Add Batch bef0e2e4-52eb-4a21-bc26-7a20ddc54716 data

.gitattributes

@@ -2087,3 +2087,67 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2025/Simpler Diffusion_ 1.5 FID on ImageNet512 with Pixel-space Diffusion/3cf16242-5862-4aa6-864f-5aba8865f5f9_content_list.json

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+        "type": "text",
+        "text": "Google Deepmind",
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+        "text": "jheek@google.com",
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+    {
+        "type": "text",
+        "text": "Kay Lamarigts",
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+        "text": "kaylamerigts@google.com",
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+    {
+        "type": "text",
+        "text": "Ruiqi Gao",
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+        "text": "ruiqig@google.com",
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+    {
+        "type": "text",
+        "text": "Tim Salimans",
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+    {
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+        "text": "Google Deepmind",
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+    {
+        "type": "text",
+        "text": "salimans@google.com",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Latent diffusion models have become the popular choice for scaling up diffusion models for high resolution image synthesis. Compared to pixel-space models that are trained end-to-end, latent models are perceived to be more efficient and to produce higher image quality at high resolution. Here we challenge these notions, and show that pixel-space models can be very competitive to latent models both in quality and efficiency, achieving 1.5 FID on ImageNet512 and new SOTA results on ImageNet128, ImageNet256 and Kinetics600.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We present a simple recipe for scaling end-to-end pixel-space diffusion models to high resolutions. 1: Use the sigmoid loss-weighting [25] with our prescribed hyperparameters. 2: Use our simplified memory-efficient architecture with fewer skip-connections. 3: Scale the model to favor processing the image at a high resolution with fewer parameters, rather than using more parameters at a lower resolution. Combining these with guidance intervals, we obtain a family of pixel-space diffusion models we call Simpler Diffusion (SiD2).",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Diffusion models have been tremendously successful in domains such as image, video and audio generation. For high resolution data, latent diffusion models [32] have been particularly successful: Through encoding the data in a lower dimensional space, these models sidestep the difficulties faced by more traditional pixel-space diffusion models in scaling up to high resolution. This makes latent diffusion models also scale better in training compute than other approaches, as shown by [20].",
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+    {
+        "type": "text",
+        "text": "However, latent models have their own challenges: It can be difficult to train the autoencoders that produce the latents,",
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+    {
+        "type": "image",
+        "img_path": "images/8b5a7ae5161b82f15e43113268a9298406651cafd4317c76bb573e36806124bf.jpg",
+        "image_caption": [
+            "Figure 1. End-to-end pixel diffusion performance on ImageNet512."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "which in practice requires careful tuning of regularization hyperparameters [32]. Even when trained well, the decoder of a latent diffusion model can produce artifacts or otherwise imperfect reconstructions, especially when it is applied to latents that are out of distribution compared to the training set. A single-stage pixel-space diffusion model does not have these issues, and so we ask the question: Can pixel-space diffusion models scale as well as latent models with the right architecture and hyperparameters?",
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+    },
+    {
+        "type": "text",
+        "text": "Over the years, end-to-end pixel-space diffusion has improved considerably (Figure 1). The main problem was that the standard schedule and loss-weighting [11] work well for small resolution images, like  $32^2$  or  $64^2$ , but not at higher resolution [3, 14]. It was further shown [25] that it can be helpful to disentangle loss weighting and time sampling for improved control over both, leading to better performance at higher resolution. However, in previous works pixels-space models still did not match the best latent models on standard benchmarks like ImageNet512.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The main contribution of this paper is to improve pixel-space diffusion on high resolution images while keeping as close to the original formulation of diffusion models as possible. Specifically, we analyze and tune the sigmoid loss weighting from [25], and show why it should be preferred over their favored EDM monotonic. We further propose architectural improvements that lead to even better perfor",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "18062",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/b18a0f4d018046d9ab7155f067e3df4b7341ad15d635e2a00a6cbc6332bde9c2.jpg",
+        "image_caption": [
+            "Figure 2. Some text-to-image samples of  $512 \\times 512$  that have been generated by SiD2."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
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+        "img_path": "images/4673782a530a2ffca3a5a3a1f6c3ddfa3d65cdd0850dc8041f8a3798bc066625.jpg",
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+    {
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+        "img_path": "images/9b3e67cdffaed8395cf0f73b870516817a0a09d2e7eec74fb72d26e6b38056ce.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/2e50436e0cea30003bd97c6bc97008729d7dedcd626988278a1604a13b1e4d6b.jpg",
+        "image_caption": [],
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+    {
+        "type": "text",
+        "text": "mance, namely flop heavy scaling and removing block skip-connections (Residual U-ViTs). Most notably, we improve the state-of-the-art of pixel-space diffusion from 2.65 to 1.48 on ImageNet512 (see also Figure 1). Further, we also achieve overall state-of-the-art on ImageNet128, ImageNet256 and Kinetics600 without heavy tuning.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1.1. Background",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A diffusion process gradually destroys data over a conceptual time  $t$ , typically with Gaussian noise as follows:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {z} _ {t} = \\alpha_ {t} \\boldsymbol {x} + \\sigma_ {t} \\boldsymbol {\\epsilon}, \\text {w h e r e} \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I}), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "which defines a distribution  $q(\\pmb{z}_t|\\pmb{x})$  such that  $\\pmb{z}_0$  is close to clean data and  $\\pmb{z}_1$  is close to Gaussian noise. In this paper we assume a variance-preserving [41] schedule, which is defined as  $\\alpha_{t} = \\sqrt{\\sigma(\\lambda_{t})}$  and  $\\sigma_t = \\sqrt{\\sigma(-\\lambda_t)}$ , with  $\\lambda_{t} = \\log \\left(\\alpha_{t}^{2} / \\sigma_{t}^{2}\\right)$  being the log signal-to-noise ratio, which monotonically decreases with time as  $t\\to 1$ , and  $\\sigma (\\cdot)$  being the sigmoid function. It can be shown that other types of schedules such as the variance-exploding schedule or the flow matching schedule [28] can always be converted to a variance-preserving schedule with a linear scaling of  $\\pmb{z}_{t}$  [25]. The key defining property of a noise schedule is the log signal-to-noise ratio  $\\lambda_{t}$ . A neural network is used to predict  $\\hat{\\pmb{x}} = \\hat{\\pmb{x}}_{\\theta}(\\pmb{z}_{t},t)$  that effectively estimates  $\\mathbb{E}[\\pmb {x}|\\pmb {z}_t]$ , which can be done by minimizing a weighted mean squared error loss:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL (\\boldsymbol {x}) = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} - \\frac {\\mathrm {d} \\lambda_ {t}}{\\mathrm {d} t} w \\left(\\lambda_ {t}\\right) \\| \\boldsymbol {x} - \\hat {\\boldsymbol {x}} \\| ^ {2}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            148,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $w(\\lambda_t)$  is the weighting function.  $-\\mathrm{d}\\lambda_{t} / \\mathrm{d}t$  cancels out the effect of the noise schedule  $\\lambda_{t}$  on the loss. In other words,  $L(\\mathbf{x})$  can be rewritten as  $\\int -w(\\lambda)\\| \\pmb {x} - \\hat{\\pmb{x}}\\| ^2 d\\lambda$  that is invariant to the choice of  $\\lambda_{t}$ . However,  $\\lambda_{t}$  still impacts the sampling efficiency of the Monte Carlo estimator of the expected loss, and thus affects the training dynamics of diffusion models. This decouples noise schedule  $\\lambda_{t}$  and weighting function  $w(\\lambda)$  as a function of  $\\lambda$  [25].",
+        "bbox": [
+            89,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The above squared error loss can be derived from the variational interpretation of diffusion models [26]. Given",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "two time steps  $s < t$ , we define the denoising distribution  $p(\\boldsymbol{z}_s|\\boldsymbol{z}_t)$  in the same formulation as the true posterior  $q(\\boldsymbol{z}_s|\\boldsymbol{z}_t,\\boldsymbol{x})$ , but replace the ground truth  $\\boldsymbol{x}$  with the learned approximation  $\\hat{\\boldsymbol{x}} \\approx \\mathbb{E}[\\boldsymbol{x}|\\boldsymbol{z}_t]$ :",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np \\left(\\boldsymbol {z} _ {s} \\mid \\boldsymbol {z} _ {t}\\right) = q \\left(\\boldsymbol {z} _ {s} \\mid \\boldsymbol {z} _ {t}, \\boldsymbol {x} = \\hat {\\boldsymbol {x}}\\right) = \\mathcal {N} \\left(\\boldsymbol {z} _ {s} \\mid \\mu_ {t \\rightarrow s}, \\sigma_ {t \\rightarrow s}\\right), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            549,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma_{t\\rightarrow s}^2 = \\left(1 / \\sigma_s^2 +\\alpha_{t|s}^2 /\\sigma_{t|s}^2\\right)^{-1}$  and  $\\mu_{t\\to s} = \\sigma_{t\\to s}^{2}\\Bigl (\\alpha_{t|s} / \\sigma_{t|s}^{2}\\pmb {z}_{t} + \\alpha_{s} / \\sigma_{s}^{2}\\pmb {x}\\Bigr)$  with  $\\alpha_{t|s} = \\alpha_t / \\alpha_s$  and  $\\sigma_{t|s}^2 = \\sigma_t^2 -\\alpha_{t|s}\\sigma_s^2$  . Note that during sampling, the standard deviation for  $p(z_{s}|z_{t})$  is chosen to be a log-linear interpolation between  $\\sigma_{t|s}$  and  $\\sigma_{t\\rightarrow s}$  of the form  $\\sigma_{t\\rightarrow s}^{\\gamma}\\sigma_{t|s}^{1 - \\gamma}$  where  $\\gamma = 0.3$  was set empirically, which is important as FID is sensitive to over-smooth or grainy images.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Simpler Diffusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Revisiting the sigmoid loss",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recall that one of the proposed losses in VDM++ [25] is the sigmoid loss. They expressed the loss with respect to  $\\epsilon$ -mse:  $L(\\pmb{x}) = \\mathbb{E}_{t \\sim \\mathcal{U}(0,1)} - \\frac{\\mathrm{d}\\lambda_t}{\\mathrm{d}t} \\tilde{w}(\\lambda_t) \\| \\pmb{\\epsilon} - \\hat{\\pmb{\\epsilon}} \\|^2$ , which is connected to  $\\pmb{x}$ -mse through  $\\| \\pmb{\\epsilon} - \\hat{\\pmb{\\epsilon}} \\|^2 = \\exp(\\lambda_t) \\| \\pmb{x} - \\hat{\\pmb{x}} \\|^2$  and  $\\tilde{w}(\\lambda_t) = \\exp(\\lambda_t) w(\\lambda_t)$ . In VDM++, viewing the loss in  $\\epsilon$ -mse enables a natural connection between the weighted loss and the ELBO and showed that losses should be monotonically decreasing on  $\\epsilon$ -mse. Hence, they propose the sigmoid loss:  $\\tilde{w}(\\lambda_t) = \\sigma(b - \\lambda_t)$ , where  $b$  denotes the bias or shift and  $\\sigma$  is the sigmoid function. However, they ultimately opted for another loss-weighting named EDM-monotonic for high resolution image generation, see Figure 3a.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Enforcing weighting monotonicity in  $x$  Revisiting the sigmoid loss, we derive its  $x$ -mse form, which turns out to conveniently be defined by a mirrored sigmoid (albeit multiplied by a constant factor):",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\sigma \\left(b - \\lambda_ {t}\\right) \\| \\boldsymbol {\\epsilon} - \\hat {\\boldsymbol {\\epsilon}} \\| ^ {2} = \\sigma \\left(b - \\lambda_ {t}\\right) \\exp \\left(\\lambda_ {t}\\right) \\| \\boldsymbol {x} - \\hat {\\boldsymbol {x}} \\| ^ {2} \\tag {4} \\\\ = \\exp (b) \\sigma \\left(\\lambda_ {t} - b\\right) \\| \\boldsymbol {x} - \\hat {\\boldsymbol {x}} \\| ^ {2}. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            531,
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "18063",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/12bc20bf77af3c4d4311affe192124ed53e769feeff62a5c95055d6236936202.jpg",
+        "image_caption": [
+            "(a) Weighting over  $\\epsilon$ -mse"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            145,
+            104,
+            439,
+            246
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/2c131284de18ff2945917ee8d0833c6474829f5f2450df0baff16c2b498b7be2.jpg",
+        "image_caption": [
+            "(b) Weighting over  $\\pmb{x}$ -mse",
+            "Figure 3. Weighting of different losses in both  $\\epsilon$  and  $x$  space. Note that the weightings are scaled to have a maximum of one."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            545,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "This reveals that the sigmoid loss is not only monotonically decreasing in  $\\epsilon$ -mse, it is also monotonically increasing in  $x$ -mse. We claim that a reasonable weighting function  $w(\\lambda_t)$  should be monotonically increasing over  $\\lambda_t$ . Observe that with less noise in  $z_t$ , there is more information available and it should be strictly easier to predict the original data, meaning that the  $x$ -mse generally decreases for higher  $\\lambda_t$ . This phenomenon is also observed in practice. If the loss weighting in  $x$ -mse also decreases, the model would be able to make worse predictions while obtaining less noisy (better) conditioning information and still achieve a lower loss. Simply put: Why put less weight on an easier problem?",
+        "bbox": [
+            88,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Studying both the form of the sigmoid and EDM-monotonic weighting functions in Figure 3, we observe that both weighting functions are monotonically decreasing in  $\\epsilon$ -mse, but only the sigmoid weighting is monotonically increasing in  $x$ -mse. Therefore, we expect the sigmoid weighting to be a better candidate to scale to high resolution generation than the EDM-monotonic version.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Loss shifting Recall that for a resolution that is two times higher in both height and width, an average (low pass) filter would see  $\\mathrm{Var}[(x_{11} + x_{12} + x_{21} + x_{22}) / 4] = 1 / 4$  of the noise, while signal strength stays the same [14, 25]. Hence, its effective logsnr is expected to increase by about  $2\\log 2\\approx 1.386\\approx 1.5$  when viewed through a low-pass filter. Suppose that the optimal setting for images of  $128\\times 128$  is a sigmoid weighting with  $b\\approx 0$ , then one would expect the optimal setting for images of  $512\\times 512$  to be roughly  $b = -3$ .<sup>1</sup> Empirically we find that slightly more aggressive shifts perform even better.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Flop heavy scaling",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "When one deals with a limited data budget, it can be difficult to balance scaling of models and regularization. Our small model version at  $512 \\times 512$  resolution starts out with  $4 \\times 4$  patching, and subsequently runs a U-ViT [14] on the  $128 \\times$",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$128 \\times 48$  input (assuming the raw input is of 3 channels). To make the model more expressive, one of the most common options is to double the number of channels for every layer, leading to  $2 \\times$  model size. However, our experiments show that this results in diminishing returns. We hypothesize that it is because the model suffers from over-fitting when trained with limited data budget such as ImageNet. Indeed, when we train using distribution augmentation [18], the best performance improves from 1.9 to 1.6. This however suggests another way to scale the model: Keep the architecture and parameter count almost the same and instead run on  $2 \\times 2$  patched input (so  $256 \\times 256 \\times 12$  for 512 inputs). Similar to  $2 \\times$  model size, reducing the patching size also increases FLOPS by roughly a factor of 4. However, we found this model performs even better to about 1.5 without the need of distribution augmentation. We call this model flop heavy, because it has a much higher flop over parameter ratio.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Flop heavy scaling has another interesting property. Suppose we have a small model trained to fit input of size  $256 \\times 256$  with  $2 \\times 2$  patching. Using the flop heavy scaling at  $512 \\times 512$  resolution enables us to directly finetune from the small model trained at  $256 \\times 256$  with exactly the same amount of parameters, whereas its counterpart version at  $512 \\times 512$  resolution and with  $4 \\times 4$  patching needs to introduce additional parameters to handle the more input channels. This method of finetuning to higher resolutions has already been popularized in the context of text-to-image generation [32]. Here we find that flop heavy scaling is a more favorable way to scale on smaller datasets such as ImageNet. Of course, in principle one could also train a model with more channels and  $4 \\times 4$  patching on a lower resolution, but this is not done in practice to train 'small' models.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Residual U-ViTs: Removing blockwise skipconnections",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "U-Nets require that sub-sampled levels (for example via average pooling) are bypassed by skip-connections. However, this makes the architecture very different from large-scale language models such as transformers, where these skip-connections are not used and residual connections suffice.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "This holds under the condition that the most important information is already contained by the  $128 \\times 128$  image, and this may for example not hold for images without global structure, e.g. that only contain textures.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "18064",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this paper we use the U-ViT model of [14], which is a variant of U-Nets with self-attention layers (with convolutional layers) being replaced by transformer blocks. Hence, that part of the architecture is closer to standard transformers.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we further simplify model definition with Residual U-ViTs, see Figure 4. The blockwise skip-connections are removed, and in their place only a single skip-connection is used per downsampling operation. To be precise, let  $f_{d}, f_{u}$  denote a down and up level of a U-ViT and let  $f_{m}$  denote the middle stage. This two-stage Residual U-ViT can now be described by:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nf (x) = f _ {u} \\left(\\mathrm {U} \\left(f _ {m} (\\mathrm {D} (h)) - \\mathrm {D} (h)\\right) + h\\right) \\text {w h e r e} h = f _ {d} (x) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $D$  is typically an average pooling and linear and  $U$  is typically a linear and nearest neighbour upsampling. Defining this network to preserve an identity function at initialization is now much easier: As long as  $f_{d}$ ,  $f_{u}$  and  $f_{m}$  are initialized to be identity, the entire  $f$  is also identity at initialization. The generalization to any-depth U-ViTs is also straightforward: we can define another two levels of U-ViTs in place of  $f_{m}$  recursively, where the nested U-ViTs can also be guaranteed to be initialized as an identity function.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For small networks, it could be helpful to keep the blockwise skip-connections, and expect to incur a slight performance degradation from removing the blockwise skip-connections. Small networks have limited capacity, so limiting skip-connections may create bottleneck issues. Experimentally, this is confirmed for the small architectures, where we observe 0.2 FID performance degradation on ImageNet512 and 0.06 FID performance degradation on ImageNet256. Because of the simplified definition, we choose to accept this performance penalty for small models. Moreover, we find that larger models perform on par or even benefit from removing the blockwise skip-connections.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The final advantage is memory consumption at evaluation. For example, a feature map at  $256^{2}$  resolution with 128 channels requires  $256^{2} \\cdot 128 \\cdot 2 / 1024^{2} = 16\\mathrm{MB}$ . With 3 blocks per level, this requires holding an extra  $3 \\cdot 16 = 48\\mathrm{MB}$  per example for the skip-connections, whereas the Residual U-ViT only requires holding  $h$  and  $D(h)$  (the latter could be cheaply recomputed), so  $16 + 8 = 24\\mathrm{MB}$  per example while computing the lower levels. For a hypothetical super-resolution model at  $4096^{2}$  resolution, this leads to a difference between  $3 \\cdot 4 = 12\\mathrm{GB}$  and only  $4 + 2 = 6\\mathrm{GB}$ . During training this advantage is usually negligible, because feature maps also need to be retained for the backward pass. A final advantage of Residual U-ViTs is that it is more straightforward to define asymmetric U-ViTs, i.e., with a different number of blocks in the downsampling (encoding) stage from the one in the upsampling (decoding) stage. In certain cases, moving blocks from the downsampling stage to the upsampling stage can increase performance.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/db47be7ec0de83b6399d13043bf84e5cd0faa4c5cc3431cd3fa9f8131560132e.jpg",
+        "image_caption": [
+            "Figure 4. Residual U-ViT with levelwise skip-connections (instead of blockwise). When the network blocks are initialized to be identity, the entire network is also an identity function at initialization."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "2.4. Distillation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Sampling from a pixel-space diffusion model naively often requires more function evaluations than sampling from a latent-space diffusion model. For example, the popular Stable Diffusion model [32] is usually sampled using 20-50 sampling steps, while pixel-space models are sampled with  $100+$  steps [14]. To reduce the number of sampling steps, we could use either more advanced solvers or distillation. Recently distillation methods show that pixel-space models can be adapted into few-step samplers that maintain high sample quality [23, 29, 36, 44, 45, 47]. In this work, we use moment matching distillation [37] which is currently one of the best distillation methods available in the few step regime. We distill our pixel-space models for use with 8-16 sampling steps, which empirically we find maintains or even improves the sample quality of our models.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The first end-to-end diffusion work that directly generated high resolution images was [4]. Given the poor performance of end-to-end models, two popular alternatives were introduced: cascaded diffusion [12] and latent diffusion [32].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": " Cascaded diffusion approaches have been shown to scale to large datasets and models to generate high quality and high resolution imagery, albeit in multiple stages [12, 40, 42, 52], or with fine-tuning [43]. Although the focus of this paper has been single stage generation up to a resolution of  $10^{24^2}$ , the loss weightings may also be used for cascaded models.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Significant improvements were made to end-to-end diffusion by shifting noise schedules [3, 14] and subsequently loss weightings [25]. Other approaches such as multi-resolution losses (and possibly architecture adaptions) [6, 7, 14] added marginal gains. However, the current best known latent model EDM2 [20] outperforms these prior end-to-end approaches by a large margin. In contrast, our models are competitive with latent models, outperforming DiT-XL/2 [31] and only performing slightly worse than EDM2.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Skip connections The U-Net architecture is a fully convolutional network with long-range skip-connections introduced for (medical) image segmentation [33, 39]. The main",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18065",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3e8b1ffcef67cfe66bf5c5c04d334ca80c64b63852d2acf792d78168f86a8358.jpg",
+        "image_caption": [
+            "Figure 5. Effect of weighting functions in the loss on the FID score of ImageNet512 over the training iterations. The proposed sigmoid weighting with  $b = -3$  shows best performance consistent across all training iterations."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "idea of U-Net is to combine a contracting path (which encodes the image semantics) with long skip-connections at the same resolution to enable precise localization.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "With the introduction of ViTs [5] as an alternative for convolutional layers, the U-Net has been converted to U-ViTs using a similar network but replacing (some) ResNet blocks with ViTs, either with spatial down-sampling [14] or without [2]. Long-range skip-connections play an pivotal role in these networks, for example for fine-tuning controllable diffusion models [17] and for the stability and training speed [15, 30]. In these latter works, it is shown that multiplying the skip-connections with a (constant) scalar  $(< 1)$  improves training stability and speed, because of the propagation of noise throughout the network. In our work, we reduce the number of skip-connections significantly and initialise the network such that it resembles an identify function.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Flop heavy fine-tuning Fine-tuning on a higher resolution at large scale was effectively done in Stable Diffusion [32] to limit the training cost, which is a form of flop heavy scaling over different resolutions. In this paper we show that flop heavy scaling is also preferred from a regularization perspective, which can be done either by finetuning from a lower resolution, or by lowering the patching size.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Sigmoid weighting versus others",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Loss weighting In this experiment, we want to understand the effect of loss weighting on the final image quality of a model. For the noise schedule, we use an interpolated cosine schedule because it has relatively broad coverage over logsnr values. We compare the weightings corresponding to the original  $\\epsilon$ -mse [11] and the multiscale  $\\epsilon$ -mse [14], the EDM shifted weightings [19], including the original and monotonic versions [19, 26], and the proposed sigmoid weighting",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0a20f14d695a3b2c1dc90f07e7e80a7af439384ddd39d007754bda786705f538.jpg",
+        "image_caption": [
+            "Figure 6. Effect of training noise schedules on the FID score of ImageNet512 over the training iterations. Fortunately, with our proposed sigmoid weighting  $(b = -3)$ , the exact choice of the noise schedules has little effect on the training process."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/efb9313d8f94b8d94214c99f76f5cc0c88c6879119bcc7ddafe1adbca754cbf4.jpg",
+        "table_caption": [
