8 and FP16 activation.
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We also compare our method with our internal trained QAT and other QAT works [57, 78]. As can be seen, with comparable accuracy results as those QAT methods, ZeroQuant can save the retraining cost from 2900s to 0s for INT8 quantization.
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Table 3: Result of $\mathbf { B E R T _ { l a r g e } }$ on the development set of GLUE benchmark (except WNLI). $+ \mathrm { { { \mathbf { W } } e } }$ extensively tuned the learning rate for QAT (see Appendix F for more details).
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<table><tr><td>Precision (Method)</td><td>CoLA</td><td>MNLI-m</td><td>MNLI-mm</td><td>MRPC</td><td>QNLI</td><td>QQP</td><td>RTE</td><td>SST-2</td><td>STS-B</td><td>Ave.</td><td>Ave. Time (s)</td></tr><tr><td>W16A16 (Baseline)</td><td>63.35</td><td>86.65</td><td>85.91</td><td>87.99/91.62</td><td>92.24</td><td>91.08/88.08</td><td>74.01</td><td>93.46</td><td>90.34/90.11</td><td>85.03</td><td>N/A</td></tr><tr><td>W8A8 [78](QAT)</td><td></td><td></td><td></td><td>/90.9</td><td>91.74</td><td></td><td></td><td></td><td>90.12/-</td><td></td><td></td></tr><tr><td>W8A8 (QAT)+</td><td>59.85</td><td>86.65</td><td>86.35</td><td>85.29/89.43</td><td>92.55</td><td>91.60/88.60</td><td>61.37</td><td>93.23</td><td>87.55/87.65</td><td>82.78</td><td>7181</td></tr><tr><td>W8A8 (PTQ)</td><td>60.57</td><td>75.69</td><td>76.94</td><td>81.13/84.93</td><td>88.49</td><td>84.04/74.35</td><td>46.93</td><td>91.74</td><td>62.75/55.77</td><td>73.54</td><td>31</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>63.38</td><td>86.52</td><td>85.64</td><td>87.75/91.50</td><td>92.31</td><td>91.09/88.05</td><td>72.56</td><td>93.35</td><td>90.45/90.19</td><td>84.81</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>16.85</td><td>33.24</td><td>68.38/80.89</td><td>51.25</td><td>63.18/0.00</td><td>52.71</td><td>52.41</td><td>-5.74/-8.51</td><td>35.73</td><td>31</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>62.99</td><td>84.77</td><td>84.42</td><td>87.50/91.16</td><td>91.63</td><td>90.03/86.41</td><td>48.01</td><td>92.16</td><td>89.49/89.28</td><td>81.23</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>63.72</td><td>84.90</td><td>84.81</td><td>87.99/91.39</td><td>91.45</td><td>90.34/86.92</td><td>51.62</td><td>92.43</td><td>89.46/89.29</td><td>81.85</td><td>550</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>62.34</td><td>84.62</td><td>84.25</td><td>87.75/91.38</td><td>91.87</td><td>89.86/86.09</td><td>47.65</td><td>91.97</td><td>89.39/89.17</td><td>81.06</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>63.51</td><td>84.70</td><td>84.71</td><td>88.73/91.99</td><td>91.73</td><td>90.25/86.74</td><td>49.82</td><td>92.09</td><td>89.34/89.08</td><td>81.62</td><td>550</td></tr></table>
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Table 4: Post training quantization result of GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ on 20 zero-shot evaluation datasets. Please see Table I.1 for the results of all 20 tasks.
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<table><tr><td>Precision (Method)</td><td>Lambada (↑)</td><td>PIQA (↑)</td><td>OpenBookQA(↑)</td><td>RTE(↑)</td><td>ReCoRd(↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td><td>Time Cost</td></tr><tr><td>W16A16</td><td>49.3</td><td>66.3</td><td>29.4</td><td>53.8</td><td>75.1</td><td>38.9</td><td>21.5</td><td>N/A</td></tr><tr><td>W8A8 (PTQ)</td><td>42.6</td><td>64.1</td><td>28.0</td><td>53.1</td><td>67.5</td><td>37.8</td><td>26.2</td><td>7 mins</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>51.0</td><td>66.5</td><td>29.2</td><td>53.4</td><td>74.9</td><td>38.7</td><td>21.7</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>51.4</td><td>30.2</td><td>52.7</td><td>16.1</td><td>28.9</td><td>1.76e5</td><td>7 mins</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>10.1</td><td>58.5</td><td>27.2</td><td>52.0</td><td>56.5</td><td>33.5</td><td>88.6</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>39.8</td><td>63.8</td><td>29.4</td><td>53.1</td><td>70.1</td><td>37.0</td><td>30.6</td><td>1.1 hours</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>10.5</td><td>57.7</td><td>28.0</td><td>52.7</td><td>55.3</td><td>33.4</td><td>92.1</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>37.4</td><td>61.8</td><td>28.2</td><td>53.1</td><td>68.5</td><td>36.6</td><td>31.1</td><td>1.1 hours</td></tr></table>
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For the more aggressive weight quantization with minimal (or no) training quantization, i.e., W4/8A16, PTQ fully loses all accuracy (pure random prediction). However, ZeroQuant can still achieve an 81.65 average score. On top of ZeroQuant, if we add our LKD, the accuracy can be further boosted to 82.35 with a cost of 31s per task using only a single GPU, which is $9 3 . 5 \mathrm { x }$ cheaper than INT8 QAT quantization. We also test ZeroQuant and ZeroQuant-LKD under the W4/8A8 quantization scheme and both of them achieve similar accuracy performance as W4/8A16. If hyper-parameter tuning is applied to LKD, ZeroQuant-LKD can achieve an 83.22 average score under W4/8A8, which is similar to QAT’s W8A8 result. Please see Appendix E for more details.
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$\mathbf { B E R T _ { l a r g e } }$ We test our methods on $\mathbf { B E R T _ { l a r g e } }$ as well and the results are shown in Table 3. Similar to $\mathrm { B E R T _ { b a s e } ^ { - } }$ , ZeroQuant achieves much better accuracy than PTQ methods. As compared to QAT methods, ZeroQuant has comparable results on larger datasets (like MNLI/QQP) and has better performance on small tasks (e.e., CoLA/MRPC/RTE). We actually tune QAT for multiple learning rates but cannot get even better performance for those small tasks (see Appendix F for more details).
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For more aggressive quantization schemes, like W4/8A16 and W4/8A8, ZeroQuant and ZeroQuantLKD still achieve good accuracy except for RTE but the model size is about $3 \mathbf { x }$ smaller than FP16 counterpart. This is aligned with the INT8 QAT results, which lose significantly more accuracy on RTE. Thanks to the lightweight cost of LKD, it only takes about 550s to finish each task even on $\mathbf { B E R T _ { l a r g e } }$ , which is $1 3 \mathrm { x }$ cheaper than QAT.
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# 5.2 Main Results of GPT-3-style Models
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$\mathbf { G P T } \mathbf { - } 3 _ { 3 5 0 \mathbf { M } }$ We first test ZeroQuant and ZeroQuant-LKD on GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ and report the result in Table 4. The first interesting finding of zero-shot evaluation on GPT-3-stype models is that the accuracy performance of accuracy-based tasks is more tolerant to quantization than generation tasks. For instance, W8A8 PTQ has a $1 . 1 \%$ average accuracy drop on 19 accuracy-based tasks as compared to 4.7 points loss on Wikitext-2. Comparing ZeroQuant with PTQ using W8A8, we can reduce the accuracy gap from $1 . 1 \%$ to $0 . 2 \%$ and the perplexity (PPL) gap from 4.7 to 0.2 with no activation range calibration cost.
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For W4/8A16 quantization scheme, PTQ can hardly predict reasonable answers for the majority of tasks and its generation performance on Wikitext-2 is fully crashed. As a comparison, ZeroQuant still achieves non-trivial performance on some tasks but its generation performance significantly degrades on Wikitext-2. LKD brings a significant performance boost for this W4/8A16 setting. Note that ZeroQuant-LKD increases the accuracy from 33.5 to 37.0 and decreases the PPL from 88.6 to 30.6 compared to ZeroQuant, and the entire cost of this is just 3.1 hours on a single A100 GPU. Note that this is about $0 . 0 2 7 \%$ GPU hours of the full pretraining cost (128 A100 GPUs for 32 hours). Similar to W4/8A16, ZeroQuant-LKD achieves much better performance than ZeroQuant on W4/8A8 by using the lightweight LKD.
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Table 5: Post training quantization result of GPT- $3 _ { 1 . 3 \mathrm { B } }$ on 20 zero-shot evaluation datasets. Please see Table I.2 for the results of all 20 tasks.
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<table><tr><td>Precision (Method)</td><td>Lambada (↑)</td><td>PIQA(↑)</td><td>OpenBookQA (↑)</td><td>RTE(↑)</td><td>ReCoRd(↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td><td>Time Cost</td></tr><tr><td>W16A16</td><td>61.3</td><td>71.4</td><td>33.6</td><td>53.1</td><td>82.6</td><td>42.4</td><td>15.3</td><td>N/A</td></tr><tr><td>W8A8 (PTQ)</td><td>54.8</td><td>67.7</td><td>16.6</td><td>54.5</td><td>75.7</td><td>40.5</td><td>18.9</td><td>13 mins</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>62.6</td><td>70.7</td><td>33.4</td><td>52.7</td><td>80.9</td><td>42.3</td><td>15.7</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>50.4</td><td>27.0</td><td>50.9</td><td>15.8</td><td>29.0</td><td>1.35e5</td><td>13 mins</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>43.9</td><td>66.5</td><td>30.0</td><td>52.7</td><td>77.3</td><td>39.38</td><td>21.9</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>59.4</td><td>69.5</td><td>31.6</td><td>52.7</td><td>79.7</td><td>41.5</td><td>17.6</td><td>3 hours</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>46.8</td><td>66.4</td><td>28.8</td><td>52.7</td><td>76.2</td><td>39.24</td><td>24.1</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>48.7</td><td>68.1</td><td>29.0</td><td>52.0</td><td>77.4</td><td>39.90</td><td>18.2</td><td>3 hours</td></tr></table>
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Table 6: The speedup of our W8A8 as compared to W16A16. We measure the end-to-end average latency for the entire BERT model, and the time reported is in milliseconds.
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<table><tr><td rowspan="2">Seq Len BS</td><td rowspan="2">Precision</td><td colspan="8">128</td><td colspan="8">256</td></tr><tr><td>2</td><td></td><td>4</td><td>8</td><td>16</td><td>16</td><td>64</td><td>128</td><td>1</td><td>2</td><td>4</td><td>8</td><td>16</td><td>16</td><td>64</td><td>128</td></tr><tr><td rowspan="3">BERTbase</td><td>W16A16</td><td>2.45</td><td>3.22</td><td>3.85</td><td>5.51</td><td>9.96</td><td>17.93</td><td>34.25</td><td>67.08</td><td>3.13</td><td>4.05</td><td>5.70</td><td>10.55</td><td>19.27</td><td>36.69</td><td>71.75</td><td>140.0</td></tr><tr><td>W8A8</td><td>1.08</td><td>1.16</td><td>1.42</td><td>1.76</td><td>2.58</td><td>3.90</td><td>6.74</td><td>12.92</td><td>1.22</td><td>1.44</td><td>2.08</td><td>2.88</td><td>4.10</td><td>7.80</td><td>14.66</td><td>28.13</td></tr><tr><td>Speedup</td><td>2.27</td><td>2.78</td><td>2.71</td><td>3.13</td><td>3.86</td><td>4.60</td><td>5.08</td><td>5.19</td><td>2.57</td><td>2.81</td><td>2.74</td><td>3.66</td><td>4.70</td><td>4.70</td><td>4.89</td><td>4.98</td></tr><tr><td rowspan="3">BERTlarge</td><td>W16A16</td><td>5.45</td><td>6.38</td><td>8.73</td><td>13.88</td><td>26.34</td><td>48.59</td><td>92.49</td><td>183.4</td><td>6.39</td><td>8.94</td><td>14.66</td><td>27.99</td><td>51.94</td><td>98.78</td><td>195.9</td><td>384.5</td></tr><tr><td>W8A8</td><td>2.08</td><td>2.58</td><td>2.84</td><td>3.79</td><td>6.21</td><td>10.28</td><td>18.86</td><td>36.62</td><td>2.55</td><td>3.36</td><td>4.16</td><td>6.88</td><td>11.61</td><td>21.20</td><td>41.24</td><td>79.90</td></tr><tr><td>Speedup</td><td>2.62</td><td>2.47</td><td>3.07</td><td>3.66</td><td>4.24</td><td>4.73</td><td>4.90</td><td>5.01</td><td>2.51</td><td>2.66</td><td>3.52</td><td>4.07</td><td>4.47</td><td>4.66</td><td>4.75</td><td>4.81</td></tr></table>
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GPT- $\mathbf { \lambda } _ { \mathbf { 3 1 . 3 B } }$ The results of GPT- $\cdot 3 _ { 1 . 3 \mathrm { B } }$ are shown in Table 5. Similar to GPT- $3 _ { 3 5 0 \mathrm { M } }$ , for W8A8, ZeroQuant has much better performance than PTQ with less no activation calibration cost, particularly for the generation task Wikitext-2 (3.2 points lower). Also, for W4/8 quantization, LKD can bring non-trivial performance gain for ZeroQuant. The cost of LKD is about $0 . 0 2 \%$ of the full pre-training cost (128 A100 GPUs for 120 hours)
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# 5.3 Latency Reduction of BERT and GPT-3-style Models
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We compare the inference speed of BERT between FP16 and our INT8 versions in Table 6 on a single 40G-A100 GPU. Using our efficient quantization kernel implementation and operator fusion, the INT8 model can achieve $2 . 2 7 { - } 5 . 1 9 \mathrm { x }$ speedup on $\mathbf { B E R T _ { b a s e } }$ and $2 . 4 7 { - } 5 . 0 1 \mathrm { x }$ on $\mathbf { B E R T _ { l a r g e } }$ .
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We also include the latency comparison of GPT-3-style models between FP16 and our INT8 version. Particularly, we use the model to generate the first 50 tokens based on a given text and measure the average latency. Our INT8 model leads to $4 . 1 6 \mathrm { x } / 4 . 0 6 \mathrm { x }$ speedup for $\mathrm { G P T } { - } 3 _ { 3 5 0 \mathrm { M } } / \mathrm { G P T } { - } 3 _ { 1 . 3 \mathrm { B } }$ as compared to the FP16 counterpart.
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# 5.4 A Showcase of GPT- $\mathbf { J _ { 6 B } }$ and GPT-NeoX20B
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To demonstrate the scalability of ZeroQuant, we applied it to two of the largest open-sourced models, i.e., $\mathrm { G P T - J _ { 6 B } }$ and G $\mathrm { P T } \mathrm { - N e o } X _ { 2 0 \mathrm { B } }$ , which have 6B and 20B parameters separately.
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We report the results of $\mathrm { G P T - J _ { 6 B } }$ in Table 7 on three generation datasets, i.e., PTB [42], Wikitext-2, and Wikitext-103 [43]. As can be seen, as compared to FP16 precision, ZeroQuant achieves similar PPL on all three different tasks. To compare the latency, we again use the average latency number to generate the first 50 tokens. Our W8A8 can get up to $3 . 6 7 \mathrm { x }$ speedup compared to the FP16 version.
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To quantize GPT- $\mathrm { \cdot N e o X _ { 2 0 B } }$ to W8A8 for all GeMMs, the accuracy significantly decreases. We retrieve the quantization of each weight matrix and of each activation, and finally find out that the activation quantization for the attention calculation (i.e., the input of self-attention) causes the accuracy loss. We conjecture that this is because of the sensitivity of the self-attention module for extra-large models (20B) but cannot verify this for other models due to the lack of open-sourced extra-large models and the full evaluation pipeline. As such, we leave the input activation for self-attention in FP16 and quantize the rest to INT8. The results are shown in Table 8. Our W8A8/16 achieves similar accuracy performance but can reduce both the GPU resource requirement (from 2 A100 GPUs to 1) and the latency from $6 5 \mathrm { m s }$ to $2 5 \mathrm { m s }$ , which together lead to $5 . 2 \mathrm { x }$ better throughput/efficiency.
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# 5.5 Ablation Study of Different Components
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To investigate the performance gain of each component we introduced in Section 4, i.e., group-wise weight quantization, token-wise activation quantization, and lightweight layer-by-layer knowledge distillation, we here do an ablation study on $\mathbf { B E R T _ { l a r g e } }$ with W4/8A8.
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Table 7: Post training quantization result of GPT$\mathrm { J } _ { 6 \mathrm { B } }$ on three zero-shot generation tasks
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<table><tr><td>Precision PTB</td><td>Wikitext-2 Wikitext-103</td><td></td><td>Latency</td></tr><tr><td>W16A16 20.47</td><td>10.35</td><td>10.35</td><td>29.13ms (1x)</td></tr><tr><td>W8A8 20.97</td><td>10.51</td><td>10.52</td><td>7.94ms (3.67x)</td></tr></table>
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Table 8: Post training quantization result of GPTNeoX20B on 19 zero-shot evaluation datasets. Please see Table I.4 for the results of all 19 tasks.
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<table><tr><td colspan="4">Precision Lambada PIQA Ave.19 Tasks Latency</td></tr><tr><td>W16A16</td><td>71.7 77.7</td><td>50.5</td><td>2×65ms (1x)</td></tr><tr><td>W8A8/16</td><td>71.9 78.3</td><td>50.4</td><td>1×25ms (5.2x)</td></tr></table>
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Table 9: Ablation study of different components for $\mathbf { B E R T _ { l a r g e } }$ on the development set of GLUE. The quantization scheme used here is W4/8A8. Here, GQ is the abbreviation of group-wise weight quantization, TQ is the abbreviation of token-wise activation quantization.
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<table><tr><td>GQ</td><td>TQ</td><td>LKD</td><td>CoLA</td><td>MNLI-m</td><td>MNLI-mm</td><td>MRPC</td><td>QNLI</td><td>QQP</td><td>RTE</td><td>SST-2</td><td>STS-B</td><td>Ave.</td></tr><tr><td></td><td></td><td>X</td><td>-0.79</td><td>33.07</td><td>32.94</td><td>68.38/80.54</td><td>49.42</td><td>63.18/0.00</td><td>52.71</td><td>52.29</td><td>-4.27/-1.90</td><td>35.85</td></tr><tr><td></td><td></td><td>X</td><td>59.81</td><td>66.63</td><td>68.79</td><td>68.63/71.17</td><td>83.87</td><td>78.24/61.30</td><td>46.93</td><td>89.45</td><td>54.58/32.52</td><td>66.52</td></tr><tr><td>x</</td><td>xx/</td><td>X</td><td>62.34</td><td>84.62</td><td>84.25</td><td>87.75/91.38</td><td>91.87</td><td>89.86/86.09</td><td>47.65</td><td>91.97</td><td>89.39/89.17</td><td>81.06</td></tr><tr><td>√</td><td>√</td><td>√</td><td>63.51</td><td>84.70</td><td>84.71</td><td>88.73/91.99</td><td>91.73</td><td>90.25/86.74</td><td>49.82</td><td>92.09</td><td>89.34/89.08</td><td>81.62</td></tr></table>
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Table 10: Post training quantization result of GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ on 20 zero-shot evaluation datesets The quantization scheme here is W4/8A8. Please see Table I.3 for the results of all 20 tasks.
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<table><tr><td>Method</td><td>Data Resource</td><td>Lambada (↑)</td><td>PIQA (↑)</td><td>OpenBookQA (↑)</td><td>RTE(↑)</td><td>ReCoRd (↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td></tr><tr><td>ZeroQuant</td><td></td><td>10.5</td><td>57.7</td><td>28.0</td><td>52.7</td><td>55.3</td><td>33.4</td><td>92.1</td></tr><tr><td>ZeroQuant-LKD</td><td>Random data</td><td>26.1</td><td>59.3</td><td>29.2</td><td>50.5</td><td>64.9</td><td>34.5</td><td>40.6</td></tr><tr><td>ZeroQuant-LKD</td><td>Wikipedia</td><td>33.9</td><td>62.4</td><td>28.0</td><td>52.7</td><td>69.5</td><td>36.2</td><td>30.4</td></tr><tr><td>ZeroQuant-LKD</td><td>Original data</td><td>37.4</td><td>61.8</td><td>28.2</td><td>53.1</td><td>68.5</td><td>36.6</td><td>31.1</td></tr></table>
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We present the results in Table 9. As can be seen, group-wise weight quantization boosts the accuracy (random-guess prediction) from PTQ to a non-trivial result (66.52). Further adding token-wise quantization improves 14.54 points accuracy performance. On top of those (i.e., ZeroQuant), LKD further brings a 0.56 point gain.
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# 5.6 No Access to The Original Training Data
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As mentioned in previous sections, the original training data are oftentimes hard to access due to the privacy and/or confidential issues. Therefore, we here study the performance of our LKD when there is no direct access to the original training data. As the distillation objective of our LKD does not depend on the label, the training data used for LKD can be very flexible.
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We compare the performance of GPT- $\cdot 3 _ { 3 5 0 \mathrm { M } }$ on W4/8A8 quantization scheme using three different training data resources, i.e., random data (using random integer number to generate token ids), Wikipedia (using Huggingface to get the data2), and original PILE dataset.
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The results are shown in Table 10. Compared to ZeroQuant, LKD using random data can boost the accuracy by $1 . 1 \%$ and reduce the PPL from 92.1 to 40.6. The reason why random data can still significantly improve the performance is that LKD does not optimize the end-to-end pipeline and it only layer-by-layer learns the internal dependency from the teacher model. Therefore, random data can also provide meaningful information. Using Wikipedia data from Huggingface can further improve the accuracy to 36.2 and reduce the PPL to 30.4, which is comparable to the results using the original data. This indicates that a clean text dataset can be used for LKD when we do not have access to the original full dataset.
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# 6 Conclusions
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With the rapid growth of large model sizes, we have reach a point to consider how to serve those models in practice. Although several works demonstrate that post-training quantization can be applied to BERT models, to the best of our knowledge, there have been no existing works on (1) billion-scale GPT-3-style models, (2) ultra-low precision post-training quantization, and (3) end-to-end solution of how to efficiently serve the quantized model online. In this work, we offer fine-grained compression schemes for both weight and activations to enable INT8 quantization for up to 20B-scale models ( $\mathrm { \bf J P T - N e o X } _ { 2 0 \mathrm { B } }$ ). We also offer a novel affordable layer-by-layer knowledge distillation for ultra-low precision quantization, which leads to $3 \mathbf { x }$ model size reduction compared to FP16 model while achieving minimal accuracy degradation. Furthermore, we provide a system backend support and show up to $5 . 1 9 \mathrm { x }$ speedup on BERT models and $5 . 2 \mathrm { x }$ better efficiency on GPT-NeoX20B.
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[69] Wenhui Wang, Furu Wei, Li Dong, Hangbo Bao, Nan Yang, and Ming Zhou. Minilm: Deep self-attention distillation for task-agnostic compression of pre-trained transformers. arXiv preprint arXiv:2002.10957, 2020.
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[70] Alex Warstadt, Amanpreet Singh, and Samuel R Bowman. Neural network acceptability judgments. arXiv preprint arXiv:1805.12471, 2018.
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[71] Adina Williams, Nikita Nangia, and Samuel Bowman. A broad-coverage challenge corpus for sentence understanding through inference. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long Papers), pages 1112–1122, 2018.
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[72] Adina Williams, Tristan Thrush, and Douwe Kiela. Anlizing the adversarial natural language inference dataset. arXiv preprint arXiv:2010.12729, 2020.
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[73] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, et al. HuggingFace’s Transformers: State-of-the-art natural language processing. ArXiv, pages arXiv–1910, 2019.
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[74] Hao Wu, Patrick Judd, Xiaojie Zhang, Mikhail Isaev, and Paulius Micikevicius. Integer quantization for deep learning inference: Principles and empirical evaluation. arXiv preprint arXiv:2004.09602, 2020.
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[75] Vikas Yadav, Steven Bethard, and Mihai Surdeanu. Quick and (not so) dirty: Unsupervised selection of justification sentences for multi-hop question answering. arXiv preprint arXiv:1911.07176, 2019.
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[76] Zhewei Yao, Linjian Ma, Sheng Shen, Kurt Keutzer, and Michael W Mahoney. Mlpruning: A multilevel structured pruning framework for transformer-based models. arXiv preprint arXiv:2105.14636, 2021.
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[77] Ali Hadi Zadeh, Isak Edo, Omar Mohamed Awad, and Andreas Moshovos. Gobo: Quantizing attention-based nlp models for low latency and energy efficient inference. In 2020 53rd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO), pages 811–824. IEEE, 2020.
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[78] Ofir Zafrir, Guy Boudoukh, Peter Izsak, and Moshe Wasserblat. Q8BERT: Quantized 8bit bert. arXiv preprint arXiv:1910.06188, 2019.
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[79] Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. Hellaswag: Can a machine really finish your sentence? arXiv preprint arXiv:1905.07830, 2019.
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[80] Sheng Zhang, Xiaodong Liu, Jingjing Liu, Jianfeng Gao, Kevin Duh, and Benjamin Van Durme. Record: Bridging the gap between human and machine commonsense reading comprehension. arXiv preprint arXiv:1810.12885, 2018.
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| 297 |
+
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| 298 |
+
# Checklist
|
| 299 |
+
|
| 300 |
+
1. For all authors...
|
| 301 |
+
|
| 302 |
+
(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
|
| 303 |
+
(b) Did you describe the limitations of your work? [Yes] Please see Appendix H.
|
| 304 |
+
(c) Did you discuss any potential negative societal impacts of your work? [N/A] ZeroQuant a common machine learning technique.
|
| 305 |
+
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
|
| 306 |
+
|
| 307 |
+
2. If you are including theoretical results...
|
| 308 |
+
|
| 309 |
+
(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
|
| 310 |
+
|
| 311 |
+
3. If you ran experiments...
|
| 312 |
+
|
| 313 |
+
(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] We have very comprehensive experimental details in Appendix A.
|
| 314 |
+
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] All details are in Appendix A.
|
| 315 |
+
(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [N/A] Our results are based on a single set of hyperparameters. So it does not rely on the randomness. However, we do provide a tuning results in Appendix E.
|
| 316 |
+
(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] Those are in Appendix A.
|
| 317 |
+
|
| 318 |
+
4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
|
| 319 |
+
|
| 320 |
+
(a) If your work uses existing assets, did you cite the creators? [Yes] We cited all dataset and github repository used in the paper.
|
| 321 |
+
(b) Did you mention the license of the assets? [N/A]
|
| 322 |
+
(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]
|
| 323 |
+
(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]
|
| 324 |
+
(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
|
| 325 |
+
|
| 326 |
+
5. If you used crowdsourcing or conducted research with human subjects...
|
| 327 |
+
|
| 328 |
+
(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
|
| 329 |
+
(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
|
| 330 |
+
(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
|
parse/dev/f-fVCElZ-G1/f-fVCElZ-G1_content_list.json
ADDED
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|
| 1 |
+
[
|
| 2 |
+
{
|
| 3 |
+
"type": "text",
|
| 4 |
+
"text": "ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers ",
|
| 5 |
+
"text_level": 1,
|
| 6 |
+
"bbox": [
|
| 7 |
+
191,
|
| 8 |
+
122,
|
| 9 |
+
813,
|
| 10 |
+
172
|
| 11 |
+
],
|
| 12 |
+
"page_idx": 0
|
| 13 |
+
},
|
| 14 |
+
{
|
| 15 |
+
"type": "text",
|
| 16 |
+
"text": "Zhewei Yao⇤ , Reza Yazdani Aminabadi, Minjia Zhang, Xiaoxia Wu, Conglong Li, Yuxiong He ",
|
| 17 |
+
"bbox": [
|
| 18 |
+
186,
|
| 19 |
+
224,
|
| 20 |
+
831,
|
| 21 |
+
241
|
| 22 |
+
],
|
| 23 |
+
"page_idx": 0
|
| 24 |
+
},
|
| 25 |
+
{
|
| 26 |
+
"type": "text",
|
| 27 |
+
"text": "Microsoft {zheweiyao, yazdani.reza, minjiaz, xiaoxiawu, conglong.li, yuxhe}@microsoft.com ",
|
| 28 |
+
"bbox": [
|
| 29 |
+
207,
|
| 30 |
+
247,
|
| 31 |
+
816,
|
| 32 |
+
275
|
| 33 |
+
],
|
| 34 |
+
"page_idx": 0
|
| 35 |
+
},
|
| 36 |
+
{
|
| 37 |
+
"type": "text",
|
| 38 |
+
"text": "Abstract ",
|
| 39 |
+
"text_level": 1,
|
| 40 |
+
"bbox": [
|
| 41 |
+
462,
|
| 42 |
+
310,
|
| 43 |
+
535,
|
| 44 |
+
327
|
| 45 |
+
],
|
| 46 |
+
"page_idx": 0
|
| 47 |
+
},
|
| 48 |
+
{
|
| 49 |
+
"type": "text",
|
| 50 |
+
"text": "How to efficiently serve ever-larger trained natural language models in practice has become exceptionally challenging even for powerful cloud servers due to their prohibitive memory/computation requirements. In this work, we present an efficient and affordable post-training quantization approach to compress large Transformer-based models, termed as ZeroQuant. ZeroQuant is an end-to-end quantization and inference pipeline with three main components: (1) a fine-grained hardware-friendly quantization scheme for both weight and activations; (2) a novel affordable layer-by-layer knowledge distillation algorithm (LKD) even without the access to the original training data; (3) a highly-optimized quantization system backend support to remove the quantization/dequantization overhead. As such, we are able to show that: (1) ZeroQuant can reduce the precision for weights and activations to INT8 in a cost-free way for both BERT and GPT-3-style models with minimal accuracy impact, which leads to up to $5 . 1 9 \\mathrm { x } / 4 . 1 6 \\mathrm { x }$ speedup on those models compared to FP16 inference; (2) ZeroQuant plus LKD affordably quantize the weights in the fully-connected module to INT4 along with INT8 weights in the attention module and INT8 activations, resulting in $3 \\mathbf { x }$ memory footprint reduction compared to the FP16 model; (3) ZeroQuant can be directly applied to two of the largest open-sourced language models, including $\\mathrm { G P T - J _ { 6 B } }$ and GPT- $\\mathrm { \\cdot N e o X _ { 2 0 B } }$ , for which our INT8 model achieves similar accuracy as the FP16 model but achieves up to $5 . 2 \\mathrm { x }$ better efficiency. ",
|
| 51 |
+
"bbox": [
|
| 52 |
+
233,
|
| 53 |
+
340,
|
| 54 |
+
764,
|
| 55 |
+
617
|
| 56 |
+
],
|
| 57 |
+
"page_idx": 0
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"type": "text",
|
| 61 |
+
"text": "1 Introduction ",
|
| 62 |
+
"text_level": 1,
|
| 63 |
+
"bbox": [
|
| 64 |
+
174,
|
| 65 |
+
641,
|
| 66 |
+
310,
|
| 67 |
+
659
|
| 68 |
+
],
|
| 69 |
+
"page_idx": 0
|
| 70 |
+
},
|
| 71 |
+
{
|
| 72 |
+
"type": "text",
|
| 73 |
+
"text": "Large-scale natural language models have been widely adopted in different applications, e.g., natural language understanding using BERT [64] and generation tasks using GPT-style models [49]. Although those models have achieved cutting-edge accuracy results, as the model size keeps increasing dramatically, the requirements of memory footprint and the computational cost to deploy them become a major bottleneck, even on cloud servers with powerful GPU devices. ",
|
| 74 |
+
"bbox": [
|
| 75 |
+
174,
|
| 76 |
+
672,
|
| 77 |
+
823,
|
| 78 |
+
741
|
| 79 |
+
],
|
| 80 |
+
"page_idx": 0
|
| 81 |
+
},
|
| 82 |
+
{
|
| 83 |
+
"type": "text",
|
| 84 |
+
"text": "One promising way to alleviate this challenge is quantization, which can reduce the bit precision for both weight and activations for lower memory footprint and faster compute (e.g., INT8 Tensor cores on T4/A100). However, quantization usually requires retraining (also known as quantization aware training, or QAT in short) to recover the accuracy degradation from representation loss of weight and activations. To enable QAT, the full training pipeline is usually required, including the training data and compute resources, to finetune the model. Access to those components is now oftentimes not available, and QAT is also a time-consuming process, particularly for those large-scale models. ",
|
| 85 |
+
"bbox": [
|
| 86 |
+
174,
|
| 87 |
+
747,
|
| 88 |
+
825,
|
| 89 |
+
845
|
| 90 |
+
],
|
| 91 |
+
"page_idx": 0
|
| 92 |
+
},
|
| 93 |
+
{
|
| 94 |
+
"type": "text",
|
| 95 |
+
"text": "Recently, zero-shot quantization [10, 47] and post-training quantization (PTQ) [46, 39] are proposed to address the training-data access and compute requirement challenges since PTQ generally requires no (or minimal) retraining. But most of those works primarily focus on computer vision problems on relatively small scales. More recently, [7] shows promising PTQ results on BERT. However, (1) its main focus is on high-precision quantization (INT8/FP16) on $\\mathbf { B E R T _ { b a s e } }$ , (2) it does not consider other billion-scale generative models (GPT-3-style models [9]). More importantly, most of these works do not report real latency improvement, putting the usefulness of these methods in improving inference latency into question. For example, existing work often do not discuss the quantization/dequantization cost associated with different quantization schemes, which in fact has a big impact to the performance benefit of using low precision. ",
|
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"text": "Besides, for extreme quantization (e.g., INT4), knowledge distillation is usually used to boost performance, which adds another source of expensive computation cost as compared to QAT. Furthermore, in order to achieve better accuracy performance, hidden-states knowledge distillation, e.g., [3, 81], is usually applied for the quantized model. This would put significant pressure on the GPU memory and the compute resource requirement since both the teacher and student models needed to be loaded into the GPU memory for training. ",
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"text": "In this paper, we present ZeroQuant, an end-to-end post-training quantization and inference pipeline, to address those challenges, targeting both INT8 and INT4/INT8 mixed-precision quantization. Specifically, our contributions are: ",
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"text": "• We apply fine-grained hardware-friendly quantization schemes on both weight and activations, i.e., group-wise quantization for weight and token-wise quantization for activations. Both quantization schemes can significantly reduce the quantization error and retain hardware acceleration properties. \n• We propose a novel layer-by-layer knowledge distillation method (LKD) for INT4/INT8 mixedprecision quantization, where the neural network is quantized layer-by-layer through distillation with minimal iterations and even without the access to the original training data. As such, at any given moment, the device memory is primarily populated only with a single extra layer’s footprint, making billion-scale model distillation feasible with limited training budget and GPU devices. \n• We develop a highly optimized inference backend, which eliminates the expensive computation cost of quantization/dequantization operators, enabling latency speedups on INT8 Tensor cores on modern GPU hardware. \n• Our empirical results show that: – ZeroQuant enables quantizing BERT and GPT-3-style models into INT8 weight and activations to retain accuracy without incurring any retraining cost. Compared to FP16 inference, our INT8 model achieves up to $5 . 1 9 \\mathrm { x } / 4 . 1 6 \\mathrm { x }$ speedup on $\\mathrm { B E R T _ { b a s e } / G P T } { - 3 _ { 3 5 0 \\mathrm { M } } }$ on A100 GPUs. ZeroQuant plus LKD can do INT4/INT8 mixed-precision quantization for BERT and GPT3-style models. This results in a $3 \\mathbf { x }$ memory footprint reduction with marginal accuracy loss as compared to the FP16 model. Also, thanks to the lightweight of LKD, we can finish the quantization process in 33s (10 minutes) for $\\mathbf { B E R T _ { b a s e } }$ $\\mathrm { ( B E R T _ { l a r g e } } ,$ ). We also demonstrate that LKD can use other datasets to achieve similar performance to the original training data. We demonstrate the scalability of ZeroQuant on two of the largest open-sourced language models, i.e, $\\mathrm { G P T - J _ { 6 B } }$ and GPT- $\\mathrm { N e o X } _ { 2 0 \\mathrm { B } }$ , with INT8 quantization. ZeroQuant can achieve $3 . 6 7 \\mathrm { x }$ speedup over the FP16 model for $\\mathrm { G P T - J _ { 6 B } }$ and (2) reduce the GPU requirement for inference from 2 to 1 and latency from $6 5 \\mathrm { m s }$ to $2 5 \\mathrm { m s }$ for GPT- $\\mathrm { \\cdot N e o X _ { 2 0 B } }$ (i.e., $5 . 2 \\mathrm { x }$ better system efficiency in total). ",
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"type": "text",
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"text": "2 Related Work ",
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"text": "Model compression has been explored from different aspects [26, 38, 40, 35, 44, 21, 25, 51, 19, 76, 41, 27, 56, 60, 29, 61, 69, 34, 15, 39, 32]. Among those, quantization is one of the most promising directions as it directly reduces the memory footprint and compute intensity. Here, we focus on quantization for NLP models and briefly discuss the related work. ",
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"text": "The majority of quantization works can be categorized into quantization-aware training (QAT). [57, 78] are the first few works to quantize BERT models using integer numbers for both weight and activations. Particularly, [57] utilizes Hessian information to push the weight bit-precision to even INT2/INT4, and it also proposes group-wise quantization to quantize the weight matrix in a more fine-grained granularity compared to single matrix quantization. [22] introduces quantization noise to alleviate the variations of QAT. [81, 3] leverage very expensive knowledge distillation [27] and data augmentation [29] to ternarize/binarize weights. [30] combines knowledge distillation [29] and learned step size quantization [20] to quantize the weight to 2–8 bits. Recently, [62] also uses knowledge distillation to compress GPT-2 models on task-specific problems to INT2. All those works quantize models using the original training datasets. More importantly they need retraining or finetuning the full model to recover the accuracy, and such compute cost on extra-large models, like [58, 12], can be hardly affordable for most research labs or practitioners. ",
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"text": "One solution to overcome the compute cost challenge is post-training quantization (PTQ). However, PTQ often induces a significant drop in accuracy because the network can be sensitive to quantization errors. Along this line, one of the first works applied to Transformer-based [65] models is [77]. The authors introduce centroid-based quantization method, where outlier numbers use FP32 format and the rest numbers are quantized using non-uniform quantization. As such, it is hard to get the real inference latency benefit on general compute accelerators, e.g., CPU and GPU, because the parallel processing units in these hardware do not support efficient computation of mixed data types. More recently, [7] introduces high-precision activation quantization (FP16) for part of the model to overcome the high dynamic activation ranges. However, to the best of our knowledge, (1) How to apply PTQ on GPT-3-style models while achieving high accuracy has not been studied in any of previous work yet; (2) How to apply PTQ on billion (or even a dozen of billions) scale model is still under-explored; (3) Efficient inference system backend is still missing, especially for fine-grained quantization schemes, making it hard to achieve low latency on commodity hardware. ZeroQuant resolves all those limitations by considering the system backend into the algorithm design and we verify its capability on both BERT and large-scale GPT-3-style (up to 20 billion, i.e., GP $\\left[ - \\mathrm { N e o } \\mathrm { X } _ { 2 0 \\mathrm { B } } \\right]$ ) models for various tasks. ",
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"text": "3 Background and Challenge ",
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"text": "3.1 Transformer Architecture ",
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"text": "The transformer architecture usually has three components: an embedding layer, a stack of encoder/decoder layers, and a final classifier. In this paper, we focus on quantizing the encoder/decoder layers, i.e., the transformer block, because it is often the most memory and compute intensive components in the entire architecture. With a transformer block, there are two sub-layers, the multi-head self-attention (MHSA) and the feed-forward connection (FFC). We give a short review later and please refer to [65] for more details. At high level, transformer models can be broadly categorized to three branches: encoder-only models (BERT) [64], decoder-only models (GPT-3-style) [49], and encoder-decoder models (T5) [50]. In this paper, we focus on encoder-only and decoder-only models but our approach can be applied to encoder-decoder models as well. ",
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"img_path": "images/e003d37e3d482fcd798a0d8e7d1be94febcf5048398aca175c49b7a253357071.jpg",
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"image_caption": [
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"Figure 1: The illustration of a Transformer-block. "
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"text": "Transformer Block Assume the input of an encoder layer is $\\boldsymbol { X }$ , the query, key, value, attention output, FFC dense, and FFC output matrices are $W _ { q }$ , $W _ { k }$ , $W _ { v }$ , $W _ { o }$ , $W _ { h - 4 h }$ , and $W _ { 4 h - h }$ , respectively. Then the forward propagation of a transformer-block is illustrated in Figure 1, where LN is the layer normalization, Softmax is the softmax operator, and GeLU is the activation function. ",
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"type": "text",
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"text": "3.2 Quantization Background ",
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"type": "text",
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"text": "Quantization maps high-precision numbers, e.g., FP16/FP32, to its low-precision counterpart, e.g., INT4/INT8, to reduce the model footprint and improve the compute performance. In this work, we use uniform symmetric scalar quantizers. That is to say, if we have a vector/matrix, $\\mathbf { x }$ , the quantization is applied as ",
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"type": "equation",
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"img_path": "images/e1035b012a5333f4a730c48890985a9581d33c82e401db1200e513dc168af1f9.jpg",
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"text": "$$\n\\mathbf { x } _ { q u a n t i z e } = r o u n d \\left( c l a m p ( \\frac { \\mathbf { x } } { S } , - 2 ^ { b i t - 1 } , 2 ^ { b i t - 1 } - 1 ) \\right) ,\n$$",
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"type": "table",
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"img_path": "images/f1291b3aec0429be45d4ac807c5c02f4bb3eced1d829c0ebd9852ea83612fd08.jpg",
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"table_caption": [
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"Table 1: Post training quantization results of GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ on 20 zero-shot evaluation datesets. Here WxAy means x-/y-bit for weight/activation. Particularly, for W4/8, we quantize the MHSA’s weight to INT8 and FFC’s weight to INT4. Please see Table I.1 for the results of all 20 tasks. "
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"table_footnote": [],
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"table_body": "<table><tr><td>Precision</td><td>Lambada (↑)</td><td>PIQA (↑)</td><td>OpenBookQA(↑)</td><td>RTE (↑)</td><td>ReCoRd (↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td></tr><tr><td>W16A16</td><td>49.3</td><td>66.3</td><td>29.4</td><td>53.8</td><td>75.1</td><td>38.9</td><td>21.5</td></tr><tr><td>W8A16</td><td>49.3</td><td>66.1</td><td>29.6</td><td>54.2</td><td>74.8</td><td>38.5</td><td>22.1</td></tr><tr><td>W16A8</td><td>44.7</td><td>64.8</td><td>28.2</td><td>52.7</td><td>69.2</td><td>37.8</td><td>24.6</td></tr><tr><td>W8A8</td><td>42.6</td><td>64.1</td><td>28.0</td><td>53.1</td><td>67.5</td><td>37.8</td><td>26.2</td></tr><tr><td>W4/8A16</td><td>0.00</td><td>51.4</td><td>30.2</td><td>52.7</td><td>16.1</td><td>28.9</td><td>1.76e5</td></tr></table>",
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"text": "where bit is the number of bit we use to represent the quantized value, and $S$ is the scaling factor. For weight matrix quantization, $S$ is generally computed as $S = m a x \\left( a b s ( \\mathbf { x } ) \\right)$ , since the weight matrix is static during inference. On the other hand, activations’ range is dynamic during inference so that an accurate $S$ requires dynamic calculation during inference. However, to achieve best latency reduction, coarse-grained static quantization is usually applied in practice, where $S$ is calibrated using training data (e.g., momentum based averaging) and fixed during inference [24]. Although static quantization achieves better latency reduction, it also limits the quantization representation for activations, which is discussed below. ",
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"type": "text",
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"text": "3.3 Post Training Quantization ",
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"type": "text",
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"text": "Post-training quantization (PTQ) exhibits great compression efficiency compared to quantizationaware training (QAT) since PTQ is usually applied to quantize the model without retraining. A common strategy of PTQ is to feed the training data to the network and calibrate the scaling factor, $S$ , using the running mean. Please see Appendix A.1 for more details. ",
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"text": "Some work has been done for $\\mathbf { B E R T _ { b a s e } }$ models [7] with INT8 weight and mixed INT8/FP16 activation quantization. However, there is no investigation for (1) even lower bit-precision PTQ on BERT models and (2) large-scale GPT-3-style models. Here, we briefly discuss the challenge of the application of PTQ on both BERT (in Appendix C) and GPT-3-style models. ",
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"img_path": "images/a2dca122815f99ddb040d073632b2d126537cbeebb4ffb4d6b36b423bca5a255.jpg",
|
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"image_caption": [
|
| 366 |
+
"Figure 2: The activation range (left) and row-wise weight range of the attention output matrix (right) of different layers on the pretrained GPT- $3 _ { 3 5 0 \\mathrm { M } }$ . See Figure C.1 for the results of $\\mathbf { B E R T _ { b a s e } }$ . "
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"type": "text",
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"text": "The results of $\\mathrm { G P T } { \\cdot } 3 _ { 3 5 0 \\mathrm { M } }$ with PTQ are shown in Table 1. As can be seen, the INT8 activation quantization (i.e., the row of W16A8) causes the primary accuracy loss. Further pushing the weight to INT8 (i.e., the row of W8A8) does not change the accuracy of zero-shot evaluation tasks but leads the causal language modeling task (Wikitext-2) to worse perplexity score, which demonstrates the sensitivity of generation tasks as compared to other zero-shot evaluation problems. For W4/8A16, on some accuracy-based tasks, GPT- $3 _ { 3 5 0 \\mathrm { M } }$ still achieves reasonable performance like OpenBookQA but it loses accuracy on the majority of the rest tasks. Particularly, for Wikitext-2, GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ with W4/8A16 cannot generate any meaningful text anymore. Please also see Appendix C for the analysis for BERT. ",
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"type": "text",
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"text": "Dynamic Activation Range To investigate why INT8 activation leads to significant accuracy drop for both BERT and GPT-3-style models, we plot the token-wise (i.e., the hidden state of each token) range of each activation for different transformer layers of GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ in Figure 2 (left). As can be seen, different tokens have dramatically different activation ranges. For example, the maximum range of the last layer is around 35 but the minimum range is close to 8. This larger variance in the activation range makes it difficult to use a fixed quantization range (usually the maximum value) for all tokens to retain the prediction accuracy, because the limited representation power for small range tokens is going to hurt the accuracy performance. ",
|
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"type": "text",
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"text": "",
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"bbox": [
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"type": "text",
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"text": "Different Ranges of Neurons in Weight Matrices Similarly, we plot the row-wise (i.e., the output dimension) weight range of the attention output matrix $( W _ { o } )$ of GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ in Figure 2 (right). There is a $1 0 \\mathrm { x }$ difference between the largest magnitudes of different rows and this leads to the worse generation performance of the INT8 weight PTQ. This also makes it very challenging when INT4 quantization is applied as the INT4 only has 16 numbers and a $1 0 \\mathrm { x }$ smaller range leads to 2 (or 3) numbers for the representations of those smaller-range rows. ",
|
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"text": "This analysis results also indicate why more expensive hidden-states knowledge distillation [3, 37] is used for ultra-low precision quantization to close the accuracy gap. However, as the training cost of knowledge distillation for large-scale models is too high, a lightweight and efficient method is desirable for PTQ. ",
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"type": "text",
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"text": "4 Methodology ",
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"type": "text",
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"text": "4.1 Fine-grained Hardware-friendly Quantization Scheme ",
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"text": "As shown in Section 3, even applying INT8 PTQ to BERT/GPT-3-style models leads to significant accuracy degradation. The key challenge is the representation of INT8 cannot fully capture the different numerical ranges of different rows in weight matrices and different activation tokens. One way to address this is to use group-wise (token-wise) quantization for the weight matrix (activations). ",
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"type": "text",
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"text": "Group-wise Quantization for Weights Group-wise weight matrix quantization has first been proposed in [57], where a weight matrix $\\mathbf { W } \\in \\mathbb { R } ^ { n \\times m }$ is partitioned in to $g$ groups, and each group is quantized separately. However, in [57], the authors only apply this for quantization aware training. More importantly, they do not consider the hardware efficiency constraint and they do not have a system backend support. As such, they lack the real latency reduction benefit. ",
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"type": "text",
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| 480 |
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"text": "In our design, we consider the hardware constraint from Ampere Architecture of GPUs (e.g, A100), where the compute unit is based on Warp Matrix Multiply and Accumulate (WMMA) tiling size [54] to achieve the best speedup. Later, we will show that our group-wise quantization leads to much better accuracy as compared to single-matrix quantization due to its finer-granularity quantization while still achieving great latency reduction. ",
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"type": "text",
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"text": "Token-wise Quantization for Activations As mentioned in Section 3 and Appendix 3.2, a common practice for existing PTQ work is to use static quantization for activation, where the min/max range is calculated at an offline calibration phase. Such a method might be sufficient for small scale models where the variance in the activation range is small. However, as analyzed in Section 3, there is a huge variance in the activation range for large-scale transformer models such as GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ and $\\mathbf { B E R T _ { b a s e } }$ . As such, a static quantization scheme (often applied to all tokens/samples) would lead to significant accuracy drop. One natural idea to overcome this issue is to adopt finer-grained token-wise quantization and dynamically calculate the min/max range for each token to reduce the quantization error from activations. Our evaluation in Section 5 also shows that token-wise quantization for activation significantly improves the accuracy of GPT-3-style and BERT models. ",
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"type": "text",
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"text": "However, directly applying token-wise quantization using existing DL frameworks, such as the PyTorch quantization suite, would lead to significant quantization and dequantization cost because token-wise quantization introduces additional operations that lead to expensive data movement overhead between the GPU compute units and the main memory. To address this issue, we build a highly optimized inference backend for token-wise quantization of transformer models. For example, the inference backend of ZeroQuant employs so called kernel fusion technique to fuse quantization operator with its previous operator, like layer normalization, to alleviate the data movement cost from token-wise quantization. Similarly, the dequantization cost of the different GeMMs’ output is alleviated by scaling the INT32 accumulation using both the weight and activation quantization scales, before writing the final FP16 result back to the main memory for the next FP16 operator (like GeLU). Those optimization will be discussed in more details in Section 4.3. ",
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{
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| 512 |
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"type": "image",
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"img_path": "images/b7ccdd045c7c258ea47e1bc5b9ae3005151b5c70d2d84b32df1fe7bed308ab3f.jpg",
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| 514 |
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"image_caption": [
|
| 515 |
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"Figure 3: The illustration of normal (left) and our fused (right) INT8 GeMM. "
|
| 516 |
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],
|
| 517 |
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|
| 518 |
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"text": "Token-wise quantization can significantly reduce the representation error for quantized activations. Also, as it does not need to calibrate the activation range, later we will show that there is no quantization-related cost (e.g., activation range calibration) for a moderate quantization scheme (INT8 weight with INT8 activation) for ZeroQuant. ",
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"text": "4.2 Layer-by-layer Knowledge Distillation with Affordable Cost ",
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"text_level": 1,
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"type": "text",
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"text": "Knowledge distillation (KD) is one of the most powerful methods to alleviate the accuracy degradation after model compression. However, there are several limitations of KD, especially for hidden-states KD on large-scale language models: (1) KD needs to hold a teacher and a student model together during the training, which dramatically increases the memory and compute cost; (2) KD usually requires full training of the student model. Therefore, several copies (gradient, first/second order momentum) of the weight parameters need to be stored in memory to update the model; (3) KD generally requires original training data, which sometimes are not accessible due to privacy/confidential issues. ",
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"type": "text",
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"text": "To address those limitations, we present our layer-by-layer distillation (LKD) algorithm. Assume the target model for quantization has $N$ transformer blocks, $L _ { 1 } , . . . , L _ { N }$ , the accessible dataset has input $( X , Y )$ , which can be the original training data or datasets from other resources. Our LKD quantizes the network layer-by-layer and uses its original (i.e., unquantized) version as the teacher model. More specifically, assume layer $L _ { k }$ is going to be quantized, and its quantized version is $\\widehat { L } _ { k }$ . Then we use the output of the $L _ { k - 1 }$ (i.e., by running inference on $X$ over the first $k - 1$ layers) as the input of $L _ { k }$ and $\\widehat { \\widehat { L } } _ { k }$ , measure the difference, and do the model update to $L _ { k }$ , i.e., ",
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"img_path": "images/4dc1348ec4ca9564e57c925fd05b8df8405884858e6719c2085062fbde315918.jpg",
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| 574 |
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"text": "$$\n\\mathcal { L } _ { L K D , k } = M S E \\left( L _ { k } \\cdot L _ { k - 1 } \\cdot L _ { k - 2 } \\cdot \\ldots \\cdot L _ { 1 } ( \\pmb { X } ) - \\widehat { L } _ { k } \\cdot L _ { k - 1 } \\cdot L _ { k - 2 } \\cdot \\ldots \\cdot L _ { 1 } ( \\pmb { X } ) \\right) ,\n$$",
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| 575 |
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| 576 |
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{
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| 585 |
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"type": "text",
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| 586 |
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"text": "where $M S E$ is the mean square loss, and it can be also replaced by other losses (e.g., KL divergence) as well. As can be seen, (1) our LKD does not need to hold a separate teacher as we use the same $L _ { 1 }$ to $L _ { k - 1 }$ for both teacher/student model. As such, the only extra model cost we have is $L _ { k }$ ; (2) the memory overhead of optimizer states are significantly reduced as the only optimizing layer is $L _ { k }$ ; (3) as we never optimize the end-to-end model, the training does not depend on the label anymore. Later, we will show that LKD does not rely on the original training data in Section 5.6. ",
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| 596 |
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"type": "text",
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| 597 |
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"text": "4.3 Quantization-Optimized Transformer Kernels ",
|
| 598 |
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"type": "text",
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"text": "Both optimizing the inference latency and model size is crucial for serving large-scale transformer models in practice. During inference, the batch size is often relatively small, so the inference latency of the model primarily depends on the time of loading inference needed data from the main memory. By quantizing the weights and activations to lower precision, we reduce the data volume needed to load those data, which allows more effective use of memory bandwidth and higher loading throughput. However, simply converting weights/activations to INT8 does not guarantee improved latency because there are additional data movement overhead associated with quantization/dequantization operations as shown in Figure 3 (red box). Such an overhead becomes expensive and in some cases surpasses the performance benefits of using low precision. To reap the accuracy improvement from token-wise quantization while obtaining improved latency, we now present our optimizations that maximize the memory bandwidth utilization to speed up inference latency for ZeroQuant. ",
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"type": "text",
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"text": "CUTLASS INT8 GeMM To support INT8 computation, we use CUTLASS [6] INT8 GeMM implementation tuned for different batch sizes. Unlike standard GPU backend library, such as cuDNN, using CUTLASS allows us to more flexibly fuse quantization operation before and after GeMM to reduce kernel launching and data-movement overhead. ",
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"type": "text",
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| 631 |
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"text": "Fusing Token-wise Activation Quantization Token-wise quantization/dequantization introduce many additional operations that lead to extra data movement cost. To eliminate these cost, we use kernel fusion [68] to fuse quantization operation for activation with its previous element-wise and/or reduction operations such as bias-add, GeLU, and LayerNorm into a single operator, as illustrated by the green box in Figure 3. For the dequantization operation (e.g., dequantizing the integer output from the GeMM operator), we similarly fuse it with our custom GeMM schedule to avoid additional read/write accesses to the main memory as illustrated by the blue box in Figure 3. ",
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| 641 |
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"type": "table",
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| 642 |
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"img_path": "images/35e7e2998b6025ee1b32ba988ce167ff17010d058caa489e86fac774cf092c38.jpg",
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| 643 |
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"table_caption": [
|
| 644 |
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"Table 2: Result of $\\mathbf { B E R T _ { b a s e } }$ on the development set of GLUE benchmark (except WNLI). $[ 5 7 ] ^ { + }$ uses 128 groups for weight matrix which is hard to get GPU acceleration. $[ 7 ] ^ { * }$ uses mixed INT8 and FP16 activation, and it directly reports the average metric of MNLI/MRPC/QQP/STS-B, which is basically the average of the two metrics we used for our runs. "
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| 645 |
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],
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| 646 |
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"table_footnote": [],
|
| 647 |
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"table_body": "<table><tr><td>Precision (Method)</td><td>CoLA</td><td>MNLI-m</td><td>MNLI-mm</td><td>MRPC</td><td>QNLI</td><td>QQP</td><td>RTE</td><td>SST-2</td><td>STS-B</td><td>Ave.</td><td>Ave. Time (s)</td></tr><tr><td>W16A16 (Baseline)</td><td>59.72</td><td>84.94</td><td>85.06</td><td>86.27/90.57</td><td>92.15</td><td>91.51/88.56</td><td>72.20</td><td>93.23</td><td>90.06/89.59</td><td>83.95</td><td>N/A</td></tr><tr><td>W8A8 [57](QAT)+</td><td></td><td>83.91</td><td>83.83</td><td></td><td></td><td></td><td></td><td>92.83</td><td></td><td></td><td></td></tr><tr><td>W8A8 [78](QAT)</td><td>58.48</td><td></td><td></td><td>-/89.56</td><td>90.62</td><td>/87.96</td><td>68.78</td><td>92.24</td><td>89.04/-</td><td></td><td></td></tr><tr><td>W8A8 (QAT)</td><td>61.21</td><td>84.80</td><td>84.64</td><td>83.82/88.85</td><td>91.29</td><td>91.29/88.28</td><td>71.12</td><td>92.89</td><td>88.39/88.18</td><td>83.37</td><td>2900</td></tr><tr><td>W8A8 (PTQ)</td><td>56.06</td><td>79.99</td><td>81.06</td><td>75.49/79.67</td><td>87.35</td><td>89.92/86.82</td><td>48.38</td><td>91.40</td><td>86.58/86.44</td><td>77.41</td><td>6</td></tr><tr><td>W8A8/16 [7](PTQ)*</td><td>58.63</td><td>82.67</td><td>82.67</td><td>88.74</td><td>90.41</td><td>89.40</td><td>68.95</td><td>92.66</td><td>88.00</td><td>82.46</td><td>Unknown</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>59.59</td><td>84.83</td><td>85.13</td><td>86.03/90.39</td><td>91.98</td><td>91.45/88.46</td><td>71.12</td><td>93.12</td><td>90.09/89.62</td><td>83.75</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>16.74</td><td>16.95</td><td>31.62/0.00</td><td>50.74</td><td>63.18/0.00</td><td>47.29</td><td>70.64</td><td>16.48/15.91</td><td>33.11</td><td>6</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>57.29</td><td>82.69</td><td>83.27</td><td>84.56/88.40</td><td>90.04</td><td>86.52/79.49</td><td>70.76</td><td>92.78</td><td>88.46/88.61</td><td>81.65</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>58.50</td><td>83.16</td><td>83.69</td><td>84.80/89.31</td><td>90.83</td><td>88.94/84.12</td><td>70.04</td><td>92.78</td><td>88.49/88.67</td><td>82.35</td><td>31</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>56.69</td><td>82.46</td><td>83.06</td><td>84.07/88.03</td><td>90.13</td><td>87.04/80.50</td><td>70.76</td><td>92.78</td><td>88.07/88.44</td><td>81.55</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>58.80</td><td>83.09</td><td>83.65</td><td>85.78/89.90</td><td>90.76</td><td>89.16/84.85</td><td>71.84</td><td>93.00</td><td>88.16/88.55</td><td>82.71</td><td>31</td></tr></table>",
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"text": "",
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"type": "text",
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"text": "By doing the above optimizations, we are able to show significant latency reduction for BERT and GPT-3-style models in Section 5. Please see Appendix D for more details about our system optimization. ",
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"type": "text",
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"text": "5 Results ",
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"type": "text",
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"text": "Experimental Details To evaluate the proposed ZeroQuant, we test it on both BERT and GPT-3 models. For BERT, we tested both $\\mathbf { B E R T _ { b a s e } }$ and $\\mathbf { B E R T _ { l a r g e } }$ on GLUE benchmark; and for GPT-3-style models, we tested the GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ (i.e., GPT-3-style model with 350M parameters) and GPT- $\\boldsymbol { \\cdot } 3 _ { 1 . 3 \\mathrm { B } }$ (i.e., GPT-3-style model with 1.3B parameters) on 20 zero-shot evaluation tasks, including 19 accuracybased tasks and 1 language modeling generation task. To illustrate the scalability of the proposed ZeroQuant, we also directly apply it to two of the largest open-sourced GPT-3-style models, i.e., $\\mathrm { G P T - J _ { 6 B } }$ [67] and GPT- $\\mathrm { N e o X } _ { 2 0 \\mathrm { B } }$ [5]. We use a fixed set of hyperparameters for all the LKD-related experiments even though tuning them may benefit our results. Please see Appendix A.2 for more training details and see Appendix A.3 for the reported metrics for BERT. To provide a comprehensive study, we also include a tuning result in Appendix E on BERT and an ablation study for different proposed components in Section 5.5. ",
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"type": "text",
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"text": "Notation Explanation We use WxAy to represent using $\\mathbf { X }$ -bit for weight quantization and y-bit for activation quantization. Unless specific explanation, for W4/8, we quantize the MHSA’s weight to INT8 and FFC’s weight to INT4; for A8/16, we use FP16 activation for self-attention calculation (i.e., the GeMM related to $W _ { q / k / v , }$ ) and use INT8 for the rest calculation. We use ZeroQuant to represent the method with only fine-grained quantization schemes and use ZeroQuant-LKD to represent the method with both fine-grained quantization schemes and LKD. ",
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"type": "text",
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"text": "A summary of results is shown in Appendix B. We also include (1) the results required by reviewers in Appendix G; (2) the speedup explanation . ",
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"type": "text",
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"text": "5.1 Main Results of BERT ",
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"text_level": 1,
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"type": "text",
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"text": "$\\mathbf { B E R T _ { b a s e } }$ We report the results of $\\mathbf { B E R T _ { b a s e } }$ in Table 2. For W8A8, the average accuracy of PTQ degrades more than 10 points. However, ZeroQuant can achieve 83.75 scores, which is only 0.2 lower than baseline. Particularly, as ZeroQuant has no activation range calibration phase, the cost of ZeroQuant is 0 which is even cheaper than standard PTQ. As compared to [7], our method achieves a better average score (1.29 higher). Meanwhile, as compared to INT8 activation used in ZeroQuant, [7] uses mixed INT8 and FP16 activation. ",
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"type": "text",
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"text": "We also compare our method with our internal trained QAT and other QAT works [57, 78]. As can be seen, with comparable accuracy results as those QAT methods, ZeroQuant can save the retraining cost from 2900s to 0s for INT8 quantization. ",
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"type": "table",
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"img_path": "images/63f77665b438db357963aba154d7f4ae3d9e19d0b1c56b5c253caa349baf73f1.jpg",
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"table_caption": [
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"Table 3: Result of $\\mathbf { B E R T _ { l a r g e } }$ on the development set of GLUE benchmark (except WNLI). $+ \\mathrm { { { \\mathbf { W } } e } }$ extensively tuned the learning rate for QAT (see Appendix F for more details). "
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],
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"table_footnote": [],
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"table_body": "<table><tr><td>Precision (Method)</td><td>CoLA</td><td>MNLI-m</td><td>MNLI-mm</td><td>MRPC</td><td>QNLI</td><td>QQP</td><td>RTE</td><td>SST-2</td><td>STS-B</td><td>Ave.</td><td>Ave. Time (s)</td></tr><tr><td>W16A16 (Baseline)</td><td>63.35</td><td>86.65</td><td>85.91</td><td>87.99/91.62</td><td>92.24</td><td>91.08/88.08</td><td>74.01</td><td>93.46</td><td>90.34/90.11</td><td>85.03</td><td>N/A</td></tr><tr><td>W8A8 [78](QAT)</td><td></td><td></td><td></td><td>/90.9</td><td>91.74</td><td></td><td></td><td></td><td>90.12/-</td><td></td><td></td></tr><tr><td>W8A8 (QAT)+</td><td>59.85</td><td>86.65</td><td>86.35</td><td>85.29/89.43</td><td>92.55</td><td>91.60/88.60</td><td>61.37</td><td>93.23</td><td>87.55/87.65</td><td>82.78</td><td>7181</td></tr><tr><td>W8A8 (PTQ)</td><td>60.57</td><td>75.69</td><td>76.94</td><td>81.13/84.93</td><td>88.49</td><td>84.04/74.35</td><td>46.93</td><td>91.74</td><td>62.75/55.77</td><td>73.54</td><td>31</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>63.38</td><td>86.52</td><td>85.64</td><td>87.75/91.50</td><td>92.31</td><td>91.09/88.05</td><td>72.56</td><td>93.35</td><td>90.45/90.19</td><td>84.81</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>16.85</td><td>33.24</td><td>68.38/80.89</td><td>51.25</td><td>63.18/0.00</td><td>52.71</td><td>52.41</td><td>-5.74/-8.51</td><td>35.73</td><td>31</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>62.99</td><td>84.77</td><td>84.42</td><td>87.50/91.16</td><td>91.63</td><td>90.03/86.41</td><td>48.01</td><td>92.16</td><td>89.49/89.28</td><td>81.23</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>63.72</td><td>84.90</td><td>84.81</td><td>87.99/91.39</td><td>91.45</td><td>90.34/86.92</td><td>51.62</td><td>92.43</td><td>89.46/89.29</td><td>81.85</td><td>550</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>62.34</td><td>84.62</td><td>84.25</td><td>87.75/91.38</td><td>91.87</td><td>89.86/86.09</td><td>47.65</td><td>91.97</td><td>89.39/89.17</td><td>81.06</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>63.51</td><td>84.70</td><td>84.71</td><td>88.73/91.99</td><td>91.73</td><td>90.25/86.74</td><td>49.82</td><td>92.09</td><td>89.34/89.08</td><td>81.62</td><td>550</td></tr></table>",
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"type": "table",
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"img_path": "images/5c42bc1fee147731d46d90ce3b65c338ffa2f0a9ec56d91148bd0be4feeb1bb4.jpg",
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"table_caption": [
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"Table 4: Post training quantization result of GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ on 20 zero-shot evaluation datasets. Please see Table I.1 for the results of all 20 tasks. "
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],
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"table_footnote": [],
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"table_body": "<table><tr><td>Precision (Method)</td><td>Lambada (↑)</td><td>PIQA (↑)</td><td>OpenBookQA(↑)</td><td>RTE(↑)</td><td>ReCoRd(↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td><td>Time Cost</td></tr><tr><td>W16A16</td><td>49.3</td><td>66.3</td><td>29.4</td><td>53.8</td><td>75.1</td><td>38.9</td><td>21.5</td><td>N/A</td></tr><tr><td>W8A8 (PTQ)</td><td>42.6</td><td>64.1</td><td>28.0</td><td>53.1</td><td>67.5</td><td>37.8</td><td>26.2</td><td>7 mins</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>51.0</td><td>66.5</td><td>29.2</td><td>53.4</td><td>74.9</td><td>38.7</td><td>21.7</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>51.4</td><td>30.2</td><td>52.7</td><td>16.1</td><td>28.9</td><td>1.76e5</td><td>7 mins</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>10.1</td><td>58.5</td><td>27.2</td><td>52.0</td><td>56.5</td><td>33.5</td><td>88.6</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>39.8</td><td>63.8</td><td>29.4</td><td>53.1</td><td>70.1</td><td>37.0</td><td>30.6</td><td>1.1 hours</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>10.5</td><td>57.7</td><td>28.0</td><td>52.7</td><td>55.3</td><td>33.4</td><td>92.1</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>37.4</td><td>61.8</td><td>28.2</td><td>53.1</td><td>68.5</td><td>36.6</td><td>31.1</td><td>1.1 hours</td></tr></table>",
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"type": "text",
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"text": "For the more aggressive weight quantization with minimal (or no) training quantization, i.e., W4/8A16, PTQ fully loses all accuracy (pure random prediction). However, ZeroQuant can still achieve an 81.65 average score. On top of ZeroQuant, if we add our LKD, the accuracy can be further boosted to 82.35 with a cost of 31s per task using only a single GPU, which is $9 3 . 5 \\mathrm { x }$ cheaper than INT8 QAT quantization. We also test ZeroQuant and ZeroQuant-LKD under the W4/8A8 quantization scheme and both of them achieve similar accuracy performance as W4/8A16. If hyper-parameter tuning is applied to LKD, ZeroQuant-LKD can achieve an 83.22 average score under W4/8A8, which is similar to QAT’s W8A8 result. Please see Appendix E for more details. ",
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"type": "text",
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"text": "$\\mathbf { B E R T _ { l a r g e } }$ We test our methods on $\\mathbf { B E R T _ { l a r g e } }$ as well and the results are shown in Table 3. Similar to $\\mathrm { B E R T _ { b a s e } ^ { - } }$ , ZeroQuant achieves much better accuracy than PTQ methods. As compared to QAT methods, ZeroQuant has comparable results on larger datasets (like MNLI/QQP) and has better performance on small tasks (e.e., CoLA/MRPC/RTE). We actually tune QAT for multiple learning rates but cannot get even better performance for those small tasks (see Appendix F for more details). ",
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"type": "text",
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"text": "For more aggressive quantization schemes, like W4/8A16 and W4/8A8, ZeroQuant and ZeroQuantLKD still achieve good accuracy except for RTE but the model size is about $3 \\mathbf { x }$ smaller than FP16 counterpart. This is aligned with the INT8 QAT results, which lose significantly more accuracy on RTE. Thanks to the lightweight cost of LKD, it only takes about 550s to finish each task even on $\\mathbf { B E R T _ { l a r g e } }$ , which is $1 3 \\mathrm { x }$ cheaper than QAT. ",
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"type": "text",
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"text": "5.2 Main Results of GPT-3-style Models ",
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"text": "$\\mathbf { G P T } \\mathbf { - } 3 _ { 3 5 0 \\mathbf { M } }$ We first test ZeroQuant and ZeroQuant-LKD on GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ and report the result in Table 4. The first interesting finding of zero-shot evaluation on GPT-3-stype models is that the accuracy performance of accuracy-based tasks is more tolerant to quantization than generation tasks. For instance, W8A8 PTQ has a $1 . 1 \\%$ average accuracy drop on 19 accuracy-based tasks as compared to 4.7 points loss on Wikitext-2. Comparing ZeroQuant with PTQ using W8A8, we can reduce the accuracy gap from $1 . 1 \\%$ to $0 . 2 \\%$ and the perplexity (PPL) gap from 4.7 to 0.2 with no activation range calibration cost. ",
|
| 837 |
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"bbox": [
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"type": "text",
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"text": "For W4/8A16 quantization scheme, PTQ can hardly predict reasonable answers for the majority of tasks and its generation performance on Wikitext-2 is fully crashed. As a comparison, ZeroQuant still achieves non-trivial performance on some tasks but its generation performance significantly degrades on Wikitext-2. LKD brings a significant performance boost for this W4/8A16 setting. Note that ZeroQuant-LKD increases the accuracy from 33.5 to 37.0 and decreases the PPL from 88.6 to 30.6 compared to ZeroQuant, and the entire cost of this is just 3.1 hours on a single A100 GPU. Note that this is about $0 . 0 2 7 \\%$ GPU hours of the full pretraining cost (128 A100 GPUs for 32 hours). Similar to W4/8A16, ZeroQuant-LKD achieves much better performance than ZeroQuant on W4/8A8 by using the lightweight LKD. ",
|
| 848 |
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"bbox": [
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| 851 |
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{
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| 857 |
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"type": "table",
|
| 858 |
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"img_path": "images/5f3f136bd119381779c24ce59f09719d375d8d63a0a580af36010e79fcb258d1.jpg",
|
| 859 |
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"table_caption": [
|
| 860 |
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"Table 5: Post training quantization result of GPT- $3 _ { 1 . 3 \\mathrm { B } }$ on 20 zero-shot evaluation datasets. Please see Table I.2 for the results of all 20 tasks. "
|
| 861 |
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],
|
| 862 |
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"table_footnote": [],
|
| 863 |
+
"table_body": "<table><tr><td>Precision (Method)</td><td>Lambada (↑)</td><td>PIQA(↑)</td><td>OpenBookQA (↑)</td><td>RTE(↑)</td><td>ReCoRd(↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td><td>Time Cost</td></tr><tr><td>W16A16</td><td>61.3</td><td>71.4</td><td>33.6</td><td>53.1</td><td>82.6</td><td>42.4</td><td>15.3</td><td>N/A</td></tr><tr><td>W8A8 (PTQ)</td><td>54.8</td><td>67.7</td><td>16.6</td><td>54.5</td><td>75.7</td><td>40.5</td><td>18.9</td><td>13 mins</td></tr><tr><td>W8A8 (ZeroQuant)</td><td>62.6</td><td>70.7</td><td>33.4</td><td>52.7</td><td>80.9</td><td>42.3</td><td>15.7</td><td>0</td></tr><tr><td>W4/8A16 (PTQ)</td><td>0.00</td><td>50.4</td><td>27.0</td><td>50.9</td><td>15.8</td><td>29.0</td><td>1.35e5</td><td>13 mins</td></tr><tr><td>W4/8A16 (ZeroQuant)</td><td>43.9</td><td>66.5</td><td>30.0</td><td>52.7</td><td>77.3</td><td>39.38</td><td>21.9</td><td>0</td></tr><tr><td>W4/8A16 (ZeroQuant-LKD)</td><td>59.4</td><td>69.5</td><td>31.6</td><td>52.7</td><td>79.7</td><td>41.5</td><td>17.6</td><td>3 hours</td></tr><tr><td>W4/8A8 (ZeroQuant)</td><td>46.8</td><td>66.4</td><td>28.8</td><td>52.7</td><td>76.2</td><td>39.24</td><td>24.1</td><td>0</td></tr><tr><td>W4/8A8 (ZeroQuant-LKD)</td><td>48.7</td><td>68.1</td><td>29.0</td><td>52.0</td><td>77.4</td><td>39.90</td><td>18.2</td><td>3 hours</td></tr></table>",
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|
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"page_idx": 8
|
| 871 |
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|
| 872 |
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{
|
| 873 |
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"type": "table",
|
| 874 |
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"img_path": "images/52f2631ffb9d46bab4bc1c10472f6d8fb72739fb1547a27b2d6447f405665435.jpg",
|
| 875 |
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"table_caption": [
|
| 876 |
+
"Table 6: The speedup of our W8A8 as compared to W16A16. We measure the end-to-end average latency for the entire BERT model, and the time reported is in milliseconds. "
|
| 877 |
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],
|
| 878 |
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"table_footnote": [],
|
| 879 |
+
"table_body": "<table><tr><td rowspan=\"2\">Seq Len BS</td><td rowspan=\"2\">Precision</td><td colspan=\"8\">128</td><td colspan=\"8\">256</td></tr><tr><td>2</td><td></td><td>4</td><td>8</td><td>16</td><td>16</td><td>64</td><td>128</td><td>1</td><td>2</td><td>4</td><td>8</td><td>16</td><td>16</td><td>64</td><td>128</td></tr><tr><td rowspan=\"3\">BERTbase</td><td>W16A16</td><td>2.45</td><td>3.22</td><td>3.85</td><td>5.51</td><td>9.96</td><td>17.93</td><td>34.25</td><td>67.08</td><td>3.13</td><td>4.05</td><td>5.70</td><td>10.55</td><td>19.27</td><td>36.69</td><td>71.75</td><td>140.0</td></tr><tr><td>W8A8</td><td>1.08</td><td>1.16</td><td>1.42</td><td>1.76</td><td>2.58</td><td>3.90</td><td>6.74</td><td>12.92</td><td>1.22</td><td>1.44</td><td>2.08</td><td>2.88</td><td>4.10</td><td>7.80</td><td>14.66</td><td>28.13</td></tr><tr><td>Speedup</td><td>2.27</td><td>2.78</td><td>2.71</td><td>3.13</td><td>3.86</td><td>4.60</td><td>5.08</td><td>5.19</td><td>2.57</td><td>2.81</td><td>2.74</td><td>3.66</td><td>4.70</td><td>4.70</td><td>4.89</td><td>4.98</td></tr><tr><td rowspan=\"3\">BERTlarge</td><td>W16A16</td><td>5.45</td><td>6.38</td><td>8.73</td><td>13.88</td><td>26.34</td><td>48.59</td><td>92.49</td><td>183.4</td><td>6.39</td><td>8.94</td><td>14.66</td><td>27.99</td><td>51.94</td><td>98.78</td><td>195.9</td><td>384.5</td></tr><tr><td>W8A8</td><td>2.08</td><td>2.58</td><td>2.84</td><td>3.79</td><td>6.21</td><td>10.28</td><td>18.86</td><td>36.62</td><td>2.55</td><td>3.36</td><td>4.16</td><td>6.88</td><td>11.61</td><td>21.20</td><td>41.24</td><td>79.90</td></tr><tr><td>Speedup</td><td>2.62</td><td>2.47</td><td>3.07</td><td>3.66</td><td>4.24</td><td>4.73</td><td>4.90</td><td>5.01</td><td>2.51</td><td>2.66</td><td>3.52</td><td>4.07</td><td>4.47</td><td>4.66</td><td>4.75</td><td>4.81</td></tr></table>",
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| 880 |
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"bbox": [
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"page_idx": 8
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| 887 |
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},
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| 888 |
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{
|
| 889 |
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"type": "text",
|
| 890 |
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"text": "GPT- $\\mathbf { \\lambda } _ { \\mathbf { 3 1 . 3 B } }$ The results of GPT- $\\cdot 3 _ { 1 . 3 \\mathrm { B } }$ are shown in Table 5. Similar to GPT- $3 _ { 3 5 0 \\mathrm { M } }$ , for W8A8, ZeroQuant has much better performance than PTQ with less no activation calibration cost, particularly for the generation task Wikitext-2 (3.2 points lower). Also, for W4/8 quantization, LKD can bring non-trivial performance gain for ZeroQuant. The cost of LKD is about $0 . 0 2 \\%$ of the full pre-training cost (128 A100 GPUs for 120 hours) ",
|
| 891 |
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"bbox": [
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| 892 |
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| 893 |
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| 895 |
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|
| 897 |
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"page_idx": 8
|
| 898 |
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},
|
| 899 |
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{
|
| 900 |
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"type": "text",
|
| 901 |
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"text": "5.3 Latency Reduction of BERT and GPT-3-style Models ",
|
| 902 |
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"text_level": 1,
|
| 903 |
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"bbox": [
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| 904 |
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| 907 |
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| 908 |
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|
| 909 |
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"page_idx": 8
|
| 910 |
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},
|
| 911 |
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{
|
| 912 |
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"type": "text",
|
| 913 |
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"text": "We compare the inference speed of BERT between FP16 and our INT8 versions in Table 6 on a single 40G-A100 GPU. Using our efficient quantization kernel implementation and operator fusion, the INT8 model can achieve $2 . 2 7 { - } 5 . 1 9 \\mathrm { x }$ speedup on $\\mathbf { B E R T _ { b a s e } }$ and $2 . 4 7 { - } 5 . 0 1 \\mathrm { x }$ on $\\mathbf { B E R T _ { l a r g e } }$ . ",
|
| 914 |
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"bbox": [
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| 915 |
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| 916 |
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|
| 917 |
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| 918 |
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|
| 919 |
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|
| 920 |
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"page_idx": 8
|
| 921 |
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},
|
| 922 |
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{
|
| 923 |
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"type": "text",
|
| 924 |
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"text": "We also include the latency comparison of GPT-3-style models between FP16 and our INT8 version. Particularly, we use the model to generate the first 50 tokens based on a given text and measure the average latency. Our INT8 model leads to $4 . 1 6 \\mathrm { x } / 4 . 0 6 \\mathrm { x }$ speedup for $\\mathrm { G P T } { - } 3 _ { 3 5 0 \\mathrm { M } } / \\mathrm { G P T } { - } 3 _ { 1 . 3 \\mathrm { B } }$ as compared to the FP16 counterpart. ",
|
| 925 |
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"bbox": [
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| 929 |
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|
| 931 |
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"page_idx": 8
|
| 932 |
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},
|
| 933 |
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{
|
| 934 |
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"type": "text",
|
| 935 |
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"text": "5.4 A Showcase of GPT- $\\mathbf { J _ { 6 B } }$ and GPT-NeoX20B ",
|
| 936 |
+
"text_level": 1,
|
| 937 |
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"bbox": [
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| 938 |
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| 939 |
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| 941 |
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|
| 943 |
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"page_idx": 8
|
| 944 |
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},
|
| 945 |
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{
|
| 946 |
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"type": "text",
|
| 947 |
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"text": "To demonstrate the scalability of ZeroQuant, we applied it to two of the largest open-sourced models, i.e., $\\mathrm { G P T - J _ { 6 B } }$ and G $\\mathrm { P T } \\mathrm { - N e o } X _ { 2 0 \\mathrm { B } }$ , which have 6B and 20B parameters separately. ",
|
| 948 |
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"bbox": [
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| 950 |
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| 952 |
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| 954 |
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| 955 |
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| 956 |
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{
|
| 957 |
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"type": "text",
|
| 958 |
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"text": "We report the results of $\\mathrm { G P T - J _ { 6 B } }$ in Table 7 on three generation datasets, i.e., PTB [42], Wikitext-2, and Wikitext-103 [43]. As can be seen, as compared to FP16 precision, ZeroQuant achieves similar PPL on all three different tasks. To compare the latency, we again use the average latency number to generate the first 50 tokens. Our W8A8 can get up to $3 . 6 7 \\mathrm { x }$ speedup compared to the FP16 version. ",
|
| 959 |
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"bbox": [
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|
| 965 |
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"page_idx": 8
|
| 966 |
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},
|
| 967 |
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{
|
| 968 |
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"type": "text",
|
| 969 |
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"text": "To quantize GPT- $\\mathrm { \\cdot N e o X _ { 2 0 B } }$ to W8A8 for all GeMMs, the accuracy significantly decreases. We retrieve the quantization of each weight matrix and of each activation, and finally find out that the activation quantization for the attention calculation (i.e., the input of self-attention) causes the accuracy loss. We conjecture that this is because of the sensitivity of the self-attention module for extra-large models (20B) but cannot verify this for other models due to the lack of open-sourced extra-large models and the full evaluation pipeline. As such, we leave the input activation for self-attention in FP16 and quantize the rest to INT8. The results are shown in Table 8. Our W8A8/16 achieves similar accuracy performance but can reduce both the GPU resource requirement (from 2 A100 GPUs to 1) and the latency from $6 5 \\mathrm { m s }$ to $2 5 \\mathrm { m s }$ , which together lead to $5 . 2 \\mathrm { x }$ better throughput/efficiency. ",
|
| 970 |
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"bbox": [
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|
| 976 |
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"page_idx": 8
|
| 977 |
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},
|
| 978 |
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{
|
| 979 |
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"type": "text",
|
| 980 |
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"text": "5.5 Ablation Study of Different Components ",
|
| 981 |
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"text_level": 1,
|
| 982 |
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"bbox": [
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| 983 |
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| 989 |
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|
| 990 |
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{
|
| 991 |
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"type": "text",
|
| 992 |
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"text": "To investigate the performance gain of each component we introduced in Section 4, i.e., group-wise weight quantization, token-wise activation quantization, and lightweight layer-by-layer knowledge distillation, we here do an ablation study on $\\mathbf { B E R T _ { l a r g e } }$ with W4/8A8. ",
|
| 993 |
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"bbox": [
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|
| 1000 |
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|
| 1001 |
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{
|
| 1002 |
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"type": "table",
|
| 1003 |
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"img_path": "images/aa57b112b2da0bf75996dd274dafd3945fd4e9d8639a886788ddc48c6442430e.jpg",
|
| 1004 |
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"table_caption": [
|
| 1005 |
+
"Table 7: Post training quantization result of GPT$\\mathrm { J } _ { 6 \\mathrm { B } }$ on three zero-shot generation tasks "
|
| 1006 |
+
],
|
| 1007 |
+
"table_footnote": [],
|
| 1008 |
+
"table_body": "<table><tr><td>Precision PTB</td><td>Wikitext-2 Wikitext-103</td><td></td><td>Latency</td></tr><tr><td>W16A16 20.47</td><td>10.35</td><td>10.35</td><td>29.13ms (1x)</td></tr><tr><td>W8A8 20.97</td><td>10.51</td><td>10.52</td><td>7.94ms (3.67x)</td></tr></table>",
|
| 1009 |
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"bbox": [
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| 1012 |
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| 1013 |
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| 1014 |
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| 1015 |
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| 1016 |
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},
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| 1017 |
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{
|
| 1018 |
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"type": "table",
|
| 1019 |
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"img_path": "images/51eb615b84a5a50a35001b81a501b0be8c9c2012d35ca6ca15983af0ddb7bda3.jpg",
|
| 1020 |
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"table_caption": [
|
| 1021 |
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"Table 8: Post training quantization result of GPTNeoX20B on 19 zero-shot evaluation datasets. Please see Table I.4 for the results of all 19 tasks. "
|
| 1022 |
+
],
|
| 1023 |
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"table_footnote": [],
|
| 1024 |
+
"table_body": "<table><tr><td colspan=\"4\">Precision Lambada PIQA Ave.19 Tasks Latency</td></tr><tr><td>W16A16</td><td>71.7 77.7</td><td>50.5</td><td>2×65ms (1x)</td></tr><tr><td>W8A8/16</td><td>71.9 78.3</td><td>50.4</td><td>1×25ms (5.2x)</td></tr></table>",
|
| 1025 |
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"bbox": [
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| 1027 |
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| 1028 |
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| 1029 |
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188
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| 1030 |
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|
| 1031 |
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"page_idx": 9
|
| 1032 |
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},
|
| 1033 |
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{
|
| 1034 |
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"type": "table",
|
| 1035 |
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"img_path": "images/f3b76b6d91260f2c1b03c248b1a4d692c58238d585e68698e5fe1ed437aefc7d.jpg",
|
| 1036 |
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"table_caption": [
|
| 1037 |
+
"Table 9: Ablation study of different components for $\\mathbf { B E R T _ { l a r g e } }$ on the development set of GLUE. The quantization scheme used here is W4/8A8. Here, GQ is the abbreviation of group-wise weight quantization, TQ is the abbreviation of token-wise activation quantization. "
|
| 1038 |
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],
|
| 1039 |
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"table_footnote": [],
|
| 1040 |
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"table_body": "<table><tr><td>GQ</td><td>TQ</td><td>LKD</td><td>CoLA</td><td>MNLI-m</td><td>MNLI-mm</td><td>MRPC</td><td>QNLI</td><td>QQP</td><td>RTE</td><td>SST-2</td><td>STS-B</td><td>Ave.</td></tr><tr><td></td><td></td><td>X</td><td>-0.79</td><td>33.07</td><td>32.94</td><td>68.38/80.54</td><td>49.42</td><td>63.18/0.00</td><td>52.71</td><td>52.29</td><td>-4.27/-1.90</td><td>35.85</td></tr><tr><td></td><td></td><td>X</td><td>59.81</td><td>66.63</td><td>68.79</td><td>68.63/71.17</td><td>83.87</td><td>78.24/61.30</td><td>46.93</td><td>89.45</td><td>54.58/32.52</td><td>66.52</td></tr><tr><td>x</</td><td>xx/</td><td>X</td><td>62.34</td><td>84.62</td><td>84.25</td><td>87.75/91.38</td><td>91.87</td><td>89.86/86.09</td><td>47.65</td><td>91.97</td><td>89.39/89.17</td><td>81.06</td></tr><tr><td>√</td><td>√</td><td>√</td><td>63.51</td><td>84.70</td><td>84.71</td><td>88.73/91.99</td><td>91.73</td><td>90.25/86.74</td><td>49.82</td><td>92.09</td><td>89.34/89.08</td><td>81.62</td></tr></table>",
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| 1041 |
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| 1050 |
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"type": "table",
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| 1051 |
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"img_path": "images/21f35abab8d7dfbf34e6d2cf5a916fb89ebde9ac663be31184d5f2b6c04070e1.jpg",
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"table_caption": [
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"Table 10: Post training quantization result of GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ on 20 zero-shot evaluation datesets The quantization scheme here is W4/8A8. Please see Table I.3 for the results of all 20 tasks. "
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"table_footnote": [],
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"table_body": "<table><tr><td>Method</td><td>Data Resource</td><td>Lambada (↑)</td><td>PIQA (↑)</td><td>OpenBookQA (↑)</td><td>RTE(↑)</td><td>ReCoRd (↑)</td><td>Ave.19 Tasks (↑)</td><td>Wikitext-2 (↓)</td></tr><tr><td>ZeroQuant</td><td></td><td>10.5</td><td>57.7</td><td>28.0</td><td>52.7</td><td>55.3</td><td>33.4</td><td>92.1</td></tr><tr><td>ZeroQuant-LKD</td><td>Random data</td><td>26.1</td><td>59.3</td><td>29.2</td><td>50.5</td><td>64.9</td><td>34.5</td><td>40.6</td></tr><tr><td>ZeroQuant-LKD</td><td>Wikipedia</td><td>33.9</td><td>62.4</td><td>28.0</td><td>52.7</td><td>69.5</td><td>36.2</td><td>30.4</td></tr><tr><td>ZeroQuant-LKD</td><td>Original data</td><td>37.4</td><td>61.8</td><td>28.2</td><td>53.1</td><td>68.5</td><td>36.6</td><td>31.1</td></tr></table>",
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"text": "We present the results in Table 9. As can be seen, group-wise weight quantization boosts the accuracy (random-guess prediction) from PTQ to a non-trivial result (66.52). Further adding token-wise quantization improves 14.54 points accuracy performance. On top of those (i.e., ZeroQuant), LKD further brings a 0.56 point gain. ",
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"text": "5.6 No Access to The Original Training Data ",
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"text": "As mentioned in previous sections, the original training data are oftentimes hard to access due to the privacy and/or confidential issues. Therefore, we here study the performance of our LKD when there is no direct access to the original training data. As the distillation objective of our LKD does not depend on the label, the training data used for LKD can be very flexible. ",
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"text": "We compare the performance of GPT- $\\cdot 3 _ { 3 5 0 \\mathrm { M } }$ on W4/8A8 quantization scheme using three different training data resources, i.e., random data (using random integer number to generate token ids), Wikipedia (using Huggingface to get the data2), and original PILE dataset. ",
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"text": "The results are shown in Table 10. Compared to ZeroQuant, LKD using random data can boost the accuracy by $1 . 1 \\%$ and reduce the PPL from 92.1 to 40.6. The reason why random data can still significantly improve the performance is that LKD does not optimize the end-to-end pipeline and it only layer-by-layer learns the internal dependency from the teacher model. Therefore, random data can also provide meaningful information. Using Wikipedia data from Huggingface can further improve the accuracy to 36.2 and reduce the PPL to 30.4, which is comparable to the results using the original data. This indicates that a clean text dataset can be used for LKD when we do not have access to the original full dataset. ",
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"text": "6 Conclusions ",
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"text": "With the rapid growth of large model sizes, we have reach a point to consider how to serve those models in practice. Although several works demonstrate that post-training quantization can be applied to BERT models, to the best of our knowledge, there have been no existing works on (1) billion-scale GPT-3-style models, (2) ultra-low precision post-training quantization, and (3) end-to-end solution of how to efficiently serve the quantized model online. In this work, we offer fine-grained compression schemes for both weight and activations to enable INT8 quantization for up to 20B-scale models ( $\\mathrm { \\bf J P T - N e o X } _ { 2 0 \\mathrm { B } }$ ). We also offer a novel affordable layer-by-layer knowledge distillation for ultra-low precision quantization, which leads to $3 \\mathbf { x }$ model size reduction compared to FP16 model while achieving minimal accuracy degradation. Furthermore, we provide a system backend support and show up to $5 . 1 9 \\mathrm { x }$ speedup on BERT models and $5 . 2 \\mathrm { x }$ better efficiency on GPT-NeoX20B. ",
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parse/dev/f-fVCElZ-G1/f-fVCElZ-G1_middle.json
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parse/dev/f-fVCElZ-G1/f-fVCElZ-G1_model.json
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parse/dev/fAdMly4ki5/fAdMly4ki5.md
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@@ -0,0 +1,564 @@
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| 1 |
+
# Diffusion Model is an Effective Planner and Data Synthesizer for Multi-Task Reinforcement Learning
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| 2 |
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| 3 |
+
Haoran He 1,2∗ Chenjia Bai2† Kang Xu2,3 Zhuoran Yang4 Weinan Zhang1
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| 4 |
+
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| 5 |
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Dong Wang2 Bin Zhao2,5 Xuelong Li2,5†
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1Shanghai Jiao Tong University 2Shanghai Artificial Intelligence Laboratory
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3Fudan University 4Yale University 5Northwestern Polytechnical University
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| 10 |
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# Abstract
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Diffusion models have demonstrated highly-expressive generative capabilities in vision and NLP. Recent studies in reinforcement learning (RL) have shown that diffusion models are also powerful in modeling complex policies or trajectories in offline datasets. However, these works have been limited to single-task settings where a generalist agent capable of addressing multi-task predicaments is absent. In this paper, we aim to investigate the effectiveness of a single diffusion model in modeling large-scale multi-task offline data, which can be challenging due to diverse and multimodal data distribution. Specifically, we propose Multi-Task Diffusion Model (MTDIFF), a diffusion-based method that incorporates Transformer backbones and prompt learning for generative planning and data synthesis in multitask offline settings. MTDIFF leverages vast amounts of knowledge available in multi-task data and performs implicit knowledge sharing among tasks. For generative planning, we find MTDIFF outperforms state-of-the-art algorithms across 50 tasks on Meta-World and 8 maps on Maze2D. For data synthesis, MTDIFF generates high-quality data for testing tasks given a single demonstration as a prompt, which enhances the low-quality datasets for even unseen tasks.