+            "Table 1. Sigmoid weighting performance (left) with the flop heavy architecture. Larger resolutions require more negative bias. Power loss performance (right) on ImageNet512 with the small model. Increasing downsampling has a similar effect as decreasing bias, hence we prefer the more simple sigmoid weighting."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"5\">(a) Sigmoid weighting</td><td colspan=\"5\">(b) Power loss weighting</td></tr><tr><td rowspan=\"2\">bias</td><td colspan=\"4\">resolution</td><td rowspan=\"2\">bias</td><td colspan=\"4\">downsample levels</td></tr><tr><td>128</td><td>256</td><td>512</td><td>1024</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td>-5</td><td>-</td><td>-</td><td>-</td><td>1.82</td><td>-4</td><td>2.19</td><td>2.58</td><td>3.62</td><td>5.11</td></tr><tr><td>-4</td><td>-</td><td>-</td><td>1.63</td><td>1.75</td><td>-3</td><td>2.19</td><td>2.32</td><td>2.85</td><td>4.02</td></tr><tr><td>-3</td><td>-</td><td>1.47</td><td>1.48</td><td>2.32</td><td>-2</td><td>2.29</td><td>2.15</td><td>2.34</td><td>3.13</td></tr><tr><td>-2</td><td>1.49</td><td>1.42</td><td>1.55</td><td>2.17</td><td>-1</td><td>2.64</td><td>2.32</td><td>2.25</td><td>2.54</td></tr><tr><td>-1</td><td>1.35</td><td>1.38</td><td>1.75</td><td>-</td><td>0</td><td>3.22</td><td>2.74</td><td>2.07</td><td>2.22</td></tr><tr><td>0</td><td>1.30</td><td>1.46</td><td>1.94</td><td>-</td><td>1</td><td>-</td><td>2.69</td><td>2.29</td><td>2.16</td></tr><tr><td>1</td><td>1.26</td><td>1.56</td><td>-</td><td>-</td><td>2</td><td>-</td><td>3.26</td><td>2.53</td><td>2.19</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "with shift  $b = -3$ . As can be seen in Figure 5, the sigmoid weighting outperforms all other weightings, with EDM monotonic shifted being the closest alternative. Appendix C contains additional experiments, where we also evaluate the sigmoid weighting against the closest competitor without guidance. Here again sigmoid weighting is consistently better. We also evaluate a time-shifted variant, where the bias depends on the progress in training.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training efficiency of noise schedules Since the training noise schedule can be decoupled from the loss weighting and it only affects the training efficiency but not the final performance, one can measure the convergence speed over the training process caused by leveraging particular noise schedules. In this experiment we test the cosine schedule [11], the shifted cosine and the interpolated cosine schedules [14] (Figure 6). For fair comparison, we fix the sampling noise schedule as the cosine interpolated schedule. Interestingly, when the sigmoid weighting is used, the choice of noise schedule does not affect the training efficiency significantly. Arguably, the shifted schedule is a bit more sample effi",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18066",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/cfba554f0499d140f421d739d32d5229f4c5d7630c45e389a8d625935e959e56.jpg",
+        "image_caption": [
+            "Figure 7. FID versus training cost on ImageNet512. Note that the EDM-2 training curves are without guidance, but the best performance with guidance intervals is reported with a separate marker, the figure source adapted has been adapted from EDM2 [20]. Following their assumptions, one training iteration is three times as expensive as evaluating the model. Our Flop Heavy (finetune) is trained by first training a small model on ImageNet256 for 400k iterations and then finetuning the same model on ImageNet512."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            119,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/584f7bccdcdfe72473e5875f5ad05299e881bc000dab70b530254646605fc7cc.jpg",
+        "image_caption": [
+            "Figure 8. The effect of scaling either channels or tokens, compared to the small model variant. FLOPS between model size  $2\\mathrm{x}$  and flop heavy are similar."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            91,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/c32f83e922fb55d924c8bf41c4c5064257dcb4a5573c063f4ece679f81f58f5a.jpg",
+        "image_caption": [
+            "Figure 9. The effect of Residual-UViTs (removing block skip connections). Although smaller models can be effected, larger models are unaffected by the simplification."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            364,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/21d9702abf3eda288b9e9681b14556e5f7071b8f2e50a14b2017ca07968d5fd0.jpg",
+        "image_caption": [
+            "Figure 10. Changing the encoder decoder architecture. Decoder blocks are more important than encoder blocks, and symmetric architectures have decent performance."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "cient initially but all schedules perform similarly towards the end. This suggests that there is a lot of transfer across different logsnr values. We also tried the EDM training noise schedule with the sigma power sampling noise schedule [19] (not plotted), with both shifted or the original version, but its narrower logsnr sampling schedule led to performance degradation, achieving about 9 FID at best. This suggests that for high resolution, a wide logsnr range is crucial to cover the important noise levels.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Bias over resolutions In Table 1a, we show the effect of the bias term  $b$  on the final performance when trained using a flop heavy model. All models use the same guidance and similar guidance intervals, where the lower bound of the guidance interval has been shifted according to resolution (again approximately 1.5 per 2x resolution change), see Appendix B for more details.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Sigmoid weighting versus the power loss In literature, high resolution generation can greatly benefit from having a multiscale loss [6, 7, 14]. To that end we create a multiscale",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "variant that we name the power loss. In addition to the sigmoid weighting that effectively upweights low frequency components of the data and downweights high frequency components, the power loss aims to amplify the loss of low sub-band (smooth) signals in the spatial domain via Haar wavelets. For details on this loss see Appendix B.2.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In Table 1b we see that the bias should be adjusted based on the number of Haar transform downsampling levels. Despite being competitive, the performance of power loss is roughly on par with the one with sigmoid weighting but without multiscaling (i.e. downsample levels  $= 0$ ), if we tune the bias of the sigmoid weighting more aggressively. Interestingly, lowering the bias has almost the same effect as increasing the scale. Therefore, building the multiscale variant is not necessary with the sigmoid weighting.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Scaling channels vs tokens on ImageNet",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section we show the difference between scaling a model 4x FLOPS, either via channels or by creating larger resolution feature maps (or put differently, feature maps with a higher token count). Note that our small model on",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "18067",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ImageNet512 is patched  $4 \\times 4$ . This model is scaled either by increasing channels by two (named model size  $2x$ ), or by reducing patching to  $2 \\times 2$  (named flop heavy, because FLOPS over params is much higher). Indeed as can be seen in Figure 8, the flop heavy model performs much better than the model size  $2x$ , when trained in a standard way on ImageNet512. Note that unlike most experiments, in these experiments it was necessary to use very different optimal guidance settings, more details in Appendix B.",
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+    {
+        "type": "text",
+        "text": "We confirm this is an issue related to overfitting, by training the model size 2x with distribution augmentation [18] the model size 2x variant performs much better, with an FID of 1.6 instead of 1.9 (latter in Figure 8). Still, without any augmentation beyond the standard horizontal flips, the flop heavy model achieves a score of 1.54.",
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+    {
+        "type": "text",
+        "text": "4.3. Removing block skip connection",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section we study the difference between the residual skip-connections and the blockwise skip-connections. As hypothesized, the small model performance drops a bit because of this. For ImageNet512 a deficit of about 0.2 FID (in Figure 9) and for Imagenet256 a deficit of about 0.05 FID. That the task of fitting ImageNet256 is less affected by removing skip-connections can be explained by the task being easier: The task of fitting ImageNet256 is a subset of fitting ImageNet512.",
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+    },
+    {
+        "type": "text",
+        "text": "For larger models, removing blockwise skip-connections in favor of a single residual connection does not degrade performance, and may even lead to slightly increased performance (see Figure 9). This is somewhat unexpected, and the phenomenon persists with different guidance settings as well. The FID curve reminds of the model size  $2\\mathrm{x}$  curve, which at first improves but flattens out over iterations. Therefore our best hypothesis is that the block skip (flop) baseline may have similar problems such as overfitting. Regardless, it shows that Residual U-ViTs scale well.",
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+    },
+    {
+        "type": "text",
+        "text": "Asymmetric U-ViT Since our U-ViT models encompass only a single skip connection for each level, we can use a different number of ResNet or ViT blocks per level. This allows to move compute from the encoder stage (the down sampling half of the model) to the decoder stage (the upsampling half of the model). From Figure 10 we observe that (a) for a fixed compute budget, it is better to add more parameters to the decoder, the encoder heavy model (E5-D1) is significantly worse than the baseline (E3-D3) and the decoder heavy model (E1-D5); (b) there needs to be some balance between the encoder and the decoder, E1-D7 works less good than E3-D5. (c) by a slightly heavier model (E3-D7, only  $10\\%$  more parameters than our small (E3-D3) model, the performance significantly increases.",
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+    {
+        "type": "table",
+        "img_path": "images/ef128d1d326e3d3a214cf0c61296f4451a59a5987594436ff51fc59603ea22ff.jpg",
+        "table_caption": [
+            "Table 2. Literature Comparison on ImageNet on FID. Note that even though certain NFEs are high (e.g. 4100 for CDM) typically these suffer minor performance degradation for lower NFEs and should not be taken too literally."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>NFE</td><td>FID</td></tr><tr><td colspan=\"3\">Imagenet 128 x 128</td></tr><tr><td>RIN [16]</td><td>1000</td><td>2.75</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>1.94</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>1.81</td></tr><tr><td>VDM+++ [25]</td><td>250</td><td>1.75</td></tr><tr><td>DisCo-Diff [46]</td><td>414</td><td>1.73</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.48</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.26</td></tr><tr><td colspan=\"3\">Imagenet 256 x 256</td></tr><tr><td>ADM-G [4]</td><td>250</td><td>4.59</td></tr><tr><td>ADM-U [4]</td><td>250</td><td>3.94</td></tr><tr><td>CDM [12]</td><td>4100</td><td>4.88</td></tr><tr><td>RIN [3, 16]</td><td>1000</td><td>3.52</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>2.44</td></tr><tr><td>MDM [7]</td><td>250</td><td>3.51</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>2.30</td></tr><tr><td>DiT-XL/2 [31]</td><td>250</td><td>2.27</td></tr><tr><td>VDM++ [25]</td><td>250</td><td>2.12</td></tr><tr><td>RDM [42]</td><td>356</td><td>1.89</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.56</td></tr><tr><td>SiD2, small (ours)</td><td>512</td><td>1.72</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.38</td></tr><tr><td colspan=\"3\">Imagenet 512 x 512</td></tr><tr><td>ADM-G [4]</td><td>250</td><td>7.72</td></tr><tr><td>RIN [3, 16]</td><td>1000</td><td>3.95</td></tr><tr><td>ADM-U [4]</td><td>250</td><td>3.85</td></tr><tr><td>LDM-4-G [32]</td><td>250</td><td>3.60</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>3.02</td></tr><tr><td>DiffiT [9]</td><td>250</td><td>2.67</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>2.40</td></tr><tr><td>DiT-XL/2 [31]</td><td>250</td><td>3.04</td></tr><tr><td>VDM++ [25]</td><td>250</td><td>2.65</td></tr><tr><td>MAGVIT-v2 [51]</td><td>64</td><td>1.91</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.80</td></tr><tr><td>EDM2-S (interval) [27]</td><td>63</td><td>1.68</td></tr><tr><td>EDM2-XXL (interval) [27]</td><td>63</td><td>1.40</td></tr><tr><td>SiD2, small (ours)</td><td>512</td><td>2.19</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.48</td></tr><tr><td>SiD2, Flop Heavy distilled (ours)</td><td>16</td><td>1.50</td></tr><tr><td colspan=\"3\">Imagenet 1024 x 1024</td></tr><tr><td>RIN [16]</td><td>1000</td><td>8.72</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.75</td></tr></table>",
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+    },
+    {
+        "type": "page_number",
+        "text": "18068",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5d6987a48d055fb4e712dfadd36587f8b0d1bf41716e0491a2aae199d07621da.jpg",
+        "table_caption": [
+            "Table 3. Zero-shot text-to-image performance evaluated on MSCOCO in  $\\mathrm{FID}_{30\\mathrm{k}}$ . Our distilled model, evaluated on the more difficult 512 setting, outperforming other works."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Size</td><td>NFE</td><td>FID30k</td></tr><tr><td>DeepFloyd [40]</td><td>256</td><td></td><td>6.7</td></tr><tr><td>eDiff-I [1]</td><td>256</td><td></td><td>6.9</td></tr><tr><td>Parti [49]</td><td>256</td><td></td><td>7.2</td></tr><tr><td>Imagen [35]</td><td>256</td><td></td><td>7.3</td></tr><tr><td>simple diffusion [14]</td><td>256</td><td></td><td>8.3</td></tr><tr><td>simple diffusion [14]</td><td>512</td><td>256</td><td>9.6</td></tr><tr><td>SDv1.5 (eval DMD2) [32]</td><td>512</td><td>200</td><td>7.2</td></tr><tr><td>DMD2 [48]</td><td>512</td><td>4</td><td>8.3</td></tr><tr><td>SiD2 (ours, bias=-3)</td><td>512</td><td>256</td><td>8.1</td></tr><tr><td>SiD2 16-step distilled (ours)</td><td>512</td><td>16</td><td>6.7</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Literature comparison",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Here we compare different models from the literature. In the first section end-to-end diffusion models are compared, and in the second section we compare between all types of generative models. In Table 2 it can be seen that our SiD2 is very competitive with existing generative models: On ImageNet128 and ImageNet256 it achieves state-of-the-art performance, on ImageNet512 it is a little worse but still competitive with the best latent diffusion model and outperforms all other models, pixel-based and latent.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparing diffusion models on compute The training cost SiD2 is another helpful way to see how the model scales, as depicted in Figure 7). Importantly, the performance of our pixel-based approach outperforms other significantly. Observe for example the performance of our small variant (using no guidance interval to keep this comparison fair), which roughly the same performance as the VDM++ while only using a third of the training cost, and a fourth of the FLOPS in a single forward pass (see Figure 16 in Appendix C). It is also competitive with the best currently known latent diffusion approach EDM2 [20], but in fairness EDM2 scales a little bit better. These models attain even better performance for a smaller training cost, and a similar story holds for forward pass complexity. End-to-end diffusion can work much better than previously demonstrated, but it is still somewhat outperformed by latent diffusion on quality versus compute comparisons for both sampling and training.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Text to image generation Finally, we show that our method can be used for end-to-end training of text-to-image models. Here, evaluation is more difficult as MSCOCO zero-shot performance depends a lot on the dataset used and is known to not necessarily correspond to actual perceived performance. Nevertheless, it is important that the model achieves performance in the right ballpark. Indeed, when we train SiD2 it performs comparable to other models in the",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/d5236b904016a7ed46178509b5d43b738cfd980c3ca046b1e34ffde478850fc2.jpg",
+        "table_caption": [
+            "Table 4. Conditional Video generation performance on Kinetics600 in FVD (resized to 64). For video generation the loss specification is important to obtain good sample quality (see ablations)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>FVD50k</td></tr><tr><td colspan=\"2\">pixel diffusion</td></tr><tr><td>Video Diffusion Models [13]</td><td>16.6</td></tr><tr><td>RIN [16]</td><td>10.8</td></tr><tr><td>Rolling Diffusion [34]</td><td>5.2</td></tr><tr><td colspan=\"2\">latent diffusion</td></tr><tr><td>MAGVIT [50]</td><td>9.9</td></tr><tr><td>MAGVITv2 [51]</td><td>4.3</td></tr><tr><td>W.A.L.T [8]</td><td>3.3</td></tr><tr><td>SiD2 (ours, sigmoid bias = 0)</td><td>2.3</td></tr><tr><td colspan=\"2\">ablations</td></tr><tr><td>eps-mse</td><td>5.7</td></tr><tr><td>sigmoid bias = +2</td><td>3.2</td></tr><tr><td>sigmoid bias = -2</td><td>2.5</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "literature on MSCOCO  $\\mathrm{FID}_{30\\mathrm{K}}$ , and detailed samples have only a small number of artifacts (Figure 2). Furthermore, the moment matching distilled version using [37] outperforms the baseline model as previously observed. This model also outperforms all other zero-shot approaches at 512 resolution as shown in Table 3.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Video Generation To test whether our approach transfers to video, we test our model on Kinetics600 following [13], by conditioning on 5 frames and generating (sometimes referred to as predicting) the subsequent 11 frames. We then compute the FVD between the training set and the generated samples both on the subsequent 11 frames. Even though our method generates at  $128 \\times 128$ , we follow [8] and resize samples to have resolution  $64 \\times 64$ . Our model achieves SOTA performance and it turns out that tuning the loss is very important to achieve this as shown in Table 4. Note that the latent approaches ([8, 50, 51]) use much less training compute than our models in pixel-space, which we discuss in more detail in the Appendix B.",
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+    {
+        "type": "text",
+        "text": "5. Discussion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper we present Simpler Diffusion (SiD2) and show how one can train end-to-end diffusion and achieve competitive performance with latent models: (1) use the sigmoid loss, (2) with a simpler U-ViT architecture, and (3) favour a flop heavy model design. As a result, our method outperforms existing end-to-end models by a large margin. Nevertheless, at this moment latent diffusion methods still seem to have slightly better scaling properties and it remains to be seen whether this gap can be closed any further. Importantly, for many applications training a separate autoencoder may not be either practical or desired. Therefore, we believe this paper is an important contribution that allows end-to-end modelling directly in the pixel-space.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "18069",
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            91,
+            89,
+            187,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+    {
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2025/Simpler Diffusion_ 1.5 FID on ImageNet512 with Pixel-space Diffusion/3cf16242-5862-4aa6-864f-5aba8865f5f9_model.json

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+        {
+            "type": "title",
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Latent diffusion models have become the popular choice for scaling up diffusion models for high resolution image synthesis. Compared to pixel-space models that are trained end-to-end, latent models are perceived to be more efficient and to produce higher image quality at high resolution. Here we challenge these notions, and show that pixel-space models can be very competitive to latent models both in quality and efficiency, achieving 1.5 FID on ImageNet512 and new SOTA results on ImageNet128, ImageNet256 and Kinetics600."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.533,
+                0.484,
+                0.684
+            ],
+            "angle": 0,
+            "content": "We present a simple recipe for scaling end-to-end pixel-space diffusion models to high resolutions. 1: Use the sigmoid loss-weighting [25] with our prescribed hyperparameters. 2: Use our simplified memory-efficient architecture with fewer skip-connections. 3: Scale the model to favor processing the image at a high resolution with fewer parameters, rather than using more parameters at a lower resolution. Combining these with guidance intervals, we obtain a family of pixel-space diffusion models we call Simpler Diffusion (SiD2)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.71,
+                0.222,
+                0.725
+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.735,
+                0.484,
+                0.87
+            ],
+            "angle": 0,
+            "content": "Diffusion models have been tremendously successful in domains such as image, video and audio generation. For high resolution data, latent diffusion models [32] have been particularly successful: Through encoding the data in a lower dimensional space, these models sidestep the difficulties faced by more traditional pixel-space diffusion models in scaling up to high resolution. This makes latent diffusion models also scale better in training compute than other approaches, as shown by [20]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.871,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "However, latent models have their own challenges: It can be difficult to train the autoencoders that produce the latents,"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.543,
+                0.366,
+                0.883,
+                0.468
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.48,
+                0.905,
+                0.495
+            ],
+            "angle": 0,
+            "content": "Figure 1. End-to-end pixel diffusion performance on ImageNet512."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.506,
+                0.906,
+                0.642
+            ],
+            "angle": 0,
+            "content": "which in practice requires careful tuning of regularization hyperparameters [32]. Even when trained well, the decoder of a latent diffusion model can produce artifacts or otherwise imperfect reconstructions, especially when it is applied to latents that are out of distribution compared to the training set. A single-stage pixel-space diffusion model does not have these issues, and so we ask the question: Can pixel-space diffusion models scale as well as latent models with the right architecture and hyperparameters?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.643,
+                0.907,
+                0.794
+            ],
+            "angle": 0,
+            "content": "Over the years, end-to-end pixel-space diffusion has improved considerably (Figure 1). The main problem was that the standard schedule and loss-weighting [11] work well for small resolution images, like \\(32^2\\) or \\(64^2\\), but not at higher resolution [3, 14]. It was further shown [25] that it can be helpful to disentangle loss weighting and time sampling for improved control over both, leading to better performance at higher resolution. However, in previous works pixels-space models still did not match the best latent models on standard benchmarks like ImageNet512."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.796,
+                0.909,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The main contribution of this paper is to improve pixel-space diffusion on high resolution images while keeping as close to the original formulation of diffusion models as possible. Specifically, we analyze and tune the sigmoid loss weighting from [25], and show why it should be preferred over their favored EDM monotonic. We further propose architectural improvements that lead to even better perfor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.945,
+                0.519,
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+            "angle": 0,
+            "content": "18062"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.088,
+                0.291,
+                0.242
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.296,
+                0.088,
+                0.496,
+                0.242
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.089,
+                0.701,
+                0.242
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.708,
+                0.089,
+                0.905,
+                0.242
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.239,
+                0.252,
+                0.757,
+                0.267
+            ],
+            "angle": 0,
+            "content": "Figure 2. Some text-to-image samples of \\(512 \\times 512\\) that have been generated by SiD2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.293,
+                0.484,
+                0.384
+            ],
+            "angle": 0,
+            "content": "mance, namely flop heavy scaling and removing block skip-connections (Residual U-ViTs). Most notably, we improve the state-of-the-art of pixel-space diffusion from 2.65 to 1.48 on ImageNet512 (see also Figure 1). Further, we also achieve overall state-of-the-art on ImageNet128, ImageNet256 and Kinetics600 without heavy tuning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.394,
+                0.222,
+                0.41
+            ],
+            "angle": 0,
+            "content": "1.1. Background"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.416,
+                0.484,
+                0.446
+            ],
+            "angle": 0,
+            "content": "A diffusion process gradually destroys data over a conceptual time \\(t\\), typically with Gaussian noise as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.16,
+                0.459,
+                0.482,
+                0.475
+            ],
+            "angle": 0,
+            "content": "\\[\n\\boldsymbol {z} _ {t} = \\alpha_ {t} \\boldsymbol {x} + \\sigma_ {t} \\boldsymbol {\\epsilon}, \\text {w h e r e} \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, \\mathbf {I}), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.487,
+                0.484,
+                0.699
+            ],
+            "angle": 0,
+            "content": "which defines a distribution \\(q(\\pmb{z}_t|\\pmb{x})\\) such that \\(\\pmb{z}_0\\) is close to clean data and \\(\\pmb{z}_1\\) is close to Gaussian noise. In this paper we assume a variance-preserving [41] schedule, which is defined as \\(\\alpha_{t} = \\sqrt{\\sigma(\\lambda_{t})}\\) and \\(\\sigma_t = \\sqrt{\\sigma(-\\lambda_t)}\\), with \\(\\lambda_{t} = \\log \\left(\\alpha_{t}^{2} / \\sigma_{t}^{2}\\right)\\) being the log signal-to-noise ratio, which monotonically decreases with time as \\(t\\to 1\\), and \\(\\sigma (\\cdot)\\) being the sigmoid function. It can be shown that other types of schedules such as the variance-exploding schedule or the flow matching schedule [28] can always be converted to a variance-preserving schedule with a linear scaling of \\(\\pmb{z}_{t}\\) [25]. The key defining property of a noise schedule is the log signal-to-noise ratio \\(\\lambda_{t}\\). A neural network is used to predict \\(\\hat{\\pmb{x}} = \\hat{\\pmb{x}}_{\\theta}(\\pmb{z}_{t},t)\\) that effectively estimates \\(\\mathbb{E}[\\pmb {x}|\\pmb {z}_t]\\), which can be done by minimizing a weighted mean squared error loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.149,
+                0.71,
+                0.482,
+                0.739
+            ],
+            "angle": 0,
+            "content": "\\[\nL (\\boldsymbol {x}) = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} - \\frac {\\mathrm {d} \\lambda_ {t}}{\\mathrm {d} t} w \\left(\\lambda_ {t}\\right) \\| \\boldsymbol {x} - \\hat {\\boldsymbol {x}} \\| ^ {2}, \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.75,
+                0.483,
+                0.87
+            ],
+            "angle": 0,
+            "content": "where \\( w(\\lambda_t) \\) is the weighting function. \\( -\\mathrm{d}\\lambda_{t} / \\mathrm{d}t \\) cancels out the effect of the noise schedule \\( \\lambda_{t} \\) on the loss. In other words, \\( L(\\mathbf{x}) \\) can be rewritten as \\( \\int -w(\\lambda)\\| \\pmb {x} - \\hat{\\pmb{x}}\\| ^2 d\\lambda \\) that is invariant to the choice of \\( \\lambda_{t} \\). However, \\( \\lambda_{t} \\) still impacts the sampling efficiency of the Monte Carlo estimator of the expected loss, and thus affects the training dynamics of diffusion models. This decouples noise schedule \\( \\lambda_{t} \\) and weighting function \\( w(\\lambda) \\) as a function of \\( \\lambda \\) [25]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.871,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The above squared error loss can be derived from the variational interpretation of diffusion models [26]. Given"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.293,
+                0.908,
+                0.355
+            ],
+            "angle": 0,
+            "content": "two time steps \\(s < t\\), we define the denoising distribution \\(p(\\boldsymbol{z}_s|\\boldsymbol{z}_t)\\) in the same formulation as the true posterior \\(q(\\boldsymbol{z}_s|\\boldsymbol{z}_t,\\boldsymbol{x})\\), but replace the ground truth \\(\\boldsymbol{x}\\) with the learned approximation \\(\\hat{\\boldsymbol{x}} \\approx \\mathbb{E}[\\boldsymbol{x}|\\boldsymbol{z}_t]\\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.55,
+                0.366,
+                0.905,
+                0.382
+            ],
+            "angle": 0,
+            "content": "\\[\np \\left(\\boldsymbol {z} _ {s} \\mid \\boldsymbol {z} _ {t}\\right) = q \\left(\\boldsymbol {z} _ {s} \\mid \\boldsymbol {z} _ {t}, \\boldsymbol {x} = \\hat {\\boldsymbol {x}}\\right) = \\mathcal {N} \\left(\\boldsymbol {z} _ {s} \\mid \\mu_ {t \\rightarrow s}, \\sigma_ {t \\rightarrow s}\\right), \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.394,
+                0.906,
+                0.518
+            ],
+            "angle": 0,
+            "content": "where \\(\\sigma_{t\\rightarrow s}^2 = \\left(1 / \\sigma_s^2 +\\alpha_{t|s}^2 /\\sigma_{t|s}^2\\right)^{-1}\\) and \\(\\mu_{t\\to s} = \\sigma_{t\\to s}^{2}\\Bigl (\\alpha_{t|s} / \\sigma_{t|s}^{2}\\pmb {z}_{t} + \\alpha_{s} / \\sigma_{s}^{2}\\pmb {x}\\Bigr)\\) with \\(\\alpha_{t|s} = \\alpha_t / \\alpha_s\\) and \\(\\sigma_{t|s}^2 = \\sigma_t^2 -\\alpha_{t|s}\\sigma_s^2\\) . Note that during sampling, the standard deviation for \\(p(z_{s}|z_{t})\\) is chosen to be a log-linear interpolation between \\(\\sigma_{t|s}\\) and \\(\\sigma_{t\\rightarrow s}\\) of the form \\(\\sigma_{t\\rightarrow s}^{\\gamma}\\sigma_{t|s}^{1 - \\gamma}\\) where \\(\\gamma = 0.3\\) was set empirically, which is important as FID is sensitive to over-smooth or grainy images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.533,
+                0.688,
+                0.55
+            ],
+            "angle": 0,
+            "content": "2. Simpler Diffusion"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.559,
+                0.753,
+                0.575
+            ],
+            "angle": 0,
+            "content": "2.1. Revisiting the sigmoid loss"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.581,
+                0.908,
+                0.764
+            ],
+            "angle": 0,
+            "content": "Recall that one of the proposed losses in VDM++ [25] is the sigmoid loss. They expressed the loss with respect to \\(\\epsilon\\)-mse: \\(L(\\pmb{x}) = \\mathbb{E}_{t \\sim \\mathcal{U}(0,1)} - \\frac{\\mathrm{d}\\lambda_t}{\\mathrm{d}t} \\tilde{w}(\\lambda_t) \\| \\pmb{\\epsilon} - \\hat{\\pmb{\\epsilon}} \\|^2\\), which is connected to \\(\\pmb{x}\\)-mse through \\(\\| \\pmb{\\epsilon} - \\hat{\\pmb{\\epsilon}} \\|^2 = \\exp(\\lambda_t) \\| \\pmb{x} - \\hat{\\pmb{x}} \\|^2\\) and \\(\\tilde{w}(\\lambda_t) = \\exp(\\lambda_t) w(\\lambda_t)\\). In VDM++, viewing the loss in \\(\\epsilon\\)-mse enables a natural connection between the weighted loss and the ELBO and showed that losses should be monotonically decreasing on \\(\\epsilon\\)-mse. Hence, they propose the sigmoid loss: \\(\\tilde{w}(\\lambda_t) = \\sigma(b - \\lambda_t)\\), where \\(b\\) denotes the bias or shift and \\(\\sigma\\) is the sigmoid function. However, they ultimately opted for another loss-weighting named EDM-monotonic for high resolution image generation, see Figure 3a."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.786,
+                0.908,
+                0.847
+            ],
+            "angle": 0,
+            "content": "Enforcing weighting monotonicity in \\( x \\) Revisiting the sigmoid loss, we derive its \\( x \\)-mse form, which turns out to conveniently be defined by a mirrored sigmoid (albeit multiplied by a constant factor):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.532,
+                0.859,
+                0.905,
+                0.897
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\sigma \\left(b - \\lambda_ {t}\\right) \\| \\boldsymbol {\\epsilon} - \\hat {\\boldsymbol {\\epsilon}} \\| ^ {2} = \\sigma \\left(b - \\lambda_ {t}\\right) \\exp \\left(\\lambda_ {t}\\right) \\| \\boldsymbol {x} - \\hat {\\boldsymbol {x}} \\| ^ {2} \\tag {4} \\\\ = \\exp (b) \\sigma \\left(\\lambda_ {t} - b\\right) \\| \\boldsymbol {x} - \\hat {\\boldsymbol {x}} \\| ^ {2}. \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18063"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.147,
+                0.106,
+                0.44,
+                0.247
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.239,
+                0.247,
+                0.359,
+                0.257
+            ],
+            "angle": 0,
+            "content": "(a) Weighting over \\(\\epsilon\\)-mse"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.547,
+                0.106,
+                0.838,
+                0.247
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.638,
+                0.247,
+                0.76,
+                0.257
+            ],
+            "angle": 0,
+            "content": "(b) Weighting over \\( \\pmb{x} \\)-mse"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.128,
+                0.269,
+                0.868,
+                0.283
+            ],
+            "angle": 0,
+            "content": "Figure 3. Weighting of different losses in both \\(\\epsilon\\) and \\(x\\) space. Note that the weightings are scaled to have a maximum of one."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.292,
+                0.483,
+                0.473
+            ],
+            "angle": 0,
+            "content": "This reveals that the sigmoid loss is not only monotonically decreasing in \\(\\epsilon\\)-mse, it is also monotonically increasing in \\(x\\)-mse. We claim that a reasonable weighting function \\(w(\\lambda_t)\\) should be monotonically increasing over \\(\\lambda_t\\). Observe that with less noise in \\(z_t\\), there is more information available and it should be strictly easier to predict the original data, meaning that the \\(x\\)-mse generally decreases for higher \\(\\lambda_t\\). This phenomenon is also observed in practice. If the loss weighting in \\(x\\)-mse also decreases, the model would be able to make worse predictions while obtaining less noisy (better) conditioning information and still achieve a lower loss. Simply put: Why put less weight on an easier problem?"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.473,
+                0.484,
+                0.581
+            ],
+            "angle": 0,
+            "content": "Studying both the form of the sigmoid and EDM-monotonic weighting functions in Figure 3, we observe that both weighting functions are monotonically decreasing in \\(\\epsilon\\)-mse, but only the sigmoid weighting is monotonically increasing in \\(x\\)-mse. Therefore, we expect the sigmoid weighting to be a better candidate to scale to high resolution generation than the EDM-monotonic version."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.597,
+                0.484,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Loss shifting Recall that for a resolution that is two times higher in both height and width, an average (low pass) filter would see \\(\\mathrm{Var}[(x_{11} + x_{12} + x_{21} + x_{22}) / 4] = 1 / 4\\) of the noise, while signal strength stays the same [14, 25]. Hence, its effective logsnr is expected to increase by about \\(2\\log 2\\approx 1.386\\approx 1.5\\) when viewed through a low-pass filter. Suppose that the optimal setting for images of \\(128\\times 128\\) is a sigmoid weighting with \\(b\\approx 0\\), then one would expect the optimal setting for images of \\(512\\times 512\\) to be roughly \\(b = -3\\).<sup>1</sup> Empirically we find that slightly more aggressive shifts perform even better."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.772,
+                0.27,
+                0.789
+            ],
+            "angle": 0,
+            "content": "2.2. Flop heavy scaling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.794,
+                0.483,
+                0.856
+            ],
+            "angle": 0,
+            "content": "When one deals with a limited data budget, it can be difficult to balance scaling of models and regularization. Our small model version at \\(512 \\times 512\\) resolution starts out with \\(4 \\times 4\\) patching, and subsequently runs a U-ViT [14] on the \\(128 \\times\\)"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.292,
+                0.908,
+                0.549
+            ],
+            "angle": 0,
+            "content": "\\(128 \\times 48\\) input (assuming the raw input is of 3 channels). To make the model more expressive, one of the most common options is to double the number of channels for every layer, leading to \\(2 \\times\\) model size. However, our experiments show that this results in diminishing returns. We hypothesize that it is because the model suffers from over-fitting when trained with limited data budget such as ImageNet. Indeed, when we train using distribution augmentation [18], the best performance improves from 1.9 to 1.6. This however suggests another way to scale the model: Keep the architecture and parameter count almost the same and instead run on \\(2 \\times 2\\) patched input (so \\(256 \\times 256 \\times 12\\) for 512 inputs). Similar to \\(2 \\times\\) model size, reducing the patching size also increases FLOPS by roughly a factor of 4. However, we found this model performs even better to about 1.5 without the need of distribution augmentation. We call this model flop heavy, because it has a much higher flop over parameter ratio."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.55,
+                0.909,
+                0.777
+            ],
+            "angle": 0,
+            "content": "Flop heavy scaling has another interesting property. Suppose we have a small model trained to fit input of size \\(256 \\times 256\\) with \\(2 \\times 2\\) patching. Using the flop heavy scaling at \\(512 \\times 512\\) resolution enables us to directly finetune from the small model trained at \\(256 \\times 256\\) with exactly the same amount of parameters, whereas its counterpart version at \\(512 \\times 512\\) resolution and with \\(4 \\times 4\\) patching needs to introduce additional parameters to handle the more input channels. This method of finetuning to higher resolutions has already been popularized in the context of text-to-image generation [32]. Here we find that flop heavy scaling is a more favorable way to scale on smaller datasets such as ImageNet. Of course, in principle one could also train a model with more channels and \\(4 \\times 4\\) patching on a lower resolution, but this is not done in practice to train 'small' models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.787,
+                0.907,
+                0.817
+            ],
+            "angle": 0,
+            "content": "2.3. Residual U-ViTs: Removing blockwise skipconnections"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.825,
+                0.909,
+                0.9
+            ],
+            "angle": 0,
+            "content": "U-Nets require that sub-sampled levels (for example via average pooling) are bypassed by skip-connections. However, this makes the architecture very different from large-scale language models such as transformers, where these skip-connections are not used and residual connections suffice."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.09,
+                0.863,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "This holds under the condition that the most important information is already contained by the \\(128 \\times 128\\) image, and this may for example not hold for images without global structure, e.g. that only contain textures."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18064"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.485,
+                0.152
+            ],
+            "angle": 0,
+            "content": "In this paper we use the U-ViT model of [14], which is a variant of U-Nets with self-attention layers (with convolutional layers) being replaced by transformer blocks. Hence, that part of the architecture is closer to standard transformers."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.153,
+                0.485,
+                0.259
+            ],
+            "angle": 0,
+            "content": "In this paper, we further simplify model definition with Residual U-ViTs, see Figure 4. The blockwise skip-connections are removed, and in their place only a single skip-connection is used per downsampling operation. To be precise, let \\( f_{d}, f_{u} \\) denote a down and up level of a U-ViT and let \\( f_{m} \\) denote the middle stage. This two-stage Residual U-ViT can now be described by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.09,
+                0.272,
+                0.484,
+                0.31
+            ],
+            "angle": 0,
+            "content": "\\[\nf (x) = f _ {u} \\left(\\mathrm {U} \\left(f _ {m} (\\mathrm {D} (h)) - \\mathrm {D} (h)\\right) + h\\right) \\text {w h e r e} h = f _ {d} (x) \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.31,
+                0.484,
+                0.446
+            ],
+            "angle": 0,
+            "content": "where \\( D \\) is typically an average pooling and linear and \\( U \\) is typically a linear and nearest neighbour upsampling. Defining this network to preserve an identity function at initialization is now much easier: As long as \\( f_{d} \\), \\( f_{u} \\) and \\( f_{m} \\) are initialized to be identity, the entire \\( f \\) is also identity at initialization. The generalization to any-depth U-ViTs is also straightforward: we can define another two levels of U-ViTs in place of \\( f_{m} \\) recursively, where the nested U-ViTs can also be guaranteed to be initialized as an identity function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.447,
+                0.485,
+                0.629
+            ],
+            "angle": 0,
+            "content": "For small networks, it could be helpful to keep the blockwise skip-connections, and expect to incur a slight performance degradation from removing the blockwise skip-connections. Small networks have limited capacity, so limiting skip-connections may create bottleneck issues. Experimentally, this is confirmed for the small architectures, where we observe 0.2 FID performance degradation on ImageNet512 and 0.06 FID performance degradation on ImageNet256. Because of the simplified definition, we choose to accept this performance penalty for small models. Moreover, we find that larger models perform on par or even benefit from removing the blockwise skip-connections."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.63,
+                0.486,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The final advantage is memory consumption at evaluation. For example, a feature map at \\(256^{2}\\) resolution with 128 channels requires \\(256^{2} \\cdot 128 \\cdot 2 / 1024^{2} = 16\\mathrm{MB}\\). With 3 blocks per level, this requires holding an extra \\(3 \\cdot 16 = 48\\mathrm{MB}\\) per example for the skip-connections, whereas the Residual U-ViT only requires holding \\(h\\) and \\(D(h)\\) (the latter could be cheaply recomputed), so \\(16 + 8 = 24\\mathrm{MB}\\) per example while computing the lower levels. For a hypothetical super-resolution model at \\(4096^{2}\\) resolution, this leads to a difference between \\(3 \\cdot 4 = 12\\mathrm{GB}\\) and only \\(4 + 2 = 6\\mathrm{GB}\\). During training this advantage is usually negligible, because feature maps also need to be retained for the backward pass. A final advantage of Residual U-ViTs is that it is more straightforward to define asymmetric U-ViTs, i.e., with a different number of blocks in the downsampling (encoding) stage from the one in the upsampling (decoding) stage. In certain cases, moving blocks from the downsampling stage to the upsampling stage can increase performance."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.518,
+                0.089,
+                0.906,
+                0.193
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.203,
+                0.908,
+                0.245
+            ],
+            "angle": 0,
+            "content": "Figure 4. Residual U-ViT with levelwise skip-connections (instead of blockwise). When the network blocks are initialized to be identity, the entire network is also an identity function at initialization."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.264,
+                0.637,
+                0.278
+            ],
+            "angle": 0,
+            "content": "2.4. Distillation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.285,
+                0.908,
+                0.513
+            ],
+            "angle": 0,
+            "content": "Sampling from a pixel-space diffusion model naively often requires more function evaluations than sampling from a latent-space diffusion model. For example, the popular Stable Diffusion model [32] is usually sampled using 20-50 sampling steps, while pixel-space models are sampled with \\(100+\\) steps [14]. To reduce the number of sampling steps, we could use either more advanced solvers or distillation. Recently distillation methods show that pixel-space models can be adapted into few-step samplers that maintain high sample quality [23, 29, 36, 44, 45, 47]. In this work, we use moment matching distillation [37] which is currently one of the best distillation methods available in the few step regime. We distill our pixel-space models for use with 8-16 sampling steps, which empirically we find maintains or even improves the sample quality of our models."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.514,
+                0.525,
+                0.655,
+                0.541
+            ],
+            "angle": 0,
+            "content": "3. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.55,
+                0.908,
+                0.611
+            ],
+            "angle": 0,
+            "content": "The first end-to-end diffusion work that directly generated high resolution images was [4]. Given the poor performance of end-to-end models, two popular alternatives were introduced: cascaded diffusion [12] and latent diffusion [32]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.611,
+                0.908,
+                0.701
+            ],
+            "angle": 0,
+            "content": " Cascaded diffusion approaches have been shown to scale to large datasets and models to generate high quality and high resolution imagery, albeit in multiple stages [12, 40, 42, 52], or with fine-tuning [43]. Although the focus of this paper has been single stage generation up to a resolution of \\(10^{24^2}\\), the loss weightings may also be used for cascaded models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.702,
+                0.909,
+                0.838
+            ],
+            "angle": 0,
+            "content": "Significant improvements were made to end-to-end diffusion by shifting noise schedules [3, 14] and subsequently loss weightings [25]. Other approaches such as multi-resolution losses (and possibly architecture adaptions) [6, 7, 14] added marginal gains. However, the current best known latent model EDM2 [20] outperforms these prior end-to-end approaches by a large margin. In contrast, our models are competitive with latent models, outperforming DiT-XL/2 [31] and only performing slightly worse than EDM2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.856,
+                0.91,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Skip connections The U-Net architecture is a fully convolutional network with long-range skip-connections introduced for (medical) image segmentation [33, 39]. The main"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18065"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.092,
+                0.087,
+                0.493,
+                0.273
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.281,
+                0.493,
+                0.338
+            ],
+            "angle": 0,
+            "content": "Figure 5. Effect of weighting functions in the loss on the FID score of ImageNet512 over the training iterations. The proposed sigmoid weighting with \\( b = -3 \\) shows best performance consistent across all training iterations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.35,
+                0.486,
+                0.395
+            ],
+            "angle": 0,
+            "content": "idea of U-Net is to combine a contracting path (which encodes the image semantics) with long skip-connections at the same resolution to enable precise localization."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.396,
+                0.486,
+                0.593
+            ],
+            "angle": 0,
+            "content": "With the introduction of ViTs [5] as an alternative for convolutional layers, the U-Net has been converted to U-ViTs using a similar network but replacing (some) ResNet blocks with ViTs, either with spatial down-sampling [14] or without [2]. Long-range skip-connections play an pivotal role in these networks, for example for fine-tuning controllable diffusion models [17] and for the stability and training speed [15, 30]. In these latter works, it is shown that multiplying the skip-connections with a (constant) scalar \\((< 1)\\) improves training stability and speed, because of the propagation of noise throughout the network. In our work, we reduce the number of skip-connections significantly and initialise the network such that it resembles an identify function."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.612,
+                0.484,
+                0.718
+            ],
+            "angle": 0,
+            "content": "Flop heavy fine-tuning Fine-tuning on a higher resolution at large scale was effectively done in Stable Diffusion [32] to limit the training cost, which is a form of flop heavy scaling over different resolutions. In this paper we show that flop heavy scaling is also preferred from a regularization perspective, which can be done either by finetuning from a lower resolution, or by lowering the patching size."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.733,
+                0.223,
+                0.75
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.758,
+                0.376,
+                0.774
+            ],
+            "angle": 0,
+            "content": "4.1. Sigmoid weighting versus others"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.78,
+                0.486,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Loss weighting In this experiment, we want to understand the effect of loss weighting on the final image quality of a model. For the noise schedule, we use an interpolated cosine schedule because it has relatively broad coverage over logsnr values. We compare the weightings corresponding to the original \\(\\epsilon\\)-mse [11] and the multiscale \\(\\epsilon\\)-mse [14], the EDM shifted weightings [19], including the original and monotonic versions [19, 26], and the proposed sigmoid weighting"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.087,
+                0.903,
+                0.273
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.281,
+                0.905,
+                0.338
+            ],
+            "angle": 0,
+            "content": "Figure 6. Effect of training noise schedules on the FID score of ImageNet512 over the training iterations. Fortunately, with our proposed sigmoid weighting \\((b = -3)\\), the exact choice of the noise schedules has little effect on the training process."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.512,
+                0.348,
+                0.908,
+                0.418
+            ],
+            "angle": 0,
+            "content": "Table 1. Sigmoid weighting performance (left) with the flop heavy architecture. Larger resolutions require more negative bias. Power loss performance (right) on ImageNet512 with the small model. Increasing downsampling has a similar effect as decreasing bias, hence we prefer the more simple sigmoid weighting."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.518,
+                0.429,
+                0.897,
+                0.564
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"5\">(a) Sigmoid weighting</td><td colspan=\"5\">(b) Power loss weighting</td></tr><tr><td rowspan=\"2\">bias</td><td colspan=\"4\">resolution</td><td rowspan=\"2\">bias</td><td colspan=\"4\">downsample levels</td></tr><tr><td>128</td><td>256</td><td>512</td><td>1024</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td>-5</td><td>-</td><td>-</td><td>-</td><td>1.82</td><td>-4</td><td>2.19</td><td>2.58</td><td>3.62</td><td>5.11</td></tr><tr><td>-4</td><td>-</td><td>-</td><td>1.63</td><td>1.75</td><td>-3</td><td>2.19</td><td>2.32</td><td>2.85</td><td>4.02</td></tr><tr><td>-3</td><td>-</td><td>1.47</td><td>1.48</td><td>2.32</td><td>-2</td><td>2.29</td><td>2.15</td><td>2.34</td><td>3.13</td></tr><tr><td>-2</td><td>1.49</td><td>1.42</td><td>1.55</td><td>2.17</td><td>-1</td><td>2.64</td><td>2.32</td><td>2.25</td><td>2.54</td></tr><tr><td>-1</td><td>1.35</td><td>1.38</td><td>1.75</td><td>-</td><td>0</td><td>3.22</td><td>2.74</td><td>2.07</td><td>2.22</td></tr><tr><td>0</td><td>1.30</td><td>1.46</td><td>1.94</td><td>-</td><td>1</td><td>-</td><td>2.69</td><td>2.29</td><td>2.16</td></tr><tr><td>1</td><td>1.26</td><td>1.56</td><td>-</td><td>-</td><td>2</td><td>-</td><td>3.26</td><td>2.53</td><td>2.19</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.58,
+                0.909,
+                0.703
+            ],
+            "angle": 0,
+            "content": "with shift \\( b = -3 \\). As can be seen in Figure 5, the sigmoid weighting outperforms all other weightings, with EDM monotonic shifted being the closest alternative. Appendix C contains additional experiments, where we also evaluate the sigmoid weighting against the closest competitor without guidance. Here again sigmoid weighting is consistently better. We also evaluate a time-shifted variant, where the bias depends on the progress in training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.72,
+                0.911,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Training efficiency of noise schedules Since the training noise schedule can be decoupled from the loss weighting and it only affects the training efficiency but not the final performance, one can measure the convergence speed over the training process caused by leveraging particular noise schedules. In this experiment we test the cosine schedule [11], the shifted cosine and the interpolated cosine schedules [14] (Figure 6). For fair comparison, we fix the sampling noise schedule as the cosine interpolated schedule. Interestingly, when the sigmoid weighting is used, the choice of noise schedule does not affect the training efficiency significantly. Arguably, the shifted schedule is a bit more sample effi"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18066"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.12,
+                0.088,
+                0.882,
+                0.281
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.089,
+                0.285,
+                0.908,
+                0.342
+            ],
+            "angle": 0,
+            "content": "Figure 7. FID versus training cost on ImageNet512. Note that the EDM-2 training curves are without guidance, but the best performance with guidance intervals is reported with a separate marker, the figure source adapted has been adapted from EDM2 [20]. Following their assumptions, one training iteration is three times as expensive as evaluating the model. Our Flop Heavy (finetune) is trained by first training a small model on ImageNet256 for 400k iterations and then finetuning the same model on ImageNet512."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.093,
+                0.358,
+                0.36,
+                0.482
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.366,
+                0.358,
+                0.633,
+                0.482
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.639,
+                0.353,
+                0.907,
+                0.482
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.491,
+                0.36,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Figure 8. The effect of scaling either channels or tokens, compared to the small model variant. FLOPS between model size \\(2\\mathrm{x}\\) and flop heavy are similar."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.364,
+                0.491,
+                0.633,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Figure 9. The effect of Residual-UViTs (removing block skip connections). Although smaller models can be effected, larger models are unaffected by the simplification."