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# 1 Introduction
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The high-capacity generative models trained on large, diverse datasets have demonstrated remarkable success across vision and language tasks. An impressive and even preternatural ability of these models, e.g. large language models (LLMs), is that the learned model can generalize among different tasks by simply conditioning the model on instructions or prompts [49, 46, 7, 12, 60, 42, 66]. The success of LLMs and vision models inspires us to utilize the recent generative model to learn from large-scale offline datasets that include multiple tasks for generalized decision-making in reinforcement learning (RL). Thus far, recent attempts in offline decision-making take advantage of the generative capability of diffusion models [54, 20] to improve long-term planning [21, 2] or enhance the expressiveness of policies [63, 11, 8]. However, these works are limited to small-scale datasets and single-task settings where broad generalization and general-purpose policies are not expected. In multi-task offline RL which considers learning a single model to solve multi-task problems, the dataset often contains noisy, multimodal, and long-horizon trajectories collected by various policies across tasks and with various qualities, which makes it more challenging to learn policies with broad generalization and transferable capabilities. Gato [47] and other generalized agents [29, 65] take transformer-based architecture [62] via sequence modeling to solve multi-task problems, while they are highly dependent on the optimality of the datasets and are expensive to train due to the huge number of parameters.
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Figure 1: Overall architecture of MTDIFF. Different colors represent different tasks. $S$ , $A$ and $R$ denote the state sequence, action sequence, and reward sequence from multi-task data, respectively. $S _ { \mathrm { p r e v } }$ and $R _ { \tau }$ represent historical states and normalized return.
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| 20 |
+
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To address the above challenges, we propose a novel diffusion model to further explore its generalizability in a multi-task setting. We formulate the learning process from multi-task data as a denoising problem, which benefits the modeling of multimodal data. Meanwhile, we develop a relatively lightweight architecture by using a GPT backbone [45] to model sequential trajectories, which has less computation burden and improved sequential modeling capability than previous U-Net-based [48] diffusion models [21, 33]. To disambiguate tasks during training and inference, instead of providing e.g. one-hot task identifiers, we leverage demonstrations as prompt conditioning, which exploits the few-shot abilities of agents [50, 64, 69].
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We name our method the Multi-Task Diffusion Model (MTDIFF). As shown in Figure 1, we investigate two variants of MTDIFF for planning and data synthesis to further exploit the utility of diffusion models, denoted as MTDIFF-P and MTDIFF-S, respectively. (a) For planning, MTDIFF-P learns a prompt embedding to extract the task-relevant representation, and then concatenates the embedding with the trajectory’s normalized return and historical states as the conditions of the model. During training, MTDIFF-P learns to predict the corresponding future action sequence given the conditions, and we call this process generative planning [78]. During inference, given few-shot prompts and the desired return, MTDIFF-P tries to denoise out the optimal action sequence starting from the current state. Surprisingly, MTDIFF-P can adapt to unseen tasks given well-constructed prompts that contain task information. (b) By slightly changing the inputs and training strategy, we can unlock the abilities of our diffusion model for data synthesis. Our insight is that the diffusion model, which compresses informative multi-task knowledge well, is more effective and generalist than previous methods that only utilize single-task data for augmentation [38, 52, 28]. Specifically, MTDIFF-S learns to estimate the joint conditional distribution of the full transitions that contain states, actions, and rewards based on the task-oriented prompt. Different from MTDIFF-P, MTDIFF-S learns to synthesize data from the underlying dynamic environments for each task. Thus MTDIFF-S only needs prompt conditioning to identify tasks. We empirically find that MTDIFF-S synthesizes high-fidelity data for multiple tasks, including both seen and unseen ones, which can be further utilized for data augmentation to expand the offline dataset and enhance policy performance.
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| 25 |
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To summarize, MTDIFF is a diffusion-based method that leverages the multimodal generative ability of diffusion models, the sequential modeling capability of GPT architecture, and the few-shot generalizability of prompt learning for multi-task RL. To the best of our knowledge, we are the first to achieve both effective planning and data synthesis for multi-task RL via diffusion models. Our contributions include: (i) we propose MTDIFF, a novel GPT-based diffusion model that illustrates the supreme effectiveness in multi-task trajectory modeling for both planning and data synthesis; (ii) we incorporate prompt learning into the diffusion framework to learn to generalize across different tasks and even adapt to unseen tasks; (iii) our experiments on Meta-World and Maze2D benchmarks demonstrate that MTDIFF is an effective planner to solve the multi-task problem, and also a powerful data synthesizer to augment offline datasets in the seen or unseen tasks.
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# 2 Preliminaries
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| 28 |
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# 2.1 Reinforcement Learning
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| 30 |
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| 31 |
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MDP and Multi-task MDP. A Markov Decision Process (MDP) is defined by a tuple $( \mathcal { S } , \mathcal { A } , \mathcal { P } , \mathcal { R } , \mu , \gamma )$ , where $s$ is the state space, $\mathcal { A }$ is the action space, $\mathcal { P } : \mathcal { S } \times \mathcal { A } \mathcal { S }$ is the transition function, $\mathcal { R } : \mathcal { S } \times \mathcal { A } \times \mathcal { S } \mathbb { R }$ is the reward function for any transition, $\gamma \in ( 0 , 1 ]$ is a discount factor, and $\mu$ is the initial state distribution. At each timestep $t$ , the agent chooses an action scalar reward $a _ { t }$ by following the policy $r _ { t }$ . In single-task RL, the goal is to learn a policy $\pi : { \mathcal { S } } \Delta _ { { \mathcal { A } } }$ . Then the agent obtains the next state $\begin{array} { r } { \pi ^ { * } = \arg \operatorname* { m a x } _ { \pi } \mathbb E _ { a _ { t } \sim \pi } \big [ \sum _ { t = 0 } ^ { \infty } \gamma ^ { t } r _ { t } \big ] } \end{array}$ $s _ { t + 1 }$ and receives a by maximizing the expected cumulative reward of the corresponding task.
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| 32 |
+
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| 33 |
+
In a multi-task setting, different tasks can have different reward functions, state spaces and transition functions. We consider all tasks to share the same action space with the same embodied agent. Given a specific task $\tau \sim p ( \mathcal { T } )$ , a task-specified MDP can be defined as $( S ^ { \mathcal { T } } , A , \mathcal { P } ^ { \mathcal { T } } , \mathcal { R } ^ { \mathcal { T } } , \mu ^ { \mathcal { T } } , \gamma )$ . Instead of solving a single MDP, the goaexpected return over all the tasks: $\begin{array} { r } { \pi ^ { * } = \arg \operatorname* { m a x } _ { \pi } \mathbb { E } _ { \mathcal { T } \sim p ( \mathcal { T } ) } \mathbb { E } _ { a _ { t } \sim \pi } \tau \Big [ \sum _ { t = 0 } ^ { \infty } \dot { \gamma } ^ { t } r _ { t } ^ { \mathcal { T } } \Big ] } \end{array}$ y that maximizes.
|
| 34 |
+
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| 35 |
+
Multi-Task Offline Decision-Making. In offline decision-making, the policy is learned from a static dataset of transitions $\{ ( s _ { j } , a _ { j } , s _ { j } ^ { \tilde { \prime } } , r _ { j } ) \} _ { j = 1 } ^ { N }$ collected by an unknown behavior policy $\pi _ { \beta }$ [30]. In the multi-task offline RL setting, the dataset $\mathcal { D }$ is partitioned into per-task subsets as $\mathcal { D } = \cup _ { i = 1 } ^ { N } \mathcal { D } _ { i }$ , where $\mathcal { D } _ { i }$ consists of experiences from task $\mathcal { T } _ { i }$ . The key issue of RL in the offline setting is the distribution shift problem caused by temporal-difference (TD) learning. In our work, we extend the idea of Decision Diffuser [2] by considering multi-task policy learning as a conditional generative process without fitting a value function. The insight is to take advantage of the powerful distribution modeling ability of diffusion models for multi-task data, avoiding facing the risk of distribution shift.
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| 36 |
+
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| 37 |
+
Offline RL learns policies from a static dataset, which makes the quality and diversity of the dataset significant [15]. One can perform data perturbation [28] to up-sample the offline dataset. Alternatively, we synthesize new transitions $( s , a , s ^ { \prime } , r )$ by capturing the underlying MDP of a given task via diffusion models, which expands the original dataset and leads to significant policy improvement.
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| 38 |
+
|
| 39 |
+
# 2.2 Diffusion Models
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| 40 |
+
|
| 41 |
+
We employ diffusion models to learn from multi-task data $\mathcal { D } = \cup _ { i = 1 } ^ { N } \mathcal { D } _ { i }$ in this paper. With $\tau$ the sampled trajectory from $\mathcal { D }$ , we denote ${ \pmb x } _ { k } ( \tau )$ as the $k$ -step denoised output of the diffusion model, and $\pmb { y } ( \tau )$ is the condition which represents the task attributes and the trajectory’s optimality (e.g., returns). A forward diffusion chain gradually adds noise to the data $\pmb { x } _ { 0 } ( \tau ) \sim q ( \pmb { x } ( \tau ) )$ in $K$ steps with a pre-defined variance schedule $\beta _ { k }$ , which can be expressed as
|
| 42 |
+
|
| 43 |
+
$$
|
| 44 |
+
q ( \pmb { x } _ { k } ( \tau ) | \pmb { x } _ { k - 1 } ( \tau ) ) : = \mathcal { N } ( \pmb { x } _ { k } ( \tau ) ; \sqrt { 1 - \beta _ { k } } \pmb { x } _ { k - 1 } ( \tau ) , \beta _ { k } \pmb { I } ) .
|
| 45 |
+
$$
|
| 46 |
+
|
| 47 |
+
In this paper, we adopt Variance Preserving (VP) beta schedule [67] and define $\beta _ { k } \quad =$ $1 ~ - ~ \mathrm { e x p } \bar { ( - \beta _ { m i n } ( \frac { 1 } { K } ) - 0 . 5 ( \beta _ { \mathrm { m a x } } - \beta _ { \mathrm { m i n } } ) \frac { 2 k - 1 } { K ^ { 2 } } ) }$ , where $\beta _ { \mathrm { m a x } } \ = \ 1 0$ and $\beta _ { \mathrm { m i n } } ~ = ~ 0 . 1$ are constants. A trainable reverse diffusion chain, constructed as $p _ { \boldsymbol { \theta } } ( \mathbf { x } _ { k - 1 } ( \tau ) | \mathbf { x } _ { k } ( \tau ) , \mathbf { y } ( \tau ) ) \ : =$ $\mathcal { N } ( \pmb { x } _ { k - 1 } ( \tau ) | \mu _ { \boldsymbol { \theta } } ( \pmb { x } _ { k } ( \tau ) , \pmb { y } ( \tau ) , k ) , \Sigma _ { k } )$ , can be optimized by a simplified surrogate loss [20]:
|
| 48 |
+
|
| 49 |
+
$$
|
| 50 |
+
\begin{array} { r } { \mathcal { L } _ { \mathrm { d e n o i s e } } : = \mathbb { E } _ { k \sim \mathcal { U } ( 1 , K ) , \pmb { x } _ { 0 } ( \tau ) \sim q , \epsilon \sim \mathcal { N } ( \mathbf { 0 } , I ) } [ \big | \epsilon - \epsilon _ { \theta } ( \pmb { x } _ { k } ( \tau ) , \pmb { y } ( \tau ) , k ) \big | \big | ^ { 2 } ] , } \end{array}
|
| 51 |
+
$$
|
| 52 |
+
|
| 53 |
+
where $\epsilon _ { \theta }$ parameterized by a deep neural network is trained to predict the noise $\epsilon \sim \mathcal { N } ( 0 , I )$ added to the dataset sample $\pmb { x } _ { 0 } ( \tau )$ to produce ${ \pmb x } _ { k } ( \tau )$ . By setting $\alpha _ { k } : = 1 - \beta _ { k }$ and $\textstyle { \bar { \alpha } } _ { k } : = \prod _ { s = 1 } ^ { k } \alpha _ { s }$ , we obtain
|
| 54 |
+
|
| 55 |
+
$$
|
| 56 |
+
\mathfrak { s } _ { k - 1 } ( \tau ) \frac { 1 } { \sqrt { \alpha _ { k } } } ( x _ { k } ( \tau ) - \frac { \beta _ { k } } { \sqrt { 1 - \bar { \alpha } _ { k } } } \epsilon _ { \theta } ( \mathbf { x } _ { k } ( \tau ) , \boldsymbol { y } ( \tau ) , \boldsymbol { k } ) ) + \sqrt { \beta _ { k } } \sigma , \sigma \sim \mathcal { N } ( \mathbf { 0 } , I ) , \mathrm { ~ f o r ~ } k = \{ K , . . . , 1 \} .
|
| 57 |
+
$$
|
| 58 |
+
|
| 59 |
+
Classifier-free guidance [19] aims to learn the conditional distribution $q ( { \pmb x } ( \tau ) | { \pmb y } ( \tau ) )$ without separately training a classifier. In the training stage, this method needs to learn both a conditional $\epsilon _ { \theta } ( { \pmb x } _ { k } ( \tau ) , { \pmb y } ( \tau ) , k )$ and an unconditional $\epsilon _ { \theta } ( { \pmb x } _ { k } ( \tau ) , \emptyset , k )$ model, where $\pmb { y } ( \tau )$ is dropped out. Then the perturbed noise $\begin{array} { r l } & { \epsilon _ { \theta } ( { \pmb x } _ { k } ( \tau ) , \emptyset , k ) + \alpha ( \epsilon _ { \theta } ( { \pmb x } _ { k } ( \tau ) , { \pmb y } ( \tau ) , k ) - \epsilon _ { \theta } ( { \pmb x } _ { k } ( \tau ) , \emptyset , k ) ) } \end{array}$ is used to generate samples latter, where $\alpha$ can be recognized as the guidance scale.
|
| 60 |
+
|
| 61 |
+
|
| 62 |
+
Figure 2: An example of the denoising process of MTDIFF. We choose 4 tasks for visualization and $\pmb { x } _ { K } ( \tau )$ is sampled from the Gaussian noise for each task. Since different tasks require different manipulation skills, the corresponding action sequences are dispersed in the embedding space. Our model learns such properties and generates task-specific sequences based on task-relevant prompts.
|
| 63 |
+
|
| 64 |
+
# 3 Methodology
|
| 65 |
+
|
| 66 |
+
# 3.1 Diffusion Formulation
|
| 67 |
+
|
| 68 |
+
To capture the multimodal distribution of the trajectories sampled from multiple MDPs, we formulate the multi-task trajectory modeling as a conditional generative problem via diffusion models:
|
| 69 |
+
|
| 70 |
+
$$
|
| 71 |
+
\begin{array} { r } { \operatorname* { m a x } _ { \boldsymbol { \theta } } \mathbb { E } _ { \tau \sim \cup _ { i } \mathcal { D } _ { i } } \big [ \log p _ { \boldsymbol { \theta } } ( \pmb { x } _ { 0 } ( \tau ) \big | \pmb { y } ( \tau ) \big ] , } \end{array}
|
| 72 |
+
$$
|
| 73 |
+
|
| 74 |
+
where $\pmb { x } _ { 0 } ( \tau )$ is the generated desired sequence and $\pmb { y } ( \tau )$ is the condition. ${ \pmb x } _ { 0 } ( \tau )$ will then be used for generative planning or data synthesis through conditional reverse denoising process $p _ { \theta }$ for specific tasks. Maximizing Eq. (3) can be approximated by maximizing a variational lower bound [20].
|
| 75 |
+
|
| 76 |
+
In terms of different inputs and outputs in generative planning and data synthesis, $\pmb { x } ( \tau )$ can be represented in different formats. We consider two choices to formulate $\pmb { x } ( \tau )$ in MTDIFF- $\mathbf { \nabla } \cdot \mathbf { P }$ and MTDIFF-S, respectively. (i) For MTDIFF-P, $\pmb { x } ( \tau )$ represents the action sequence for planning. We model the action sequence defined as:
|
| 77 |
+
|
| 78 |
+
$$
|
| 79 |
+
\pmb { x } _ { k } ^ { p } ( \tau ) : = ( a _ { t } , a _ { t + 1 } , . . . , a _ { t + H - 1 } ) _ { k } ,
|
| 80 |
+
$$
|
| 81 |
+
|
| 82 |
+
with the context condition as
|
| 83 |
+
|
| 84 |
+
$$
|
| 85 |
+
\textit { \textbf { y } } ( \tau ) : = \big [ \pmb { y } ^ { \prime } ( \tau ) , R ( \tau ) \big ] , \quad \pmb { y } ^ { \prime } ( \tau ) : = ( Z , s _ { t - L + 1 } , . . . , s _ { t } ) ,
|
| 86 |
+
$$
|
| 87 |
+
|
| 88 |
+
where $t$ , $H$ , $R ( \tau )$ and $L$ denote the time visited in trajectory $\tau$ , the length of the input sequence $_ { \textbf { \em x } }$ , the normalized cumulative return under $\tau$ and the length of the observed state history, respectively. $Z$ is the task-relevant information as prompt. We use $y ^ { \prime } ( \tau )$ as an ordinary condition that is injected into the model during both training and testing, while considering $R ( \tau )$ as the classifier-free guidance to obtain the optimal action sequence for a given task. (ii) For data synthesis in MTDIFF-S, the inputs and outputs become the transition sequence that contains states, actions, and rewards, and then the outputs are utilized for data augmentation. We define the transition sequence as:
|
| 89 |
+
|
| 90 |
+
$$
|
| 91 |
+
\pmb { x } _ { k } ^ { s } ( \tau ) : = \left[ \begin{array} { l l l l } { s _ { t } } & { s _ { t + 1 } } & { \cdot \cdot \cdot } & { s _ { t + H - 1 } } \\ { a _ { t } } & { a _ { t + 1 } } & { \cdot \cdot \cdot } & { a _ { t + H - 1 } } \\ { r _ { t } } & { r _ { t + 1 } } & { \cdot \cdot \cdot } & { r _ { t + H - 1 } } \end{array} \right] ,
|
| 92 |
+
$$
|
| 93 |
+
|
| 94 |
+
with the condition:
|
| 95 |
+
|
| 96 |
+
$$
|
| 97 |
+
\begin{array} { r } { \pmb { y } ^ { s } ( \tau ) : = [ Z ] , } \end{array}
|
| 98 |
+
$$
|
| 99 |
+
|
| 100 |
+
where $\pmb { y } ^ { s } ( \tau )$ takes the same conditional approach as $y ^ { \prime } ( \tau )$ . Figure 2 illustrates the reverse denoising process of MTDIFF-P learned on multi-task datasets collected in Meta-World [73]. The result demonstrates that our diffusion model successfully distinguishes different tasks and finally generates the desired $\pmb { x } _ { 0 } ( \tau )$ . We illustrate the data distribution of $\pmb { x } _ { 0 } ( \tau )$ in a 2D space with dimensional reduction via T-SNE [61], as well as the rendered states after executing the action sequence. The result shows that, with different task-specific prompts as conditions, the generated planning sequence for a specific task will be separate from sequences of other tasks, which verifies that MTDIFF can learn the distribution of multimodal trajectories based on $\pmb { y } ( \tau )$ .
|
| 101 |
+
|
| 102 |
+
# 3.2 Prompt, Training and Sampling
|
| 103 |
+
|
| 104 |
+
In multi-task RL and LLM-driven decision-making, existing works use one-hot task identifiers [56, 74] or language descriptions [1, 6] as conditions in multi-task training. Nevertheless, we argue that the one-hot encoding for each task [22, 14] suffices for learning a repertoire of training tasks while cannot generalize to novel tasks since it does not leverage semantic similarity between tasks. In addition, the language descriptions [51, 1, 6, 41, 40] of tasks require large amounts of human labor to annotate and encounter challenges related to ambiguity [72]. In MTDIFF, we use expert demonstrations consisting of a few trajectory segments to construct more expressive prompts in multitask settings. The incorporation of prompt learning improves the model’s ability for generalization and extracting task-relevant information to facilitate both generative planning and data synthesis. We remark that a similar method has also been used in PromptDT [69]. Nonetheless, how such a prompt contributes within a diffusion-based framework remains to be investigated.
|
| 105 |
+
|
| 106 |
+
Specifically, we formulate the task-specific label $Z$ as trajectory prompts that contain states and actions:
|
| 107 |
+
|
| 108 |
+
$$
|
| 109 |
+
Z : = \left[ \begin{array} { l l l l } { s _ { i } ^ { * } } & { s _ { i + 1 } ^ { * } } & { \cdot \cdot } & { s _ { i + J - 1 } ^ { * } } \\ { a _ { i } ^ { * } } & { a _ { i + 1 } ^ { * } } & { \cdot \cdot \cdot } & { a _ { i + J - 1 } ^ { * } } \end{array} \right] ,
|
| 110 |
+
$$
|
| 111 |
+
|
| 112 |
+
where each element with star-script is associated with a trajectory prompt, and $J$ is the number of environment steps for identifying tasks. With the prompts as conditions, MTDIFF can specify the task by implicitly capturing the transition model and the reward function stored in the prompts for better generalization to unseen tasks without additional parameter-tuning.
|
| 113 |
+
|
| 114 |
+
In terms of decision-making in MTDIFF-P, we aim to devise the optimal behaviors that maximize return. Our approach is to utilize the diffusion model for action planning via classifier-free guidance [19]. Formally, an optimal action sequence $\pmb { x } _ { 0 } ^ { p } ( \tau )$ is sampled by starting with Gaussian noise $\pmb { x } _ { K } ( \tau )$ and refining $\pmb { x } _ { k } ^ { p } ( \tau )$ into $\pmb { x } _ { k - 1 } ^ { p } ( \tau )$ at each intermediate timestep with the perturbed noise:
|
| 115 |
+
|
| 116 |
+
$$
|
| 117 |
+
\epsilon _ { \theta } \big ( { \pmb x } _ { k } ^ { p } ( \tau ) , { \pmb y } ^ { \prime } ( \tau ) , \emptyset , k \big ) + \alpha \big ( \epsilon _ { \theta } ( { \pmb x } _ { k } ^ { p } ( \tau ) , { \pmb y } ^ { \prime } ( \tau ) , R ( \tau ) , k ) - \epsilon _ { \theta } ( { \pmb x } _ { k } ^ { p } ( \tau ) , { \pmb y } ^ { \prime } ( \tau ) , \emptyset , k ) \big ) ,
|
| 118 |
+
$$
|
| 119 |
+
|
| 120 |
+
where $y ^ { \prime } ( \tau )$ is defined in Eq. (5). $R ( \tau )$ is the normalized return of $\tau$ , and $\alpha$ is a hyper-parameter that seeks to augment and extract the best portions of trajectories in the dataset with high return. During training, we follow DDPM [20] as well as classifier-free guidance [19] to train the reverse diffusion process $p _ { \theta }$ , parameterized through the noise model $\epsilon _ { \theta }$ , with the following loss:
|
| 121 |
+
|
| 122 |
+
$$
|
| 123 |
+
\begin{array} { r } { \colon ( \theta ) : = \mathbb { E } _ { k \sim \mathcal { U } ( 1 , K ) , x _ { 0 } ( \tau ) \sim q , \epsilon \sim \mathcal { N } ( \mathbf { 0 } , I ) , \beta \sim \mathrm { B e r n } ( \mathrm { p } ) } \big [ \big \| \epsilon - \epsilon _ { \theta } \big ( \mathbf { x } _ { k } ( \tau ) , y ^ { \prime } ( \tau ) , ( 1 - \beta ) R ( \tau ) + \beta \mathcal { Q } , k \big ) \big \| _ { * } ^ { 2 } \big ] . } \end{array}
|
| 124 |
+
$$
|
| 125 |
+
|
| 126 |
+
Note that with probability $p$ sampled from a Bernoulli distribution, we ignore the conditioning return $R ( \tau )$ . During inference, we adopt the low-temperature sampling technique [2] to produce high-likelihood sequences. We sample $\begin{array} { r } { \pmb { x } _ { k - 1 } ^ { p } ( \tau ) \sim \hat { \mathcal { N } } ( \mu _ { \theta } ( \pmb { x } _ { k - 1 } ^ { p } , \pmb { y } ^ { \prime } ( \tau ) , R _ { \operatorname* { m a x } } ( \tau ) , k - 1 ) , \bar { \beta } \Sigma _ { k - 1 } ) } \end{array}$ , where the variance is reduced by $\beta \in [ 0 , 1 )$ for generating action sequences with higher optimality.
|
| 127 |
+
|
| 128 |
+
For MTDIFF-S, since the model aims to synthesize diverse trajectories for data augmentation, which does not need to take any guidance like $R ( \tau )$ , we have the following loss:
|
| 129 |
+
|
| 130 |
+
$$
|
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\begin{array} { r } { \mathcal { L } \mathbf { \Psi } ( \mathbf { \theta } ) : = \mathbb { E } _ { k \sim \mathcal { U } ( 1 , K ) , \mathbf { x } _ { 0 } ( \tau ) \sim q , \epsilon \sim \mathcal { N } ( \mathbf { 0 } , I ) } \left[ \left| \left| \epsilon - \epsilon _ { \theta } ( \mathbf { x } _ { k } ( \tau ) , \boldsymbol { y } _ { \mathbf { \alpha } } ( \tau ) , k ) \right| \right| ^ { 2 } \right] . } \end{array}
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$$
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We sample $\pmb { x } _ { k - 1 } ^ { s } ( \tau ) \sim \mathcal { N } ( \mu _ { \theta } ( \pmb { x } _ { k - 1 } ^ { s } , \pmb { y } ^ { s } ( \tau ) , k - 1 ) , \Sigma _ { k - 1 } )$ . The evaluation process is given in Fig. 3.
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# 3.3 Architecture Design
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Notably, the emergence of Transformer [62] and its applications on generative modeling [44, 5, 47, 6] provides a promising solution to capture interactions between modalities of different tasks. Naturally, instead of U-Net [48] which is commonly used in previous single-task diffusion RL works [21, 2, 33], we parameterize $\epsilon _ { \theta }$ with a novel transformer architecture. We adopt GPT2 [45] architecture for implementation, which excels in sequential modeling and offers a favorable balance between performance and computational efficiency. Our key insight is to train the diffusion model in a unified manner to model multi-task data, treating different inputs as tokens in a unified architecture, which is expected to enhance the efficiency of diverse information exploitation.
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Figure 3: Model architecture of MTDIFF, which treats different inputs as tokens in a unified architecture. The two key designs are (i) the trainable GPT2 Transformer which enhances sequential modeling, and (ii) the MLPs and prediction head which enable efficient training.
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As shown in Figure 3, first, different raw inputs $x$ are embedded into embeddings $h$ of the same size $^ d$ via separate MLPs $f$ , which can be expressed as:
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$$
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\begin{array} { l } { { h _ { \mathit { P } } = f _ { \mathit { P } } ( x ^ { \mathrm { { p r o m p t } } } ) , h _ { \mathit { T } i } = f _ { T i } ( x ^ { \mathrm { { t i m e s t e p } } } ) , \mathrm { { \beta _ { \mathit { P } } } \vdash \mathrm { { f o r ~ p r o m p t ~ a n d ~ d i f f u s i o n ~ t i m e s t e p } } } } } \\ { { h _ { \mathit { T r } } ^ { s } = f _ { T r } ( x ^ { \mathrm { { t r a n s i t i o n s } } } ) , \mathrm { { \beta _ { \mathit { P } } \vdash \mathrm { { f o r ~ M T D I F F - S } } } } } } \\ { { h _ { \mathit { A } } ^ { p } = f _ { A } ( x ^ { \mathrm { { a c t i o n s } } } ) , h _ { \mathit { H } } ^ { p } = f _ { H } ( x ^ { \mathrm { { h i s t o r y } } } ) , h _ { \mathit { R } } ^ { p } = f _ { R } ( x ^ { \mathrm { { r e t u r n } } } ) . \mathrm { { \beta _ { \mathit { P } } \mathrm { { f o r ~ M T D I F F - P } } } } } } \end{array}
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$$
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Then, the embeddings $h _ { P }$ and $h _ { T i }$ are prepended as follows to formulate input tokens for MTDIFF-P and MTDIFF-S, respectively:
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$\iota _ { \mathrm { t o k e n s } } = \mathrm { L N } ( h _ { T i } \times [ h _ { P } , h _ { T i } , h _ { R } , h _ { H } , h _ { A } ] + h _ { R } + E ^ { \mathrm { p o s } } ) , h _ { \mathrm { t o k e n s } } = \mathrm { L N } ( h _ { T i } \times [ h _ { P } , h _ { T i } , h _ { T r } ] + E ^ { \mathrm { p o s } } ) ,$ where $E ^ { \mathrm { p o s } }$ is the positional embedding, and LN denotes layer normalization [3] for stabilizing training. In our implementation, we strengthen the condition of the stacked inputs through multiplication with the diffusion timestep $h _ { T i }$ and addition with the return $h _ { R } ^ { p }$ . GPT2 is a decoder-only transformer that incorporates a self-attention mechanism to capture dependencies between different positions in the input sequence. We employ the GPT2 architecture as a trainable backbone in MTDIFF to handle sequential inputs. It outputs an updated representation as:
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$$
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h _ { \mathrm { o u t } } ^ { p } = \mathrm { t r a n s f o r m e r } ( h _ { \mathrm { t o k e n s } } ^ { p } ) , \quad h _ { \mathrm { o u t } } ^ { s } = \mathrm { t r a n s f o r m e r } ( h _ { \mathrm { t o k e n s } } ^ { s } ) .
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$$
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Finally, given the output representation, we use a prediction head consisting of fully connected layers to predict the corresponding noise at diffusion timestep $k$ . Notice that the predicted noise shares the same dimensional space as the original inputs, which differs from the representation size $^ d$ . This noise is used in the reverse denoising process $p _ { \theta }$ during inference. We summarize the details of the training process, architecture and hyperparameters used in MTDIFF in Appendix A.
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# 4 Related Work
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Diffusion Models in RL. Diffusion models have emerged as a powerful family of deep generative models with a record-breaking performance in many applications across vision, language and combinatorial optimization [49, 46, 17, 31, 32]. Recent works in RL have demonstrated the capability of diffusion models to learn the multimodal distribution of offline policies [63, 43, 11] or human behaviors [8]. Other works formulate the sequential decision-making problem as a conditional generative process [2] and learn to generate the trajectories satisfying conditioned constraints. However, these works are limited to the single-task settings, while we further study the trajectory modeling and generalization problems of diffusion models in multi-task settings.
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Multi-Task RL and Few-Shot RL. Multi-task RL aims to learn a shared policy for a diverse set of tasks. The main challenge of multi-task RL is the conflicting gradients among different tasks, and previous online RL works address this problem via gradient surgery [74], conflict-averse learning [34], and parameter composition [70, 56]. Instead, MTDIFF addresses such a problem in an offline setting through a conditional generative process via a novel transformer architecture. Previous Decision-Transformer (DT)-based methods [47, 29, 72] which consider handling multi-task problems, mainly rely on expert trajectories and entail substantial training expenses. Scaled-QL [26] adopts separate networks for different tasks and is hard to generalize to new tasks. Instead of focusing on the performance of training tasks in multi-task RL, few-shot RL aims to improve the generalizability in novel tasks based on the learned multi-task knowledge. Nevertheless, these methods need additional context encoders [77, 79] or gradient descents in the finetuning stage [57, 58, 29]. In contrast, we use prompts for few-shot generalization without additional parameter-tuning.
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Data Augmentation for RL. Data augmentation [13, 39] has been verified to be effective in RL. Previous methods incorporate various data augmentations (e.g. adding noise, random translation) on observations for visual-based RL [71, 28, 52, 27], which ensure the agents learn on multiple views of the same observation. Differently, we focus on data augmentation via synthesizing new experiences rather than perturbing the origin one. Recent works [76, 10] consider augmenting the observations of robotic control using a text-guided diffusion model whilst maintaining the same action, which differs from our approach that can synthesize novel action and reward labels. The recently proposed SynthER [38] is closely related to our method by generating transitions of trained tasks via a diffusion model. However, SynthER is studied in single-task settings, while we investigate whether a diffusion model can accommodate all knowledge of multi-task datasets and augment the data for novel tasks.
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# 5 Experiments
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In this section, we conduct extensive experiments to answer the following questions: (1) How does MTDIFF-P compare to other offline and online baselines in the multi-task regime? (2) Does MTDIFFS synthesize high-fidelity data and bring policy improvement? (3) How is MTDIFF-S compared with other augmentation methods for single-task RL? (4) Does the synthetic data of MTDIFF-S match the original data distribution? (5) Can both MTDIFF-P and MTDIFF-S generalize to unseen tasks?
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# 5.1 Environments and Baselines
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Meta-World Tasks The Meta-World benchmark [73] contains 50 qualitatively-distinct manipulation tasks. The tasks share similar dynamics and require a Sawyer robot to interact with various objects with different shapes, joints, and connectivity. In this setup, the state space and reward functions of different tasks are different since the robot is manipulating different objects with different objectives. At each timestep, the Sawyer robot receives a 4-dimensional fine-grained action, representing the 3D position movements of the end effector and the variation of gripper openness. The original Meta-World environment is configured with a fixed goal, which is more restrictive and less realistic in robotic learning. Following recent works [70, 56], we extend all the tasks to a random-goal setting and refer to it as MT50-rand. We use the average success rate of all tasks as the evaluation metric.
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By training a SAC [18] agent for each task in isolation, we utilize the experience collected in the replay buffer as our offline dataset. Similar to [26], we consider two different dataset compositions: (i) Near-optimal dataset consisting of the experience (100M transitions) from random to expert (convergence) in SAC-Replay, and (ii) Sub-optimal dataset consisting of the initial $50 \%$ of the trajectories (50M transitions) from the replay buffer for each task, where the proportion of expert data decreases a lot. We summarize more details about the dataset in Appendix G.
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Maze2D Tasks Maze2D [15] is a navigation task that requires an agent to traverse from a randomly designated location to a fixed goal in the 2D map. The reward is 1 if succeed and 0 otherwise. Maze2D can evaluate the ability of RL algorithms to stitch together previously collected sub-trajectories, which helps the agent find the shortest path to evaluation goals. We use the agent’s scores as the evaluation metric. The offline dataset is collected by selecting random goal locations and using a planner to generate sequences of waypoints by following a PD controller.
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Baselines We compare our proposed MTDIFF (MTDIFF-P and MTDIFF-S) with the following baselines. Each baseline has the same batch size and training steps as MTDIFF. For MTDIFF-P, we have following baselines: (i) PromptDT. PromptDT [69] built on Decision-Transformer (DT) [9] aims to learn from multi-task data and generalize the policy to unseen tasks. PromptDT generates actions based on the trajectory prompts and reward-to-go. We use the same GPT2-network as in MTDIFF-P. The main difference between our method and PromptDT is that we employ diffusion models for generative planning. (ii) MTDT. We extend the DT architecture [9] to learn from multitask data. Specifically, MTDT concatenates an embedding $z$ and a state $s$ as the input tokens, where $z$ is the encoding of task ID. In evaluation, the reward-to-go and task ID are fed into the Transformer to provide task-specific information. MTDT also uses the same GPT2-network as in MTDIFF-P. Compared to MTDT, our model incorporates prompt and diffusion framework to learn from the multi-task data. (iii) MTCQL. Following scaled-QL [26], we extend CQL [25] with multi-head critic networks and a task-ID conditioned actor for multi-task policy learning. (iv) MTIQL. We extend IQL [24] for multi-task learning using a similar revision of MTCQL. The TD-based baselines (i.e., MTCQL and MTIQL) are used to demonstrate the effectiveness of conditional generative modeling for multi-task planning. (v) MTBC. We extend Behavior cloning (BC) to multi-task offline policy learning via network scaling and a task-ID conditioned actor that is similar to MTCQL and MTIQL.
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As for MTDIFF-S, we compare it with two baselines that perform direct data augmentation in offline RL. (i) RAD. We adopt the random amplitude scaling [28] that multiplies a random variable to states, i.e., $s ^ { \prime } = s \times z$ , where $z \sim \mathrm { U n i f o r m } [ \alpha , \beta ]$ . This augmentation technique has been verified to be effective for state-based RL. (ii) S4RL. We adopt the adversarial state training [52] by taking gradients with respect to the value function to obtain a new state, i.e. $s ^ { \prime } s + \epsilon \nabla _ { s } \mathbb { J } _ { Q } ( \pi ( s ) )$ , where $\mathbb { J } _ { Q }$ is the policy evaluation update performed via a $Q$ function, and $\epsilon$ is the size of gradient steps. We summarize the details of all the baselines in Appendix B.
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# 5.2 Result Comparison for Planning
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# How does MTDIFF-P compare to baselines in the multi-task regime? For a fair comparison,
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we add MTDIFF-P-ONEHOT as a variant of MTDIFF-P by replacing the prompt with a one-hot task-ID, which is used in the baselines except for PromptDT. The first action generated by MTDIFF-P is used to interact with the environment. According to Tab. 1, we have the following key observations. (i) Our method achieves better performance than baselines in both near-optimal and sub-optimal settings. For near-optimal datasets, MTDIFF-P and MTDIFF-P-ONEHOT achieve about $60 \%$ success rate, significantly outperforming other methods and performing comparably with MTBC. However, the performance of MTBC decreases a lot in sub-optimal datasets. BC is hard to handle the conflict behaviors in experi
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Table 1: Average success rate across 3 seeds on MetaWorld-V2 MT50 with random goals (MT50-rand). Each task is evaluated for 50 episodes.
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<table><tr><td>Methods</td><td>Near-optimal</td><td>Sub-optimal</td></tr><tr><td>CARE [53] (Online)</td><td>50.8 ± 1.0</td><td>一</td></tr><tr><td>PaCo [56] (Online)</td><td>57.3 ± 1.3</td><td>1</td></tr><tr><td>MTDT</td><td>20.99 ± 2.66</td><td>20.63 ± 2.21</td></tr><tr><td>PromptDT</td><td>45.68 ± 1.84</td><td>39.76 ± 2.79</td></tr><tr><td>MTBC</td><td>60.39 ±0.86</td><td>34.53 ± 1.25</td></tr><tr><td>MTCQL</td><td></td><td></td></tr><tr><td>MTIQL</td><td>56.21 ± 1.39</td><td>43.28 ± 0.90</td></tr><tr><td>MTDIFF-p (ours)</td><td>59.53 ± 1.12</td><td>48.67 ± 1.32</td></tr><tr><td>MTDIFF-P-ONEHOT (ours)</td><td>61.32 ± 0.89</td><td>48.94± 0.95</td></tr></table>
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ences sampled by a mixture of policies with different returns, which has also been verified in previous offline imitation methods [35, 68]. In contrast, both MTDIFF-P and MTDIFF-ONEHOT perform the best in sub-optimal datasets. (ii) We compare MTDIFF-P with two SOTA multi-task online RL methods, CARE [53] and PaCo [56], which are trained for 100M steps in MT50-rand. MTDIFF-P outperforms both of them given the near-optimal dataset, demonstrating the potential of solving the multi-task RL problems in an offline setting. (iii) MTDT is limited in distinguishing different tasks with task ID while PromptDT performs better, which demonstrates the effect of prompts in multi-task settings. (iv) As for TD-based baselines, we find MTCQL almost fails while MTIQL performs well. We hypothesize that since MTCQL penalizes the OOD actions for each task, it will hinder other tasks’ learning since different tasks can choose remarkably different actions when facing similar states. In contrast, IQL learns a value function without querying the values of OOD actions.
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We remark that MTDIFF-P based on GPT network outperforms that with U-Net in similar model size, and detailed results are given in Appendix C. Overall, MTDIFF-P is an effective planner in multi-task settings including sub-optimal datasets where we must stitch useful segments of suboptimal trajectories, and near-optimal datasets where we mimic the best behaviors. Meanwhile, we argue that although MTDIFF-P-ONEHOT performs well, it cannot generalize to unseen tasks without prompts.
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Figure 1: Seen and unseen maps of Maze2D with long planning path. Goal position is denoted as .Figure 4: Seen and unseen maps of Maze2D with long planning path. Goal position is denoted as .
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Figure 5: Average scores obtained in 8 Maze2D maps.
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Does MTDIFF-P generalize to unseen tasks? We further carry out experiments on Maze2D Diffusion Model is an Effective Planner and Data to evaluate the generalizability of MTDIFF-P. We select PromptDT as our baseline, as it has Synthesizer for Multi-Task RL demonstrated both competitive performances on training tasks and adaptation ability for unseen tasks [69]. We use 8 different maps for training and one new map for adaptation evaluation. The setup details are given in Appendix D. We evaluate these two methods on both seen maps and an unseen map. The average scores obtained in 8 training maps are referred to Figure 5. To further illustrate Affiliation the advantages of our method compared to PromptDT, we select one difficult training map and the Address unseen map for visualization, as shown in Figure 4. According to the visualized path, we find that (1) for seen maps in training, MTDIFF-P generates a shorter and smoother path, and (2) for unseen maps, PromptDT fails to obtain a reasonable path while MTDIFF-P succeed, which verifies that MTDIFF-P can perform few-shot adaptation based on trajectory prompts and the designed architecture.
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# 5.3 Results for Augmentation via Data Synthesis
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Does MTDIFF-S synthesize high-fidelity data and bring policy improvement? We train MTDIFFS on near-optimal datasets from 45 tasks to evaluate its generalizability. We select 3 training tasks and 3 unseen tasks, and measure the policy improvement of offline RL training (i.e., TD3-BC [16]) with data augmentation. For each evaluated task, MTDIFF-S synthesizes 2M transitions to expand the original 1M dataset. From the results summarized in Table 2, MTDIFF-S can boost the offline performance for all tasks and significantly increases performance by about $180 \%$ , $131 \%$ , and $161 \%$ for box-close, hand-insert, and coffee-push, respectively.
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Figure 7: Average success rate across 3 seeds on coffee-push. Dataset is augmented by MTDIFF-S trained under different number of tasks.
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Figure 6: Results of multi-task and single- task augmentation
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How does MTDiff-s perform and benefit from multi-task training? From Table 2, we find MTDIFF-S achieves superior policy improvement in seen tasks compared with previous SOTA augmentation methods (i.e., S4RL and RAD) that are developed in single-task RL. We hypothesize that, by absorbing vast knowledge of multi-task data in training, MTDIFF-S can perform implicit data sharing [75] by integrating other tasks’ knowledge into data synthesis of the current task. To verify this hypothesis, we select three tasks (i.e., coffee-push, disassemble and dial-turn) to re-train MTDIFF-S on the corresponding single-task dataset. We denote this variant as MTDIFF-S-SINGLE. We implement SynthER [38] to further confirm the benefits of multi-task training. SynthER also utilizes diffusion models to enhance offline datasets for policy improvement, but it doesn’t take into account the aspect of learning from multi-task data. We observe that MTDIFF-S outperforms both two methods, as shown in Figure 6. What’s more, we re-train MTDIFF-S on 10, 20, and 30 tasks respectively, in order to obtain the relationship between the performance gains and the number of training tasks. Our findings, as outlined in Fig. 7, provide compelling evidence in support of our hypothesis: MTDIFF-S exhibits progressively superior data synthesis performance with increasing task diversity.
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Does MTDIFF-S generalize to unseen tasks? We answer this question by conducting offline RL training on the augmented datasets of 3 unseen tasks. According to Table 2, MTDIFF-S is wellgeneralized and obtains significant improvement compared to the success rate of original datasets. MTDIFF-S boost the policy performance by $131 \%$ , $180 \%$ and $32 \%$ for hand-insert, box-close and bin-picking, respectively. We remark that S4RL performs the best on the two unseen tasks, i.e., box-close and bin-picking, since it utilizes the entire datasets to train $Q$ -functions and obtains the augmented states. Nevertheless, we use much less information (i.e., a single trajectory as prompts) for augmentation.
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Table 2: Average success rate across 3 seeds on Meta-World-V2 single task with random goals. Each selected task is evaluated for 500 episodes.
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<table><tr><td colspan="2">Tasks</td><td>Original</td><td>S4RL</td><td>RAD</td><td>MTDIFF-S(OURS)</td></tr><tr><td rowspan="2">Unseen Tasks</td><td>box-close</td><td>23.46 ± 7.11</td><td>73.13±3.51(个211%)</td><td>71.20±4.84(个203%)</td><td>65.73±8.36 (↑180%)</td></tr><tr><td>hand-insert bin-picking</td><td>30.60±9.77</td><td>60.20 ± 1.57 (↑ 96%)</td><td>43.79 ±3.44 (↑43%)</td><td>70.87 ± 3.59 (↑ 131%)</td></tr><tr><td rowspan="2">Seen Tasks</td><td>sweep-into</td><td>42.13 ± 14.33 91.8 ±1.14</td><td>72.20 ± 4.17(↑ 71%) 90.53 ±3.52(↓ 1%)</td><td>43.27 ± 4.38(↑ 2%)</td><td>55.73 ± 7.63(↑32%)</td></tr><tr><td>coffee-push</td><td>28.60 ± 14.55</td><td>28.73±8.44(个 0.4%)</td><td>88.06±9.86(↓4%)</td><td>92.87 ± 1.11(↑ 1%)</td></tr><tr><td rowspan="2"></td><td>disassemble</td><td></td><td></td><td>33.19 ± 2.86(个 16%)</td><td>74.67 ± 6.79(↑ 161%)</td></tr><tr><td></td><td>60.20 ±16.29</td><td>52.20 ± 5.68(↓12%)</td><td>60.93 ± 20.80(个1%)</td><td>69.00 ± 4.72(↑ 14.6%)</td></tr></table>
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Does the synthetic data of MTDIFF-S match the original data distribution? We select 4 tasks and use T-SNE [61] to visualize the distribution of original data and synthetic data. We find the synthetic data overlap and expand the original data distribution while also keeping consistency with the underlying MDP. The visualization results and further analyses are given in Appendix E.
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# 6 Conclusion
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We propose MTDIFF, a diffusion-based effective planner and data synthesizer for multi-task RL. With the trajectory prompt and unified GPT-based architecture, MTDIFF can model multi-task data and generalize to unseen tasks. We show that in the MT50-rand benchmark containing fine-grained manipulation tasks, MTDIFF-P generates desirable behavior for each task via few-shot prompts. By compressing multi-task knowledge in a single model, we demonstrate that MTDIFF-S greatly boosts policy performance by augmenting original offline datasets. In future research, we aim to develop a practical multi-task algorithm for real robots to trade off the sample speed and generative quality. We further discuss the limitations and broader impacts of MTDIFF in Appendix F.
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# Acknowledgments
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This work is supported by the National Natural Science Foundation of China (Grant No.62306242&62076161), the National Key R&D Program of China (Grant No.2022ZD0160100), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102) and Shanghai Artificial Intelligence Laboratory.
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# A The Details of MTDIFF
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In this section, we give the pseudocodes of MTDIFF-P and MTDIFF-S in Alg. 1 and Alg. 2, respectively. Then we describe various details of the training process, architecture and hyperparameters:
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��� We set the per-task batch size as 8, so the total batch size is 400. We train our model using Adam optimizer [23] with $2 e ^ { - 4 }$ learning rate for $2 e ^ { 6 }$ train steps.
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• We train MTDIFF on NVIDIA GeForce RTX 3080 for around 50 hours.
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• We represent the noise model as the transformer-based architecture described in Section 3.3. MLP $f _ { P }$ which processes prompt is a 3-layered MLP (prepended by a layer norm [3] and with Mish activation). MLP $f _ { T i }$ which processes diffusion timestep $f _ { R }$ is a 2-layered MLP (prepended by a Sinusoidal embedding and with Mish activation). $f _ { R }$ which processes conditioned Return and $f _ { H }$ which processes state history are 3-layered MLPs with Mish activation. $f _ { A }$ which processes actions, $f _ { T R }$ which process transitions and prediction head are 2-layered MLPs with Mish activation. The GPT2 transformer is configured as 6 hidden layers and 4 attention heads. The code of GPT2 is borrowed from https://github.com/kzl/decision-transformer.
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• We choose the probability $p$ of removing the conditioning information to be 0.25.
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• In MTDIFF-P, we choose the state history length $L = 2$ for Meta-World and $L = 5$ for Maze2D.
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• We choose the trajectory prompt length $J = 2 0$ .
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• We use $K = 2 0 0$ for diffusion steps.
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• We set guidance scale $\alpha = 1 . 2$ for extracting near-optimal behavior.
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• We choose $\beta = 0 . 5$ for low temperature sampling.