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.639,
+                0.491,
+                0.908,
+                0.547
+            ],
+            "angle": 0,
+            "content": "Figure 10. Changing the encoder decoder architecture. Decoder blocks are more important than encoder blocks, and symmetric architectures have decent performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.574,
+                0.483,
+                0.709
+            ],
+            "angle": 0,
+            "content": "cient initially but all schedules perform similarly towards the end. This suggests that there is a lot of transfer across different logsnr values. We also tried the EDM training noise schedule with the sigma power sampling noise schedule [19] (not plotted), with both shifted or the original version, but its narrower logsnr sampling schedule led to performance degradation, achieving about 9 FID at best. This suggests that for high resolution, a wide logsnr range is crucial to cover the important noise levels."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.73,
+                0.484,
+                0.837
+            ],
+            "angle": 0,
+            "content": "Bias over resolutions In Table 1a, we show the effect of the bias term \\( b \\) on the final performance when trained using a flop heavy model. All models use the same guidance and similar guidance intervals, where the lower bound of the guidance interval has been shifted according to resolution (again approximately 1.5 per 2x resolution change), see Appendix B for more details."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.856,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Sigmoid weighting versus the power loss In literature, high resolution generation can greatly benefit from having a multiscale loss [6, 7, 14]. To that end we create a multiscale"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.574,
+                0.907,
+                0.664
+            ],
+            "angle": 0,
+            "content": "variant that we name the power loss. In addition to the sigmoid weighting that effectively upweights low frequency components of the data and downweights high frequency components, the power loss aims to amplify the loss of low sub-band (smooth) signals in the spatial domain via Haar wavelets. For details on this loss see Appendix B.2."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.666,
+                0.909,
+                0.803
+            ],
+            "angle": 0,
+            "content": "In Table 1b we see that the bias should be adjusted based on the number of Haar transform downsampling levels. Despite being competitive, the performance of power loss is roughly on par with the one with sigmoid weighting but without multiscaling (i.e. downsample levels \\(= 0\\)), if we tune the bias of the sigmoid weighting more aggressively. Interestingly, lowering the bias has almost the same effect as increasing the scale. Therefore, building the multiscale variant is not necessary with the sigmoid weighting."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.817,
+                0.857,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.2. Scaling channels vs tokens on ImageNet"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.84,
+                0.908,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this section we show the difference between scaling a model 4x FLOPS, either via channels or by creating larger resolution feature maps (or put differently, feature maps with a higher token count). Note that our small model on"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "18067"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.091,
+                0.482,
+                0.228
+            ],
+            "angle": 0,
+            "content": "ImageNet512 is patched \\(4 \\times 4\\). This model is scaled either by increasing channels by two (named model size \\(2x\\)), or by reducing patching to \\(2 \\times 2\\) (named flop heavy, because FLOPS over params is much higher). Indeed as can be seen in Figure 8, the flop heavy model performs much better than the model size \\(2x\\), when trained in a standard way on ImageNet512. Note that unlike most experiments, in these experiments it was necessary to use very different optimal guidance settings, more details in Appendix B."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.23,
+                0.483,
+                0.321
+            ],
+            "angle": 0,
+            "content": "We confirm this is an issue related to overfitting, by training the model size 2x with distribution augmentation [18] the model size 2x variant performs much better, with an FID of 1.6 instead of 1.9 (latter in Figure 8). Still, without any augmentation beyond the standard horizontal flips, the flop heavy model achieves a score of 1.54."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.34,
+                0.376,
+                0.356
+            ],
+            "angle": 0,
+            "content": "4.3. Removing block skip connection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.364,
+                0.483,
+                0.501
+            ],
+            "angle": 0,
+            "content": "In this section we study the difference between the residual skip-connections and the blockwise skip-connections. As hypothesized, the small model performance drops a bit because of this. For ImageNet512 a deficit of about 0.2 FID (in Figure 9) and for Imagenet256 a deficit of about 0.05 FID. That the task of fitting ImageNet256 is less affected by removing skip-connections can be explained by the task being easier: The task of fitting ImageNet256 is a subset of fitting ImageNet512."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.504,
+                0.483,
+                0.655
+            ],
+            "angle": 0,
+            "content": "For larger models, removing blockwise skip-connections in favor of a single residual connection does not degrade performance, and may even lead to slightly increased performance (see Figure 9). This is somewhat unexpected, and the phenomenon persists with different guidance settings as well. The FID curve reminds of the model size \\(2\\mathrm{x}\\) curve, which at first improves but flattens out over iterations. Therefore our best hypothesis is that the block skip (flop) baseline may have similar problems such as overfitting. Regardless, it shows that Residual U-ViTs scale well."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.689,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Asymmetric U-ViT Since our U-ViT models encompass only a single skip connection for each level, we can use a different number of ResNet or ViT blocks per level. This allows to move compute from the encoder stage (the down sampling half of the model) to the decoder stage (the upsampling half of the model). From Figure 10 we observe that (a) for a fixed compute budget, it is better to add more parameters to the decoder, the encoder heavy model (E5-D1) is significantly worse than the baseline (E3-D3) and the decoder heavy model (E1-D5); (b) there needs to be some balance between the encoder and the decoder, E1-D7 works less good than E3-D5. (c) by a slightly heavier model (E3-D7, only \\(10\\%\\) more parameters than our small (E3-D3) model, the performance significantly increases."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.09,
+                0.905,
+                0.145
+            ],
+            "angle": 0,
+            "content": "Table 2. Literature Comparison on ImageNet on FID. Note that even though certain NFEs are high (e.g. 4100 for CDM) typically these suffer minor performance degradation for lower NFEs and should not be taken too literally."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.536,
+                0.147,
+                0.885,
+                0.869
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>NFE</td><td>FID</td></tr><tr><td colspan=\"3\">Imagenet 128 x 128</td></tr><tr><td>RIN [16]</td><td>1000</td><td>2.75</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>1.94</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>1.81</td></tr><tr><td>VDM+++ [25]</td><td>250</td><td>1.75</td></tr><tr><td>DisCo-Diff [46]</td><td>414</td><td>1.73</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.48</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.26</td></tr><tr><td colspan=\"3\">Imagenet 256 x 256</td></tr><tr><td>ADM-G [4]</td><td>250</td><td>4.59</td></tr><tr><td>ADM-U [4]</td><td>250</td><td>3.94</td></tr><tr><td>CDM [12]</td><td>4100</td><td>4.88</td></tr><tr><td>RIN [3, 16]</td><td>1000</td><td>3.52</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>2.44</td></tr><tr><td>MDM [7]</td><td>250</td><td>3.51</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>2.30</td></tr><tr><td>DiT-XL/2 [31]</td><td>250</td><td>2.27</td></tr><tr><td>VDM++ [25]</td><td>250</td><td>2.12</td></tr><tr><td>RDM [42]</td><td>356</td><td>1.89</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.56</td></tr><tr><td>SiD2, small (ours)</td><td>512</td><td>1.72</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.38</td></tr><tr><td colspan=\"3\">Imagenet 512 x 512</td></tr><tr><td>ADM-G [4]</td><td>250</td><td>7.72</td></tr><tr><td>RIN [3, 16]</td><td>1000</td><td>3.95</td></tr><tr><td>ADM-U [4]</td><td>250</td><td>3.85</td></tr><tr><td>LDM-4-G [32]</td><td>250</td><td>3.60</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>3.02</td></tr><tr><td>DiffiT [9]</td><td>250</td><td>2.67</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>2.40</td></tr><tr><td>DiT-XL/2 [31]</td><td>250</td><td>3.04</td></tr><tr><td>VDM++ [25]</td><td>250</td><td>2.65</td></tr><tr><td>MAGVIT-v2 [51]</td><td>64</td><td>1.91</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.80</td></tr><tr><td>EDM2-S (interval) [27]</td><td>63</td><td>1.68</td></tr><tr><td>EDM2-XXL (interval) [27]</td><td>63</td><td>1.40</td></tr><tr><td>SiD2, small (ours)</td><td>512</td><td>2.19</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.48</td></tr><tr><td>SiD2, Flop Heavy distilled (ours)</td><td>16</td><td>1.50</td></tr><tr><td colspan=\"3\">Imagenet 1024 x 1024</td></tr><tr><td>RIN [16]</td><td>1000</td><td>8.72</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.75</td></tr></table>"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.956
+            ],
+            "angle": 0,
+            "content": "18068"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.09,
+                0.089,
+                0.486,
+                0.133
+            ],
+            "angle": 0,
+            "content": "Table 3. Zero-shot text-to-image performance evaluated on MSCOCO in \\(\\mathrm{FID}_{30\\mathrm{k}}\\). Our distilled model, evaluated on the more difficult 512 setting, outperforming other works."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.134,
+                0.143,
+                0.444,
+                0.314
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Size</td><td>NFE</td><td>FID30k</td></tr><tr><td>DeepFloyd [40]</td><td>256</td><td></td><td>6.7</td></tr><tr><td>eDiff-I [1]</td><td>256</td><td></td><td>6.9</td></tr><tr><td>Parti [49]</td><td>256</td><td></td><td>7.2</td></tr><tr><td>Imagen [35]</td><td>256</td><td></td><td>7.3</td></tr><tr><td>simple diffusion [14]</td><td>256</td><td></td><td>8.3</td></tr><tr><td>simple diffusion [14]</td><td>512</td><td>256</td><td>9.6</td></tr><tr><td>SDv1.5 (eval DMD2) [32]</td><td>512</td><td>200</td><td>7.2</td></tr><tr><td>DMD2 [48]</td><td>512</td><td>4</td><td>8.3</td></tr><tr><td>SiD2 (ours, bias=-3)</td><td>512</td><td>256</td><td>8.1</td></tr><tr><td>SiD2 16-step distilled (ours)</td><td>512</td><td>16</td><td>6.7</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.33,
+                0.303,
+                0.346
+            ],
+            "angle": 0,
+            "content": "4.4. Literature comparison"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.351,
+                0.486,
+                0.489
+            ],
+            "angle": 0,
+            "content": "Here we compare different models from the literature. In the first section end-to-end diffusion models are compared, and in the second section we compare between all types of generative models. In Table 2 it can be seen that our SiD2 is very competitive with existing generative models: On ImageNet128 and ImageNet256 it achieves state-of-the-art performance, on ImageNet512 it is a little worse but still competitive with the best latent diffusion model and outperforms all other models, pixel-based and latent."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.506,
+                0.487,
+                0.765
+            ],
+            "angle": 0,
+            "content": "Comparing diffusion models on compute The training cost SiD2 is another helpful way to see how the model scales, as depicted in Figure 7). Importantly, the performance of our pixel-based approach outperforms other significantly. Observe for example the performance of our small variant (using no guidance interval to keep this comparison fair), which roughly the same performance as the VDM++ while only using a third of the training cost, and a fourth of the FLOPS in a single forward pass (see Figure 16 in Appendix C). It is also competitive with the best currently known latent diffusion approach EDM2 [20], but in fairness EDM2 scales a little bit better. These models attain even better performance for a smaller training cost, and a similar story holds for forward pass complexity. End-to-end diffusion can work much better than previously demonstrated, but it is still somewhat outperformed by latent diffusion on quality versus compute comparisons for both sampling and training."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.781,
+                0.486,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Text to image generation Finally, we show that our method can be used for end-to-end training of text-to-image models. Here, evaluation is more difficult as MSCOCO zero-shot performance depends a lot on the dataset used and is known to not necessarily correspond to actual perceived performance. Nevertheless, it is important that the model achieves performance in the right ballpark. Indeed, when we train SiD2 it performs comparable to other models in the"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.089,
+                0.909,
+                0.133
+            ],
+            "angle": 0,
+            "content": "Table 4. Conditional Video generation performance on Kinetics600 in FVD (resized to 64). For video generation the loss specification is important to obtain good sample quality (see ablations)."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.597,
+                0.143,
+                0.828,
+                0.347
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>FVD50k</td></tr><tr><td colspan=\"2\">pixel diffusion</td></tr><tr><td>Video Diffusion Models [13]</td><td>16.6</td></tr><tr><td>RIN [16]</td><td>10.8</td></tr><tr><td>Rolling Diffusion [34]</td><td>5.2</td></tr><tr><td colspan=\"2\">latent diffusion</td></tr><tr><td>MAGVIT [50]</td><td>9.9</td></tr><tr><td>MAGVITv2 [51]</td><td>4.3</td></tr><tr><td>W.A.L.T [8]</td><td>3.3</td></tr><tr><td>SiD2 (ours, sigmoid bias = 0)</td><td>2.3</td></tr><tr><td colspan=\"2\">ablations</td></tr><tr><td>eps-mse</td><td>5.7</td></tr><tr><td>sigmoid bias = +2</td><td>3.2</td></tr><tr><td>sigmoid bias = -2</td><td>2.5</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.362,
+                0.909,
+                0.453
+            ],
+            "angle": 0,
+            "content": "literature on MSCOCO \\(\\mathrm{FID}_{30\\mathrm{K}}\\), and detailed samples have only a small number of artifacts (Figure 2). Furthermore, the moment matching distilled version using [37] outperforms the baseline model as previously observed. This model also outperforms all other zero-shot approaches at 512 resolution as shown in Table 3."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.47,
+                0.909,
+                0.669
+            ],
+            "angle": 0,
+            "content": "Video Generation To test whether our approach transfers to video, we test our model on Kinetics600 following [13], by conditioning on 5 frames and generating (sometimes referred to as predicting) the subsequent 11 frames. We then compute the FVD between the training set and the generated samples both on the subsequent 11 frames. Even though our method generates at \\(128 \\times 128\\), we follow [8] and resize samples to have resolution \\(64 \\times 64\\). Our model achieves SOTA performance and it turns out that tuning the loss is very important to achieve this as shown in Table 4. Note that the latent approaches ([8, 50, 51]) use much less training compute than our models in pixel-space, which we discuss in more detail in the Appendix B."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "5. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.704,
+                0.911,
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+            ],
+            "angle": 0,
+            "content": "In this paper we present Simpler Diffusion (SiD2) and show how one can train end-to-end diffusion and achieve competitive performance with latent models: (1) use the sigmoid loss, (2) with a simpler U-ViT architecture, and (3) favour a flop heavy model design. As a result, our method outperforms existing end-to-end models by a large margin. Nevertheless, at this moment latent diffusion methods still seem to have slightly better scaling properties and it remains to be seen whether this gap can be closed any further. Importantly, for many applications training a separate autoencoder may not be either practical or desired. Therefore, we believe this paper is an important contribution that allows end-to-end modelling directly in the pixel-space."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "18069"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "References"
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2025/Simpler Diffusion_ 1.5 FID on ImageNet512 with Pixel-space Diffusion/3cf16242-5862-4aa6-864f-5aba8865f5f9_origin.pdf

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2025/Simpler Diffusion_ 1.5 FID on ImageNet512 with Pixel-space Diffusion/full.md

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+# Simpler Diffusion: 1.5 FID on ImageNet512 with pixel-space diffusion
+
+Emiel Hoogeboom
+
+Google Deepmind
+
+emielh@google.com
+
+Thomas Mensink
+
+Google Deepmind
+
+mensink@google.com
+
+Jonathan Heek
+
+Google Deepmind
+
+jheek@google.com
+
+Kay Lamarigts
+
+Google Research
+
+kaylamerigts@google.com
+
+Ruiqi Gao
+
+Google Deepmind
+
+ruiqig@google.com
+
+Tim Salimans
+
+Google Deepmind
+
+salimans@google.com
+
+# Abstract
+
+Latent diffusion models have become the popular choice for scaling up diffusion models for high resolution image synthesis. Compared to pixel-space models that are trained end-to-end, latent models are perceived to be more efficient and to produce higher image quality at high resolution. Here we challenge these notions, and show that pixel-space models can be very competitive to latent models both in quality and efficiency, achieving 1.5 FID on ImageNet512 and new SOTA results on ImageNet128, ImageNet256 and Kinetics600.
+
+We present a simple recipe for scaling end-to-end pixel-space diffusion models to high resolutions. 1: Use the sigmoid loss-weighting [25] with our prescribed hyperparameters. 2: Use our simplified memory-efficient architecture with fewer skip-connections. 3: Scale the model to favor processing the image at a high resolution with fewer parameters, rather than using more parameters at a lower resolution. Combining these with guidance intervals, we obtain a family of pixel-space diffusion models we call Simpler Diffusion (SiD2).
+
+# 1. Introduction
+
+Diffusion models have been tremendously successful in domains such as image, video and audio generation. For high resolution data, latent diffusion models [32] have been particularly successful: Through encoding the data in a lower dimensional space, these models sidestep the difficulties faced by more traditional pixel-space diffusion models in scaling up to high resolution. This makes latent diffusion models also scale better in training compute than other approaches, as shown by [20].
+
+However, latent models have their own challenges: It can be difficult to train the autoencoders that produce the latents,
+
+![](images/8b5a7ae5161b82f15e43113268a9298406651cafd4317c76bb573e36806124bf.jpg)  
+Figure 1. End-to-end pixel diffusion performance on ImageNet512.
+
+which in practice requires careful tuning of regularization hyperparameters [32]. Even when trained well, the decoder of a latent diffusion model can produce artifacts or otherwise imperfect reconstructions, especially when it is applied to latents that are out of distribution compared to the training set. A single-stage pixel-space diffusion model does not have these issues, and so we ask the question: Can pixel-space diffusion models scale as well as latent models with the right architecture and hyperparameters?
+
+Over the years, end-to-end pixel-space diffusion has improved considerably (Figure 1). The main problem was that the standard schedule and loss-weighting [11] work well for small resolution images, like  $32^2$  or  $64^2$ , but not at higher resolution [3, 14]. It was further shown [25] that it can be helpful to disentangle loss weighting and time sampling for improved control over both, leading to better performance at higher resolution. However, in previous works pixels-space models still did not match the best latent models on standard benchmarks like ImageNet512.
+
+The main contribution of this paper is to improve pixel-space diffusion on high resolution images while keeping as close to the original formulation of diffusion models as possible. Specifically, we analyze and tune the sigmoid loss weighting from [25], and show why it should be preferred over their favored EDM monotonic. We further propose architectural improvements that lead to even better perfor
+
+![](images/b18a0f4d018046d9ab7155f067e3df4b7341ad15d635e2a00a6cbc6332bde9c2.jpg)  
+Figure 2. Some text-to-image samples of  $512 \times 512$  that have been generated by SiD2.