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# Algorithm 1 MTDIFF-P Training and Evaluation
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# Training Process
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Initialize: training tasks ${ \mathcal { T } } ^ { t r a i n }$ , training iterations $N$ , multi-task dataset $\mathcal { D }$ , per-task batch size $M$ multi-task trajectory prompts $Z$
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+
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+
1: for $n = 1$ to $N$ do
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+
2: for Each task $\mathcal { T } _ { i } \in \mathcal { T } ^ { t r a i n } ~ ,$ do
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+
3: Sample action sequences $\pmb { x } _ { 0 } ( \tau _ { i } )$ of length $H$ and corresponding state history $S _ { i } ^ { \mathrm { p r e v } }$ of length
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+
$L$ from $\mathcal { D } _ { i }$ with batch size $M$
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+
4: Compute normalized return $R ( \tau _ { i } )$ under $\tau _ { i }$
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+
5: Sample trajectory prompts $\boldsymbol { \tau } _ { i } ^ { * }$ of length $J$ from $Z _ { i }$ with batch size $M$
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+
6: end for
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+
7: Get a batch $\begin{array} { r } { \mathbb { B } = \{ \pmb { x } _ { 0 } ^ { p } ( \tau _ { i } ) , \tau _ { i } ^ { * } , S _ { i } ^ { \mathrm { p r e v } } , R ( \tau _ { i } ) \} _ { i = 1 } ^ { | \mathcal { T } ^ { t r a i n } | } } \end{array}$
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+
8: Randomly sample a diffusion timestep $k \sim \mathcal { U } ( 1 , K )$ and obtain noisy sequences $\pmb { x } _ { k } ^ { p } ( \tau _ { i } )$
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+
9: Omit the $R ( \tau )$ condition with probability $\beta \sim \mathrm { B e r n } ( p )$
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+
10: Compute ${ \mathcal { L } } ^ { p } ( \theta )$ and update MTDIFF-P model
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+
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# 11: end for
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+
# Evaluation Process
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| 426 |
+
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+
1: Given a task, reset the environment and set desired return $R _ { \mathrm { m a x } } ( \tau )$
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+
2: Obtain the initial state history $h _ { 0 }$ , few-shot prompts $Z$
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+
3: Set low-temperature sampling scale $\beta$ , classifier-free guidance scale $\alpha$
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+
4: for $t = 0$ to $t _ { \mathrm { m a x } }$ do
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| 431 |
+
5: Initialize $\pmb { x } _ { K } ^ { p } ( \tau ) \sim { \mathcal { N } } ( \mathbf { 0 } , \beta \pmb { I } )$
|
| 432 |
+
6: Sample $\tau ^ { * } \sim Z$ , and formulate $\pmb { y } ^ { \prime } ( \tau ) = [ h _ { t } , \tau ^ { * } ]$
|
| 433 |
+
7: for $k = K$ to 1 do
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| 434 |
+
8: $\begin{array} { r l } & \dot { \mathbf { \Xi } } _ { k } ^ { \mathrm { ~ ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \dot { \Xi } _ { k } ^ { \mathrm { ~ ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \Lambda } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \dot { \Xi } _ { k } ^ { \mathrm { ~ } } = \epsilon _ { \theta } \big ( \mathbf { \Delta } \mathbf { x } _ { k } ( \tau ) , \mathbf { \Xi } \mathbf { y } ^ { \prime } ( \tau ) , \mathcal { Q } , k \big ) + \alpha \big ( \epsilon _ { \theta } \big ( \mathbf { \Delta } \mathbf { x } _ { k } ( \tau ) , \mathbf { \Xi } \mathbf { y } ^ { \prime } ( \tau ) , R _ { \operatorname* { m a x } } ( \tau ) , k \big ) - \epsilon _ { \theta } \big ( \mathbf { \Delta } \mathbf { x } _ { k } ( \tau ) , \mathbf { \Xi } \mathbf { y } ^ { \prime } ( \tau ) , \mathcal { Q } , k \big ) \big ) } \\ & { \left( \mu _ { k - 1 } , \Sigma _ { k - 1 } \right) \gets \mathrm { ~ D e n o i s e } ( \mathbf { \Delta } \mathbf { x } _ { k } ( \tau ) , \hat { \mathbf { \Xi } } \mathbf { \Lambda } \mathbf { \Lambda } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \mathrm { ~ } \Omega ) } \\ & { \mathbf { \Delta } \mathbf { x } _ { k - 1 } ^ { \mathrm { ~ } } ( \tau ) \sim \mathcal { N } ( \mu _ { k - 1 } , \beta \Sigma _ { k - 1 } ) } \end{array}$
|
| 435 |
+
9:
|
| 436 |
+
10:
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| 437 |
+
11: end for
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| 438 |
+
12: Execute the first action from $\pmb { x } _ { 0 } ( \tau )$ as the current action to interact with the environment
|
| 439 |
+
13: Obtain the next state, and update $h _ { t }$
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| 440 |
+
14: end for
|
| 441 |
+
|
| 442 |
+
# Training Process
|
| 443 |
+
|
| 444 |
+
Initialize: training tasks ${ \mathcal { T } } ^ { t r a i n }$ , training iterations $N$ , multi-task dataset $\mathcal { D }$ , per-task batch size $M$ multi-task trajectory prompts $Z$
|
| 445 |
+
|
| 446 |
+
1: for $n = 1$ to $N$ do
|
| 447 |
+
2: for Each task ${ \mathcal { T } } _ { i } \in { \mathcal { T } } ^ { t r a i n }$ do
|
| 448 |
+
3: Sample transition sequences $\pmb { x } _ { 0 } ( \tau _ { i } )$ of length $H$ from $\mathcal { D } _ { i }$ with batch size $M$
|
| 449 |
+
4: Sample trajectory prompts $\boldsymbol { \tau } _ { i } ^ { * }$ of length $J$ from $Z _ { i }$ with batch size $M$
|
| 450 |
+
5: end for
|
| 451 |
+
6: Get a batch $\boldsymbol { B } = \{ \boldsymbol { x } _ { 0 } ^ { s } ( \tau _ { i } ) , \tau _ { i } ^ { * } \} _ { i = 1 } ^ { | \mathcal { T } ^ { t r a i n } | }$ p
|
| 452 |
+
7: Randomly sample a diffusion timestep $k \sim \mathcal { U } ( 1 , K )$ and obtain noisy sequences $\pmb { x } _ { k } ^ { s } ( \tau _ { i } )$
|
| 453 |
+
8: Compute ${ \mathcal { L } } ^ { s } ( \theta )$ and update MTDIFF-S model
|
| 454 |
+
|
| 455 |
+
# Data Synthesis Process
|
| 456 |
+
|
| 457 |
+
Initialize: synthetic dataset $\mathcal { D } = \varnothing$ , synthesizing times $M$
|
| 458 |
+
|
| 459 |
+
1: Given a task, obtain few-shot prompts $Z$
|
| 460 |
+
2: for $m = 1$ to $M$ do
|
| 461 |
+
3: Initialize $\mathbf { \boldsymbol { x } } _ { K } ( \tau ) \sim \mathcal { N } ( \mathbf { \boldsymbol { 0 } } , I )$
|
| 462 |
+
4: Sample $\tau ^ { * } \sim Z$ , and formulate $\pmb { y } _ { k } ^ { s } ( \tau ) = [ \tau ^ { * } ]$
|
| 463 |
+
5: for $k = K$ to 1 do
|
| 464 |
+
6: $\begin{array} { r l } & { \hat { \epsilon } = \epsilon _ { \theta } \big ( \pmb { x } _ { k } ( \tau ) , \pmb { y } _ { \mathbf { \lambda } } ( \tau ) , k \big ) } \\ & { ( \mu _ { k - 1 } , \Sigma _ { k - 1 } ) \mathrm { D e n o i s e } ( \pmb { x } _ { k } ( \tau ) , \hat { \epsilon } ) } \\ & { \pmb { x } _ { k - 1 } ( \tau ) \sim \mathcal { N } ( \mu _ { k - 1 } , \Sigma _ { k - 1 } ) } \end{array}$
|
| 465 |
+
7:
|
| 466 |
+
8:
|
| 467 |
+
9: end for
|
| 468 |
+
10: Update $\mathcal { D } = \mathcal { D } \cup \pmb { x } _ { 0 } ^ { s } ( \tau )$
|
| 469 |
+
11: end for
|
| 470 |
+
|
| 471 |
+
# B The Details of Baselines
|
| 472 |
+
|
| 473 |
+
In this section, we describe the implementation details of the baselines:
|
| 474 |
+
|
| 475 |
+
• PromptDT uses the same prompts and GPT2 transformer in MTDIFF-P for taining. We borrow the code from https://github.com/mxu34/prompt-dt for implementation.
|
| 476 |
+
|
| 477 |
+
• MTDT embeds the tskaID which indicates the task to a embedding $z$ with size 12, then $z$ is concatenated with the raw state. With such conditioning, we broaden the original state space to equip DT with the ability to identify tasks in this multi-task setting. We keep other hyperparameters and implementation details the same as the official version https://github.com/kzl/ decision-transformer/.
|
| 478 |
+
|
| 479 |
+
• MTIQL uses a multi-head critic network to predict the $Q$ value for each task, and each head is parameterized with a 3-layered MLP (with Mish activation). The actor-network is parameterized with a 3-layered MLP (with Mish activation). During training and inference, the scalar taskID is embedded via 3-layered MLP (with Mish activation) into latent variable $z$ , and the input of the actor becomes the concatenation of the original state and $z$ . We build MTIQL based on the code https://github.com/tinkoff-ai/CORL [59].
|
| 480 |
+
|
| 481 |
+
• MTCQL is applied with a similar revision in MTIQL. The main difference is that MTCQL is based on CQL [25] algorithm instead of the IQL algorithm [24]. We build MTCQL based on the code https://github.com/tinkoff-ai/CORL [59].
|
| 482 |
+
|
| 483 |
+
• MTBC uses a similar taskID-cognitional actor in MTIQL and MTCQL. For training and inference, the scalar taskID is embedded via a 3-layered MLP (with Mish activation) into latent variable $z$ , and the input of the actor becomes the concatenation of the original state and $z$ . The actor is parameterized with a 3-layered MLP and outputs predicted actions.
|
| 484 |
+
|
| 485 |
+
• RAD adopts the random amplitude scaling [28] that multiplies a random variable to states during training, i.e., $s ^ { \prime } = s \times z$ , where $z \sim \mathrm { U n i f o r m } [ \alpha , \beta ]$ . We choose $\alpha = 0 . 8$ and $\beta = 1 . 2$ .
|
| 486 |
+
|
| 487 |
+
• S4RL adopts the adversarial state training [52] by taking gradients with respect to the value function to obtain a new state, i.e. $s ^ { \prime } \bar { s } + \epsilon \nabla _ { s } \bar { \mathbb { J } } _ { Q } ( \pi ( s \bar { ) } )$ , where $\mathbb { J } _ { Q }$ is the policy evaluation update performed via a $Q$ function, and $\epsilon$ is the size of gradient steps. We choose $\epsilon = 0 . 0 1$ .
|
| 488 |
+
|
| 489 |
+
# C Ablation Study on Model Architecture
|
| 490 |
+
|
| 491 |
+
The architecture described in $\ S 3 . 3$ handles input types of different modalities as tokens that share similar formats, actively capturing interactions between modalities. The incorporation of a transformer is also helpful for sequential modeling. To ablate the effectiveness of our architecture design, we train MTDIFF-P using U-Net with a similar model size to ours on the near-optimal dataset. We use a Temporal Convolutional Network (TCN) [4] to encode the prompt into an embedding $z _ { p }$ , and inject it in the U-Net layers as a condition. We follow the conditional approach in [2] and borrow the code for temporal U-Net from https://github.com/jannerm/diffuser [21]. The results summarized in Table 3 show that our model architecture outperforms U-Net to learn from multi-task datasets.
|
| 492 |
+
|
| 493 |
+
Table 3: Average success rate across 3 different seeds of MTDIFF-P and MTDIFF-P (U-Net) on MT50-rand.
|
| 494 |
+
|
| 495 |
+
<table><tr><td>Methods</td><td>Success rate on near-optimal dataset (%）Success rate on sub-optimal dataset (%)</td><td></td></tr><tr><td>MTDIFF-P</td><td>59.53±1.12</td><td>48.67 ±1.32</td></tr><tr><td>MTDIFF-P (U-Net)</td><td>55.67 ± 1.27</td><td>47.42 ± 0.74</td></tr></table>
|
| 496 |
+
|
| 497 |
+
# D Environmental Details of Maze2D
|
| 498 |
+
|
| 499 |
+
|
| 500 |
+
Figure 8: 2D visualization of eight training maps designed in Maze2D.
|
| 501 |
+
|
| 502 |
+
We design eight different training maps for multi-task training, which are shown at Fig. 8. Different tasks have different reward functions and transition functions. For generalizability evaluation, we have designed one new unseen map. Although in Fig. 4, MTDIFF is able to generalize on new maps while PromptDT fails, we should acknowledged that MTDIFF may fail at some difficult unseen cases, as shown in Fig. 9. The reasons may lie in 2 folds: One is the inherent difficulty of the case itself, and the other is that the case’s deviation from the distribution of the training cases surpasses the upper threshold of generalizability of MTDIFF. We also provide another map where MTDIFF succeeds while PromptDT fails in Fig. 10.
|
| 503 |
+
|
| 504 |
+
We collect $3 5 \mathrm { k }$ episodes together to train our model and PromptDT. The episodic length is set as 600 for training and 200 for evaluation. After training with 512 batch size for 2e5 gradient steps, we evaluate these methods on seen and unseen maps.
|
| 505 |
+
|
| 506 |
+
|
| 507 |
+
Figure 9: 2D visualization of 2 difficult cases where both PromptDT and MTDIFF both fail. These 2 cases are both unseen during training. Goal position is denoted as $\mathbf { F }$ .
|
| 508 |
+
|
| 509 |
+
|
| 510 |
+
Figure 10: Unseen maps of Maze2D with long planning path. MTDIFF-P reach the goal while PromptDT fails. Goal position is denoted as $\mathbf { F }$ .
|
| 511 |
+
|
| 512 |
+
# E Data Analysis
|
| 513 |
+
|
| 514 |
+
# E.1 Distribution Visualization
|
| 515 |
+
|
| 516 |
+
We find the synthetic data is high-fidelity, covering or even broadening the original data distribution, which makes the offline RL method performs better in the augmented dataset. The distribution visualization is shown in Fig. 11.
|
| 517 |
+
|
| 518 |
+
|
| 519 |
+
Figure 11: 2D visualization of sampled synthetic data and original data via T-SNE [61]. The data is sampled from tasks coffee-push, disassemble, hand-insert and box-close respectively.
|
| 520 |
+
|
| 521 |
+
# E.2 Statistical Analysis
|
| 522 |
+
|
| 523 |
+
Following SynthER [38], we measure the Dynamics Error (MSE between the augmented next state and true next state), and L2 Distance from Dataset (minimum L2 distance of each datapoint from the dataset) for the augmented data of each method (i.e., MTDIFF-S, S4RL and RAD), as shown in Table 4. Since S4RL performs data augmentation by adding data within the $\epsilon$ -ball of the original data points, it has the smallest dynamics error with a small ϵ. RAD performs random amplitude scaling and causes the largest dynamics error. We remark that S4RL performs local data augmentation around the original data and can be limited in expanding the data coverage of offline datasets. In contrast, our method generates data via diffusion model without explicit constraints to the original data points, which also has small dynamics error and significantly improves the data coverage, benefiting the offline RL training.
|
| 524 |
+
|
| 525 |
+
Table 4: Comparing L2 distance from the training dataset and dynamics error under each method.
|
| 526 |
+
|
| 527 |
+
<table><tr><td rowspan=1 colspan=1>Methods</td><td rowspan=1 colspan=1>Dynamics Error</td><td rowspan=1 colspan=1>L2 Distance from Dataset</td></tr><tr><td rowspan=1 colspan=1>MTDIFF-S</td><td rowspan=1 colspan=1>0.0174</td><td rowspan=1 colspan=1>0.4552</td></tr><tr><td rowspan=1 colspan=1>S4RL</td><td rowspan=1 colspan=1>0.0001</td><td rowspan=1 colspan=1>0.4024</td></tr><tr><td rowspan=1 colspan=1>RAD</td><td rowspan=1 colspan=1>0.0641</td><td rowspan=1 colspan=1>0.4617</td></tr></table>
|
| 528 |
+
|
| 529 |
+
# F Limitations and Discussions
|
| 530 |
+
|
| 531 |
+
In this section, we will discuss the limitations and broader impacts of our proposed method MTDIFF.
|
| 532 |
+
|
| 533 |
+
Limitation. Diffusion models are bottlenecked by their slow sampling speed, which caps the potential of MTDIFF for real-time control. How to trade off the sampling speed and generative quality remains to be a crucial research topic. For a concrete example in MetaWorld, it takes on average 1.9s in wall-clock time to generate one action sequence for planning (hardware being a 3090 GPU). We can improve the inference speed by leveraging a recent sampler called DPM-solver [37, 36] to decrease the diffusion steps required to $0 . 2 \times$ without any loss in performance, and using a larger batch size (leveraging the parallel computing power of GPUs) to evaluate multiple environments at once. Thus the evaluation run-time roughly matches the run-time of non-diffusion algorithms (diffusion step is 1). In addition, consistency models [55] are recently proposed to support one-step and few-step generation, while the upper performance of what such models can achieve is still vague.
|
| 534 |
+
|
| 535 |
+
Broader Impacts. As far as we know, MTDIFF is the first proposed diffusion-based approach for multi-task reinforcement learning. It could be applied to multi-task decision-making, and also could be used to synthesize more data to boost policy improvement. MTDIFF provides a solution for achieving generalization in reinforcement learning.
|
| 536 |
+
|
| 537 |
+
# G Dataset collection
|
| 538 |
+
|
| 539 |
+
Meta-World. We train Soft Actor-Critic (SAC) [18] policy in isolation for each task from scratch until convergence. Then we collect 1M transitions from the SAC replay buffer for each task, consisting of recording samples in the replay buffer observed during training until the policy reaches the convergence of performance. For this benchmark, we have two different dataset compositions:
|
| 540 |
+
|
| 541 |
+
• Near-optimal dataset consisting of the experience (100M transitions) from random to expert (convergence) in SAC-Replay. • Sub-optimal dataset consisting of the initial $50 \%$ of the trajectories (50M transitions) of the near-optimal dataset for each task, where the proportion of expert data decreases a lot.
|
| 542 |
+
|
| 543 |
+
To visualize the optimality of each dataset clearly, we plot the univariate distribution of return in each kind of dataset in Fig. 12. Our dataset is available at https://bit.ly/3MWf40w.
|
| 544 |
+
|
| 545 |
+
|
| 546 |
+
Figure 12: Density visualization of the normalized return in the dataset.
|
| 547 |
+
|
| 548 |
+
Maze2D The offline dataset is collected by selecting random goal locations and using a planner to generate sequences of waypoints by following a PD controller. We borrow the code from https: //github.com/Farama-Foundation/D4RL [15] to generate datasets for 8 training maps. We collect $3 5 \mathrm { k }$ episodes in total.
|
| 549 |
+
|
| 550 |
+
# H Differences Between PromptDT and MTDIFF-P
|
| 551 |
+
|
| 552 |
+
The remarkable superiority of MTDIFF-P over PromptDT emerges from our elegant incorporation of transformer architecture and trajectory prompt within the diffusion model framework, effectively modeling the multi-task trajectory distribution. PromptDT is built on Decision Transformer and it is trained in an autoregressive manner, which is limited to predicting actions step by step. However, MTDIFF-P leverages the potency of sequence modeling, empowering it to perform trajectory generation adeptly. MTDIFF-P has demonstrated SOTA performance in both multi-task decision-making and data synthesis empirical experiments, while PromptDT fails to contribute to data synthesis. Technically, MTDIFF-P extends Decision Diffuser [2] into the multi-task scenario, utilizing classifier-free guidance for generative planning to yield high expected returns. To further verify our claim, we train our model on the publicly available PromptDT datasets [69], i.e., Cheetah-vel and Ant-dir. These chosen environments have been judiciously selected due to their inherent diversity of tasks, serving as a robust test to validate the capability of multi-task learning. We report the scores (mean and std for 3 seeds) in Table 5.
|
| 553 |
+
|
| 554 |
+
Table 5: Average scores obtained by MTDIFF-P and PromptDT across 3 seeds. We observed that MTDIFF-P outperforms PromptDT largely, demonstrating its high efficacy and potency.
|
| 555 |
+
|
| 556 |
+
<table><tr><td rowspan=1 colspan=1>Methods</td><td rowspan=1 colspan=1>Cheetah-vel</td><td rowspan=1 colspan=1>Ant-dir</td></tr><tr><td rowspan=1 colspan=1>MTDIFF-P</td><td rowspan=1 colspan=1>-29.09± 0.31</td><td rowspan=1 colspan=1>602.17 ± 1.68</td></tr><tr><td rowspan=1 colspan=1>PromptDT</td><td rowspan=1 colspan=1>-34.43±2.33</td><td rowspan=1 colspan=1>409.81士9.69</td></tr></table>
|
| 557 |
+
|
| 558 |
+
# I Single-Task Performance
|
| 559 |
+
|
| 560 |
+
We train one MTDIFF-P model on MT50-rand and evaluate the performance for each task for 50 episodes. We report the average evaluated return in Table 6.
|
| 561 |
+
|
| 562 |
+
Table 6: Evaluated return of MTDIFF-P for each task in MT50-rand. We report the mean and standard deviation for 50 episodes for each task.
|
| 563 |
+
|
| 564 |
+
<table><tr><td>Tasks</td><td>Return on near-optimal datasetReturn on sub-optimal dataset</td><td></td></tr><tr><td>basketball-v2</td><td>2735.7 ±1927.7</td><td>2762.7±1928.8</td></tr><tr><td>bin-picking-v2</td><td>733.7 ± 1211.8</td><td>59.6 ± 32.3</td></tr><tr><td>button-press-topdown-v2</td><td>1491.6 ± 390.9</td><td>1395.8 ± 332.6</td></tr><tr><td>button-press-v2</td><td>2419.2 ± 413.7</td><td>2730.4 ± 514.3</td></tr><tr><td>button-press-wall-v2</td><td>3474.7 ± 887.6</td><td>2613.1 ± 906.8</td></tr><tr><td>coffee-button-v2</td><td>3157.9 ± 1274.3</td><td>1649.4 ± 869.5</td></tr><tr><td>coffee-pull-v2</td><td>437.5 ± 597.3</td><td>98.8 ± 115.4</td></tr><tr><td>coffee-push-v2</td><td>463.7 ± 729.1</td><td>71.3 ± 55.7</td></tr><tr><td>dial-turn-v2</td><td>2848.1 ± 996.3</td><td>2244.5 ± 881.5</td></tr><tr><td>disassemble-v2</td><td>369.9 ± 265.4</td><td>372.3 ± 623.2</td></tr><tr><td>door-close-v2</td><td>4325.2 ± 377.6</td><td>4270.4 ± 460.1</td></tr><tr><td>door-lock-v2</td><td>3215.1 ± 857.5</td><td>3082.4±1041.4</td></tr><tr><td>door-open-v2</td><td>3458.1 ± 960.5</td><td>2457.0 ± 833.0</td></tr><tr><td>door-unlock-v2</td><td>2082.6 ± 1568.4</td><td>3078.8 ± 1158.1</td></tr><tr><td>hand-insert-v2</td><td>927.9 ± 1527.6</td><td>288.8 ± 932.1</td></tr><tr><td>drawer-close-v2</td><td>4824.5 ± 8.8</td><td>4825.3 ± 22.3</td></tr><tr><td>drawer-open-v2</td><td>3530.4 ± 1512.6</td><td>2218.8 ± 529.3</td></tr><tr><td>faucet-open-v2</td><td>3877.4± 598.1</td><td>4245.6 ± 575.2</td></tr><tr><td>faucet-close-v2</td><td>4167.1 ± 418.8</td><td>4624.1 ± 107.5</td></tr><tr><td>handle-press-side-v2</td><td>3423.3 ± 1075.6</td><td>3995.8 ± 1130.0</td></tr><tr><td>handle-press-v2</td><td>3397.9 ±1752.1</td><td>3125.4 ± 1724.7</td></tr><tr><td>handle-pull-side-v2</td><td>3141.5 ± 1775.4</td><td>1474.2 ±1392.9</td></tr><tr><td>handle-pull-v2</td><td>2845.7 ± 1970.6</td><td>2856.8 ± 1699.8</td></tr><tr><td>lever-pull-v2</td><td>3383.5 ±1299.2</td><td>3125.6 ±1433.1</td></tr><tr><td>peg-insert-side-v2</td><td>915.1 ± 1624.8</td><td>497.8 ± 1015.3</td></tr><tr><td>pick-place-wall-v2</td><td>649.8 ± 1288.6</td><td>288.2± 988.1</td></tr><tr><td>pick-out-of-hole-v2</td><td>1792.8 ± 1959.9</td><td>700.5 ± 1190.3</td></tr><tr><td>reach-v2</td><td>4144.2 ± 645.4</td><td>966.4 ± 842.9</td></tr><tr><td>push-back-v2</td><td>97.2 ± 611.3</td><td>566.3 ± 1042.9</td></tr><tr><td>push-v2</td><td>142.0 ± 335.7</td><td>64.6 ± 98.2</td></tr><tr><td>pick-place-v2</td><td>166.0 ± 759.2</td><td>7.3 ± 4.8</td></tr><tr><td>plate-slide-v2</td><td>4096.4 ± 1202.5</td><td>4306.3 ± 495.8</td></tr><tr><td>plate-slide-side-v2</td><td>2910.3 ± 616.1</td><td>2989.0± 1044.1</td></tr><tr><td>plate-slide-back-v2</td><td>4378.5 ± 373.0</td><td>3963.4 ± 927.3</td></tr><tr><td>plate-slide-back-side-v2</td><td>3872.0 ± 1151.6</td><td>4186.5 ± 772.6</td></tr><tr><td>soccer-v2</td><td>443.5 ± 785.5</td><td>480.4 ± 994.8</td></tr><tr><td>push-wall-v2</td><td>873.9 ± 1718.3</td><td>705.2 ± 1535.7</td></tr><tr><td>shelf-place-v2</td><td>204.5 ± 714.3</td><td>366.1 ± 919.0</td></tr><tr><td>sweep-into-v2</td><td>1297.9 ± 1661.5</td><td>506.2 ± 1368.5</td></tr><tr><td>sweep-v2</td><td>1397.1 ± 1922.3</td><td>599.1 ± 1359.2</td></tr><tr><td>window-open-v2</td><td>1453.6 ± 1101.4</td><td>3095.5 ± 751.1</td></tr><tr><td>window-close-v2</td><td>2963.9 ± 875.3</td><td>3177.6± 737.8</td></tr><tr><td>assembly-v2</td><td>2470.7 ± 1758.6</td><td>663.7± 28.7</td></tr><tr><td>button-press-topdown-wall-v2</td><td>1270.9 ± 214.5</td><td>1199.9 ± 203.7</td></tr><tr><td>hammer-v2</td><td>868.7± 983.4</td><td>1024.4 ± 1024.3</td></tr><tr><td>peg-unplug-side-v2</td><td>1439.1 ± 1817.8</td><td>136.4 ± 508.6</td></tr><tr><td>reach-wall-v2</td><td>4249.9 ± 536.0</td><td>4191.4± 412.9</td></tr><tr><td>stick-push-v2</td><td>1288.5 ± 1587.3</td><td>790.1 ± 1097.6</td></tr><tr><td>stick-pull-v2</td><td>601.4± 1346.3</td><td>287.1 ± 922.8</td></tr><tr><td>box-close-v2</td><td>2683.7 ± 1823.4</td><td>2273.3 ± 1707.3</td></tr></table>
|
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| 1 |
+
# Secure Split Learning against Property Inference and Data Reconstruction Attacks
|
| 2 |
+
|
| 3 |
+
Anonymous Author(s)
|
| 4 |
+
Affiliation
|
| 5 |
+
Address
|
| 6 |
+
email
|
| 7 |
+
|
| 8 |
+
# Abstract
|
| 9 |
+
|
| 10 |
+
1 Split learning of deep neural networks (SplitNN) has provided a promising solu
|
| 11 |
+
2 tion to learning jointly for the mutual interest of a guest and a host, which may
|
| 12 |
+
3 come from different backgrounds, holding features partitioned vertically. How
|
| 13 |
+
4 ever, SplitNN creates a new attack surface for the adversarial participant, holding
|
| 14 |
+
5 back its practical use in the real world. By investigating the adversarial effects
|
| 15 |
+
6 of two highly threatening attacks, i.e., property inference and data reconstruction,
|
| 16 |
+
7 adapted from security studies of federated learning, we identify the underlying
|
| 17 |
+
8 vulnerability of SplitNN. To prevent potential threats and ensure learning guaran
|
| 18 |
+
9 tees of SplitNN, we design a privacy-preserving tunnel for information exchange
|
| 19 |
+
10 between the guest and the host. The intuition behind our design is to perturb the
|
| 20 |
+
11 propagation of knowledge in each direction with a controllable unified solution.
|
| 21 |
+
12 To this end, we propose a new activation function named $\mathtt { R } ^ { 3 } \mathtt { e L U }$ , transferring pri
|
| 22 |
+
13 vate smashed data and partial loss into randomized responses in forward and back
|
| 23 |
+
14 ward propagations, respectively. Moreover, we give the first attempt to achieve
|
| 24 |
+
15 a fine-grained privacy budget allocation scheme for SplitNN. The analysis of pri
|
| 25 |
+
16 vacy loss proves that our privacy-preserving SplitNN solution provides a tight
|
| 26 |
+
17 privacy budget, while the experimental result shows that our solution outperforms
|
| 27 |
+
18 existing solutions in attack defense and model usability.
|
| 28 |
+
|
| 29 |
+
# 19 1 Introduction
|
| 30 |
+
|
| 31 |
+
20 Collaborative learning enables participants from different backgrounds to learn jointly for mutual
|
| 32 |
+
21 interests. A well-known collaborative learning paradigm is federated learning (FL) [25], focusing
|
| 33 |
+
22 on the coordination of distributed participants. Meanwhile, another paradigm, split neural network
|
| 34 |
+
23 learning (SplitNN for short) [19, 11, 4], is designed for vertically partitioned features. The emer
|
| 35 |
+
24 gence of SplitNN provides a promising solution to building cooperative models such as two-towers
|
| 36 |
+
25 recommendation systems [37, 39]. By combining different features, SplitNN is supposed to be more
|
| 37 |
+
26 expressive for tasks like user profiling and recommendation.
|
| 38 |
+
27 However, collaborative learning paradigms are faced with severe security issues. Roughly speak
|
| 39 |
+
28 ing, there are three kinds of known threats, inference attack [9, 30], reconstruction attack [17, 31],
|
| 40 |
+
29 and poisoning attack [33, 18]. The inference attack discloses properties or membership information
|
| 41 |
+
30 of data samples, while the reconstruction attack seeks to recover participants’ private data samples.
|
| 42 |
+
31 Unlike these two kinds of threats, the poisoning attack [33, 18] aims to put harmful data into collab
|
| 43 |
+
32 orative learning for malicious purposes rather than stealing private information. As a result, some
|
| 44 |
+
33 defensive solutions have been proposed for federated learning. According to their techniques, these
|
| 45 |
+
34 solutions can be classified into three categories: differential privacy solutions [36, 32], homomorphic
|
| 46 |
+
35 encryption solutions [38, 21], and secure multiparty computation solutions [12, 27].
|
| 47 |
+
Submitted to 36th Conference on Neural Information Processing Systems (NeurIPS 2022). Do not distribute.
|
| 48 |
+
36 Unfortunately, defense solutions for SplitNN are barely discussed, but threatening attacks are con
|
| 49 |
+
37 tinuously emerging. We note that the workflow of SplitNN has a unique asymmetric design, which
|
| 50 |
+
38 is quite different from FL. Therefore, most solutions for secure FL are not suitable for SplitNN.
|
| 51 |
+
39 Secure multiparty computation solutions and homomorphic encryption solutions can achieve ideal
|
| 52 |
+
40 data confidentiality in SplitNN. But the overhead introduced is still far away from practical uses.
|
| 53 |
+
41 Thus, for the first attempt at a secure SplitNN solution, we will concentrate on privacy leakage is
|
| 54 |
+
42 sues caused by property inference and data reconstruction attacks in this paper because they share
|
| 55 |
+
43 similar adversarial goals. Instead, poisoning attacks need to be studied separately [7, 24].
|
| 56 |
+
44 We note an inherent contradiction [6] between privacy preservation and model utility in SplitNN.
|
| 57 |
+
45 To investigate the privacy leakage risk of SplitNN, we evaluate the adversarial effect of property
|
| 58 |
+
46 inference and data reconstruction attacks against recommendation and image classification models
|
| 59 |
+
47 built using SplitNN. The results in semi-honest and malicious settings show that both attacks have
|
| 60 |
+
48 sufficiently high success rates when disclosing the privacy of the guest or the host. To secure SplitNN
|
| 61 |
+
49 against these attacks [17, 30, 29], we give the first privacy-preserving SplitNN solution, stemming
|
| 62 |
+
50 privacy leakage from either direction with dynamic privacy budget allocation.
|
| 63 |
+
51 Contribution. Through a thorough investigation of the privacy leakage issue in SplitNN, we con
|
| 64 |
+
52 firm that the best option of defensive solution for SplitNN is to construct a privacy-preserving tunnel
|
| 65 |
+
53 between the split surfaces of the host and guest sides. To this end, we propose a novel activation
|
| 66 |
+
54 function named $\mathtt { R } ^ { 3 } \mathtt { e L U }$ , responding to forward and backward propagations in a randomized manner.
|
| 67 |
+
55 Furthermore, we propose a fine-grained privacy budget allocation scheme for SplitNN to achieve
|
| 68 |
+
56 more efficient perturbations, dynamically allocating the privacy budget in spatial dimension (feature
|
| 69 |
+
57 level) and temporal dimension (epoch level). The analysis of privacy loss shows that our solution
|
| 70 |
+
58 provides a differential privacy guarantee regarding activations. The evaluation results regarding rec
|
| 71 |
+
59 ommendation and classification models show that our solution can outperform the existing solutions
|
| 72 |
+
60 in privacy preservation and model usability.
|
| 73 |
+
|
| 74 |
+
# 2 Problem Statement
|
| 75 |
+
|
| 76 |
+
# 2.1 Split Learning
|
| 77 |
+
|
| 78 |
+
Given a training dataset $\boldsymbol { X }$ and model parameters $\pmb { \theta }$ , a learning task is to find approximately optimal $\pmb { \theta }$ by minimizing a pre-defined loss function $\mathcal { L }$ . We assume that the optimizer used is a mini-batch stochastic gradient descent (SGD) algorithm, which updates $\pmb { \theta }$ with a batch input of $\boldsymbol { X }$ iteratively. Assuming the batch size is $N$ , then the total loss of $\pmb \theta$ for a batch input $\pmb { x } = \{ x _ { i } | x _ { i } \in X , i \in$ $[ 1 , N ] \}$ should be $\textstyle \sum _ { x \in x } { \mathcal { L } } ( \theta , x )$ in the $t { \cdot }$ -th training iteration. The gradients of $\pmb { \theta }$ for model updating should be estimated by $\begin{array} { r } { \frac { 1 } { N } \sum _ { x \in x } \nabla _ { \pmb { \theta } } \mathcal { L } ( \pmb { \theta } , x ) } \end{array}$ approximately. Hence, parameters $\pmb { \theta }$ can be updated as $\begin{array} { r } { \pmb { \theta } ^ { t + 1 } = \pmb { \theta } ^ { t } - \frac { 1 } { N } \sum _ { x \in \pmb { x } } \tilde { \nabla } _ { \pmb { \theta } } \tilde { \mathcal { L } } ( \pmb { \theta } , x ) } \end{array}$ . This mini-batch SGD based optimizing procedure should be repeated until the model usability meets the requirement or the maximal count of iterations reaches.
|
| 79 |
+
|
| 80 |
+
71 Generally, there are two roles in a two-party SplitNN. We denote by the guest who holds features
|
| 81 |
+
72 only and the host who holds both features and labels. According to related studies [34, 14], there
|
| 82 |
+
73 exist several split configurations of neural networks. We will focus on the SplitNN designed for
|
| 83 |
+
74 vertically partitioned features with labels held by the host only [4, 11]. We denote by $\pmb { \theta } ^ { g }$ , $\pmb \theta ^ { h }$ the
|
| 84 |
+
75 partial models of the guest and the host after split and $\pmb { \theta } ^ { k }$ the rest part of the original model. Then
|
| 85 |
+
76 the forwarding result Forwar $\mathbb { I } ( \pmb { x } ^ { g } , \pmb { \theta } ^ { g } )$ of the guest should be evaluated locally and passed to the
|
| 86 |
+
77 host. The host should merge Forwar $\mathsf { d } ( \boldsymbol { \mathbf { \mathit { x } } } ^ { h } , \boldsymbol { \theta } ^ { h } )$ with Forward $\mathbf { \delta } _ { \cdot } ( { \mathbf { x } } ^ { g } , \mathbf { \delta } ^ { g } )$ using a predefined strategy
|
| 87 |
+
78 such as concatenating and averaging. Then the host finishes the rest of the forward propagation
|
| 88 |
+
79 $\mathcal { L } ( \mathtt { M e r g e } ( \mathtt { F o r w a r d } ( x ^ { g } , \theta ^ { g } ) , \mathtt { F o r w a r d } ( x ^ { h } , \theta ^ { h } ) ) , \theta ^ { k } )$ and initiates backward propagation, sending
|
| 89 |
+
80 the partial loss regarding $\pmb { x } ^ { g }$ and $\pmb { \theta } ^ { g }$ back to the guest.
|
| 90 |
+
81 We take a SplitNN based recommendation system as an example and give a benchmark in Table 1.
|
| 91 |
+
82 Different merging strategies and two public datasets, MovieLens [15] and BookCrossing [40], have
|
| 92 |
+
83 been evaluated. In case of misaligned features, zero padding will be used to retain the shape of fea
|
| 93 |
+
|
| 94 |
+
84 ture vectors. We notice that concatenating and element-wise averaging with padding have relatively stable and desirable performance, which will be used as the default setting in the rest of this work.
|
| 95 |
+
|
| 96 |
+
Table 1: Top-10 hit ratio of SplitNN based recommendation using different merging strategies.
|
| 97 |
+
|
| 98 |
+
<table><tr><td rowspan="2"></td><td rowspan="2"></td><td rowspan="2">concatenate</td><td colspan="4">element-wise</td><td rowspan="2">no split</td></tr><tr><td>max</td><td>sum</td><td>average</td><td>min</td></tr><tr><td rowspan="2">MovieLens</td><td>padding</td><td>56.62%</td><td>56.26%</td><td>56.35%</td><td>56.89%</td><td>57.19%</td><td rowspan="2">57.21%</td></tr><tr><td>non-padding</td><td>55.38%</td><td>54.75%</td><td>54.95%</td><td>55.72%</td><td>55.08%</td></tr><tr><td rowspan="2">Book Crossing</td><td>padding</td><td>61.70%</td><td>60.84%</td><td>60.21%</td><td>61.16%</td><td>60.98%</td><td rowspan="2">61.92%</td></tr><tr><td>non-padding</td><td>58.80%</td><td>59.34%</td><td>59.44%</td><td>59.10%</td><td>59.02%</td></tr></table>
|
| 99 |
+
|
| 100 |
+
# 86 2.2 Threat Model
|
| 101 |
+
|
| 102 |
+
In SplitNN, interactions between the guest and the host pose threats to each other. Thus, we will investigate private data leakage threats from either direction. We first assume that the host and the guest are honest but curious about the private data of each other. Moreover, we will consider a more powerful threat model [29], where the guest or the host could be malicious, hijacking the feature space during split learning. In both cases, we take into account property inference and data reconstruction attacks, which are highly threatening attacks identified in collaborative learning.
|
| 103 |
+
|
| 104 |
+
93 Property inference attack. Since either role of SplitNN has access to the output of the other’s local
|
| 105 |
+
94 model, the adversary can mount a property inference attack [9, 22], inferring properties of private
|
| 106 |
+
95 data through observing query input and the corresponding output. By constructing shadow models
|
| 107 |
+
96 elaborately, the adversary can steal substantial information from the target. In this way, the adversary
|
| 108 |
+
97 acquires the capability of inferring some properties (such as gender and age) of the data samples used
|
| 109 |
+
98 for training. Denoted by $F , T$ and $\mathcal { L } _ { F }$ the inference model, target model, and the loss function used
|
| 110 |
+
99 for $F$ , the adversarial goal of property inference attack is
|
| 111 |
+
|
| 112 |
+
$$
|
| 113 |
+
\mathcal { A } _ { P I A } = \arg \operatorname* { m i n } _ { F } \sum _ { x _ { i } \in \pmb { x } } \mathcal { L } _ { F } ( F ( T ( x _ { i } ) ) , l _ { i } ) , l _ { i } \in \{ 0 , 1 \} .
|
| 114 |
+
$$
|
| 115 |
+
|
| 116 |
+
100 Data reconstruction attack. By taking advantage of generative adversarial networks (GANs) [13], a
|
| 117 |
+
101 data reconstruction attack [17, 29] becomes possible in collaborative learning. To mount the attack,
|
| 118 |
+
102 the adversary augments the training data per iteration by inserting fake samples $_ z$ generated by a
|
| 119 |
+
103 generator $G$ . The target model will serve as a discriminator $D$ . The adversary affects the target
|
| 120 |
+
104 model by deceiving the target with fake training samples. For correcting the adversary, the target
|
| 121 |
+
105 participant is supposed to put more private information into the learning. In this game-style training,
|
| 122 |
+
106 the adversary can obtain a generator to reconstruct data samples similar to target private data. The
|
| 123 |
+
107 adversarial goal of the data reconstruction attack can be given as
|
| 124 |
+
|
| 125 |
+
$$
|
| 126 |
+
\mathcal { A } _ { D R A } = \operatorname* { m i n } _ { G } \operatorname* { m a x } _ { D } \frac { 1 } { | x | } \sum _ { x \in \pmb { x } } l o g D ( x ) + \frac { 1 } { | x | } \sum _ { z \in z } l o g ( 1 - D ( G ( z ) ) ) .
|
| 127 |
+
$$
|
| 128 |
+
|
| 129 |
+
108 Feature space hijacking. The property inference and data reconstruction attacks adapted from FL
|
| 130 |
+
109 can be mounted by a semi-honest participant, who follows the split learning protocol normally. How
|
| 131 |
+
110 ever, a recent attack study dedicated to SplitNN has revealed that a malicious host can achieve more
|
| 132 |
+
111 impressive adversarial effects on property inference or data reconstruction by explicitly distorting
|
| 133 |
+
112 the objective of split learning. Thus, we also consider the defensive effect of our solution against
|
| 134 |
+
113 property inference and data reconstruction attacks using this feature space hijacking approach.
|
| 135 |
+
|
| 136 |
+
# 114 3 Privacy-Preserving Split Learning
|
| 137 |
+
|
| 138 |
+
115 Our goal is to design an unified defense solution to preserving privacy from both the host and guest’s
|
| 139 |
+
116 perspectives. Ideally, the guest wants to collaborate with the host under the condition that the host
|
| 140 |
+
117 could disclose no private information and vice versa. According to recent studies [3, 23, 16], artifi
|
| 141 |
+
118 cial perturbations of data samples or parameters could prevent privacy leakage effectively. However,
|
| 142 |
+
119 different from conventional model publishing scenarios, the host and guest in SplitNN will keep
|
| 143 |
+
120 exchanging intermediate results during training. These continuous queries significantly increase the
|
| 144 |
+
121 risk of privacy leakage for both sides. Moreover, the attack surface of splitNN is in the middle of
|
| 145 |
+
122 neural network propagations, which makes things tricky. Thus, our primary idea to tackle this prob
|
| 146 |
+
123 lem is to construct a bidirectional privacy-preserving tunnel for interactions. Recent studies such as
|
| 147 |
+
124 [10] have proved that activation functions are more adaptive for perturbed operands than other neu
|
| 148 |
+
125 ral network components. Moreover, activation functions have various forms [2], which are flexible
|
| 149 |
+
126 for configuration. As a result, we propose a new variant of ReLU as a privacy-preserving interface.
|
| 150 |
+
|
| 151 |
+
# 3.1 ${ \bf R } ^ { 3 }$ eLU: Randomized-Response ReLU
|
| 152 |
+
|
| 153 |
+
128 Inspired by a randomized response approach [35], we propose a new activation function named
|
| 154 |
+
129 $\mathtt { R } ^ { 3 } \mathtt { e L U }$ . The original randomized response method is good at statistical analysis of item sets. But
|
| 155 |
+
130 the result of an activation function is commonly a continuous variable. Hence, they cannot be easily
|
| 156 |
+
131 combined together. It should also be noted that it is risky to perturb activation functions directly
|
| 157 |
+
132 because non-activated results may be flipped unexpectedly. Recall that the original formula of ReLU
|
| 158 |
+
133 is $f ( x ) = \operatorname* { m a x } ( 0 , x )$ , $x \in \mathcal { R }$ . Our randomized-response variant will yield a proper substitute for
|
| 159 |
+
134 replacing the real activation with a probability of $p$ . If we yield 0 as the substitute, then we can
|
| 160 |
+
135 randomly inactivate a part of ReLU results. But nothing has been changed for $x \le 0$ . Because
|
| 161 |
+
136 $f ( x ) = 0$ when $x \leq 0$ . Hence, the variant is not completely privacy preserved since $f ( x ) = 0$ also
|
| 162 |
+
137 reveals useful information to the adversary. For the completeness of the variant, we generate noisy
|
| 163 |
+
138 activations $x ^ { \prime } \ L \mathrm { a p l a c e } ( 0 , \sigma )$ for $x \leq 0$ . Now, we can give the definition of $\mathtt { R } ^ { 3 } \mathtt { e L U }$ as
|
| 164 |
+
|
| 165 |
+
$$
|
| 166 |
+
R ^ { 3 } e L U ( x ) = \left\{ \begin{array} { l l } { \mathrm { m a x } ( 0 , x + x ^ { \prime } ) , } & { \mathrm { ~ w i t h ~ p r o b a b i l i t y } \ p , } \\ { 0 , } & { \mathrm { ~ w i t h ~ p r o b a b i l i t y } \ ( 1 - p ) . } \end{array} \right.
|
| 167 |
+
$$
|
| 168 |
+
|
| 169 |
+
139 We remark that the way $\mathtt { R } ^ { 3 } \mathtt { e L U }$ handles non-activated results is dangerous, although learning ac
|
| 170 |
+
140 curacy is often traded off for privacy. But we will mitigate the side effect through privacy budget
|
| 171 |
+
141 allocation. Then the risk of applying $\mathtt { R } ^ { 3 } \mathtt { e L U }$ will not be a problem.
|
| 172 |
+
|
| 173 |
+
# 3.2 Forward Propagation with $\mathbf { R ^ { 3 } e L U }$
|
| 174 |
+
|
| 175 |
+
143 Now we show how to apply $\mathtt { R } ^ { 3 } \mathtt { e L U }$ in the forward pass of SplitNN regarding the guest’s privacy.
|
| 176 |
+
144 Generally, when the $t$ -th training iteration begins, the guest randomly samples a mini-batch $_ { \textbf { \em x } }$ from
|
| 177 |
+
145 private training dataset $\chi ( g )$ . Assuming that an embedding procedure Embedding() : $\mathcal { R } ^ { M } \gets$
|
| 178 |
+
146 $\mathcal { X }$ is publicly available, raw data samples in the mini-batch can be encoded into feature vectors
|
| 179 |
+
147 $V = \{ \pmb { v } _ { 1 } , \pmb { v } _ { 2 } , \ldots , \pmb { v } _ { N } \}$ , $\pmb { v _ { i } } = \{ v _ { 1 } , v _ { 2 } , \dots , v _ { M } \}$ , $i \in [ 1 , N ]$ , and $M$ is the dimension of feature
|
| 180 |
+
148 representing space. From the functional perspective, we assume that $\mathcal { L } ( \boldsymbol { v } ^ { h } , \boldsymbol { v } ^ { g } , \boldsymbol { \theta } )$ is equivalent to
|
| 181 |
+
149 $\mathcal { L } ( \mathrm { F o r w a r d } ( v ^ { h } , \pmb \theta ^ { h } )$ , Forwar $\mathfrak { l } ( v ^ { g } , \theta ^ { g } ) , \theta ^ { k } )$ , where Forward $( ) : \mathcal { R } ^ { N _ { s } } \gets \mathcal { R } ^ { M }$ is a function to yield
|
| 182 |
+
150 the feedforward result of hidden units for a given neural network, and $N _ { s }$ indicates the output shape.
|
| 183 |
+
151 We now make the minimal modification of the forward propagation of SplitNN while leaving the
|
| 184 |
+
152 rest part unchanged. Denoted by Forward- $\cdot \mathtt { R } ^ { 3 } \mathtt { e L U ( ) }$ the feedforward result of neural network by
|
| 185 |
+
153 replacing the activation functions of the guest’s output layer with $\mathtt { R } ^ { 3 } \mathtt { e L U }$ . Then the feedforward
|
| 186 |
+
154 result transmitted to the host should be $\pmb { a } ^ { g } = \mathtt { F o r w a r d - R } ^ { 3 } \mathtt { e L U } ( \pmb { v } ^ { g } , \pmb { \theta } ^ { g } )$ . Next, the host executes a pre
|
| 187 |
+
155 defined aggregation procedure taking as input $\pmb { a } ^ { g }$ and $\pmb { a } ^ { h }$ . Finally, the loss function will be evaluated
|
| 188 |
+
156 by $\mathcal { L } ( \mathrm { F o r w a r d - R } ^ { 3 } \mathrm { e L U } ( v ^ { g } , \pmb { \theta } ^ { g } )$ , Forwar $\mathfrak { i } ( v ^ { h } , \theta ^ { h } ) , \theta ^ { k } )$ . Algorithm 1 in the appendix integrates the
|
| 189 |
+
157 above forward propagation using $\mathtt { R } ^ { 3 } \mathtt { e L U }$ into SplitNN.
|
| 190 |
+
|
| 191 |
+
# 158 3.3 Privacy-Preserving Backward Propagation
|
| 192 |
+
|
| 193 |
+
159 According to recent studies of privacy leakage in backward propagation [26, 31, 8], model updating
|
| 194 |
+
160 information may cause severe leakage of private training data. Since the partial loss will be propa
|
| 195 |
+
161 gated to the guest in SplitNN, it is crucial to protect the host’s privacy from being disclosed. Fortu
|
| 196 |
+
162 nately, our $\mathtt { R } ^ { 3 } \mathtt { e L U }$ is adaptable to noisy partial losses and we design $\mathbb { R } ^ { 3 }$ eLU-Diff in a randomized
|
| 197 |
+
|
| 198 |
+
$$
|
| 199 |
+
\begin{array} { r } { \mathrm { R } ^ { 3 } \mathrm { e L U - D i f f } ( \delta ^ { g } , a ^ { g } , v ^ { g } ) = \left\{ \begin{array} { l l } { \delta ^ { g } \times \mathrm { R e L U - D i f f } ( a ^ { g } , v ^ { g } ) + x ^ { \prime } , } & { \mathrm { ~ w i t h ~ p r o b a b i l i t y ~ } ( 1 - p ) , } \\ { 0 , } & { \mathrm { ~ w i t h ~ p r o b a b i l i t y ~ } p . } \end{array} \right. } \end{array}
|
| 200 |
+
$$
|
| 201 |
+
|
| 202 |
+
164 Noting that the derivative value of ReLU for any input is either one or zero, randomly flipping the
|
| 203 |
+
165 derivative value may still disclose $\delta _ { t } ^ { g }$ when value ones are not flipped. Therefore, we integrate a
|
| 204 |
+
166 Laplace mechanism into the $\mathbb { R } ^ { 3 }$ eLU-Diff. Please also note that the constructions of $\mathbb { R } ^ { 3 }$ eLU-Diff and
|
| 205 |
+
167 $\mathtt { R } ^ { 3 } \mathtt { e L U }$ are in a similar way. This is helpful to obtain uniform analysis results of two parties, which
|
| 206 |
+
168 will be shown in the privacy analysis part.
|
| 207 |
+
169 We sketch the backward propagation using $\mathbb { R } ^ { 3 }$ eLU-Diff in Algorithm 2 in the appendix. Briefly,
|
| 208 |
+
170 when the $t$ -th backward propagation begins, the host calculates the partial loss $\delta ^ { k } = \nabla _ { \pmb { a } ^ { k } } \mathcal { L } ( l , \bar { \pmb { a } } , \pmb { \theta } _ { t } ^ { k } )$
|
| 209 |
+
171 for $\pmb { \theta } ^ { k }$ regarding the total loss $l$ obtained in forward propagation, where $\bar { \bf a }$ is the averaged activation
|
| 210 |
+
172 result. Then a Backward $( ) : \mathcal { R } ^ { N _ { r } } \gets \mathcal { R } ^ { N _ { s } }$ procedure calculates the gradients of model parameters,
|
| 211 |
+
173 where $N _ { r }$ is the shape of parameters. To update the guest model, the host sends partial loss $\delta ^ { g }$ for
|
| 212 |
+
174 $\pmb { \theta } ^ { g }$ to the guest. To preserve the host’s privacy within $\delta ^ { g }$ , we disturb the partial loss $\delta ^ { g }$ propagating
|
| 213 |
+
175 to the guest and keep the partial loss on the host side unchanged.
|
| 214 |
+
|
| 215 |
+
# 176 3.4 Dynamic Privacy Budget Allocation
|
| 216 |
+
|
| 217 |
+
177 It has been proved that the importance of a parameter can be quantified by the error introduced when
|
| 218 |
+
178 it is removed from the model [28]. Thus, we define the importance $I _ { j }$ of a given SplitNN parameter
|
| 219 |
+
179 $\theta _ { j } \in \pmb \theta$ as the squared difference of prediction errors caused by removing $\theta _ { j }$ ,
|
| 220 |
+
|
| 221 |
+
$$
|
| 222 |
+
I _ { j } = ( \mathcal { L } ( \pmb { x } , \pmb { \theta } ) - \mathcal { L } ( \pmb { x } , \pmb { \theta } \setminus \{ \theta _ { j } \} ) ) ^ { 2 } .
|
| 223 |
+
$$
|
| 224 |
+
|
| 225 |
+
180 Due to the consideration of efficiency, it is suggested in [28] to estimating the importance by a
|
| 226 |
+
181 first-order Taylor expansion approximately. Then the importance of $\theta _ { j }$ is estimated as
|
| 227 |
+
|
| 228 |
+
$$
|
| 229 |
+
\hat { I } _ { j } = ( g _ { j } \cdot \theta _ { j } ) ^ { 2 } ,
|
| 230 |
+
$$
|
| 231 |
+
|
| 232 |
+
182 where $g _ { j }$ is the gradient of the parameter $\theta _ { j }$ regarding a specific sample when $\pmb { \theta }$ is well-trained.
|
| 233 |
+
183 Given parameter importance, the importance of features can be derived further. Specifically, the
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184 importance of a neuron (or a feature) $U _ { j }$ , $j \in [ 1 , N _ { u } ]$ , where $N _ { u }$ is the total number of neurons
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185 in the model, can be calculated as a joint importance of relevant parameters by summing up the
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186 importance of all relevant parameters. Hence, $\begin{array} { r } { U _ { j } \ = \ \sum _ { \theta _ { k } \in \tilde { \pmb { \theta } } _ { j } } \hat { I } _ { k } } \end{array}$ , where $\tilde { \theta } _ { j }$ denotes the set of all
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187 parameters directly connected to the $j$ -th neuron.
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188 However, the above importance estimation method is designed for a well-trained model and cannot
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189 be directly applied to intermediate models during training. To tackle this problem, we give a dynamic
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190 estimation method by deriving the original method into a cumulative form. The importance of a
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191 feature will be accumulated as the training epoch increases. Specifically, the importance of the $j$ -th
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192 feature in the $q$ -th training epoch is
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+
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$$
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U _ { j } ^ { q } = \frac { \sum _ { \theta _ { k } \in \tilde { \theta } _ { j } } \hat { I } _ { k } + U _ { j } ^ { q - 1 } \times ( q \times \lfloor T / n _ { t } \rfloor + ( t \bmod n _ { t } ) - 1 ) } { q \times \lfloor T / n _ { t } \rfloor + ( t \bmod n _ { t } ) } ,
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$$
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+
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193 where $n _ { t }$ indicates the iteration number within a training epoch, $T$ is the maximum training iteration
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194 number, and $t$ is the current training iteration globally. Generally, we assume that $T / n _ { t } = n _ { q }$
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195 $n _ { q } \in \mathcal N$ , which also means that $q \in [ 1 , n _ { q } ]$ . We give the importance estimation results of different
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196 neurons in Figure 3 in the appendix, showing the correctness of our dynamic importance estimation
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197 method and the existence of unbalanced feature importance.
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198 Given the parameter importance estimated dynamically, we are capable of allocating privacy budgets
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199 regarding different features. The intuition is to give larger budgets to more important features while
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200 smaller budgets to less important ones. Before the $q$ -th training epoch begins, we estimate the
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201 feature importance vector $\boldsymbol { U } = \{ U _ { 1 } ^ { q } , U _ { 2 } ^ { q } , \ldots , U _ { N _ { u } } ^ { q } \}$ . Based on $U$ , the corresponding privacy budget
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202 to be allocated should be $\epsilon _ { j } \times U _ { j } ^ { q }$ , $j \in [ 1 , N _ { u } ]$ . And the total privacy budget for all features is
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203 $\begin{array} { r } { \epsilon _ { F } = \sum _ { j = \in [ 1 , N _ { u } ] } \epsilon _ { j } } \end{array}$ . On the other hand, we can also dynamically allocate privacy budgets for
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204 different iterations to optimize the total privacy budget further. Given the total privacy budget $\epsilon _ { T }$
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205 for all iterations, we assign the privacy budget $\begin{array} { r } { \epsilon _ { i } = \frac { \epsilon _ { T } } { 2 ^ { i } } } \end{array}$ to the $i$ -th iteration. Since $\begin{array} { r } { \sum _ { i = 1 } ^ { \infty } \frac { \epsilon _ { T } } { 2 ^ { i } } = \epsilon _ { T } } \end{array}$ ,
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206 according to the sequential composition theory of differential privacy, we can still ensure that the
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207 whole training process achieves $\epsilon _ { T }$ -differential privacy.
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+
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# 3.5 Privacy Analysis
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209 We will give the privacy analysis for the host and the guest respectively. In forward propagation,
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210 we recall that $\pmb { v } ^ { g } , \pmb { \theta } ^ { g }$ , and $\pmb { a } ^ { g }$ are input features, model parameters, and activation results of the
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211 guest. According to the definition of $\mathtt { R } ^ { 3 } \mathtt { e L U }$ , $\pmb { a } ^ { g }$ should be randomly flipped with probability $p$ . For
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212 brevity, we denote by $f ( )$ the evaluation of neural network before activation. Then the probability
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213 of observing any activation $a _ { o }$ for a given input $v$ should be
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+
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$$
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+
\begin{array} { l } { \displaystyle P ( a _ { o } = 0 | v ) = p + ( 1 - p ) \int _ { - \infty } ^ { - f ( v ) _ { o } } \frac { 1 } { 2 b } \exp ( - \frac { | v | } { b } ) d v = p + \frac { 1 - p } { 2 } \exp ( \frac { - f ( v ) _ { o } } { b } ) , } \\ { \displaystyle P ( a _ { o } > 0 | v ) = \frac { 1 - p } { 2 b } \exp ( - \frac { | a _ { 0 } - f ( v ) _ { o } | } { b } ) . } \end{array}
|
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+
$$
|
| 275 |
+
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214 Then we can give the following conclusion regarding the guest model. The proof is in the appendix.
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+
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Corollary 1. When forward propagation of the guest model is activated by215 $R ^ { 3 } e L U$ in split learning, 216 the activation result is $\epsilon$ -DP, given Laplace noise scale $\sigma _ { g }$ .
|
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+
|
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217 For a fine-grained privacy budget allocation, we introduce dynamic budget allocation in our solution.
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218 We now give the analysis of feature-specific privacy budget. Given the estimated feature importance
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219 vector $\boldsymbol { U } = \{ U _ { 1 } ^ { q } , U _ { 2 } ^ { q } , \dots , U _ { N _ { u } } ^ { q } \}$ , we allocate privacy budget $\epsilon _ { i } = \epsilon U _ { i } ^ { q }$ to each feature. Thus, if the
|
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220 divergence of features can be bounded by their privacy budgets, then the total privacy budget will
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221 be bounded. Denoted by $b _ { i }$ and $c _ { i }$ the noise parameter and bound of the $i$ -th feature. Then we can
|
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222 account the divergence of features as
|
| 286 |
+
|
| 287 |
+
$$
|
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+
\begin{array} { r l } & { \frac { P \left( a _ { i } > 0 | v \right) } { P \left( a _ { i } > 0 | v ^ { \prime } \right) } = \frac { \frac { 1 - p } { 2 b } \exp \left( - \frac { \left| a _ { i } - f ( v ) _ { i } \right| } { b _ { i } } \right) } { \frac { 1 - p } { 2 b } \exp \left( - \frac { \left| a _ { i } - f ( v ^ { \prime } ) _ { i } \right| } { b _ { i } } \right) } \leq \exp ( \frac { \left| a _ { i } - f ( v ^ { \prime } ) _ { i } \right| - \left| a _ { i } - f ( v ) _ { i } \right| } { b _ { i } } ) \leq \exp ( \frac { 2 c _ { i } } { b _ { i } } ) } \\ & { \frac { P \left( a _ { i } = 0 | v \right) } { P \left( a _ { i } = 0 | v ^ { \prime } \right) } = \frac { p + \frac { 1 - p } { 2 } e x p \left( - \frac { f ( v ) _ { i } } { b _ { i } } \right) } { p + \frac { 1 - p } { 2 } e x p \left( - \frac { f ( v ^ { \prime } ) _ { i } } { b _ { i } } \right) } \leq \frac { p + \frac { 1 - p } { 2 } e x p \left( \frac { c _ { i } } { b _ { i } } \right) } { p + \frac { 1 - p } { 2 } e x p \left( \frac { - c _ { i } } { b _ { i } } \right) } \leq \exp ( \frac { 2 c _ { i } } { b _ { i } } ) } \end{array}
|
| 289 |
+
$$
|
| 290 |
+
|
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+
223 Basing on this result, we can conclude the following corollary.
|
| 292 |
+
|
| 293 |
+
Corollary 2. In forward propagation with $R ^ { 3 } e L U ,$ , the privacy budget of the $i$ -th feature can be bounded by $\epsilon _ { i }$ if we choose $b _ { i }$ to satisfy $\begin{array} { r } { \exp \bigl ( \frac { 2 c _ { i } } { b _ { i } } \bigr ) \leq \exp ( \epsilon _ { i } ) , \forall p \in [ 0 , 1 ] . } \end{array}$ .
|
| 294 |
+
|
| 295 |
+
The last analysis result of the guest is privacy budget allocation during the whole training stage. Since we have allocated $\begin{array} { r } { \epsilon = \sum _ { i \in [ 1 , N _ { u } ] } \epsilon _ { i } } \end{array}$ for all features, we can directly conclude that each training step is $\gamma \epsilon$ -DP by following the privacy amplification theory, where $\begin{array} { r } { \gamma = \frac { B } { N } } \end{array}$ is the sampling ratio of a batch regarding the whole training dataset. Now we can give the total privacy budget of the whole training stage using the strong composition theorem.
|
| 296 |
+
|
| 297 |
+
Corollary 3. The total privacy budget of the whole training process using $R ^ { 3 } e L U$ is $( \epsilon _ { g } ^ { \prime } , \delta _ { g } ^ { \prime } )$ -DP, where $\begin{array} { r } { \epsilon _ { g } ^ { \prime } = \gamma \epsilon \sqrt { 2 T \ln ( \frac { 1 } { \delta _ { g } ^ { \prime } } ) } + \gamma \epsilon T ( e ^ { \gamma \epsilon } - 1 ) . } \end{array}$ .
|
| 298 |
+
|
| 299 |
+
So far, we have given the privacy analysis from the guest perspective. Since we construct $\mathtt { R } ^ { 3 } \mathtt { e L U }$ and $\mathbb { R } ^ { 3 }$ eLU-Diff using the same way and same technique, these two procedures have the same analysis result if we choose the noise scale of host $\sigma _ { h } = \sigma _ { g }$ . In this way, we can conclude the following result for the host.
|
| 300 |
+
|
| 301 |
+
Corollary 4. In backward propagation with $R ^ { 3 } e L U$ -Diff, the privacy budget of the host can be bounded by $\epsilon _ { h }$ if we choose $\sigma _ { h } = \sigma _ { g }$ . The total privacy budget of the host in the whole training process is $( \epsilon _ { h } ^ { \prime } , \delta _ { h } ^ { \prime } )$ -DP, where $\begin{array} { r } { \epsilon _ { h } ^ { \prime } = \gamma \epsilon _ { h } \sqrt { 2 T \ln ( \frac { 1 } { \delta _ { h } ^ { \prime } } ) } + \gamma \epsilon _ { h } T ( e ^ { \gamma \epsilon _ { h } } - 1 ) . } \end{array}$ .
|
| 302 |
+
|
| 303 |
+
241 We evaluate our privacy-preserving SplitNN solution from two aspects model usability and privacy
|
| 304 |
+
242 loss. To be comprehensive, we will compare our solution with the baseline (without any protection)
|
| 305 |
+
243 and the most relevant defense solutions, i.e., a primitive Laplace mechanism [5] and DPSGD [1],
|
| 306 |
+
244 the most well-known privacy-preserving deep learning solution, in the same setting. We will use
|
| 307 |
+
245 the same fixed total privacy budget and the same split way (shown in the appendix) for all solutions.
|
| 308 |
+
246 We adapt solutions into recommendation models using two real-world datasets, MovieLens [15],
|
| 309 |
+
247 BookCrossing [40], and an image classification model using MNIST [20] dataset. The MovieLens
|
| 310 |
+
248 1-M dataset contains 1 million ratings of 4,000 movies collected from 6,000 users and users’ de
|
| 311 |
+
249 mographic information such as gender and age. The BookCrossing dataset includes 278,858 users’
|
| 312 |
+
250 demographic information and 1,149,780 ratings of 271,379 books. The MNIST database has 70,000
|
| 313 |
+
251 handwriting image examples. We will use a 32 batch size, a 0.01 learning rate and an Adam opti
|
| 314 |
+
252 mizer as default. Since different datasets and defense solutions may require various epochs for split
|
| 315 |
+
253 learning, we calculate the metrics when the learning converges, or the privacy budget is drained. All
|
| 316 |
+
experimental results are averaged across multiple runs.
|
| 317 |
+
|
| 318 |
+
Table 2: Model usability results while preserving the privacy of the guest.
|
| 319 |
+
|
| 320 |
+
<table><tr><td rowspan="2">E</td><td colspan="3">MovieLens</td><td colspan="3">BookCrossing</td><td colspan="3">MNIST</td></tr><tr><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td></tr><tr><td>0.1</td><td>30.84%</td><td>32.29%</td><td>34.03%</td><td>57.02%</td><td>55.89%</td><td>58.18%</td><td>17.43%</td><td>30.21%</td><td>32.41%</td></tr><tr><td>0.5</td><td>41.25%</td><td>43.69%</td><td>43.87%</td><td>57.67%</td><td>56.14%</td><td>58.54%</td><td>27.33%</td><td>58.43%</td><td>60.38%</td></tr><tr><td>1.0</td><td>48.16%</td><td>49.09%</td><td>50.56%</td><td>58.02%</td><td>56.56%</td><td>58.42%</td><td>31.05%</td><td>75.58%</td><td>76.60%</td></tr><tr><td>2.0</td><td>49.32%</td><td>50.38%</td><td>50.49%</td><td>58.74%</td><td>56.91%</td><td>59.24%</td><td>38.92%</td><td>92.90%</td><td>93.53%</td></tr><tr><td>4.0</td><td>49.26%</td><td>50.86%</td><td>50.73%</td><td>59.01%</td><td>57.16%</td><td>59.26%</td><td>95.37%</td><td>95.87%</td><td>94.12%</td></tr></table>
|
| 321 |
+
|
| 322 |
+
Table 3: Model usability results while preserving the privacy of the host.
|
| 323 |
+
|
| 324 |
+
<table><tr><td rowspan="2">E</td><td colspan="3">MovieLens</td><td colspan="3">BookCrossing</td><td colspan="3">MNIST</td></tr><tr><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td></tr><tr><td>0.1</td><td>31.47%</td><td>30.68%</td><td>33.98%</td><td>57.37%</td><td>57.46%</td><td>58.26%</td><td>27.64%</td><td>33.45%</td><td>32.36%</td></tr><tr><td>0.5</td><td>41.75%</td><td>42.31%</td><td>42.67%</td><td>58.62%</td><td>58.24%</td><td>58.59%</td><td>55.38%</td><td>65.28%</td><td>67.83%</td></tr><tr><td>1.0</td><td>47.43%</td><td>48.29%</td><td> 50.39%</td><td>59.49%</td><td>58.44%</td><td>59.77%</td><td>71.95%</td><td>89.74%</td><td>88.14%</td></tr><tr><td>2.0</td><td>49.86%</td><td>50.43%</td><td> 51.47%</td><td>59.34%</td><td>59.97%</td><td>60.27%</td><td>89.15%</td><td>92.66%</td><td>92.52%</td></tr><tr><td>4.0</td><td>49.57%</td><td>50.09%</td><td>51.62%</td><td>59.55%</td><td>60.75%</td><td>60.66%</td><td>94.61%</td><td>95.37%</td><td>95.01%</td></tr></table>
|
| 325 |
+
|
| 326 |
+
# 4.1 Model Usability
|
| 327 |
+
|
| 328 |
+
Since artificial perturbation may affect the learning procedure, we will evaluate how SplitNN is affected by privacy-preserving solutions. Moreover, two asymmetric parties of SplitNN may have different privacy concerns and affect learning differently. Thus, we will evaluate model usability concerning privacy from the perspective of the guest or the host. We use an averaged test accuracy across all test samples for the evaluation. Precisely, the test accuracy of a recommendation model is calculated using a top-10 hit ratio, while the test accuracy of an image classifier is the prediction accuracy. In Table 2 and Table 3, we show the model usability results regarding various privacy budget values of two parties. We note that model accuracy baselines of Movielens, BookCrossing, and MNIST are $5 6 . 6 2 \%$ , $6 1 . 7 0 \%$ , and $9 8 . 0 0 \%$ , respectively.
|
| 329 |
+
|
| 330 |
+
265 For the MovieLens model, our solution achieves the best model usability in most cases, especially
|
| 331 |
+
266 with less privacy budget. DPSGD has a better result when $\epsilon = 4$ for the guest. But DPSGD will
|
| 332 |
+
267 cause a significant privacy leakage in this case. For the BookCrossing model, the model usability of
|
| 333 |
+
268 our solution is relatively high in cases of protecting the guest and the host. Similarly, DPSGD has a
|
| 334 |
+
269 better result when $\epsilon = 4$ for the host, sacrificing the privacy guarantee. Things are a bit different for
|
| 335 |
+
270 the MNIST model. DPSGD gets some better results when protecting the host. The reason is that split
|
| 336 |
+
271 learning for an image classification model segments image samples roughly, making our dynamic
|
| 337 |
+
272 budget allocation approach malfunction. Meanwhile, DPSGD is not designed for protecting partial
|
| 338 |
+
273 loss in SplitNN, leading to an optimistic estimation of the threat against the host. Apart from these
|
| 339 |
+
274 exceptional cases, our solution outperforms other solutions on model usability.
|
| 340 |
+
|
| 341 |
+
We will evaluate the performance of privacy preservation by comparing attack results against SplitNN with and without the defense. We will mount property inference and data reconstruction attacks against the guest and the host, respectively. Prediction accuracy of the adversary’s inference model will be used to measure the performance of the property inference attack. As for the data reconstruction attack, the adversary tries to generate data samples as similar as possible to the target’s private data. In this case, we can use a mean squared error (MSE) between a generated sample and a target data sample to measure the adversarial effect.
|
| 342 |
+
|
| 343 |
+
Table 4: Results of defending the guest against property inference attack.
|
| 344 |
+
|
| 345 |
+
<table><tr><td rowspan="2">E</td><td colspan="3">MovieLens</td><td colspan="3">BookCrossing</td><td colspan="3">MNIST</td></tr><tr><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td></tr><tr><td>0.1</td><td>66.99%</td><td>77.71%</td><td>60.99%</td><td>54.76%</td><td>73.29%</td><td>55.78%</td><td>43.27%</td><td>53.95%</td><td>44.33%</td></tr><tr><td>0.5</td><td>66.16%</td><td>74.23%</td><td>64.16%</td><td>54.97%</td><td>74.52%</td><td>56.33%</td><td>46.92%</td><td>54.23%</td><td>45.59%</td></tr><tr><td>1.0</td><td>67.19%</td><td>78.65%</td><td>68.18%</td><td>55.03%</td><td>74.96%</td><td>58.65%</td><td>47.58%</td><td>54.26%</td><td>47.51%</td></tr><tr><td>2.0</td><td>68.65%</td><td>73.06%</td><td>68.56%</td><td>54.85%</td><td>74.26%</td><td>58.14%</td><td>48.06%</td><td>54.65%</td><td>52.87%</td></tr><tr><td>4.0</td><td>69.14%</td><td>76.18%</td><td>71.91%</td><td>54.92%</td><td>74.33%</td><td>60.76%</td><td>48.47%</td><td>54.57%</td><td>55.73%</td></tr></table>
|
| 346 |
+
|
| 347 |
+
Table 5: Results of defending the host against property inference attack.
|
| 348 |
+
|
| 349 |
+
<table><tr><td rowspan="2">E</td><td colspan="3">MovieLens</td><td colspan="3">BookCrossing</td><td colspan="3">MNIST</td></tr><tr><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td></tr><tr><td>0.1</td><td>53.46%</td><td>78.59%</td><td>51.86%</td><td>54.55%</td><td>74.35%</td><td>59.42%</td><td>60.34%</td><td>80.29%</td><td>48.74%</td></tr><tr><td>0.5</td><td>53.46%</td><td>75.64%</td><td>51.89%</td><td>54.62%</td><td>74.36%</td><td>59.42%</td><td>59.82%</td><td>81.92%</td><td>49.71%</td></tr><tr><td>1.0</td><td>53.46%</td><td>73.54%</td><td>52.75%</td><td>54.95%</td><td>74.39%</td><td>59.52%</td><td>59.74%</td><td>82.80%</td><td>50.48%</td></tr><tr><td>2.0</td><td>53.47%</td><td>75.05%</td><td>59.77%</td><td>54.40%</td><td>74.39%</td><td>58.13%</td><td>60.38%</td><td>88.88%</td><td>50.57%</td></tr><tr><td>4.0</td><td> 53.48%</td><td>79.28%</td><td>56.52%</td><td> 54.95%</td><td>74.39&</td><td>62.04%</td><td>60.62%</td><td>89.73%</td><td>50.47%</td></tr></table>
|
| 350 |
+
|
| 351 |
+
Defense against property inference attack. We give evaluation results of the defensive effect of the guest and the host in Table 4 and Table 5, respectively, inferring the property of users in MovieLens and BookCrossing and an image patch in MNIST. The attack accuracy against baselines of MovieLens, BookCrossing, and MNIST models can achieve above $80 \%$ , $79 \%$ , and $94 \%$ by an adversarial host, $80 \%$ , $78 \%$ , and $57 \%$ by an adversarial guest, respectively. However, our SplitNN solution can effectively mitigate the adversarial effect during training and decrease the attack accuracy significantly. It should be noted that the primitive Laplace mechanism frustrates the inference attack badly because the artificial noise added by the mechanism is indiscriminate, leading to conspicuous damages to the model usability. Even so, our solution has significant advantages on MovieLens and MNIST datasets. In contrast, the primitive Laplace mechanism cannot cover image classification cases, while DPSGD cannot defeat the attack.
|
| 352 |
+
|
| 353 |
+
Table 6: Results of defending the guest against data reconstruction attack.
|
| 354 |
+
|
| 355 |
+
<table><tr><td rowspan="2">E</td><td colspan="3">MovieLens</td><td colspan="3">BookCrossing</td><td colspan="3">MNIST</td></tr><tr><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td></tr><tr><td>0.1</td><td>0.2459</td><td>0.2455</td><td>0.3223</td><td>0.3216</td><td>0.2907</td><td>0.3329</td><td>1.8849</td><td>1.8885</td><td>2.0181</td></tr><tr><td>0.5</td><td>0.2453</td><td>0.2451</td><td>0.3222</td><td>0.3202</td><td>0.2902</td><td>0.3329</td><td>1.8024</td><td>1.8137</td><td>1.9875</td></tr><tr><td>1.0</td><td>0.2453</td><td>0.2451</td><td>0.3222</td><td>0.3202</td><td>0.2902</td><td>0.3221</td><td>1.7857</td><td>1.7509</td><td>1.9533</td></tr><tr><td>2.0</td><td>0.2452</td><td>0.2451</td><td>0.3222</td><td>0.3202</td><td>0.2902</td><td>0.3221</td><td>1.7336</td><td>1.7469</td><td>1.9391</td></tr><tr><td>4.0</td><td>0.2452</td><td>0.2451</td><td>0.3222</td><td>0.3202</td><td>0.2902</td><td>0.3221</td><td>1.7014</td><td>1.7440</td><td>1.9206</td></tr></table>
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Defense against data reconstruction attack. We show the defense results against an adversarial host and an adversarial guest in Table 6 and Table 7, respectively. We note that the MSE is measured after the attack model has been trained sufficiently in all cases. The MSEs measured for the attack against baselines of MovieLens, BookCrossing, and MNIST models are 0.2412, 0.2629, and 0.9612 by an adversarial host, 0.2369, 0.2402, and 1.6998 by an adversarial guest, respectively. Please note that these attack results against the baselines are frustrating because the reconstruction attack is hard to succeed in the semi-honest setting. Meanwhile, data samples in two recommendation datasets are similar and embedded with the same feature vectors. This leads to similar reconstruction results and similar MSEs. But we can still conclude from the results that our solution has dominant performance in the defense against reconstruction attacks mounted by either side.
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Table 7: Results of defending the host against data reconstruction attack.
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<table><tr><td rowspan="2">E</td><td colspan="3">MovieLens</td><td colspan="2">BookCrossing</td><td colspan="3">MNIST</td></tr><tr><td>Laplace</td><td>DPSGD</td><td>Ours</td><td>Laplace DPSGD</td><td>Ours</td><td>Laplace</td><td>DPSGD</td><td>Ours</td></tr><tr><td>0.1</td><td>0.4032</td><td>0.2417</td><td>0.5486</td><td>0.4237</td><td>0.2758 0.5066</td><td>1.2887</td><td>1.0875</td><td>1.8257</td></tr><tr><td>0.5</td><td>0.4024</td><td>0.2419</td><td>0.5357</td><td>0.4222</td><td>0.2756 0.5149</td><td>1.2778</td><td>1.0685</td><td>1.7758</td></tr><tr><td>1.0</td><td>0.4008</td><td>0.2422</td><td>0.5285</td><td>0.4217</td><td>0.2743 0.5235</td><td>1.2602</td><td>1.0422</td><td>1.7528</td></tr><tr><td>2.0</td><td>0.3982</td><td>0.2421</td><td>0.5083</td><td>0.4214</td><td>0.2697 0.5150</td><td>1.2613</td><td>1.0333</td><td>1.7334</td></tr><tr><td>4.0</td><td>0.3960</td><td>0.2422</td><td>0.4819</td><td>0.4194</td><td>0.2683 0.5046</td><td>1.2549</td><td>0.9996</td><td>1.7262</td></tr></table>
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Defense against feature space hijacking attacks (FSHA). Please note that property inference and data reconstruction attacks implemented in [29] hijack the learning objective, offering the adversary an advantage over the previous attacks we straightforwardly adapted from FL. In this setting, the malicious attacker trains a generator using the split neural network as a discriminator during the split learning process and uses a gradient-scaling trick to train the generator. Since the generating part is critical to FSHA, we will focus on the defense against the reconstruction. If the generating part fails, the inference attack will be impossible. Here we give the defense results of the MNIST model because FSHA [29] is mainly evaluated using this dataset. We also evaluate our solution for other datasets against FSHA, and the results are given in the appendix. In Figure 1 and Figure 2, we give the reconstruction results of FHSA mounted by an adversarial host and guest against target samples used in [29]. The second row of two figures shows the results of FSHA against baselines. The following rows show that our solution can effectively preserve private data for both the guest and the host, even the privacy budget is relaxed to 4. More practical privacy budget values for defending against FSHA are presented in the appendix.
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Figure 1: Reconstruction results of FSHA against the guest’s data in the first row. The following rows are attack results against the original SplitNN and our solution $\epsilon = 0 . 1 , 1 . 0 , 4 . 0 )$ , respectively.
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Figure 2: Reconstruction results of FSHA against the host’s data in the first row. The following rows are attack results against the original SplitNN and our solution $\mathsf { \bar { \epsilon } } = 0 . 1 , 1 . 0 , 4 . 0 )$ , respectively.
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# 318 5 Conclusion and Limitation
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319 Our privacy-preserving SplitNN solution, built upon a new activation function $\mathtt { R } ^ { 3 } \mathtt { e L U }$ and its deriva
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320 tive $\mathbb { R } ^ { 3 }$ eLU-Diff in a randomized-response manner, significantly reduces privacy leakage risk for
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321 both the guest and the host. We show that our solution can provide a tight privacy budget for split
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322 learning through the privacy analysis. The model usability and privacy loss can be further balanced
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323 by our dynamic privacy budget allocation. The experimental evaluation using different datasets
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324 shows that our solution outperforms the existing privacy-preserving SplitNN solutions in model us
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325 ability and privacy protection. We note that our solution deals with property inference and data
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326 reconstruction attacks in a feature level, but a clustering-based label inference attack [8] is out of
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327 our reach, which is an interesting topic to be studied in future work.
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References [1] Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. Deep learning with differential privacy. In ACM SIGSAC conference on computer and communications security, pages 308–318, 2016. [2] Andrea Apicella, Francesco Donnarumma, Francesco Isgrò, and Roberto Prevete. A survey on modern trainable activation functions. Neural Networks, 2021.
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[3] Eugene Bagdasaryan, Omid Poursaeed, and Vitaly Shmatikov. Differential privacy has disparate impact on model accuracy. Advances in Neural Information Processing Systems, 32: 15479–15488, 2019. [4] Iker Ceballos, Vivek Sharma, Eduardo Mugica, Abhishek Singh, Alberto Roman, Praneeth Vepakomma, and Ramesh Raskar. Splitnn-driven vertical partitioning. arXiv preprint arXiv:2008.04137, 2020. [5] Cynthia Dwork, Aaron Roth, et al. The algorithmic foundations of differential privacy. Foundations and Trends® in Theoretical Computer Science, pages 211–407, 2014. [6] Ege Erdogan, Alptekin Kupcu, and A Ercument Cicek. Unsplit: Data-oblivious model inversion, model stealing, and label inference attacks against split learning. arXiv preprint arXiv:2108.09033, 2021.
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[7] Minghong Fang, Neil Zhenqiang Gong, and Jia Liu. Influence function based data poisoning attacks to top-n recommender systems. In Proceedings of The Web Conference, pages 3019– 3025, 2020. [8] Chong Fu, Xuhong Zhang, Shouling Ji, Jinyin Chen, Jingzheng Wu, Shanqing Guo, Jun Zhou, Alex X Liu, and Ting Wang. Label inference attacks against vertical federated learning. In USENIX Security Symposium, 2022.
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[9] Karan Ganju, Qi Wang, Wei Yang, Carl A Gunter, and Nikita Borisov. Property inference attacks on fully connected neural networks using permutation invariant representations. In ACM SIGSAC conference on computer and communications security, pages 619–633, 2018.
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[10] Hongyang Gao, Lei Cai, and Shuiwang Ji. Adaptive convolutional relus. In AAAI Conference on Artificial Intelligence, volume 34, pages 3914–3921, 2020.
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[11] Yansong Gao, Minki Kim, Sharif Abuadbba, Yeonjae Kim, Chandra Thapa, Kyuyeon Kim, Seyit A Camtep, Hyoungshick Kim, and Surya Nepal. End-to-end evaluation of federated learning and split learning for internet of things. In International Symposium on Reliable Distributed Systems, pages 91–100, 2020.
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[12] Ran Gilad-Bachrach, Nathan Dowlin, Kim Laine, Kristin Lauter, Michael Naehrig, and John Wernsing. Cryptonets: Applying neural networks to encrypted data with high throughput and accuracy. In International conference on machine learning, pages 201–210, 2016.
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[13] Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pages 2672–2680, 2014.
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[14] Otkrist Gupta and Ramesh Raskar. Distributed learning of deep neural network over multiple agents. Journal of Network and Computer Applications, 116:1–8, 2018.
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[15] Attribution F Maxwell Harper and Joseph A Konstan. The movielens datasets: History and context. ACM Transactions on Interactive Intelligent Systems, 5(4), 2015.
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[16] Xinlei He and Yang Zhang. Quantifying and mitigating privacy risks of contrastive learning. In ACM Conference on Computer and Communications Security, 2021.
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[17] Briland Hitaj, Giuseppe Ateniese, and Fernando Perez-Cruz. Deep models under the gan: information leakage from collaborative deep learning. In ACM SIGSAC Conference on Computer and Communications Security, pages 603–618, 2017.
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[18] Hai Huang, Jiaming Mu, Neil Zhenqiang Gong, Qi Li, Bin Liu, and Mingwei Xu. Data poisoning attacks to deep learning based recommender systems. In Annual Network and Distributed System Security Symposium, 2021.
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[19] Juyong Kim, Yookoon Park, Gunhee Kim, and Sung Ju Hwang. Splitnet: Learning to semantically split deep networks for parameter reduction and model parallelization. In International Conference on Machine Learning, pages 1866–1874, 2017.
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[20] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998.
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[21] Yang Liu, Zhuo Ma, Yilong Yang, Ximeng Liu, Jianfeng Ma, and Kui Ren. Revfrf: Enabling cross-domain random forest training with revocable federated learning. IEEE Transactions on Dependable and Secure Computing, 2021.
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[22] Xinjian Luo, Yuncheng Wu, Xiaokui Xiao, and Beng Chin Ooi. Feature inference attack on model predictions in vertical federated learning. In IEEE International Conference on Data Engineering, pages 181–192, 2021.
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[23] Yunlong Mao, Wenbo Hong, Boyu Zhu, Zhifei Zhu, Yuan Zhang, and Sheng Zhong. Secure deep neural network models publishing against membership inference attacks via training task parallelism. IEEE Transactions on Parallel and Distributed Systems, 2021.
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[24] Yunlong Mao, Xinyu Yuan, Xinyang Zhao, and Sheng Zhong. Romoa: Robust model aggregation for the resistance of federated learning to model poisoning attacks. In European Symposium on Research in Computer Security, pages 476–496, 2021.
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[25] Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication-efficient learning of deep networks from decentralized data. In Artificial intelligence and statistics, pages 1273–1282, 2017.
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[26] Luca Melis, Congzheng Song, Emiliano De Cristofaro, and Vitaly Shmatikov. Exploiting unintended feature leakage in collaborative learning. In IEEE Symposium on Security and Privacy, pages 691–706. IEEE, 2019.
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[27] Payman Mohassel and Yupeng Zhang. Secureml: A system for scalable privacy-preserving machine learning. In IEEE symposium on security and privacy, pages 19–38, 2017.
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[28] Pavlo Molchanov, Arun Mallya, Stephen Tyree, Iuri Frosio, and Jan Kautz. Importance estimation for neural network pruning. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11264–11272, 2019.
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[29] Dario Pasquini, Giuseppe Ateniese, and Massimo Bernaschi. Unleashing the tiger: Inference attacks on split learning. ACM SIGSAC Conference on Computer and Communications Security, 2021.
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[30] Ahmed Salem, Yang Zhang, Mathias Humbert, Mario Fritz, and Michael Backes. Ml-leaks: Model and data independent membership inference attacks and defenses on machine learning models. In Annual Network and Distributed Systems Security Symposium, 2019.
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[31] Ahmed Salem, Apratim Bhattacharya, Michael Backes, Mario Fritz, and Yang Zhang. Updatesleak: Data set inference and reconstruction attacks in online learning. In USENIX Security Symposium, pages 1291–1308, 2020.
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[32] Lichao Sun, Jianwei Qian, and Xun Chen. LDP-FL: practical private aggregation in federated learning with local differential privacy. In International Joint Conference on Artificial Intelligence, pages 1571–1578, 2021.
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[33] Vale Tolpegin, Stacey Truex, Mehmet Emre Gursoy, and Ling Liu. Data poisoning attacks against federated learning systems. In European Symposium on Research in Computer Security, pages 480–501, 2020.
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[34] Praneeth Vepakomma, Otkrist Gupta, Tristan Swedish, and Ramesh Raskar. Split learning for health: Distributed deep learning without sharing raw patient data. arXiv preprint arXiv:1812.00564, 2018.
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[35] Stanley L Warner. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309):63–69, 1965.
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[36] Kang Wei, Jun Li, Ming Ding, Chuan Ma, Howard H Yang, Farhad Farokhi, Shi Jin, Tony QS Quek, and H Vincent Poor. Federated learning with differential privacy: Algorithms and performance analysis. IEEE Transactions on Information Forensics and Security, 15:3454–3469, 2020.
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[37] Ji Yang, Xinyang Yi, Derek Zhiyuan Cheng, Lichan Hong, Yang Li, Simon Xiaoming Wang, Taibai Xu, and Ed H Chi. Mixed negative sampling for learning two-tower neural networks in recommendations. In Proceedings of the Web Conference, pages 441–447, 2020.
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[38] Chengliang Zhang, Suyi Li, Junzhe Xia, Wei Wang, Feng Yan, and Yang Liu. Batchcrypt: Efficient homomorphic encryption for cross-silo federated learning. In USENIX Annual Technical Conference, 2020.
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[39] Yin Zhang, Derek Zhiyuan Cheng, Tiansheng Yao, Xinyang Yi, Lichan Hong, and Ed H Chi. A model of two tales: Dual transfer learning framework for improved long-tail item recommendation. In Proceedings of the Web Conference, pages 2220–2231, 2021.
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[40] Cai-Nicolas Ziegler, Sean M McNee, Joseph A Konstan, and Georg Lausen. Improving recommendation lists through topic diversification. In International Conference on World Wide Web, pages 22–32, 2005.
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# 442 Checklist
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The checklist follows the references. Please read the checklist guidelines carefully for information on how to answer these questions. For each question, change the default [TODO] to [Yes] , [No] , or [N/A] . You are strongly encouraged to include a justification to your answer, either by referencing the appropriate section of your paper or providing a brief inline description. For example:
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• Did you include the license to the code and datasets? [Yes] See Section ??.
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• Did you include the license to the code and datasets? [No] The code and the data are proprietary.
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• Did you include the license to the code and datasets? [N/A]
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451 Please do not modify the questions and only use the provided macros for your answers. Note that the
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452 Checklist section does not count towards the page limit. In your paper, please delete this instructions
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453 block and only keep the Checklist section heading above along with the questions/answers below.
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1. For all authors...
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
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(b) Did you describe the limitations of your work? [Yes]
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(c) Did you discuss any potential negative societal impacts of your work? [N/A] (d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
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2. If you are including theoretical results...
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(a) Did you state the full set of assumptions of all theoretical results? [Yes] (b) Did you include complete proofs of all theoretical results? [Yes]
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3. If you ran experiments...
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(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]
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(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes]
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(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes]
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(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]
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4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
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+
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(a) If your work uses existing assets, did you cite the creators? [Yes]
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(b) Did you mention the license of the assets? [Yes]
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(c) Did you include any new assets either in the supplemental material or as a URL? [No]
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(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]
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(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
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5. If you used crowdsourcing or conducted research with human subjects...
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(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
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(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
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(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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# A.1 Split Leaning with490 $\mathbf { R } ^ { 3 }$ eLU
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491 We give the forward propagation procedure of SplitNN using our $\mathtt { R } ^ { 3 } \mathtt { e L U }$ in Algorithm 1, and the 492 backward propagation procedure of SplitNN using our $\mathbb { R } ^ { 3 }$ eLU-Diff in Algorithm 2. The two algorithms are supplementary materials for Section 3.2 and 3.3.
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# Algorithm 1: forward propagation with $\mathtt { R } ^ { 3 } \mathtt { e L U }$
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Input: batch size $N$ , data batch $\mathbf { \Delta } _ { \mathbf { \boldsymbol { x } } ^ { g } , \mathbf { \boldsymbol { x } } ^ { h } }$ , encoded label $\textbf { { y } }$ , training indicator $I$ , noise scale $\sigma$ .
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Output: loss or prediction.
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+
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+
$$
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+
\textbf { 1 } \theta ^ { h } \overset { r } { \longleftarrow } \mathcal { N } ( 0 , 1 ) , \theta ^ { k } \overset { r } { \longleftarrow } \mathcal { N } ( 0 , 1 ) , \theta ^ { g } \overset { r } { \longleftarrow } \mathcal { N } ( 0 , 1 )
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| 474 |
+
$$
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+
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+
// initial
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+
|
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+
# Guest:
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+
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+
2 for $i \gets 1$ to $N$ do
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+
3 $\begin{array} { r l } { | } & { { } v _ { i } ^ { g } E m b e d d i n g ( x _ { i } ^ { g } ) } \end{array}$ ;
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+
4 end
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+
5 $\pmb { v } ^ { g } \{ v _ { 1 } ^ { g } , v _ { 2 } ^ { g } , \dots , v _ { N } ^ { g } \}$
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+
6 $\pmb { a } ^ { g } \gets F o r u a r d - \mathbb { A } ^ { 3 } e L U ( \pmb { v } ^ { g } , \pmb { \theta } ^ { g } )$
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+
Host:
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+
7 for $i \gets 1$ to $N$ do
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8 $\begin{array} { r l } { \Bigl | } & { { } v _ { i } ^ { h } \gets E m b e d d i n g ( x _ { i } ^ { h } ) } \end{array}$ ;
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+
9 end
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10 $\pmb { v } ^ { h } \{ v _ { 1 } ^ { h } , v _ { 2 } ^ { h } , . . . , v _ { N } ^ { h } \}$
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+
11 $\pmb { a } ^ { h } \gets F o r u a r d ( \pmb { v } ^ { h } , \pmb { \theta } ^ { h } )$
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+
12 $\bar { \mathbf { \ b { a } } } \gets A v e r a g e ( \mathbf { \ b { a } } ^ { g } , \mathbf { \ b { a } } ^ { h } )$
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+
13 $\pmb { o } ^ { k } \gets F o r u a r d ( \bar { \pmb { a } } , \pmb { \theta } ^ { k } )$
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+
14 if $I = =$ train then
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+
15 $l o s s \mathcal { L } ( o ^ { k } , \pmb { y } )$
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+
16 else
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+
17 pred ← Softmax(ok)
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+
18 end
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+
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+
// predicting
|
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+
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| 501 |
+
Algorithm 2: backward propagation with R3eLU-Diff
|
| 502 |
+
|
| 503 |
+
Input: batch size $N$ , feature vectors ${ \pmb v } ^ { g } , { \pmb v } ^ { h }$ , forward results $\pmb { a } ^ { g }$ , $\mathbf { \Omega } _ { \mathbf { { \mathfrak { a } } } ^ { h } }$ , $\bar { \bf a }$ , total loss $l$ , encoded label $\textbf { { y } }$ , learning rate $\eta ^ { g } , \eta ^ { h } , \eta ^ { k }$ , clipping bound $C$ , noise scale $\sigma$ .
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+
|
| 505 |
+
$\theta _ { t + 1 } ^ { g }$ $\theta _ { t + 1 } ^ { h }$ $\widehat { \theta _ { t + 1 } ^ { k } }$
|
| 506 |
+
|
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+
# Host:
|
| 508 |
+
|
| 509 |
+
1 $\delta ^ { k } \gets \nabla _ { \pmb { a } ^ { k } } \mathcal { L } ( l , \bar { \pmb { a } } , \pmb { \theta } _ { t } ^ { k } )$
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+
2 $\pmb { g } _ { t } ^ { k } \gets \tt B a c k w a r d ( \delta ^ { k } , \bar { \pmb { a } } , \pmb { \theta } _ { t } ^ { k } )$
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| 511 |
+
3 $\delta ^ { h } \gets \nabla _ { \mathbf { \boldsymbol { a } } ^ { h } } \mathcal { L } ( \delta ^ { k } , \mathbf { \boldsymbol { a } } ^ { h } , \mathbf { \boldsymbol { \theta } } _ { t } ^ { h } )$ , δ g ← ∇a g L(δ k , a g , θ kt )
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+
4 $\pmb { g } _ { t } ^ { h } \mathtt { B a c k w a r d } ( \delta ^ { h } , \pmb { v } ^ { h } , \pmb { \theta } _ { t } ^ { h } )$
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+
5 $\begin{array} { r } { \bar { g } _ { t } ^ { k } \gets \frac { 1 } { N } \sum _ { i \in [ 1 , N ] } g _ { i , t } ^ { k } } \end{array}$ , g¯ht ← 1N Pi∈[1,N ] ghi,t
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| 514 |
+
6 $\pmb { \theta } _ { t + 1 } ^ { k } \pmb { \theta } _ { t } ^ { k } - \eta ^ { k } \bar { \pmb { g } } _ { t } ^ { k }$ , θ ht+ 1 ← θ ht − η h g¯ ht
|
| 515 |
+
7 $\begin{array} { r } { \hat { \delta } ^ { g } \gets \delta ^ { g } / \operatorname* { m a x } ( 1 , \frac { | | \delta ^ { g } | | _ { 1 } } { C } ) } \end{array}$
|
| 516 |
+
8 ${ \tilde { \delta } } ^ { g } \gets R ^ { 3 } e L U - D i f f ( \hat { \delta } ^ { g } , { \pmb a } ^ { g } , { \pmb v } ^ { g } )$
|
| 517 |
+
|
| 518 |
+
# Guest:
|
| 519 |
+
|
| 520 |
+
10 9 $\pmb { \mathscr { g } } _ { t } ^ { g } \gets \tt B a c k w a r d ( \tilde { \delta } ^ { g } , \pmb { a } ^ { g } , \pmb { \theta } _ { t } ^ { g } )$ $\begin{array} { r } { \bar { g } _ { t } ^ { g } \frac { 1 } { N } \sum _ { i \in [ 1 , N ] } g _ { i , t } ^ { g } } \end{array}$
|
| 521 |
+
11 $\pmb { \theta } _ { t + 1 } ^ { g } \pmb { \theta } _ { t } ^ { g } - \eta ^ { g } \bar { \pmb { g } } _ { t } ^ { g }$
|
| 522 |
+
|
| 523 |
+
495 Here we give the proof of our Corollary 1 in detail for the privacy analysis in Section 3.5.
|
| 524 |
+
|
| 525 |
+
496 Proof. Without loss of generality, we assume an activation result $\pmb { a } = \{ a _ { 1 } = 0 , a _ { 2 } = 0 , . . . , a _ { o } =$
|
| 526 |
+
497 $0 , a _ { o + 1 } > 0 , . . . , a _ { N _ { s } } > 0 \}$ . Then the difference of activations for two neighboring feature vectors
|
| 527 |
+
498 $v , v ^ { \prime }$ can be bounded by
|
| 528 |
+
|
| 529 |
+
$$
|
| 530 |
+
\begin{array} { r l } & { \frac { \hat { \rho } _ { \mathrm { e f f } } } { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } } \\ & { = \underset { \hat { \rho } _ { \mathrm { e f f } } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } } \\ & { = \underset { \hat { \rho } _ { \mathrm { e f f } } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } + \underset { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } ( \frac { 1 - \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } ) ^ { 2 } \underset { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } - \underset { \hat { \rho } { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } - \underset { \hat { \rho } { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } } } { \frac { \hat { \rho } { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } } } \\ & - \underset { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } ( \frac { 1 - \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } ) + \underset { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } \frac { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } } \\ & \underset { \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { \sum } \frac \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } ( \frac { 1 - \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } } { 2 } ) + \underset { \hat { \rho } _ { \mathrm { e f f } } } { \sum } \frac \hat { \rho } _ { \mathrm { e f f } } ^ { ( 0 ) } ( \frac 1 - \hat { \rho } _ \ \end{array}
|
| 531 |
+
$$
|
| 532 |
+
|
| 533 |
+
We assume 499 $| f ( \boldsymbol { v } ) _ { i } | \le c _ { g }$ and $\begin{array} { r } { b \leq \frac { c _ { g } } { l n 2 } } \end{array}$ , then the RHS
|
| 534 |
+
|
| 535 |
+
$$
|
| 536 |
+
\begin{array} { r l } & { \leq \displaystyle \prod _ { i = 1 } ^ { o } \frac { 1 + p } { p \exp \left( \frac { - c _ { q } } { b } \right) + \frac { 1 - p } { 2 } } \times \prod _ { i = o + 1 } ^ { N _ { s } } \exp ( \frac { | f ( v ^ { \prime } ) _ { i } - f ( v ) _ { i } | } { b } ) } \\ & { \leq \displaystyle \prod _ { i = 1 } ^ { o } \frac { \frac { 1 + p } { 2 } } { \exp \left( \frac { - c _ { q } } { b } \right) } \times \prod _ { i = o + 1 } ^ { N _ { s } } \exp ( \frac { | f ( v ^ { \prime } ) _ { i } - f ( v ) _ { i } | } { b } ) } \\ & { \leq ( \frac { \frac { 1 + p } { 2 } } { \exp \left( \frac { - c _ { q } } { b } \right) } ) ^ { o } \times \exp ( \frac { \Delta f } { b } ) } \\ & { = \exp ( \epsilon ) } \end{array}
|
| 537 |
+
$$
|
| 538 |
+
|
| 539 |
+
Thus, we have 500 $\begin{array} { r } { N _ { S } ( \frac { c _ { g } } { \sigma _ { g } } + \ln ( \frac { 1 + p } { 2 } ) ) + \frac { \Delta f } { \sigma _ { g } } = \epsilon } \end{array}$
|
| 540 |
+
|
| 541 |
+
# 01 A.3 Evaluation of Dynamic Parameter Importance Estimation
|
| 542 |
+
|
| 543 |
+
502 Additionally, we evaluate the effectiveness of our feature importance estimation method and give
|
| 544 |
+
503 the result here. We compare the estimating results between parameter importance estimated in the
|
| 545 |
+
504 model’s finally stable state and parameter importance estimated in our dynamic manner. The result
|
| 546 |
+
505 is shown in Figure 3. We can conclude from the result that our dynamic parameter importance
|
| 547 |
+
506 estimation approach can achieve desirable effectiveness.
|
| 548 |
+
507 We aim to estimate the importance of parameters precisely during privacy-preserving split learning.
|
| 549 |
+
508 But it is difficult to get the same result with the estimation in a non-perturbed case. By carefully
|
| 550 |
+
509 constructing the dynamic estimation method, we can obtain dynamic estimation results of noisy pa
|
| 551 |
+
510 rameters quite close to a baseline estimation result in the stable state without any privacy protection.
|
| 552 |
+
511 In Figure 4, we show the result of our dynamic importance estimation approach. We can find that
|
| 553 |
+
|
| 554 |
+
|
| 555 |
+
Figure 3: Comparison of parameter importance estimation results.
|
| 556 |
+
|
| 557 |
+
512 artificial noise introduced by our privacy-preserving SplitNN solution will affect the estimation of 513 parameter importance. But the growth tendency keep the same as the baseline. This is good enough 514 for us since we use the proportionality factor of each parameter to calculate the budget allocation, which will not be influenced by the magnitude.
|
| 558 |
+
|
| 559 |
+
|
| 560 |
+
Figure 4: Importance of noisy parameters estimated dynamically in logarithm.
|
| 561 |
+
|
| 562 |
+
# 516 A.4 Supplementary Results for Evaluation
|
| 563 |
+
|
| 564 |
+
517 The neural networks we used for the MovieLens, BookCrossing, and MNIST datasets after split are
|
| 565 |
+
518 shown in Tab 8, Table 9, and Table 10. These networks are commonly used in related studies. We
|
| 566 |
+
519 split them according to the interpretation of SplitNN in [4, 11, 29].
|
| 567 |
+
520 To further investigate how our solution affects the learning process of SplitNN, we report learning
|
| 568 |
+
521 results of a MovieLens recommendation model protecting the privacy of the guest and the host
|
| 569 |
+
522 in Figure 5 and 6, respectively. In each plot, we show trends of training loss, training accuracy,
|
| 570 |
+
523 and testing accuracy as the training epoch increases. We can conclude from these figures that our
|
| 571 |
+
524 solution achieve satisfying model usability with small privacy budget for either side of SplitNN.
|
| 572 |
+
525 We notice that FSHA is sensitive to our privacy-preserving SplitNN solution. In Figure 1 and Fig
|
| 573 |
+
526 ure 2, we find that neither an adversarial host nor an adversarial guest can reconstruct meaningful
|
| 574 |
+
527 samples, even if the target’s privacy budget is $\epsilon = 4$ . Therefore, we are curious about a practical
|
| 575 |
+
528 choice of the privacy budget when dealing with FSHA. To this end, we give more defense results
|
| 576 |
+
529 of our solution against FSHA using various privacy budget values in Table 11. We can conclude
|
| 577 |
+
530 from the MSE results that two recommendation models prefer relatively low privacy budget, such
|
| 578 |
+
531 as $\epsilon = 1 . 0$ . However, it is interesting to see that FSHA attack against an image classification model
|
| 579 |
+
532 using SplitNN can be frustrated by our solution using relatively high privacy budget, which also
|
| 580 |
+
means a high model usability.
|
| 581 |
+
|
| 582 |
+
<table><tr><td>Guest Layer</td><td>Output Shape</td><td>Param #</td></tr><tr><td>Linear(160,128)+ReLU</td><td>(None,128)</td><td>20608</td></tr><tr><td>Host Layer</td><td>Output Shape</td><td>Param #</td></tr><tr><td>Linear(160,128)+ReLU</td><td>(None,128)</td><td>20608</td></tr><tr><td>Merge Guest Linear(128,128)+ReLU</td><td>(None,128)</td><td>16512</td></tr><tr><td>Linear(128,64)+ReLU</td><td>(None,64)</td><td>8256</td></tr><tr><td>Linear(64,3952)+Softmax</td><td>(None,3952)</td><td>256880</td></tr></table>
|
| 583 |
+
|
| 584 |
+
Table 8: The MovieLens model.
|
| 585 |
+
|
| 586 |
+
<table><tr><td>Guest Layer</td><td>Output Shape</td><td>Param #</td></tr><tr><td>Linear(160,128)+ReLU</td><td>(None,128)</td><td>20608</td></tr><tr><td>Host Layer</td><td>Output Shape</td><td>Param #</td></tr><tr><td>Linear(160,128)+ReLU</td><td>(None,128)</td><td>20608</td></tr><tr><td>Merge Guest</td><td></td><td></td></tr><tr><td>Linear(128,256)+ReLU Linear(256,128)+ReLU</td><td>(None,256)</td><td>33024</td></tr><tr><td></td><td>(None,128)</td><td>32896</td></tr><tr><td>Linear(128,17384)+Softmax</td><td>(None,10)</td><td>2242536</td></tr></table>
|
| 587 |
+
|
| 588 |
+
Table 9: The BookCrossing model.
|
| 589 |
+
|
| 590 |
+
<table><tr><td>Guest Layer</td><td>Output Shape</td><td>Param #</td></tr><tr><td>Linear(28*14,128)</td><td>(None,128)</td><td>50304</td></tr><tr><td>BatchNorm+ReLU Linear(128,64)</td><td>(None,128) (None,64)</td><td>8256</td></tr><tr><td></td><td></td><td></td></tr><tr><td>Host Layer</td><td>Output Shape</td><td>Param #</td></tr><tr><td>Linear(28*14,128) BatchNorm+ReLU</td><td>(None,128)</td><td>50304</td></tr><tr><td></td><td>(None,128)</td><td></td></tr><tr><td>Linear(128.64) BatchNorm+ReLU</td><td>(None,64)</td><td>8256</td></tr><tr><td>Merge Guest</td><td>(None,64)</td><td></td></tr><tr><td></td><td></td><td></td></tr><tr><td>Linear(64,64)</td><td>(None,64)</td><td>4160</td></tr><tr><td>BatchNorm+ReLU</td><td>(None,64)</td><td></td></tr><tr><td>Linear(64,10)+Softmax</td><td>(None,10)</td><td>650</td></tr></table>
|
| 591 |
+
|
| 592 |
+
Table 10: The MNIST model.
|
| 593 |
+
|
| 594 |
+
Table 11: Defense results against FSHA mounted by an adversarial host.
|
| 595 |
+
|
| 596 |
+
<table><tr><td rowspan="3">E</td><td colspan="2">MovieLens</td><td colspan="2">BookCrossing</td><td colspan="2">MNIST</td></tr><tr><td>baseline</td><td>Ours</td><td>baseline</td><td>Ours</td><td>baseline</td><td>Ours</td></tr><tr><td>1200Epochs</td><td>5000 Epochs 455.5676</td><td>1200Epochs</td><td>5000 Epochs 500.1487</td><td>9000Epochs</td><td>9000 Epochs 1.98257</td></tr><tr><td>0.25</td><td rowspan="10">0.2652 ×10-3</td><td>73.7824</td><td rowspan="10"></td><td>83.7606</td><td rowspan="10"></td><td></td></tr><tr><td></td><td></td><td></td><td>1.9788</td></tr><tr><td>0.5</td><td>21.1706</td><td>30.2905</td><td>1.9703</td></tr><tr><td>0.75</td><td>9.5312</td><td>8.5984</td><td>1.9534</td></tr><tr><td>1.0</td><td>4.4903</td><td>6.1267</td><td>1.9442</td></tr><tr><td>2.0</td><td>1.1559</td><td>1.7047</td><td>1.9283</td></tr><tr><td>4.0</td><td>0.2719</td><td>0.2478</td><td>1.9209</td></tr><tr><td>6.0</td><td>0.1091</td><td>0.1638</td><td>1.9135</td></tr><tr><td>8.0</td><td>0.0975</td><td>0.0846</td><td>1.9116</td></tr></table>
|
| 597 |
+
|
| 598 |
+
|
| 599 |
+
Figure 5: SplitNN learning curve with the guest’s privacy protected by our solution.
|
| 600 |
+
|
| 601 |
+
|
| 602 |
+
Figure 6: SplitNN learning curve with the host’s privacy protected by our solution.
|
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# Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures
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Shitong $\mathbf { L u o ^ { 1 * } }$ , Yufeng $\mathbf { S u ^ { 2 * } }$ , Xingang Peng3, Sheng Wang4, Jian Peng1,2, Jianzhu Ma1,5
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1 Helixon Research 2 University of Illinois Urbana-Champaign 3 School of Intelligence Science and Technology, Peking University 4 Paul G. Allen School of Computer Science, University of Washington 5 Institute for AI Industry Research, Tsinghua University luost@helixon.com,luost26@gmail.com swang@cs.washington.edu,jianpeng@illinois.edu,majianzhu@tsinghua.edu.cn
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# Abstract
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Antibodies are immune system proteins that protect the host by binding to specific antigens such as viruses and bacteria. The binding between antibodies and antigens is mainly determined by the complementarity-determining regions (CDR) of the antibodies. In this work, we develop a deep generative model that jointly models sequences and structures of CDRs based on diffusion probabilistic models and equivariant neural networks. Our method is the first deep learning-based method that generates antibodies explicitly targeting specific antigen structures and is one of the earliest diffusion probabilistic models for protein structures. The model is a “Swiss Army Knife” capable of sequence-structure co-design, sequence design for given backbone structures, and antibody optimization. We conduct extensive experiments to evaluate the quality of both sequences and structures of designed antibodies. We find that our model could yield competitive results in binding affinity measured by biophysical energy functions and other protein design metrics.
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# 1 Introduction
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Antibodies are important immune proteins generated during an immune response to recognize and neutralize the pathogen [Janeway et al., 2001]. As illustrated in Figure 1a, an antibody contains two heavy chains and two light chains, and their overall structure is similar. Six variable regions determine the specificity of an antibody to the antigens. They are called the Complementarity Determining Regions (CDRs), denoted as H1, H2, H3, L1, L2, and L3. Therefore, the most important step for developing effective therapeutic antibodies is to design CDRs that bind to the specific antigen [Presta, 1992, Akbar et al., 2022a].
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Similar to other protein design tasks, the search space of CDRs is vast. A CDR sequence with $L$ amino acids has up to $\mathrm { 2 0 } ^ { L }$ possible protein sequences. It is not feasible to test all the possible sequences using experimental approaches, so computational methods are needed. Traditional computational approaches rely on sampling protein sequences and structures from complex biophysical energy functions [Pantazes and Maranas, 2010, Lapidoth et al., 2015, Adolf-Bryfogle et al., 2018, Warszawski et al., 2019]. They are generally time-consuming and are prone to get trapped in local optima. Recently, various deep generative models have been developed to design antibodies [Saka et al., 2021, Akbar et al., 2022b, Jin et al., 2022]. Compared to conventional algorithms, deep generative models could directly capture higher-order interactions among amino acids on antibodies and antigens and generate antibodies more efficiently [Akbar et al., 2022a]. Recently, Jin et al. proposed a generative model for antibody structure-sequence co-design. Their model addresses two important computational challenges: First is how to model the intrinsic relation between CDR sequences and 3D structures, and second is how to model the distribution of CDRs conditional on the rest of the antibody sequence. However, there is still a large gap to fill before generative models become practical for antibody design.
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Figure 1: (a) Antibody-antigen complex structure and CDR structure. (b) The orientations of amino acids (represented by triangles) determine their side-chain orientations, which are key to inter-aminoacid interactions.
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Here, we identify another three challenges for antibody sequence-structure co-design. First, the model should be explicitly conditional on the 3D structures of the antigen and generate CDRs that fit the antigen structure in the 3D space. This is indispensable for the model to generalize to new antigens. Second, the interactions between amino acids are mainly determined by side-chains which are groups of atoms stretching out from the protein backbone (Figure 1b) [Liljas et al., 2016]. Therefore, the model should be able to consider both the position and orientation of amino acids. Third, in drug discovery, pharmacologists collect multiple initial antibodies either from humanized mice or patients [Presta, 1992, Barlow et al., 2018, Warszawski et al., 2019]. Therefore, instead of de novo design, the model should be applicable to another realistic scenario: optimizing a particular antibody to increase the binding affinity to the antigen. To the best of our knowledge, no previous machine learning model satisfies all of the above design principles.
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To address these challenges, we propose a diffusion-based generative model [Sohl-Dickstein et al., 2015, Song and Ermon, 2019, Ho et al., 2020, Yang et al., 2022] capable of jointly sampling antibody CDR sequences and structures. More importantly, the joint distribution of a CDR sequence and its structure is directly conditional on antigen structures. Given a protein complex consisting of an antigen and an antibody framework as input2 (as illustrated in Figure 2), we first initialize the CDR with an arbitrary sequence, positions, and orientations. The diffusion model first aggregates information from the antigen and the antibody framework. Then, it iteratively updates the amino acid type, position, and orientation of each amino acid on CDRs. In the last step, we reconstruct the CDR structure at the atom level using side-chain packing algorithms based on the predicted orientations [Alford et al., 2017]. From the perspective of model capability, one of the most important reasons for us to choose the diffusion-based model over other generative models such as generative adversarial networks [Goodfellow et al., 2014] and variational auto-encoders [Kingma and Welling, 2013] is that it generates CDR candidates iteratively in the sequence-structure space so that we can interfere and impose constraints on the sampling process to support a broader range of design tasks.
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Figure 2: The task in this work is to design CDRs for a given antigen structure and an antibody framework.
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We summarize our contributions as follows:
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• We propose the first deep learning models to perform antibody sequence-structure design by considering the 3D structures of the antigen. • In our model, we not only design protein sequences and coordinates but also side-chain orientations (represented as SO(3) element) of each amino acid. It is the first deep learning model that could achieve atomic-resolution antibody design and is equivariant to rotation and translation.
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• We show that our model can be applied to a wide range of antibody design tasks, including sequence-structure co-design, fix-backbone CDR design, and antibody optimization.
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# 2 Related Work
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Computational Antibody Design Conventional computational approaches are mainly based on sampling algorithms over hand-crafted and statistical energy functions and iteratively modify protein sequences and structures [Adolf-Bryfogle et al., 2018, Lapidoth et al., 2015, Warszawski et al., 2019, Pantazes and Maranas, 2010, Ruffolo et al., 2021]. These methods are inefficient and prone to getting stuck at local optima due to the rough energy landscape. In recent years, deep learning methods have shown potential in antibody design by using language models to generate protein sequences [Alley et al., 2019, Shin et al., 2021, Saka et al., 2021, Akbar et al., 2022b]. Although much more efficient, the sequence-based methods can only generate new antibodies based on previously observed antibodies but can hardly generate antibodies for specific antigen structures.
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Jin et al. proposed the first CDR sequence-structure co-design deep generative model which focuses on designing antibodies to neutralize SARS-CoV-2. It relies on an additional antigen-specific predictor to predict the neutralization of the designed antibodies, which is not generalizable to arbitrary antigens. In comparison to their model, we explicitly model the 3D structure of an antigen, opening the door to generalizing the prediction to unseen antigens with solved 3D structures. Another advantage of our model is that we consider not only backbone atom coordinates but also the orientation of amino acids. The orientation is critical to protein-protein interactions as most of the atoms interacting between antibodies and antigens are in the side-chain [Liljas et al., 2016] (as illustrated in Figure 1b). Lastly, the model proposed by Jin et al. is not equivariant by construction, which is fundamental in molecular modeling.
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Protein Structure Prediction Protein structure prediction algorithms take protein sequences and Multiple Sequence Alignments (MSAs) as input and translate them to 3D structures [Jumper et al., 2021, Baek et al., 2021, Yang et al., 2020]. Accurate protein structure prediction models predict not only the position of amino acids but also their orientation [Jumper et al., 2021, Yang et al., 2020]. The orientation of amino acids determines the direction in which its side chain stretches, so it is indispensable for reconstructing full-atom structures. AlphaFold2 [Jumper et al., 2021] predicts per-amino-acid orientations in an iterative fashion, similar to our proposed model. However, it is not generative, unable to efficiently sample diverse structures for protein design. Recently, based on prior protein structure prediction algorithms, methods for predicting antibody CDR structures have emerged [Ruffolo et al., 2022b,a], but they are not able to design CDR sequences.
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Diffusion-Based Generative Models Diffusion probabilistic models learn to generate data via denoising samples from a prior distribution [Sohl-Dickstein et al., 2015, Song and Ermon, 2019, Ho et al., 2020]. Recently, progress has been made in developing equivariant diffusion models for molecular 3D structures [Shi et al., 2021, Hoogeboom et al., 2022, Jing et al., 2022, Xu et al., 2022]. Atoms in a molecule do not have natural orientations, so the generation process differs from generating protein structures. Diffusion models have also been extended to non-Euclidean data, such as data in the Riemannian manifolds [Leach et al., 2022, De Bortoli et al., 2022]. These models are relevant to modeling orientations which are represented by elements in SO(3). In addition, diffusion models can also be used to generate discrete categorical data [Hoogeboom et al., 2021, Austin et al., 2021]. Concurrently with this work, various diffusion probabilistic models have been developed for proteins [Anand and Achim, 2022, Trippe et al., 2022, Wu et al., 2022].
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# 3 Methods
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This section is organized as follows: Section 3.1 introduces notations used throughout the paper and formally states the problem. Section 3.2 formulates the diffusion process for modeling antibodies. Section 3.3 introduces details about the neural network parameterization for the diffusion processes. Section 3.4 presents sampling algorithms for various antibody design tasks.
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# 3.1 Definitions and Notations
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An amino acid in a protein complex can be represented by its type, $\mathrm { C } _ { \alpha }$ atom coordinate, and the orientation, denoted as $s _ { i } \in \left\{ \tt A C D E F G H I K L M N P Q R S T V W Y \right\}$ , $\dot { \pmb { x } } _ { i } \in \mathbb { R } ^ { \bar { 3 } } , O _ { i } \in \mathrm { S O ( 3 ) }$ , respectively. Here $i = 1 \ldots N$ , and $N$ is the number of amino acids in the protein complex3.
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In this work, we assume the antigen structure and the antibody framework is given (Figure 2), and we focus on designing CDRs on the antibody framework. Assume the CDR to be generated has $m$ amino acids with index from $l + 1$ to $l + m$ . They are denoted as $\mathcal { R } = \{ ( \mathbf { s } _ { j } , \mathbf { x } _ { j } , \mathbf { O } _ { j } ) \mid \bar { j } = l + 1 , \ldots , l + m \}$ Formally, our goal is to jointly model the distribution of $\mathcal { R }$ given the structure of the antibody-antigen complex $\mathcal { C } = \bar { \{ } ( s _ { i } , \mathbf { x } _ { i } , \bar { \mathbf { O } } _ { i } ) | \dot { \ i } \in \{ 1 \ldots N \} \backslash \{ l + 1 , \ldots , l + m \} \}$ .
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# 3.2 Diffusion Processes
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A diffusion probabilistic model defines two Markov chains of diffusion processes. The forward diffusion process gradually adds noise to the data until the data distribution approximately reaches the prior distribution. The generative diffusion process starts from the prior distribution and iteratively transforms it to the desired distribution. Training the model relies on the forward diffusion process to simulate the noisy data. Let $\left( \mathbf { s } _ { j } ^ { t } , \mathbf { x } _ { j } ^ { t } , \mathbf { O } _ { j } ^ { t } \right)$ denote the intermediate state of amino acid $j$ at time step $t$ . $\mathcal { R } ^ { t } = \{ \mathbf { s } _ { j } ^ { t } , \mathbf { x } _ { j } ^ { t } , \mathbf { O } _ { j } ^ { t } \} _ { j = l + 1 } ^ { l + m }$ represents the sequence and structure sampled at step $t$ . $t = 0$ represents the state of real data (observed sequences and structures of CDRs) and $t = T$ represents samples from the prior distribution. Forward diffusion goes from $t = 0$ to $T$ , and generative diffusion proceeds in the opposite way. The diffusion processes for amino acid types $\mathrm { s } _ { j } ^ { t }$ , coordinates $\mathbf { x } _ { j } ^ { t }$ , and orientations $\mathbf { O } _ { j } ^ { t }$ are defined as follows:
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Multinomial Diffusion for Amino Acid Types The forward diffusion process for amino acid types is based on the multinomial distribution defined as follows [Hoogeboom et al., 2021]:
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$$
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q ( \mathbf { s } _ { j } ^ { t } | \mathbf { s } _ { j } ^ { t - 1 } ) = \mathrm { M u l t i n o m i a l } \left( ( 1 - \beta _ { \mathrm { t y p e } } ^ { t } ) \cdot \mathsf { o n e h o t } ( \mathbf { s } _ { j } ^ { t - 1 } ) + \beta _ { \mathrm { t y p e } } ^ { t } \cdot \frac { 1 } { 2 0 } \cdot \mathbf { 1 } \right) ,
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$$
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where onehot represents a function that converts amino acid type to a 20-dimensional one-hot vector and 1 is an all-one vector. $\beta _ { \mathrm { t y p e } } ^ { t }$ is the probability of resampling another amino acid over 20 types uniformly. When $t \to T$ , $\beta _ { \mathrm { t y p e } } ^ { t }$ is set close to 1 and the distribution is closer to the uniform distribution. The following probability density provides an efficient way to perturb $\mathbf { s } _ { j } ^ { 0 }$ for timestep $t$ during training [Hoogeboom et al., 2021]:
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$$
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q ( \mathrm { s } _ { j } ^ { t } | \mathrm { s } _ { j } ^ { 0 } ) = \mathrm { M u l t i n o m i a l } \left( \bar { \alpha } _ { \mathrm { t y p e } } ^ { t } \cdot \mathrm { o n e h o t } ( \mathrm { s } _ { j } ^ { 0 } ) + ( 1 - \bar { \alpha } _ { \mathrm { t y p e } } ^ { t } ) \cdot \frac { 1 } { 2 0 } \cdot \mathbf { 1 } \right) ,
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$$
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where $\begin{array} { r } { \bar { \alpha } _ { \mathrm { t y p e } } ^ { t } = \prod _ { \tau = 1 } ^ { t } ( 1 - \beta _ { \mathrm { t y p e } } ^ { \tau } ) } \end{array}$
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The generative diffusion process is defined as:
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$$
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p ( \mathbf { s } _ { j } ^ { t - 1 } | \mathcal { R } ^ { t } , \mathcal { C } ) = \mathrm { M u l t i n o m i a l } \left( F ( \mathcal { R } ^ { t } , \mathcal { C } ) [ j ] \right) ,
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$$
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where $F ( \cdot ) [ j ]$ is a neural network model taking the structure context (antigen and antibody framework) and the CDR state from the previous step as input and predicts the probability of the amino acid type for the $j$ -th amino acid on the CDR. Note that, different from the forward diffusion process, the generative diffusion process must rely on the structure context $\mathcal { C }$ and the CDR state of the previous step including positions and orientations. The main difference between these two processes is that the forward diffusion process adds noise to data so it is irrelevant to data or contexts but the generative diffusion process depends on the given condition and full observation of the previous step. The generative diffusion process needs to approximate the posterior $\boldsymbol { q } ( \mathrm { s } _ { j } ^ { t - 1 } | \mathrm { s } _ { j } ^ { t } , \mathrm { s } _ { j } ^ { 0 } )$ derived from Eq.1 and Eq.2 to denoise. Therefore, the objective of training the generative diffusion process for amino acid types is to minimize the expected KL divergence between Eq.3 and the posterior distribution:
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$$
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L _ { \mathrm { t y p e } } ^ { t } = \mathbb { E } _ { \mathcal { R } ^ { t } \sim p } \left[ \frac { 1 } { m } \sum _ { j } D _ { \mathrm { K L } } \left( q ( \mathbf { s } _ { j } ^ { t - 1 } | \mathbf { s } _ { j } ^ { t } , \mathbf { s } _ { j } ^ { 0 } ) \Big | \Big | p ( \mathbf { s } _ { j } ^ { t - 1 } | \mathcal { R } ^ { t } , \mathcal { C } ) \right) \right] .
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$$
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Figure 3: Illustration of the generative diffusion process. At each step, the network takes the current CDR state as input and parameterizes the distribution of the CDR’s sequences, positions, and orientations for the next step. In the end, full-atom structures are constructed by the side-chain packing algorithm.
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Diffusion for $\mathrm { C } _ { \alpha }$ Coordinates As the coordinate of an atom could be an arbitrary value, we scale and shift the coordinates of the whole structure such that the distribution of atom coordinates roughly match the standard normal distribution. We define the forward diffusion for the normalized $\mathrm { C } _ { \alpha }$ coordinate $\mathbf { x } _ { j }$ as follows:
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$$
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\begin{array} { r } { q \left( \mathbf { x } _ { j } ^ { t } \mid \mathbf { x } _ { j } ^ { t - 1 } \right) = \mathcal { N } \left( \mathbf { x } _ { j } ^ { t } \Big | \sqrt { 1 - \beta _ { \mathrm { p o s } } ^ { t } } \cdot \mathbf { x } _ { j } ^ { t - 1 } , \beta _ { \mathrm { p o s } } ^ { t } I \right) , } \\ { q \left( \mathbf { x } _ { j } ^ { t } \mid \mathbf { x } _ { j } ^ { 0 } \right) = \mathcal { N } \left( \mathbf { x } _ { j } ^ { t } \Big | \sqrt { \bar { \alpha } _ { \mathrm { p o s } } ^ { 0 } } \cdot \mathbf { x } _ { j } ^ { 0 } , ( 1 - \bar { \alpha } _ { \mathrm { p o s } } ^ { 0 } ) I \right) , } \end{array}
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$$
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where $\beta _ { \mathrm { p o s } } ^ { t }$ controls the rate of diffusion and its value increases from 0 to 1 as time step goes from 0 to $t$ , and $\begin{array} { r } { \bar { \alpha } _ { \mathrm { p o s } } ^ { t } = \prod _ { \tau = 1 } ^ { t } ( 1 - \beta _ { \mathrm { p o s } } ^ { \tau } ) } \end{array}$ . Using the reparameterization trick proposed by Ho et al., the generative diffusion process is defined as:
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$$
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\begin{array} { r l } & { p \left( \mathbf { x } _ { j } ^ { t - 1 } \middle | \mathcal { R } ^ { t } , \mathcal { C } \right) = \mathcal { N } \left( \mathbf { x } _ { j } ^ { t - 1 } \middle | \mu _ { p } \left( \mathcal { R } ^ { t } , \mathcal { C } \right) , \beta _ { \mathrm { p o s } } ^ { t } I \right) , } \\ & { ~ \mu _ { p } \left( \mathcal { R } ^ { t } , \mathcal { C } \right) = \frac { 1 } { \sqrt { \alpha _ { \mathrm { p o s } } ^ { t } } } \left( \mathbf { x } _ { j } ^ { t } - \frac { \beta _ { \mathrm { p o s } } ^ { t } } { \sqrt { 1 - \bar { \alpha } _ { \mathrm { p o s } } ^ { t } } } G ( \mathcal { R } ^ { t } , \mathcal { C } ) [ j ] \right) . } \end{array}
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$$
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Here, $G ( \cdot ) [ j ]$ is a neural network that predicts the standard Gaussian noise $\epsilon _ { j } \sim \mathcal { N } ( \mathbf { 0 } , I )$ added to $\sqrt { \bar { \alpha } _ { \mathrm { p o s } } ^ { 0 } } \mathbf { x } _ { j } ^ { 0 }$ (scaled coordinate of amino acid $j$ ) based on the reparameterization of Eq.6: $\mathbf { x } _ { j } ^ { t } = $ $\sqrt { \bar { \alpha } _ { \mathrm { p o s } } ^ { 0 } } \mathbf { x } _ { j } ^ { 0 } + \sqrt { 1 - \bar { \alpha } _ { \mathrm { p o s } } ^ { 0 } } \epsilon _ { j }$ . The objective function of training the generative process is the expected MSE between $G$ and $\epsilon _ { j }$ , which is simplified from aligning distribution $p$ to the posterior $q ( \mathbf { x } _ { j } ^ { t - 1 } \mid$ $\mathbf { x } _ { j } ^ { t } , \mathbf { x } _ { j } ^ { 0 } )$ [Ho et al., 2020]:
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$$
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L _ { \mathrm { p o s } } ^ { t } = \mathbb { E } \left[ \frac { 1 } { m } \sum _ { j } \left\| \epsilon _ { j } - G ( \mathcal { R } ^ { t } , \mathcal { C } ) \right\| ^ { 2 } \right] .
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$$
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SO(3) Denoising for Amino Acid Orientations We empirically formulate an iterative perturbdenoise scheme for learning and generating amino acid orientations represented by SO(3) elements [Leach et al., 2022]. Note that we do not use the term diffusion because the formulation does not strictly follow the framework of diffusion probabilistic models though the overall principle is the same. Similar to the typical diffusion process, the distribution of orientations perturbed for $t$ steps is defined as, according to Leach et al. [2022]:
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$$
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q \left( \mathbf { O } _ { j } ^ { t } \mid \mathbf { O } _ { j } ^ { 0 } \right) = \mathcal { Z } \mathcal { G } _ { \mathrm { S O ( 3 ) } } \left( \mathbf { O } _ { j } ^ { t } \middle | \mathrm { S c a l e R o t } \left( \sqrt { \bar { \alpha } _ { \mathrm { o r i } } ^ { t } } , \mathbf { O } _ { j } ^ { 0 } \right) , 1 - \bar { \alpha } _ { \mathrm { o r i } } ^ { t } \right) .
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$$
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$\mathcal { T G } _ { \mathrm { S O ( 3 ) } }$ denotes the isotropic Gaussian distribution on SO(3) parameterized by a mean rotation and a scalar variance [Leach et al., 2022, Matthies et al., 1970, Nikolayev and Savyolov, 1970]. ScaleRot modifies the rotation matrix by scaling its rotation angle with the rotation axis fixed [Gallier and Xu,
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2003]. $\begin{array} { r } { \bar { \alpha } _ { \mathrm { o r i } } ^ { t } = \prod _ { \tau = 1 } ^ { t } ( 1 - \beta _ { \mathrm { o r i } } ^ { \tau } ) } \end{array}$ , where $\beta _ { \mathrm { o r i } } ^ { t }$ is the variance increases with the step $t$ . The conditional distribution used for the generation process of orientations is defined as:
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$$
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p \left( \mathbf { O } _ { j } ^ { t - 1 } \Big | \mathcal { R } ^ { t } , \mathcal { C } \right) = \mathcal { Z } \mathcal { G } _ { \mathrm { S O ( 3 ) } } \left( \mathbf { O } _ { j } ^ { t - 1 } \Big | H ( \mathcal { R } ^ { t } , \mathcal { C } ) [ j ] , \beta _ { \mathrm { o r i } } ^ { t } \right) ,
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$$
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where $H ( \cdot ) [ j ]$ is a neural network that denoises the orientation and outputs the denoised orientation matrix of amino acid $j$ . Training the conditional distribution requires aligning the predicted orientation from $H ( \cdot )$ to the real orientation. Hence, we formulate the training object that minimizes the expected discrepancy measured by the inner product between the real and the predicted orientation matrices:
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$$
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L _ { \mathrm { o r i } } ^ { t } = \mathbb { E } \left[ \frac { 1 } { m } \sum _ { j } \left. \left( \mathbf { O } _ { j } ^ { 0 } \right) ^ { \intercal } \widehat { \mathbf { O } } _ { j } ^ { t - 1 } - I \right. _ { F } ^ { 2 } \right] ,
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$$
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where $\widehat { \mathbf { O } } _ { j } ^ { t - 1 } = H ( \cdot ) [ j ]$ is the predicted orientation for amino acid $j$ .
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The Overall Training Objective By summing Eq.4, 9, and 12 and taking the expectation w.r.t. $t$ , we obtain the final training objective function:
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$$
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L = \mathbb { E } _ { t \sim \mathrm { U n i f o r m } ( 1 . . . T ) } \left[ L _ { \mathrm { t y p e } } ^ { t } + L _ { \mathrm { p o s } } ^ { t } + L _ { \mathrm { o r i } } ^ { t } \right] .
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$$
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To train the model, we first sample a time step $t$ and then sample noisy states $\{ \mathbf { s } _ { j } ^ { t } , \mathbf { x } _ { j } ^ { t } , \mathbf { O } _ { j } ^ { t } \} _ { j = l + 1 } ^ { l + m } \sim p$ by adding noise to the training sample using the diffusion process defined by Eq.2, 6, and 10. We compute the loss using the noisy data and backpropagate the loss to update model parameters.
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# 3.3 Parameterization with Neural Networks
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In this section, we briefly introduce the neural network architectures used in different components of the diffusion process. The purpose of the networks is to encode the CDR state at a time step along with the context structure: $\{ \mathbf { s } _ { j } ^ { t } , \mathbf { x } _ { j } ^ { t } , \mathbf { O } _ { j } ^ { t } \} _ { j = l + 1 } ^ { l + m } \cup \{ s _ { i } ^ { t } , \mathbf { x } _ { i } ^ { t } , O _ { i } ^ { t } \} _ { i = \{ 1 \ldots N \} \setminus \{ l + 1 \ldots l + m \} }$ , and then denoises the CDR amino acid types $( F )$ , positions $( G )$ , and orientations $( H )$ .
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First, we adopt Multiple Layer Perceptrons (MLPs) to generate embeddings for single and pairs of amino acids. The single amino-acid embedding MLP creates vector $e _ { i }$ for amino acid $i$ , which encodes the information of amino acid types, torsional angles, and 3D coordinates of all the heavy atoms. The pairwise embedding MLP encodes the Euclidean distances and dihedral angles between amino acid $i$ and $j$ to feature vectors $z _ { i j }$ . We adopt IPA [Jumper et al., 2021], an orientation-aware roto-translation invariant network to transform $e _ { i }$ and $z _ { i j }$ into hidden representations $\boldsymbol { h } _ { i }$ , which aims to represent the amino acid itself and its environment. Next, the representations are fed to three different MLPs to denoise the amino acid types, 3D positions, and orientations of the CDR, respectively.
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In particular, the MLP for denoising amino acid types outputs a 20-dimensional vector representing the posterior probabilities. The MLP for denoising $\mathrm { C } _ { \alpha }$ coordinates predicts the scaled change of the coordinate in terms of the current orientation of the amino acid. As the coordinate deviation is calculated in the local frame, we left-multiply it by the orientation matrix and transform it back to the global frame. Formally, this can be expressed as $\hat { \epsilon } _ { j } = \mathbf { O } _ { j } ^ { t } \mathrm { M L P } _ { G } \left( h _ { j } \right)$ . Predicting coordinate deviations in the local frame and projecting it to the global frame ensures the equivariance of the prediction, as when the entire 3D structure rotates by a particular angle, the coordinate deviations also rotate by the same angle. The MLP for denoising orientations first predicts a $s o ( 3 )$ vector [Gallier and Xu, 2003]. The vector is converted to a rotation matrix $M _ { j } \in \mathrm { S O } ( 3 )$ right-multiplied to the orientation to produce a new mean orientation for the next generative step: $\widehat { \mathbf { O } } _ { j } ^ { t - 1 } \gets \mathbf { O } _ { j } ^ { t } M _ { j }$ . The proposed networks are equivariant to the rotation and translation of the overall structure:
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Proposition 1. For any proper rotation matrix $R \in \mathrm { S O } ( 3 )$ and any $3 D$ vector $\pmb { r } \in \mathbb { R } ^ { 3 }$ (rigid transformation $( R , r ) \in \mathrm { S E } ( 3 )$ ), $F$ , $G$ and $H$ satisfy the following equivariance properties:
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$$
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\begin{array} { r l } & { F ( R \mathcal { R } ^ { t } + r , R \mathcal { C } + r ) = F ( \mathcal { R } ^ { t } , \mathcal { C } ) , } \\ & { G ( R \mathcal { R } ^ { t } + r , R \mathcal { C } + r ) = R G ( \mathcal { R } ^ { t } , \mathcal { C } ) , } \\ & { H ( R \mathcal { R } ^ { t } + r , R \mathcal { C } + r ) = R H ( \mathcal { R } ^ { t } , \mathcal { C } ) , } \end{array}
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$$
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where $R \mathcal { R } ^ { t } { + } r : = \{ \mathrm { s } _ { j } ^ { t } , \mathrm { \mathbf { x } } _ { j } ^ { t } { + } r , R \mathbf { O } _ { j } ^ { t } \} _ { j = l + 1 } ^ { l { + } m }$ and $R { \mathcal { C } } + r : = \{ s _ { i } , x _ { i } + r , R O _ { i } \} _ { i \in \{ 1 . . . N \} \setminus \{ l + 1 , . . . , l + m \} }$ denote the rotated and translated structure. Note that $F$ , $G$ , and $H$ are not single MLPs. Each of them includes the shared encoder and a specific MLP.
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# 3.4 Sampling Algorithms
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The sampling algorithm first samples amino acid types from the uniform distribution over 20 classes: $s _ { j } ^ { T } \sim \bar { \mathrm { U n i f o r m } ( 2 0 ) }$ , $\mathrm { C } _ { \alpha }$ positions from the standard normal distribution: $\mathbf { x } _ { j } ^ { T } \sim \mathcal { N } ( \mathbf { 0 } , I _ { 3 } )$ , and orientations from the uniform distribution over SO(3): $\mathbf { O } _ { j } ^ { T } \sim \mathrm { U n i f o r m } ( \bar { \mathrm { S O } } ( 3 ) )$ . Note that we normalize the coordinates of the structure in the same way as training such that $\mathrm { C } _ { \alpha }$ positions in the CDR roughly follow the standard normal distribution. Next, we iteratively sample sequences and structures from the generative diffusion kernel by denoising amino acid types, $\mathrm { C } _ { \alpha }$ coordinates, and orientations until $t = 0$ . To build a full atom 3D structure, we construct the coordinates of N, $\mathrm { C } _ { \alpha }$ , C, O, and side-chain $\mathrm { C } _ { \beta }$ (except glycine that does not have $\mathrm { C } _ { \beta }$ ) according to their ideal local coordinates relative to the $\mathrm { C } _ { \alpha }$ position and orientation of each amino acid [Engh and Huber, 2012]. Based on the five reconstructed atoms, the rest of the side-chain atoms are constructed using the side-chain packing function implemented in Rosetta [Alford et al., 2017]. In the end, we adopt the AMBER99 force field [Lindorff-Larsen et al., 2010] in OpenMM [Eastman et al., 2017] to refine the full atom structure.
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In addition to the joint design of sequences and structures, we can constrain partial states for other design tasks. For example, by fixing the backbone structure (positions and orientations) and sampling only sequences, we can do fix-backbone sequence design. Another usage is to optimize an existing antibody. Specifically, we first add noise to the existing antibody for $t$ steps and denoise the perturbed antibody sequence starting from the $t$ -th step of the generative diffusion process.
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# 4 Experiments
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We present the application of our model, named DiffAb4, in three antibody design tasks: sequencestructure co-design (Section 4.1), antibody sequence design based on antibody backbones (Section 4.2), and antibody optimization (Section 4.3). In Section 4.4, we show how to use our model without known antibody frameworks bound to the antigen.
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# 4.1 Sequence-Structure Co-design
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The dataset for training the model is derived from the SAbDab database[Dunbar et al., 2014]. We first remove structures whose resolution is worse than $4 \mathring \mathrm { A }$ and discard antibodies targeting non-protein antigens. We cluster antibodies in the database according to CDR-H3 sequences at $50 \%$ sequence identity. We manually select five clusters as the test set, containing 19 antibody-antigen complexes in total. The test set includes antigens from several well-known pathogens including SARS-CoV-2, MERS, influenza, and so on. Structures in the remaining clusters are used for training.
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To evaluate the performance, we remove the original CDR from the antibody-antigen complex in the test set and sample both the sequence and structure of the removed region. We set the length of the CDR to be identical to the length of the original CDR for simplicity. In practice, one can enumerate different lengths of CDRs. We compare our model to RosettaAntibodyDesign (RAbD) [Adolf-Bryfogle et al., 2018], an antibody design software based on Rosetta energy functions. For each model, we draw 100 samples for each CDR. Both the original structures and designed structures from different methods are refined by OpenMM and Rosetta.
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We use the following metrics to evaluate designed antibodies: (1) IMP: is the percentage of designed CDRs with lower (better) binding energy $( \Delta G )$ than the original CDR. The binding energy is calculated by InterfaceAnalyzer in the Rosetta software package [Alford et al., 2017]. (2) RMSD: is the $\mathrm { C } _ { \alpha }$ root-mean-square deviation (RMSD) between the generated structure and the original structure with only antibody frameworks aligned. (3) AAR: is the amino acid recovery rate measured by the sequence identity between the reference CDR sequences and the generated sequences [AdolfBryfogle et al., 2018]. Note that different from Jin et al. [2022], we do not use neutralization prediction models because they are sequence-based and are specified to a limited class of antigens, which deviates from our goal of developing a general antibody design model.
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Table 1 shows that our model (DiffAb) recovers CDR sequences more accurately than RAbD (higher AAR). The RMSDs of CDRs generated by DiffAb are higher in CDR-H3, which indicates that our generated samples are more diverse structurally. The IMP score of DiffAb is on par with RAbD in
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<table><tr><td>CDR</td><td>Method</td><td>AAR</td><td>RMSD</td><td>IMP</td></tr><tr><td rowspan="2">H1</td><td>RAbD</td><td>22.85%</td><td>2.261A</td><td rowspan="2">43.88% 53.63%</td></tr><tr><td>DiffAb</td><td>65.75%</td><td>1.188A</td></tr><tr><td rowspan="2">H2</td><td>RAbD</td><td>25.50%</td><td>1.641A</td><td>53.50%</td></tr><tr><td>DiffAb</td><td>49.31%</td><td>1.076A</td><td>29.84%</td></tr><tr><td rowspan="2">H3</td><td>RAbD</td><td>22.14%</td><td>2.900A</td><td>23.25%</td></tr><tr><td>DiffAb</td><td>26.78%</td><td>3.597A</td><td>23.63%</td></tr></table>
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Table 1: Evaluation of the generated antibody CDRs (sequence-structure co-design) by RAbD and our DiffAb model.
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<table><tr><td>CDR</td><td>Method</td><td>AAR</td><td>RMSD</td><td>IMP</td></tr><tr><td rowspan="2">L1</td><td>RAbD</td><td>34.27%</td><td>1.204A</td><td rowspan="2">46.81% 45.58%</td></tr><tr><td>DiffAb</td><td>56.67%</td><td>1.388A</td></tr><tr><td rowspan="2">L2</td><td>RAbD</td><td>26.30%</td><td>1.767A</td><td rowspan="2">56.94% 49.95%</td></tr><tr><td>DiffAb</td><td>59.32%</td><td>1.373A</td></tr><tr><td rowspan="2">L3</td><td>RAbD</td><td>20.73%</td><td>1.624A</td><td>55.63%</td></tr><tr><td>DiffAb</td><td>46.47%</td><td>1.627A</td><td>47.32%</td></tr></table>
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Figure 4: Examples of CDR-H3 designed by the sequence-structure co-design method and the distribution of their interaction energy and RMSD. The antigen-antibody template is derived from PDB:7chf, where the antigen is SARS-CoV-2 RBD. Sample 1 has better complementarity to the antigen while Sample 3 fits the antigen worse. This could explain their difference in the binding energy $( \Delta G )$ .
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CDR-H3, and lower in other CDRs. However, it should be noted that RAbD optimizes the Rosetta energy function, which is also used for evaluation. Our model achieves reasonably good binding energy without explicit supervision signal from Rosetta energy functions. Figure 4 presents three generated examples of CDR-H3 targeting SARS-CoV-2 RBD. Sample 1 has the lowest binding energy and it can be observed that it has better complementarity to the antigen. The binding energy of Sample 3 is higher than the original one and visually, the shape of the CDR does not fit the antigen well.
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# 4.2 Fix-Backbone Sequence Design and Structure Prediction
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In this setting, the backbone structure of CDRs is given and we only need to design the CDR sequence, which transforms the task into a constrained sampling problem. Fix-backbone design is a common setting in the area of protein design [Ingraham et al., 2019, Hsu et al., 2022, Anishchenko et al., 2021, Strokach et al., 2020, Tischer et al., 2020]. For this task, we consider FixBB, a Rosetta-based sequence design software given CDR backbone structure, as the baseline. We use the AAR metric introduced in Section 4.1 to evaluate the designed CDRs.
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As shown in Table 2, our model achieves better AAR in all the CDRs. This shows that our model is also powerful in modeling the conditional probability of sequences given backbone structures. Admittedly, the training data is clustered only by CDR-H3 sequences, so the model might have seen other CDRs in the test set during training, leading to even higher AAR. However, we believe this is not an issue as CDRs other than H3 are generally conserved and contribute less to the specificity $\mathrm { X u }$ and Davis [2000].
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Our model can predict CDR structures by fixing the sequence. Table 3 shows that it accurately predicts the structure of CDR H1, H2, L1, L2, and L3 $\mathrm { R i M S D } \le 1 . 5 \mathring \mathrm { A } ;$ ). The accuracy of CDR-H3 prediction is lower due to the high variability. Figure 5a separately shows the accuracy of different CDR-H3 lengths. The prediction is generally more accurate for shorter ones. When the CDR-H3 contains more than 10 amino acids, the prediction accuracy drops.
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Table 2: Comparison of FixBB and DiffAb in terms of amino acid recovery (AAR) in the fix-backbone CDR design task. DiffAb achieves higher AAR. The AAR of DiffAb on CDR-H3 is lower than other CDRs since H3 is much more versatile.
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<table><tr><td>CDR</td><td>Method</td><td>AAR</td><td>CDR</td><td>Method</td><td>AAR</td></tr><tr><td>H1</td><td>FixBB DiffAb</td><td>37.14% 87.83%</td><td>L1</td><td>FixBB DiffAb</td><td>33.80% 86.63%</td></tr><tr><td>H2</td><td>FixBB DiffAb</td><td>43.08% 79.70%</td><td>L2</td><td>FixBB DiffAb</td><td>28.54% 88.91%</td></tr><tr><td>H3</td><td>FixBB DiffAb</td><td>30.74% 59.48%</td><td>L3</td><td>FixBB DiffAb</td><td>17.92% 78.69%</td></tr></table>
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Table 3: The accuracy of CDR structures predicted by DiffAb in RMSD.
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<table><tr><td>CDR</td><td>RMSD</td></tr><tr><td>H1</td><td>0.901A</td></tr><tr><td>H2</td><td>1.044A</td></tr><tr><td>H3</td><td>3.246A</td></tr><tr><td>L1</td><td>1.365A</td></tr><tr><td>L2</td><td>1.321A</td></tr><tr><td></td><td></td></tr><tr><td>L3</td><td>1.492A</td></tr></table>
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Figure 5: (a) RMSD of predicted CDR-H3 structures grouped by lengths. (b) The antibody optimization algorithm first perturbs the initial CDR for $t$ steps using the forward diffusion process and then denoises it by the backward diffusion process into the optimized CDR. (c) IMP, RMSD, and SeqID of the CDRs optimized with different numbers of steps. Dashed lines represent the results of de novo design. When $t = 4$ , the optimized CDRs reach an IMP score close to de novo CDRs but remain structurally similar to the original one.
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# 4.3 Antibody Optimization
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We use our model to optimize existing antibodies which is another common pharmaceutical application. To optimize an antibody, we first perturb the CDR sequence and structure for $t$ steps using the forward diffusion process. Then, we denoise the sequences starting from the $( T - t )$ -th step $t$ steps remaining) of the generative diffusion process and obtain a set of optimized antibodies. This process is illustrated in Figure 5b. We optimize CDR-H3 of the antibodies in the test set with various $t$ values. For each antibody and $t$ , we perturb the CDR independently 100 times and collect 100 optimized CDRs different from the original CDR. We report the percentage of optimized antibodies with improved binding energy (IMP), RMSD, and sequence identity (SeqID) of the optimized CDR in comparison to the original antibody. We also compare the optimized antibodies with the de novo ( $t = T = 1 0 0$ ) designed antibodies introduced in Section 4.1. As shown in Table 4 and Figure 5c, the optimization method could produce antibodies with improved binding energy measured by the Rosetta energy function. In contrast to redesigning CDRs, optimization improves binding energy while keeping the optimized CDR similar to the original one, which is desired in many practical applications.
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Table 4: Evaluation of optimized CDR-H3s with different numbers of optimization steps. In contrast to redesigning the CDR, the optimization method can improve binding energy while keeping the optimized CDR similar to the original one. Figure 5c shows the line plot of the results.
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<table><tr><td>t</td><td>IMP</td><td>RMSD</td><td>SeqID</td></tr><tr><td>1</td><td>18.52%</td><td>1.194A</td><td>92.42%</td></tr><tr><td>2</td><td>16.67%</td><td>1.252A</td><td>91.61%</td></tr><tr><td>4</td><td>23.29%</td><td>1.290A</td><td>91.16%</td></tr><tr><td>8</td><td>22.01%</td><td>1.447A</td><td>88.78%</td></tr><tr><td>16</td><td>18.02%</td><td>1.759A</td><td>78.43%</td></tr><tr><td>32</td><td>16.43%</td><td>2.623A</td><td>40.58%</td></tr><tr><td>64</td><td>15.47%</td><td>3.380A</td><td>27.30%</td></tr><tr><td>T</td><td>23.63%</td><td>3.597A</td><td>26.78%</td></tr></table>
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Figure 6: A human antibody framework docked to SARS-CoV-2 Omicron RBD using HDOCK. CDR-H3s are designed based on the docking structure.