+
+![](images/4673782a530a2ffca3a5a3a1f6c3ddfa3d65cdd0850dc8041f8a3798bc066625.jpg)
+
+![](images/9b3e67cdffaed8395cf0f73b870516817a0a09d2e7eec74fb72d26e6b38056ce.jpg)
+
+![](images/2e50436e0cea30003bd97c6bc97008729d7dedcd626988278a1604a13b1e4d6b.jpg)
+
+mance, namely flop heavy scaling and removing block skip-connections (Residual U-ViTs). Most notably, we improve the state-of-the-art of pixel-space diffusion from 2.65 to 1.48 on ImageNet512 (see also Figure 1). Further, we also achieve overall state-of-the-art on ImageNet128, ImageNet256 and Kinetics600 without heavy tuning.
+
+# 1.1. Background
+
+A diffusion process gradually destroys data over a conceptual time  $t$ , typically with Gaussian noise as follows:
+
+$$
+\boldsymbol {z} _ {t} = \alpha_ {t} \boldsymbol {x} + \sigma_ {t} \boldsymbol {\epsilon}, \text {w h e r e} \boldsymbol {\epsilon} \sim \mathcal {N} (0, \mathbf {I}), \tag {1}
+$$
+
+which defines a distribution  $q(\pmb{z}_t|\pmb{x})$  such that  $\pmb{z}_0$  is close to clean data and  $\pmb{z}_1$  is close to Gaussian noise. In this paper we assume a variance-preserving [41] schedule, which is defined as  $\alpha_{t} = \sqrt{\sigma(\lambda_{t})}$  and  $\sigma_t = \sqrt{\sigma(-\lambda_t)}$ , with  $\lambda_{t} = \log \left(\alpha_{t}^{2} / \sigma_{t}^{2}\right)$  being the log signal-to-noise ratio, which monotonically decreases with time as  $t\to 1$ , and  $\sigma (\cdot)$  being the sigmoid function. It can be shown that other types of schedules such as the variance-exploding schedule or the flow matching schedule [28] can always be converted to a variance-preserving schedule with a linear scaling of  $\pmb{z}_{t}$  [25]. The key defining property of a noise schedule is the log signal-to-noise ratio  $\lambda_{t}$ . A neural network is used to predict  $\hat{\pmb{x}} = \hat{\pmb{x}}_{\theta}(\pmb{z}_{t},t)$  that effectively estimates  $\mathbb{E}[\pmb {x}|\pmb {z}_t]$ , which can be done by minimizing a weighted mean squared error loss:
+
+$$
+L (\boldsymbol {x}) = \mathbb {E} _ {t \sim \mathcal {U} (0, 1)} - \frac {\mathrm {d} \lambda_ {t}}{\mathrm {d} t} w \left(\lambda_ {t}\right) \| \boldsymbol {x} - \hat {\boldsymbol {x}} \| ^ {2}, \tag {2}
+$$
+
+where  $w(\lambda_t)$  is the weighting function.  $-\mathrm{d}\lambda_{t} / \mathrm{d}t$  cancels out the effect of the noise schedule  $\lambda_{t}$  on the loss. In other words,  $L(\mathbf{x})$  can be rewritten as  $\int -w(\lambda)\| \pmb {x} - \hat{\pmb{x}}\| ^2 d\lambda$  that is invariant to the choice of  $\lambda_{t}$ . However,  $\lambda_{t}$  still impacts the sampling efficiency of the Monte Carlo estimator of the expected loss, and thus affects the training dynamics of diffusion models. This decouples noise schedule  $\lambda_{t}$  and weighting function  $w(\lambda)$  as a function of  $\lambda$  [25].
+
+The above squared error loss can be derived from the variational interpretation of diffusion models [26]. Given
+
+two time steps  $s < t$ , we define the denoising distribution  $p(\boldsymbol{z}_s|\boldsymbol{z}_t)$  in the same formulation as the true posterior  $q(\boldsymbol{z}_s|\boldsymbol{z}_t,\boldsymbol{x})$ , but replace the ground truth  $\boldsymbol{x}$  with the learned approximation  $\hat{\boldsymbol{x}} \approx \mathbb{E}[\boldsymbol{x}|\boldsymbol{z}_t]$ :
+
+$$
+p \left(\boldsymbol {z} _ {s} \mid \boldsymbol {z} _ {t}\right) = q \left(\boldsymbol {z} _ {s} \mid \boldsymbol {z} _ {t}, \boldsymbol {x} = \hat {\boldsymbol {x}}\right) = \mathcal {N} \left(\boldsymbol {z} _ {s} \mid \mu_ {t \rightarrow s}, \sigma_ {t \rightarrow s}\right), \tag {3}
+$$
+
+where  $\sigma_{t\rightarrow s}^2 = \left(1 / \sigma_s^2 +\alpha_{t|s}^2 /\sigma_{t|s}^2\right)^{-1}$  and  $\mu_{t\to s} = \sigma_{t\to s}^{2}\Bigl (\alpha_{t|s} / \sigma_{t|s}^{2}\pmb {z}_{t} + \alpha_{s} / \sigma_{s}^{2}\pmb {x}\Bigr)$  with  $\alpha_{t|s} = \alpha_t / \alpha_s$  and  $\sigma_{t|s}^2 = \sigma_t^2 -\alpha_{t|s}\sigma_s^2$  . Note that during sampling, the standard deviation for  $p(z_{s}|z_{t})$  is chosen to be a log-linear interpolation between  $\sigma_{t|s}$  and  $\sigma_{t\rightarrow s}$  of the form  $\sigma_{t\rightarrow s}^{\gamma}\sigma_{t|s}^{1 - \gamma}$  where  $\gamma = 0.3$  was set empirically, which is important as FID is sensitive to over-smooth or grainy images.
+
+# 2. Simpler Diffusion
+
+# 2.1. Revisiting the sigmoid loss
+
+Recall that one of the proposed losses in VDM++ [25] is the sigmoid loss. They expressed the loss with respect to  $\epsilon$ -mse:  $L(\pmb{x}) = \mathbb{E}_{t \sim \mathcal{U}(0,1)} - \frac{\mathrm{d}\lambda_t}{\mathrm{d}t} \tilde{w}(\lambda_t) \| \pmb{\epsilon} - \hat{\pmb{\epsilon}} \|^2$ , which is connected to  $\pmb{x}$ -mse through  $\| \pmb{\epsilon} - \hat{\pmb{\epsilon}} \|^2 = \exp(\lambda_t) \| \pmb{x} - \hat{\pmb{x}} \|^2$  and  $\tilde{w}(\lambda_t) = \exp(\lambda_t) w(\lambda_t)$ . In VDM++, viewing the loss in  $\epsilon$ -mse enables a natural connection between the weighted loss and the ELBO and showed that losses should be monotonically decreasing on  $\epsilon$ -mse. Hence, they propose the sigmoid loss:  $\tilde{w}(\lambda_t) = \sigma(b - \lambda_t)$ , where  $b$  denotes the bias or shift and  $\sigma$  is the sigmoid function. However, they ultimately opted for another loss-weighting named EDM-monotonic for high resolution image generation, see Figure 3a.
+
+Enforcing weighting monotonicity in  $x$  Revisiting the sigmoid loss, we derive its  $x$ -mse form, which turns out to conveniently be defined by a mirrored sigmoid (albeit multiplied by a constant factor):
+
+$$
+\begin{array}{l} \sigma \left(b - \lambda_ {t}\right) \| \boldsymbol {\epsilon} - \hat {\boldsymbol {\epsilon}} \| ^ {2} = \sigma \left(b - \lambda_ {t}\right) \exp \left(\lambda_ {t}\right) \| \boldsymbol {x} - \hat {\boldsymbol {x}} \| ^ {2} \tag {4} \\ = \exp (b) \sigma \left(\lambda_ {t} - b\right) \| \boldsymbol {x} - \hat {\boldsymbol {x}} \| ^ {2}. \\ \end{array}
+$$
+
+![](images/12bc20bf77af3c4d4311affe192124ed53e769feeff62a5c95055d6236936202.jpg)  
+(a) Weighting over  $\epsilon$ -mse
+
+![](images/2c131284de18ff2945917ee8d0833c6474829f5f2450df0baff16c2b498b7be2.jpg)  
+(b) Weighting over  $\pmb{x}$ -mse  
+Figure 3. Weighting of different losses in both  $\epsilon$  and  $x$  space. Note that the weightings are scaled to have a maximum of one.
+
+This reveals that the sigmoid loss is not only monotonically decreasing in  $\epsilon$ -mse, it is also monotonically increasing in  $x$ -mse. We claim that a reasonable weighting function  $w(\lambda_t)$  should be monotonically increasing over  $\lambda_t$ . Observe that with less noise in  $z_t$ , there is more information available and it should be strictly easier to predict the original data, meaning that the  $x$ -mse generally decreases for higher  $\lambda_t$ . This phenomenon is also observed in practice. If the loss weighting in  $x$ -mse also decreases, the model would be able to make worse predictions while obtaining less noisy (better) conditioning information and still achieve a lower loss. Simply put: Why put less weight on an easier problem?
+
+Studying both the form of the sigmoid and EDM-monotonic weighting functions in Figure 3, we observe that both weighting functions are monotonically decreasing in  $\epsilon$ -mse, but only the sigmoid weighting is monotonically increasing in  $x$ -mse. Therefore, we expect the sigmoid weighting to be a better candidate to scale to high resolution generation than the EDM-monotonic version.
+
+Loss shifting Recall that for a resolution that is two times higher in both height and width, an average (low pass) filter would see  $\mathrm{Var}[(x_{11} + x_{12} + x_{21} + x_{22}) / 4] = 1 / 4$  of the noise, while signal strength stays the same [14, 25]. Hence, its effective logsnr is expected to increase by about  $2\log 2\approx 1.386\approx 1.5$  when viewed through a low-pass filter. Suppose that the optimal setting for images of  $128\times 128$  is a sigmoid weighting with  $b\approx 0$ , then one would expect the optimal setting for images of  $512\times 512$  to be roughly  $b = -3$ .<sup>1</sup> Empirically we find that slightly more aggressive shifts perform even better.
+
+# 2.2. Flop heavy scaling
+
+When one deals with a limited data budget, it can be difficult to balance scaling of models and regularization. Our small model version at  $512 \times 512$  resolution starts out with  $4 \times 4$  patching, and subsequently runs a U-ViT [14] on the  $128 \times$
+
+$128 \times 48$  input (assuming the raw input is of 3 channels). To make the model more expressive, one of the most common options is to double the number of channels for every layer, leading to  $2 \times$  model size. However, our experiments show that this results in diminishing returns. We hypothesize that it is because the model suffers from over-fitting when trained with limited data budget such as ImageNet. Indeed, when we train using distribution augmentation [18], the best performance improves from 1.9 to 1.6. This however suggests another way to scale the model: Keep the architecture and parameter count almost the same and instead run on  $2 \times 2$  patched input (so  $256 \times 256 \times 12$  for 512 inputs). Similar to  $2 \times$  model size, reducing the patching size also increases FLOPS by roughly a factor of 4. However, we found this model performs even better to about 1.5 without the need of distribution augmentation. We call this model flop heavy, because it has a much higher flop over parameter ratio.
+
+Flop heavy scaling has another interesting property. Suppose we have a small model trained to fit input of size  $256 \times 256$  with  $2 \times 2$  patching. Using the flop heavy scaling at  $512 \times 512$  resolution enables us to directly finetune from the small model trained at  $256 \times 256$  with exactly the same amount of parameters, whereas its counterpart version at  $512 \times 512$  resolution and with  $4 \times 4$  patching needs to introduce additional parameters to handle the more input channels. This method of finetuning to higher resolutions has already been popularized in the context of text-to-image generation [32]. Here we find that flop heavy scaling is a more favorable way to scale on smaller datasets such as ImageNet. Of course, in principle one could also train a model with more channels and  $4 \times 4$  patching on a lower resolution, but this is not done in practice to train 'small' models.
+
+# 2.3. Residual U-ViTs: Removing blockwise skipconnections
+
+U-Nets require that sub-sampled levels (for example via average pooling) are bypassed by skip-connections. However, this makes the architecture very different from large-scale language models such as transformers, where these skip-connections are not used and residual connections suffice.
+
+In this paper we use the U-ViT model of [14], which is a variant of U-Nets with self-attention layers (with convolutional layers) being replaced by transformer blocks. Hence, that part of the architecture is closer to standard transformers.
+
+In this paper, we further simplify model definition with Residual U-ViTs, see Figure 4. The blockwise skip-connections are removed, and in their place only a single skip-connection is used per downsampling operation. To be precise, let  $f_{d}, f_{u}$  denote a down and up level of a U-ViT and let  $f_{m}$  denote the middle stage. This two-stage Residual U-ViT can now be described by:
+
+$$
+f (x) = f _ {u} \left(\mathrm {U} \left(f _ {m} (\mathrm {D} (h)) - \mathrm {D} (h)\right) + h\right) \text {w h e r e} h = f _ {d} (x) \tag {5}
+$$
+
+where  $D$  is typically an average pooling and linear and  $U$  is typically a linear and nearest neighbour upsampling. Defining this network to preserve an identity function at initialization is now much easier: As long as  $f_{d}$ ,  $f_{u}$  and  $f_{m}$  are initialized to be identity, the entire  $f$  is also identity at initialization. The generalization to any-depth U-ViTs is also straightforward: we can define another two levels of U-ViTs in place of  $f_{m}$  recursively, where the nested U-ViTs can also be guaranteed to be initialized as an identity function.
+
+For small networks, it could be helpful to keep the blockwise skip-connections, and expect to incur a slight performance degradation from removing the blockwise skip-connections. Small networks have limited capacity, so limiting skip-connections may create bottleneck issues. Experimentally, this is confirmed for the small architectures, where we observe 0.2 FID performance degradation on ImageNet512 and 0.06 FID performance degradation on ImageNet256. Because of the simplified definition, we choose to accept this performance penalty for small models. Moreover, we find that larger models perform on par or even benefit from removing the blockwise skip-connections.
+
+The final advantage is memory consumption at evaluation. For example, a feature map at  $256^{2}$  resolution with 128 channels requires  $256^{2} \cdot 128 \cdot 2 / 1024^{2} = 16\mathrm{MB}$ . With 3 blocks per level, this requires holding an extra  $3 \cdot 16 = 48\mathrm{MB}$  per example for the skip-connections, whereas the Residual U-ViT only requires holding  $h$  and  $D(h)$  (the latter could be cheaply recomputed), so  $16 + 8 = 24\mathrm{MB}$  per example while computing the lower levels. For a hypothetical super-resolution model at  $4096^{2}$  resolution, this leads to a difference between  $3 \cdot 4 = 12\mathrm{GB}$  and only  $4 + 2 = 6\mathrm{GB}$ . During training this advantage is usually negligible, because feature maps also need to be retained for the backward pass. A final advantage of Residual U-ViTs is that it is more straightforward to define asymmetric U-ViTs, i.e., with a different number of blocks in the downsampling (encoding) stage from the one in the upsampling (decoding) stage. In certain cases, moving blocks from the downsampling stage to the upsampling stage can increase performance.
+
+![](images/db47be7ec0de83b6399d13043bf84e5cd0faa4c5cc3431cd3fa9f8131560132e.jpg)  
+Figure 4. Residual U-ViT with levelwise skip-connections (instead of blockwise). When the network blocks are initialized to be identity, the entire network is also an identity function at initialization.
+
+# 2.4. Distillation
+
+Sampling from a pixel-space diffusion model naively often requires more function evaluations than sampling from a latent-space diffusion model. For example, the popular Stable Diffusion model [32] is usually sampled using 20-50 sampling steps, while pixel-space models are sampled with  $100+$  steps [14]. To reduce the number of sampling steps, we could use either more advanced solvers or distillation. Recently distillation methods show that pixel-space models can be adapted into few-step samplers that maintain high sample quality [23, 29, 36, 44, 45, 47]. In this work, we use moment matching distillation [37] which is currently one of the best distillation methods available in the few step regime. We distill our pixel-space models for use with 8-16 sampling steps, which empirically we find maintains or even improves the sample quality of our models.
+
+# 3. Related Work
+
+The first end-to-end diffusion work that directly generated high resolution images was [4]. Given the poor performance of end-to-end models, two popular alternatives were introduced: cascaded diffusion [12] and latent diffusion [32].
+
+Cascaded diffusion approaches have been shown to scale to large datasets and models to generate high quality and high resolution imagery, albeit in multiple stages [12, 40, 42, 52], or with fine-tuning [43]. Although the focus of this paper has been single stage generation up to a resolution of  $10^{24^2}$ , the loss weightings may also be used for cascaded models.
+
+Significant improvements were made to end-to-end diffusion by shifting noise schedules [3, 14] and subsequently loss weightings [25]. Other approaches such as multi-resolution losses (and possibly architecture adaptions) [6, 7, 14] added marginal gains. However, the current best known latent model EDM2 [20] outperforms these prior end-to-end approaches by a large margin. In contrast, our models are competitive with latent models, outperforming DiT-XL/2 [31] and only performing slightly worse than EDM2.
+
+Skip connections The U-Net architecture is a fully convolutional network with long-range skip-connections introduced for (medical) image segmentation [33, 39]. The main
+
+![](images/3e8b1ffcef67cfe66bf5c5c04d334ca80c64b63852d2acf792d78168f86a8358.jpg)  
+Figure 5. Effect of weighting functions in the loss on the FID score of ImageNet512 over the training iterations. The proposed sigmoid weighting with  $b = -3$  shows best performance consistent across all training iterations.
+
+idea of U-Net is to combine a contracting path (which encodes the image semantics) with long skip-connections at the same resolution to enable precise localization.
+
+With the introduction of ViTs [5] as an alternative for convolutional layers, the U-Net has been converted to U-ViTs using a similar network but replacing (some) ResNet blocks with ViTs, either with spatial down-sampling [14] or without [2]. Long-range skip-connections play an pivotal role in these networks, for example for fine-tuning controllable diffusion models [17] and for the stability and training speed [15, 30]. In these latter works, it is shown that multiplying the skip-connections with a (constant) scalar  $(< 1)$  improves training stability and speed, because of the propagation of noise throughout the network. In our work, we reduce the number of skip-connections significantly and initialise the network such that it resembles an identify function.
+
+Flop heavy fine-tuning Fine-tuning on a higher resolution at large scale was effectively done in Stable Diffusion [32] to limit the training cost, which is a form of flop heavy scaling over different resolutions. In this paper we show that flop heavy scaling is also preferred from a regularization perspective, which can be done either by finetuning from a lower resolution, or by lowering the patching size.
+
+# 4. Experiments
+
+# 4.1. Sigmoid weighting versus others
+
+Loss weighting In this experiment, we want to understand the effect of loss weighting on the final image quality of a model. For the noise schedule, we use an interpolated cosine schedule because it has relatively broad coverage over logsnr values. We compare the weightings corresponding to the original  $\epsilon$ -mse [11] and the multiscale  $\epsilon$ -mse [14], the EDM shifted weightings [19], including the original and monotonic versions [19, 26], and the proposed sigmoid weighting
+
+![](images/0a20f14d695a3b2c1dc90f07e7e80a7af439384ddd39d007754bda786705f538.jpg)  
+Figure 6. Effect of training noise schedules on the FID score of ImageNet512 over the training iterations. Fortunately, with our proposed sigmoid weighting  $(b = -3)$ , the exact choice of the noise schedules has little effect on the training process.
+
+Table 1. Sigmoid weighting performance (left) with the flop heavy architecture. Larger resolutions require more negative bias. Power loss performance (right) on ImageNet512 with the small model. Increasing downsampling has a similar effect as decreasing bias, hence we prefer the more simple sigmoid weighting.  
+
+<table><tr><td colspan="5">(a) Sigmoid weighting</td><td colspan="5">(b) Power loss weighting</td></tr><tr><td rowspan="2">bias</td><td colspan="4">resolution</td><td rowspan="2">bias</td><td colspan="4">downsample levels</td></tr><tr><td>128</td><td>256</td><td>512</td><td>1024</td><td>0</td><td>1</td><td>2</td><td>3</td></tr><tr><td>-5</td><td>-</td><td>-</td><td>-</td><td>1.82</td><td>-4</td><td>2.19</td><td>2.58</td><td>3.62</td><td>5.11</td></tr><tr><td>-4</td><td>-</td><td>-</td><td>1.63</td><td>1.75</td><td>-3</td><td>2.19</td><td>2.32</td><td>2.85</td><td>4.02</td></tr><tr><td>-3</td><td>-</td><td>1.47</td><td>1.48</td><td>2.32</td><td>-2</td><td>2.29</td><td>2.15</td><td>2.34</td><td>3.13</td></tr><tr><td>-2</td><td>1.49</td><td>1.42</td><td>1.55</td><td>2.17</td><td>-1</td><td>2.64</td><td>2.32</td><td>2.25</td><td>2.54</td></tr><tr><td>-1</td><td>1.35</td><td>1.38</td><td>1.75</td><td>-</td><td>0</td><td>3.22</td><td>2.74</td><td>2.07</td><td>2.22</td></tr><tr><td>0</td><td>1.30</td><td>1.46</td><td>1.94</td><td>-</td><td>1</td><td>-</td><td>2.69</td><td>2.29</td><td>2.16</td></tr><tr><td>1</td><td>1.26</td><td>1.56</td><td>-</td><td>-</td><td>2</td><td>-</td><td>3.26</td><td>2.53</td><td>2.19</td></tr></table>
+
+with shift  $b = -3$ . As can be seen in Figure 5, the sigmoid weighting outperforms all other weightings, with EDM monotonic shifted being the closest alternative. Appendix C contains additional experiments, where we also evaluate the sigmoid weighting against the closest competitor without guidance. Here again sigmoid weighting is consistently better. We also evaluate a time-shifted variant, where the bias depends on the progress in training.
+
+Training efficiency of noise schedules Since the training noise schedule can be decoupled from the loss weighting and it only affects the training efficiency but not the final performance, one can measure the convergence speed over the training process caused by leveraging particular noise schedules. In this experiment we test the cosine schedule [11], the shifted cosine and the interpolated cosine schedules [14] (Figure 6). For fair comparison, we fix the sampling noise schedule as the cosine interpolated schedule. Interestingly, when the sigmoid weighting is used, the choice of noise schedule does not affect the training efficiency significantly. Arguably, the shifted schedule is a bit more sample effi
+
+![](images/cfba554f0499d140f421d739d32d5229f4c5d7630c45e389a8d625935e959e56.jpg)  
+Figure 7. FID versus training cost on ImageNet512. Note that the EDM-2 training curves are without guidance, but the best performance with guidance intervals is reported with a separate marker, the figure source adapted has been adapted from EDM2 [20]. Following their assumptions, one training iteration is three times as expensive as evaluating the model. Our Flop Heavy (finetune) is trained by first training a small model on ImageNet256 for 400k iterations and then finetuning the same model on ImageNet512.