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# 4.4 Design Without Bound Antibody Frameworks
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In the last experiment, we consider designing antibodies without a known binding pose against the antigen, a more general and challenging setting. We show that this challenging task could be achieved with docking software. Specifically, we create an antibody template from an existing antibody structure by removing its CDR-H3. This is because CDR-H3 is the most variable one and accounts for most of the specificity, while other CDRs are much more conserved [Xu and Davis, 2000]. Next, we use HDOCK [Yan et al., 2017] to dock the antibody template to the target antigen to produce the antibody-antigen complex. In this way, the problem reduces to the original problem so we can adapt our model to design the CDR-H3 sequence and structure and re-design other CDRs. We demonstrate using this method to design antibodies for the SARS-CoV-2 Omicron RDB structure (PDB: 7wvn, residue A322-A590, the structure is not bound to any antibodies). The antibody template is derived from a human antibody against influenza (PDB: 3qhf). Figure 6 shows the docking structure, five designed CDR-H3s, and the binding energy distribution. It is hard to confidently conclude that the generated antibodies are effective without a reference antibody. However, according to the binding energy distribution, we can still say the generated antibodies are at least reasonable.
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# 5 Conclusions and Limitations
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In this work, we propose a diffusion-based generative model for antibody design. Our model is capable of a wide range of antibody design tasks and can achieve competitive performance. One main limitation of this work is that it relies on an antibody framework bound to the target antigen. Therefore, we leave it for future work to design an effective model for generating antibodies without bound structures. Another limitation is that it remains unclear whether the generated antibodies can be produced in the wet lab and actually binds to the target. More efforts are needed to design a biologically effective antibody.
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# Acknowledgments and Disclosure of Funding
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Supported by National Key R&D Program of China No. 2021YFF1201600.
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parse/dev/jSorGn2Tjg/jSorGn2Tjg_content_list.json
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| 1 |
+
[
|
| 2 |
+
{
|
| 3 |
+
"type": "text",
|
| 4 |
+
"text": "Antigen-Specific Antibody Design and Optimization with Diffusion-Based Generative Models for Protein Structures ",
|
| 5 |
+
"text_level": 1,
|
| 6 |
+
"bbox": [
|
| 7 |
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186,
|
| 8 |
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122,
|
| 9 |
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813,
|
| 10 |
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196
|
| 11 |
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],
|
| 12 |
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"page_idx": 0
|
| 13 |
+
},
|
| 14 |
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{
|
| 15 |
+
"type": "text",
|
| 16 |
+
"text": "Shitong $\\mathbf { L u o ^ { 1 * } }$ , Yufeng $\\mathbf { S u ^ { 2 * } }$ , Xingang Peng3, Sheng Wang4, Jian Peng1,2, Jianzhu Ma1,5 ",
|
| 17 |
+
"bbox": [
|
| 18 |
+
187,
|
| 19 |
+
246,
|
| 20 |
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803,
|
| 21 |
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262
|
| 22 |
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],
|
| 23 |
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"page_idx": 0
|
| 24 |
+
},
|
| 25 |
+
{
|
| 26 |
+
"type": "text",
|
| 27 |
+
"text": "1 Helixon Research 2 University of Illinois Urbana-Champaign 3 School of Intelligence Science and Technology, Peking University 4 Paul G. Allen School of Computer Science, University of Washington 5 Institute for AI Industry Research, Tsinghua University luost@helixon.com,luost26@gmail.com swang@cs.washington.edu,jianpeng@illinois.edu,majianzhu@tsinghua.edu.cn ",
|
| 28 |
+
"bbox": [
|
| 29 |
+
192,
|
| 30 |
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262,
|
| 31 |
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803,
|
| 32 |
+
361
|
| 33 |
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],
|
| 34 |
+
"page_idx": 0
|
| 35 |
+
},
|
| 36 |
+
{
|
| 37 |
+
"type": "text",
|
| 38 |
+
"text": "Abstract ",
|
| 39 |
+
"text_level": 1,
|
| 40 |
+
"bbox": [
|
| 41 |
+
462,
|
| 42 |
+
396,
|
| 43 |
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535,
|
| 44 |
+
412
|
| 45 |
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],
|
| 46 |
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"page_idx": 0
|
| 47 |
+
},
|
| 48 |
+
{
|
| 49 |
+
"type": "text",
|
| 50 |
+
"text": "Antibodies are immune system proteins that protect the host by binding to specific antigens such as viruses and bacteria. The binding between antibodies and antigens is mainly determined by the complementarity-determining regions (CDR) of the antibodies. In this work, we develop a deep generative model that jointly models sequences and structures of CDRs based on diffusion probabilistic models and equivariant neural networks. Our method is the first deep learning-based method that generates antibodies explicitly targeting specific antigen structures and is one of the earliest diffusion probabilistic models for protein structures. The model is a “Swiss Army Knife” capable of sequence-structure co-design, sequence design for given backbone structures, and antibody optimization. We conduct extensive experiments to evaluate the quality of both sequences and structures of designed antibodies. We find that our model could yield competitive results in binding affinity measured by biophysical energy functions and other protein design metrics. ",
|
| 51 |
+
"bbox": [
|
| 52 |
+
233,
|
| 53 |
+
428,
|
| 54 |
+
766,
|
| 55 |
+
608
|
| 56 |
+
],
|
| 57 |
+
"page_idx": 0
|
| 58 |
+
},
|
| 59 |
+
{
|
| 60 |
+
"type": "text",
|
| 61 |
+
"text": "1 Introduction ",
|
| 62 |
+
"text_level": 1,
|
| 63 |
+
"bbox": [
|
| 64 |
+
174,
|
| 65 |
+
632,
|
| 66 |
+
310,
|
| 67 |
+
650
|
| 68 |
+
],
|
| 69 |
+
"page_idx": 0
|
| 70 |
+
},
|
| 71 |
+
{
|
| 72 |
+
"type": "text",
|
| 73 |
+
"text": "Antibodies are important immune proteins generated during an immune response to recognize and neutralize the pathogen [Janeway et al., 2001]. As illustrated in Figure 1a, an antibody contains two heavy chains and two light chains, and their overall structure is similar. Six variable regions determine the specificity of an antibody to the antigens. They are called the Complementarity Determining Regions (CDRs), denoted as H1, H2, H3, L1, L2, and L3. Therefore, the most important step for developing effective therapeutic antibodies is to design CDRs that bind to the specific antigen [Presta, 1992, Akbar et al., 2022a]. ",
|
| 74 |
+
"bbox": [
|
| 75 |
+
174,
|
| 76 |
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|
| 77 |
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825,
|
| 78 |
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761
|
| 79 |
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],
|
| 80 |
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"page_idx": 0
|
| 81 |
+
},
|
| 82 |
+
{
|
| 83 |
+
"type": "text",
|
| 84 |
+
"text": "Similar to other protein design tasks, the search space of CDRs is vast. A CDR sequence with $L$ amino acids has up to $\\mathrm { 2 0 } ^ { L }$ possible protein sequences. It is not feasible to test all the possible sequences using experimental approaches, so computational methods are needed. Traditional computational approaches rely on sampling protein sequences and structures from complex biophysical energy functions [Pantazes and Maranas, 2010, Lapidoth et al., 2015, Adolf-Bryfogle et al., 2018, Warszawski et al., 2019]. They are generally time-consuming and are prone to get trapped in local optima. Recently, various deep generative models have been developed to design antibodies [Saka et al., 2021, Akbar et al., 2022b, Jin et al., 2022]. Compared to conventional algorithms, deep generative models could directly capture higher-order interactions among amino acids on antibodies and antigens and generate antibodies more efficiently [Akbar et al., 2022a]. Recently, Jin et al. proposed a generative model for antibody structure-sequence co-design. Their model addresses two important computational challenges: First is how to model the intrinsic relation between CDR sequences and 3D structures, and second is how to model the distribution of CDRs conditional on the rest of the antibody sequence. However, there is still a large gap to fill before generative models become practical for antibody design. ",
|
| 85 |
+
"bbox": [
|
| 86 |
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174,
|
| 87 |
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|
| 88 |
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825,
|
| 89 |
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878
|
| 90 |
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],
|
| 91 |
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"page_idx": 0
|
| 92 |
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},
|
| 93 |
+
{
|
| 94 |
+
"type": "image",
|
| 95 |
+
"img_path": "images/b13068984583b136a9a4b5a96fdef9461462ae5998653b129d3d19f3058c2a91.jpg",
|
| 96 |
+
"image_caption": [
|
| 97 |
+
"Figure 1: (a) Antibody-antigen complex structure and CDR structure. (b) The orientations of amino acids (represented by triangles) determine their side-chain orientations, which are key to inter-aminoacid interactions. "
|
| 98 |
+
],
|
| 99 |
+
"image_footnote": [],
|
| 100 |
+
"bbox": [
|
| 101 |
+
220,
|
| 102 |
+
88,
|
| 103 |
+
777,
|
| 104 |
+
202
|
| 105 |
+
],
|
| 106 |
+
"page_idx": 1
|
| 107 |
+
},
|
| 108 |
+
{
|
| 109 |
+
"type": "text",
|
| 110 |
+
"text": "",
|
| 111 |
+
"bbox": [
|
| 112 |
+
173,
|
| 113 |
+
256,
|
| 114 |
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826,
|
| 115 |
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353
|
| 116 |
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],
|
| 117 |
+
"page_idx": 1
|
| 118 |
+
},
|
| 119 |
+
{
|
| 120 |
+
"type": "text",
|
| 121 |
+
"text": "Here, we identify another three challenges for antibody sequence-structure co-design. First, the model should be explicitly conditional on the 3D structures of the antigen and generate CDRs that fit the antigen structure in the 3D space. This is indispensable for the model to generalize to new antigens. Second, the interactions between amino acids are mainly determined by side-chains which are groups of atoms stretching out from the protein backbone (Figure 1b) [Liljas et al., 2016]. Therefore, the model should be able to consider both the position and orientation of amino acids. Third, in drug discovery, pharmacologists collect multiple initial antibodies either from humanized mice or patients [Presta, 1992, Barlow et al., 2018, Warszawski et al., 2019]. Therefore, instead of de novo design, the model should be applicable to another realistic scenario: optimizing a particular antibody to increase the binding affinity to the antigen. To the best of our knowledge, no previous machine learning model satisfies all of the above design principles. ",
|
| 122 |
+
"bbox": [
|
| 123 |
+
173,
|
| 124 |
+
359,
|
| 125 |
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825,
|
| 126 |
+
511
|
| 127 |
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],
|
| 128 |
+
"page_idx": 1
|
| 129 |
+
},
|
| 130 |
+
{
|
| 131 |
+
"type": "text",
|
| 132 |
+
"text": "To address these challenges, we propose a diffusion-based generative model [Sohl-Dickstein et al., 2015, Song and Ermon, 2019, Ho et al., 2020, Yang et al., 2022] capable of jointly sampling antibody CDR sequences and structures. More importantly, the joint distribution of a CDR sequence and its structure is directly conditional on antigen structures. Given a protein complex consisting of an antigen and an antibody framework as input2 (as illustrated in Figure 2), we first initialize the CDR with an arbitrary sequence, positions, and orientations. The diffusion model first aggregates information from the antigen and the antibody framework. Then, it iteratively updates the amino acid type, position, and orientation of each amino acid on CDRs. In the last step, we reconstruct the CDR structure at the atom level using side-chain packing algorithms based on the predicted orientations [Alford et al., 2017]. From the perspective of model capability, one of the most important reasons for us to choose the diffusion-based model over other generative models such as generative adversarial networks [Goodfellow et al., 2014] and variational auto-encoders [Kingma and Welling, 2013] is that it generates CDR candidates iteratively in the sequence-structure space so that we can interfere and impose constraints on the sampling process to support a broader range of design tasks. ",
|
| 133 |
+
"bbox": [
|
| 134 |
+
174,
|
| 135 |
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|
| 136 |
+
549,
|
| 137 |
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683
|
| 138 |
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],
|
| 139 |
+
"page_idx": 1
|
| 140 |
+
},
|
| 141 |
+
{
|
| 142 |
+
"type": "image",
|
| 143 |
+
"img_path": "images/bb8be12f301b7bc8947974b8f56749b9807a630d717934dc48f1a85c6efbf65e.jpg",
|
| 144 |
+
"image_caption": [
|
| 145 |
+
"Figure 2: The task in this work is to design CDRs for a given antigen structure and an antibody framework. "
|
| 146 |
+
],
|
| 147 |
+
"image_footnote": [],
|
| 148 |
+
"bbox": [
|
| 149 |
+
566,
|
| 150 |
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522,
|
| 151 |
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816,
|
| 152 |
+
618
|
| 153 |
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],
|
| 154 |
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"page_idx": 1
|
| 155 |
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},
|
| 156 |
+
{
|
| 157 |
+
"type": "text",
|
| 158 |
+
"text": "",
|
| 159 |
+
"bbox": [
|
| 160 |
+
174,
|
| 161 |
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684,
|
| 162 |
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826,
|
| 163 |
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780
|
| 164 |
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],
|
| 165 |
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"page_idx": 1
|
| 166 |
+
},
|
| 167 |
+
{
|
| 168 |
+
"type": "text",
|
| 169 |
+
"text": "We summarize our contributions as follows: ",
|
| 170 |
+
"bbox": [
|
| 171 |
+
176,
|
| 172 |
+
786,
|
| 173 |
+
462,
|
| 174 |
+
800
|
| 175 |
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],
|
| 176 |
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"page_idx": 1
|
| 177 |
+
},
|
| 178 |
+
{
|
| 179 |
+
"type": "text",
|
| 180 |
+
"text": "• We propose the first deep learning models to perform antibody sequence-structure design by considering the 3D structures of the antigen. • In our model, we not only design protein sequences and coordinates but also side-chain orientations (represented as SO(3) element) of each amino acid. It is the first deep learning model that could achieve atomic-resolution antibody design and is equivariant to rotation and translation. ",
|
| 181 |
+
"bbox": [
|
| 182 |
+
217,
|
| 183 |
+
813,
|
| 184 |
+
825,
|
| 185 |
+
869
|
| 186 |
+
],
|
| 187 |
+
"page_idx": 1
|
| 188 |
+
},
|
| 189 |
+
{
|
| 190 |
+
"type": "text",
|
| 191 |
+
"text": "",
|
| 192 |
+
"bbox": [
|
| 193 |
+
225,
|
| 194 |
+
92,
|
| 195 |
+
823,
|
| 196 |
+
118
|
| 197 |
+
],
|
| 198 |
+
"page_idx": 2
|
| 199 |
+
},
|
| 200 |
+
{
|
| 201 |
+
"type": "text",
|
| 202 |
+
"text": "• We show that our model can be applied to a wide range of antibody design tasks, including sequence-structure co-design, fix-backbone CDR design, and antibody optimization. ",
|
| 203 |
+
"bbox": [
|
| 204 |
+
220,
|
| 205 |
+
119,
|
| 206 |
+
823,
|
| 207 |
+
147
|
| 208 |
+
],
|
| 209 |
+
"page_idx": 2
|
| 210 |
+
},
|
| 211 |
+
{
|
| 212 |
+
"type": "text",
|
| 213 |
+
"text": "2 Related Work ",
|
| 214 |
+
"text_level": 1,
|
| 215 |
+
"bbox": [
|
| 216 |
+
174,
|
| 217 |
+
176,
|
| 218 |
+
321,
|
| 219 |
+
194
|
| 220 |
+
],
|
| 221 |
+
"page_idx": 2
|
| 222 |
+
},
|
| 223 |
+
{
|
| 224 |
+
"type": "text",
|
| 225 |
+
"text": "Computational Antibody Design Conventional computational approaches are mainly based on sampling algorithms over hand-crafted and statistical energy functions and iteratively modify protein sequences and structures [Adolf-Bryfogle et al., 2018, Lapidoth et al., 2015, Warszawski et al., 2019, Pantazes and Maranas, 2010, Ruffolo et al., 2021]. These methods are inefficient and prone to getting stuck at local optima due to the rough energy landscape. In recent years, deep learning methods have shown potential in antibody design by using language models to generate protein sequences [Alley et al., 2019, Shin et al., 2021, Saka et al., 2021, Akbar et al., 2022b]. Although much more efficient, the sequence-based methods can only generate new antibodies based on previously observed antibodies but can hardly generate antibodies for specific antigen structures. ",
|
| 226 |
+
"bbox": [
|
| 227 |
+
174,
|
| 228 |
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202,
|
| 229 |
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825,
|
| 230 |
+
327
|
| 231 |
+
],
|
| 232 |
+
"page_idx": 2
|
| 233 |
+
},
|
| 234 |
+
{
|
| 235 |
+
"type": "text",
|
| 236 |
+
"text": "Jin et al. proposed the first CDR sequence-structure co-design deep generative model which focuses on designing antibodies to neutralize SARS-CoV-2. It relies on an additional antigen-specific predictor to predict the neutralization of the designed antibodies, which is not generalizable to arbitrary antigens. In comparison to their model, we explicitly model the 3D structure of an antigen, opening the door to generalizing the prediction to unseen antigens with solved 3D structures. Another advantage of our model is that we consider not only backbone atom coordinates but also the orientation of amino acids. The orientation is critical to protein-protein interactions as most of the atoms interacting between antibodies and antigens are in the side-chain [Liljas et al., 2016] (as illustrated in Figure 1b). Lastly, the model proposed by Jin et al. is not equivariant by construction, which is fundamental in molecular modeling. ",
|
| 237 |
+
"bbox": [
|
| 238 |
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173,
|
| 239 |
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333,
|
| 240 |
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|
| 241 |
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472
|
| 242 |
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],
|
| 243 |
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"page_idx": 2
|
| 244 |
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| 245 |
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{
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| 246 |
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"type": "text",
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| 247 |
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"text": "Protein Structure Prediction Protein structure prediction algorithms take protein sequences and Multiple Sequence Alignments (MSAs) as input and translate them to 3D structures [Jumper et al., 2021, Baek et al., 2021, Yang et al., 2020]. Accurate protein structure prediction models predict not only the position of amino acids but also their orientation [Jumper et al., 2021, Yang et al., 2020]. The orientation of amino acids determines the direction in which its side chain stretches, so it is indispensable for reconstructing full-atom structures. AlphaFold2 [Jumper et al., 2021] predicts per-amino-acid orientations in an iterative fashion, similar to our proposed model. However, it is not generative, unable to efficiently sample diverse structures for protein design. Recently, based on prior protein structure prediction algorithms, methods for predicting antibody CDR structures have emerged [Ruffolo et al., 2022b,a], but they are not able to design CDR sequences. ",
|
| 248 |
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"text": "Diffusion-Based Generative Models Diffusion probabilistic models learn to generate data via denoising samples from a prior distribution [Sohl-Dickstein et al., 2015, Song and Ermon, 2019, Ho et al., 2020]. Recently, progress has been made in developing equivariant diffusion models for molecular 3D structures [Shi et al., 2021, Hoogeboom et al., 2022, Jing et al., 2022, Xu et al., 2022]. Atoms in a molecule do not have natural orientations, so the generation process differs from generating protein structures. Diffusion models have also been extended to non-Euclidean data, such as data in the Riemannian manifolds [Leach et al., 2022, De Bortoli et al., 2022]. These models are relevant to modeling orientations which are represented by elements in SO(3). In addition, diffusion models can also be used to generate discrete categorical data [Hoogeboom et al., 2021, Austin et al., 2021]. Concurrently with this work, various diffusion probabilistic models have been developed for proteins [Anand and Achim, 2022, Trippe et al., 2022, Wu et al., 2022]. ",
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"type": "text",
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"text": "3 Methods ",
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| 270 |
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"text_level": 1,
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| 271 |
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"type": "text",
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"text": "This section is organized as follows: Section 3.1 introduces notations used throughout the paper and formally states the problem. Section 3.2 formulates the diffusion process for modeling antibodies. Section 3.3 introduces details about the neural network parameterization for the diffusion processes. Section 3.4 presents sampling algorithms for various antibody design tasks. ",
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"type": "text",
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"text": "3.1 Definitions and Notations ",
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"text": "An amino acid in a protein complex can be represented by its type, $\\mathrm { C } _ { \\alpha }$ atom coordinate, and the orientation, denoted as $s _ { i } \\in \\left\\{ \\tt A C D E F G H I K L M N P Q R S T V W Y \\right\\}$ , $\\dot { \\pmb { x } } _ { i } \\in \\mathbb { R } ^ { \\bar { 3 } } , O _ { i } \\in \\mathrm { S O ( 3 ) }$ , respectively. Here $i = 1 \\ldots N$ , and $N$ is the number of amino acids in the protein complex3. ",
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"type": "text",
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"text": "In this work, we assume the antigen structure and the antibody framework is given (Figure 2), and we focus on designing CDRs on the antibody framework. Assume the CDR to be generated has $m$ amino acids with index from $l + 1$ to $l + m$ . They are denoted as $\\mathcal { R } = \\{ ( \\mathbf { s } _ { j } , \\mathbf { x } _ { j } , \\mathbf { O } _ { j } ) \\mid \\bar { j } = l + 1 , \\ldots , l + m \\}$ Formally, our goal is to jointly model the distribution of $\\mathcal { R }$ given the structure of the antibody-antigen complex $\\mathcal { C } = \\bar { \\{ } ( s _ { i } , \\mathbf { x } _ { i } , \\bar { \\mathbf { O } } _ { i } ) | \\dot { \\ i } \\in \\{ 1 \\ldots N \\} \\backslash \\{ l + 1 , \\ldots , l + m \\} \\}$ . ",
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"type": "text",
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"text": "3.2 Diffusion Processes ",
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"type": "text",
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"text": "A diffusion probabilistic model defines two Markov chains of diffusion processes. The forward diffusion process gradually adds noise to the data until the data distribution approximately reaches the prior distribution. The generative diffusion process starts from the prior distribution and iteratively transforms it to the desired distribution. Training the model relies on the forward diffusion process to simulate the noisy data. Let $\\left( \\mathbf { s } _ { j } ^ { t } , \\mathbf { x } _ { j } ^ { t } , \\mathbf { O } _ { j } ^ { t } \\right)$ denote the intermediate state of amino acid $j$ at time step $t$ . $\\mathcal { R } ^ { t } = \\{ \\mathbf { s } _ { j } ^ { t } , \\mathbf { x } _ { j } ^ { t } , \\mathbf { O } _ { j } ^ { t } \\} _ { j = l + 1 } ^ { l + m }$ represents the sequence and structure sampled at step $t$ . $t = 0$ represents the state of real data (observed sequences and structures of CDRs) and $t = T$ represents samples from the prior distribution. Forward diffusion goes from $t = 0$ to $T$ , and generative diffusion proceeds in the opposite way. The diffusion processes for amino acid types $\\mathrm { s } _ { j } ^ { t }$ , coordinates $\\mathbf { x } _ { j } ^ { t }$ , and orientations $\\mathbf { O } _ { j } ^ { t }$ are defined as follows: ",
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"text": "Multinomial Diffusion for Amino Acid Types The forward diffusion process for amino acid types is based on the multinomial distribution defined as follows [Hoogeboom et al., 2021]: ",
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"img_path": "images/89f3dc6e30e46a1238a22bfc5b4b6f1c11ff8a0ba7b480b9c194183c2a242965.jpg",
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"text": "$$\nq ( \\mathbf { s } _ { j } ^ { t } | \\mathbf { s } _ { j } ^ { t - 1 } ) = \\mathrm { M u l t i n o m i a l } \\left( ( 1 - \\beta _ { \\mathrm { t y p e } } ^ { t } ) \\cdot \\mathsf { o n e h o t } ( \\mathbf { s } _ { j } ^ { t - 1 } ) + \\beta _ { \\mathrm { t y p e } } ^ { t } \\cdot \\frac { 1 } { 2 0 } \\cdot \\mathbf { 1 } \\right) ,\n$$",
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"text": "where onehot represents a function that converts amino acid type to a 20-dimensional one-hot vector and 1 is an all-one vector. $\\beta _ { \\mathrm { t y p e } } ^ { t }$ is the probability of resampling another amino acid over 20 types uniformly. When $t \\to T$ , $\\beta _ { \\mathrm { t y p e } } ^ { t }$ is set close to 1 and the distribution is closer to the uniform distribution. The following probability density provides an efficient way to perturb $\\mathbf { s } _ { j } ^ { 0 }$ for timestep $t$ during training [Hoogeboom et al., 2021]: ",
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"type": "equation",
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"text": "$$\nq ( \\mathrm { s } _ { j } ^ { t } | \\mathrm { s } _ { j } ^ { 0 } ) = \\mathrm { M u l t i n o m i a l } \\left( \\bar { \\alpha } _ { \\mathrm { t y p e } } ^ { t } \\cdot \\mathrm { o n e h o t } ( \\mathrm { s } _ { j } ^ { 0 } ) + ( 1 - \\bar { \\alpha } _ { \\mathrm { t y p e } } ^ { t } ) \\cdot \\frac { 1 } { 2 0 } \\cdot \\mathbf { 1 } \\right) ,\n$$",
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"type": "text",
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"text": "where $\\begin{array} { r } { \\bar { \\alpha } _ { \\mathrm { t y p e } } ^ { t } = \\prod _ { \\tau = 1 } ^ { t } ( 1 - \\beta _ { \\mathrm { t y p e } } ^ { \\tau } ) } \\end{array}$ ",
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"type": "text",
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"text": "The generative diffusion process is defined as: ",
|
| 409 |
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| 416 |
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},
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| 417 |
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{
|
| 418 |
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"type": "equation",
|
| 419 |
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"img_path": "images/842d25c79251ce5ea5f55f20efcf380a2a0a772aeb246de3f4766e2c59e93a4d.jpg",
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"text": "$$\np ( \\mathbf { s } _ { j } ^ { t - 1 } | \\mathcal { R } ^ { t } , \\mathcal { C } ) = \\mathrm { M u l t i n o m i a l } \\left( F ( \\mathcal { R } ^ { t } , \\mathcal { C } ) [ j ] \\right) ,\n$$",
|
| 421 |
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"text_format": "latex",
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"bbox": [
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{
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"type": "text",
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"text": "where $F ( \\cdot ) [ j ]$ is a neural network model taking the structure context (antigen and antibody framework) and the CDR state from the previous step as input and predicts the probability of the amino acid type for the $j$ -th amino acid on the CDR. Note that, different from the forward diffusion process, the generative diffusion process must rely on the structure context $\\mathcal { C }$ and the CDR state of the previous step including positions and orientations. The main difference between these two processes is that the forward diffusion process adds noise to data so it is irrelevant to data or contexts but the generative diffusion process depends on the given condition and full observation of the previous step. The generative diffusion process needs to approximate the posterior $\\boldsymbol { q } ( \\mathrm { s } _ { j } ^ { t - 1 } | \\mathrm { s } _ { j } ^ { t } , \\mathrm { s } _ { j } ^ { 0 } )$ derived from Eq.1 and Eq.2 to denoise. Therefore, the objective of training the generative diffusion process for amino acid types is to minimize the expected KL divergence between Eq.3 and the posterior distribution: ",
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"type": "equation",
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"text": "$$\nL _ { \\mathrm { t y p e } } ^ { t } = \\mathbb { E } _ { \\mathcal { R } ^ { t } \\sim p } \\left[ \\frac { 1 } { m } \\sum _ { j } D _ { \\mathrm { K L } } \\left( q ( \\mathbf { s } _ { j } ^ { t - 1 } | \\mathbf { s } _ { j } ^ { t } , \\mathbf { s } _ { j } ^ { 0 } ) \\Big | \\Big | p ( \\mathbf { s } _ { j } ^ { t - 1 } | \\mathcal { R } ^ { t } , \\mathcal { C } ) \\right) \\right] .\n$$",
|
| 445 |
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"text_format": "latex",
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{
|
| 455 |
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"type": "image",
|
| 456 |
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"img_path": "images/763df5ad9ab18b5b5ffb241a7ba532baf80459a901f750f4f12452181b94276c.jpg",
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"image_caption": [
|
| 458 |
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"Figure 3: Illustration of the generative diffusion process. At each step, the network takes the current CDR state as input and parameterizes the distribution of the CDR’s sequences, positions, and orientations for the next step. In the end, full-atom structures are constructed by the side-chain packing algorithm. "
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"text": "Diffusion for $\\mathrm { C } _ { \\alpha }$ Coordinates As the coordinate of an atom could be an arbitrary value, we scale and shift the coordinates of the whole structure such that the distribution of atom coordinates roughly match the standard normal distribution. We define the forward diffusion for the normalized $\\mathrm { C } _ { \\alpha }$ coordinate $\\mathbf { x } _ { j }$ as follows: ",
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"type": "equation",
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"text": "$$\n\\begin{array} { r } { q \\left( \\mathbf { x } _ { j } ^ { t } \\mid \\mathbf { x } _ { j } ^ { t - 1 } \\right) = \\mathcal { N } \\left( \\mathbf { x } _ { j } ^ { t } \\Big | \\sqrt { 1 - \\beta _ { \\mathrm { p o s } } ^ { t } } \\cdot \\mathbf { x } _ { j } ^ { t - 1 } , \\beta _ { \\mathrm { p o s } } ^ { t } I \\right) , } \\\\ { q \\left( \\mathbf { x } _ { j } ^ { t } \\mid \\mathbf { x } _ { j } ^ { 0 } \\right) = \\mathcal { N } \\left( \\mathbf { x } _ { j } ^ { t } \\Big | \\sqrt { \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { 0 } } \\cdot \\mathbf { x } _ { j } ^ { 0 } , ( 1 - \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { 0 } ) I \\right) , } \\end{array}\n$$",
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"text_format": "latex",
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| 485 |
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"type": "text",
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"text": "where $\\beta _ { \\mathrm { p o s } } ^ { t }$ controls the rate of diffusion and its value increases from 0 to 1 as time step goes from 0 to $t$ , and $\\begin{array} { r } { \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { t } = \\prod _ { \\tau = 1 } ^ { t } ( 1 - \\beta _ { \\mathrm { p o s } } ^ { \\tau } ) } \\end{array}$ . Using the reparameterization trick proposed by Ho et al., the generative diffusion process is defined as: ",
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"text": "$$\n\\begin{array} { r l } & { p \\left( \\mathbf { x } _ { j } ^ { t - 1 } \\middle | \\mathcal { R } ^ { t } , \\mathcal { C } \\right) = \\mathcal { N } \\left( \\mathbf { x } _ { j } ^ { t - 1 } \\middle | \\mu _ { p } \\left( \\mathcal { R } ^ { t } , \\mathcal { C } \\right) , \\beta _ { \\mathrm { p o s } } ^ { t } I \\right) , } \\\\ & { ~ \\mu _ { p } \\left( \\mathcal { R } ^ { t } , \\mathcal { C } \\right) = \\frac { 1 } { \\sqrt { \\alpha _ { \\mathrm { p o s } } ^ { t } } } \\left( \\mathbf { x } _ { j } ^ { t } - \\frac { \\beta _ { \\mathrm { p o s } } ^ { t } } { \\sqrt { 1 - \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { t } } } G ( \\mathcal { R } ^ { t } , \\mathcal { C } ) [ j ] \\right) . } \\end{array}\n$$",
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| 519 |
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"text": "Here, $G ( \\cdot ) [ j ]$ is a neural network that predicts the standard Gaussian noise $\\epsilon _ { j } \\sim \\mathcal { N } ( \\mathbf { 0 } , I )$ added to $\\sqrt { \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { 0 } } \\mathbf { x } _ { j } ^ { 0 }$ (scaled coordinate of amino acid $j$ ) based on the reparameterization of Eq.6: $\\mathbf { x } _ { j } ^ { t } = $ $\\sqrt { \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { 0 } } \\mathbf { x } _ { j } ^ { 0 } + \\sqrt { 1 - \\bar { \\alpha } _ { \\mathrm { p o s } } ^ { 0 } } \\epsilon _ { j }$ . The objective function of training the generative process is the expected MSE between $G$ and $\\epsilon _ { j }$ , which is simplified from aligning distribution $p$ to the posterior $q ( \\mathbf { x } _ { j } ^ { t - 1 } \\mid$ $\\mathbf { x } _ { j } ^ { t } , \\mathbf { x } _ { j } ^ { 0 } )$ [Ho et al., 2020]: ",
|
| 520 |
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"bbox": [
|
| 521 |
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| 522 |
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| 526 |
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| 527 |
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| 528 |
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|
| 529 |
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"type": "equation",
|
| 530 |
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"img_path": "images/50b8eec6b760b0bd7883b0edf90f639196eb06033fe80bc4230dddbda681e913.jpg",
|
| 531 |
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"text": "$$\nL _ { \\mathrm { p o s } } ^ { t } = \\mathbb { E } \\left[ \\frac { 1 } { m } \\sum _ { j } \\left\\| \\epsilon _ { j } - G ( \\mathcal { R } ^ { t } , \\mathcal { C } ) \\right\\| ^ { 2 } \\right] .\n$$",
|
| 532 |
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"text_format": "latex",
|
| 533 |
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"bbox": [
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|
| 541 |
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| 542 |
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"type": "text",
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| 543 |
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"text": "SO(3) Denoising for Amino Acid Orientations We empirically formulate an iterative perturbdenoise scheme for learning and generating amino acid orientations represented by SO(3) elements [Leach et al., 2022]. Note that we do not use the term diffusion because the formulation does not strictly follow the framework of diffusion probabilistic models though the overall principle is the same. Similar to the typical diffusion process, the distribution of orientations perturbed for $t$ steps is defined as, according to Leach et al. [2022]: ",
|
| 544 |
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"bbox": [
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| 552 |
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| 553 |
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"type": "equation",
|
| 554 |
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"img_path": "images/d00c6690b905578b29a576e27de973bc7d01f6b6aa7014713d6ba09b93fedd65.jpg",
|
| 555 |
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"text": "$$\nq \\left( \\mathbf { O } _ { j } ^ { t } \\mid \\mathbf { O } _ { j } ^ { 0 } \\right) = \\mathcal { Z } \\mathcal { G } _ { \\mathrm { S O ( 3 ) } } \\left( \\mathbf { O } _ { j } ^ { t } \\middle | \\mathrm { S c a l e R o t } \\left( \\sqrt { \\bar { \\alpha } _ { \\mathrm { o r i } } ^ { t } } , \\mathbf { O } _ { j } ^ { 0 } \\right) , 1 - \\bar { \\alpha } _ { \\mathrm { o r i } } ^ { t } \\right) .\n$$",
|
| 556 |
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"text_format": "latex",
|
| 557 |
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"bbox": [
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| 564 |
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|
| 565 |
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|
| 566 |
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"type": "text",
|
| 567 |
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"text": "$\\mathcal { T G } _ { \\mathrm { S O ( 3 ) } }$ denotes the isotropic Gaussian distribution on SO(3) parameterized by a mean rotation and a scalar variance [Leach et al., 2022, Matthies et al., 1970, Nikolayev and Savyolov, 1970]. ScaleRot modifies the rotation matrix by scaling its rotation angle with the rotation axis fixed [Gallier and Xu, ",
|
| 568 |
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"bbox": [
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| 575 |
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|
| 576 |
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|
| 577 |
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"type": "text",
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| 578 |
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"text": "2003]. $\\begin{array} { r } { \\bar { \\alpha } _ { \\mathrm { o r i } } ^ { t } = \\prod _ { \\tau = 1 } ^ { t } ( 1 - \\beta _ { \\mathrm { o r i } } ^ { \\tau } ) } \\end{array}$ , where $\\beta _ { \\mathrm { o r i } } ^ { t }$ is the variance increases with the step $t$ . The conditional distribution used for the generation process of orientations is defined as: ",
|
| 579 |
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"type": "equation",
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"img_path": "images/86274340918522b0d70c179ccae1736e92a9fa9442a2d425a564897fea687b22.jpg",
|
| 590 |
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"text": "$$\np \\left( \\mathbf { O } _ { j } ^ { t - 1 } \\Big | \\mathcal { R } ^ { t } , \\mathcal { C } \\right) = \\mathcal { Z } \\mathcal { G } _ { \\mathrm { S O ( 3 ) } } \\left( \\mathbf { O } _ { j } ^ { t - 1 } \\Big | H ( \\mathcal { R } ^ { t } , \\mathcal { C } ) [ j ] , \\beta _ { \\mathrm { o r i } } ^ { t } \\right) ,\n$$",
|
| 591 |
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"text_format": "latex",
|
| 592 |
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"bbox": [
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| 599 |
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},
|
| 600 |
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|
| 601 |
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"type": "text",
|
| 602 |
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"text": "where $H ( \\cdot ) [ j ]$ is a neural network that denoises the orientation and outputs the denoised orientation matrix of amino acid $j$ . Training the conditional distribution requires aligning the predicted orientation from $H ( \\cdot )$ to the real orientation. Hence, we formulate the training object that minimizes the expected discrepancy measured by the inner product between the real and the predicted orientation matrices: ",
|
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| 611 |
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| 612 |
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"type": "equation",
|
| 613 |
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"img_path": "images/5729a6f7cb44a327d9839b8f1c3b331fa8dd1c38d94fe9438692a1b4c5258d40.jpg",
|
| 614 |
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"text": "$$\nL _ { \\mathrm { o r i } } ^ { t } = \\mathbb { E } \\left[ \\frac { 1 } { m } \\sum _ { j } \\left. \\left( \\mathbf { O } _ { j } ^ { 0 } \\right) ^ { \\intercal } \\widehat { \\mathbf { O } } _ { j } ^ { t - 1 } - I \\right. _ { F } ^ { 2 } \\right] ,\n$$",
|
| 615 |
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"text_format": "latex",
|
| 616 |
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"bbox": [
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| 621 |
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| 622 |
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"page_idx": 5
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| 623 |
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},
|
| 624 |
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|
| 625 |
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"type": "text",
|
| 626 |
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"text": "where $\\widehat { \\mathbf { O } } _ { j } ^ { t - 1 } = H ( \\cdot ) [ j ]$ is the predicted orientation for amino acid $j$ . ",
|
| 627 |
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"bbox": [
|
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|
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"type": "text",
|
| 637 |
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"text": "The Overall Training Objective By summing Eq.4, 9, and 12 and taking the expectation w.r.t. $t$ , we obtain the final training objective function: ",
|
| 638 |
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"bbox": [
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"img_path": "images/e61a380294985e4edc109f88e511f63fc2478c16b817ada7892dc00d00fb8775.jpg",
|
| 649 |
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"text": "$$\nL = \\mathbb { E } _ { t \\sim \\mathrm { U n i f o r m } ( 1 . . . T ) } \\left[ L _ { \\mathrm { t y p e } } ^ { t } + L _ { \\mathrm { p o s } } ^ { t } + L _ { \\mathrm { o r i } } ^ { t } \\right] .\n$$",
|
| 650 |
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"text_format": "latex",
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| 651 |
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"bbox": [
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| 659 |
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"type": "text",
|
| 661 |
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"text": "To train the model, we first sample a time step $t$ and then sample noisy states $\\{ \\mathbf { s } _ { j } ^ { t } , \\mathbf { x } _ { j } ^ { t } , \\mathbf { O } _ { j } ^ { t } \\} _ { j = l + 1 } ^ { l + m } \\sim p$ by adding noise to the training sample using the diffusion process defined by Eq.2, 6, and 10. We compute the loss using the noisy data and backpropagate the loss to update model parameters. ",
|
| 662 |
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"bbox": [
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| 669 |
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},
|
| 670 |
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|
| 671 |
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"type": "text",
|
| 672 |
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"text": "3.3 Parameterization with Neural Networks ",
|
| 673 |
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"text_level": 1,
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| 674 |
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| 683 |
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| 684 |
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"text": "In this section, we briefly introduce the neural network architectures used in different components of the diffusion process. The purpose of the networks is to encode the CDR state at a time step along with the context structure: $\\{ \\mathbf { s } _ { j } ^ { t } , \\mathbf { x } _ { j } ^ { t } , \\mathbf { O } _ { j } ^ { t } \\} _ { j = l + 1 } ^ { l + m } \\cup \\{ s _ { i } ^ { t } , \\mathbf { x } _ { i } ^ { t } , O _ { i } ^ { t } \\} _ { i = \\{ 1 \\ldots N \\} \\setminus \\{ l + 1 \\ldots l + m \\} }$ , and then denoises the CDR amino acid types $( F )$ , positions $( G )$ , and orientations $( H )$ . ",
|
| 685 |
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|
| 694 |
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| 695 |
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"text": "First, we adopt Multiple Layer Perceptrons (MLPs) to generate embeddings for single and pairs of amino acids. The single amino-acid embedding MLP creates vector $e _ { i }$ for amino acid $i$ , which encodes the information of amino acid types, torsional angles, and 3D coordinates of all the heavy atoms. The pairwise embedding MLP encodes the Euclidean distances and dihedral angles between amino acid $i$ and $j$ to feature vectors $z _ { i j }$ . We adopt IPA [Jumper et al., 2021], an orientation-aware roto-translation invariant network to transform $e _ { i }$ and $z _ { i j }$ into hidden representations $\\boldsymbol { h } _ { i }$ , which aims to represent the amino acid itself and its environment. Next, the representations are fed to three different MLPs to denoise the amino acid types, 3D positions, and orientations of the CDR, respectively. ",
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"text": "In particular, the MLP for denoising amino acid types outputs a 20-dimensional vector representing the posterior probabilities. The MLP for denoising $\\mathrm { C } _ { \\alpha }$ coordinates predicts the scaled change of the coordinate in terms of the current orientation of the amino acid. As the coordinate deviation is calculated in the local frame, we left-multiply it by the orientation matrix and transform it back to the global frame. Formally, this can be expressed as $\\hat { \\epsilon } _ { j } = \\mathbf { O } _ { j } ^ { t } \\mathrm { M L P } _ { G } \\left( h _ { j } \\right)$ . Predicting coordinate deviations in the local frame and projecting it to the global frame ensures the equivariance of the prediction, as when the entire 3D structure rotates by a particular angle, the coordinate deviations also rotate by the same angle. The MLP for denoising orientations first predicts a $s o ( 3 )$ vector [Gallier and Xu, 2003]. The vector is converted to a rotation matrix $M _ { j } \\in \\mathrm { S O } ( 3 )$ right-multiplied to the orientation to produce a new mean orientation for the next generative step: $\\widehat { \\mathbf { O } } _ { j } ^ { t - 1 } \\gets \\mathbf { O } _ { j } ^ { t } M _ { j }$ . The proposed networks are equivariant to the rotation and translation of the overall structure: ",
|
| 707 |
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"bbox": [
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|
| 716 |
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"type": "text",
|
| 717 |
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"text": "Proposition 1. For any proper rotation matrix $R \\in \\mathrm { S O } ( 3 )$ and any $3 D$ vector $\\pmb { r } \\in \\mathbb { R } ^ { 3 }$ (rigid transformation $( R , r ) \\in \\mathrm { S E } ( 3 )$ ), $F$ , $G$ and $H$ satisfy the following equivariance properties: ",
|
| 718 |
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"bbox": [
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| 727 |
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"type": "equation",
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"img_path": "images/cdd2d4e9b8b2712a936383573efb0f8f6bc1626bf931b1abf04734122fa50f6e.jpg",
|
| 729 |
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"text": "$$\n\\begin{array} { r l } & { F ( R \\mathcal { R } ^ { t } + r , R \\mathcal { C } + r ) = F ( \\mathcal { R } ^ { t } , \\mathcal { C } ) , } \\\\ & { G ( R \\mathcal { R } ^ { t } + r , R \\mathcal { C } + r ) = R G ( \\mathcal { R } ^ { t } , \\mathcal { C } ) , } \\\\ & { H ( R \\mathcal { R } ^ { t } + r , R \\mathcal { C } + r ) = R H ( \\mathcal { R } ^ { t } , \\mathcal { C } ) , } \\end{array}\n$$",
|
| 730 |
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| 731 |
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"bbox": [
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| 739 |
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|
| 740 |
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"type": "text",
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| 741 |
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"text": "where $R \\mathcal { R } ^ { t } { + } r : = \\{ \\mathrm { s } _ { j } ^ { t } , \\mathrm { \\mathbf { x } } _ { j } ^ { t } { + } r , R \\mathbf { O } _ { j } ^ { t } \\} _ { j = l + 1 } ^ { l { + } m }$ and $R { \\mathcal { C } } + r : = \\{ s _ { i } , x _ { i } + r , R O _ { i } \\} _ { i \\in \\{ 1 . . . N \\} \\setminus \\{ l + 1 , . . . , l + m \\} }$ denote the rotated and translated structure. Note that $F$ , $G$ , and $H$ are not single MLPs. Each of them includes the shared encoder and a specific MLP. ",
|
| 742 |
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|
| 751 |
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| 752 |
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"text": "3.4 Sampling Algorithms ",
|
| 753 |
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"text_level": 1,
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| 754 |
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| 762 |
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"type": "text",
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| 764 |
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"text": "The sampling algorithm first samples amino acid types from the uniform distribution over 20 classes: $s _ { j } ^ { T } \\sim \\bar { \\mathrm { U n i f o r m } ( 2 0 ) }$ , $\\mathrm { C } _ { \\alpha }$ positions from the standard normal distribution: $\\mathbf { x } _ { j } ^ { T } \\sim \\mathcal { N } ( \\mathbf { 0 } , I _ { 3 } )$ , and orientations from the uniform distribution over SO(3): $\\mathbf { O } _ { j } ^ { T } \\sim \\mathrm { U n i f o r m } ( \\bar { \\mathrm { S O } } ( 3 ) )$ . Note that we normalize the coordinates of the structure in the same way as training such that $\\mathrm { C } _ { \\alpha }$ positions in the CDR roughly follow the standard normal distribution. Next, we iteratively sample sequences and structures from the generative diffusion kernel by denoising amino acid types, $\\mathrm { C } _ { \\alpha }$ coordinates, and orientations until $t = 0$ . To build a full atom 3D structure, we construct the coordinates of N, $\\mathrm { C } _ { \\alpha }$ , C, O, and side-chain $\\mathrm { C } _ { \\beta }$ (except glycine that does not have $\\mathrm { C } _ { \\beta }$ ) according to their ideal local coordinates relative to the $\\mathrm { C } _ { \\alpha }$ position and orientation of each amino acid [Engh and Huber, 2012]. Based on the five reconstructed atoms, the rest of the side-chain atoms are constructed using the side-chain packing function implemented in Rosetta [Alford et al., 2017]. In the end, we adopt the AMBER99 force field [Lindorff-Larsen et al., 2010] in OpenMM [Eastman et al., 2017] to refine the full atom structure. ",
|
| 765 |
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| 773 |
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|
| 774 |
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"type": "text",
|
| 775 |
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"text": "In addition to the joint design of sequences and structures, we can constrain partial states for other design tasks. For example, by fixing the backbone structure (positions and orientations) and sampling only sequences, we can do fix-backbone sequence design. Another usage is to optimize an existing antibody. Specifically, we first add noise to the existing antibody for $t$ steps and denoise the perturbed antibody sequence starting from the $t$ -th step of the generative diffusion process. ",
|
| 776 |
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| 784 |
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{
|
| 785 |
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"type": "text",
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| 786 |
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"text": "4 Experiments ",
|
| 787 |
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"text": "We present the application of our model, named DiffAb4, in three antibody design tasks: sequencestructure co-design (Section 4.1), antibody sequence design based on antibody backbones (Section 4.2), and antibody optimization (Section 4.3). In Section 4.4, we show how to use our model without known antibody frameworks bound to the antigen. ",
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"type": "text",
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"text": "4.1 Sequence-Structure Co-design ",
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"text": "The dataset for training the model is derived from the SAbDab database[Dunbar et al., 2014]. We first remove structures whose resolution is worse than $4 \\mathring \\mathrm { A }$ and discard antibodies targeting non-protein antigens. We cluster antibodies in the database according to CDR-H3 sequences at $50 \\%$ sequence identity. We manually select five clusters as the test set, containing 19 antibody-antigen complexes in total. The test set includes antigens from several well-known pathogens including SARS-CoV-2, MERS, influenza, and so on. Structures in the remaining clusters are used for training. ",
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"text": "To evaluate the performance, we remove the original CDR from the antibody-antigen complex in the test set and sample both the sequence and structure of the removed region. We set the length of the CDR to be identical to the length of the original CDR for simplicity. In practice, one can enumerate different lengths of CDRs. We compare our model to RosettaAntibodyDesign (RAbD) [Adolf-Bryfogle et al., 2018], an antibody design software based on Rosetta energy functions. For each model, we draw 100 samples for each CDR. Both the original structures and designed structures from different methods are refined by OpenMM and Rosetta. ",
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"text": "We use the following metrics to evaluate designed antibodies: (1) IMP: is the percentage of designed CDRs with lower (better) binding energy $( \\Delta G )$ than the original CDR. The binding energy is calculated by InterfaceAnalyzer in the Rosetta software package [Alford et al., 2017]. (2) RMSD: is the $\\mathrm { C } _ { \\alpha }$ root-mean-square deviation (RMSD) between the generated structure and the original structure with only antibody frameworks aligned. (3) AAR: is the amino acid recovery rate measured by the sequence identity between the reference CDR sequences and the generated sequences [AdolfBryfogle et al., 2018]. Note that different from Jin et al. [2022], we do not use neutralization prediction models because they are sequence-based and are specified to a limited class of antigens, which deviates from our goal of developing a general antibody design model. ",
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"text": "Table 1 shows that our model (DiffAb) recovers CDR sequences more accurately than RAbD (higher AAR). The RMSDs of CDRs generated by DiffAb are higher in CDR-H3, which indicates that our generated samples are more diverse structurally. The IMP score of DiffAb is on par with RAbD in ",
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"type": "table",
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"img_path": "images/8931ecf11c3f565643b0f9bc6dd5619fe4ff7cc34d6808e27f466a73a84f6f55.jpg",
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"table_caption": [],
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"table_body": "<table><tr><td>CDR</td><td>Method</td><td>AAR</td><td>RMSD</td><td>IMP</td></tr><tr><td rowspan=\"2\">H1</td><td>RAbD</td><td>22.85%</td><td>2.261A</td><td rowspan=\"2\">43.88% 53.63%</td></tr><tr><td>DiffAb</td><td>65.75%</td><td>1.188A</td></tr><tr><td rowspan=\"2\">H2</td><td>RAbD</td><td>25.50%</td><td>1.641A</td><td>53.50%</td></tr><tr><td>DiffAb</td><td>49.31%</td><td>1.076A</td><td>29.84%</td></tr><tr><td rowspan=\"2\">H3</td><td>RAbD</td><td>22.14%</td><td>2.900A</td><td>23.25%</td></tr><tr><td>DiffAb</td><td>26.78%</td><td>3.597A</td><td>23.63%</td></tr></table>",
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"type": "table",
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"img_path": "images/e5fa29ac9336d028e91f86e196add41ab084af4f7e220b118898356864616525.jpg",
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"table_caption": [
|
| 881 |
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"Table 1: Evaluation of the generated antibody CDRs (sequence-structure co-design) by RAbD and our DiffAb model. "
|
| 882 |
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| 883 |
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"table_footnote": [],
|
| 884 |
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"table_body": "<table><tr><td>CDR</td><td>Method</td><td>AAR</td><td>RMSD</td><td>IMP</td></tr><tr><td rowspan=\"2\">L1</td><td>RAbD</td><td>34.27%</td><td>1.204A</td><td rowspan=\"2\">46.81% 45.58%</td></tr><tr><td>DiffAb</td><td>56.67%</td><td>1.388A</td></tr><tr><td rowspan=\"2\">L2</td><td>RAbD</td><td>26.30%</td><td>1.767A</td><td rowspan=\"2\">56.94% 49.95%</td></tr><tr><td>DiffAb</td><td>59.32%</td><td>1.373A</td></tr><tr><td rowspan=\"2\">L3</td><td>RAbD</td><td>20.73%</td><td>1.624A</td><td>55.63%</td></tr><tr><td>DiffAb</td><td>46.47%</td><td>1.627A</td><td>47.32%</td></tr></table>",
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"img_path": "images/f841f961e4a52f14035e6f02665232d757f1ac6b45b7af9b9c24aa229956fe8e.jpg",
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"image_caption": [
|
| 897 |
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"Figure 4: Examples of CDR-H3 designed by the sequence-structure co-design method and the distribution of their interaction energy and RMSD. The antigen-antibody template is derived from PDB:7chf, where the antigen is SARS-CoV-2 RBD. Sample 1 has better complementarity to the antigen while Sample 3 fits the antigen worse. This could explain their difference in the binding energy $( \\Delta G )$ . "
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"text": "CDR-H3, and lower in other CDRs. However, it should be noted that RAbD optimizes the Rosetta energy function, which is also used for evaluation. Our model achieves reasonably good binding energy without explicit supervision signal from Rosetta energy functions. Figure 4 presents three generated examples of CDR-H3 targeting SARS-CoV-2 RBD. Sample 1 has the lowest binding energy and it can be observed that it has better complementarity to the antigen. The binding energy of Sample 3 is higher than the original one and visually, the shape of the CDR does not fit the antigen well. ",
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"text": "4.2 Fix-Backbone Sequence Design and Structure Prediction ",
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"text": "In this setting, the backbone structure of CDRs is given and we only need to design the CDR sequence, which transforms the task into a constrained sampling problem. Fix-backbone design is a common setting in the area of protein design [Ingraham et al., 2019, Hsu et al., 2022, Anishchenko et al., 2021, Strokach et al., 2020, Tischer et al., 2020]. For this task, we consider FixBB, a Rosetta-based sequence design software given CDR backbone structure, as the baseline. We use the AAR metric introduced in Section 4.1 to evaluate the designed CDRs. ",
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"text": "As shown in Table 2, our model achieves better AAR in all the CDRs. This shows that our model is also powerful in modeling the conditional probability of sequences given backbone structures. Admittedly, the training data is clustered only by CDR-H3 sequences, so the model might have seen other CDRs in the test set during training, leading to even higher AAR. However, we believe this is not an issue as CDRs other than H3 are generally conserved and contribute less to the specificity $\\mathrm { X u }$ and Davis [2000]. ",
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"text": "Our model can predict CDR structures by fixing the sequence. Table 3 shows that it accurately predicts the structure of CDR H1, H2, L1, L2, and L3 $\\mathrm { R i M S D } \\le 1 . 5 \\mathring \\mathrm { A } ;$ ). The accuracy of CDR-H3 prediction is lower due to the high variability. Figure 5a separately shows the accuracy of different CDR-H3 lengths. The prediction is generally more accurate for shorter ones. When the CDR-H3 contains more than 10 amino acids, the prediction accuracy drops. ",
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"type": "table",
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"img_path": "images/c3538dca10f1c2723716ec36881ebcb0ff708b8b1bc08f1fc1b511717f514629.jpg",
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| 967 |
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"table_caption": [
|
| 968 |
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"Table 2: Comparison of FixBB and DiffAb in terms of amino acid recovery (AAR) in the fix-backbone CDR design task. DiffAb achieves higher AAR. The AAR of DiffAb on CDR-H3 is lower than other CDRs since H3 is much more versatile. "
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| 969 |
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| 970 |
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"table_footnote": [],
|
| 971 |
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"table_body": "<table><tr><td>CDR</td><td>Method</td><td>AAR</td><td>CDR</td><td>Method</td><td>AAR</td></tr><tr><td>H1</td><td>FixBB DiffAb</td><td>37.14% 87.83%</td><td>L1</td><td>FixBB DiffAb</td><td>33.80% 86.63%</td></tr><tr><td>H2</td><td>FixBB DiffAb</td><td>43.08% 79.70%</td><td>L2</td><td>FixBB DiffAb</td><td>28.54% 88.91%</td></tr><tr><td>H3</td><td>FixBB DiffAb</td><td>30.74% 59.48%</td><td>L3</td><td>FixBB DiffAb</td><td>17.92% 78.69%</td></tr></table>",
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| 972 |
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| 981 |
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"type": "table",
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"img_path": "images/d4e7d80fc6f41d9f3e9c65bc15a8ab9e9bb95ac3876de13e9994b1fecc51e691.jpg",
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| 983 |
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"table_caption": [
|
| 984 |
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"Table 3: The accuracy of CDR structures predicted by DiffAb in RMSD. "
|
| 985 |
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],
|
| 986 |
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"table_footnote": [],
|
| 987 |
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"table_body": "<table><tr><td>CDR</td><td>RMSD</td></tr><tr><td>H1</td><td>0.901A</td></tr><tr><td>H2</td><td>1.044A</td></tr><tr><td>H3</td><td>3.246A</td></tr><tr><td>L1</td><td>1.365A</td></tr><tr><td>L2</td><td>1.321A</td></tr><tr><td></td><td></td></tr><tr><td>L3</td><td>1.492A</td></tr></table>",
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"type": "image",
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| 998 |
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"img_path": "images/27850727702d41cefe4304b703014b0bd35e4cfc0f6ac13def48512bdc838705.jpg",
|
| 999 |
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"image_caption": [
|
| 1000 |
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"Figure 5: (a) RMSD of predicted CDR-H3 structures grouped by lengths. (b) The antibody optimization algorithm first perturbs the initial CDR for $t$ steps using the forward diffusion process and then denoises it by the backward diffusion process into the optimized CDR. (c) IMP, RMSD, and SeqID of the CDRs optimized with different numbers of steps. Dashed lines represent the results of de novo design. When $t = 4$ , the optimized CDRs reach an IMP score close to de novo CDRs but remain structurally similar to the original one. "
|
| 1001 |
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],
|
| 1002 |
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|
| 1003 |
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"type": "text",
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| 1013 |
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"text": "4.3 Antibody Optimization ",
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| 1014 |
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"type": "text",
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"text": "We use our model to optimize existing antibodies which is another common pharmaceutical application. To optimize an antibody, we first perturb the CDR sequence and structure for $t$ steps using the forward diffusion process. Then, we denoise the sequences starting from the $( T - t )$ -th step $t$ steps remaining) of the generative diffusion process and obtain a set of optimized antibodies. This process is illustrated in Figure 5b. We optimize CDR-H3 of the antibodies in the test set with various $t$ values. For each antibody and $t$ , we perturb the CDR independently 100 times and collect 100 optimized CDRs different from the original CDR. We report the percentage of optimized antibodies with improved binding energy (IMP), RMSD, and sequence identity (SeqID) of the optimized CDR in comparison to the original antibody. We also compare the optimized antibodies with the de novo ( $t = T = 1 0 0$ ) designed antibodies introduced in Section 4.1. As shown in Table 4 and Figure 5c, the optimization method could produce antibodies with improved binding energy measured by the Rosetta energy function. In contrast to redesigning CDRs, optimization improves binding energy while keeping the optimized CDR similar to the original one, which is desired in many practical applications. ",
|
| 1026 |
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| 1035 |
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"type": "table",
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| 1036 |
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"img_path": "images/088925f0f84512174818eb9019ef663a91d41d53127277120d435d57e368cbc7.jpg",
|
| 1037 |
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"table_caption": [
|
| 1038 |
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"Table 4: Evaluation of optimized CDR-H3s with different numbers of optimization steps. In contrast to redesigning the CDR, the optimization method can improve binding energy while keeping the optimized CDR similar to the original one. Figure 5c shows the line plot of the results. "
|
| 1039 |
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|
| 1040 |
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"table_footnote": [],
|
| 1041 |
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"table_body": "<table><tr><td>t</td><td>IMP</td><td>RMSD</td><td>SeqID</td></tr><tr><td>1</td><td>18.52%</td><td>1.194A</td><td>92.42%</td></tr><tr><td>2</td><td>16.67%</td><td>1.252A</td><td>91.61%</td></tr><tr><td>4</td><td>23.29%</td><td>1.290A</td><td>91.16%</td></tr><tr><td>8</td><td>22.01%</td><td>1.447A</td><td>88.78%</td></tr><tr><td>16</td><td>18.02%</td><td>1.759A</td><td>78.43%</td></tr><tr><td>32</td><td>16.43%</td><td>2.623A</td><td>40.58%</td></tr><tr><td>64</td><td>15.47%</td><td>3.380A</td><td>27.30%</td></tr><tr><td>T</td><td>23.63%</td><td>3.597A</td><td>26.78%</td></tr></table>",
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| 1042 |
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| 1051 |
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"text": "",
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| 1053 |
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"type": "image",
|
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"img_path": "images/4fe2809ba79f7e335832e5954a3e35332119a5205e0e71d7925506c427f1a016.jpg",
|
| 1064 |
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"image_caption": [
|
| 1065 |
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"Figure 6: A human antibody framework docked to SARS-CoV-2 Omicron RBD using HDOCK. CDR-H3s are designed based on the docking structure. "
|
| 1066 |
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],
|
| 1067 |
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88,
|
| 1071 |
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794,
|
| 1072 |
+
284
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| 1073 |
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|
| 1074 |
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|
| 1075 |
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},
|
| 1076 |
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{
|
| 1077 |
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"type": "text",
|
| 1078 |
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"text": "4.4 Design Without Bound Antibody Frameworks ",
|
| 1079 |
+
"text_level": 1,
|
| 1080 |
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| 1081 |
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|
| 1088 |
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|
| 1089 |
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"type": "text",
|
| 1090 |
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"text": "In the last experiment, we consider designing antibodies without a known binding pose against the antigen, a more general and challenging setting. We show that this challenging task could be achieved with docking software. Specifically, we create an antibody template from an existing antibody structure by removing its CDR-H3. This is because CDR-H3 is the most variable one and accounts for most of the specificity, while other CDRs are much more conserved [Xu and Davis, 2000]. Next, we use HDOCK [Yan et al., 2017] to dock the antibody template to the target antigen to produce the antibody-antigen complex. In this way, the problem reduces to the original problem so we can adapt our model to design the CDR-H3 sequence and structure and re-design other CDRs. We demonstrate using this method to design antibodies for the SARS-CoV-2 Omicron RDB structure (PDB: 7wvn, residue A322-A590, the structure is not bound to any antibodies). The antibody template is derived from a human antibody against influenza (PDB: 3qhf). Figure 6 shows the docking structure, five designed CDR-H3s, and the binding energy distribution. It is hard to confidently conclude that the generated antibodies are effective without a reference antibody. However, according to the binding energy distribution, we can still say the generated antibodies are at least reasonable. ",
|
| 1091 |
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| 1097 |
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|
| 1098 |
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},
|
| 1099 |
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{
|
| 1100 |
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"type": "text",
|
| 1101 |
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"text": "5 Conclusions and Limitations ",
|
| 1102 |
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"text_level": 1,
|
| 1103 |
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"bbox": [
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|
| 1111 |
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|
| 1112 |
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"type": "text",
|
| 1113 |
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"text": "In this work, we propose a diffusion-based generative model for antibody design. Our model is capable of a wide range of antibody design tasks and can achieve competitive performance. One main limitation of this work is that it relies on an antibody framework bound to the target antigen. Therefore, we leave it for future work to design an effective model for generating antibodies without bound structures. Another limitation is that it remains unclear whether the generated antibodies can be produced in the wet lab and actually binds to the target. More efforts are needed to design a biologically effective antibody. ",
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| 1114 |
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| 1120 |
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| 1121 |
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| 1122 |
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{
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| 1123 |
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"type": "text",
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| 1124 |
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"text": "Acknowledgments and Disclosure of Funding ",
|
| 1125 |
+
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| 1126 |
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"bbox": [
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| 1133 |
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| 1134 |
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| 1135 |
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"type": "text",
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| 1136 |
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"text": "Supported by National Key R&D Program of China No. 2021YFF1201600. ",
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"text": "References ",
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|
| 1 |
+
# Simple and Controllable Music Generation
|
| 2 |
+
|
| 3 |
+
Jade Copet♠♢ Felix Kreuk♠♢ Itai Gat Tal Remez David Kant Gabriel Synnaeve ♢ Yossi Adi∗♢ Alexandre Défossez ♢ $\spadesuit$ : equal contributions, $\diamondsuit$ : core team Meta AI {jadecopet, felixkreuk, adiyoss}@meta.com
|
| 4 |
+
|
| 5 |
+
# Abstract
|
| 6 |
+
|
| 7 |
+
We tackle the task of conditional music generation. We introduce MUSICGEN, a single Language Model (LM) that operates over several streams of compressed discrete music representation, i.e., tokens. Unlike prior work, MUSICGEN is comprised of a single-stage transformer LM together with efficient token interleaving patterns, which eliminates the need for cascading several models, e.g., hierarchically or upsampling. Following this approach, we demonstrate how MUSICGEN can generate high-quality samples, both mono and stereo, while being conditioned on textual description or melodic features, allowing better controls over the generated output. We conduct extensive empirical evaluation, considering both automatic and human studies, showing the proposed approach is superior to the evaluated baselines on a standard text-to-music benchmark. Through ablation studies, we shed light over the importance of each of the components comprising MUSICGEN. Music samples, code, and models are available at github.com/facebookresearch/audiocraft.
|
| 8 |
+
|
| 9 |
+
# 1 Introduction
|
| 10 |
+
|
| 11 |
+
Text-to-music is the task of generating musical pieces given text descriptions, e.g., “90s rock song with a guitar riff”. Generating music is a challenging task as it requires modeling long range sequences. Unlike speech, music requires the use of the full frequency spectrum [Müller, 2015]. That means sampling the signal at a higher rate, i.e., the standard sampling rates of music recordings are 44.1 $\mathrm { k H z }$ or $4 8 ~ \mathrm { k H z }$ vs. $1 6 \ \mathrm { k H z }$ for speech. Moreover, music contains harmonies and melodies from different instruments, which create complex structures. Human listeners are highly sensitive to disharmony [Fedorenko et al., 2012, Norman-Haignere et al., 2019], hence generating music does not leave a lot of room for making melodic errors. Lastly, the ability to control the generation process in a diverse set of methods, e.g., key, instruments, melody, genre, etc. is essential for music creators.
|
| 12 |
+
|
| 13 |
+
Recent advances in self-supervised audio representation learning [Balestriero et al., 2023], sequential modeling [Touvron et al., 2023], and audio synthesis [Tan et al., 2021] provide the conditions to develop such models. To make audio modeling more tractable, recent studies proposed representing audio signals as multiple streams of discrete tokens representing the same signal [Défossez et al., 2022]. This allows both high-quality audio generation and effective audio modeling. However, this comes at the cost of jointly modeling several parallel dependent streams.
|
| 14 |
+
|
| 15 |
+
Kharitonov et al. [2022], Kreuk et al. [2022] proposed modeling multi-streams of speech tokens in parallel following a delay approach, i.e., introduce offsets between the different streams. Agostinelli et al. [2023] proposed representing musical segments using multiple sequences of discrete tokens at different granularity and model them using a hierarchy of autoregressive models. In parallel, Donahue et al. [2023] follows a similar approach but for the task of singing to accompaniment generation. Recently, Wang et al. [2023] proposed tackling this problem in two stages: (i) modeling the first stream of tokens only; (ii) then, apply a post-network to jointly model the rest of the streams in a non-autoregressive manner.
|
| 16 |
+
|
| 17 |
+
|
| 18 |
+
Figure 1: Codebook interleaving patterns presented in Section 2.2. Each time step $t _ { 1 } , t _ { 2 } , \ldots , t _ { n }$ is composed of 4 quantized values (corresponding to $k _ { 1 } , \ldots , k _ { 4 } )$ . When doing autoregressive modelling, we can flatten or interleave them in various ways, resulting in a new sequence with 4 parallel streams and steps $s _ { 1 } , s _ { 2 } , \ldots , s _ { m }$ . The total number of sequence steps $S$ depends on the pattern and original number of steps $T , 0$ is a special token indicating empty positions in the pattern.
|
| 19 |
+
|
| 20 |
+
In this work, we introduce MUSICGEN, a simple and controllable music generation model, which is able to generate high-quality music given textual description. We propose a general framework for modeling multiple parallel streams of acoustic tokens, which serves as a generalization of previous studies (see Figure 1). We show how this framework allows to extend generation to stereo audio at no extra computational cost. To improve controllability of the generated samples, we additionally introduce unsupervised melody conditioning, which allows the model to generate music that matches a given harmonic and melodic structure. We conduct an extensive evaluation of MUSICGEN and show the proposed method is superior to the evaluated baselines by a large margin, with a subjective rating of 84.8 out of 100 for MUSICGEN against 80.5 for the best baseline. We additionally provide an ablation study which sheds light on the importance of each of the components on the overall model performance. Lastly, human evaluation suggests that MUSICGEN yields high quality samples which are better melodically aligned with a given harmonic structure, while adhering to a textual description.
|
| 21 |
+
|
| 22 |
+
Our contribution: (i) We introduce a simple and efficient model to generate high quality music at $3 2 \mathrm { k H z }$ . We show that MUSICGEN can generate consistent music with a single-stage language model through an efficient codebook interleaving strategy. (ii) We present a single model to perform both text and melody-conditioned generation and demonstrate that the generated audio is coherent with the provided melody and faithful to the text conditioning information. (iii) We provide extensive objective and human evaluations on the key design choices behind our method.
|
| 23 |
+
|
| 24 |
+
# 2 Method
|
| 25 |
+
|
| 26 |
+
MUSICGEN consists in an autoregressive transformer-based decoder [Vaswani et al., 2017], conditioned on a text or melody representation. The (language) model is over the quantized units from an EnCodec [Défossez et al., 2022] audio tokenizer, which provides high fidelity reconstruction from a low frame rate discrete representation. Compression models such as [Défossez et al., 2022, Zeghidour et al., 2021] employ Residual Vector Quantization (RVQ) which results in several parallel streams. Under this setting, each stream is comprised of discrete tokens originating from different learned codebooks. Prior work, proposed several modeling strategies to handle this issue [Kharitonov et al., 2022, Agostinelli et al., 2023, Wang et al., 2023]. In this work, we introduce a novel modeling framework, which generalizes to various codebook interleaving patterns, and we explore several
|
| 27 |
+
|
| 28 |
+
variants. Through patterns, we can leverage the internal structure of the quantized audio tokens.
|
| 29 |
+
Finally, MUSICGEN supports conditional generation based on either text or melody.
|
| 30 |
+
|
| 31 |
+
# 2.1 Audio tokenization
|
| 32 |
+
|
| 33 |
+
We use EnCodec [Défossez et al., 2022], a convolutional auto-encoder with a latent space quantized using Residual Vector Quantization (RVQ) [Zeghidour et al., 2021], and an adversarial reconstruction loss. Given a reference audio random variable $\breve { X } \in \mathbb { R } ^ { d \cdot f _ { s } }$ with $d$ the audio duration and $f _ { s }$ the sample rate, EnCodec encodes it into a continuous tensor with a frame rate $f _ { r } \ll f _ { s }$ . This representation is then quantized into $Q \in \{ 1 , \dots , M \} ^ { d \cdot f _ { r } \times K }$ , with $K$ being the number of codebooks used in RVQ and $M$ being the codebook size. Notice, after quantization we are left with $K$ parallel discrete tokens sequences, each of length $T = d \cdot f _ { r }$ , representing the audio sample. In RVQ, each quantizer encodes the quantization error left by the previous quantizer, thus quantized values for different codebooks are in general not independent, and the first codebook is the most important one.
|
| 34 |
+
|
| 35 |
+
# 2.2 Codebook interleaving patterns (see Figure 1)
|
| 36 |
+
|
| 37 |
+
Exact flattened autoregressive decomposition. An autoregressive model requires a discrete random sequence $U \in \{ 1 , \dotsc , \bar { M } \} ^ { S }$ with $S$ the sequence length. By convention, we will take $U _ { 0 } = 0$ , a deterministic special token indicating the beginning of the sequence. We can then model the distribution
|
| 38 |
+
|
| 39 |
+
$$
|
| 40 |
+
\forall t > 0 , p _ { t } ( U _ { t - 1 } , \ldots , U _ { 0 } ) \triangleq \mathbb { P } \left[ U _ { t } | U _ { t - 1 } , \ldots , U _ { 0 } \right] .
|
| 41 |
+
$$
|
| 42 |
+
|
| 43 |
+
Let us build a second sequence of random variables $\tilde { U }$ using the auto-regressive density $p$ , e.g. we define recursively $\tilde { U } _ { 0 } = \bar { 0 }$ , and for all $t > 0$ ,
|
| 44 |
+
|
| 45 |
+
$$
|
| 46 |
+
\forall t > 0 , \mathbb { P } \left[ \tilde { U } _ { t } | \tilde { U } _ { t - 1 } \dots , \tilde { U } _ { 0 } \right] = p _ { t } \left( \tilde { U } _ { t - 1 } , \dots , \tilde { U } _ { 0 } \right) .
|
| 47 |
+
$$
|
| 48 |
+
|
| 49 |
+
Then, we immediately have that $U$ and $\tilde { U }$ follow the same distribution. This means that if we can fit a perfect estimate $\hat { p }$ of $p$ with a deep learning model, then we can fit exactly the distribution of $U$ .
|
| 50 |
+
|
| 51 |
+
As stated before, the main issue with the representation $Q$ we obtained from the EnCodec model is that there are $K$ codebooks for each time step. One solution would be to flatten out $Q$ , thus taking $S = d \cdot f _ { r } \cdot K$ , e.g. first predicting the first codebook of the first time step, then the second codebook of the first time step, etc. Then, using eq. (1) and eq. (2), we could theoretically fit an exact model of the distribution of $Q$ . The downside however is the increased complexity, with part of the gain coming from the lowest sample rate $f _ { r }$ being lost.
|
| 52 |
+
|
| 53 |
+
More than one possible flattening exists, and not all the $\hat { p } _ { t }$ functions need to be estimated through a single model. For instance, MusicLM [Agostinelli et al., 2023] uses two models, one modeling the flattened first $K / 2$ codebooks, and a second one the other $K / 2$ flattened codebooks, conditioned on the decision of the first model. In that case, the number of autoregressive steps is still $d f _ { r } \cdot K$ .
|
| 54 |
+
|
| 55 |
+
Inexact autoregressive decomposition. Another possibility is to consider an autoregressive decomposition, where some codebooks are predicted in parallel. For instance, let us define another sequence with $V _ { 0 } = 0$ and for all $t \in \{ 1 , \ldots , T \}$ , $k \in \{ 1 , \ldots , K \}$ , $V _ { t , k } = Q _ { t , k }$ . When dropping the codebook index $k$ , e.g. $V _ { t }$ , we mean the concatenation of all the codebooks at time $t$ .
|
| 56 |
+
|
| 57 |
+
$$
|
| 58 |
+
p _ { t , k } \left( V _ { t - 1 } , \ldots , V _ { 0 } \right) \triangleq \mathbb { P } \left[ V _ { t , k } | V _ { t - 1 } , \cdot , \ldots , V _ { 0 } \right] .
|
| 59 |
+
$$
|
| 60 |
+
|
| 61 |
+
Let’s define again recursively $\tilde { V } _ { 0 } = 0$ and for all $t > 0$ ,
|
| 62 |
+
|
| 63 |
+
$$
|
| 64 |
+
\forall t > 0 , \forall k , \mathbb { P } \left[ \tilde { V } _ { t , k } \right] = p _ { t , k } \left( \tilde { V } _ { t - 1 } , \ldots , \tilde { V } _ { 0 } \right) .
|
| 65 |
+
$$
|
| 66 |
+
|
| 67 |
+
Unlike in (2), we no longer have in the general case that $\tilde { V }$ follows the same distribution as $V$ , even assuming we have access to the exact distribution $_ { p _ { t , k } }$ . In fact, we would only have a proper generative model if for all $t$ , $( V _ { t , k } ) _ { k }$ are independent conditionally on $V _ { t - 1 } , \ldots , V _ { 0 }$ . As $t$ increases, the errors will compound and the two distributions can grow further apart. Such a decomposition is inexact, but allows to keep the original frame rate which can considerably speed up training and inference, especially for long sequences.
|
| 68 |
+
|
| 69 |
+
Arbitrary codebook interleaving patterns. In order to experiment with various such decompositions, and measure exactly the impact of using an inexact decomposition, we introduce codebook interleaving patterns. Let us consider $\Omega = \{ ( t , \bar { k } ) : \{ 1 , \dots , d \cdot f _ { r } \} , k \in \{ 1 , \dots , K \} \}$ be the set of all pairs of time steps and codebook indexes. A codebook pattern is a sequence $P = ( P _ { 0 } , P _ { 1 } , P _ { 2 } , . . . , P _ { S } )$ , with $P _ { 0 } = \emptyset$ , and for all $0 < s \le S$ , $P _ { s } \subset \Omega$ , such that $P$ is partition of $\Omega$ . We model $Q$ by predicting in parallel all the positions in $P _ { s }$ , conditionally on all the positions in $P _ { 0 } , P _ { 1 } , \dots , P _ { s - 1 }$ . Pragmatically, we restrict ourselves to patterns where each codebook index appears at most once in any of the $P _ { s }$ .
|
| 70 |
+
|
| 71 |
+
We can now easily define a number of decompositions, for instance the “parallel” pattern given by
|
| 72 |
+
|
| 73 |
+
$$
|
| 74 |
+
P _ { s } = \{ ( s , k ) : k \in \{ 1 , \ldots , K \} \} .
|
| 75 |
+
$$
|
| 76 |
+
|
| 77 |
+
It is also possible to introduce a “delay” between the codebooks, as in Kharitonov et al. [2022], e.g.,
|
| 78 |
+
|
| 79 |
+
$$
|
| 80 |
+
P _ { s } = \{ ( s - k + 1 , k ) : k \in \{ 1 , \ldots , K \} , s - k \geq 0 \} .
|
| 81 |
+
$$
|
| 82 |
+
|
| 83 |
+
Through empirical evaluations, we show the benefits and drawbacks of various codebook patterns, shedding light on the importance of exact modeling of the parallel codebook sequences.
|
| 84 |
+
|
| 85 |
+
# 2.3 Model conditioning
|
| 86 |
+
|
| 87 |
+
Text conditioning. Given a textual description matching the input audio $X$ , we compute a conditioning tensor $\check { C } \in \mathbb { R } ^ { T _ { C } \times D }$ with $D$ being the inner dimension used in the autoregressive model. Generally, there are three main approaches for representing text for conditional audio generation. Kreuk et al. [2022] proposed using a pretrained text encoder, specifically T5 [Raffel et al., 2020]. Chung et al. [2022] show that using instruct-based language models provide superior performance. Lastly, Agostinelli et al. [2023], Liu et al. [2023], Huang et al. [2023a], Sheffer and Adi [2023] claimed that joint text-audio representation, such as CLAP $\mathrm { [ W u ^ { * } }$ et al., 2023], provides better-quality generations. We experiment with all of the above, respectively: T5 encoder, FLAN-T5, and CLAP.
|
| 88 |
+
|
| 89 |
+
Melody conditioning. While text is the prominent approach in conditional generative models nowadays, a more natural approach for music is conditioning on a melodic structure from another audio track or even whistling or humming. Such an approach also allows for an iterative refinement of the model’s output. To support that, we experiment with controlling the melodic structure via jointly conditioning on the input’s chromagram and text description. In preliminary experiments, we observed that conditioning on the raw chromagram often led to reconstructing the original sample, resulting in overfitting. To reduce it, we introduce an information bottleneck by choosing the dominant time-frequency bin in each time step. While a similar capability was shown in Agostinelli et al. [2023], the authors used supervised proprietary data, which is tedious and costly to collect. In this work, we take an unsupervised approach, eliminating the requirement for supervised data.
|
| 90 |
+
|
| 91 |
+
# 2.4 Model architecture
|
| 92 |
+
|
| 93 |
+
Codebook projection and positional embedding. Given a codebook pattern, only some codebooks are present at each pattern step $P _ { s }$ . We retrieve from $Q$ the values corresponding to the indices in $P _ { s }$ . As noted in Section 2.2, each codebook is present at most once in $P _ { s }$ or not at all. If it is present, we use a learned embedding table with $N$ entries and dimension $D$ to represent the associated value from $Q$ . Otherwise, we use a special token indicating its absence. We sum the contribution from each codebook after this transformation. As $P _ { 0 } = \emptyset$ , the first input is always the sum of all the special tokens. Finally, we sum a sinusoidal embedding to encode the current step $s$ [Vaswani et al., 2017].
|
| 94 |
+
|
| 95 |
+
Transformer decoder. The input is fed into a transformer with $L$ layers and a dimension $D$ . Each layer consists of a causal self-attention block. We then use a cross-attention block that is fed with the conditioning signal $C$ . When using melody conditioning, we instead provide the conditioning tensor $C$ as a prefix to the transformer input. The layer ends with a fully connected block consisting of a linear layer from $D$ to $4 \cdot D$ channels, a ReLU, and a linear layer back to $D$ channels. The attention and fully connected blocks are wrapped with a residual skip connection. Layer normalization [Ba et al., 2016] is applied to each block before being summed with the residual skip connection (“pre-norm”).
|
| 96 |
+
|
| 97 |
+
Logits prediction. The output from the transformer decoder at pattern step $P _ { s }$ is transformed into logits prediction for the values of $Q$ taken at the indices given by $P _ { s + 1 }$ . Each codebook is present at most once in $P _ { s + 1 }$ . If a codebook is present, the logits prediction is obtained by applying a codebook specific linear layer from $D$ channels to $N$ .
|
| 98 |
+
|
| 99 |
+
# 3 Experimental setup
|
| 100 |
+
|
| 101 |
+
# 3.1 Models and hyperparameters
|
| 102 |
+
|
| 103 |
+
Audio tokenization model. We use a non-causal five layers EnCodec model for $3 2 \mathrm { k H z }$ monophonic audio with a stride of 640, resulting in a frame rate of $5 0 \mathrm { H z }$ , and an initial hidden size of 64, doubling at each of the model’s five layers. The embeddings are quantized with a RVQ with four quantizers, each with a codebook size of 2048. We follow Défossez et al. [2022] to train the model on one-second audio segments cropped at random in the audio sequence.