+
+![](images/584f7bccdcdfe72473e5875f5ad05299e881bc000dab70b530254646605fc7cc.jpg)  
+Figure 8. The effect of scaling either channels or tokens, compared to the small model variant. FLOPS between model size  $2\mathrm{x}$  and flop heavy are similar.
+
+![](images/c32f83e922fb55d924c8bf41c4c5064257dcb4a5573c063f4ece679f81f58f5a.jpg)  
+Figure 9. The effect of Residual-UViTs (removing block skip connections). Although smaller models can be effected, larger models are unaffected by the simplification.
+
+![](images/21d9702abf3eda288b9e9681b14556e5f7071b8f2e50a14b2017ca07968d5fd0.jpg)  
+Figure 10. Changing the encoder decoder architecture. Decoder blocks are more important than encoder blocks, and symmetric architectures have decent performance.
+
+cient initially but all schedules perform similarly towards the end. This suggests that there is a lot of transfer across different logsnr values. We also tried the EDM training noise schedule with the sigma power sampling noise schedule [19] (not plotted), with both shifted or the original version, but its narrower logsnr sampling schedule led to performance degradation, achieving about 9 FID at best. This suggests that for high resolution, a wide logsnr range is crucial to cover the important noise levels.
+
+Bias over resolutions In Table 1a, we show the effect of the bias term  $b$  on the final performance when trained using a flop heavy model. All models use the same guidance and similar guidance intervals, where the lower bound of the guidance interval has been shifted according to resolution (again approximately 1.5 per 2x resolution change), see Appendix B for more details.
+
+Sigmoid weighting versus the power loss In literature, high resolution generation can greatly benefit from having a multiscale loss [6, 7, 14]. To that end we create a multiscale
+
+variant that we name the power loss. In addition to the sigmoid weighting that effectively upweights low frequency components of the data and downweights high frequency components, the power loss aims to amplify the loss of low sub-band (smooth) signals in the spatial domain via Haar wavelets. For details on this loss see Appendix B.2.
+
+In Table 1b we see that the bias should be adjusted based on the number of Haar transform downsampling levels. Despite being competitive, the performance of power loss is roughly on par with the one with sigmoid weighting but without multiscaling (i.e. downsample levels  $= 0$ ), if we tune the bias of the sigmoid weighting more aggressively. Interestingly, lowering the bias has almost the same effect as increasing the scale. Therefore, building the multiscale variant is not necessary with the sigmoid weighting.
+
+# 4.2. Scaling channels vs tokens on ImageNet
+
+In this section we show the difference between scaling a model 4x FLOPS, either via channels or by creating larger resolution feature maps (or put differently, feature maps with a higher token count). Note that our small model on
+
+ImageNet512 is patched  $4 \times 4$ . This model is scaled either by increasing channels by two (named model size  $2x$ ), or by reducing patching to  $2 \times 2$  (named flop heavy, because FLOPS over params is much higher). Indeed as can be seen in Figure 8, the flop heavy model performs much better than the model size  $2x$ , when trained in a standard way on ImageNet512. Note that unlike most experiments, in these experiments it was necessary to use very different optimal guidance settings, more details in Appendix B.
+
+We confirm this is an issue related to overfitting, by training the model size 2x with distribution augmentation [18] the model size 2x variant performs much better, with an FID of 1.6 instead of 1.9 (latter in Figure 8). Still, without any augmentation beyond the standard horizontal flips, the flop heavy model achieves a score of 1.54.
+
+# 4.3. Removing block skip connection
+
+In this section we study the difference between the residual skip-connections and the blockwise skip-connections. As hypothesized, the small model performance drops a bit because of this. For ImageNet512 a deficit of about 0.2 FID (in Figure 9) and for Imagenet256 a deficit of about 0.05 FID. That the task of fitting ImageNet256 is less affected by removing skip-connections can be explained by the task being easier: The task of fitting ImageNet256 is a subset of fitting ImageNet512.
+
+For larger models, removing blockwise skip-connections in favor of a single residual connection does not degrade performance, and may even lead to slightly increased performance (see Figure 9). This is somewhat unexpected, and the phenomenon persists with different guidance settings as well. The FID curve reminds of the model size  $2\mathrm{x}$  curve, which at first improves but flattens out over iterations. Therefore our best hypothesis is that the block skip (flop) baseline may have similar problems such as overfitting. Regardless, it shows that Residual U-ViTs scale well.
+
+Asymmetric U-ViT Since our U-ViT models encompass only a single skip connection for each level, we can use a different number of ResNet or ViT blocks per level. This allows to move compute from the encoder stage (the down sampling half of the model) to the decoder stage (the upsampling half of the model). From Figure 10 we observe that (a) for a fixed compute budget, it is better to add more parameters to the decoder, the encoder heavy model (E5-D1) is significantly worse than the baseline (E3-D3) and the decoder heavy model (E1-D5); (b) there needs to be some balance between the encoder and the decoder, E1-D7 works less good than E3-D5. (c) by a slightly heavier model (E3-D7, only  $10\%$  more parameters than our small (E3-D3) model, the performance significantly increases.
+
+Table 2. Literature Comparison on ImageNet on FID. Note that even though certain NFEs are high (e.g. 4100 for CDM) typically these suffer minor performance degradation for lower NFEs and should not be taken too literally.  
+
+<table><tr><td>Method</td><td>NFE</td><td>FID</td></tr><tr><td colspan="3">Imagenet 128 x 128</td></tr><tr><td>RIN [16]</td><td>1000</td><td>2.75</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>1.94</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>1.81</td></tr><tr><td>VDM+++ [25]</td><td>250</td><td>1.75</td></tr><tr><td>DisCo-Diff [46]</td><td>414</td><td>1.73</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.48</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.26</td></tr><tr><td colspan="3">Imagenet 256 x 256</td></tr><tr><td>ADM-G [4]</td><td>250</td><td>4.59</td></tr><tr><td>ADM-U [4]</td><td>250</td><td>3.94</td></tr><tr><td>CDM [12]</td><td>4100</td><td>4.88</td></tr><tr><td>RIN [3, 16]</td><td>1000</td><td>3.52</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>2.44</td></tr><tr><td>MDM [7]</td><td>250</td><td>3.51</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>2.30</td></tr><tr><td>DiT-XL/2 [31]</td><td>250</td><td>2.27</td></tr><tr><td>VDM++ [25]</td><td>250</td><td>2.12</td></tr><tr><td>RDM [42]</td><td>356</td><td>1.89</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.56</td></tr><tr><td>SiD2, small (ours)</td><td>512</td><td>1.72</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.38</td></tr><tr><td colspan="3">Imagenet 512 x 512</td></tr><tr><td>ADM-G [4]</td><td>250</td><td>7.72</td></tr><tr><td>RIN [3, 16]</td><td>1000</td><td>3.95</td></tr><tr><td>ADM-U [4]</td><td>250</td><td>3.85</td></tr><tr><td>LDM-4-G [32]</td><td>250</td><td>3.60</td></tr><tr><td>SD, U-ViT-L [14]</td><td>512</td><td>3.02</td></tr><tr><td>DiffiT [9]</td><td>250</td><td>2.67</td></tr><tr><td>StyleGAN-XL [38]</td><td>1</td><td>2.40</td></tr><tr><td>DiT-XL/2 [31]</td><td>250</td><td>3.04</td></tr><tr><td>VDM++ [25]</td><td>250</td><td>2.65</td></tr><tr><td>MAGVIT-v2 [51]</td><td>64</td><td>1.91</td></tr><tr><td>PaGoDA [22]</td><td>1</td><td>1.80</td></tr><tr><td>EDM2-S (interval) [27]</td><td>63</td><td>1.68</td></tr><tr><td>EDM2-XXL (interval) [27]</td><td>63</td><td>1.40</td></tr><tr><td>SiD2, small (ours)</td><td>512</td><td>2.19</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.48</td></tr><tr><td>SiD2, Flop Heavy distilled (ours)</td><td>16</td><td>1.50</td></tr><tr><td colspan="3">Imagenet 1024 x 1024</td></tr><tr><td>RIN [16]</td><td>1000</td><td>8.72</td></tr><tr><td>SiD2, Flop Heavy (ours)</td><td>512</td><td>1.75</td></tr></table>
+
+Table 3. Zero-shot text-to-image performance evaluated on MSCOCO in  $\mathrm{FID}_{30\mathrm{k}}$ . Our distilled model, evaluated on the more difficult 512 setting, outperforming other works.  
+
+<table><tr><td>Method</td><td>Size</td><td>NFE</td><td>FID30k</td></tr><tr><td>DeepFloyd [40]</td><td>256</td><td></td><td>6.7</td></tr><tr><td>eDiff-I [1]</td><td>256</td><td></td><td>6.9</td></tr><tr><td>Parti [49]</td><td>256</td><td></td><td>7.2</td></tr><tr><td>Imagen [35]</td><td>256</td><td></td><td>7.3</td></tr><tr><td>simple diffusion [14]</td><td>256</td><td></td><td>8.3</td></tr><tr><td>simple diffusion [14]</td><td>512</td><td>256</td><td>9.6</td></tr><tr><td>SDv1.5 (eval DMD2) [32]</td><td>512</td><td>200</td><td>7.2</td></tr><tr><td>DMD2 [48]</td><td>512</td><td>4</td><td>8.3</td></tr><tr><td>SiD2 (ours, bias=-3)</td><td>512</td><td>256</td><td>8.1</td></tr><tr><td>SiD2 16-step distilled (ours)</td><td>512</td><td>16</td><td>6.7</td></tr></table>
+
+# 4.4. Literature comparison
+
+Here we compare different models from the literature. In the first section end-to-end diffusion models are compared, and in the second section we compare between all types of generative models. In Table 2 it can be seen that our SiD2 is very competitive with existing generative models: On ImageNet128 and ImageNet256 it achieves state-of-the-art performance, on ImageNet512 it is a little worse but still competitive with the best latent diffusion model and outperforms all other models, pixel-based and latent.
+
+Comparing diffusion models on compute The training cost SiD2 is another helpful way to see how the model scales, as depicted in Figure 7). Importantly, the performance of our pixel-based approach outperforms other significantly. Observe for example the performance of our small variant (using no guidance interval to keep this comparison fair), which roughly the same performance as the VDM++ while only using a third of the training cost, and a fourth of the FLOPS in a single forward pass (see Figure 16 in Appendix C). It is also competitive with the best currently known latent diffusion approach EDM2 [20], but in fairness EDM2 scales a little bit better. These models attain even better performance for a smaller training cost, and a similar story holds for forward pass complexity. End-to-end diffusion can work much better than previously demonstrated, but it is still somewhat outperformed by latent diffusion on quality versus compute comparisons for both sampling and training.
+
+Text to image generation Finally, we show that our method can be used for end-to-end training of text-to-image models. Here, evaluation is more difficult as MSCOCO zero-shot performance depends a lot on the dataset used and is known to not necessarily correspond to actual perceived performance. Nevertheless, it is important that the model achieves performance in the right ballpark. Indeed, when we train SiD2 it performs comparable to other models in the
+
+Table 4. Conditional Video generation performance on Kinetics600 in FVD (resized to 64). For video generation the loss specification is important to obtain good sample quality (see ablations).  
+
+<table><tr><td>Method</td><td>FVD50k</td></tr><tr><td colspan="2">pixel diffusion</td></tr><tr><td>Video Diffusion Models [13]</td><td>16.6</td></tr><tr><td>RIN [16]</td><td>10.8</td></tr><tr><td>Rolling Diffusion [34]</td><td>5.2</td></tr><tr><td colspan="2">latent diffusion</td></tr><tr><td>MAGVIT [50]</td><td>9.9</td></tr><tr><td>MAGVITv2 [51]</td><td>4.3</td></tr><tr><td>W.A.L.T [8]</td><td>3.3</td></tr><tr><td>SiD2 (ours, sigmoid bias = 0)</td><td>2.3</td></tr><tr><td colspan="2">ablations</td></tr><tr><td>eps-mse</td><td>5.7</td></tr><tr><td>sigmoid bias = +2</td><td>3.2</td></tr><tr><td>sigmoid bias = -2</td><td>2.5</td></tr></table>
+
+literature on MSCOCO  $\mathrm{FID}_{30\mathrm{K}}$ , and detailed samples have only a small number of artifacts (Figure 2). Furthermore, the moment matching distilled version using [37] outperforms the baseline model as previously observed. This model also outperforms all other zero-shot approaches at 512 resolution as shown in Table 3.
+
+Video Generation To test whether our approach transfers to video, we test our model on Kinetics600 following [13], by conditioning on 5 frames and generating (sometimes referred to as predicting) the subsequent 11 frames. We then compute the FVD between the training set and the generated samples both on the subsequent 11 frames. Even though our method generates at  $128 \times 128$ , we follow [8] and resize samples to have resolution  $64 \times 64$ . Our model achieves SOTA performance and it turns out that tuning the loss is very important to achieve this as shown in Table 4. Note that the latent approaches ([8, 50, 51]) use much less training compute than our models in pixel-space, which we discuss in more detail in the Appendix B.
+
+# 5. Discussion
+
+In this paper we present Simpler Diffusion (SiD2) and show how one can train end-to-end diffusion and achieve competitive performance with latent models: (1) use the sigmoid loss, (2) with a simpler U-ViT architecture, and (3) favour a flop heavy model design. As a result, our method outperforms existing end-to-end models by a large margin. Nevertheless, at this moment latent diffusion methods still seem to have slightly better scaling properties and it remains to be seen whether this gap can be closed any further. Importantly, for many applications training a separate autoencoder may not be either practical or desired. Therefore, we believe this paper is an important contribution that allows end-to-end modelling directly in the pixel-space.
+
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+    {
+        "type": "text",
+        "text": "Simplification Is All You Need against Out-of-Distribution Overconfidence",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Keke Tang $^{1*}$ , Chao Hou $^{1*}$ , Weilong Peng $^{1\\dagger}$ , Xiang Fang $^{2}$ , Zhize Wu $^{3}$ , Yongwei Nie $^{4}$ , Wenping Wang $^{5}$ , Zhihong Tian $^{1}$",
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+        "type": "text",
+        "text": "$^{1}$ Guangzhou University  $^{2}$ Nanyang Technological University  $^{3}$ Hefei University  $^{4}$ South China University of Technology  $^{5}$ Texas A&M University",
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+        "type": "text",
+        "text": "tangbohutbh@gmail.com, houchaohk@gmail.com, wlpeng@tju.edu.cn, xfang9508@gmail.com, wuzz@hfuu.edu.cn, nieyongwei@scut.edu.cn, wenping@amu.edu, tianzhihong@gzhu.edu.cn",
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Deep neural networks (DNNs) often exhibit out-of-distribution (OOD) overconfidence, producing overly confident predictions on OOD samples. We attribute this issue to the inherent over-complexity of DNNs and investigate two key aspects: capacity and nonlinearity. First, we demonstrate that reducing model capacity through knowledge distillation can effectively mitigate OOD overconfidence. Second, we show that selectively reducing nonlinearity by removing ReLU operations further alleviates the issue. Building on these findings, we present a practical guide to model simplification, combining both strategies to significantly reduce OOD overconfidence. Extensive experiments validate the effectiveness of this approach in mitigating OOD overconfidence and demonstrate its superiority over state-of-the-art methods. Additionally, our simplification strategies can be combined with existing OOD detection techniques to further enhance OOD detection performance.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Deep neural networks (DNNs) have revolutionized image classification tasks, consistently achieving state-of-the-art performance [8, 15, 25, 45, 46]. Despite this success, DNN classifiers are inherently designed for static, closed-world environments [2], limiting their ability to adapt to novel, unforeseen concepts encountered in real-world scenarios, known as out-of-distribution (OOD) samples. Indeed, many recent studies demonstrate that DNN classifiers suffer from OOD overconfidence, generating overly confident predictions on OOD samples [13, 34]. This issue significantly impacts the reliability and safety of DNNs in real-world applications, highlighting an urgent need for effective solutions.",
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+        "image_caption": [
+            "Figure 1. Histograms (logarithmic scale) of maximum confidence values for the teacher network (ResNet-50), the distilled student network (ResNet-18), and its variant with additional ReLU removal. All models are trained on CIFAR-100 and evaluated on OOD datasets: (a) SVHN, (b) LSUN-R, (c) iSUN, and (d) TinyImageNet-R. The  $y$ -axis represents the frequency of samples, and the  $x$ -axis represents confidence scores."
+        ],
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+    {
+        "type": "text",
+        "text": "Extensive research has been dedicated to addressing the OOD overconfidence issue. One common approach involves calibrating outputs for both in-distribution (ID) and OOD samples to improve discrimination [20], enabling OOD detectors to proactively reject OOD inputs. While these methods can reduce the impact of overconfidence, they do not fundamentally resolve the issue within DNN classifiers. Moreover, their effectiveness heavily depends on the classifiers' ability to adequately separate predictive distributions; they fail when the classifiers cannot achieve this separation [26]. As a more intrinsic solution, another approach trains DNN classifiers to suppress predictions on a subset of typical OOD samples, with the expectation that this behavior will generalize to other OOD data [18, 20].",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "CVF",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "*Joint first authors. †Corresponding author.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "5030",
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+    {
+        "type": "text",
+        "text": "However, given the vast diversity of potential OOD samples, the effectiveness of this method remains limited.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "DNNs can indeed be regarded as complex systems, often characterized by over-parameterization, in which the number of parameters exceeds the amount of available training data [66]. This excessive complexity can cause DNNs to exhibit emergent behaviors, leading to unpredictable outcomes, as observed in other complex systems [31]. Consequently, when presented with certain OOD inputs, DNNs may unexpectedly but confidently misclassify them as ID classes. Therefore, investigating the relationship between model complexity and OOD overconfidence presents a promising path toward effectively addressing this issue.",
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+    {
+        "type": "text",
+        "text": "In this paper, we explore two key aspects of model complexity: capacity and nonlinearity, and their roles in influencing OOD overconfidence. For capacity, we use knowledge distillation to examine how varying the student network's capacity affects OOD overconfidence, finding that an appropriately reduced capacity can significantly alleviate this issue (see Fig. 1). For nonlinearity, we investigate selective ReLU removal at different ratios and locations within the network, observing that controlled reductions in nonlinearity similarly mitigate OOD overconfidence (see Fig. 1). Based on these insights, we present a practical guide to model simplification that combines these two strategies to mitigate the OOD overconfidence issue in DNNs more effectively, achieving superior results compared to state-of-the-art methods. Furthermore, we demonstrate that our approach can be effectively combined with existing OOD detection techniques to further enhance performance.",
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+        "text": "Overall, our contribution is summarized as follows:",
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+    {
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+        "list_items": [
+            "- We are the first to attribute the OOD overconfidence issue in DNNs to their over-complexity, identifying model simplification as a crucial and effective solution.",
+            "- We systematically investigate two fundamental aspects of complexity: capacity and nonlinearity, analyzing their effects on OOD overconfidence through knowledge distillation and selective ReLU removal.",
+            "- We present a practical guide for model simplification and demonstrate through extensive experiments its effectiveness in significantly mitigating OOD overconfidence."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Mitigating OOD Overconfidence. The issue of OOD overconfidence, where DNNs assign excessively high confidence scores to OOD samples, presents a substantial security risk for real-world applications [18, 42, 56]. Current approaches often incorporate auxiliary data to improve OOD sensitivity, using techniques such as adding random noise and image shuffling [26], leveraging large volumes of unlabeled data [51, 55, 60], relying on external OOD datasets [20], or generating synthetic OOD samples via models like Chamfer GAN [41]. Additionally, some",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "methods, including VOS [9] and NPOS [47], create virtual features in feature space rather than explicit OOD instances. However, these approaches typically require substantial volumes of OOD data.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In contrast, our approach addresses OOD overconfidence by reducing model complexity, thus eliminating the need for auxiliary OOD data. Through extensive experiments, we systematically explore the effects of capacity reduction and selective activation removal, presenting a data-independent alternative for mitigating OOD overconfidence.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "OD Detection. Another approach to managing OOD overconfidence is to develop scoring or normalization techniques that increase the distinction between ID and OOD samples [11, 17, 36, 43]. A foundational method, maximum softmax probability, introduced by Hendrycks and Gimpel [19], demonstrates that classifiers typically assign lower confidence to OOD samples. Follow-up methods, including ODIN [28] with temperature scaling and input perturbation, Energy Score [29], and density-based scores [27, 40], further enhance this ID-OOD separation. To improve robustness, several techniques refine feature representations: feature activation rectification [39, 62], feature selection [67], neuron pruning [3], and methods like CORES [44], which identify layer-specific relevant kernels for OOD detection. In contrast, our approach inherently addresses OOD overconfidence through model simplification. By tackling the root of the overconfidence issue, our method naturally enhances OOD detection performance as a result.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Knowledge Distillation. Knowledge distillation transfers knowledge from a larger teacher model to a smaller student model, enabling the student to approximate the teacher's performance [22]. It typically utilizes response-based knowledge (soft logits) [1, 22, 32], feature-based knowledge (intermediate feature maps) [37, 50, 53], and relation-based knowledge (layer/sample relationships) [57, 58]. We use distillation to reduce model capacity and mitigate OOD overconfidence.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "ReLU Activation. ReLU  $(f(x) = \\max(0, x))$  introduces nonlinearity while maintaining efficiency, making it widely used in deep learning [10, 12]. However, ReLU networks are prone to OOD overconfidence [18]. We address this by selectively removing ReLU activations to mitigate OOD overconfidence.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. How Complexity Affects Overconfidence?",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "The complexity of a neural network is influenced by various factors. To investigate whether model complexity affects the degree of OOD overconfidence in DNNs, we focus on two key aspects: capacity and nonlinearity. In this section, we examine each of these factors individually to better understand their impact on OOD overconfidence.",
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+    {
+        "type": "text",
+        "text": "Evaluation Metrics. To assess the severity of OOD overconfidence across different DNNs, we use the mean max",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "5031",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/75ec9c1ad56e1ef40ee44c7598cc1dadae5d9442f505313699ce8ac33cf9ef87.jpg",
+        "table_caption": [
+            "Table 1. Comparison of MMC and OOD detection performance for student models (ResNet-18) distilled from a teacher model (ResNet-50) using different knowledge distillation methods on CIFAR datasets. Results are averaged across multiple OOD datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ID</td><td colspan=\"3\">CIFAR-10</td><td colspan=\"3\">CIFAR-100</td></tr><tr><td>Method</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>Teacher</td><td>79.58</td><td>54.23</td><td>91.78</td><td>72.12</td><td>83.67</td><td>74.73</td></tr><tr><td>KD [22]</td><td>76.81</td><td>49.81</td><td>92.42</td><td>62.69</td><td>79.77</td><td>76.31</td></tr><tr><td>FitNet [37]</td><td>79.46</td><td>50.58</td><td>92.26</td><td>60.60</td><td>77.53</td><td>77.78</td></tr><tr><td>AT [64]</td><td>77.90</td><td>48.09</td><td>92.69</td><td>64.11</td><td>82.14</td><td>75.51</td></tr><tr><td>SP [48]</td><td>78.81</td><td>50.52</td><td>92.22</td><td>58.75</td><td>77.12</td><td>80.01</td></tr></table>",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "imum confidence (MMC) on OOD samples as our evaluation metric. Additionally, to analyze how OOD overconfidence impacts the model's ability for ID/OOD discrimination, we also report the area under the receiver operating characteristic curve (AUROC) [6], the false positive rate at a true positive rate of  $95\\%$  (FPR95) [28], and the area under the precision-recall curve, with ID samples specified as positives (AUPRin) [38].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Capacity",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To investigate whether model capacity affects the severity of OOD overconfidence, we employ knowledge distillation to transfer knowledge from a large-capacity teacher network to a smaller-capacity student network. Specifically, we examine how different knowledge distillation strategies and varying student network capacities influence OOD overconfidence. Since DNN capacity is influenced by various factors, such as depth, width, and number of parameters, we ensure a fair comparison by testing networks with the same architecture but different depths.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Effectiveness of Knowledge Distillation. To validate the effectiveness of knowledge distillation in mitigating OOD overconfidence, we select ResNet-50 as the teacher network and ResNet-18 as the student network, applying four distinct knowledge distillation methods: KD [22], FitNet [37], AT [64], and SP [48]. Experiments are conducted using CIFAR-10 and CIFAR-100 as ID datasets, with SVHN, LSUN-R, iSUN, Textures, and TinyImageNet-R as OOD datasets. The results, shown in Tab. 1, indicate that all four distillation methods lead to reductions in MMC and enhancements in AUROC and FPR95 metrics, demonstrating that knowledge distillation effectively mitigates the OOD overconfidence issue.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Analysis of Student Networks with Varying Capacities. We conduct experiments on two datasets using KD [22] with student networks of varying capacities. For CIFAR-100, we set ResNet-101 as the teacher and evaluate student networks with capacities ranging from ResNet-50, ResNet-34, ResNet-18, to ResNet-10. For ImageNet-100, we use ResNet-152 as the teacher, with ResNet-101, ResNet-50, ResNet-34, and ResNet-18 as student models. As shown in Fig. 2, on CIFAR-100, reducing the student",
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+        "img_path": "images/4ffa6e7764a95fff13f73b17cd996d9e5cf871addff07cfe74f627858ec654f7.jpg",
+        "table_caption": [
+            "Table 2. Comparison of MMC and OOD detection performance for different ReLU removal proportions using ResNet-101 as the classifier. Results are averaged across multiple OOD datasets."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>ID</td><td colspan=\"3\">CIFAR-10</td><td colspan=\"3\">CIFAR-100</td></tr><tr><td>Ratio</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>0%</td><td>83.46</td><td>51.92</td><td>92.53</td><td>73.84</td><td>84.41</td><td>73.03</td></tr><tr><td>1%</td><td>84.46</td><td>57.58</td><td>90.48</td><td>69.14</td><td>82.43</td><td>76.22</td></tr><tr><td>2%</td><td>77.18</td><td>43.00</td><td>93.69</td><td>72.26</td><td>83.07</td><td>75.25</td></tr><tr><td>3%</td><td>77.91</td><td>46.93</td><td>93.06</td><td>69.37</td><td>78.74</td><td>78.12</td></tr><tr><td>5%</td><td>83.07</td><td>56.53</td><td>90.71</td><td>68.71</td><td>78.57</td><td>79.43</td></tr><tr><td>10%</td><td>79.60</td><td>50.06</td><td>92.25</td><td>71.24</td><td>80.94</td><td>77.70</td></tr><tr><td>20%</td><td>80.78</td><td>50.31</td><td>92.30</td><td>73.54</td><td>82.73</td><td>74.81</td></tr><tr><td>50%</td><td>79.22</td><td>48.34</td><td>92.73</td><td>70.40</td><td>82.22</td><td>75.40</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "network capacity to ResNet-18 improves OOD overconfidence and enhances ID/OOD discrimination. However, further reducing capacity to ResNet-10 results in degraded performance, likely due to insufficient capacity to effectively handle CIFAR-100 classification. A similar trend is observed on ImageNet-100, where reducing the student network capacity to ResNet-50 continues to yield improvements, but further reductions impair performance, likely due to the dataset's increased complexity. These findings suggest that reducing network capacity to a moderate level can effectively alleviate the OOD overconfidence issue.",
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+    {
+        "type": "text",
+        "text": "3.2. Nonlinearity",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Nonlinearity in DNNs arises from activation functions, e.g., ReLU and Sigmoid. The more activation operations are applied, the greater the degree of nonlinearity. In this subsection, we investigate whether the degree of nonlinearity affects the severity of OOD overconfidence. Given that ReLU is one of the most widely used activation functions, we focus on examining the effect of removing ReLU operations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Specifically, we examine the impact of removing ReLU operations at different proportions and locations, similar to the approach in [4]. as we will detail in Sec. 4, to evaluate their effect on mitigating OOD overconfidence. Additionally, we assess the influence of initiating ReLU removal at various stages of training. For these experiments, CIFAR-10 and CIFAR-100 are used as the ID datasets, with SVHN, LSUN-R, iSUN, Textures, and TinyImageNet-R as the OOD datasets, using ResNet-18/101 as the classifier.",
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+    {
+        "type": "text",
+        "text": "Analysis of Different Removal Proportions. To assess the impact of varying removal proportions, we introduce the Negative Response Ratio (NRO), which measures the proportion of negative responses that are passed to ReLU operations:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nN R O = \\frac {\\text {N u m b e r o f n e g a t i v e c o n v o l u t i o n a l r e s p o n s e s}}{\\text {T o t a l n u m b e r o f c o n v o l u t i o n a l r e s p o n s e s}}. \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "A smaller NRO indicates fewer activations requiring truncation, suggesting that the corresponding ReLU layers contribute less to overall nonlinearity. Based on NRO values, we selectively remove ReLU operations with the low",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "5032",
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+    {
+        "type": "image",
+        "img_path": "images/19135528d01fbdfee79fa48fbdcda4f0bbc6b063ba79534135e0e1344c342092.jpg",
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+    {
+        "type": "image",
+        "img_path": "images/b8889e50737340affa915d527572fc1e1bb309e3feca8bf34d0bc30c4f98eaf6.jpg",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/b7bbd30e25a50659fc0a95cd265e3c0a4fa6a07ed765e9a686a75683f3190403.jpg",
+        "image_caption": [
+            "Figure 2. Comparison of MMC and OOD detection metrics, including FPR95, AUROC, and AUPRin, for student models with varying capacities (e.g., ResNet models) across datasets: (a) CIFAR-100 and (b) ImageNet-100."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "image",
+        "img_path": "images/0b695f5d3704bfe92f4f6a91eb4ec4f0903c73dcfe1cfa4ecbbaa9cafc7e32d6.jpg",
+        "image_caption": [],
+        "image_footnote": [
+            "Teacher Student"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/301ad9c7ffc67ad80272d3b6901be0ab800881fe239a99c2e8aa6d17f490666a.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/521aa6f536e610a027968e764225eecf6777f02685bbb4831f6844b2bd32fd44.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/01f77a8c33e4dc7cae2ae8746efb3e495b5e1a150cbfd698a4aca7d73c6ef79a.jpg",
+        "image_caption": [
+            "Figure 3. Comparison of MMC and FPR95 for ResNet-101 with ReLU removal applied at different network locations."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            114,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "est NRO scores at proportions of  $1\\%$ ,  $2\\%$ ,  $3\\%$ ,  $5\\%$ ,  $10\\%$ ,  $20\\%$ , and  $50\\%$ , starting at the 40th epoch and continuing through the 100th epoch. As shown in Tab. 2, removing a certain proportion of ReLU operations reduces OOD overconfidence and enhances OOD detection. For example, removing  $2\\%$  of ReLU operations on CIFAR-10 and  $5\\%$  on CIFAR-100 yields the best results.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Analysis of Different Removal Locations. To identify which ReLU operations are most suitable for removal, we compare the effects of removing ReLU operations from shallow, middle, and deep layers, as well as from layers with the lowest NRO values. Following previous findings, we remove  $2\\%$  of ReLU operations for CIFAR-10 and  $5\\%$  for CIFAR-100, initiating removal at the 40th epoch. As shown in Fig. 3, each removal strategy effectively reduces OOD overconfidence, with the best results achieved by removing ReLU operations based on NRO values.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Impact of ReLU Removal Initiation Points. We also",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/09125d787ec7e270736996341582f23c8db509209b4a91dacf06d71b306f5a76.jpg",
+        "image_caption": [
+            "Figure 4. Comparison of MMC and FPR95 for ResNet-18 with ReLU removal initiated at different training epochs."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "analyze the effects of initiating ReLU removal at different stages during training. As illustrated in Fig. 4, the specific stage at which ReLU removal begins has only a moderate impact on overall performance. The best results are achieved when removal is initiated around the middle of the training process, such as at the 40th epoch.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4. A Practical Guide to Model Simplification",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Based on our findings reported in Sec. 3, we present a practical guide to model simplification for addressing the OOD overconfidence issue in DNNs. For models that exhibit high OOD overconfidence, we suggest reducing complexity through a combination of knowledge distillation and selective ReLU removal. Please refer to Fig. 5 for demonstration. Knowledge Distillation with a Moderately-Sized Student. The first step is to choose a small student model with a capacity suited to the task requirements. This student model should be sufficiently compact to reduce complexity but still capable of performing well on the original task. We then apply knowledge distillation (e.g., KD) to transfer es",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5033",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/bf8fc906eb6da835625877dfe77bf98c2395802d61b870b8320876d358dc070b.jpg",
+        "image_caption": [
+            "Figure 5. Illustration of our model simplification pipeline. Given a complex teacher model with high capacity and nonlinearity, we use knowledge distillation to transfer information to a low-capacity student model. During distillation, ReLU operations are selectively replaced with Leaky ReLU, and the negative slope is iteratively adjusted from 0 to 1, ultimately transforming ReLU into an identity function."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "sential knowledge from the larger teacher model to the student. This process enables the student to approximate the teacher's performance while operating with a reduced capacity, thereby alleviating the OOD overconfidence issue.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Selective ReLU Removal During Distillation. To further streamline the model, we selectively remove ReLU operations. Using the NRO metric defined in Eq. (1), we identify ReLU operations that contribute minimally to the model's responses. Following the approach in [4], we replace these selected ReLU operations with Leaky ReLU, initially setting the negative slope to 0 and gradually increasing it to 1 midway through the distillation process. This controlled transition effectively transforms ReLU into an identity function, thereby reducing the model's nonlinearity.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This practical guide, combining knowledge distillation for capacity reduction with selective ReLU removal for nonlinearity reduction, provides an accessible approach to mitigate OOD overconfidence issue in DNNs.",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "5. Experimental Results",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "5.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Implementation Details. We employ KD [22] to transfer knowledge from teacher to student models, with a weight ratio of 1.5:1 between KD loss and cross-entropy (CE) loss. All student models are trained for 100 epochs, with selective ReLU removal starting at the 40th epoch and continuing through the end of training, similar to the approach in [4]. We remove  $2\\%$  of ReLU operations for models trained on CIFAR-10,  $5\\%$  for models trained on CIFAR-100, and  $5\\%$  for models trained on ImageNet-1k [7]. All experiments are implemented in PyTorch [35] and conducted on a workstation equipped with dual 2.40 GHz CPUs, 128 GB RAM, and eight NVIDIA RTX 3090Ti GPUs.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Setup. For (1) Mitigating OOD Overconfidence, we use CIFAR-10 and CIFAR-100 [24] as ID datasets, with SVHN [33], LSUN-R [59], iSUN [54], Textures [5], and TINR, a resized variant of TinyImageNet uniformly scaled to  $32 \\times 32$ , as the OOD datasets. For (2) OOD Detection, we use the same CIFAR-based configuration as in (1). For large-scale evaluations, we use ImageNet-1k [7] as the ID dataset, with SUN [52], Places [65], Textures [5], and OpenImage-O [49] as the OOD datasets. We train ResNet-50 and ResNet-101 [16] on CIFAR-10 and CIFAR-100, and train DenseNet-201 [23] and WideResNet-101-2 (WRN-101) [63] on ImageNet-1k [7], following the training protocols specified in their respective original papers.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Setting of Our Approach. We designate ResNet-18 and WideResNet-16-10 (WRN-16) as student networks for ResNet-50, and ResNet-34 and WideResNet-28-10 (WRN-28) as students for ResNet-101 on CIFAR datasets. For the ImageNet-1k dataset, DenseNet-161 serves as the student for DenseNet-201, and WideResNet-50-2 (WRN-50) for WRN-101. All student models are trained using the SGD optimizer with a momentum of 0.9 and an initial learning rate of 0.1. On the ImageNet-1k benchmark, the learning rate is reduced by a factor of 10 every 30 epochs, while on the CIFAR benchmarks, the learning rate is adjusted using the CosineAnnealingLR scheduler. For simplicity, we refer to our method as \"Ours (student)\" in subsequent sections to indicate the specific student network employed.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Baselines. For (1) Mitigating OOD Overconfidence, we select three state-of-the-art baselines: ACET [18], CEDA [18], and CCUs [30]. For (2) OOD Detection, we benchmark our approach against five post-hoc methods: maximum softmax probability (MSP) [19], MaxLogit [21], Energy [29], ReAct [39], and FeatureNorm [61].",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "page_number",
+        "text": "5034",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/a91d1c4df56b66c6db7db4329e9c32041400b2e2012c7a1d597cb46e2c4d64fc.jpg",
+        "table_caption": [