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Transformer model. We train autoregressive transformer models at different sizes: 300M, 1.5B, 3.3B parameters. We use a memory efficient Flash attention [Dao et al., 2022] from the xFormers package [Lefaudeux et al., 2022] to improve both speed and memory usage with long sequences. We study the impact of the size of the model in Section 4. We use the 300M-parameter model for all of our ablations. We train on 30-second audio crops sampled at random from the full track. We train the models for 1M steps with the AdamW optimizer [Loshchilov and Hutter, 2017], a batch size of 192 examples, $\beta _ { 1 } = 0 . 9$ , $\beta _ { 2 } = 0 . 9 5$ , a decoupled weight decay of 0.1 and gradient clipping of 1.0. We further rely on D-Adaptation based automatic step-sizes [Defazio and Mishchenko, 2023] for the 300M model as it improves model convergence but showed no gain for the bigger models. We use a cosine learning rate schedule with a warmup of 4000 steps. Additionally, we use an exponential moving average with a decay of 0.99. We train the 300M, 1.5B and 3.3B parameter models, using respectively 32, 64 and 96 GPUs, with mixed precision. More specifically, we use float16 as bfloat16 was leading to instabilities in our setup. Finally, for sampling, we employ top- $\mathbf { \nabla } \cdot \mathbf { k }$ sampling [Fan et al., 2018] with keeping the top 250 tokens and a temperature of 1.0.
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Text preprocessing. Kreuk et al. [2022] proposed a text normalization scheme, in which stop words are omitted and the remaining text is lemmatized. We denote this method by text-normalization. When considering musical datasets, additional annotations tags such as musical key, tempo, type of instruments, etc. are often available. We also experiment with concatenating such annotations to the text description. We denote this approach by condition-merging. Finally, we explored using word dropout as another text augmentation strategy. For the final models, we used condition-merging with a probability of 0.25. Upon merging, we apply a text description dropout with a probability of 0.5. We use a word dropout with a probability of 0.3 on the resulting text. A full comparison of the different text preprocessing strategies can be found in Appendix A.2.
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Codebook patterns and conditioning. We use the “delay” interleaving pattern from Section 2.2, This translates 30 seconds of audio into 1500 autoregressive steps. For text conditioning, we use the T5 [Raffel et al., 2020] text encoder, optionally with the addition of the melody conditioning presented in Section 2.3. We also experiment with FLAN-T5 [Chung et al., 2022], and CLAP $\mathrm { [ W u ^ { * } }$ et al., 2023] and compare the performance of MUSICGEN using each of these text encoders in the Appendix A.2. For melody conditioning, we compute the chromagrams with a window size of $2 ^ { 1 4 }$ and a hop size of $2 ^ { 1 2 }$ . Using a large window prevents the model from recovering fine temporal details. We further quantize the chromagram by taking the argmax at each time step. We follow a similar approach to Kreuk et al. [2022] and implement classifier-free guidance when sampling from the model’s logits. Specifically, during training we drop the condition with a probability of 0.2 and during inference we use a guidance scale of 3.0.
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# 3.2 Datasets
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Training datasets. We use 20K hours of licensed music to train MUSICGEN. Specifically, we rely on an internal dataset of 10K high-quality music tracks, and on the ShutterStock and Pond5 music data collections2 with respectively 25K and 365K instrument-only music tracks. All datasets consist of full-length music sampled at $3 2 \mathrm { k H z }$ with metadata composed of a textual description and information such as the genre, BPM, and tags. We downmix the audio to mono unless stated otherwise.
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Evaluation datasets. For the main results and comparison with prior work, we evaluate the proposed method on the MusicCaps benchmark [Agostinelli et al., 2023]. MusicCaps is composed of 5.5K samples (ten-second long) prepared by expert musicians and a 1K subset balanced across genres. We report objective metrics on the unbalanced set, while we sample examples from the genre-balanced set for qualitative evaluations. For melody evaluation and the ablation studies, we use samples from an in-domain held out evaluation set of 528 music tracks, with no artist overlap with the training set.
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Table 1: Text-to-Music generation. We compare objective and subjective metrics for MUSICGEN against a number of baselines. We report both mean and CI95 scores. The Mousai model is retrained on the same dataset, while for MusicLM we use the public API for human studies. We report the original FAD on MusicCaps for Noise2Music and MusicLM. “MUSICGEN w. random melody” refers to MUSICGEN trained with chromagram and text. At evaluation time, we sample the chromagrams at random from a held-out set.
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<table><tr><td rowspan="2">MODEL</td><td colspan="5">MUSICCAPS Test Set</td></tr><tr><td>FADugg</td><td>KL↓</td><td>CLAPscr↑</td><td>OvL. ↑</td><td>REL.个</td></tr><tr><td>Riffusion</td><td>14.8</td><td>2.06</td><td>0.19</td><td>79.31±1.37</td><td>74.20±2.17</td></tr><tr><td>Mousai</td><td>7.5</td><td>1.59</td><td>0.23</td><td>76.11±1.56</td><td>77.35±1.72</td></tr><tr><td>MusicLM</td><td>4.0</td><td>1</td><td>1</td><td>80.51±1.07</td><td>82.35±1.36</td></tr><tr><td>Noise2Music</td><td>2.1</td><td>1</td><td>1</td><td>1</td><td>1</td></tr><tr><td>MUSICGEN w.o melody (300M)</td><td>3.1</td><td>1.28</td><td>0.31</td><td>78.43±1.30</td><td>81.11±1.31</td></tr><tr><td>MUSICGEN w.o melody (1.5B)</td><td>3.4</td><td>1.23</td><td>0.32</td><td>80.74±1.17</td><td>83.70±1.21</td></tr><tr><td>MUSICGEN w.o melody (3.3B)</td><td>3.8</td><td>1.22</td><td>0.31</td><td>84.81±0.95</td><td>82.47±1.25</td></tr><tr><td>MUSICGEN w. random melody (1.5B)</td><td>5.0</td><td>1.31</td><td>0.28</td><td>81.30±1.29</td><td>81.98±1.79</td></tr></table>
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# 3.3 Evaluation
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Baselines. We compare MUSICGEN to two baselines for text-to-music generation: Riffusion [Forsgren and Martiros] and Mousai [Schneider et al., 2023]. We use the open source Riffusion model to run inference 3. For Mousai, we train a model using our dataset for a fair comparison, using the open source implementation provided by the authors4. Additionally, when possible, we compare to MusicLM [Agostinelli et al., 2023] and Noise2Music [Huang et al., 2023b].
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Evaluation metrics. We evaluate the proposed method using objective and subjective metrics. For the objective methods, we use three metrics: the Fréchet Audio Distance (FAD), the Kullback-Leiber Divergence (KL) and the CLAP score (CLAP). We report the FAD [Kilgour et al., 2018] using the official implementation in Tensorflow with the VGGish model 5. A low FAD score indicates the generated audio is plausible. Following Kreuk et al. [2022], we use a state-of-the-art audio classifier trained for classification on AudioSet [Koutini et al., 2021] to compute the KL-divergence over the probabilities of the labels between the original and the generated music. The generated music is expected to share similar concepts with the reference music when the KL is low. Last, the CLAP score $[ \mathrm { W u ^ { * } }$ et al., 2023, Huang et al., 2023a] is computed between the track description and the generated audio to quantify audio-text alignment, using the official pretrained CLAP model 6.
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For the human studies, we follow the same setup as in Kreuk et al. [2022]. We ask human raters to evaluate two aspects of the audio samples (i) overall quality (OVL), and (ii) relevance to the text input (REL). For the overall quality test, raters were asked to rate the perceptual quality of the provided samples in a range of 1 to 100. For the text relevance test, raters were asked to rate the match between audio and text on a scale of 1 to 100. Raters were recruited using the Amazon Mechanical Turk platform. We evaluate randomly sampled files, where each sample was evaluated by at least 5 raters. We use the CrowdMOS package7 to filter noisy annotations and outliers. We remove annotators who did not listen to the full recordings, annotators who rate the reference recordings less than 85, and the rest of the recommended recipes from CrowdMOS [Ribeiro et al., 2011]. For fairness, all samples are normalized at −14dB LUFS [ITU-R, 2017].
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Table 2: We report cosine similarity between reference and generated melody (SIM.) and subjective metrics including alignment with the melody (MEL.). All results are reported for MUSICGEN 1.5B.
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<table><tr><td colspan="3"></td><td colspan="3">In Domain Test Set</td></tr><tr><td>TRAIN CONDITION</td><td>TEST CONDITION</td><td>SIM.↑|</td><td>MEL.个</td><td>OvL. ↑</td><td>REL.个</td></tr><tr><td>Text</td><td>Text</td><td>0.10</td><td>64.44±0.83</td><td>82.18±1.21</td><td>81.54±1.22</td></tr><tr><td>Text+Chroma</td><td>Text</td><td>0.10</td><td>61.89±0.96</td><td>81.65±1.13</td><td>82.50±0.98</td></tr><tr><td>Text+Chroma</td><td>Text+Chroma</td><td>0.66</td><td>72.87±0.93</td><td>83.94±1.99</td><td>80.28±1.06</td></tr></table>
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# 4 Results
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We start by presenting results of the proposed method on the task of text-to-music generation and compare MUSICGEN to prior work in the field. Next, we evaluate the ability of the proposed method to generate music conditioned on melodic features. We further show how to simply extend our codebook patterns for stereo audio generation. We conclude with an ablation study. Music samples, code, and models are available at github.com/facebookresearch/audiocraft.
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# 4.1 Comparison with the baselines
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Table 1 presents the comparison of the proposed method against Mousai, Riffusion, MusicLM, and Noise2Music. As there is no official implementation of Noise2Music, nor pre-trained model, we report only FAD on MusicCaps, which is reported in the Noise2Music manuscript. Similarly, MusicLM implementation is not public. We use the MusicLM public demo8 for our subjective tests while reporting the FAD as reported by the authors. While the original MusicLM model is trained on data with vocals, the model behind the API is instrument-only. For the human study, we restrict ourselves to 40 instrument-only samples from MusicCaps. To prevent leakage in MUSICGEN trained with chromagram, we sample chromagrams at random from a held-out set during test time.
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Results suggest that MUSICGEN performs better than the evaluated baselines as evaluated by human listeners, both in terms of audio quality and adherence to the provided text description. Noise2Music performs the best in terms of FAD on MusicCaps, followed by MUSICGEN trained with text conditioning. Interestingly, adding a melody conditioning degrades the objective metrics, however, it does not significantly affect human ratings, while still being superior to the evaluated baselines.
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We notice that for the worst rated model, the FAD is correlated with the overall subjective rating, but it is not the case for the best rated models. We noticed that a large number of samples in MusicCaps [Agostinelli et al., 2023] contains a description stating that the recording is "noisy". It is possible that due to those noisy samples, improvements in the quality of the generated audio might deteriorate the FAD on MusicCaps once a certain quality threshold is achieved.
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# 4.2 Melody evaluation
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We evaluate MUSICGEN, conditioned jointly on textual and melodic representations, using objective and subjective metric on the held out evaluation set. For the objective evaluation, we introduce a new metric: chroma cosine-similarity, which measures the average cosine-similarity between frames corresponding to the same time steps, taken from the quantized chroma of the reference and the generated samples. We evaluate using 1000 randomly sampled files from a held-out set. To better evaluate the relation between the conditioned melody to the generated music, we introduce another human study. To that end, we present human raters with a reference musical piece, followed by a set of generated pieces. For each generated sample, the listeners are asked to rate how well the melody of the generated piece matches that of the reference on a scale of 1 to 100. We use 40 samples of 10 seconds at random from the held-out set. Results are reported in Table 2. Results suggest that MUSICGEN trained with chromagram conditioning successfully generates music that follows a given melody. Thus, allowing for better control over the generated output. Interestingly, MUSICGEN is robust to dropping the chroma at inference time with both OVL. and REL. staying roughly the same.
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(a) Visualizing codebook patterns for stereo models with two possible interleaving of the left (blue) and right (red) codebooks. For a given codebook index, the “stereo delay” pattern uses different delays for the left and right channels, while the “stereo partial delay” predicts the two channels in parallel.
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(b) Memorization results for the first codebook tokens on 5-second audio generations, considering exact (solid line) and $80 \%$ partial (dashed line) matches when prompted with extracts of varying duration from the train set.
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Figure 2: Stereo codebooks (left) and memorization results (right)
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Table 3: Stereophonic Text-to-Music generation. EnCodec processes separately the left and right channels, giving us 8 codebooks instead of 4. We experiment with two codebook patterns, depicted in Figure 2a. We also measure one of the stereo model after being downmixed to mono. We use a 1.5B MUSICGEN model conditioned only on text.
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<table><tr><td rowspan="2">CB.PATTERN STEREO?</td><td rowspan="2"></td><td colspan="2">MUSICCAPS Test Set</td></tr><tr><td>OvL. ↑</td><td>REL. 个</td></tr><tr><td>Mono Delay</td><td>X</td><td>84.95±1.60</td><td>80.61±1.22</td></tr><tr><td>Stereo Partial Delay</td><td>X*</td><td>84.49±1.80</td><td>79.39±1.16</td></tr><tr><td>Stereo Partial Delay</td><td>√</td><td>86.73±1.06</td><td>80.41±1.15</td></tr><tr><td>Stereo Delay</td><td>√</td><td>85.51±1.21</td><td>78.32 ±1.21</td></tr></table>
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\*: downmixed to mono after generation.
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# 4.3 Fine-tuning for stereophonic generation
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We experiment with for extending generation to stereophonic data. We use the same EnCodec tokenizer, which we applied independently to the left and right channels, providing $2 \cdot K = 8$ codebooks per frame. Starting from a pre-trained monophonic MUSICGEN model, we fine tune it for 200K batches the same dataset with stereo audio. We reuse the “delay” pattern, with two possible variations: (i) “stereo delay” introduces a delay between the left and right channels for the same codebook level, while (ii) “stereo partial delay” apply the same delay to the left and right channel codebooks for a given level, as depicted in Figure 2a. Note that using this simple strategy, we can generate stereo audio at no extra computational cost. We provide in Table 3 the subjective evaluations for those models. We notice that when downmixing the stereo output to mono, we are almost equivalent in perceived quality to a mono model. Stereo audio was overall rated higher than the mono counterpart, and the “stereo partial delay” benefits from a small boost both in overall quality and text relevance compared with the “stereo delay” pattern.
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# 4.4 Ablation
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This section provides an ablation study for the different codebook patterns, together with results for model scales and a memorization study. Additionally, we present results for different text augmentation strategies, text encoders, and audio tokenization models in Appendix A.2. All ablations are performed using 1K samples of 30 seconds, randomly sampled from the held-out evaluation set.
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The effect of the codebook interleaving patterns. We evaluate various codebook patterns using the framework from Section 2.2, with $K = 4$ , given by the audio tokenization model. Table 1 reports results with the “delay” pattern. The “partial delay” consists in delaying by the same amount the codebooks 2, 3, and 4. The “parallel” pattern predicts all the codebooks from the same time step in parallel. The “coarse first” pattern first predicts codebook 1 for all steps, then predicts in parallel codebooks 2, 3, and 4. Thus, this pattern has twice the steps compared to other patterns. “Partial flattening” is similar, but instead of sampling first codebook 1 for all steps, it interleaves them with the parallel sampling of codebooks 2, 3, and 4. Finally, the “flattening” pattern consists in flattening all the codebooks, similar to MusicLM [Agostinelli et al., 2023]. We report objective and subjective evaluations in Table 4. While flattening improves generation, it comes at a high computational cost and similar performance can be reached for a fraction of this cost using a simple delay approach.
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Table 4: Codebook patterns. We compare different codebook interleaving patterns on 30-seconds, audio sequences. The “flattening” pattern achieves the best scores. The “delay” and “partial flattening” patterns achieve similar scores, while “parallel” obtains worse scores.
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<table><tr><td></td><td></td><td colspan="5">In Domain Test Set</td></tr><tr><td>CONFIGURATION丨Nb. steps</td><td></td><td>FADvgg</td><td>KL↓</td><td>CLAPscr↑|</td><td>OvL.↑</td><td>REL.个</td></tr><tr><td>Delay</td><td>1500</td><td>0.96</td><td>0.52</td><td>0.35</td><td>79.69±1.46</td><td>79.67±1.41</td></tr><tr><td>Partial delay</td><td>1500</td><td>1.51</td><td>0.54</td><td>0.32</td><td>79.13±1.56</td><td>79.67±1.46</td></tr><tr><td>Parallel</td><td>1500</td><td>2.58</td><td>0.62</td><td>0.27</td><td>72.21±2.49</td><td>80.30±1.43</td></tr><tr><td>Partial flattening</td><td>3000</td><td>1.32</td><td>0.54</td><td>0.34</td><td>78.56±1.86</td><td>79.18±1.49</td></tr><tr><td>Coarse first</td><td>3000</td><td>1.98</td><td>0.56</td><td>0.30</td><td>74.42±2.28</td><td>76.55±1.67</td></tr><tr><td>Flattening</td><td>6000</td><td>0.86</td><td>0.51</td><td>0.37</td><td>79.71±1.58</td><td>82.03±1.1</td></tr></table>
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Table 5: Model scale. We compare 3 scales for our method, and evaluate it on an internal test set to limit the impact of the out of domain prediction issues we observed with MusicCaps. In terms of objective metrics we observe a continuous improvement of the metrics, although subjective quality stop improving at 1.5B parameters. A 3.3B model however seems to better fit the text prompt.
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<table><tr><td colspan="8"></td><td></td><td></td></tr><tr><td>Dim.</td><td>Heads</td><td>Depth</td><td>#Param.</td><td>PPL↓</td><td>FADvgg</td><td>KL↓</td><td>CLAPscr 个</td><td>OvL. ↑</td><td>REL.个</td></tr><tr><td>1024</td><td>16</td><td>24</td><td>300M</td><td>56.1</td><td>0.96</td><td>0.52</td><td>0.35</td><td>78.3±1.4</td><td>82.5 ±1.6</td></tr><tr><td>1536</td><td>24</td><td>48</td><td>1.5B</td><td>48.4</td><td>0.86</td><td>0.50</td><td>0.35</td><td>81.9±1.4</td><td>82.9±1.5</td></tr><tr><td>2048</td><td>32</td><td>48</td><td>3.3B</td><td>46.1</td><td>0.82</td><td>0.50</td><td>0.36</td><td>79.2±1.3</td><td>83.5±1.3</td></tr></table>
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The effect of model size. In Table 5 we report results for different model sizes, namely 300M, 1.5B, and 3.3B parameter models. As expected, scaling the model size results in better scores, however this comes at the expense of longer training and inference time. Regarding subjective evaluations, the overall quality is optimal at 1.5B, but a larger model can better understand the text prompt.
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Memorization experiment. Following [Agostinelli et al., 2023], we analyze the memorization abilities of MUSICGEN. We only consider the first stream of codebooks from MUSICGEN as it contains the coarser-grain information. We randomly select $N = 2 0$ , 000 examples from our training set and for each one we feed the model with a prompt of EnCodec codebooks corresponding to the original audio and the conditioning information. We generate a continuation of 250 audio tokens (5 second-long audio) using greedy decoding. We report exact matches as the fraction of examples for which the generated audio tokens and source audio tokens are identical over the whole sequence. In addition, we report partial matches as the fraction of the training examples for which the generated and source sequences have at least $8 0 \%$ of the audio tokens matching. We present the memorization results for the different model sizes when varying the length of the audio prompt in Figure 2b.
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# 5 Related work
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Audio representation. In recent years, the prominent approach is to represent the music signals in a compressed representation, discrete or continuous, and apply a generative model on top of it. Lakhotia et al. [2021] proposed quantizing speech representation using $\mathbf { k }$ -means to construct speech language models. Recently, Défossez et al. [2022], Zeghidour et al. [2021] proposed to apply a VQ-VAE directly on the raw waveform using residual vector quantization. Later, several studies used such representation for text-to-audio generation. Next, we discuss the recent research in audio generation.
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Music generation. Music generation has been long studied under various setups. Dong et al. [2018] proposed a GAN-based approach for symbolic music generation. Bassan et al. [2022] proposed an unsupervised segmentation for symbolic music which can be later used for generation. Ycart et al.
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[2017] proposed modeling polyphonic music modeling using recurrent neural networks. Ji et al.
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[2020] conducted a comprehensive survey therein for deep learning methods for music generation.
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Dhariwal et al. [2020] proposed representing music samples in multiple streams of discrete representations using a hierarchical VQ-VAE. Next, two sparse transformers applied over the sequences to generate music. Gan et al. [2020] proposed generating music for a given video, while predicting its midi notes. Recently, Agostinelli et al. [2023] proposed representing music using multiple streams of “semantic tokens” and “acoustic tokens”. Then, they applied a cascade of transformer decoders conditioned on a textual-music joint representation [Huang et al., 2022]. Donahue et al. [2023] followed a similar modeling approach, but for the task of singing-to-accompaniment generation.
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An alternative approach is using diffusion models. Schneider et al. [2023], Huang et al. [2023b], Maina [2023], Forsgren and Martiros proposed using a latent diffusion model for the task of text-to-music. Schneider et al. [2023] proposed using diffusion models for both audio encoder-decoder and latent generation. Huang et al. [2023b] proposed a cascade of diffusion model to generate audio and gradually increase its sampling rate. Forsgren and Martiros proposed fine-tuning Stable Diffusion Rombach et al. [2022] using spectrograms to generate five-second segments, then, using image-to-image mapping and latent interpolation to generate long sequences.
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Audio generation. Several studies were proposed for text-to-audio (environmental sounds) generation. Yang et al. [2022] proposed representing audio spectrograms using a VQ-VAE, then applying a discrete diffusion model conditioned on textual CLIP embeddings for the generation part [Radford et al., 2021]. Kreuk et al. [2022] proposed applying a transformer language model over discrete audio representation, obtained by quantizing directly time-domain signals using EnCodec [Défossez et al., 2022]. Sheffer and Adi [2023] followed a similar approach to Kreuk et al. [2022] for image-to-audio generation. Huang et al. [2023a], Liu et al. [2023] proposed using latent diffusion models for the task of text-to-audio, while extending it to various other tasks such as inpainting, image-to-audio, etc.
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# 6 Discussion
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We introduced MUSICGEN, a state-of-the-art single stage controllable music generation model that can be conditioned on text and melody. We demonstrated that simple codebook interleaving strategies can be used to achieve high quality generation, even in stereo, while reducing the number of autoregressive time steps compared to the flattening approach. We provided a comprehensive study of the impact of model sizes, conditioning methods, and text pre-processing techniques. We also introduced a simple chromagram-based conditioning for controlling the melody of the generated audio.
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Limitations Our simple generation method does not allow us to have fine-grained control over adherence of the generation to the conditioning, we rely mostly on CF guidance. Also, while it is relatively straightforward to do data augmentation for text conditioning, conditioning on audio warrants further research on data augmentation, types and amount of guidance.
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Broader impact. Large scale generative models present ethical challenges. We first ensured that all the data we trained on was covered by legal agreements with the right holders, in particular through an agreement with ShutterStock. A second aspect is the potential lack of diversity in the dataset we used, which contains a larger proportion of western-style music. However, we believe the simplification we operate in this work, e.g., using a single stage language model and a reduced number of auto-regressive steps, can help broaden the applications to new datasets. Generative models can represent an unfair competition for artists, which is an open problem. Open research can ensure that all actors have equal access to these models. Through the development of more advanced controls, such as the melody conditioning we introduced, we hope that such models can become useful both to music amateurs and professionals.
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# Acknowledgements.
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The authors would like to thank Mary Williamson, Rashel Moritz and Joelle Pineau for supporting this project, thank Justin Luk, Prash Jain, Sidd Srinivasan, Rod Duenes, and Philip Woods for the dataset, and thank the xformers team: Daniel Haziza, Francisco Massa, and Michael Ramamonjisoa for the technical discussions.
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Authors note. This paper was submitted in the wake of the tragic terror attack perpetrated by Hamas on October 7, 2023, which has left the Israeli nation profoundly devastated. The assault greatly impacted us at a personal level, thereby significantly impacting the course of this research work. This paper was finalized while we grieve and mourn our friends and family, under great stress, with scientific considerations being the last thing on our minds. It may contain subtle errors.
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In memory of the countless lives shattered by Hamas actions.
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Figure A.1: Visualizing partial flattening and partial delays codebook patterns applied on a sequence with 4 parallel streams of quantized values (corresponding to $k _ { 1 } , \ldots , k _ { 4 } )$ and $N$ time steps $( t _ { 1 } , \ldots$ $k _ { n , \astrosun }$ ). “Partial flattening” separates the first codebook in dedicated steps and interleaves them with the parallel sampling of codebooks 2, 3, and 4, leading the number of interleaved sequences steps $M$ to be twice the number of original steps $N$ . The “partial delay” pattern consists in delaying by the same amount the codebooks 2, 3, and 4, in our case we use a delay of 1. The total number of steps of the interleave sequences is $N$ (excluding the last step for simplicity).
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# A.1 Experimental details
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Codebook interleaving patterns. Figure A.1 provides a visual description of the additional codebook patterns introduced for the ablation in Section 4, namely “partial flattening” and “partial delay” patterns. The intuition behind such patterns is driven by the fact that the first codebook from RVQ is the most important one and predicting the rest of the codebooks in parallel would allow to limit the introduced flattening or delay while maintaining good modeling performance.
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Melody conditioning. In this work, we provide an unsupervised approach for melody conditioning through conditioning on the chromagram representation. As shown in Figure A.2, chromagram-based conditioning successfully preserves the melodic structure when generating novel music samples. In preliminary experiments, we noticed that the chromagram tends to be dominated by the lower frequency instruments, mainly by the drums and bass. To mitigate that, we used Demucs [Défossez et al., 2019] to first decompose the reference track into four components: drums, bass, vocals, and other. Next, we omit the drums and bass to recover the melodic structure of the residual waveform. Finally, we extract the quantized chromagram to create the conditioning that is later fed to the model.
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Distribution of genres. We provide in Figure A.3 a histogram of the top 50 musical genres present in the dataset. We notice a clear dominance of the Dance/EDM genre, which in our experience is also one of the genres that is best generated by MUSICGEN. While we tried to explore a number of resampling scheme to boost the importance of other genres, we observed that oversampling less represented genres would often lead to a worse model overall.
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# A.2 Additional experimental results
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We provide further ablation studies on the core components of MUSICGEN, namely the text encoder used for text conditioning described in Section 2.3, text augmentation strategies presented in Section 3.1, and the used audio tokenization model. We report results on the MusicCaps dataset to better understand out-of-domain generalization abilities of the different approaches. Finally, we share additional experimental results on optimization methods.
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The effect of text encoder. We investigate the impact of the text encoder, comparing three different encoders: T5 [Raffel et al., 2020] 9, Flan-T5 [Chung et al., $2 0 2 2 ] ^ { 1 0 }$ and CLAP $[ \mathrm { W u ^ { * } }$ et al., 2023] 11 with a quantization bottleneck. For the CLAP-based encoder, similarly to Agostinelli et al. [2023] we rely on the music embeddings during training and the text embeddings at inference time and we train a RVQ layer on top of the extracted embeddings. More specifically, we first normalize the embeddings and use RVQ with 12 quantizers, each with a codebook size of 1024. Quantizing the CLAP embeddings leads to a homogeneous representation with the discrete tokens further reducing the gap between the audio encoding used at train time and text encoding at test time. We report results for the different text encoders in Table A.1. Both T5 and Flan-T5 perform similarly in terms of objective metrics, the overall quality being slighly better for T5. The CLAP-based model however suffers worse objective and subjective metrics, with the exception of the CLAP score which rely on the same underlying audio and text encoder.
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Table A.1: Text encoder results. We report results for T5, Flan-T5, and CLAP as text encoders. We observe similar results for T5 and Flan-T5 on all the objective metrics. Note that T5 is the text encoder used for the main MUSICGEN models. CLAP encoder performs consistently worse on all the metrics but CLAP score. All comparisons are done with a 300M MUSICGEN model using text conditioning only.
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<table><tr><td rowspan="2">MODEL</td><td colspan="5">MUSICCAPS Test Set</td></tr><tr><td>FADugg</td><td>KL↓</td><td>CLAPscr 个</td><td>OvL. ↑</td><td>REL.↑</td></tr><tr><td>T5</td><td>3.12</td><td>1.29</td><td>0.31</td><td>85.04±1.23</td><td>87.33±1.9</td></tr><tr><td>Flan-T5</td><td>3.36</td><td>1.30</td><td>0.32</td><td>85.54±1.01</td><td>85.00±1.63</td></tr><tr><td>CLAP</td><td>4.16</td><td>1.36</td><td>0.35</td><td>82.13±1.29</td><td>83.56±1.54</td></tr><tr><td>CLAP (no normalization)</td><td>4.14</td><td>1.38</td><td>0.35</td><td>84.87±1.25</td><td>85.06±1.72</td></tr><tr><td>CLAP (no quantization)</td><td>5.07</td><td>1.37</td><td>0.37</td><td>84.13±1.02</td><td>84.67±1.42</td></tr></table>
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Table A.2: Text augmentations strategies results. We report objective metrics using only the original text description (no augmentation) and for different text augmentation strategies: using condition merging to augment the text description with metadata, using text-normalization (text-norm.) and applying word dropout on the resulting text. We use 300M MUSICGEN models trained for 500K steps. Condition merging improves the result over training only over the original text description. Other augmentations perform worst on all metrics. We use the Condition Merging with Word dropout, showing the best text relevance, in our main models.
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<table><tr><td rowspan="2">CONFIGURATION</td><td colspan="5">MUSICCAPs Test Set</td></tr><tr><td>FADugg√</td><td>KL↓</td><td>CLAPscr</td><td>OVL. ↑</td><td>REL.↑</td></tr><tr><td>No augmentation</td><td>3.68</td><td>1.28</td><td>0.31</td><td>83.40±1.44</td><td>81.16±1.29</td></tr><tr><td>Condition Merging (CM)</td><td>3.28</td><td>1.26</td><td>0.31</td><td>82.60±1.41</td><td>84.45 ±1.16</td></tr><tr><td>CM+ Text-norm. (TN)</td><td>3.78</td><td>1.30</td><td>0.29</td><td>80.57±2.14</td><td>82.40±1.09</td></tr><tr><td>CM+ Word dropout (WD)</td><td>3.31</td><td>1.31</td><td>0.30</td><td>82.52±1.55</td><td>85.27±0.97</td></tr><tr><td>CM + TN+ WD</td><td>3.41</td><td>1.39</td><td>0.30</td><td>81.18±1.91</td><td>84.32 ±1.59</td></tr></table>
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The effect of text augmentations. We examine the impact of text augmentation strategies for the proposed method. In particular, we study the use of condition merging (i.e. concatenating additional metadata to the text description), text normalization (text-norm.) and word dropout. We report objective metrics for the different augmentation strategies in Table A.2. We observe a gain in FAD and KL when leveraging the additional metadata with condition merging. However, neither text normalization or word dropout improves the results in terms of objective metrics.
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The effect of the audio tokenizer. We experiment with replacing EnCodec with Descript Audio Codec (DAC) [Kumar et al., $2 0 2 3 ] ^ { 1 2 }$ , a similar audio compression models, that uses a different training set, a similar adversarial loss enhanced with multiband discriminators, but performs quantization in a lower dimension space to improve codebook usage. DAC compresses audio at $4 4 . 1 \mathrm { k H z }$ with 9 codebooks, and a framerate of $8 6 \mathrm { H z }$ . We trained a small (300M parameters) and a medium (1.5B parameters) MUSICGEN model using both DAC and EnCodec as an audio tokenizer, on a vocal-free version of our dataset. The results provided in Table A.3 show a worse FAD and KL on our in domain test set. On MusicCaps, the FAD is improved by using DAC, although the KL is worse, as well as the subjective evaluations. The EnCodec model used in this work was specifically designed to operate at a lower frame rate $( 5 0 \ : \mathrm { H z } )$ than DAC $( 8 6 ~ \mathrm { H z } )$ ), thus reducing by $40 \%$ the inference runtime for producing the same audio. Note finally that DAC was trained on a different dataset than EnCodec, and further experiments would be required to understand exactly what influences the fitness of such compression models to be used with auto-regressive language models.
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Table A.3: We test replacing EnCodec with DAC [Kumar et al., 2023] using their implementation. DAC is a $4 4 . 1 \mathrm { k H z }$ model with 9 codebooks and a frame rate of $8 6 \mathrm { H z }$ . Those models are trained on a vocal-free version of our dataset, hence the objective metrics will not match those reported in the other tables. We report objective metrics both on our in domain test set and MusicCaps [Agostinelli et al., 2023], and subjective metrics only on MusicCaps.
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<table><tr><td rowspan="2">MODEL</td><td colspan="2">In Domain Test Set</td><td colspan="3">MUSICCAPS Test Set</td></tr><tr><td>FADvgg↓</td><td>KL←</td><td>FADvgg</td><td>KL↓</td><td>OvL.↑</td></tr><tr><td>MUSICGEN + DAC small</td><td>3.45</td><td>0.58</td><td>4.46</td><td>1.35</td><td>83.32±0.95</td></tr><tr><td>MUSICGEN + DAC medium</td><td>2.42</td><td>0.57</td><td>4.32</td><td>1.30</td><td>84.46±0.97</td></tr><tr><td>MUSICGEN + EnCodec small</td><td>0.67</td><td>0.54</td><td>5.26</td><td>1.27</td><td>84.69±0.90</td></tr><tr><td>MUSICGEN + EnCodec medium</td><td>0.49</td><td>0.52</td><td>5.05</td><td>1.23</td><td>86.09±0.88</td></tr></table>
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# Effect of D-Adaptation.
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D-Adaptation is a novel automated way of selecting the overall learning rate of the Adam optimizer, i.e. its $\alpha$ parameter, dynamically throughout the training, introduced by Defazio and Mishchenko [2023]. We observed improved convergence for the 300M parameter model, although for larger models, e.g. 1.5B and 3.3B, we observed the automated rule led to deteriorated performance, both on the train and validation set. Further investigation is required to better understand the effect of D-Adaptation, and whether it can scale to the largest model. The convergence for both methods can be observed on the train and validation set in Figure A.4.
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Figure A.2: Visualization of quantized chromagram bins over time from reference melody (left), generated music conditioned on chroma and text (middle) and generated music with text-only conditioning (right). Each row is generated using a different chroma condition, all rows share the same text condition: “90s rock song with electric guitar and heavy drums”. We observe strong adherence to the input melody for the music samples generated with chroma conditioning while rendering novel styles guided by the input text.
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Figure A.3: Histogram of the top 50 musical genres in the training dataset.
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Figure A.4: Comparison of Adam and Adam with D-Adaptation [Defazio and Mishchenko, 2023]. While D-Adaptation provided consistent gains for the 300M parameters model, we observed worse convergence both on the train (left) and validation (right) set for the 1.5B parameters model.
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| 1 |
+
# DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining
|
| 2 |
+
|
| 3 |
+
Sang Michael Xie1,2, Hieu Pham1, Xuanyi $\mathbf { D o n g } ^ { 1 }$ , $\mathbf { N a n D u } ^ { 1 }$ , Hanxiao Liu1, Yifeng ${ { \bf { L } } { \bf { u } } ^ { 1 } }$ , Percy Liang2, Quoc V. Le1, Tengyu $\mathbf { M } \mathbf { a } ^ { 2 }$ , and Adams Wei ${ { \bf { Y } } { \bf { u } } ^ { 1 } }$
|
| 4 |
+
|
| 5 |
+
1Google DeepMind
|
| 6 |
+
2Stanford University
|
| 7 |
+
|
| 8 |
+
# Abstract
|
| 9 |
+
|
| 10 |
+
The mixture proportions of pretraining data domains (e.g., Wikipedia, books, web text) greatly affect language model (LM) performance. In this paper, we propose Domain Reweighting with Minimax Optimization (DoReMi), which first trains a small proxy model using group distributionally robust optimization (Group DRO) over domains to produce domain weights (mixture proportions) without knowledge of downstream tasks. We then resample a dataset with these domain weights and train a larger, full-sized model. In our experiments, we use DoReMi on a 280Mparameter proxy model to set the domain weights for training an 8B-parameter model $3 0 \mathrm { x }$ larger) more efficiently. On The Pile, DoReMi improves perplexity across all domains, even when it downweights a domain. DoReMi improves average few-shot downstream accuracy by $6 . 5 \%$ points over a baseline model trained using The Pile’s default domain weights and reaches the baseline accuracy with $2 . 6 \mathbf { x }$ fewer training steps. On the GLaM dataset, DoReMi, which has no knowledge of downstream tasks, even matches the performance of using domain weights tuned on downstream tasks.
|
| 11 |
+
|
| 12 |
+
# 1 Introduction
|
| 13 |
+
|
| 14 |
+
Datasets for training language models (LMs) are typically sampled from a mixture of many domains [17; 13; 10; 9]. For example, The Pile [17], a large publicly available dataset, is composed of $24 \%$ web data, $9 \%$ Wikipedia, $4 \%$ GitHub, etc.1 The composition of the pretraining data greatly affects the effectiveness of an LM [13; 20; 55]. However, it is unclear how much of each domain to include to produce a model that performs well for a wide variety of downstream tasks.
|
| 15 |
+
|
| 16 |
+
Existing works determine domain weights (the sampling probabilities for each domain) by using intuition or a set of downstream tasks. For example, The Pile uses heuristically-chosen domain weights, which could be suboptimal. On the other hand, existing LMs such as PaLM [10] and GLaM [13] tune the domain weights based on a set of downstream tasks, but requires training potentially thousands of LMs on different domain weights and risks overfitting to the particular set of downstream tasks.
|
| 17 |
+
|
| 18 |
+
Instead of optimizing domain weights based on a set of downstream tasks, our approach aims to find domain weights which lead to models that perform well on all domains by minimizing the worst-case excess loss over domains, following Oren et al. [35]; Mindermann et al. [30]. The excess loss is the loss gap between the model being evaluated and a pretrained reference model.
|
| 19 |
+
|
| 20 |
+
This motivates our algorithm, Domain Reweighting with Minimax Optimization (DoReMi), which leverages distributionally robust optimization (DRO) to tune the domain weights without knowledge of downstream tasks (Figure 1). First, DoReMi trains a small reference model (e.g., 280M parameters)
|
| 21 |
+
|
| 22 |
+
|
| 23 |
+
Figure 1: Given a dataset with a set of domains, Domain Reweighting with Minimax Optimization (DoReMi) optimizes the domain weights to improve language models trained on the dataset. First, DoReMi uses some initial reference domain weights to train a reference model (Step 1). The reference model is used to guide the training of a small proxy model using group distributionally robust optimization (Group DRO) over domains [35; 43; 34], which we adapt to output domain weights instead of a robust model (Step 2). We then use the tuned domain weights to train a large model (Step 3).
|
| 24 |
+
|
| 25 |
+
|
| 26 |
+
Figure 2: DoReMi optimizes domain weights with a small model (280M params) and uses these domain weights to train a much larger model (8B params, $3 0 \mathrm { x }$ larger). Here, optimizing the domain weights (training a small model twice) takes $8 \%$ of the compute of training the large model. DoReMi improves average one-shot downstream accuracy by $6 . 5 \%$ points and reaches the baseline accuracy $2 . 6 \mathbf { x }$ faster when pretraining on The Pile.
|
| 27 |
+
|
| 28 |
+
in a standard way. Second, DoReMi trains a small distributionally robust language model (DRO-LM) [35], which minimizes the worst-case excess loss (relative to the reference’s model’s loss) across all domains. Notably, rather than using the robust LM, we take the domain weights produced by DRO training. Finally, we train a large (8B) LM on a new dataset defined by these domain weights.
|
| 29 |
+
|
| 30 |
+
Our approach adapts the DRO-LM framework [35] to optimize domain weights instead of producing a robust model. To do this, DoReMi uses the online learning-based optimizer from Group DRO [43; 34], which dynamically updates domain weights according to the loss on each domain for rescaling the training objective, instead of sub-selecting examples from a minibatch as in Oren et al. [35]; Mindermann et al. [30]. Finally, DoReMi takes the averaged domain weights over DRO training steps.
|
| 31 |
+
|
| 32 |
+
In Section 3, we run DoReMi on 280M proxy and reference models to optimize domain weights on The Pile [17] and the GLaM dataset [13] (used in PaLM [10]). The DoReMi domain weights are used to train an 8B parameter LM (over $3 0 \mathrm { x }$ larger). On The Pile, DoReMi reduces perplexity on all domains over baseline domain weights, even when it downweights a domain. DoReMi improves average downstream accuracy over a baseline model trained on The Pile’s default domain weights by $6 . 5 \%$ points on generative few-shot tasks and achieves the baseline downstream accuracy $2 . 6 \mathbf { x }$ faster (Figure 2). In Section 4, we find that DoReMi consistently improves LM training when varying the sizes of the proxy model and the main model trained with optimized domain weights. On the
|
| 33 |
+
|
| 34 |
+
GLaM dataset where domain weights tuned on downstream tasks are available, DoReMi even performs comparably to tuning domain weights on downstream task performance.2
|
| 35 |
+
|
| 36 |
+
# 2 Domain Reweighting with Minimax Optimization (DoReMi)
|
| 37 |
+
|
| 38 |
+
In this section we define DoReMi, an algorithm for using a small proxy model to optimize the domain weights of a language modeling dataset, which then improves the training of a large model.
|
| 39 |
+
|
| 40 |
+
Setup. Suppose that we have $k$ domains (e.g., Wikipedia, GitHub), where for each domain $i$ , we have a set of examples $D _ { i }$ . Domain weights $\alpha \in \bar { \Delta } ^ { k }$ specify a probability distribution over the $k$ domains, and consequently a distribution over the training data: $\begin{array} { r } { P _ { \alpha } = \sum _ { i = 1 } ^ { k } \alpha _ { i } \cdot \mathbf { u n i f } ( D _ { i } ) } \end{array}$ where $\mathrm { u n i f } ( D ) =$ $\textstyle { \frac { 1 } { | D | } } \sum _ { x \in D } \delta _ { x }$ is the uniform distribution over the examples in $D$ and $\delta _ { x } ( x ^ { \prime } )$ is 1 if $x ^ { \prime } = x$ and 0 otherwise.
|
| 41 |
+
|
| 42 |
+
DoReMi. The inputs of DoReMi are the data $D _ { 1 } , \ldots , D _ { k }$ , reference domain weights $\alpha _ { \mathrm { r e f } }$ (e.g., uniform or based on raw token count of each domain), and training hyperparameters for the large, full-size model (number of training steps $T$ and batch size $b$ ). DoReMi returns optimized domain weights $\bar { \alpha }$ and ultimately, a large model trained on $P _ { \bar { \alpha } }$ .
|
| 43 |
+
|
| 44 |
+
Step 1: Obtain a small reference model. We first train a model $p _ { \mathrm { r e f } }$ on some reference domain weights $\alpha _ { \mathrm { r e f } }$ (e.g., based on raw token count as a default) for $T$ steps, batch size $b$ . This model serves as the reference model for step 2 and captures a baseline level of difficulty of each example/domain. The reference model can be a relatively small model (280M parameters in our experiments).
|
| 45 |
+
|
| 46 |
+
Step 2: Train proxy model with Group DRO to obtain domain weights. To obtain domain weights, we train a small proxy model $p _ { \theta }$ in the distributionally robust language modeling (DROLM) [35] framework with the Group DRO optimizer [43], where $\theta$ are the weights of the proxy model. This framework trains a robust model by optimizing the worst-case loss over domains, which is equivalent to the following minimax objective:
|
| 47 |
+
|
| 48 |
+
$$
|
| 49 |
+
\operatorname* { m i n } _ { \theta } \operatorname* { m a x } _ { \alpha \in \Delta ^ { k } } L ( \theta , \alpha ) : = \sum _ { i = 1 } ^ { k } \alpha _ { i } \cdot \left[ \frac { 1 } { \sum _ { \boldsymbol { x } \in D _ { i } } \left| \boldsymbol { x } \right| } \sum _ { \boldsymbol { x } \in D _ { i } } \ell _ { \theta } ( \boldsymbol { x } ) - \ell _ { \mathrm { r e f } } ( \boldsymbol { x } ) \right]
|
| 50 |
+
$$
|
| 51 |
+
|
| 52 |
+
where the losses $\ell _ { \theta } ( x ) = - \log \ p _ { \theta } ( x )$ and $\ell _ { \mathrm { { r e f } } } ( x ) = - \log \ p _ { \mathrm { { r e f } } } ( x )$ are the negative log-likelihoods of the proxy and reference models respectively in this paper, and $| x |$ is the number of tokens in an example $x$ . The objective aims to minimize the worst-case excess loss across domains because the inner maximization over $\alpha$ puts all the weight on the domain with the highest excess loss.
|
| 53 |
+
|
| 54 |
+
Intuitively, the excess loss $( \ell _ { \theta } ( x ) - \ell _ { \mathrm { r e f } } ( x ) )$ measures the headroom for the proxy model to improve, with respect to the reference model, on example $x$ . Examples with higher excess loss are those where the reference model achieves low loss (such that the example is “learnable”) but the proxy model still has high loss. Examples with low excess loss may be very high entropy (i.e. optimal loss is high, and thus the reference loss is high) or very low entropy (i.e., easy to learn, and thus the proxy loss is low). The Group DRO optimizer works by interleaving exponentiated gradient ascent updates on domain weights $\alpha _ { t }$ with gradient updates on the proxy model weights $\theta _ { t }$ over training steps $t$ . The optimizer updates $\alpha _ { t }$ to upweight domains with high excess loss, which scales up the proxy model’s gradient update on examples from these domains. Following Nemirovski et al. [34], we return the average weights over the training trajectory $\begin{array} { r } { \bar { \alpha } = \frac { 1 } { T } \sum _ { i = 1 } ^ { T } \alpha _ { t } } \end{array}$ as the optimized domain weights to use in step 3.
|
| 55 |
+
|
| 56 |
+
Step 3: Train large model with new domain weights. The tuned domain weights $\bar { \alpha }$ define a new training distribution $P _ { \bar { \alpha } }$ . We resample the data from this new distribution to train a main model (larger than the reference/proxy models), using a standard training procedure.
|
| 57 |
+
|
| 58 |
+
Details for Step 2. Algorithm 1 provides the pseudocode for Step 2. The main structure of Algorithm 1 is a training loop which updates the proxy model over $T$ steps. At each step, we follow Sagawa et al. [43] and sample a minibatch with uniform domain weights (regardless of the reference domain weights $\alpha _ { \mathrm { r e f } }$ , which only affects the reference model). We then compute the per-domain excess losses, normalized by the total number of tokens in each domain, and use them to update the domain weights $\alpha _ { t }$ at each step. We first compute the per-domain excess loss at a per-token level and then aggregate, where the token-level losses at index $j$ are $\ell _ { \theta _ { t - 1 } , j } ( \boldsymbol { x } ) = - \mathrm { l o g } p _ { \theta _ { t - 1 } } \bar { ( x _ { j } | x _ { 1 } , \ldots , x _ { j - 1 } ) }$ and $\bar { \ell _ { \mathrm { r e f } , j } } ( \bar { x } ) = - \log p _ { \mathrm { r e f } } ( x _ { j } | x _ { 1 } , . . . , x _ { j - 1 } )$ . Since the Group DRO optimizer [43] requires a non-negative loss, we clip the per-token excess loss at 0. Finally, we update the proxy model for the objective $L ( \theta _ { t - 1 } , \alpha _ { t } )$ using a standard optimizer such as Adam [26] or Adafactor [46]. All experiments in this paper use Adafactor. We set the domain weight update step size to $\eta = 1$ and the smoothing parameter to $c { = } 1 \mathrm { e } { - } 3$ in all our experiments and did not extensively tune these hyperparameters.
|
| 59 |
+
|
| 60 |
+
Algorithm 1 DoReMi domain reweighting (Step 2)
|
| 61 |
+
|
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<table><tr><td>Require: Domain data D1,.,Dk,number of training steps T, batch size b,step size n, smoothing parameterc∈ [0,1] (e.g.,c=1e-3 in our implementation).</td><td></td></tr><tr><td>Initialize proxy weights 0o</td><td></td></tr><tr><td>Initialize domain weights αo = 11</td><td></td></tr><tr><td>for t from 1 to T do</td><td>Sample minibatch B={xi1,,xj} of size b from Pu, where u= 1</td></tr><tr><td>Let |x| be the token length of example x (|x|≤ L)</td><td></td></tr><tr><td></td><td>Compute per-domain excess losses for each domain i∈ {1,2,.,k} (le.,j(x) is j-th token-level</td></tr><tr><td>loss): 1 1|x</td><td>max{lθt-1,j(x)-lref,j(x),0}</td></tr><tr><td>入t[i]←Ω∈BnD ∑xEBnDi∑j=11 |x</td><td>Update domain weights (exp is entrywise): αt ← αt-1exp(n入t)</td></tr><tr><td>Renormalize and smooth domain weights: αt ← (1-c)</td><td>a +cu</td></tr><tr><td></td><td></td></tr><tr><td>end for</td><td>Update proxy model weights 0t for the objective L(0t-1,αt) (using Adam, Adafactor, etc.)</td></tr></table>
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Iterated DoReMi. We extend DoReMi by running it for multiple rounds, setting the reference domain weights $\alpha _ { \mathrm { r e f } }$ for the next round to be $\bar { \alpha }$ from the previous round. We call this iterated DoReMi. The entire iterated process still only uses small models for tuning domain weights. We stop iterating when the domain weights converge, which we define as when maximum change in any domain weight $\left\| \bar { \alpha } - \alpha _ { \mathrm { r e f } } \right\| _ { \infty }$ is less than 1e-3. Empirically, this takes only 3 rounds on the GLaM dataset (Section 3.2).
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# 3 DoReMi Improves LM Training Efficiency and Performance
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In this section, we use DoReMi domain weights optimized with a 280M-parameter proxy model to train a 8B-parameter main model $3 0 \mathrm { x }$ larger). We consider two datasets, The Pile [17] and the GLaM dataset [13]. On The Pile, DoReMi reduces perplexity significantly on every domain, improves average downstream accuracy on generative one-shot tasks by $6 . 5 \%$ , and achieves the baseline accuracy $2 . 6 \mathbf { x }$ faster. On the GLaM dataset where domain weights tuned on downstream datasets are available, DoReMi finds domain weights with comparable performance to downstream-tuned domain weights.
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# 3.1 Experimental setup
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The Pile dataset. The Pile [17] is a 800GB text dataset with 22 domains (Table 1). The default domain weights were determined heuristically. We use the default domain weights from The Pile dataset to train the baseline and as the reference domain weights $\alpha _ { \mathrm { r e f } }$ in DoReMi (see Appendix C).
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GLaM dataset. The GLaM dataset [13] (also used in training PaLM [10]) includes text from 8 domains (Table 2). For comparison, the GLaM domain weights (downstream-tuned) were tuned according to the downstream performance of models trained on each domain and the size of each domain [13]. We consider this an oracle comparison, since these domain weights are tuned on downstream tasks that are in our evaluation set. We use uniform domain weights both for training the baseline and the reference domain weights $\alpha _ { \mathrm { r e f } }$ for DoReMi.
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Training setup. We train Transformer [51] decoder-only LMs with the standard next-token language modeling loss. We conduct a controlled comparison by equalizing the amount of compute, measured by the number of tokens processed during training. For The Pile, we train each model for $2 0 0 \mathrm { k }$ steps; for the GLaM dataset, we train each model for 300k steps. All models use a batch size of 512 and maximum token length of 1024. The proxy and reference models have 280M parameters. All models are trained from scratch (other hyperparameters are in Appendix C).
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Evaluation. We use held-out validation data to measure the perplexity on each domain. For downstream evaluation, we use the generative one-shot tasks from the GPT-3 paper [9]: TriviaQA [21], NaturalQuestions [27], WebQuestions [5], SQuADv2 [41], and LAMBADA [36]. We use the standard exact-match accuracy metric for the these datasets. The performance on these datasets (particularly TriviaQA) has been shown to correlate well with model scale even at the 100M–1B range [9].
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Compute used for optimizing domain weights. We train two 280M models (the reference and proxy models) to optimize the domain weights. This is $8 \%$ of the FLOPs required to train the main 8B model. All FLOPs come from standard forward and backward passes.
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Notation for model sizes in DoReMi. We denote the size of the reference/proxy models (which are always the same size in our experiments) and the size of the main model trained with DoReMi domain weights as “DoReMi (size of reference/proxy size of main model)”: for example, DoReMi $( 2 8 0 \mathbf { M } \partial \mathbf { B }$ ). When we are discussing the optimized domain weights independently of the main model, we only include one number (e.g., DoReMi (280M)) which refers to the reference/proxy model size.
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Figure 3: Average one-shot downstream accuracy (exact match) on 5 tasks, with 8B parameter models trained on The Pile (left) and the GLaM dataset (right). On The Pile, DoReMi improves downstream accuracy by $6 . 5 \%$ points and achieves the baseline accuracy $2 . 6 \mathbf { x }$ faster (same plot as Figure 2). On the GLaM dataset, iterated DoReMi (round 2) attains comparable performance to oracle domain weights tuned with downstream tasks that are in our evaluation set.
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Figure 4: Per-domain log-perplexity of 8B models on The Pile. Despite downweighting some domains, DoReMi improves log-perplexity on all domains.
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Table 1: Domain weights on The Pile. Baseline domain weights are computed from the default Pile dataset. DoReMi (280M) uses a 280M proxy model to optimize the domain weights.
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<table><tr><td>Domain</td><td>Baseline</td><td>DoReMi (280M)</td><td>Difference</td><td>Domain</td><td>Baseline</td><td>DoReMi(280M)</td><td>Difference</td></tr><tr><td>Pile-CC</td><td>0.1121</td><td>0.6057</td><td>+0.4936</td><td>DMMathematics</td><td>0.0198</td><td>0.0018</td><td>-0.0180</td></tr><tr><td>YoutubeSubtitles</td><td>0.0042</td><td>0.0502</td><td>+0.0460</td><td>Wikipedia (en)</td><td>0.0919</td><td>0.0699</td><td>-0.0220</td></tr><tr><td>PhilPapers</td><td>0.0027</td><td>0.0274</td><td>+0.0247</td><td>OpenWebText2</td><td>0.1247</td><td>0.1019</td><td>-0.0228</td></tr><tr><td>HackerNews</td><td>0.0075</td><td>0.0134</td><td>+0.0059</td><td>Github</td><td>0.0427</td><td>0.0179</td><td>-0.0248</td></tr><tr><td>Enron Emails</td><td>0.0030</td><td>0.0070</td><td>+0.0040</td><td>FreeLaw</td><td>0.0386</td><td>0.0043</td><td>-0.0343</td></tr><tr><td>EuroParl</td><td>0.0043</td><td>0.0062</td><td>+0.0019</td><td>USPTO Backgrounds</td><td>0.0420</td><td>0.0036</td><td>-0.0384</td></tr><tr><td>Ubuntu IRC</td><td>0.0074</td><td>0.0093</td><td>+0.0019</td><td>Books3</td><td>0.0676</td><td>0.0224</td><td>-0.0452</td></tr><tr><td>BookCorpus2</td><td>0.0044</td><td>0.0061</td><td>+0.0017</td><td>PubMed Abstracts</td><td>0.0845</td><td>0.0113</td><td>-0.0732</td></tr><tr><td>NIH ExPorter</td><td>0.0052</td><td>0.0063</td><td>+0.0011</td><td>StackExchange</td><td>0.0929</td><td>0.0153</td><td>-0.0776</td></tr><tr><td>OpenSubtitles</td><td>0.0124</td><td>0.0047</td><td>-0.0077</td><td>ArXiv</td><td>0.1052</td><td>0.0036</td><td>-0.1016</td></tr><tr><td>Gutenberg (PG-19)</td><td>0.0199</td><td>0.0072</td><td>-0.0127</td><td>PubMed Central</td><td>0.1071</td><td>0.0046</td><td>-0.1025</td></tr></table>
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Table 2: Domain weights in the GLaM dataset. Iterated DoReMi (280M) converges within 3 rounds, with a similar overall pattern to domain weights tuned on downstream tasks.
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<table><tr><td></td><td>Round 1</td><td>Round 2</td><td>Round 3</td><td>Downstream-tuned</td></tr><tr><td>Wikipedia</td><td>0.09</td><td>0.05</td><td>0.05</td><td>0.06</td></tr><tr><td>Filtered webpages</td><td>0.44</td><td>0.51</td><td>0.51</td><td>0.42</td></tr><tr><td>Conversations</td><td>0.10</td><td>0.22</td><td>0.22</td><td>0.27</td></tr><tr><td>Forums</td><td>0.16</td><td>0.04</td><td>0.04</td><td>0.02</td></tr><tr><td>Books</td><td>0.11</td><td>0.17</td><td>0.17</td><td>0.20</td></tr><tr><td>News</td><td>0.10</td><td>0.02</td><td>0.02</td><td>0.02</td></tr></table>
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# 3.2 DoReMi improves perplexity and downstream accuracy
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We show that DoReMi significantly improves both the perplexity and downstream accuracy of 8B models trained on The Pile and the GLaM dataset over their respective baseline domain weights.
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Downstream accuracy improves on The Pile. Figure 3 (left) shows the average downstream performance for baseline and DoReMi $2 8 0 { \mathbf { M } } { } 8 { \mathbf { B } }$ ) models on The Pile. DoReMi improves the downstream accuracy by $6 . 5 \%$ points and achieves the baseline accuracy within $7 5 \mathrm { k }$ steps — $2 . 6 \mathbf { x }$ faster than the baseline (200k steps). Thus, DoReMi can dramatically speed up training and improve downstream performance.
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DoReMi can reduce perplexity across all domains without a tradeoff. Figure 4 shows the per-domain log-perplexity of the 8B models on The Pile. DoReMi significantly reduces the perplexity over the baseline across all domains, despite allocating lower weight to some domains. How can this occur? One hypothesis is that the domains with the lowest and highest entropy can be downweighted without impacting the perplexity much. The lowest entropy domains statistically require few samples to learn. The highest entropy domains have token distributions that are close to common uniform priors — for example, models at random initialization tend to output a uniform next token distribution. Thus, we need less samples to fit these domains. Positive transfer from allocating more samples to medium entropy domains can then improve perplexity on all domains. In Appendix D, we provide a simple example where reweighting domains can improve perplexity on all domains and DoReMi finds such domain weights in simulations.
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Iterated DoReMi achieves performance of downstream-tuned weights on the GLaM dataset. We employ iterated DoReMi on the GLaM dataset over 3 rounds. We find that the second and third round domain weights are almost identical (Table 2). Figure 3 (right) shows one-shot results for the first two rounds of iterated DoReMi. After the first round, the DoReMi main model has comparable downstream accuracy to the baseline (uniform domain weights). After the second round, the DoReMi main model achieves comparable downstream accuracy to oracle domain weights tuned on downstream tasks in our evaluation set. Overall, domain reweighting has a smaller effect on GLaM, possibly because there are only 8 domains compared to 22 in The Pile.
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Inspecting the DoReMi domain weights. Tables 1 and 2 present the DoReMi domain weights for The Pile and the GLaM dataset. When running DoReMi on a 280M proxy model (DoReMi (280M)), most weight is put on the diverse Pile-CC web text domain. Note that Wikipedia is downweighted in comparison to the baseline, but DoReMi still improves the downstream accuracy on tasks derived from Wikipedia (e.g., TriviaQA, Appendix Table 5). Domain weights for a 1B proxy model (Appendix 8)
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Figure 5: Average one-shot downstream accuracy across 4 model scales (280M, 510M, 760M, 1B) where the reference/proxy models for DoReMi are the same size as the main model trained with DoReMi domain weights. DoReMi consistently improves downstream accuracy across scales, with a similar $3 \%$ accuracy gap at $2 0 0 \mathrm { k }$ steps at most scales (except for 510M). DoReMi achieves the baseline accuracy 4x faster on average across scales.
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shows a different trend, where OpenWebText is the mostly upweighted instead of Pile-CC. This suggests that there may be multiple possible local minima in the domain weight space. On the GLaM dataset, the DoReMi weights have the same general pattern as the downstream-tuned domain weights. DoReMi is able to recover a similar set of domain weights by starting from uniform initial reference domain weights, without any use of downstream data.
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# 4 Ablations and Analysis Across Scales
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Previously in Section 3, we showed that DoReMi finds domain weights using 280M models that can improve training of 8B models. In this section, we conduct an analysis of DoReMi where we vary the scale of the proxy model in relation to the main model and ablate the components of the excess loss objective.
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DoReMi improves LMs consistently across scales. We consider using proxy and main models of the same size to analyze DoReMi’s behavior in a simple setting, without the need for the domain weights to generalize across scales. Note that this is just for scientific purposes since this does not save compute in practice. In particular, we run DoReMi $( \mathrm { X } { \to } \mathrm { X } )$ where X is 280M, 510M, 760M, or 1B on The Pile. Figure 5 shows that DoReMi consistently improves downstream accuracy over the baseline by $2 \%$ and achieves the baseline accuracy $4 \mathbf { x }$ faster on average across scales, and this improvement does not shrink with larger model size. DoReMi improves the worst-case perplexity on all scales and improves 18 of 22 individual domain perplexities on average across scales (Appendix Table 6). These experiments give a rough picture of how much is lost when using a smaller proxy model; our DoReMi $( 2 8 0 \mathbf { M } \partial \mathbf { B }$ ) model achieves the baseline accuracy $2 . 6 \mathbf { x }$ faster, while matching the proxy and main model sizes results in a $4 \mathbf { x }$ average speedup.
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Proxy model underperforms main model, especially at larger sizes. Recall that DoReMi uses Group DRO to train a proxy model, which reweights the objective with the domain weights. In contrast, the main model is trained by resampling on the domain weights from DoReMi. When the proxy model and the main model are the same size, which one is the better model? Table 3b shows that the proxy
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Figure 6: Average downstream accuracy for models trained on The Pile. (Left) Increasing the size of the reference/proxy models from 70M to 280M in DoReMi improves downstream accuracy for a 8B main model, but the trend does not continue for the 1B proxy model. We hypothesize that the Group DRO optimizer is worse for larger proxy models. Right) Optimizing for the hardest or easiest domains rather than excess loss (which combines both) do not achieve the same average downstream accuracy as DoReMi (280M models).
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Table 3: Summary of per-domain log-perplexities on The Pile (22 total domains). Average log-perplexity is an unweighted average of the per-domain log-perplexities.
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(a) Varying the size of the proxy/reference model and training at 8B.
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<table><tr><td></td><td>Worst-case log-ppl</td><td>Avg log-ppl</td><td>#domains beating baseline</td></tr><tr><td>Baseline (8B)</td><td>1.71</td><td>1.64</td><td>0/22</td></tr><tr><td>DoReMi(70M->8B)</td><td>1.63</td><td>1.53</td><td>22/22</td></tr><tr><td>DoReMi(150M->8B)</td><td>1.56</td><td>1.52</td><td>22/22</td></tr><tr><td>DoReMi(280M->8B)</td><td>1.46</td><td>1.40</td><td>22/22</td></tr><tr><td>DoReMi(1B->8B)</td><td>1.58</td><td>1.54</td><td>22/22</td></tr></table>
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(b) Perplexity of the DoReMi main model and proxy model of the same size. Although the 1B proxy model is relatively poor quality, the resulting domain weights still improve the main model.
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<table><tr><td></td><td>Worst-case log-ppl</td><td>Avg log-ppl</td><td>#domains beating baseline</td></tr><tr><td>Baseline (280M)</td><td>2.39</td><td>2.32</td><td>0/22</td></tr><tr><td>DoReMi(280M->280M)</td><td>2.19</td><td>2.13</td><td>22/22</td></tr><tr><td>Proxy (280M)</td><td>2.33</td><td>2.27</td><td>19/22</td></tr><tr><td>Baseline (1B)</td><td>1.94</td><td>1.87</td><td>0/22</td></tr><tr><td>DoReMi(1B->1B)</td><td>1.92</td><td>1.83</td><td>19/22</td></tr><tr><td>Proxy (1B)</td><td>2.11</td><td>2.02</td><td>0/22</td></tr></table>
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model typically underperforms the main model in this case. The gap between the proxy and main model increases with scale, as the 1B proxy model not only underperforms the 1B main model but also the 1B baseline model, while the 280M proxy model achieves better perplexity than the 280M baseline model on 19/22 domains. Despite the relatively poor quality of the 1B proxy model, the domain weights still allow the 1B main model to achieve the baseline performance over $2 \mathbf { x }$ faster. This suggests that DoReMi can succeed even if the proxy model is not trained well. However, we hypothesize that the mismatch between the proxy and main model training (loss reweighting vs. resampling) explains their performance difference and therefore a resampling-based Group DRO optimizer may improve DoReMi for larger proxy models.
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Effect of proxy model scale on larger main model’s performance. We consider 70M, 150M, 280M, and 1B scales for the DoReMi proxy model while fixing the main model size at 8B (DoReMi $( \mathrm { X } \to 8 \mathrm { B } )$ ). From 70M to 280M, increasing the proxy model size improves downstream accuracy at 8B (Figure 6 left). We hypothesize that this trend does not continue for the 1B proxy model because the Group DRO optimizer is worse at larger scales (Table 3b). While DoReMi $2 8 0 { \mathbf { M } } { } 8 { \mathbf { B } }$ ) results in the most improvement at 8B, DoReMi ( $1 5 0 { \mathbf { M } } { } 8 { \mathbf { B } }$ ) and DoReMi ( $1 \mathrm { B } \to 8 \mathrm { B }$ ) still achieve the baseline accuracy almost $2 \mathbf { x }$ faster. This suggests that DoReMi is robust to the proxy model scale. In practice, we suggest choosing a relatively small proxy model size (280M) to save compute.
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Choosing the easiest or hardest domains do not suffice. We ablate the components of the excess loss metric $\ell _ { \theta } ( x ) - \ell _ { \mathrm { r e f } } ( x )$ by running DoReMi using only the loss of the proxy model $p _ { \theta }$ on example $x$ , i.e. $\ell _ { \theta } ( x )$ (prefer hardest domains for the proxy model) or only the negative loss of the reference $- \ell _ { \mathrm { r e f } } ( x )$ (prefer easiest domains for the reference model). Figure 6 (right) shows that neither of the components of the excess loss alone are sufficient to achieve the gains of DoReMi.
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# 5 Related Work
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Curating pretraining data for LMs. Most closely related is the GLaM dataset [13] (also used for training PaLM [10]), which has domain weights that are tuned using downstream data. Optimizing domain weights for downstream tasks can be expensive and could require search/zero-order optimization [48], RL [56], or heuristic assumptions on how positive/negative transfer between domains work. Example-level filtering also brings benefits for LM training. The C4 dataset [39] shows gains over CommonCrawl via heuristic data cleaning methods. Du et al. [13]; Xie et al. [55] show that filtering the data at an example level for high-quality text that look like Wikipedia and books can significantly improve downstream performance for LMs. In contrast to these works, DoReMi sets domain weights automatically with only two small LM training runs and does not make assumptions about the type of data to prefer (Wikipedia-like, etc.).
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General data selection methods. Moore-Lewis selection [32; 3; 15] selects examples with high cross-entropy difference (similar to excess log-perplexity) between language models trained on target and raw data. In contrast, DoReMi reweights the data without a target distribution. Coleman et al. [11] select examples based on the uncertainty of a small proxy model for active learning, while DoReMi uses DRO on the excess loss with respect to a reference model, and focuses on data mixture reweighting. Mindermann et al. [30] select examples in an online fashion by taking the top $k$ examples in a minibatch according to excess loss. DoReMi optimizes the data mixture before training, allowing the larger main model to train in a standard way. Many other works on data selection are in vision [49; 22; 24; 23; 25; 53; 54; 38; 31; 45] and mainly focus on example-level subset selection with metrics such as gradient matching. Overall, these methods do not address data selection for pretraining, where the downstream data distribution may be very different from the pretraining distribution. DoReMi aims to address the pretraining/downstream distribution shift with a robust optimization approach. To the best of our knowledge, we are the first to show that reweighting the data according to losses of a small proxy LM can improve the training efficiency of much larger LM.
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Distributionally robust optimization. Within DRO methods for deep learning [4; 47; 35; 43], we target a restricted form of shift called group shifts [14; 35; 43], where the test distribution can be an unknown mixture of groups (domains). We follow DRO-LM [35], which employs DRO for LMs in the group shift setting. DRO-LM also uses a baselined loss, but with a simple bigram reference model. DoReMi uses a reference model of the same size and architecture as the proxy model to ensure that the losses are on a similar scale. During optimization, DRO-LM takes a worst-case subset of each minibatch to update the model on, while we use the Group DRO optimizer [43] which doesn’t require online subselection. If we equalize the number of examples in each minibatch used for gradient updates, online subselelction is more expensive than Group DRO since it requires running forward passes on a larger minibatch (e.g., double the minibatch size) before selecting a subset to update the model with. In comparison, the Group DRO optimizer updates the model on all examples in a weighted fashion. Overall, in contrast to these DRO methods which aim to produce robust models, we use DRO to optimize the data for training larger models more efficiently.
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Data-centric AI. Large-scale datasets and benchmarks have driven much of the recent progress in AI, including vision, NLP, and multimodal models [12; 42; 52; 40; 39; 17; 44; 16]. However, most datasets are still painstakingly created with human-generated data, manual work, and heuristics [12; 39; 17; 44; 16]. DoReMi is a principled data-centric method that aims to improve language model training efficiency. We hope that DoReMi can provide a starting point for a general data-centric framework for language modeling via robust optimization.
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# 6 Discussion and Limitations
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Saving compute in DoReMi with extrapolation. In Section 2, we run DoReMi for the number of training steps that will be used to train the final model, which could be unnecessarily expensive. A future direction for saving compute would be to stop running DoReMi at an early step and extrapolate the domain weights for the desired number of steps, since we found that most of the variation in the domain weights during a DoReMi run seems to occur in the beginning of training (Appendix Figure 8).
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Choice of reference model. The choice of reference model can affect the domain weights found by DoReMi. For example, iterated DoReMi (Section 3) improves performance by using a reference model trained on the tuned domain weights from a previous round of DoReMi. Further directions include varying the reference model size and using specialized reference models to optimize domain weights for a specific application area.
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What is a domain? We define a domain by data provenance in our experiments, but this only enables coarse-grained control. Using fine-grained domains could improve the gains from DoReMi. For example, DoReMi is more effective on The Pile (22 domains) than the GLaM dataset (8 domains). Open directions include automatically finding fine-grained domains (e.g., via clustering as in DRO-LM [35]) and reweighting the data at an example level. When domains are very fine-grained, it will be important to control the pessimism of DRO (e.g., DRO can put all the weight on a small set of worst-case examples).
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Transferability of domain weights across scales. We optimized the domain weights with a small proxy model (280M) and directly used these domain weights to improve training at a larger scale (8B). Understanding why the domain weights can be transferred across scales and the limits of how far these domain weights transfer are important questions to answer in future work.
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Broader impacts. Large language models are We hope to improve training efficiency and reduce the environmental impact of training large LMs [50; 28; 37; 29]. In particular, by reducing the training time by $2 \mathbf { x }$ , we can halve the cost and energy consumption of training large language models. Since such efficiency improvements may be used to develop even larger models, there may be no absolute improvement in energy consumption. Ultimately, we hope to improve the training efficiency and cost of developing future language models relative to existing methods.
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Large LMs have also been well-documented to have risks and biases [1; 33; 7; 6; 18]. For example, GPT-3 tends to have an anti-Muslim bias, where Muslims are frequently related to violence or terrorism in analogy and completion tasks [1]. As large language models are increasingly relied upon in applications, the magnitude of the risks increases [8]. Distributionally robust optimization (DRO), which is used in DoReMi to optimize the data mixture, can have a favorable impact on fairness [19]. While the standard approach of minimizing the average loss can lead to disparate performance on minority subgroups that do not contribute heavily to the loss [2], DRO promotes good performance on all groups via a worst-case loss. In this way, DRO-style data-centric methods such as DoReMi can improve the representation disparity between majority and minority subgroups in a dataset.
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# 7 Conclusion
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We introduced DoReMi, an algorithm reweighting data domains for training language models. DoReMi is able to run on small models and transfer the benefits to $3 0 \mathrm { x }$ larger models, resulting in a $2 . 6 \mathrm { x }$ speedup in training on the Pile just by changing the sampling probabilities on domains. We hope to instigate more research on data-centric approaches for improving language model training efficiency.
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# Acknowledgments
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We thank Xiangning Chen, Andrew Dai, Zoubin Ghahramani, Balaji Lakshminarayanan, Paul Michel, Yonghui Wu, Steven Zheng, Chen Zhu, anonymous reviewers, and the broader Google Bard team members for insightful discussions and pointers.
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Figure 7: Average one-shot downstream accuracy across 4 model scales, where the reference/proxy models for DoReMi are the same size as the final model trained with DoReMi domain weights. All models in this figure are trained on the GLaM dataset. DoReMi consistently improves downstream accuracy across scales.
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# A Results Across Scales on the GLaM dataset
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Figure 7 presents results across different scales (280M, 510M, 760M, 1B) on the GLaM dataset, where the proxy/reference models are the same size as the main model trained with DoReMi domain weights. Across all scales, DoReMi is comparable or better than both the baseline (uniform) domain weights and downstream-tuned domain weights. Interestingly, for iterated DoReMi at the 280M scale, the second round weights achieve slightly worse downstream accuracy than the round 1 weights when used to train 280M models, but transfer better to training 8B models.
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# B Detailed Results for The Pile
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Per-domain perplexities for 8B models. Table 4 shows per-domain perplexities for 8B models trained on the Pile. The reference/proxy models in this case are 70M, 150M, 280M, and 1B. DoReMi improves the perplexity on each domain compared to the baseline domain weights.
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Per-task accuracies for 8B models. Table 5 shows the accuracies on one-shot generative tasks for various reference/proxy model sizes from 70M to 1B. All DoReMi models improve downstream performance significantly over the baseline.
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Summary of perplexity results across scales. Table 6 shows a summary of per-domain perplexities for DoReMi across 4 scales (280M, 510M, 760M, 1B). Here, the reference/proxy models are the same size as the main model trained with DoReMi domain weights. On average, DoReMi improves perplexity on 18.25 out of 22 domains from The Pile. The worst-case perplexity is always reduced (or comparable in the 510M case) with respect to the baseline domain weights.
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Table 4: Per-domain log-perplexities for 8B models trained on The Pile where the reference/proxy models are or smaller sizes (70M, 150M, 280M, 1B). Models trained with DoReMi domain weights have lower perplexity on all domains than the baseline weights.
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<table><tr><td></td><td>Baseline (8B)</td><td>DoReMi(70M->8B)</td><td>DoReMi(150M->8B)</td><td>DoReMi(280M->8B)</td><td>DoReMi(1B->8B)</td></tr><tr><td>Pile-CC</td><td>1.64</td><td>1.51</td><td>1.48</td><td>1.41</td><td>1.55</td></tr><tr><td>PubMed Central</td><td>1.60</td><td>1.58</td><td>1.54</td><td>1.46</td><td>1.56</td></tr><tr><td>Books3</td><td>1.65</td><td>1.52</td><td>1.50</td><td>1.42</td><td>1.57</td></tr><tr><td>OpenWebText2</td><td>1.66</td><td>1.48</td><td>1.54</td><td>1.36</td><td>1.58</td></tr><tr><td>ArXiv</td><td>1.64</td><td>1.56</td><td>1.53</td><td>1.38</td><td>1.51</td></tr><tr><td>Github</td><td>1.65</td><td>1.55</td><td>1.54</td><td>1.42</td><td>1.53</td></tr><tr><td>FreeLaw</td><td>1.64</td><td>1.55</td><td>1.54</td><td>1.45</td><td>1.55</td></tr><tr><td>StackExchange</td><td>1.61</td><td>1.52</td><td>1.54</td><td>1.39</td><td>1.55</td></tr><tr><td>USPTO Backgrounds</td><td>1.70</td><td>1.53</td><td>1.50</td><td>1.41</td><td>1.56</td></tr><tr><td>PubMed Abstracts</td><td>1.61</td><td>1.56</td><td>1.51</td><td>1.44</td><td>1.55</td></tr><tr><td>Gutenberg (PG-19)</td><td>1.70</td><td>1.56</td><td>1.54</td><td>1.35</td><td>1.52</td></tr><tr><td>OpenSubtitles</td><td>1.58</td><td>1.56</td><td>1.52</td><td>1.40</td><td>1.55</td></tr><tr><td>Wikipedia (en)</td><td>1.66</td><td>1.49</td><td>1.53</td><td>1.35</td><td>1.56</td></tr><tr><td>DMMathematics</td><td>1.63</td><td>1.50</td><td>1.56</td><td>1.38</td><td>1.48</td></tr><tr><td>Ubuntu IRC</td><td>1.71</td><td>1.53</td><td>1.49</td><td>1.42</td><td>1.48</td></tr><tr><td>BookCorpus2</td><td>1.64</td><td>1.57</td><td>1.54</td><td>1.43</td><td>1.57</td></tr><tr><td>EuroParl</td><td>1.59</td><td>1.52</td><td>1.51</td><td>1.37</td><td>1.53</td></tr><tr><td>HackerNews</td><td>1.66</td><td>1.50</td><td>1.55</td><td>1.45</td><td>1.55</td></tr><tr><td>YoutubeSubtitles</td><td>1.67</td><td>1.63</td><td>1.55</td><td>1.42</td><td>1.53</td></tr><tr><td>PhilPapers</td><td>1.67</td><td>1.55</td><td>1.49</td><td>1.39</td><td>1.53</td></tr><tr><td>NIHExPorter</td><td>1.63</td><td>1.51</td><td>1.48</td><td>1.36</td><td>1.52</td></tr><tr><td>Enron Emails</td><td>1.62</td><td>1.48</td><td>1.52</td><td>1.44</td><td>1.56</td></tr></table>
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Table 5: Per-task exact-match accuracies for generative one-shot tasks. All DoReMi models improve downstream performance significantly over the baseline domain weights.
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<table><tr><td></td><td>Baseline</td><td>DoReMi(1B->8B)</td><td>DoReMi(280M->8B)</td><td>DoReMi(150M->8B)</td><td>DoReMi(70M->8B)</td></tr><tr><td>LAMBADA</td><td>20.10</td><td>22.55</td><td>29.19</td><td>20.59</td><td>26.20</td></tr><tr><td>NaturalQuestions</td><td>4.35</td><td>6.01</td><td>7.73</td><td>6.26</td><td>5.10</td></tr><tr><td>SQuADv2</td><td>44.43</td><td>42.22</td><td>51.89</td><td>46.53</td><td>40.99</td></tr><tr><td>TriviaQA</td><td>24.55</td><td>32.25</td><td>34.86</td><td>30.01</td><td>26.30</td></tr><tr><td>WebQuestions</td><td>6.74</td><td>8.71</td><td>9.15</td><td>9.15</td><td>6.99</td></tr><tr><td>Average</td><td>20.03</td><td>22.35</td><td>26.56</td><td>22.51</td><td>21.11</td></tr></table>
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Table 6: Summary of per-domain log-perplexities for 280M, 510M, 760M, and 1B models trained on The Pile, where the reference/proxy models are the same size. DoReMi improves the worst-case and average perplexity of the baseline domain weights in all cases. On average, DoReMi improves perplexity on 18 out of 22 domains.
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<table><tr><td>Worst-case log-ppl</td><td>Avg log-ppl</td><td># domains beating baseline</td></tr><tr><td>Baseline (280M)</td><td>2.39</td><td>2.32 0/22</td></tr><tr><td>DoReMi(280M->280M)</td><td>2.19</td><td>2.13 22/22</td></tr><tr><td>Proxy (280M)</td><td>2.33 2.27</td><td>19/22</td></tr><tr><td>Baseline (510M)</td><td>2.14</td><td>2.08 0/22</td></tr><tr><td>DoReMi(510M->510M)</td><td>2.14</td><td>2.06 15/22</td></tr><tr><td>Proxy (510M)</td><td>2.23</td><td>2.18 0/22</td></tr><tr><td>Baseline (760M)</td><td>2.05</td><td>1.97 0/22</td></tr><tr><td>DoReMi(760M->760M)</td><td>2.00</td><td>1.94 17/22</td></tr><tr><td>Proxy (760M)</td><td>2.15 2.10</td><td>0/22</td></tr><tr><td>Baseline (1B)</td><td>1.94</td><td>1.87 0/22</td></tr><tr><td>DoReMi(1B->1B)</td><td>1.92</td><td>1.83 19/22</td></tr><tr><td>Proxy (1B)</td><td>2.11 2.02</td><td>0/22</td></tr></table>
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+
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Table 7: Summary of perplexity results for ablations on the DRO objective (excess loss). The individual components (which prefer hardest and easiest domains respectively) do not reduce perplexity over the baseline.
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+
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<table><tr><td></td><td>Worst-case log-ppl</td><td>Avg log-ppl</td><td>#domains beating baseline</td></tr><tr><td>Baseline (280M)</td><td>2.39</td><td>2.32</td><td>0</td></tr><tr><td>DoReMi(280M->280M)</td><td>2.19</td><td>2.13</td><td>22/22</td></tr><tr><td>Hardest (280M->280M)</td><td>2.66</td><td>2.62</td><td>0/22</td></tr><tr><td>Easiest (280M->280M)</td><td>4.27</td><td>4.18</td><td>0/22</td></tr></table>
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+
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Figure 8: Exponential moving average of domain weights throughout a DoReMi run for 280M and 1B reference/proxy models. In the beginning of the run, the domain weights change quickly and then become more stable after $5 0 \mathrm { k }$ steps. This suggests that 1) smaller compute budgets may require drastically different domain weights, and 2) we may be able to save compute by extrapolating the domain weights after 50k steps.
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Perplexity results for ablations. Table 7 shows the perplexities for ablations on the DRO objective. We change the DRO objective and use these to tune domain weights on 280M reference/proxy models. These tuned domain weights are then used to train a main 280M model. Hardest refers to optimizing the domain-level log-perplexity without baselining with a reference model. Easiest refers to optimizing for the domains with lowest log-perplexity under the reference model. Both ablations do not improve perplexity on any domain over the baseline. Optimizing for the “hardest” domain does not actually result in improving worst-case perplexity, supporting the results of Oren et al. [35], which also employs DRO for language modeling with a baselined loss.
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Trajectory of domain weights. Figure 8 shows the exponential moving average (smoothing parameter 0.99) of domain weights during a run of DoReMi. In both cases, there are domains with very high weight initially and decrease in weight very quickly (within 50k steps). Since we compute the final domain weights by integrating these curves over steps and normalizing, this suggests that if we have a smaller compute budget, these domains could become more important — this highlights the dependence of the mixture weights on the compute budget. At the same time, the domain weights tend to quickly stabilize after 50k steps, suggesting that the optimal domain weights should be similar for larger compute budgets. We may also be able to take advantage of this stability after $5 0 \mathrm { k }$ steps to run DoReMi for a smaller number of steps and extrapolate the domain weights to save compute.
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Comparison of domain weights for 280M and 1B. Table 8 presents the DoReMi domain weights for The Pile at 280M and 1B proxy models. Different proxy model sizes can result in different domain weights, which suggests that there may be multiple local minima in domain weight space. With a 280M proxy model, most of the weight is put on the Pile-CC web text domain, while DoReMi with a
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Table 8: Domain weights on The Pile. Baseline domain weights are computed from the default Pile dataset. With different proxy model sizes, DoReMi (280M) and DoReMi (1B) result in different domain weights. Despite the differences, the qualitative patterns are similar other than the which web domain has the most weight.
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<table><tr><td></td><td>Baseline</td><td>DoReMi(280M)</td><td>DoReMi(1B)</td></tr><tr><td>Pile-CC</td><td>0.1121</td><td>0.6057</td><td>0.1199</td></tr><tr><td>PubMed Central</td><td>0.1071</td><td>0.0046</td><td>0.0149</td></tr><tr><td>Books3</td><td>0.0676</td><td>0.0224</td><td>0.0739</td></tr><tr><td>OpenWebText2</td><td>0.1247</td><td>0.1019</td><td>0.3289</td></tr><tr><td>ArXiv</td><td>0.1052</td><td>0.0036</td><td>0.0384</td></tr><tr><td>Github</td><td>0.0427</td><td>0.0179</td><td>0.0129</td></tr><tr><td>FreeLaw</td><td>0.0386</td><td>0.0043</td><td>0.0148</td></tr><tr><td>StackExchange</td><td>0.0929</td><td>0.0153</td><td>0.0452</td></tr><tr><td>USPTO Backgrounds</td><td>0.0420</td><td>0.0036</td><td>0.0260</td></tr><tr><td>PubMed Abstracts</td><td>0.0845</td><td>0.0113</td><td>0.1461</td></tr><tr><td>Gutenberg (PG-19)</td><td>0.0199</td><td>0.0072</td><td>0.0250</td></tr><tr><td>OpenSubtitles</td><td>0.0124</td><td>0.0047</td><td>0.0017</td></tr><tr><td>Wikipedia (en)</td><td>0.0919</td><td>0.0699</td><td>0.0962</td></tr><tr><td>DMMathematics</td><td>0.0198</td><td>0.0018</td><td>0.0004</td></tr><tr><td>Ubuntu IRC</td><td>0.0074</td><td>0.0093</td><td>0.0044</td></tr><tr><td>BookCorpus2</td><td>0.0044</td><td>0.0061</td><td>0.0029</td></tr><tr><td>EuroParl</td><td>0.0043</td><td>0.0062</td><td>0.0078</td></tr><tr><td>HackerNews</td><td>0.0075</td><td>0.0134</td><td>0.0058</td></tr><tr><td>YoutubeSubtitles</td><td>0.0042</td><td>0.0502</td><td>0.0159</td></tr><tr><td>PhilPapers</td><td>0.0027</td><td>0.0274</td><td>0.0063</td></tr><tr><td>NIHExPorter</td><td>0.0052</td><td>0.0063</td><td>0.0094</td></tr><tr><td>Enron Emails</td><td>0.0030</td><td>0.0070</td><td>0.0033</td></tr></table>
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+
1B proxy model puts most of the weight on OpenWebText2. The overall pattern of the domain weights for the rest of the domains are similar.
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+
# C Training Details
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Data preprocessing. For all datasets, we preprocessed the data by chunking into length 1024 examples with respect to a SentencePiece tokenizer with $2 5 6 \mathrm { k }$ vocabulary size. The examples are separated by domain to facilitate hierarchical sampling (first sample a domain according to some domain weights, then sample an example from that domain at random). To reduce the amount of padding tokens, we made an effort to pack examples (possibly from different domains) together into the same sequence. When doing such a packing, we compute the domain perplexities on a per-token level in DoReMi.
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+
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Baseline domain weights for The Pile. The baseline domain weights for The Pile were computed from The Pile dataset and the number of epochs for each domain given in Gao et al. [17]. After chunking into length 1024 examples, we counted the number of examples in each domain and multiplied by the number of epochs that domain specified in Gao et al. [17]. We then normalized these counts to obtain the baseline domain weights.
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+
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Training setup. For all training runs (including DRO runs), we train with a batch size of 512, initial learning rate of 1e-3, weight decay of 1e-2, and gradient clipping to norm 1. We decay the learning rate exponentially until it reaches a minimum of 1e-4 at the end of training, with a linear warmup of $6 \%$ of the total training steps. We train for 200k steps on The Pile and 300k steps on the GLaM dataset. Models under 1B parameters were trained with TPUv3 accelerators, while 1B and 8B models were trained with TPUv4.
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+
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Model architectures. Table 9 shows the architecture hyperparameters for the model sizes used in the paper. All the models we use are vanilla Transformer decoder-only models with a 256k vocab size.
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+
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+
# D Simple Example Where Data Reweighting Has No Tradeoff
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+
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Motivated by the findings in Section 3.2, we present a simple language modeling example where reweighting the training data from different domains improves perplexity on all domains. The example shows that DoReMi downweights domains that are extremely high or low entropy.
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+
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Setup. Suppose the ground-truth distribution of text $p ^ { * }$ is a mixture over $k$ domains, where each domain $z \in \left\{ 1 , . . . , k \right\}$ is defined by a different unigram distribution $p ^ { * } ( x | z )$ over $m$ tokens. Given a budget of $n$ training samples, the goal is choose domain weights $p ( z )$ $k$ scalars that add to 1) to sample training data with such that we learn the parameters of the unigram distributions $p ^ { * } ( \cdot | z )$ well for all $z$ from 1 to $k$ . Notably, we do not aim to estimate the ground truth mixture proportions across domains.
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+
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| 318 |
+
Table 9: Architecture hyperparameters for various model scales used in the paper. All models are vanilla Transformer decoder-only models and use vocabulary size 256k.
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+
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| 320 |
+
<table><tr><td></td><td>Layers</td><td>Attention heads</td><td>Attention head dim</td><td>Model dim</td><td>Hidden dim</td></tr><tr><td>70M</td><td>3</td><td>4</td><td>64</td><td>256</td><td>1024</td></tr><tr><td>150M</td><td>6</td><td>8</td><td>64</td><td>512</td><td>2048</td></tr><tr><td>280M</td><td>12</td><td>12</td><td>64</td><td>768</td><td>3072</td></tr><tr><td>510M</td><td>12</td><td>16</td><td>64</td><td>1024</td><td>8192</td></tr><tr><td>760M</td><td>12</td><td>20</td><td>64</td><td>1280</td><td>8192</td></tr><tr><td>1B</td><td>16</td><td>32</td><td>64</td><td>2048</td><td>8192</td></tr><tr><td>8B</td><td>32</td><td>32</td><td>128</td><td>4096</td><td>24576</td></tr></table>
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+
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+
Data. Given some domain weights $p ( z )$ , we sample training data hierarchically: first we determine the number of samples $n _ { z }$ per domain $z$ by drawing from a multinomial distribution over $k$ possibilities with probabilities defined by $p ( z )$ and $n$ total trials. Then, for each domain $z$ , we sample $n _ { z }$ tokens from $p ^ { * } ( \cdot | z )$ , forming a vector of tokens $X _ { z }$ with length $n _ { z }$ .
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| 323 |
+
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| 324 |
+
Model. For each domain $z$ , we consider a Bayesian model of the unigram distribution $p ( x | z ; \theta )$ with a Dirichlet prior $p ( \boldsymbol { \theta } | \boldsymbol { z } ; \beta )$ over the unigram distribution parameters $\theta \in \Delta ^ { m }$ . The Dirichlet prior has hyperparameters $\beta \in \mathbb { R } ^ { m }$ , which can be viewed as a “pseudo-count” for each token. For each domain $z$ , we estimate the parameters $\hat { \theta } _ { z }$ by computing the mean of the posterior distribution conditioned on the data:
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| 325 |
+
|
| 326 |
+
$$
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| 327 |
+
\hat { \theta } _ { z } ( x ) = \frac { 1 } { n _ { z } + s _ { z } } \left[ \lambda _ { z } ( x ) + \sum _ { i = 1 } ^ { n _ { z } } \mathbf { 1 } [ X _ { z } [ i ] = x ] \right] \mathrm { ~ f o r ~ a l l ~ } x \in \{ 1 , . . . , m \}
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| 328 |
+
$$
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| 329 |
+
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| 330 |
+
where $s _ { z } = \sum _ { x } \lambda _ { z } ( x )$ is the sum of pseudocounts.
|
| 331 |
+
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| 332 |
+
For a domain $z$ , we can write the parameter error of this estimator as a function of the “difficulty” $H _ { z }$ of predicting the next token and the “quality” of the prior $\Delta _ { z }$ , defined below.
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| 333 |
+
|
| 334 |
+
Lemma D.1. For domain index $z$ with $n _ { z }$ samples, the parameter error is
|
| 335 |
+
|
| 336 |
+
$$
|
| 337 |
+
\sum _ { x } \mathbb { E } [ ( \hat { \theta } _ { z } ( x ) - p ^ { * } ( x \mid z ) ) ^ { 2 } ] = \frac { n _ { z } H _ { z } + s _ { z } ^ { 2 } \Delta _ { z } } { ( n _ { z } + s _ { z } ) ^ { 2 } }
|
| 338 |
+
$$
|
| 339 |
+
|
| 340 |
+
where
|
| 341 |
+
|
| 342 |
+
$$
|
| 343 |
+
\begin{array} { l } { \displaystyle { H _ { z } = \sum _ { x } p ^ { * } ( x \mid z ) ( 1 - p ^ { * } ( x \mid z ) ) } } \\ { \displaystyle { \Delta _ { z } = \sum _ { x } \biggl ( p ^ { * } ( x \mid z ) - \frac { \lambda _ { z } ( x ) } { s _ { z } } \biggr ) ^ { 2 } . } } \end{array}
|
| 344 |
+
$$
|
| 345 |
+
|
| 346 |
+
Proof. The parameter error is
|
| 347 |
+
|
| 348 |
+
$$
|
| 349 |
+
\sum _ { x } \mathbb { E } [ ( \hat { \theta } _ { z } ( x ) - p ^ { * } ( x | z ) ) ^ { 2 } ] = \sum _ { x } \mathbb { E } [ \hat { \theta } _ { z } ( x ) ^ { 2 } ] - 2 \mathbb { E } [ \hat { \theta } _ { z } ( x ) ] p ^ { * } ( x | z ) + p ^ { * } ( x | z ) ^ { 2 } .
|
| 350 |
+
$$
|
| 351 |
+
|
| 352 |
+
Evaluating the terms separately,
|
| 353 |
+
|
| 354 |
+
$$
|
| 355 |
+
\begin{array} { l } { \displaystyle \mathbb { E } [ \hat { \theta } _ { z } ( x ) ] = \frac { 1 } { n _ { z } + s _ { z } } \Bigg [ \lambda _ { z } ( x ) + \sum _ { i = 1 } ^ { n _ { z } } \mathbf { 1 } [ X _ { z } [ i ] = x ] \Bigg ] } \\ { \displaystyle \quad = \frac { 1 } { n _ { z } + s _ { z } } ( \lambda _ { z } ( x ) + n _ { z } p ^ { * } ( x | z ) ) } \\ { \displaystyle \mathbb { E } [ \hat { \theta } _ { z } ( x ) ^ { 2 } ] = \frac { 1 } { ( n _ { z } + s _ { z } ) ^ { 2 } } \mathbb { E } [ ( \lambda _ { z } ( x ) + \sum _ { i = 1 } ^ { n _ { z } } \mathbf { 1 } [ X _ { z } [ i ] = x ] ) ^ { 2 } ] } \\ { \displaystyle \quad = \frac { 1 } { ( n _ { z } + s _ { z } ) ^ { 2 } } [ \lambda _ { z } ( x ) ^ { 2 } + 2 \lambda _ { z } ( x ) n _ { z } p ^ { * } ( x | z ) + n _ { z } p ^ { * } ( x | z ) + ( n _ { z } ^ { 2 } - n _ { z } ) p ^ { * } ( x | z ) ^ { 2 } ] } \end{array}
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| 356 |
+
$$
|
| 357 |
+
|
| 358 |
+
Putting it all together, the parameter error can be written as
|
| 359 |
+
|
| 360 |
+
$$
|
| 361 |
+
\begin{array} { c l } { { \displaystyle \sum _ { x } \mathbb { E } [ ( \hat { \theta } _ { z } ( x ) - p ^ { * } ( x \mid z ) ) ^ { 2 } ] = \sum _ { x } \frac { ( s _ { z } ^ { 2 } - n _ { z } ) p ^ { * } ( x \mid z ) ^ { 2 } + \lambda _ { z } ( x ) ^ { 2 } + ( n _ { z } - 2 s _ { z } \lambda _ { z } ( x ) ) p ^ { * } ( x \mid z ) } { ( n _ { z } + s _ { z } ) ^ { 2 } } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \end{array} = \sum _ { x } \frac { n _ { z } p ^ { * } ( x \mid z ) ( 1 - p ^ { * } ( x \mid z ) ) + s _ { z } ^ { 2 } \Big ( p ^ { * } ( x \mid z ) - \frac { \lambda _ { z } ( x ) } { s _ { z } } \Big ) ^ { 2 } } { ( n _ { z } + s _ { z } ) ^ { 2 } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { { { } } } \\ { } \\ { { { { } } } } \\ { } \\
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| 362 |
+
$$
|
| 363 |
+
|
| 364 |
+
No-tradeoff example. Suppose there are 3 domains $z \in \{ 1 , 2 , 3 \}$ and $m = 3$ vocabulary tokens $x \in \{ 1 , 2 , 3 \}$ . We use a symmetric Dirichlet prior (preferring a uniform token distribution) where $\lambda _ { z } ( x ) = 1 / 3$ for all tokens $x$ and domains $z$ . Here, $\begin{array} { r } { \bar { s _ { z } } = \sum _ { x } \bar { \lambda _ { z } } ( x ) = 1 } \end{array}$ . In this setting, we show that there is a set of domain weights that has strictly lower parameter error than the baseline where we sample the same number of tokens from each domain: $n _ { z }$ are equal for all domains $z$ .
|
| 365 |
+
|
| 366 |
+
Suppose the ground truth paramaters for the unigram distributions are
|
| 367 |
+
|
| 368 |
+
$$
|
| 369 |
+
\begin{array} { r } { \left[ \begin{array} { c c c } { 1 } & { 0 } & { 0 } \\ { 0 . 7 } & { 0 . 2 } & { 0 . 1 } \\ { 1 / 3 } & { 1 / 3 } & { 1 / 3 } \end{array} \right] , } \end{array}
|
| 370 |
+
$$
|
| 371 |
+
|
| 372 |
+
where row $z$ contains the parameters for domain $z$ . For example, token 1 has probability 1 under domain 1’s unigram distribution.
|
| 373 |
+
|
| 374 |
+
For domain $z = 1$ (non-noisy domain), we have $H _ { 1 } = 0$ so the parameter error (according to Lemma D.1) is
|
| 375 |
+
|
| 376 |
+
$$
|
| 377 |
+
\frac { s _ { 1 } ^ { 2 } \Delta _ { 1 } } { ( n _ { 1 } + s _ { 1 } ) ^ { 2 } }
|
| 378 |
+
$$
|
| 379 |
+
|
| 380 |
+
which is strictly decreasing in the number of samples $n _ { 1 }$
|
| 381 |
+
|
| 382 |
+
For domain $z = 3$ (noisy domain), we have $\Delta _ { 3 } = 0$ so the parameter error is
|
| 383 |
+
|
| 384 |
+
$$
|
| 385 |
+
\frac { n _ { 3 } H _ { 3 } } { ( n _ { 3 } + s _ { 3 } ) ^ { 2 } } ,
|
| 386 |
+
$$
|
| 387 |
+
|
| 388 |
+
by Lemma D.1. This error is minimized to zero at $n _ { 3 } = 0$ (no samples). This means that we can allocate samples elsewhere while still reducing error.
|
| 389 |
+
|
| 390 |
+
For $z = 2$ (intermediate entropy domain), we have $\Delta _ { 2 } = 0 . 2 0 7$ and $H _ { 2 } = 0 . 4 6$ . The derivative of the parameter error with respect to the number of samples $n _ { 2 }$ is
|
| 391 |
+
|
| 392 |
+
$$
|
| 393 |
+
\frac { \partial } { \partial n _ { 2 } } \frac { n _ { 2 } H _ { 2 } + s _ { 2 } ^ { 2 } \Delta _ { 2 } } { ( n _ { 2 } + s _ { 2 } ) ^ { 2 } } = \frac { H _ { 2 } ( s _ { 2 } - n _ { 2 } ) - 2 s _ { 2 } ^ { 2 } \Delta _ { 2 } } { ( n _ { 2 } + s _ { 2 } ) ^ { 3 } }
|
| 394 |
+
$$
|
| 395 |
+
|
| 396 |
+
which is negative when
|
| 397 |
+
|
| 398 |
+
$$
|
| 399 |
+
n _ { 2 } > s _ { 2 } - \frac { 2 s _ { 2 } ^ { 2 } \Delta _ { 2 } } { H _ { 2 } } .
|
| 400 |
+
$$
|
| 401 |
+
|
| 402 |
+
This inequality holds in this case since $\begin{array} { r } { \frac { 2 \Delta _ { 2 } } { H _ { 2 } } < 1 } \end{array}$ and $s _ { 2 } = 1$ . Therefore the parameter error is decreasing in the number of samples $n _ { 2 }$ .
|
| 403 |
+
|
| 404 |
+
Thus, any domain weights that reallocate the examples from domain 3 to domains 1 and 2 reduces the parameter error for all domains.
|
| 405 |
+
|
| 406 |
+
What kind of domains are downweighted? Intuitively, we can downweight the very noisy (high entropy/difficulty) domain 3 because the initialization perfectly matches the ground truth. This allows us to reallocate samples to the other domains 1 and 2. Between these, domain 1 requires less additional samples since the parameter error decreases very quickly with the number of samples $n _ { 1 }$ (the difficulty $H _ { 1 }$ is zero). Thus, the easiest domains should also receive relatively less weight. In practice, positive transfer between domains (which is not captured here) can also contribute to scenarios where reweighting results in no tradeoff across domains.
|
| 407 |
+
|
| 408 |
+
Simulation with DoReMi. We consider running DoReMi on the above no-tradeoff instance of the simple example with the ground truth unigram distributions in Equation 14. Note that DoReMi’s domain reweighting step (Step 2, Algorithm 1) involves a loop over $T$ iterative model updates, while the estimator from Equation 2 is computed in closed form. To adapt the estimator for DoReMi, we consider an iterative version where the average is computed in an online fashion. We run DoReMi for $T = 5 0 0$ steps using minibatch size 1 over the $n { = } 5 0 0$ training examples with domain weight update rate $\eta { = } 0 . 5$ . For the model update at step $t$ on an example $x$ from domain $z$ , we increase the pseudo-count $\widehat { \theta } _ { z } ( x )$ by the current domain weight $\alpha _ { t }$ corresponding to domain $z$ . Instead of using the examples in the minibatch (which is only size 1 and doesn’t represent all domains), we compute the per-domain excess log-perplexities in Algorithm 1 using a fixed, independent evaluation set of 30 examples.
|
| 409 |
+
|
| 410 |
+
We compare DoReMi against a model trained with baseline domain weights, which are uniform over the 3 domains. All models are trained on $n { = } 5 0 0$ training examples. We evaluate the log-perplexity of a model on each domain in closed form using the ground truth unigram distribution parameters.
|
| 411 |
+
|
| 412 |
+
On this simple example, DoReMi returns domain weights [0.39,0.61,0.0] after rounding to 2 decimal places. These weights correspond to our intuitions — the first domain (non-noisy) is increased by a small amount, the third domain (noisy) is decreased to 0 weight, and most of the weight is allocated to the second domain. We use these domain weights to generate a new dataset of 500 examples. The model trained with this new dataset improves over the baseline model in perplexity on all domains.
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| 1 |
+
# Dataset Distillation via Factorization
|
| 2 |
+
|
| 3 |
+
Songhua Liu Kai Wang Xingyi Yang Jingwen Ye Xinchao Wang National University of Singapore {songhua.liu,e0823044,xyang}@u.nus.edu, {jingweny,xinchao}@nus.edu.sg
|
| 4 |
+
|
| 5 |
+
# Abstract
|
| 6 |
+
|
| 7 |
+
In this paper, we study dataset distillation (DD), from a novel perspective and introduce a dataset factorization approach, termed HaBa, which is a plug-andplay strategy portable to any existing DD baseline. Unlike conventional DD approaches that aim to produce distilled and representative samples, HaBa explores decomposing a dataset into two components: data Hallucination networks and Bases, where the latter is fed into the former to reconstruct image samples. The flexible combinations between bases and hallucination networks, therefore, equip the distilled data with exponential informativeness gain, which largely increase the representation capability of distilled datasets. To furthermore increase the data efficiency of compression results, we further introduce a pair of adversarial contrastive constraints on the resultant hallucination networks and bases, which increase the diversity of generated images and inject more discriminant information into the factorization. Extensive comparisons and experiments demonstrate that our method can yield significant improvement on downstream classification tasks compared with previous state of the arts, while reducing the total number of compressed parameters by up to $65 \%$ . Moreover, distilled datasets by our approach also achieve ${ \sim } 1 0 \%$ higher accuracy than baseline methods in cross-architecture generalization. Our code is available here.
|
| 8 |
+
|
| 9 |
+
# 1 Introduction
|
| 10 |
+
|
| 11 |
+
The success of deep models on a variety of vision tasks, such as image classification [23, 9, 34], object detection [33, 32], and semantic segmentation [39, 49, 25], is largely attributed to the huge amount of data used for training and various pre-trained models [50]. However, the sheer amount of data introduces significant obstacles for storage, transmission, and data pre-processing. Besides, publishing raw data inevitably brings about privacy or copyright issue in practice [40, 8]. To alleviate these problems, Wang et al. [47] pioneer the research of dataset distillation (DD), to distill a large dataset into a synthetic one with only a limited number of samples, so that the training efforts with the distilled dataset for downstream models on the original dataset can be largely reduced, which facilitates a series of applications like continual learning [37, 36, 48, 27] and black-box optimization [6]. Due the significant practical value of DD, many endeavours have been made on this area [55, 53, 54, 46, 21, 5, 56] to design novel supervision signals to train the synthetic datasets and to further improve their performances.
|
| 12 |
+
|
| 13 |
+
Nevertheless, there is a potential drawback in conventional settings of DD: it largely treats each synthetic sample independently and ignores the inter coherence and relationship between different instances. As such, the information embraced by each sample, despite distilled, is by nature limited. Using the synthetic samples for training downstream models, therefore, inevitably leads to the loss of dataset information. Moreover, the few distilled samples are incompatible with the enormous number of parameters in a deep model and may yield the risk of overfitting.
|
| 14 |
+
|
| 15 |
+
To verify these potential issues, we conduct a pre-experiment on CIFAR10 dataset with 10 synthetic images per class, using MTT [5], the current SOTA solution on DD, as the baseline. In addition to the baseline setting, we also incorporate all the checkpoint synthetic datasets after each $1 0 0 \mathrm { D D }$ iterations in the convergent stage to train the downstream model. Since the synthetic images are fine-tuned during this stage, multiple checkpoints can be viewed as related but different, which may somehow increase the diversity. As a result, it yields overall lower test loss and hence better final results in downstream training, as shown in the blue and green curves in Fig. 2, which indicates that current DD solutions can be potentially improved by leveraging some sample-wise relationships to diversify the distilled data. Nevertheless, simply involving more data samples may also increase the memory overhead. This fact motivates us to ask: is it possible to encode some shared relationships in a dataset implicitly, instead of storing samples directly, to avoid such additional storage costs?
|
| 16 |
+
|
| 17 |
+
|
| 18 |
+
Figure 1: Intuition of our hallucinator-basis factorization for dataset distillation.
|
| 19 |
+
|
| 20 |
+
We show in this paper that, it can indeed be made possible through reformulating the DD task as a factorization problem. As shown in Fig. 1, we propose a novel perspective dubbed HaBa, to factorize a dataset into two compositions: data Hallucination networks and Bases. A data hallucination network, or hallucinator, can take any basis as input and output the corresponding hallucinated image. Supervised by the training objective of DD, a set of hallucinators can synthesize multiple samples from a common basis and are optimized to extract effective relationships among different samples in original datasets explicitly. In this way, information of $| { \mathcal { H } } | \times | B |$ images can be included for a factorization result with $| \mathcal { H } |$ hallucinators and $| B |$ bases via arbitrary pair-wise combination, which improves the data efficiency of traditional DD exponentially. As shown in the yellow curve in Fig. 2, with the same budget on the storage, our strategy achieves better test performance compared with the MTT baseline.
|
| 21 |
+
|
| 22 |
+
|
| 23 |
+
Figure 2: Visualization of test loss using synthetic datasets generated by MTT, MTT with multiple checkpoints, and ours.
|
| 24 |
+
|
| 25 |
+
To further increase the informativeness of factorized results, we introduce a pair of adversarial contrastive constraints to promote sample-wise diversity. The goal of HaBa is to minimize the correlation among images composed of different hallucinators but a common basis, while an adversary tries to maximize it. Such an adversarial scheme, in turn, enforces the hallucinators to produce diversified images and increases the amount of useful information.
|
| 26 |
+
|
| 27 |
+
Notably, HaBa is a versatile strategy that can be built upon existing DD baselines, since it is compatible with any training objective for measuring the similarity between downstream performances as shown in Fig. 1, We conduct extensive experiments to demonstrate the advantages of the proposed method over baseline ones. In all benchmarks and comparisons, HaBa produces significant and consistent improvement on training downstream models, while reducing the total number of compressed parameters by up to $65 \%$ . Furthermore, it demonstrates strong cross-architecture generalization ability with accuracy improvement higher than $10 \%$ . Our contributions are summarized as follows:
|
| 28 |
+
|
| 29 |
+
• We study dataset factorization, a novel perspective to explore dataset distillation, and propose a novel approach termed HaBa for hallucinator-basis factorization. • We present a pair of adversarial contrastive objectives to further increase the data diversity and information capability.
|
| 30 |
+
|
| 31 |
+
• HaBa is a plug-and-play scheme compatible with all existing training objectives of DD and can yield significant and consistent improvement over the state of the arts.
|
| 32 |
+
|
| 33 |
+
# 2 Related Works
|
| 34 |
+
|
| 35 |
+
The goal of dataset distillation (DD) is to optimize a smaller synthetic dataset such that it is capable to take place of original one for training downstream tasks, which is different from coreset selection [1, 7, 13, 38, 44], another branch for dataset compression, directly selecting samples from raw datasets. In this section, we provide a detailed review of previous methods in DD.
|
| 36 |
+
|
| 37 |
+
Motivated from knowledge distillation [15, 12, 52, 51] aiming at model compression, Wang et al. [47] introduce the concept of dataset distillation for dataset compression. The idea is to optimize the synthetic images so that they can minimize loss functions of downstream tasks, where a bilevel optimization algorithm [11] is involved. Following this routine, several works further consider learnable labels beyond samples [3, 42]. Subsequently, Zhao et al. [55] and several following approaches [53, 24] consider matching gradients of a downstream model produced by synthetic samples and real images, which improve the performance significantly. Most recently, Cazenavette et al. [5] argue that single-iteration gradient matching may lead to inferior performance due to error accumulation across multiple steps and thereby propose to match long-range training dynamics of an expert trained on the original dataset. As an alternative method to profile training effects produced by different sets, Nguyen et al. [29, 30] also introduce the kernel ridge-regression approach based on the Neural Tangent Kernel (NTK) in infinitely wide convolutional networks [17].
|
| 38 |
+
|
| 39 |
+
Apart from matching training effects, there are also methods matching data distributions between original and synthetic datasets. For instance, Zhao et al. [54] propose a simple but effective Maximum Mean Discrepancy (MMD) constraint for DD, which does not involve the training of downstream models and enjoys superior training efficiency. Wang et al. [46] propose CAFE, explicitly attempting to align the synthetic and real distributions in the feature space of a downstream network.
|
| 40 |
+
|
| 41 |
+
Above mentioned methods are dedicated to exploring suitable training objectives and pipelines for DD. However, there are few works concerning improving the data efficiency for distilled samples. Although Zhao et al. [53] propose differentiable siamese augmentation (DSA) to enrich the training data, the augmentation operations used, e.g., crop, flip, scale, and rotation, cannot encode any information about the target datasets. In this paper, we study the task in a factorization perspective, to factorize a dataset into two different compositions: data hallucination networks and bases. Both parts carry important knowledge of the raw dataset. For downstream training, hallucinators and bases can perform arbitrary pair-wise combination, i.e., sending any basis to any hallucinator, to create a training sample. The idea of factorization can improve the diversity of distilled training datasets significantly, without introducing additional costs for storage. It is also a versatile strategy compatible with all aforementioned DD methods, which will be demonstrated in the experiment part.
|
| 42 |
+
|
| 43 |
+
Concurrent Works on Efficient Distilled Dataset Parameterization: As a concurrent work, Kim et al. [21] propose IDC for efficient synthetic data parameterization. It reveals that only storing down-sample version of synthetic images and conducting bilinear upsampling in downstream training would not hurt the performance much. Thus, given the same budget of storage, it can store $4 \times$ number of $2 \times$ down-sample synthetic images compared with the baseline. Both IDC and HaBa in this paper are dedicated to improving the data efficiency of synthetic parameters. Interestingly, according to the definition of our hallucinator-basis factorization, IDC can in fact be treated as a special case of HaBa, where the hallucinator is a parameter-free upsampling function and each basis has a smaller spatial size. Nevertheless, the main focuses for IDC and HaBa are different and they are in fact two orthogonal techniques, which can readily join force to enhance the baseline performance, as discussed in Sec. 4.2.
|
| 44 |
+
|
| 45 |
+
# 3 Methods
|
| 46 |
+
|
| 47 |
+
In this section, we elaborate our proposed method HaBa for dataset distillation (DD). Assume that there is an original dataset $\mathcal { T } = \{ ( x _ { i } , y _ { i } ) \} _ { i = 1 } ^ { | T | }$ with $| \tau |$ pairs of a training sample $x _ { i }$ and the corresponding label $y _ { i }$ . DD targets a synthetic dataset $\boldsymbol { S } = \{ ( \hat { x } _ { i } , \hat { y } _ { i } ) \} _ { i = 1 } ^ { | S | }$ with $| S | \ll | T |$ and expects that a model trained on $s$ can have similar performance than that trained on $\tau$ .
|
| 48 |
+
|
| 49 |
+
|
| 50 |
+
Figure 3: Left: Overall pipeline of the proposed hallucinator-basis factorization. $B , \mathcal { H }$ , and $\tau$ denote sets of bases, hallucinators, and original data respectively. Adv. denotes an adversary model. We adopt batch size 2 here for clarity; Right: Architecture of a hallucinator in detail.
|
| 51 |
+
|
| 52 |
+
Traditional DD methods treat each synthetic sample independently and ignore the inner relationship between different samples within a dataset, which results in poor data/information efficiency. Focusing on such drawback, we study DD from a novel perspective and redefine it as a hallucinator-basis factorization problem:
|
| 53 |
+
|
| 54 |
+
$$
|
| 55 |
+
\begin{array} { r } { \mathcal { S } = \{ H _ { \theta _ { j } } \} _ { j = 1 } ^ { | \mathcal { H } | } \cup \{ ( \hat { x } _ { i } , \hat { y } _ { i } ) \} _ { i = 1 } ^ { | \mathcal { B } | } , } \end{array}
|
| 56 |
+
$$
|
| 57 |
+
|
| 58 |
+
where there are $| \mathcal { H } |$ hallucination networks and $| B |$ bases. The $j$ -th hallucinator is parameterized by $\theta _ { i }$ and we denote it by $H _ { \theta _ { i } }$ for $1 \leq j \leq | \mathcal { H } |$ . For downstream training, a training data pair $( \tilde { x } _ { i j } , \tilde { y } _ { i j } )$ is created online via sending the $i$ -th basis, with any $1 \leq i \leq | \boldsymbol { B } |$ , to the $j$ -th hallucinator, with any $1 \leq j \leq | \mathcal { H } |$ , i.e., $\tilde { x } _ { i j } = H _ { \theta _ { j } } ( \hat { x } _ { i } )$ . In this paper, the label $\tilde { y } _ { i j }$ is simply taken as $\hat { y } _ { i }$ .
|
| 59 |
+
|
| 60 |
+
An overview of our method is shown in Fig. 3(Left). To go deeper into the technical details, we first start with the introduction of our basis and data hallucination network in Sec. 3.1. Then, we propose an adversarial contrastive constraint to increase data diversity in Sec. 3.2. Finally, we present the whole training pipeline of the hallucinator-basis factorization for DD in Sec. 3.3.
|
| 61 |
+
|
| 62 |
+
# 3.1 Basis and Hallucinator
|
| 63 |
+
|
| 64 |
+
Basis: Typically, for an image classification dataset $\mathcal { T } = \{ ( x _ { i } , y _ { i } ) \} _ { i = 1 } ^ { | \mathcal { T } | }$ , $x _ { i } \in \mathbb { R } ^ { h \times w \times c }$ and $y _ { i } \in$ $\{ 0 , 1 , . . . , C - 1 \}$ for each $1 \leq i \leq | \mathcal { T } |$ , where each $x _ { i }$ is a $c$ -channel image with a resolution of $h \times w$ , and $C$ is the total number of classes. In previous DD methods, the format/shape of synthetic data pairs $( \hat { x } , \hat { y } )$ has to be held the same as that of real data, so as to make sure the consistency between input and output formats in the training and test time for downstream models. By contrast, since hallucinator networks are capable of spatial-wise and channel-wise transformation, the shape of each ${ \hat { x } } _ { i }$ , $1 \leq i \leq | \boldsymbol { B } |$ , denoted as $\mathbf { \bar { } } h ^ { \prime } \times w ^ { \prime } \times \bar { c } ^ { \prime }$ , is not necessarily the same as that of original samples and thus more flexible. And for a classification problem, we do not modify its label space in this paper for simplicity and maintain the categorical format.
|
| 65 |
+
|
| 66 |
+
Hallucinator: Given a basis $\hat { \boldsymbol { x } } \in \mathbb { R } ^ { h ^ { \prime } \times w ^ { \prime } \times c ^ { \prime } }$ , a data hallucination network, aims to create a new image $\tilde { x } \in \mathbb R ^ { h \times w \times c }$ based on $\hat { x }$ , which can be viewed as a conditional image generation problem. Inspired by image style transfer [19, 16, 18, 26], a typical conditional image generation problem, we devise an encoder-transformation-decoder based architecture for hallucinators, as shown in Fig. 3(Right). Specifically, the encoder, denoted as enc, is composed of CNN blocks, which non-linearly maps an input $\hat { x }$ to a feature space $\mathbb { R } ^ { h ^ { \prime \prime } \times w ^ { \prime \prime } \times c ^ { \prime \prime } }$ . Then, an affine transformation with scale $\sigma$ and shift $\mu$ is conducted on the derived feature, where $\sigma$ and $\mu$ are treated as network parameters in this paper. At last, the decoder $d e c$ under a symmetric CNN architecture with enc projects the transformed feature back to the image space. Formally, this process can be written as:
|
| 67 |
+
|
| 68 |
+
$$
|
| 69 |
+
\hat { f } = e n c ( \hat { x } ) , ~ \tilde { f } = \sigma \times \hat { f } + \mu , ~ \tilde { x } = d e c ( \tilde { f } ) ,
|
| 70 |
+
$$
|
| 71 |
+
|
| 72 |
+
where the multiplication is element-wise operation. There are $| { \mathcal { H } } |$ hallucinators in the whole factorization pipeline and each would be trained to implicitly encode some sample-wise relations by its network parameters.
|
| 73 |
+
|
| 74 |
+
# 3.2 Adversarial Contrastive Constraint
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Ideally, the knowledge encoded by different hallucinators should be as different/orthogonal as possible to get the most benefits for each individual. To instantiate such regularization, let’s consider two composed images $\tilde { x } _ { i j }$ and $\tilde { x } _ { i k }$ from two different hallucinators $H _ { \theta _ { j } }$ and $H _ { \theta _ { k } }$ but a common basis ${ \hat { x } } _ { i }$ The divergence between $\tilde { x } _ { i j }$ and $\tilde { x } _ { i k }$ is expected to be large. To measure the divergence, a feature extractor is required to map an input image to a feature space, and how to train such a feature extractor to find an appropriate feature space is of great importance.
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In this paper, we formalize the training of hallucinators and the feature extractor as a min-max game in a self-consistent manner, where the feature extractor desires to minimize the divergence between $\tilde { x } _ { i j }$ and $\tilde { x } _ { i k }$ while hallucinators, as well as bases, are optimized to maximize it so that the two players can reinforce each other. In specific, the feature extractor, denoted as $F$ and parameterized by $\psi$ , is typically a CNN structure for the downstream task and we adopt features at the last hidden layer before the output layer, denoted as $F _ { - 1 } ( \tilde { x } _ { i j } )$ and $F _ { - 1 } ( \tilde { x } _ { i k } )$ . $F$ is optimized to maximize the correlation between the two feature vectors, which can be quantified by the metric of mutual information (MI). Inspired by the lower bound of MI [45], the objective to minimize the divergence for $F$ is given by the following contrastive form:
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$$
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\mathcal { L } _ { c o n . } = - \frac { 1 } { | \mathcal { H } | ^ { 2 } } \frac { 1 } { | \mathcal { B } | } \sum _ { \substack { 1 \leq j , k \leq | \mathcal { H } | , i = 1 } } \sum _ { i = 1 } ^ { | \mathcal { B } | } \log \frac { \exp { \{ F _ { - 1 } ^ { \top } ( \tilde { x } _ { i j } ) F _ { - 1 } ( \tilde { x } _ { i k } ) / \tau \} } } { \sum _ { u = 1 } ^ { | \mathcal { B } | } \exp { \{ F _ { - 1 } ^ { \top } ( \tilde { x } _ { i j } ) F _ { - 1 } ( \tilde { x } _ { u k } ) / \tau \} } } ,
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$$
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where $\tau$ is a scalar temperature coefficient. For the classification problem, we can alternatively adopt the supervised form of the contrastive loss ${ \mathcal { L } } _ { c o n . }$ ., where $\tilde { x } _ { u k }$ with the same class label as $\tilde { x } _ { i j }$ are also taken into consideration as positive samples in Eq. 3. The supervised contrastive loss can benefit to increase the correlation of samples from the same class [20] for a more reasonable feature representation.
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In addition, the feature space is expected to reflect the task-specific property for a meaningful representation. Thus, we also incorporate the task loss $\mathcal { L } _ { t a s k }$ , e.g., cross-entropy loss in classification tasks, over the synthetic dataset as a supervision signal for $F$ . In this way, the overall training objective for $F$ is defined as:
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$$
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\operatorname* { m i n } _ { \psi } \mathcal { L } _ { F } = \lambda _ { c o n . } \mathcal { L } _ { c o n . } + \lambda _ { t a s k } \mathcal { L } _ { t a s k } ,
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$$
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where $\lambda _ { c o n }$ . and $\lambda _ { t a s k }$ are hyper-parameters controlling the weight for each term.
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$F$ acts as an adversary to minimize the divergence between $\tilde { x } _ { i j }$ and $\tilde { x } _ { i k }$ , while the synthetic dataset is expected to maximize it to increase data diversity. To this ends, the similarity between $F _ { - 1 } ( \tilde { x } _ { i j } )$ and $\bar { F } _ { - 1 } ( \tilde { x } _ { i k } )$ becomes one loss term for hallucinator-basis factorization. In this paper, we adopt the cosine-similarity and the objective $\mathcal { L } _ { c o s }$ . is given by:
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$$
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\mathcal { L } _ { c o s . } = \frac { 1 } { | \mathcal { H } | ^ { 2 } } \frac { 1 } { | \mathcal { B } | } \sum _ { 1 \le j , k \le | \mathcal { H } | , i = 1 \atop j \ne k } \sum _ { i = 1 } ^ { | \mathcal { B } | } \frac { F _ { - 1 } ^ { \top } ( \tilde { x } _ { i j } ) F _ { - 1 } ( \tilde { x } _ { i k } ) } { \| F _ { - 1 } ( \tilde { x } _ { i j } ) \| _ { 2 } \| F _ { - 1 } ( \tilde { x } _ { i k } ) \| _ { 2 } } .
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$$
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During training, the feature extractor and the factorized components are updated alternately to play this min-max game.
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# 3.3 Factorization Training Pipeline
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Following previous paradigms [55, 54, 5, 46], the synthetic dataset $s$ is updated in an iterative algorithm. In each iteration, we randomly sample a batch of hallucinators and bases and conduct pair-wise combinations. The composed images are evaluated by the objective of dataset distillation $\mathcal { L } _ { D D }$ and the similarity metric in Eq. 5:
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$$
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\operatorname* { m i n } _ { S } \mathcal { L } _ { S } = \lambda _ { D D } \mathcal { L } _ { D D } + \lambda _ { c o s . } \mathcal { L } _ { c o s . } ,
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$$
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where hyper-parameters $\lambda _ { D D }$ and $\lambda _ { c o s }$ . balance the loss.
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Notably, the hallucinator-basis factorization is compatible with a variety of configurations of $\mathcal { L } _ { D D }$ by previous arts, which makes it a versatile and effective strategy for DD. In this paper, we adopt the trajectories matching loss in Cazenavette et al. [5] as $\mathcal { L } _ { D D }$ by default thanks to its superior performance. The basic idea is to update a downstream model from a cached checkpoint $\phi _ { t } ^ { * }$ at iteration $t$ , using the synthetic dataset $s$ for $N$ times, and using the real dataset $\tau$ for $M$ times respectively. The updated parameters by the two cases, $\hat { \phi } _ { t + N }$ and $\phi _ { t + M } ^ { * }$ are enforced to be consistent:
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$$
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\begin{array} { r l } & { \hat { \phi } _ { t + n + 1 } \hat { \phi } _ { t + n } - \alpha \nabla _ { \hat { \phi } _ { t + n } } \mathcal { L } _ { t a s k } ( S ) , \quad \hat { \phi } _ { t } \phi _ { t } ^ { * } , \quad 0 \leq n < N , } \\ & { \quad \quad \phi _ { t + m + 1 } ^ { * } \phi _ { t + m } ^ { * } - \beta \nabla _ { \phi _ { t + m } ^ { * } } \mathcal { L } _ { t a s k } ( T ) , \quad 0 \leq m < M , } \\ & { \quad \quad \quad \mathcal { L } _ { D D } = \frac { \| \hat { \phi } _ { t + N } - \phi _ { t + M } ^ { * } \| _ { 2 } ^ { 2 } } { \| \phi _ { t } ^ { * } - \phi _ { t + M } ^ { * } \| _ { 2 } ^ { 2 } } , } \end{array}
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$$
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where $\alpha$ and $\beta$ are learning rates with $s$ and $\tau$ respectively. $\alpha$ is learnable in the framework while $\beta$ is a hyper-parameter. In Sec. 4.2, we also experiment with other settings of $\mathcal { L } _ { D D }$ .
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Based on the supervised signals in Eq. 6, the gradients are backward propagated to the composed images and finally to the sampled hallucinators and bases so as to be updated using a decent algorithm such as SGD. Since all the operations are differentiable, the training can be completed end-to-end.
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# 4 Experiments
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# 4.1 Datasets and Implementing Details
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We conduct evaluations of our method on three standard image classification benchmarks: SVHN [28], CIFAR10, and CIFAR100 [22]. There are 60,000 images for real-world digit recognition in SVHN. For CIFAR10 and CIFAR100, there are 50,000 training images in total. The number of classes for the three datasets are 10, 10, and 100 respectively. All the images are under $3 2 \times 3 2$ resolution in 3-channel RGB format. Following previous works [5], we use ZCA for image preprocessing with Kornia implementation [35] before all the experiments. Experiments with more datasets, including images in larger spatial scales, can be found in the supplement.
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In this paper, for convenience of comparisons with prior works, we maintain the same size with images in original datasets, i.e., $h ^ { \prime } = \bar { h }$ , $w ^ { \prime } = w$ , and $c ^ { \prime } = 3$ for bases. We also experiment with other sizes of bases in Sec. 4.3. For hallucinators, the encoder and decoder contain 1 Conv-ReLU blocks. The number of feature channel $c ^ { \prime \prime }$ is 3. We use 5 hallucinators by default. The learning rates of hallucinators and bases, $\eta _ { H }$ and $\eta _ { B }$ , are the same and for the feature extractor, the learning rate $\eta _ { F }$ is 0.001. Hyper-parameters $\lambda _ { c o n }$ ., $\lambda _ { t a s k }$ , $\lambda _ { D D }$ , and $\lambda _ { c o s }$ . are set as 0.1, 1, 1, and 0.1 empirically. Sensitivities of these hyper-parameters are analyzed in Sec. 4.3. The adversary network has the same architecture as that for computing $\mathcal { L } _ { D D }$ . In experiments on SVHN and CIFAR10, we incorporate all the bases in each iteration, while in experiments on CIFAR100, we adopt a batch size of 300 when the total number of bases is greater than 1,000. We only consider random 2 hallucinators in one iteration for simplicity. The maximal configuration of computational resources is 4 24GB 3090 GPUs. The GPU memory consumption is dependent on that of the baseline method for $\mathcal { L } _ { D D }$ and is slightly higher than it due to the computation of $\mathcal { L } _ { c o s }$ . and ${ \mathcal { L } } _ { c o n . }$ . The baseline method for $\mathcal { L } _ { D D }$ is MTT [5] if not specified. Other settings related to DD hold the same as the baseline. All the quantitative results are based on the mean and standard deviation over 5 repeated experiments. To make sure fair comparisons, the dataset size in our method is equal to the number of bases $| B |$ and the hallucinators are treated as parameterized data augmentors working online in downstream training, just as general data augmentations, which means that the dataset size does not increase compared with the baselines.
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# 4.2 Comparisons
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Comparisons with State of the Arts: We compare HaBa with previous state of the arts for DD in standard settings, to synthesize 1, 10, and 50 images per class (IPC) respectively. In our setting, the number of parameters in a hallucinator is is approximately equal to that for 2 synthetic images, while the size of a basis is equal to that of an image. Taking the storage cost of 5 hallucinators into consideration, we set the number of bases per class (BPC) as IPC minus 1 in each IPC configuration when IPC is greater than 1, to make the comparisons as fair as possible. Candidates are coreset based methods including Random [7, 31], Herding [4, 2], K-Center [10, 38], and Forgetting [43], meta learning based methods including DD [47] and LD [3], training matching based methods including DC [55], DSA [53], and MTT [5], and distribution matching based methods including DM [54] and CAFE [46]. The comparisons follow the standard protocol adopting a 3-layer Conv-InstanceNorm-ReLU-AvgPool ConvNet with 128 channels in training and testing.
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<table><tr><td></td><td>Dataset</td><td></td><td>SVHN</td><td></td><td></td><td>CIFAR10</td><td></td><td></td><td>CIFAR100</td><td></td></tr><tr><td rowspan="2"></td><td>IPC Ratio %</td><td>1 0.014</td><td>10 0.14</td><td>50 0.7</td><td>1 0.02</td><td>10</td><td>50</td><td>1</td><td>10</td><td>50</td></tr><tr><td>Random</td><td></td><td></td><td></td><td></td><td>0.2</td><td>1</td><td>0.2</td><td>2</td><td>10</td></tr><tr><td rowspan="4">Coreset</td><td>Herding</td><td></td><td>14.6±1.6 35.1±4.1 20.9±1.3 50.5±3.3</td><td>70.9±0.9 72.6±0.8</td><td>14.4±2.0 26.0±1.2 43.4±1.0</td><td></td><td></td><td>4.2±0.3</td><td>14.6±0.5 30.0±0.4</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>21.5±1.3 31.6±0.7 40.4±0.6</td><td></td><td></td><td>8.4±0.3</td><td>17.3±0.3 33.7±0.5</td><td></td></tr><tr><td>K-Center</td><td></td><td>21.0±1.5 14.0±1.3 20.1±1.4</td><td></td><td>21.5±1.3 14.7±0.9 27.0±1.4</td><td></td><td></td><td>8.3±0.3</td><td>7.1±0.2 30.5±0.3</td><td></td></tr><tr><td>Forgetting</td><td>12.1±1.7</td><td>16.8±1.2</td><td>227.2±1.5</td><td>13.5±1.2</td><td></td><td>23.3±1.0 23.3±1.1</td><td>4.5±0.3</td><td>9.8±0.2</td><td></td></tr><tr><td rowspan="6">Distillation</td><td>DD+ [47] LD+ [3]</td><td></td><td></td><td></td><td></td><td>36.8±1.2</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>25.7±0.7 38.3±0.4 42.5±0.4</td><td></td><td></td><td>11.5±0.4</td><td></td><td></td></tr><tr><td>DC [55]</td><td></td><td>31.2±1.4 76.1±0.6 82.3±0.3</td><td></td><td>28.3±0.5 44.9±0.5 53.9±0.5</td><td></td><td></td><td>12.8±0.3 25.2±0.3</td><td></td><td></td></tr><tr><td>DSA[53]</td><td></td><td>27.5±1.4 79.2±0.5 84.4±0.4</td><td></td><td>28.8±0.7 52.1±0.5 60.6±0.5</td><td></td><td></td><td>13.9±0.3</td><td>32.3±0.3 42.8±0.4</td><td></td></tr><tr><td>DM [54]</td><td></td><td></td><td></td><td>26.0±0.8 48.9±0.6 63.0±0.4</td><td></td><td></td><td>11.4±0.3</td><td>29.7±0.3 43.6±0.4</td><td></td></tr><tr><td>CAFE[46] CAFE+DSA[46]</td><td></td><td>42.6±3.3 75.9±0.6 81.3±0.3</td><td></td><td>30.3±1.1 46.3±0.6 55.5±0.6</td><td></td><td></td><td></td><td>12.9±0.3 27.8±0.3 37.9±0.3</td><td></td></tr><tr><td rowspan="3"></td><td>MTT[5]</td><td>58.5±1.4 70.8±1.8 85.7±0.1</td><td>42.9±3.0 77.9±0.6 82.3±0.4</td><td></td><td>31.6±0.8 50.9±0.5 62.3±0.4 46.3±0.8 65.3±0.7 71.6±0.2</td><td></td><td></td><td>14.0±0.3 31.5±0.2 24.3±0.3</td><td>39.0±0.1</td><td>42.9±0.2 46.1±0.2</td></tr><tr><td>BPC</td><td></td><td></td><td>49</td><td></td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>Ratio % HaBa</td><td>1 9 0.028</td><td></td><td></td><td>1</td><td></td><td>49</td><td>1</td><td>9</td><td>49</td></tr><tr><td colspan="2">Factorization</td><td>69.8±1.3 83.2±0.4 88.3±0.1</td><td>0.14</td><td>0.7</td><td>0.04 48.3±0.8 69.9±0.4 74.0±0.2</td><td>0.2</td><td>1</td><td>0.22 33.4±0.4 40.2±0.2 47.0±0.2</td><td>1.82</td><td>9.82</td></tr><tr><td colspan="2">Whole Dataset</td><td></td><td>95.4±0.1</td><td></td><td></td><td>84.8±0.1</td><td></td><td></td><td>56.2±0.3</td><td></td></tr></table>
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Table 1: The performance (test accuracy $\%$ ) comparison to state-of-the-art methods. LD† and DD† use AlexNet for CIFAR10, while the rest use ConvNet for training and testing. IPC: Number of Images Per Class; BPC: Number of Bases Per Class; Ratio $( \% )$ : the ratio of distilled images to whole training set. Underline denotes results by our implementation.
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Figure 4: Visualization of factorized results by our HaBa $7 0 . 2 7 \%$ test acc.) and baseline MTT $( 6 5 . 9 2 \%$ test acc.). Zoom-in for better comparisons.
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The comparison results are shown in Tab. 1 and we can observe that HaBa achieves state-of-the-art performance in all datasets and settings. Especially when the ratio of distilled images to the whole training set is less than $1 \%$ , our method can yield significant improvement over all the candidate methods, which demonstrates that the scheme of hallucinator-basis factorization improves the data efficiency for the task of dataset distillation.
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Qualitative Comparisons: We visualize the factorized results by our method as well as the baseline on CIFAR10 dataset with 10 BPC in Fig. 4. Due to the space limitation, we only provide images generated by 2 hallucinators here. More results can be found in the supplement. As shown in the figure, we can find that bases mainly store some main structures and contour information. Different hallucinators would render a basis with diverse styles and details. Thanks to the dataset factorization scheme, the diversity of distilled images by our method is higher than that by the baseline.
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Building upon Different Baselines: To reflect the versatility of the insight, we implement HaBa on multiple state-of-the-art training pipelines of DD, including DC, DM, and MTT. We evaluate the performance of synthetic datasets on CIFAR10 and maintain the IPC of baseline methods as BPC plus 1, which makes storage costs for synthetic datasets as close as possible for fairness. As shown in Tab. 2, when training and testing on ConvNet, the strategy of HaBa can make a consistent improvement over all the baselines, which demonstrates that factorization is a general idea to improve the data efficiency in DD.
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Cross-Architecture Performance: For DD, a satisfactory distilled dataset should have similar training effects to the original one on downstream models with arbitrary architectures. Thus, crossarchitecture generalization performance is an important metric for DD. We use the synthetic datasets trained on ConvNet to train models with different structures including ResNet [14], VGG [41], and AlexNet [23]. The results can be found in Tab. 2. Benefiting from the increased data diversity, HaBa can improve the across-architecture accuracy significantly with a performance gain up to $\mathrm { \bar { 1 } 7 . 5 7 \% }$ . The consistent and significant improvement validates the superior ability of our method to capture the informative features and thus original datasets can be replaced by the synthetic ones better.
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<table><tr><td></td><td>|Method</td><td colspan="3">DC [55]</td><td colspan="3">DM [54]</td><td colspan="3">MTT[5]</td></tr><tr><td></td><td>IPC BPC</td><td>2</td><td>11</td><td>51</td><td>2</td><td>11</td><td>51</td><td>2</td><td>11</td><td>51</td></tr><tr><td></td><td>Baseline</td><td>1 |31.36±0.16 45.29±0.30 54.24±0.61</td><td>10</td><td>50</td><td>1 134.57±0.52 50.35±0.36 62.03±0.29|50.59±0.95 63.90±0.29 69.81±0.48</td><td>10</td><td>50</td><td>1</td><td>10</td><td>50</td></tr><tr><td></td><td>ConvNet w.HaBa Gain Baseline</td><td>34.11±0.47 49.88±0.52 58.91±0.23 +2.75 18.10±0.7618.36±0.3622.14±0.38|</td><td>+4.59</td><td>+4.67</td><td>+2.75</td><td>37.32±0.13 56.83±0.11 64.44±0.40 +6.48 3|22.25±1.00 40.00±1.49 53.40±0.68|35.15±0.96 45.05±1.46 54.47±0.95</td><td>+2.41</td><td>+6.17</td><td>56.76±0.38 69.48±0.26 73.25±0.21 +5.58</td><td>+3.44</td></tr><tr><td>ResNet</td><td>w.HaBa Gain Baseline</td><td>24.49±0.55 24.27±0.56 31.08±0.32 +6.39 28.02±0.26 35.88±0.67 38.73±0.482</td><td>+6.11</td><td>+8.94</td><td>+9.09</td><td>31.34±0.7247.57±0.4959.61±0.35 +7.57</td><td>+6.21</td><td>+12.24 322.28±1.0341.64±0.64 55.17±0.54|38.04±1.19 50.49±1.02 61.36±0.30</td><td>47.39±0.7157.97±0.8864.35±0.60 +12.92</td><td>+9.88</td></tr><tr><td>VGG</td><td>w.HaBa Gain</td><td>29.42±0.93 37.03±0.42 41.91±0.55 +1.40</td><td>+1.15</td><td>+3.18</td><td>26.93±0.62 49.41±0.36 67.47±0.43 +4.65</td><td>+7.77</td><td>+12.30</td><td>+10.22</td><td>48.26±0.54 60.47±0.56 67.47±0.43 +9.98</td><td>+6.11</td></tr><tr><td>AlexNet</td><td>w. HaBa Gain</td><td>Baseline|20.02±1.312.42±1.3529.48±0.8720.67±3.6437.04±0.9249.14±0.94|26.06±1.0135.95±1.5249.20±1.27 22.24±1.14 33.02±0.91 33.42±1.39 +2.22</td><td>+10.60</td><td>+3.94</td><td>+11.47</td><td>32.14±0.60 44.14±0.67 53.09±0.89 +7.10</td><td>+3.95</td><td>43.63±1.46 48.96±3.00 60.07±1.37 +17.57</td><td>+13.01</td><td>+10.87</td></tr></table>
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Table 2: Cross-architecture performance (test accuracy $\%$ ) comparison to different baseline methods of DD HaBa built upon.
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Comparisons under the Same Number of Final Images: In the default comparison protocol, we compare our method with the baselines using the same budget of storage, where our method can store information of exponentially more images than the baselines with the same number of parameters. In this part, we also examine the performance of HaBa under the condition that the number of final images, i.e., $| { \mathcal { H } } | \times | B |$ , is equal to that used by the baseline. Intuitively, given that the objective functions of our method and the baseline are the same exactly, the performance of the baseline can be viewed as an upper bound of ours, since there are significantly less parameters in our method to carry the information of final images in this case. Therefore, we first remove the term $\mathcal { L } _ { c o s }$ . from the loss function of DD in Eq. 6 to guarantee a consistent optimization objective with the baseline. Then, we compare the performance of HaBa and the baseline using 10, 20, 30, 40, and 50 final images respectively. Here, the number of hallucinators $| \mathcal { H } |$ is 2 and the number of bases is thus half of the number of final images. As shown in the red and green curves in Fig. 7, performance of the baseline can be well approximated by ours with only half of the number of parameters, especially when the number of images is relatively large. Remarkably, with the proposed adversary contrastive constraint, our method can even outperform the baseline consistently, as shown in the blue curve, which further demonstrates the effectiveness of the proposed solution.
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Comparisons with Concurrent Works on Efficient Distilled Dataset Parameterization: As a concurrent work on efficient distilled dataset parameterization, IDC [21] is proposed to store $4 \times$ number of $2 \times$ down-sample synthetic images compared with the baseline. The core is to reduce the spatial size for efficient parameterization. For HaBa of this paper, instead, we do not modify the spatial size of bases in the default setting for better qualitative explainablity and more intuitive comparisons with the baselines. In this sense, IDC and HaBa are in fact two orthogonal techniques and they can readily join force to enhance the baseline performance. Here, we try using the technique of IDC and adopting $2 \times$ down-sample synthetic images on the baseline MTT, based on which we further consider adding our HaBa and involving 5 hallucinators. As shown in Tab. 3, with the efficient parameterization of IDC, the performance of baseline can be improved. With HaBa in this paper, the performance can even be further improved a lot: $5 . 1 4 \%$ , $1 . 2 9 \%$ , and $4 . 3 0 \%$ in the three settings respectively, which demonstrates that IDC and HaBa work in different ways.
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Applications in Continual Learning: To further demonstrate the advantage of the proposed method for improving data efficiency, following the setting of DM [54], we conduct experiments on the setting of continual learning on CIFAR-100, with 20 random classes per stage. The average number of parameters per class is $2 0 \times 3 2 \times 3 2 \times 3$ . The synthetic datasets are trained with a ConvNet with 3 blocks. We evaluate synthetic datasets by our method and the DM baseline on the same ConvNet architecture and ResNet18. The results in Fig. 5 demonstrate that the proposed method increases the informativeness of synthetic datasets and thus produce significantly better performance, especially in the cross-architecture setting.
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# 4.3 Ablation Studies
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Loss Terms: To validate the effectiveness of the proposed adversarial contrastive constraints, we design ablation studies on the CIFAR10 dataset over three loss terms: $\mathcal { L } _ { c o s }$ . in Eq. 5, $\mathcal { L } _ { c o n }$ . in Eq. 3, and the task-specific loss $\mathcal { L } _ { t a s k }$ . Through the results in Tab. 4, we can find that deleting any one of them would hurt the performance. We also experiment with involving $\mathcal { L } _ { c o n }$ . for downstream training, to enforce the similarity among images composed of different hallucinators and a common basis. Observed from the last row of Tab. 4, the performance can be further improved, since $\mathcal { L } _ { c o n }$ . helps the representation learning of related samples [20]. Note that we do not use this loss term for downstream training in other experiments for fair and standard comparison.
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Table 3: Comparisons with concurrent work IDC [21] on efficient synthetic parameterization.
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<table><tr><td>#ofParam./Class 2×32×32×3 11×32×32×3 51×32×32×3</td><td></td><td></td><td></td></tr><tr><td>Baseline</td><td>49.89±0.95</td><td>65.92±0.62</td><td>70.73±0.52</td></tr><tr><td>w. IDC</td><td>56.13±0.38</td><td>70.85±0.43</td><td>71.01±0.41</td></tr><tr><td>w. IDC&HaBa</td><td>61.27±0.34</td><td>72.14±0.22</td><td>75.31±0.27</td></tr></table>
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Figure 5: Comparisons on the setting of continual setting. Results on the ConvNet3 (Left) and ResNet18 (Right) architectures are shown.
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<table><tr><td>BPC</td><td>1</td><td>10</td><td>50</td></tr><tr><td>HaBa w/o Lcos.</td><td>54.56±0.61</td><td></td><td>70.16±0.44 73.93±0.21</td></tr><tr><td>HaBa w/o Lcon.</td><td>54.91±0.49</td><td>70.07±0.48</td><td>72.50±0.39</td></tr><tr><td>HaBa W/o Ltask</td><td>54.62±0.42</td><td></td><td>：70.07±0.16 72.74±0.20</td></tr><tr><td>HaBa Full</td><td>55.66±0.29</td><td>70.27±0.63</td><td>74.04±0.16</td></tr><tr><td>HaBawLcon. Downstream</td><td>56.78±0.22</td><td>70.44±0.15</td><td>75.00±0.52</td></tr></table>
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Table 4: Results of ablation study on loss terms in HaBa: $\mathcal { L } _ { c o s . }$ ., ${ \mathcal { L } } _ { c o n . }$ ., and $\mathcal { L } _ { t a s k }$ .
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Figure 6: Impacts of different $\lambda _ { c o s }$ . and $\lambda _ { c o n }$ . on the test accuracy.
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We examine the sensitivities of hyper-parameters $\lambda _ { c o s }$ . and $\lambda _ { c o n }$ . used to balance the weights of loss terms $\mathcal { L } _ { c o s }$ . and $\mathcal { L } _ { c o n }$ . respectively in Fig. 6. The results are evaluated on the CIFAR10 dataset with 10 BPC. We can observe that the overall performance is not sensitive to the selection of these hyper-parameters and our method makes a consistent improvement over the baseline with 11 IPC.
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Class-Independent Hallucinators v.s. Shared Hallucinators: In the default setting of HaBa, each class maintains a certain number of bases independently and all the classes share the same set of hallucinators. But what about the case that hallucinators are also made class-independent? We study this problem experimentally in Tab. 5. Given the same BPC, class-independent hallucinators can indeed somehow improve the performance when there are fewer synthetic samples, e.g., 1 BPC. However, when BPC is higher, equipping each class with an independent set of hallucinators would not benefit the performance. There are probably two reasons: (1) shared hallucinators across all the classes extract global information of the whole dataset, which encodes more representative and universal knowledge; and (2) the class-independent case would make the number of hallucinators 10 times for the CIFAR10 dataset, which leaves a heavy burden for the optimization process. Thus, as indicated in Tab. 5, a better solution is to make room for more bases using the memory allocated to store class-independent hallucinators initially, which would result in more satisfactory data efficiency.
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Number of Channels Used by Basis: By default, the shape of a basis is the same as that of a real image, which is generally in RGB 3-channel format. In fact, in Fig. 8(Left), we also verify that it is also possible to use single-channel basis, which can reduce the memory cost by nearly 2/3 without hurting the performance too much. Interestingly, if the memory cost is held the same, we can choose to use 3 times BPC to store single-channel bases, rather than 3-channel ones. This would yield impressive improvement on the test accuracy when BPC is small. Note that for baseline results, IPC is set as the corresponding BPC plus 1.
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Number of Hallucinators: We study the impact of the number of hallucinators, i.e., $| { \mathcal { H } } |$ , in Fig. 8(Right). We can observe that when BPC is small, including more hallucinators is helpful for the performance. Nevertheless, when BPC is 10 or 50, the performance would not improve with more hallucinators when $| \mathcal { H } | > 1 0$ . One reason is that when $| \mathcal { H } |$ is large, the sampling of hallucinators in each iteration is sparse, which makes the joint optimization of all the hallucinators more difficult.
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Data Augmentation: The similarity between our hallucinator set and data augmentation lies that both of them can contribute to generating more samples and increasing the diversity. However, the essential difference is that our hallucinators are optimized to encode sample-wise relationships in
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Figure 7: Comparisons with the baseline under the same number of final images.
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<table><tr><td>BPC</td><td>1</td><td>10</td><td>50</td></tr><tr><td>w/o Share</td><td>55.96±0.51</td><td>69.00±0.20</td><td>69.81±0.56</td></tr><tr><td>Share</td><td>55.66±0.29</td><td>70.27±0.63</td><td>74.04±0.16</td></tr><tr><td>Baseline (IPC=BPC)</td><td>45.29±0.86</td><td>62.77±0.56</td><td>71.09±0.34</td></tr><tr><td>Share (Same Memory)</td><td>70.27±0.63</td><td>72.17±0.30</td><td>74.89±0.15</td></tr><tr><td>Baseline (Same Memory)</td><td>65.92±0.62</td><td>68.58±0.49</td><td>73.55±0.48</td></tr></table>
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Table 5: Study on whether all the classes should share the same set of hallucinators.
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Figure 8: Study on the number of channels used by bases and the number of hallucinators.
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Table 6: Impact of data augmentation.
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<table><tr><td></td><td>ConvNet</td><td>ResNet</td><td>VGG</td><td>AlexNet</td></tr><tr><td>w/o aug.</td><td>60.63±0.21</td><td>43.24±0.83 48.02±0.53</td><td></td><td>30.58±1.44</td></tr><tr><td>Baseline</td><td>63.90±0.29</td><td>45.05±1.46 50.49±1.02</td><td></td><td>35.95±1.52</td></tr><tr><td>w/o aug. Ours</td><td>68.08±0.23 69.48±0.26</td><td>56.37±0.11 57.97±0.88</td><td></td><td>59.04±0.50 48.27±3.04 60.47±0.56 48.96±3.00</td></tr></table>
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a dataset, while data augmentation is based on some prior and heuristic knowledge of images. By default, both our method and the baseline adopt the data augmentation strategy DSA [53]. To study the relationship between the two schemes experimentally, we attempt to remove DSA from baseline and our method and report the corresponding results in Tab. 6. The evaluation is on CIFAR10 with 11 IPC for baseline and 10 BPC for ours. Through the results, we can find that (1) our method without data augmentation can also outperform the baseline method with augmentation significantly, which means that the mechanism of HaBa can benefit the dataset distillation task more with the learning of global information of a dataset in hallucinators; and (2) with data augmentation, our performance can be further improved, which indicates that HaBa and DSA work in different manners.
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# 5 Conclusions, Limitations, and Future Works
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This paper proposes a novel hallucinator-basis factorization method dubbed HaBa for dataset distillation (DD). It uses hallucinators to encode inner relations between different samples in original datasets, which can largely improve the data efficiency of distilled results. To diversify the knowledge captured by different hallucinators, a pair of adversarial contrastive constraints is further introduced. Extensive evaluations and comparisons on multiple benchmark datasets demonstrate that HaBa is capable of significantly improving the performance of downstream models trained on the synthetic dataset, using only $3 5 \%$ cost of memory for storage. Moreover, it is a versatile strategy that is compatible with different configurations of DD frameworks and yields consistent improvement.
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Despite the superior performance of the proposed hallucinator-basis factorization (HaBa) scheme, there are also some potential limitations. On the one hand, compared with the baseline method HaBa built upon, the process of online pairwise combination between hallucinators and bases in training increases the cost of time and GPU memory slightly, although light-weight hallucinators are adopted. On the other hand, it may inherited the limitations of baseline methods. For example, when the number of images is large, further increasing the number would produce limited performance gain.
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For future works, beyond the training efficiency of HaBa, introducing class-wise relationship may also be a potential research direction. For example, it is probably optimal that one class shares hallucinators with some specific classes but does not share with others. It is also promising to explore more advance factorization for a dataset to further improve the performance.
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# Acknowledgement
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This research is supported by the National Research Foundation, Singapore under its Medium Sized Centre for Advanced Robotics Technology Innovation (WBS: A-0009428-09-00). Xinchao Wang is the corresponding author.
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# Checklist
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1. For all authors...
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]
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(b) Did you describe the limitations of your work? [Yes] Please refer to the supplement.
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(c) Did you discuss any potential negative societal impacts of your work? [N/A]
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(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
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2. If you are including theoretical results...
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(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
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3. If you ran experiments...
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(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] Please refer to the supplement.
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(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] Please refer to Sec. 4.1.
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(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We run all the experiments 5 times and report the mean and standard deviation of the performance.
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(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] Please refer to Sec. 4.1.
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(a) If your work uses existing assets, did you cite the creators? [Yes]
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(b) Did you mention the license of the assets? [Yes]
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(c) Did you include any new assets either in the supplemental material or as a URL? [Yes]
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(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]
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(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
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(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]
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(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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|
| 1 |
+
[
|
| 2 |
+
{
|
| 3 |
+
"type": "text",
|
| 4 |
+
"text": "Dataset Distillation via Factorization ",
|
| 5 |
+
"text_level": 1,
|
| 6 |
+
"bbox": [
|
| 7 |
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| 8 |
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| 9 |
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| 10 |
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| 11 |
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],
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| 12 |
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"page_idx": 0
|
| 13 |
+
},
|
| 14 |
+
{
|
| 15 |
+
"type": "text",
|
| 16 |
+
"text": "Songhua Liu Kai Wang Xingyi Yang Jingwen Ye Xinchao Wang National University of Singapore {songhua.liu,e0823044,xyang}@u.nus.edu, {jingweny,xinchao}@nus.edu.sg ",
|
| 17 |
+
"bbox": [
|
| 18 |
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| 19 |
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| 20 |
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| 21 |
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| 22 |
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| 23 |
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"page_idx": 0
|
| 24 |
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},
|
| 25 |
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{
|
| 26 |
+
"type": "text",
|
| 27 |
+
"text": "Abstract ",
|
| 28 |
+
"text_level": 1,
|
| 29 |
+
"bbox": [
|
| 30 |
+
462,
|
| 31 |
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| 32 |
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| 33 |
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| 34 |
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| 35 |
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"page_idx": 0
|
| 36 |
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},
|
| 37 |
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{
|
| 38 |
+
"type": "text",
|
| 39 |
+
"text": "In this paper, we study dataset distillation (DD), from a novel perspective and introduce a dataset factorization approach, termed HaBa, which is a plug-andplay strategy portable to any existing DD baseline. Unlike conventional DD approaches that aim to produce distilled and representative samples, HaBa explores decomposing a dataset into two components: data Hallucination networks and Bases, where the latter is fed into the former to reconstruct image samples. The flexible combinations between bases and hallucination networks, therefore, equip the distilled data with exponential informativeness gain, which largely increase the representation capability of distilled datasets. To furthermore increase the data efficiency of compression results, we further introduce a pair of adversarial contrastive constraints on the resultant hallucination networks and bases, which increase the diversity of generated images and inject more discriminant information into the factorization. Extensive comparisons and experiments demonstrate that our method can yield significant improvement on downstream classification tasks compared with previous state of the arts, while reducing the total number of compressed parameters by up to $65 \\%$ . Moreover, distilled datasets by our approach also achieve ${ \\sim } 1 0 \\%$ higher accuracy than baseline methods in cross-architecture generalization. Our code is available here. ",
|
| 40 |
+
"bbox": [
|
| 41 |
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| 42 |
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| 43 |
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| 44 |
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| 45 |
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],
|
| 46 |
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"page_idx": 0
|
| 47 |
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},
|
| 48 |
+
{
|
| 49 |
+
"type": "text",
|
| 50 |
+
"text": "1 Introduction ",
|
| 51 |
+
"text_level": 1,
|
| 52 |
+
"bbox": [
|
| 53 |
+
174,
|
| 54 |
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| 55 |
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| 56 |
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| 57 |
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|
| 58 |
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"page_idx": 0
|
| 59 |
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},
|
| 60 |
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{
|
| 61 |
+
"type": "text",
|
| 62 |
+
"text": "The success of deep models on a variety of vision tasks, such as image classification [23, 9, 34], object detection [33, 32], and semantic segmentation [39, 49, 25], is largely attributed to the huge amount of data used for training and various pre-trained models [50]. However, the sheer amount of data introduces significant obstacles for storage, transmission, and data pre-processing. Besides, publishing raw data inevitably brings about privacy or copyright issue in practice [40, 8]. To alleviate these problems, Wang et al. [47] pioneer the research of dataset distillation (DD), to distill a large dataset into a synthetic one with only a limited number of samples, so that the training efforts with the distilled dataset for downstream models on the original dataset can be largely reduced, which facilitates a series of applications like continual learning [37, 36, 48, 27] and black-box optimization [6]. Due the significant practical value of DD, many endeavours have been made on this area [55, 53, 54, 46, 21, 5, 56] to design novel supervision signals to train the synthetic datasets and to further improve their performances. ",
|
| 63 |
+
"bbox": [
|
| 64 |
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| 65 |
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| 66 |
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| 67 |
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| 68 |
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],
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| 69 |
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"page_idx": 0
|
| 70 |
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},
|
| 71 |
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{
|
| 72 |
+
"type": "text",
|
| 73 |
+
"text": "Nevertheless, there is a potential drawback in conventional settings of DD: it largely treats each synthetic sample independently and ignores the inter coherence and relationship between different instances. As such, the information embraced by each sample, despite distilled, is by nature limited. Using the synthetic samples for training downstream models, therefore, inevitably leads to the loss of dataset information. Moreover, the few distilled samples are incompatible with the enormous number of parameters in a deep model and may yield the risk of overfitting. ",
|
| 74 |
+
"bbox": [
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| 75 |
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| 76 |
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| 77 |
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| 78 |
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| 79 |
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],
|
| 80 |
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"page_idx": 0
|
| 81 |
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},
|
| 82 |
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{
|
| 83 |
+
"type": "text",
|
| 84 |
+
"text": "To verify these potential issues, we conduct a pre-experiment on CIFAR10 dataset with 10 synthetic images per class, using MTT [5], the current SOTA solution on DD, as the baseline. In addition to the baseline setting, we also incorporate all the checkpoint synthetic datasets after each $1 0 0 \\mathrm { D D }$ iterations in the convergent stage to train the downstream model. Since the synthetic images are fine-tuned during this stage, multiple checkpoints can be viewed as related but different, which may somehow increase the diversity. As a result, it yields overall lower test loss and hence better final results in downstream training, as shown in the blue and green curves in Fig. 2, which indicates that current DD solutions can be potentially improved by leveraging some sample-wise relationships to diversify the distilled data. Nevertheless, simply involving more data samples may also increase the memory overhead. This fact motivates us to ask: is it possible to encode some shared relationships in a dataset implicitly, instead of storing samples directly, to avoid such additional storage costs? ",
|
| 85 |
+
"bbox": [
|
| 86 |
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| 87 |
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| 88 |
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| 89 |
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| 90 |
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|
| 91 |
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"page_idx": 0
|
| 92 |
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},
|
| 93 |
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{
|
| 94 |
+
"type": "image",
|
| 95 |
+
"img_path": "images/d54c5382aee43c1876cd442f8b0734b400fc447b73082889e580be83543cb7c8.jpg",
|
| 96 |
+
"image_caption": [
|
| 97 |
+
"Figure 1: Intuition of our hallucinator-basis factorization for dataset distillation. "
|
| 98 |
+
],
|
| 99 |
+
"image_footnote": [],
|
| 100 |
+
"bbox": [
|
| 101 |
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| 102 |
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| 103 |
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| 104 |
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| 105 |
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|
| 106 |
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"page_idx": 1
|
| 107 |
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},
|
| 108 |
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{
|
| 109 |
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"type": "text",
|
| 110 |
+
"text": "",
|
| 111 |
+
"bbox": [
|
| 112 |
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173,
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| 113 |
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| 114 |
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| 115 |
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| 116 |
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],
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| 117 |
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"page_idx": 1
|
| 118 |
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},
|
| 119 |
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{
|
| 120 |
+
"type": "text",
|
| 121 |
+
"text": "We show in this paper that, it can indeed be made possible through reformulating the DD task as a factorization problem. As shown in Fig. 1, we propose a novel perspective dubbed HaBa, to factorize a dataset into two compositions: data Hallucination networks and Bases. A data hallucination network, or hallucinator, can take any basis as input and output the corresponding hallucinated image. Supervised by the training objective of DD, a set of hallucinators can synthesize multiple samples from a common basis and are optimized to extract effective relationships among different samples in original datasets explicitly. In this way, information of $| { \\mathcal { H } } | \\times | B |$ images can be included for a factorization result with $| \\mathcal { H } |$ hallucinators and $| B |$ bases via arbitrary pair-wise combination, which improves the data efficiency of traditional DD exponentially. As shown in the yellow curve in Fig. 2, with the same budget on the storage, our strategy achieves better test performance compared with the MTT baseline. ",
|
| 122 |
+
"bbox": [
|
| 123 |
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| 126 |
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| 127 |
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| 128 |
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"page_idx": 1
|
| 129 |
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},
|
| 130 |
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{
|
| 131 |
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"type": "image",
|
| 132 |
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"img_path": "images/43a4d3d0bb0608da3953376c445989ec5f8437bf4c1e7987ce40ad4016188b39.jpg",
|
| 133 |
+
"image_caption": [
|
| 134 |
+
"Figure 2: Visualization of test loss using synthetic datasets generated by MTT, MTT with multiple checkpoints, and ours. "
|
| 135 |
+
],
|
| 136 |
+
"image_footnote": [],
|
| 137 |
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"bbox": [
|
| 138 |
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| 139 |
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| 140 |
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| 141 |
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| 142 |
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|
| 143 |
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"page_idx": 1
|
| 144 |
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},
|
| 145 |
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{
|
| 146 |
+
"type": "text",
|
| 147 |
+
"text": "To further increase the informativeness of factorized results, we introduce a pair of adversarial contrastive constraints to promote sample-wise diversity. The goal of HaBa is to minimize the correlation among images composed of different hallucinators but a common basis, while an adversary tries to maximize it. Such an adversarial scheme, in turn, enforces the hallucinators to produce diversified images and increases the amount of useful information. ",
|
| 148 |
+
"bbox": [
|
| 149 |
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|
| 150 |
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| 151 |
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| 152 |
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| 153 |
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|
| 154 |
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"page_idx": 1
|
| 155 |
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},
|
| 156 |
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{
|
| 157 |
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"type": "text",
|
| 158 |
+
"text": "Notably, HaBa is a versatile strategy that can be built upon existing DD baselines, since it is compatible with any training objective for measuring the similarity between downstream performances as shown in Fig. 1, We conduct extensive experiments to demonstrate the advantages of the proposed method over baseline ones. In all benchmarks and comparisons, HaBa produces significant and consistent improvement on training downstream models, while reducing the total number of compressed parameters by up to $65 \\%$ . Furthermore, it demonstrates strong cross-architecture generalization ability with accuracy improvement higher than $10 \\%$ . Our contributions are summarized as follows: ",
|
| 159 |
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| 160 |
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|
| 166 |
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|
| 167 |
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{
|
| 168 |
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"type": "text",
|
| 169 |
+
"text": "• We study dataset factorization, a novel perspective to explore dataset distillation, and propose a novel approach termed HaBa for hallucinator-basis factorization. • We present a pair of adversarial contrastive objectives to further increase the data diversity and information capability. ",
|
| 170 |
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| 178 |
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{
|
| 179 |
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"type": "text",
|
| 180 |
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"text": "• HaBa is a plug-and-play scheme compatible with all existing training objectives of DD and can yield significant and consistent improvement over the state of the arts. ",
|
| 181 |
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},
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| 189 |
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{
|
| 190 |
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"type": "text",
|
| 191 |
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"text": "2 Related Works ",
|
| 192 |
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"text_level": 1,
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| 193 |
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"type": "text",
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| 203 |
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"text": "The goal of dataset distillation (DD) is to optimize a smaller synthetic dataset such that it is capable to take place of original one for training downstream tasks, which is different from coreset selection [1, 7, 13, 38, 44], another branch for dataset compression, directly selecting samples from raw datasets. In this section, we provide a detailed review of previous methods in DD. ",
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"text": "Motivated from knowledge distillation [15, 12, 52, 51] aiming at model compression, Wang et al. [47] introduce the concept of dataset distillation for dataset compression. The idea is to optimize the synthetic images so that they can minimize loss functions of downstream tasks, where a bilevel optimization algorithm [11] is involved. Following this routine, several works further consider learnable labels beyond samples [3, 42]. Subsequently, Zhao et al. [55] and several following approaches [53, 24] consider matching gradients of a downstream model produced by synthetic samples and real images, which improve the performance significantly. Most recently, Cazenavette et al. [5] argue that single-iteration gradient matching may lead to inferior performance due to error accumulation across multiple steps and thereby propose to match long-range training dynamics of an expert trained on the original dataset. As an alternative method to profile training effects produced by different sets, Nguyen et al. [29, 30] also introduce the kernel ridge-regression approach based on the Neural Tangent Kernel (NTK) in infinitely wide convolutional networks [17]. ",
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"text": "Apart from matching training effects, there are also methods matching data distributions between original and synthetic datasets. For instance, Zhao et al. [54] propose a simple but effective Maximum Mean Discrepancy (MMD) constraint for DD, which does not involve the training of downstream models and enjoys superior training efficiency. Wang et al. [46] propose CAFE, explicitly attempting to align the synthetic and real distributions in the feature space of a downstream network. ",
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"text": "Above mentioned methods are dedicated to exploring suitable training objectives and pipelines for DD. However, there are few works concerning improving the data efficiency for distilled samples. Although Zhao et al. [53] propose differentiable siamese augmentation (DSA) to enrich the training data, the augmentation operations used, e.g., crop, flip, scale, and rotation, cannot encode any information about the target datasets. In this paper, we study the task in a factorization perspective, to factorize a dataset into two different compositions: data hallucination networks and bases. Both parts carry important knowledge of the raw dataset. For downstream training, hallucinators and bases can perform arbitrary pair-wise combination, i.e., sending any basis to any hallucinator, to create a training sample. The idea of factorization can improve the diversity of distilled training datasets significantly, without introducing additional costs for storage. It is also a versatile strategy compatible with all aforementioned DD methods, which will be demonstrated in the experiment part. ",
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"text": "Concurrent Works on Efficient Distilled Dataset Parameterization: As a concurrent work, Kim et al. [21] propose IDC for efficient synthetic data parameterization. It reveals that only storing down-sample version of synthetic images and conducting bilinear upsampling in downstream training would not hurt the performance much. Thus, given the same budget of storage, it can store $4 \\times$ number of $2 \\times$ down-sample synthetic images compared with the baseline. Both IDC and HaBa in this paper are dedicated to improving the data efficiency of synthetic parameters. Interestingly, according to the definition of our hallucinator-basis factorization, IDC can in fact be treated as a special case of HaBa, where the hallucinator is a parameter-free upsampling function and each basis has a smaller spatial size. Nevertheless, the main focuses for IDC and HaBa are different and they are in fact two orthogonal techniques, which can readily join force to enhance the baseline performance, as discussed in Sec. 4.2. ",
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"text": "3 Methods ",
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"text": "In this section, we elaborate our proposed method HaBa for dataset distillation (DD). Assume that there is an original dataset $\\mathcal { T } = \\{ ( x _ { i } , y _ { i } ) \\} _ { i = 1 } ^ { | T | }$ with $| \\tau |$ pairs of a training sample $x _ { i }$ and the corresponding label $y _ { i }$ . DD targets a synthetic dataset $\\boldsymbol { S } = \\{ ( \\hat { x } _ { i } , \\hat { y } _ { i } ) \\} _ { i = 1 } ^ { | S | }$ with $| S | \\ll | T |$ and expects that a model trained on $s$ can have similar performance than that trained on $\\tau$ . ",
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"type": "image",
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"img_path": "images/994ecdccd369f7082395e0bc2c84828eb75d9355cc1584bd82df700450ac580c.jpg",
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"image_caption": [
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"Figure 3: Left: Overall pipeline of the proposed hallucinator-basis factorization. $B , \\mathcal { H }$ , and $\\tau$ denote sets of bases, hallucinators, and original data respectively. Adv. denotes an adversary model. We adopt batch size 2 here for clarity; Right: Architecture of a hallucinator in detail. "
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"text": "Traditional DD methods treat each synthetic sample independently and ignore the inner relationship between different samples within a dataset, which results in poor data/information efficiency. Focusing on such drawback, we study DD from a novel perspective and redefine it as a hallucinator-basis factorization problem: ",
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"text": "$$\n\\begin{array} { r } { \\mathcal { S } = \\{ H _ { \\theta _ { j } } \\} _ { j = 1 } ^ { | \\mathcal { H } | } \\cup \\{ ( \\hat { x } _ { i } , \\hat { y } _ { i } ) \\} _ { i = 1 } ^ { | \\mathcal { B } | } , } \\end{array}\n$$",
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"text": "where there are $| \\mathcal { H } |$ hallucination networks and $| B |$ bases. The $j$ -th hallucinator is parameterized by $\\theta _ { i }$ and we denote it by $H _ { \\theta _ { i } }$ for $1 \\leq j \\leq | \\mathcal { H } |$ . For downstream training, a training data pair $( \\tilde { x } _ { i j } , \\tilde { y } _ { i j } )$ is created online via sending the $i$ -th basis, with any $1 \\leq i \\leq | \\boldsymbol { B } |$ , to the $j$ -th hallucinator, with any $1 \\leq j \\leq | \\mathcal { H } |$ , i.e., $\\tilde { x } _ { i j } = H _ { \\theta _ { j } } ( \\hat { x } _ { i } )$ . In this paper, the label $\\tilde { y } _ { i j }$ is simply taken as $\\hat { y } _ { i }$ . ",
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"text": "An overview of our method is shown in Fig. 3(Left). To go deeper into the technical details, we first start with the introduction of our basis and data hallucination network in Sec. 3.1. Then, we propose an adversarial contrastive constraint to increase data diversity in Sec. 3.2. Finally, we present the whole training pipeline of the hallucinator-basis factorization for DD in Sec. 3.3. ",
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"text": "3.1 Basis and Hallucinator ",
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"text_level": 1,
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"text": "Basis: Typically, for an image classification dataset $\\mathcal { T } = \\{ ( x _ { i } , y _ { i } ) \\} _ { i = 1 } ^ { | \\mathcal { T } | }$ , $x _ { i } \\in \\mathbb { R } ^ { h \\times w \\times c }$ and $y _ { i } \\in$ $\\{ 0 , 1 , . . . , C - 1 \\}$ for each $1 \\leq i \\leq | \\mathcal { T } |$ , where each $x _ { i }$ is a $c$ -channel image with a resolution of $h \\times w$ , and $C$ is the total number of classes. In previous DD methods, the format/shape of synthetic data pairs $( \\hat { x } , \\hat { y } )$ has to be held the same as that of real data, so as to make sure the consistency between input and output formats in the training and test time for downstream models. By contrast, since hallucinator networks are capable of spatial-wise and channel-wise transformation, the shape of each ${ \\hat { x } } _ { i }$ , $1 \\leq i \\leq | \\boldsymbol { B } |$ , denoted as $\\mathbf { \\bar { } } h ^ { \\prime } \\times w ^ { \\prime } \\times \\bar { c } ^ { \\prime }$ , is not necessarily the same as that of original samples and thus more flexible. And for a classification problem, we do not modify its label space in this paper for simplicity and maintain the categorical format. ",
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"text": "Hallucinator: Given a basis $\\hat { \\boldsymbol { x } } \\in \\mathbb { R } ^ { h ^ { \\prime } \\times w ^ { \\prime } \\times c ^ { \\prime } }$ , a data hallucination network, aims to create a new image $\\tilde { x } \\in \\mathbb R ^ { h \\times w \\times c }$ based on $\\hat { x }$ , which can be viewed as a conditional image generation problem. Inspired by image style transfer [19, 16, 18, 26], a typical conditional image generation problem, we devise an encoder-transformation-decoder based architecture for hallucinators, as shown in Fig. 3(Right). Specifically, the encoder, denoted as enc, is composed of CNN blocks, which non-linearly maps an input $\\hat { x }$ to a feature space $\\mathbb { R } ^ { h ^ { \\prime \\prime } \\times w ^ { \\prime \\prime } \\times c ^ { \\prime \\prime } }$ . Then, an affine transformation with scale $\\sigma$ and shift $\\mu$ is conducted on the derived feature, where $\\sigma$ and $\\mu$ are treated as network parameters in this paper. At last, the decoder $d e c$ under a symmetric CNN architecture with enc projects the transformed feature back to the image space. Formally, this process can be written as: ",
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"img_path": "images/83371c7062eba8a23618919cdaa5ec5189e6ebc09175e165cd63bf21be151338.jpg",
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"text": "$$\n\\hat { f } = e n c ( \\hat { x } ) , ~ \\tilde { f } = \\sigma \\times \\hat { f } + \\mu , ~ \\tilde { x } = d e c ( \\tilde { f } ) ,\n$$",
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"text": "where the multiplication is element-wise operation. There are $| { \\mathcal { H } } |$ hallucinators in the whole factorization pipeline and each would be trained to implicitly encode some sample-wise relations by its network parameters. ",
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"text": "3.2 Adversarial Contrastive Constraint ",
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"text": "Ideally, the knowledge encoded by different hallucinators should be as different/orthogonal as possible to get the most benefits for each individual. To instantiate such regularization, let’s consider two composed images $\\tilde { x } _ { i j }$ and $\\tilde { x } _ { i k }$ from two different hallucinators $H _ { \\theta _ { j } }$ and $H _ { \\theta _ { k } }$ but a common basis ${ \\hat { x } } _ { i }$ The divergence between $\\tilde { x } _ { i j }$ and $\\tilde { x } _ { i k }$ is expected to be large. To measure the divergence, a feature extractor is required to map an input image to a feature space, and how to train such a feature extractor to find an appropriate feature space is of great importance. ",
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"text": "In this paper, we formalize the training of hallucinators and the feature extractor as a min-max game in a self-consistent manner, where the feature extractor desires to minimize the divergence between $\\tilde { x } _ { i j }$ and $\\tilde { x } _ { i k }$ while hallucinators, as well as bases, are optimized to maximize it so that the two players can reinforce each other. In specific, the feature extractor, denoted as $F$ and parameterized by $\\psi$ , is typically a CNN structure for the downstream task and we adopt features at the last hidden layer before the output layer, denoted as $F _ { - 1 } ( \\tilde { x } _ { i j } )$ and $F _ { - 1 } ( \\tilde { x } _ { i k } )$ . $F$ is optimized to maximize the correlation between the two feature vectors, which can be quantified by the metric of mutual information (MI). Inspired by the lower bound of MI [45], the objective to minimize the divergence for $F$ is given by the following contrastive form: ",
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"text": "$$\n\\mathcal { L } _ { c o n . } = - \\frac { 1 } { | \\mathcal { H } | ^ { 2 } } \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\substack { 1 \\leq j , k \\leq | \\mathcal { H } | , i = 1 } } \\sum _ { i = 1 } ^ { | \\mathcal { B } | } \\log \\frac { \\exp { \\{ F _ { - 1 } ^ { \\top } ( \\tilde { x } _ { i j } ) F _ { - 1 } ( \\tilde { x } _ { i k } ) / \\tau \\} } } { \\sum _ { u = 1 } ^ { | \\mathcal { B } | } \\exp { \\{ F _ { - 1 } ^ { \\top } ( \\tilde { x } _ { i j } ) F _ { - 1 } ( \\tilde { x } _ { u k } ) / \\tau \\} } } ,\n$$",
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"text": "where $\\tau$ is a scalar temperature coefficient. For the classification problem, we can alternatively adopt the supervised form of the contrastive loss ${ \\mathcal { L } } _ { c o n . }$ ., where $\\tilde { x } _ { u k }$ with the same class label as $\\tilde { x } _ { i j }$ are also taken into consideration as positive samples in Eq. 3. The supervised contrastive loss can benefit to increase the correlation of samples from the same class [20] for a more reasonable feature representation. ",
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"text": "In addition, the feature space is expected to reflect the task-specific property for a meaningful representation. Thus, we also incorporate the task loss $\\mathcal { L } _ { t a s k }$ , e.g., cross-entropy loss in classification tasks, over the synthetic dataset as a supervision signal for $F$ . In this way, the overall training objective for $F$ is defined as: ",
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"img_path": "images/cb8c4585fa59ded769783751a9724f35353b92cb0cefb77ce29786f435b06473.jpg",
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"text": "$$\n\\operatorname* { m i n } _ { \\psi } \\mathcal { L } _ { F } = \\lambda _ { c o n . } \\mathcal { L } _ { c o n . } + \\lambda _ { t a s k } \\mathcal { L } _ { t a s k } ,\n$$",
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"text": "where $\\lambda _ { c o n }$ . and $\\lambda _ { t a s k }$ are hyper-parameters controlling the weight for each term. ",
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"text": "$F$ acts as an adversary to minimize the divergence between $\\tilde { x } _ { i j }$ and $\\tilde { x } _ { i k }$ , while the synthetic dataset is expected to maximize it to increase data diversity. To this ends, the similarity between $F _ { - 1 } ( \\tilde { x } _ { i j } )$ and $\\bar { F } _ { - 1 } ( \\tilde { x } _ { i k } )$ becomes one loss term for hallucinator-basis factorization. In this paper, we adopt the cosine-similarity and the objective $\\mathcal { L } _ { c o s }$ . is given by: ",
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"text": "$$\n\\mathcal { L } _ { c o s . } = \\frac { 1 } { | \\mathcal { H } | ^ { 2 } } \\frac { 1 } { | \\mathcal { B } | } \\sum _ { 1 \\le j , k \\le | \\mathcal { H } | , i = 1 \\atop j \\ne k } \\sum _ { i = 1 } ^ { | \\mathcal { B } | } \\frac { F _ { - 1 } ^ { \\top } ( \\tilde { x } _ { i j } ) F _ { - 1 } ( \\tilde { x } _ { i k } ) } { \\| F _ { - 1 } ( \\tilde { x } _ { i j } ) \\| _ { 2 } \\| F _ { - 1 } ( \\tilde { x } _ { i k } ) \\| _ { 2 } } .\n$$",
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"text": "During training, the feature extractor and the factorized components are updated alternately to play this min-max game. ",
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"text": "3.3 Factorization Training Pipeline ",
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"text": "Following previous paradigms [55, 54, 5, 46], the synthetic dataset $s$ is updated in an iterative algorithm. In each iteration, we randomly sample a batch of hallucinators and bases and conduct pair-wise combinations. The composed images are evaluated by the objective of dataset distillation $\\mathcal { L } _ { D D }$ and the similarity metric in Eq. 5: ",
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"img_path": "images/87ab72e54ffafbe400b2effbad477a262a83d6dd3116707e22d81606588f539a.jpg",
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"text": "$$\n\\operatorname* { m i n } _ { S } \\mathcal { L } _ { S } = \\lambda _ { D D } \\mathcal { L } _ { D D } + \\lambda _ { c o s . } \\mathcal { L } _ { c o s . } ,\n$$",
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"text": "where hyper-parameters $\\lambda _ { D D }$ and $\\lambda _ { c o s }$ . balance the loss. ",
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"text": "Notably, the hallucinator-basis factorization is compatible with a variety of configurations of $\\mathcal { L } _ { D D }$ by previous arts, which makes it a versatile and effective strategy for DD. In this paper, we adopt the trajectories matching loss in Cazenavette et al. [5] as $\\mathcal { L } _ { D D }$ by default thanks to its superior performance. The basic idea is to update a downstream model from a cached checkpoint $\\phi _ { t } ^ { * }$ at iteration $t$ , using the synthetic dataset $s$ for $N$ times, and using the real dataset $\\tau$ for $M$ times respectively. The updated parameters by the two cases, $\\hat { \\phi } _ { t + N }$ and $\\phi _ { t + M } ^ { * }$ are enforced to be consistent: ",
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"text": "$$\n\\begin{array} { r l } & { \\hat { \\phi } _ { t + n + 1 } \\hat { \\phi } _ { t + n } - \\alpha \\nabla _ { \\hat { \\phi } _ { t + n } } \\mathcal { L } _ { t a s k } ( S ) , \\quad \\hat { \\phi } _ { t } \\phi _ { t } ^ { * } , \\quad 0 \\leq n < N , } \\\\ & { \\quad \\quad \\phi _ { t + m + 1 } ^ { * } \\phi _ { t + m } ^ { * } - \\beta \\nabla _ { \\phi _ { t + m } ^ { * } } \\mathcal { L } _ { t a s k } ( T ) , \\quad 0 \\leq m < M , } \\\\ & { \\quad \\quad \\quad \\mathcal { L } _ { D D } = \\frac { \\| \\hat { \\phi } _ { t + N } - \\phi _ { t + M } ^ { * } \\| _ { 2 } ^ { 2 } } { \\| \\phi _ { t } ^ { * } - \\phi _ { t + M } ^ { * } \\| _ { 2 } ^ { 2 } } , } \\end{array}\n$$",
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"text": "where $\\alpha$ and $\\beta$ are learning rates with $s$ and $\\tau$ respectively. $\\alpha$ is learnable in the framework while $\\beta$ is a hyper-parameter. In Sec. 4.2, we also experiment with other settings of $\\mathcal { L } _ { D D }$ . ",
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"text": "Based on the supervised signals in Eq. 6, the gradients are backward propagated to the composed images and finally to the sampled hallucinators and bases so as to be updated using a decent algorithm such as SGD. Since all the operations are differentiable, the training can be completed end-to-end. ",
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"text": "4 Experiments ",
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"text": "4.1 Datasets and Implementing Details ",
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"text": "We conduct evaluations of our method on three standard image classification benchmarks: SVHN [28], CIFAR10, and CIFAR100 [22]. There are 60,000 images for real-world digit recognition in SVHN. For CIFAR10 and CIFAR100, there are 50,000 training images in total. The number of classes for the three datasets are 10, 10, and 100 respectively. All the images are under $3 2 \\times 3 2$ resolution in 3-channel RGB format. Following previous works [5], we use ZCA for image preprocessing with Kornia implementation [35] before all the experiments. Experiments with more datasets, including images in larger spatial scales, can be found in the supplement. ",
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"text": "In this paper, for convenience of comparisons with prior works, we maintain the same size with images in original datasets, i.e., $h ^ { \\prime } = \\bar { h }$ , $w ^ { \\prime } = w$ , and $c ^ { \\prime } = 3$ for bases. We also experiment with other sizes of bases in Sec. 4.3. For hallucinators, the encoder and decoder contain 1 Conv-ReLU blocks. The number of feature channel $c ^ { \\prime \\prime }$ is 3. We use 5 hallucinators by default. The learning rates of hallucinators and bases, $\\eta _ { H }$ and $\\eta _ { B }$ , are the same and for the feature extractor, the learning rate $\\eta _ { F }$ is 0.001. Hyper-parameters $\\lambda _ { c o n }$ ., $\\lambda _ { t a s k }$ , $\\lambda _ { D D }$ , and $\\lambda _ { c o s }$ . are set as 0.1, 1, 1, and 0.1 empirically. Sensitivities of these hyper-parameters are analyzed in Sec. 4.3. The adversary network has the same architecture as that for computing $\\mathcal { L } _ { D D }$ . In experiments on SVHN and CIFAR10, we incorporate all the bases in each iteration, while in experiments on CIFAR100, we adopt a batch size of 300 when the total number of bases is greater than 1,000. We only consider random 2 hallucinators in one iteration for simplicity. The maximal configuration of computational resources is 4 24GB 3090 GPUs. The GPU memory consumption is dependent on that of the baseline method for $\\mathcal { L } _ { D D }$ and is slightly higher than it due to the computation of $\\mathcal { L } _ { c o s }$ . and ${ \\mathcal { L } } _ { c o n . }$ . The baseline method for $\\mathcal { L } _ { D D }$ is MTT [5] if not specified. Other settings related to DD hold the same as the baseline. All the quantitative results are based on the mean and standard deviation over 5 repeated experiments. To make sure fair comparisons, the dataset size in our method is equal to the number of bases $| B |$ and the hallucinators are treated as parameterized data augmentors working online in downstream training, just as general data augmentations, which means that the dataset size does not increase compared with the baselines. ",
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"text": "4.2 Comparisons ",
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"text": "Comparisons with State of the Arts: We compare HaBa with previous state of the arts for DD in standard settings, to synthesize 1, 10, and 50 images per class (IPC) respectively. In our setting, the number of parameters in a hallucinator is is approximately equal to that for 2 synthetic images, while the size of a basis is equal to that of an image. Taking the storage cost of 5 hallucinators into consideration, we set the number of bases per class (BPC) as IPC minus 1 in each IPC configuration when IPC is greater than 1, to make the comparisons as fair as possible. Candidates are coreset based methods including Random [7, 31], Herding [4, 2], K-Center [10, 38], and Forgetting [43], meta learning based methods including DD [47] and LD [3], training matching based methods including DC [55], DSA [53], and MTT [5], and distribution matching based methods including DM [54] and CAFE [46]. The comparisons follow the standard protocol adopting a 3-layer Conv-InstanceNorm-ReLU-AvgPool ConvNet with 128 channels in training and testing. ",
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"type": "table",
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"img_path": "images/e849279a0e4a8bb085b7d15a5984c2a9a34fd9dddd4e74b4e878d056acdccf64.jpg",
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"table_body": "<table><tr><td></td><td>Dataset</td><td></td><td>SVHN</td><td></td><td></td><td>CIFAR10</td><td></td><td></td><td>CIFAR100</td><td></td></tr><tr><td rowspan=\"2\"></td><td>IPC Ratio %</td><td>1 0.014</td><td>10 0.14</td><td>50 0.7</td><td>1 0.02</td><td>10</td><td>50</td><td>1</td><td>10</td><td>50</td></tr><tr><td>Random</td><td></td><td></td><td></td><td></td><td>0.2</td><td>1</td><td>0.2</td><td>2</td><td>10</td></tr><tr><td rowspan=\"4\">Coreset</td><td>Herding</td><td></td><td>14.6±1.6 35.1±4.1 20.9±1.3 50.5±3.3</td><td>70.9±0.9 72.6±0.8</td><td>14.4±2.0 26.0±1.2 43.4±1.0</td><td></td><td></td><td>4.2±0.3</td><td>14.6±0.5 30.0±0.4</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>21.5±1.3 31.6±0.7 40.4±0.6</td><td></td><td></td><td>8.4±0.3</td><td>17.3±0.3 33.7±0.5</td><td></td></tr><tr><td>K-Center</td><td></td><td>21.0±1.5 14.0±1.3 20.1±1.4</td><td></td><td>21.5±1.3 14.7±0.9 27.0±1.4</td><td></td><td></td><td>8.3±0.3</td><td>7.1±0.2 30.5±0.3</td><td></td></tr><tr><td>Forgetting</td><td>12.1±1.7</td><td>16.8±1.2</td><td>227.2±1.5</td><td>13.5±1.2</td><td></td><td>23.3±1.0 23.3±1.1</td><td>4.5±0.3</td><td>9.8±0.2</td><td></td></tr><tr><td rowspan=\"6\">Distillation</td><td>DD+ [47] LD+ [3]</td><td></td><td></td><td></td><td></td><td>36.8±1.2</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>25.7±0.7 38.3±0.4 42.5±0.4</td><td></td><td></td><td>11.5±0.4</td><td></td><td></td></tr><tr><td>DC [55]</td><td></td><td>31.2±1.4 76.1±0.6 82.3±0.3</td><td></td><td>28.3±0.5 44.9±0.5 53.9±0.5</td><td></td><td></td><td>12.8±0.3 25.2±0.3</td><td></td><td></td></tr><tr><td>DSA[53]</td><td></td><td>27.5±1.4 79.2±0.5 84.4±0.4</td><td></td><td>28.8±0.7 52.1±0.5 60.6±0.5</td><td></td><td></td><td>13.9±0.3</td><td>32.3±0.3 42.8±0.4</td><td></td></tr><tr><td>DM [54]</td><td></td><td></td><td></td><td>26.0±0.8 48.9±0.6 63.0±0.4</td><td></td><td></td><td>11.4±0.3</td><td>29.7±0.3 43.6±0.4</td><td></td></tr><tr><td>CAFE[46] CAFE+DSA[46]</td><td></td><td>42.6±3.3 75.9±0.6 81.3±0.3</td><td></td><td>30.3±1.1 46.3±0.6 55.5±0.6</td><td></td><td></td><td></td><td>12.9±0.3 27.8±0.3 37.9±0.3</td><td></td></tr><tr><td rowspan=\"3\"></td><td>MTT[5]</td><td>58.5±1.4 70.8±1.8 85.7±0.1</td><td>42.9±3.0 77.9±0.6 82.3±0.4</td><td></td><td>31.6±0.8 50.9±0.5 62.3±0.4 46.3±0.8 65.3±0.7 71.6±0.2</td><td></td><td></td><td>14.0±0.3 31.5±0.2 24.3±0.3</td><td>39.0±0.1</td><td>42.9±0.2 46.1±0.2</td></tr><tr><td>BPC</td><td></td><td></td><td>49</td><td></td><td>9</td><td></td><td></td><td></td><td></td></tr><tr><td>Ratio % HaBa</td><td>1 9 0.028</td><td></td><td></td><td>1</td><td></td><td>49</td><td>1</td><td>9</td><td>49</td></tr><tr><td colspan=\"2\">Factorization</td><td>69.8±1.3 83.2±0.4 88.3±0.1</td><td>0.14</td><td>0.7</td><td>0.04 48.3±0.8 69.9±0.4 74.0±0.2</td><td>0.2</td><td>1</td><td>0.22 33.4±0.4 40.2±0.2 47.0±0.2</td><td>1.82</td><td>9.82</td></tr><tr><td colspan=\"2\">Whole Dataset</td><td></td><td>95.4±0.1</td><td></td><td></td><td>84.8±0.1</td><td></td><td></td><td>56.2±0.3</td><td></td></tr></table>",
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"text": "Table 1: The performance (test accuracy $\\%$ ) comparison to state-of-the-art methods. LD† and DD† use AlexNet for CIFAR10, while the rest use ConvNet for training and testing. IPC: Number of Images Per Class; BPC: Number of Bases Per Class; Ratio $( \\% )$ : the ratio of distilled images to whole training set. Underline denotes results by our implementation. ",
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"type": "image",
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"img_path": "images/5072ad7bd998dd1dbc9b70dd70fd5b93f1273567fc493164380350adcc0d35b5.jpg",
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"image_caption": [
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| 739 |
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"Figure 4: Visualization of factorized results by our HaBa $7 0 . 2 7 \\%$ test acc.) and baseline MTT $( 6 5 . 9 2 \\%$ test acc.). Zoom-in for better comparisons. "
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"type": "text",
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"text": "The comparison results are shown in Tab. 1 and we can observe that HaBa achieves state-of-the-art performance in all datasets and settings. Especially when the ratio of distilled images to the whole training set is less than $1 \\%$ , our method can yield significant improvement over all the candidate methods, which demonstrates that the scheme of hallucinator-basis factorization improves the data efficiency for the task of dataset distillation. ",
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"type": "text",
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"text": "Qualitative Comparisons: We visualize the factorized results by our method as well as the baseline on CIFAR10 dataset with 10 BPC in Fig. 4. Due to the space limitation, we only provide images generated by 2 hallucinators here. More results can be found in the supplement. As shown in the figure, we can find that bases mainly store some main structures and contour information. Different hallucinators would render a basis with diverse styles and details. Thanks to the dataset factorization scheme, the diversity of distilled images by our method is higher than that by the baseline. ",
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"text": "Building upon Different Baselines: To reflect the versatility of the insight, we implement HaBa on multiple state-of-the-art training pipelines of DD, including DC, DM, and MTT. We evaluate the performance of synthetic datasets on CIFAR10 and maintain the IPC of baseline methods as BPC plus 1, which makes storage costs for synthetic datasets as close as possible for fairness. As shown in Tab. 2, when training and testing on ConvNet, the strategy of HaBa can make a consistent improvement over all the baselines, which demonstrates that factorization is a general idea to improve the data efficiency in DD. ",
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"text": "Cross-Architecture Performance: For DD, a satisfactory distilled dataset should have similar training effects to the original one on downstream models with arbitrary architectures. Thus, crossarchitecture generalization performance is an important metric for DD. We use the synthetic datasets trained on ConvNet to train models with different structures including ResNet [14], VGG [41], and AlexNet [23]. The results can be found in Tab. 2. Benefiting from the increased data diversity, HaBa can improve the across-architecture accuracy significantly with a performance gain up to $\\mathrm { \\bar { 1 } 7 . 5 7 \\% }$ . The consistent and significant improvement validates the superior ability of our method to capture the informative features and thus original datasets can be replaced by the synthetic ones better. ",
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"type": "table",
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"img_path": "images/880d99cedbbc7037b40012349ffeaaa5e4a4974f9b8b42451f18d7e777e52f7c.jpg",
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"table_caption": [],
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"table_footnote": [
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"Table 2: Cross-architecture performance (test accuracy $\\%$ ) comparison to different baseline methods of DD HaBa built upon. "
|
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],
|
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"table_body": "<table><tr><td></td><td>|Method</td><td colspan=\"3\">DC [55]</td><td colspan=\"3\">DM [54]</td><td colspan=\"3\">MTT[5]</td></tr><tr><td></td><td>IPC BPC</td><td>2</td><td>11</td><td>51</td><td>2</td><td>11</td><td>51</td><td>2</td><td>11</td><td>51</td></tr><tr><td></td><td>Baseline</td><td>1 |31.36±0.16 45.29±0.30 54.24±0.61</td><td>10</td><td>50</td><td>1 134.57±0.52 50.35±0.36 62.03±0.29|50.59±0.95 63.90±0.29 69.81±0.48</td><td>10</td><td>50</td><td>1</td><td>10</td><td>50</td></tr><tr><td></td><td>ConvNet w.HaBa Gain Baseline</td><td>34.11±0.47 49.88±0.52 58.91±0.23 +2.75 18.10±0.7618.36±0.3622.14±0.38|</td><td>+4.59</td><td>+4.67</td><td>+2.75</td><td>37.32±0.13 56.83±0.11 64.44±0.40 +6.48 3|22.25±1.00 40.00±1.49 53.40±0.68|35.15±0.96 45.05±1.46 54.47±0.95</td><td>+2.41</td><td>+6.17</td><td>56.76±0.38 69.48±0.26 73.25±0.21 +5.58</td><td>+3.44</td></tr><tr><td>ResNet</td><td>w.HaBa Gain Baseline</td><td>24.49±0.55 24.27±0.56 31.08±0.32 +6.39 28.02±0.26 35.88±0.67 38.73±0.482</td><td>+6.11</td><td>+8.94</td><td>+9.09</td><td>31.34±0.7247.57±0.4959.61±0.35 +7.57</td><td>+6.21</td><td>+12.24 322.28±1.0341.64±0.64 55.17±0.54|38.04±1.19 50.49±1.02 61.36±0.30</td><td>47.39±0.7157.97±0.8864.35±0.60 +12.92</td><td>+9.88</td></tr><tr><td>VGG</td><td>w.HaBa Gain</td><td>29.42±0.93 37.03±0.42 41.91±0.55 +1.40</td><td>+1.15</td><td>+3.18</td><td>26.93±0.62 49.41±0.36 67.47±0.43 +4.65</td><td>+7.77</td><td>+12.30</td><td>+10.22</td><td>48.26±0.54 60.47±0.56 67.47±0.43 +9.98</td><td>+6.11</td></tr><tr><td>AlexNet</td><td>w. HaBa Gain</td><td>Baseline|20.02±1.312.42±1.3529.48±0.8720.67±3.6437.04±0.9249.14±0.94|26.06±1.0135.95±1.5249.20±1.27 22.24±1.14 33.02±0.91 33.42±1.39 +2.22</td><td>+10.60</td><td>+3.94</td><td>+11.47</td><td>32.14±0.60 44.14±0.67 53.09±0.89 +7.10</td><td>+3.95</td><td>43.63±1.46 48.96±3.00 60.07±1.37 +17.57</td><td>+13.01</td><td>+10.87</td></tr></table>",
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"type": "text",
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"text": "Comparisons under the Same Number of Final Images: In the default comparison protocol, we compare our method with the baselines using the same budget of storage, where our method can store information of exponentially more images than the baselines with the same number of parameters. In this part, we also examine the performance of HaBa under the condition that the number of final images, i.e., $| { \\mathcal { H } } | \\times | B |$ , is equal to that used by the baseline. Intuitively, given that the objective functions of our method and the baseline are the same exactly, the performance of the baseline can be viewed as an upper bound of ours, since there are significantly less parameters in our method to carry the information of final images in this case. Therefore, we first remove the term $\\mathcal { L } _ { c o s }$ . from the loss function of DD in Eq. 6 to guarantee a consistent optimization objective with the baseline. Then, we compare the performance of HaBa and the baseline using 10, 20, 30, 40, and 50 final images respectively. Here, the number of hallucinators $| \\mathcal { H } |$ is 2 and the number of bases is thus half of the number of final images. As shown in the red and green curves in Fig. 7, performance of the baseline can be well approximated by ours with only half of the number of parameters, especially when the number of images is relatively large. Remarkably, with the proposed adversary contrastive constraint, our method can even outperform the baseline consistently, as shown in the blue curve, which further demonstrates the effectiveness of the proposed solution. ",
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"text": "Comparisons with Concurrent Works on Efficient Distilled Dataset Parameterization: As a concurrent work on efficient distilled dataset parameterization, IDC [21] is proposed to store $4 \\times$ number of $2 \\times$ down-sample synthetic images compared with the baseline. The core is to reduce the spatial size for efficient parameterization. For HaBa of this paper, instead, we do not modify the spatial size of bases in the default setting for better qualitative explainablity and more intuitive comparisons with the baselines. In this sense, IDC and HaBa are in fact two orthogonal techniques and they can readily join force to enhance the baseline performance. Here, we try using the technique of IDC and adopting $2 \\times$ down-sample synthetic images on the baseline MTT, based on which we further consider adding our HaBa and involving 5 hallucinators. As shown in Tab. 3, with the efficient parameterization of IDC, the performance of baseline can be improved. With HaBa in this paper, the performance can even be further improved a lot: $5 . 1 4 \\%$ , $1 . 2 9 \\%$ , and $4 . 3 0 \\%$ in the three settings respectively, which demonstrates that IDC and HaBa work in different ways. ",
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"text": "Applications in Continual Learning: To further demonstrate the advantage of the proposed method for improving data efficiency, following the setting of DM [54], we conduct experiments on the setting of continual learning on CIFAR-100, with 20 random classes per stage. The average number of parameters per class is $2 0 \\times 3 2 \\times 3 2 \\times 3$ . The synthetic datasets are trained with a ConvNet with 3 blocks. We evaluate synthetic datasets by our method and the DM baseline on the same ConvNet architecture and ResNet18. The results in Fig. 5 demonstrate that the proposed method increases the informativeness of synthetic datasets and thus produce significantly better performance, especially in the cross-architecture setting. ",
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"text": "4.3 Ablation Studies ",
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| 846 |
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| 857 |
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"text": "Loss Terms: To validate the effectiveness of the proposed adversarial contrastive constraints, we design ablation studies on the CIFAR10 dataset over three loss terms: $\\mathcal { L } _ { c o s }$ . in Eq. 5, $\\mathcal { L } _ { c o n }$ . in Eq. 3, and the task-specific loss $\\mathcal { L } _ { t a s k }$ . Through the results in Tab. 4, we can find that deleting any one of them would hurt the performance. We also experiment with involving $\\mathcal { L } _ { c o n }$ . for downstream training, to enforce the similarity among images composed of different hallucinators and a common basis. Observed from the last row of Tab. 4, the performance can be further improved, since $\\mathcal { L } _ { c o n }$ . helps the representation learning of related samples [20]. Note that we do not use this loss term for downstream training in other experiments for fair and standard comparison. ",
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"type": "table",
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"img_path": "images/a4eefcda8945f1880f0d359443a3b6ad445f9049a4ae2d9f57bb9ec3519e0351.jpg",
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"table_caption": [
|
| 870 |
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"Table 3: Comparisons with concurrent work IDC [21] on efficient synthetic parameterization. "
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| 871 |
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"table_footnote": [],
|
| 873 |
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"table_body": "<table><tr><td>#ofParam./Class 2×32×32×3 11×32×32×3 51×32×32×3</td><td></td><td></td><td></td></tr><tr><td>Baseline</td><td>49.89±0.95</td><td>65.92±0.62</td><td>70.73±0.52</td></tr><tr><td>w. IDC</td><td>56.13±0.38</td><td>70.85±0.43</td><td>71.01±0.41</td></tr><tr><td>w. IDC&HaBa</td><td>61.27±0.34</td><td>72.14±0.22</td><td>75.31±0.27</td></tr></table>",
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"type": "image",
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"img_path": "images/e2a14eb6eccb88b733214c9ad471026600c942bd31b8ad594d3a8e25f3401183.jpg",
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| 885 |
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"image_caption": [
|
| 886 |
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"Figure 5: Comparisons on the setting of continual setting. Results on the ConvNet3 (Left) and ResNet18 (Right) architectures are shown. "
|
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"type": "table",
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"img_path": "images/3849b306a765ebefc59780354a4183220a9e1f5d6d51bf9e9f4bb0bdf9bb7f59.jpg",
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| 900 |
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"table_caption": [],
|
| 901 |
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"table_footnote": [
|
| 902 |
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"Table 4: Results of ablation study on loss terms in HaBa: $\\mathcal { L } _ { c o s . }$ ., ${ \\mathcal { L } } _ { c o n . }$ ., and $\\mathcal { L } _ { t a s k }$ . "
|
| 903 |
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],
|
| 904 |
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"table_body": "<table><tr><td>BPC</td><td>1</td><td>10</td><td>50</td></tr><tr><td>HaBa w/o Lcos.</td><td>54.56±0.61</td><td></td><td>70.16±0.44 73.93±0.21</td></tr><tr><td>HaBa w/o Lcon.</td><td>54.91±0.49</td><td>70.07±0.48</td><td>72.50±0.39</td></tr><tr><td>HaBa W/o Ltask</td><td>54.62±0.42</td><td></td><td>：70.07±0.16 72.74±0.20</td></tr><tr><td>HaBa Full</td><td>55.66±0.29</td><td>70.27±0.63</td><td>74.04±0.16</td></tr><tr><td>HaBawLcon. Downstream</td><td>56.78±0.22</td><td>70.44±0.15</td><td>75.00±0.52</td></tr></table>",
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"img_path": "images/3f3dbfd01f6c2c868d5bb3b105d79e406e69260d0d26752d8a5fe18a91635a05.jpg",
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"image_caption": [
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"Figure 6: Impacts of different $\\lambda _ { c o s }$ . and $\\lambda _ { c o n }$ . on the test accuracy. "
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"text": "We examine the sensitivities of hyper-parameters $\\lambda _ { c o s }$ . and $\\lambda _ { c o n }$ . used to balance the weights of loss terms $\\mathcal { L } _ { c o s }$ . and $\\mathcal { L } _ { c o n }$ . respectively in Fig. 6. The results are evaluated on the CIFAR10 dataset with 10 BPC. We can observe that the overall performance is not sensitive to the selection of these hyper-parameters and our method makes a consistent improvement over the baseline with 11 IPC. ",
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"text": "Class-Independent Hallucinators v.s. Shared Hallucinators: In the default setting of HaBa, each class maintains a certain number of bases independently and all the classes share the same set of hallucinators. But what about the case that hallucinators are also made class-independent? We study this problem experimentally in Tab. 5. Given the same BPC, class-independent hallucinators can indeed somehow improve the performance when there are fewer synthetic samples, e.g., 1 BPC. However, when BPC is higher, equipping each class with an independent set of hallucinators would not benefit the performance. There are probably two reasons: (1) shared hallucinators across all the classes extract global information of the whole dataset, which encodes more representative and universal knowledge; and (2) the class-independent case would make the number of hallucinators 10 times for the CIFAR10 dataset, which leaves a heavy burden for the optimization process. Thus, as indicated in Tab. 5, a better solution is to make room for more bases using the memory allocated to store class-independent hallucinators initially, which would result in more satisfactory data efficiency. ",
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"text": "Number of Channels Used by Basis: By default, the shape of a basis is the same as that of a real image, which is generally in RGB 3-channel format. In fact, in Fig. 8(Left), we also verify that it is also possible to use single-channel basis, which can reduce the memory cost by nearly 2/3 without hurting the performance too much. Interestingly, if the memory cost is held the same, we can choose to use 3 times BPC to store single-channel bases, rather than 3-channel ones. This would yield impressive improvement on the test accuracy when BPC is small. Note that for baseline results, IPC is set as the corresponding BPC plus 1. ",
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"text": "Number of Hallucinators: We study the impact of the number of hallucinators, i.e., $| { \\mathcal { H } } |$ , in Fig. 8(Right). We can observe that when BPC is small, including more hallucinators is helpful for the performance. Nevertheless, when BPC is 10 or 50, the performance would not improve with more hallucinators when $| \\mathcal { H } | > 1 0$ . One reason is that when $| \\mathcal { H } |$ is large, the sampling of hallucinators in each iteration is sparse, which makes the joint optimization of all the hallucinators more difficult. ",
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"text": "Data Augmentation: The similarity between our hallucinator set and data augmentation lies that both of them can contribute to generating more samples and increasing the diversity. However, the essential difference is that our hallucinators are optimized to encode sample-wise relationships in ",
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"Figure 7: Comparisons with the baseline under the same number of final images. "
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"table_body": "<table><tr><td>BPC</td><td>1</td><td>10</td><td>50</td></tr><tr><td>w/o Share</td><td>55.96±0.51</td><td>69.00±0.20</td><td>69.81±0.56</td></tr><tr><td>Share</td><td>55.66±0.29</td><td>70.27±0.63</td><td>74.04±0.16</td></tr><tr><td>Baseline (IPC=BPC)</td><td>45.29±0.86</td><td>62.77±0.56</td><td>71.09±0.34</td></tr><tr><td>Share (Same Memory)</td><td>70.27±0.63</td><td>72.17±0.30</td><td>74.89±0.15</td></tr><tr><td>Baseline (Same Memory)</td><td>65.92±0.62</td><td>68.58±0.49</td><td>73.55±0.48</td></tr></table>",
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"text": "Table 5: Study on whether all the classes should share the same set of hallucinators. ",
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"Figure 8: Study on the number of channels used by bases and the number of hallucinators. "
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"table_body": "<table><tr><td></td><td>ConvNet</td><td>ResNet</td><td>VGG</td><td>AlexNet</td></tr><tr><td>w/o aug.</td><td>60.63±0.21</td><td>43.24±0.83 48.02±0.53</td><td></td><td>30.58±1.44</td></tr><tr><td>Baseline</td><td>63.90±0.29</td><td>45.05±1.46 50.49±1.02</td><td></td><td>35.95±1.52</td></tr><tr><td>w/o aug. Ours</td><td>68.08±0.23 69.48±0.26</td><td>56.37±0.11 57.97±0.88</td><td></td><td>59.04±0.50 48.27±3.04 60.47±0.56 48.96±3.00</td></tr></table>",
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"text": "a dataset, while data augmentation is based on some prior and heuristic knowledge of images. By default, both our method and the baseline adopt the data augmentation strategy DSA [53]. To study the relationship between the two schemes experimentally, we attempt to remove DSA from baseline and our method and report the corresponding results in Tab. 6. The evaluation is on CIFAR10 with 11 IPC for baseline and 10 BPC for ours. Through the results, we can find that (1) our method without data augmentation can also outperform the baseline method with augmentation significantly, which means that the mechanism of HaBa can benefit the dataset distillation task more with the learning of global information of a dataset in hallucinators; and (2) with data augmentation, our performance can be further improved, which indicates that HaBa and DSA work in different manners. ",
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"text": "5 Conclusions, Limitations, and Future Works ",
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"text": "This paper proposes a novel hallucinator-basis factorization method dubbed HaBa for dataset distillation (DD). It uses hallucinators to encode inner relations between different samples in original datasets, which can largely improve the data efficiency of distilled results. To diversify the knowledge captured by different hallucinators, a pair of adversarial contrastive constraints is further introduced. Extensive evaluations and comparisons on multiple benchmark datasets demonstrate that HaBa is capable of significantly improving the performance of downstream models trained on the synthetic dataset, using only $3 5 \\%$ cost of memory for storage. Moreover, it is a versatile strategy that is compatible with different configurations of DD frameworks and yields consistent improvement. ",
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"text": "Despite the superior performance of the proposed hallucinator-basis factorization (HaBa) scheme, there are also some potential limitations. On the one hand, compared with the baseline method HaBa built upon, the process of online pairwise combination between hallucinators and bases in training increases the cost of time and GPU memory slightly, although light-weight hallucinators are adopted. On the other hand, it may inherited the limitations of baseline methods. For example, when the number of images is large, further increasing the number would produce limited performance gain. ",
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"text": "For future works, beyond the training efficiency of HaBa, introducing class-wise relationship may also be a potential research direction. For example, it is probably optimal that one class shares hallucinators with some specific classes but does not share with others. It is also promising to explore more advance factorization for a dataset to further improve the performance. ",
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"text": "Acknowledgement ",
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"text": "This research is supported by the National Research Foundation, Singapore under its Medium Sized Centre for Advanced Robotics Technology Innovation (WBS: A-0009428-09-00). Xinchao Wang is the corresponding author. ",
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Representation learning with contrastive predictive coding. arXiv e-prints, pages arXiv–1807, 2018. \n[46] Kai Wang, Bo Zhao, Xiangyu Peng, Zheng Zhu, Shuo Yang, Shuo Wang, Guan Huang, Hakan Bilen, Xinchao Wang, and Yang You. Cafe: Learning to condense dataset by aligning features. arXiv preprint arXiv:2203.01531, 2022. \n[47] Tongzhou Wang, Jun-Yan Zhu, Antonio Torralba, and Alexei A Efros. Dataset distillation. arXiv preprint arXiv:1811.10959, 2018. \n[48] Felix Wiewel and Bin Yang. Condensed composite memory continual learning. In Proceedings of the International Joint Conference on Neural Networks (IJCNN), pages 1–8, 2021. \n[49] Enze Xie, Wenhai Wang, Zhiding Yu, Anima Anandkumar, Jose M Alvarez, and Ping Luo. Segformer: Simple and efficient design for semantic segmentation with transformers. arXiv preprint arXiv:2105.15203, 2021. \n[50] Xingyi Yang, Jingwen Ye, and Xinchao Wang. Factorizing knowledge in neural networks. 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Dataset distillation using neural feature regression. arXiv preprint arXiv:2206.00719, 2022. ",
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"text": "Checklist ",
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"text": "1. For all authors... ",
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"text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] \n(b) Did you describe the limitations of your work? [Yes] Please refer to the supplement. \n(c) Did you discuss any potential negative societal impacts of your work? [N/A] \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
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"text": "2. If you are including theoretical results... ",
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| 1222 |
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{
|
| 1223 |
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"type": "text",
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| 1224 |
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"text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ",
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| 1225 |
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"text": "3. If you ran experiments... ",
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"type": "text",
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"text": "(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] Please refer to the supplement. \n(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] Please refer to Sec. 4.1. \n(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We run all the experiments 5 times and report the mean and standard deviation of the performance. \n(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] Please refer to Sec. 4.1. ",
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"text": "4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... ",
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| 1267 |
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"type": "text",
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| 1268 |
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"text": "(a) If your work uses existing assets, did you cite the creators? [Yes] \n(b) Did you mention the license of the assets? [Yes] \n(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] \n(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A] \n(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A] ",
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| 1277 |
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| 1278 |
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"type": "text",
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| 1279 |
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"text": "5. If you used crowdsourcing or conducted research with human subjects... ",
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| 1280 |
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| 1288 |
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| 1289 |
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"type": "text",
|
| 1290 |
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"text": "(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] \n(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] \n(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A] ",
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|
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parse/dev/ne6zeqLFCZ/ne6zeqLFCZ_content_list.json
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