+            "Table 3. Comparison of MMC on OOD datasets for ResNet-50 and ResNet-101 models trained on CIFAR-10 and CIFAR-100, evaluated using various OOD overconfidence mitigation techniques. Underlined values denote the best performance for a single method, while bolded values indicate the best performance across all methods, including both individual and combined methods."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Method</td><td colspan=\"5\">ID: CIFAR-10</td><td rowspan=\"2\">Average</td><td colspan=\"5\">ID: CIFAR-100</td><td rowspan=\"2\">Average</td></tr><tr><td>SVHN</td><td>LSUN-R</td><td>iSUN</td><td>Textures</td><td>TINR</td><td>SVHN</td><td>LSUN-R</td><td>iSUN</td><td>Textures</td><td>TINR</td></tr><tr><td rowspan=\"9\">ResNet-50</td><td>—</td><td>75.34</td><td>79.64</td><td>79.86</td><td>81.53</td><td>81.53</td><td>79.58</td><td>72.50</td><td>72.07</td><td>72.20</td><td>72.74</td><td>71.11</td><td>72.12</td></tr><tr><td>CEDA</td><td>74.73</td><td>70.91</td><td>72.02</td><td>73.37</td><td>78.64</td><td>73.93</td><td>55.64</td><td>54.77</td><td>56.25</td><td>62.85</td><td>55.42</td><td>56.99</td></tr><tr><td>ACET</td><td>74.29</td><td>67.35</td><td>67.72</td><td>70.37</td><td>69.87</td><td>69.92</td><td>63.68</td><td>62.49</td><td>62.19</td><td>64.44</td><td>61.15</td><td>62.79</td></tr><tr><td>CCUs</td><td>69.56</td><td>63.51</td><td>63.10</td><td>68.64</td><td>68.92</td><td>66.75</td><td>57.33</td><td>52.30</td><td>54.71</td><td>61.25</td><td>54.89</td><td>56.09</td></tr><tr><td>Ours (ResNet-18)</td><td>78.24</td><td>73.29</td><td>74.37</td><td>79.51</td><td>76.98</td><td>76.48</td><td>54.75</td><td>43.65</td><td>42.27</td><td>61.40</td><td>39.69</td><td>48.35</td></tr><tr><td>Ours (WRN-16)</td><td>63.65</td><td>66.32</td><td>68.49</td><td>77.09</td><td>70.18</td><td>69.15</td><td>43.06</td><td>51.76</td><td>51.99</td><td>57.96</td><td>52.37</td><td>51.43</td></tr><tr><td>CEDA + Ours (WRN-16)</td><td>61.31</td><td>67.40</td><td>69.64</td><td>70.09</td><td>73.54</td><td>68.40</td><td>47.84</td><td>59.40</td><td>60.69</td><td>59.24</td><td>60.00</td><td>57.43</td></tr><tr><td>ACET + Ours (WRN-16)</td><td>67.44</td><td>61.28</td><td>62.36</td><td>70.05</td><td>65.48</td><td>65.32</td><td>52.54</td><td>59.45</td><td>61.59</td><td>60.82</td><td>60.48</td><td>58.98</td></tr><tr><td>CCUs + Ours (WRN-16)</td><td>65.97</td><td>58.81</td><td>61.32</td><td>64.84</td><td>65.96</td><td>63.38</td><td>50.88</td><td>49.04</td><td>51.85</td><td>58.40</td><td>51.82</td><td>52.40</td></tr><tr><td rowspan=\"9\">ResNet-101</td><td>—</td><td>83.44</td><td>82.13</td><td>83.02</td><td>84.56</td><td>84.17</td><td>83.46</td><td>65.25</td><td>77.21</td><td>78.03</td><td>73.38</td><td>75.32</td><td>73.84</td></tr><tr><td>CEDA</td><td>70.07</td><td>68.26</td><td>68.42</td><td>74.42</td><td>74.02</td><td>71.04</td><td>58.82</td><td>58.18</td><td>59.00</td><td>66.23</td><td>58.47</td><td>60.14</td></tr><tr><td>ACET</td><td>75.82</td><td>53.69</td><td>55.00</td><td>64.50</td><td>59.98</td><td>61.80</td><td>63.62</td><td>59.57</td><td>58.44</td><td>60.34</td><td>58.01</td><td>60.00</td></tr><tr><td>CCUs</td><td>73.56</td><td>65.72</td><td>64.98</td><td>66.94</td><td>69.83</td><td>68.21</td><td>58.45</td><td>54.53</td><td>56.52</td><td>59.80</td><td>56.32</td><td>57.12</td></tr><tr><td>Ours (ResNet-34)</td><td>75.22</td><td>74.81</td><td>75.94</td><td>82.08</td><td>78.86</td><td>77.38</td><td>63.62</td><td>58.42</td><td>60.13</td><td>66.69</td><td>59.89</td><td>61.75</td></tr><tr><td>Ours (WRN-28)</td><td>71.21</td><td>74.73</td><td>76.03</td><td>81.80</td><td>77.89</td><td>76.33</td><td>55.69</td><td>47.84</td><td>51.20</td><td>63.69</td><td>54.09</td><td>54.50</td></tr><tr><td>CEDA + Ours (WRN-28)</td><td>67.15</td><td>68.21</td><td>70.59</td><td>76.77</td><td>73.83</td><td>71.31</td><td>56.51</td><td>65.12</td><td>66.59</td><td>62.51</td><td>66.77</td><td>63.50</td></tr><tr><td>ACET + Ours (WRN-28)</td><td>59.33</td><td>52.70</td><td>53.07</td><td>66.95</td><td>58.05</td><td>58.02</td><td>56.10</td><td>62.48</td><td>63.94</td><td>58.34</td><td>63.86</td><td>60.95</td></tr><tr><td>CCUs + Ours (WRN-28)</td><td>67.79</td><td>61.74</td><td>64.20</td><td>65.95</td><td>68.80</td><td>65.70</td><td>53.71</td><td>50.96</td><td>53.58</td><td>57.86</td><td>54.52</td><td>54.13</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/2a70a23a637a5e8fe3f704e446e6090892e643e0f8fa1c4cf8befca0eb7c2718.jpg",
+        "image_caption": [
+            "(a)",
+            "(b)"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/5450420c4e84847d0faa06662c292c27f4cd299cf0f3c2763cd43382beb50d1f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/154d7c306de00cb139e4e86ecf243644f310051d2d3e7abe9102816e300c8e5b.jpg",
+        "image_caption": [
+            "ACET"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            274,
+            440,
+            419,
+            513
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/d683d1fef2149b66067bae02fe792dedf427a55d07dac875bffc6d84f9c63b0a.jpg",
+        "image_caption": [
+            "CEDA"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            421,
+            440,
+            568,
+            513
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/c58ce1c74130b039c4d9056eca9d0802ac214005ae37fab257fa844c8d247a26.jpg",
+        "image_caption": [
+            "CCUs"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            570,
+            440,
+            715,
+            513
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/195006fd2e1c97a2d69f08dae8f6f38e157e8e06aeab95d519a2cb87a577b88b.jpg",
+        "image_caption": [
+            "Ours (ResNet-18)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            718,
+            440,
+            864,
+            513
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/e81ef09903ff89a34b2893ed9cc7fe4e1630ab89cf858bd580e0130fe071d9ec.jpg",
+        "image_caption": [
+            "(c)",
+            "(d)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            125,
+            609,
+            272,
+            684
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/c0844b9b5ba1f2864d2361bc5eb81364dc23e04710ccf26e08a3dae0c41f836d.jpg",
+        "image_caption": [
+            "Figure 6. Histograms (logarithmic scale) of MMC values for (a, b) ResNet-50 and (c, d) ResNet-101, w/ and w/o applying mitigation techniques: ACET, CEDA, CCUs, and Ours. All models are trained on CIFAR-100 and evaluated on OOD datasets: (a, c) LSUN-R and (d) TinyImageNet-R. In our approach, ResNet-18 and WRN-28 serve as students for ResNet-50 and ResNet-101, respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            125,
+            688,
+            272,
+            762
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/5f3f12b6ef1143b59a059d7d12e983c1526e867a2d63a304238575ebc2ac6b72.jpg",
+        "image_caption": [
+            "ACET"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            274,
+            609,
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+            684
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/ff89139269c01983fdda6fe307d4f08114af96d0a9f4a0bcb690b1f1e5430d4c.jpg",
+        "image_caption": [
+            "CEDA"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            421,
+            609,
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+            683
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/011606af33bf67277ae955b252a1ece844b99209b093b7d7ddd7cd2b207b2f9c.jpg",
+        "image_caption": [
+            "CCUs"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            570,
+            609,
+            715,
+            683
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/196b6591331d6b3a402901ff99e39d9e570fed47804d5134bef54eed362cd2e0.jpg",
+        "image_caption": [
+            "Ours (WRN-28)"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            718,
+            611,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results of Mitigating OOD Overconfidence",
+        "text_level": 1,
+        "bbox": [
+            125,
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+            838
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Comparison with State-of-the-art Methods. To assess the effectiveness and superiority of our approach, we conduct comparative experiments evaluating OOD overconfi",
+        "bbox": [
+            89,
+            854,
+            480,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "dence for ResNet-50 and ResNet-101 trained on CIFAR-10 and CIFAR-100. The results in Tab. 3 demonstrate that our approach consistently reduces the mean maximum confidence (MMC) across different student networks in all cases, validating its effectiveness. In comparison, methods such",
+        "bbox": [
+            511,
+            823,
+            906,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "5035",
+        "bbox": [
+            482,
+            945,
+            514,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/5fe2cce378dda2cce1d573c8a6201f09a59af1e5463fa9acc29c6edd94c89e71.jpg",
+        "table_caption": [
+            "Table 4. Comparison of OOD detection performance for various methods on the CIFAR-10 and CIFAR-100 datasets. Underlined values indicate results enhanced by applying our approach to the baseline, while bolded values denote the best performance."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">ID</td><td rowspan=\"3\">Model</td><td rowspan=\"3\">Method</td><td colspan=\"11\">OOD</td><td rowspan=\"2\" colspan=\"2\">Average</td></tr><tr><td colspan=\"2\">SVHN</td><td colspan=\"2\">LSUN-R</td><td colspan=\"2\">iSUN</td><td colspan=\"2\">Textures</td><td colspan=\"3\">TINR</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td></td></tr><tr><td rowspan=\"15\">CIFAR-10</td><td rowspan=\"15\">ResNet-50</td><td>MSP</td><td>43.75</td><td>94.19</td><td>54.32</td><td>91.96</td><td>55.46</td><td>91.66</td><td>59.01</td><td>90.31</td><td>58.61</td><td>90.80</td><td>54.23</td><td>91.78</td><td></td></tr><tr><td>MSP + Ours (ResNet-18)</td><td>51.82</td><td>93.27</td><td>41.93</td><td>93.89</td><td>44.86</td><td>93.27</td><td>55.64</td><td>90.57</td><td>50.18</td><td>91.97</td><td>48.89</td><td>92.59</td><td></td></tr><tr><td>MSP + Ours (WRN-16)</td><td>28.18</td><td>96.12</td><td>35.74</td><td>95.01</td><td>39.78</td><td>94.34</td><td>57.00</td><td>89.79</td><td>42.35</td><td>93.75</td><td>40.61</td><td>93.80</td><td></td></tr><tr><td>MaxLogit</td><td>22.07</td><td>96.31</td><td>32.03</td><td>94.95</td><td>34.95</td><td>94.53</td><td>46.33</td><td>91.39</td><td>44.96</td><td>92.57</td><td>36.07</td><td>93.95</td><td></td></tr><tr><td>MaxLogit + Ours (ResNet-18)</td><td>30.25</td><td>94.94</td><td>25.06</td><td>95.34</td><td>27.91</td><td>94.73</td><td>44.50</td><td>91.71</td><td>36.75</td><td>92.73</td><td>32.89</td><td>93.89</td><td></td></tr><tr><td>MaxLogit + Ours (WRN-16)</td><td>17.61</td><td>96.96</td><td>18.54</td><td>96.92</td><td>21.69</td><td>96.39</td><td>47.70</td><td>89.58</td><td>27.81</td><td>95.55</td><td>26.67</td><td>95.08</td><td></td></tr><tr><td>Energy</td><td>20.35</td><td>96.40</td><td>29.79</td><td>95.11</td><td>32.80</td><td>94.67</td><td>45.41</td><td>91.44</td><td>43.76</td><td>92.64</td><td>34.42</td><td>94.05</td><td></td></tr><tr><td>Energy + Ours (ResNet-18)</td><td>28.53</td><td>95.07</td><td>23.99</td><td>95.43</td><td>26.55</td><td>94.83</td><td>44.13</td><td>89.70</td><td>35.92</td><td>92.79</td><td>31.82</td><td>93.56</td><td></td></tr><tr><td>Energy + Ours (WRN-16)</td><td>18.80</td><td>96.88</td><td>18.07</td><td>97.02</td><td>20.91</td><td>96.50</td><td>47.89</td><td>89.54</td><td>27.63</td><td>95.61</td><td>26.66</td><td>95.11</td><td></td></tr><tr><td>ReAct</td><td>37.66</td><td>91.10</td><td>16.24</td><td>96.64</td><td>19.65</td><td>95.84</td><td>46.72</td><td>86.29</td><td>30.79</td><td>93.46</td><td>30.21</td><td>92.67</td><td></td></tr><tr><td>ReAct + Ours (ResNet-18)</td><td>31.59</td><td>94.62</td><td>23.87</td><td>95.51</td><td>26.78</td><td>94.86</td><td>43.60</td><td>90.19</td><td>35.87</td><td>92.92</td><td>32.34</td><td>93.62</td><td></td></tr><tr><td>ReAct + Ours (WRN-16)</td><td>19.07</td><td>96.84</td><td>17.90</td><td>97.03</td><td>20.66</td><td>96.51</td><td>47.45</td><td>89.84</td><td>27.24</td><td>95.68</td><td>26.46</td><td>95.18</td><td></td></tr><tr><td>FeatureNorm</td><td>9.25</td><td>97.97</td><td>77.34</td><td>82.07</td><td>70.29</td><td>83.96</td><td>48.97</td><td>84.16</td><td>67.71</td><td>84.49</td><td>54.71</td><td>86.53</td><td></td></tr><tr><td>FeatureNorm + Ours (ResNet-18)</td><td>2.73</td><td>99.35</td><td>24.34</td><td>95.75</td><td>21.04</td><td>96.28</td><td>22.82</td><td>94.89</td><td>29.52</td><td>94.36</td><td>20.09</td><td>96.13</td><td></td></tr><tr><td>FeatureNorm + Ours (WRN-16)</td><td>3.37</td><td>99.26</td><td>22.03</td><td>96.43</td><td>21.54</td><td>96.47</td><td>53.67</td><td>78.85</td><td>29.35</td><td>94.50</td><td>25.99</td><td>93.10</td><td></td></tr><tr><td rowspan=\"15\">CIFAR-100</td><td rowspan=\"15\">ResNet-101</td><td>MSP</td><td>76.30</td><td>81.14</td><td>86.67</td><td>69.76</td><td>88.11</td><td>69.06</td><td>85.69</td><td>73.73</td><td>85.27</td><td>71.47</td><td>84.41</td><td>73.03</td><td></td></tr><tr><td>MSP + Ours (ResNet-34)</td><td>77.48</td><td>78.92</td><td>72.74</td><td>83.09</td><td>74.83</td><td>82.14</td><td>82.50</td><td>77.26</td><td>74.52</td><td>82.20</td><td>76.41</td><td>80.72</td><td></td></tr><tr><td>MSP + Ours (WRN-28)</td><td>74.87</td><td>81.39</td><td>62.57</td><td>85.71</td><td>66.94</td><td>83.93</td><td>83.28</td><td>76.33</td><td>69.44</td><td>81.70</td><td>71.42</td><td>81.81</td><td></td></tr><tr><td>MaxLogit</td><td>68.05</td><td>86.77</td><td>82.84</td><td>74.34</td><td>84.94</td><td>73.40</td><td>87.25</td><td>74.81</td><td>81.92</td><td>75.05</td><td>81.00</td><td>76.87</td><td></td></tr><tr><td>MaxLogit + Ours (ResNet-34)</td><td>71.69</td><td>83.47</td><td>63.74</td><td>87.26</td><td>65.69</td><td>86.54</td><td>81.74</td><td>78.46</td><td>66.88</td><td>86.44</td><td>69.95</td><td>84.43</td><td></td></tr><tr><td>MaxLogit + Ours (WRN-28)</td><td>73.84</td><td>82.61</td><td>54.30</td><td>89.11</td><td>60.29</td><td>87.26</td><td>83.62</td><td>77.06</td><td>64.12</td><td>84.98</td><td>67.23</td><td>84.20</td><td></td></tr><tr><td>Energy</td><td>68.38</td><td>86.94</td><td>82.38</td><td>74.64</td><td>84.21</td><td>73.67</td><td>88.03</td><td>74.62</td><td>81.40</td><td>75.25</td><td>80.88</td><td>77.02</td><td></td></tr><tr><td>Energy + Ours (ResNet-34)</td><td>69.20</td><td>84.14</td><td>58.83</td><td>88.05</td><td>61.10</td><td>87.37</td><td>81.68</td><td>78.51</td><td>62.89</td><td>87.18</td><td>66.74</td><td>85.05</td><td></td></tr><tr><td>Energy + Ours (WRN-28)</td><td>74.17</td><td>82.61</td><td>48.60</td><td>90.07</td><td>55.05</td><td>88.12</td><td>84.10</td><td>77.01</td><td>60.41</td><td>85.71</td><td>64.47</td><td>84.70</td><td></td></tr><tr><td>ReAct</td><td>65.68</td><td>88.14</td><td>86.44</td><td>69.18</td><td>86.97</td><td>69.09</td><td>83.44</td><td>80.13</td><td>83.80</td><td>71.59</td><td>81.27</td><td>75.63</td><td></td></tr><tr><td>ReAct + Ours (ResNet-34)</td><td>60.26</td><td>88.30</td><td>57.94</td><td>86.49</td><td>58.11</td><td>86.52</td><td>63.07</td><td>85.78</td><td>60.03</td><td>85.69</td><td>59.88</td><td>86.56</td><td></td></tr><tr><td>ReAct + Ours (WRN-28)</td><td>71.89</td><td>86.73</td><td>47.34</td><td>89.20</td><td>53.66</td><td>87.46</td><td>80.57</td><td>81.48</td><td>58.97</td><td>84.66</td><td>62.49</td><td>85.91</td><td></td></tr><tr><td>FeatureNorm</td><td>31.88</td><td>94.59</td><td>99.54</td><td>34.11</td><td>99.10</td><td>39.02</td><td>53.42</td><td>82.32</td><td>98.22</td><td>42.32</td><td>76.43</td><td>58.47</td><td></td></tr><tr><td>FeatureNorm + Ours (ResNet-34)</td><td>41.47</td><td>90.47</td><td>92.46</td><td>71.49</td><td>91.41</td><td>72.89</td><td>65.18</td><td>80.33</td><td>89.99</td><td>69.00</td><td>76.10</td><td>76.84</td><td></td></tr><tr><td>FeatureNorm + Ours (WRN-28)</td><td>54.17</td><td>89.08</td><td>80.86</td><td>79.52</td><td>80.69</td><td>79.91</td><td>71.49</td><td>74.37</td><td>78.00</td><td>80.74</td><td>73.04</td><td>80.72</td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "as CEDA, ACET, and CCUs, which employ specific techniques to suppress confidence scores during training, also significantly mitigate OOD overconfidence in DNNs. However, our approach, which does not incorporate specific confidence suppression measures, still outperforms these state-of-the-art methods, particularly in the more challenging CIFAR-100 scenario. This further highlights the robustness and effectiveness of our strategy.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "On CIFAR-10, while our base method may not show a pronounced advantage over others, combining our approach with confidence suppression techniques provides additional improvements, surpassing the performance of these state-of-the-art methods. These results reinforce the effectiveness of our approach in addressing OOD overconfidence.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Visualization. We visualize the maximum confidence scores predicted by various DNN classifiers as histograms (logarithmic scale) in Fig. 6. As shown, applying OOD overconfidence mitigation solutions shifts the confidence distributions of the Baseline to the left, substantially reducing the number of samples with high confidence scores. Notably, our approach achieves the most pronounced shift, un",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "derscoring its effectiveness and validating its superiority in mitigating OOD overconfidence.",
+        "bbox": [
+            511,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Results of Enhancing OOD Detection",
+        "text_level": 1,
+        "bbox": [
+            511,
+            617,
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+            633
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "CIFAR Experiments. We evaluate the effectiveness of our approach in enhancing OOD detection. The results in Tab. 4 demonstrate that applying our method to existing OOD detection approaches leads to significant performance improvements. Even when directly applied to the classifier without any advanced post-hoc processing, i.e., MSP, the performance enhancement is still noticeable. These improvements are consistent across different student model configurations, datasets, and classifiers, validating the effectiveness of our approach in boosting OOD detection.",
+        "bbox": [
+            511,
+            642,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ImageNet Experiments. We further validate the effectiveness of our approach in enhancing OOD detection on the ImageNet-1k dataset. The results in Tab. 5 indicate that, similar to the CIFAR experiments, applying our approach significantly improves OOD detection performance across methods, demonstrating the robustness and scalability of our approach in large-scale settings.",
+        "bbox": [
+            511,
+            795,
+            908,
+            902
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "5036",
+        "bbox": [
+            482,
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+            516,
+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6c83316610385ef32e2e9572156dfe65487b7f6951758bec3c7e77f4fa41d3d3.jpg",
+        "table_caption": [
+            "Table 5. Comparison of OOD detection performance for various methods on the ImageNet-1k dataset."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Model</td><td rowspan=\"3\">Method</td><td colspan=\"9\">OOD</td><td rowspan=\"2\" colspan=\"2\">Average</td></tr><tr><td colspan=\"2\">SUN</td><td colspan=\"2\">Places</td><td colspan=\"2\">Textures</td><td colspan=\"3\">OpenImage-O</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td></td></tr><tr><td rowspan=\"10\">DenseNet-201</td><td>MSP</td><td>65.76</td><td>82.24</td><td>69.53</td><td>81.14</td><td>67.82</td><td>79.36</td><td>64.92</td><td>84.47</td><td>67.01</td><td>81.80</td><td></td></tr><tr><td>MSP + Ours (DenseNet-161)</td><td>66.31</td><td>81.72</td><td>68.61</td><td>81.32</td><td>66.97</td><td>79.55</td><td>62.12</td><td>85.10</td><td>66.00</td><td>81.92</td><td></td></tr><tr><td>MaxLogit</td><td>55.44</td><td>86.06</td><td>61.89</td><td>83.99</td><td>58.48</td><td>83.45</td><td>59.64</td><td>86.94</td><td>58.86</td><td>85.11</td><td></td></tr><tr><td>MaxLogit + Ours (DenseNet-161)</td><td>55.33</td><td>87.67</td><td>59.95</td><td>86.26</td><td>55.80</td><td>85.84</td><td>60.03</td><td>88.60</td><td>57.78</td><td>87.09</td><td></td></tr><tr><td>Energy</td><td>52.87</td><td>86.04</td><td>60.46</td><td>83.71</td><td>56.13</td><td>83.35</td><td>59.87</td><td>86.65</td><td>57.33</td><td>84.94</td><td></td></tr><tr><td>Energy + Ours (DenseNet-161)</td><td>50.88</td><td>88.25</td><td>56.90</td><td>86.60</td><td>52.25</td><td>86.45</td><td>58.76</td><td>88.60</td><td>54.70</td><td>87.48</td><td></td></tr><tr><td>ReAct</td><td>46.00</td><td>90.81</td><td>57.46</td><td>86.11</td><td>55.14</td><td>84.19</td><td>69.32</td><td>74.43</td><td>56.98</td><td>83.89</td><td></td></tr><tr><td>ReAct + Ours (DenseNet-161)</td><td>49.21</td><td>88.55</td><td>55.02</td><td>86.94</td><td>50.99</td><td>86.75</td><td>57.61</td><td>88.64</td><td>53.21</td><td>87.72</td><td></td></tr><tr><td>FeatureNorm</td><td>43.06</td><td>90.05</td><td>55.71</td><td>85.42</td><td>50.46</td><td>79.90</td><td>79.97</td><td>67.22</td><td>57.30</td><td>80.65</td><td></td></tr><tr><td>FeatureNorm + Ours (DenseNet-161)</td><td>36.52</td><td>91.79</td><td>49.24</td><td>87.50</td><td>56.73</td><td>78.29</td><td>82.20</td><td>65.49</td><td>56.17</td><td>80.77</td><td></td></tr><tr><td rowspan=\"10\">WRN-101</td><td>MSP</td><td>66.93</td><td>82.44</td><td>70.48</td><td>81.35</td><td>65.14</td><td>80.91</td><td>59.87</td><td>86.13</td><td>65.61</td><td>82.71</td><td></td></tr><tr><td>MSP + Ours (WRN-50)</td><td>67.75</td><td>82.80</td><td>69.07</td><td>81.81</td><td>66.38</td><td>80.96</td><td>60.91</td><td>86.78</td><td>66.03</td><td>83.09</td><td></td></tr><tr><td>MaxLogit</td><td>63.25</td><td>84.75</td><td>68.40</td><td>82.69</td><td>57.39</td><td>84.38</td><td>55.84</td><td>88.43</td><td>61.22</td><td>85.06</td><td></td></tr><tr><td>MaxLogit + Ours (WRN-50)</td><td>61.92</td><td>86.18</td><td>64.34</td><td>84.40</td><td>56.74</td><td>85.60</td><td>55.69</td><td>89.25</td><td>59.67</td><td>86.36</td><td></td></tr><tr><td>Energy</td><td>65.06</td><td>84.46</td><td>70.32</td><td>82.27</td><td>57.11</td><td>84.37</td><td>58.04</td><td>88.02</td><td>62.63</td><td>84.78</td><td></td></tr><tr><td>Energy + Ours (WRN-50)</td><td>63.18</td><td>85.96</td><td>66.06</td><td>84.00</td><td>55.90</td><td>85.68</td><td>57.87</td><td>88.77</td><td>60.75</td><td>86.10</td><td></td></tr><tr><td>ReAct</td><td>52.22</td><td>88.11</td><td>58.76</td><td>85.47</td><td>57.09</td><td>84.99</td><td>49.63</td><td>87.82</td><td>54.43</td><td>86.60</td><td></td></tr><tr><td>ReAct + Ours (WRN-50)</td><td>37.02</td><td>92.24</td><td>48.54</td><td>88.70</td><td>50.90</td><td>87.36</td><td>54.49</td><td>85.92</td><td>47.74</td><td>88.56</td><td></td></tr><tr><td>FeatureNorm</td><td>70.07</td><td>78.89</td><td>78.61</td><td>73.23</td><td>20.98</td><td>94.79</td><td>75.09</td><td>74.81</td><td>61.19</td><td>80.43</td><td></td></tr><tr><td>FeatureNorm + Ours (WRN-50)</td><td>60.22</td><td>83.67</td><td>74.01</td><td>75.96</td><td>17.71</td><td>96.09</td><td>69.94</td><td>78.90</td><td>55.47</td><td>83.66</td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/fde2ce04aaca16c76111726c9f84627990c92ae2e4070b9d447cfb428d1867da.jpg",
+        "table_caption": [
+            "Table 6. Comparison of MMC and OOD detection performance for ResNet-50 enhanced by Ours (ResNet-18) and its variants w/o knowledge distillation (KD) and ReLU removal (RR), using CIFAR-10 as the ID dataset, and SVHN, LSUN-R, iSUN, Textures, and TINR as the OOD datasets. Results are averaged."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>KD</td><td>RR</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td></td><td></td><td>79.58</td><td>54.23</td><td>91.78</td></tr><tr><td>✓</td><td></td><td>76.81</td><td>49.81</td><td>92.42</td></tr><tr><td></td><td>✓</td><td>78.46</td><td>50.50</td><td>91.76</td></tr><tr><td>✓</td><td>✓</td><td>76.48</td><td>48.89</td><td>92.59</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4. Ablation Studies and More Analysis",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Importance of Knowledge Distillation and ReLU Removal. We conduct comprehensive ablation studies to evaluate the impact of knowledge distillation and ReLU removal, the two essential components of our approach. As shown in Tab. 6, excluding either component notably diminishes the effectiveness of our method in mitigating OOD overconfidence and complicates the accuracy of OOD detection. These findings validate the critical importance of both knowledge distillation and selective ReLU removal in achieving optimal performance with our approach.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Knowledge Distillation vs. Network Pruning for Capacity Reduction. We further investigate an alternative capacity reduction method for our approach by applying network pruning. To facilitate a fair comparison with knowledge distillation, we evaluate ResNet-50 and ResNet-101 models trained on CIFAR-10, applying two strategies: (1) using KD [22] to reduce ResNet-50 to ResNet-18 and ResNet-101 to WRN-28, and (2) applying Prune [14] to ResNet-50 and ResNet-101, reducing them to parameter counts comparable to ResNet-18 and WRN-28, respectively. The re",
+        "bbox": [
+            89,
+            750,
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+            900
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/60035a89324ec8924f96fb8ab61cb275242cae4d322d35e32b3d47d66f281b7f.jpg",
+        "table_caption": [
+            "Table 7. Comparison of MMC and OOD detection performance for ResNet-50 and ResNet-101 reduced to comparable parameter counts via KD [22] and Prune [14]. CIFAR-10 serves as the ID dataset, with SVHN, LSUN-R, iSUN, Textures, and TINR as OOD datasets. Results are averaged across all five OOD datasets"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Capacity Reduction</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td rowspan=\"3\">ResNet-50</td><td>—</td><td>79.58</td><td>54.23</td><td>91.78</td></tr><tr><td>Prune</td><td>77.34</td><td>52.55</td><td>92.27</td></tr><tr><td>KD (ResNet-18)</td><td>76.81</td><td>49.81</td><td>92.42</td></tr><tr><td rowspan=\"3\">ResNet-101</td><td>—</td><td>83.46</td><td>51.92</td><td>92.53</td></tr><tr><td>Prune</td><td>78.20</td><td>50.92</td><td>91.61</td></tr><tr><td>KD (WRN-28)</td><td>77.01</td><td>41.09</td><td>92.56</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "sults in Tab. 7 show that both methods effectively reduce OOD overconfidence and improve OOD detection; however, knowledge distillation consistently delivers a more substantial improvement than network pruning. Additionally, knowledge distillation offers greater stability and flexibility during training, making it a more suitable choice for capacity reduction in our approach.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion and Future Work",
+        "text_level": 1,
+        "bbox": [
+            511,
+            709,
+            782,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This paper has presented a comprehensive investigation into mitigating OOD overconfidence in DNNs through model simplification. By reducing model capacity via knowledge distillation and decreasing nonlinearity through selective ReLU removal, we demonstrate that OOD overconfidence in DNN classifiers can be significantly mitigated. Furthermore, these strategies can be effectively combined with OOD detection methods to enhance overall performance. In future work, we plan to study the effects of model simplification on OOD overconfidence in greater depth and from a theoretical perspective.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "5037",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
+            91,
+            90,
+            259,
+            107
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We sincerely thank the anonymous reviewers for their valuable comments. This work was supported in part by the National Natural Science Foundation of China (62472117, U2436208, 62406095), the Guangdong Basic and Applied Basic Research Foundation (2025A1515010157, 2024A1515012064), the Science and Technology Projects in Guangzhou (2025A03J0137, SL2022A04J01112), and the Academician Bixing Fang's Specialized Class.",
+        "bbox": [
+            89,
+            114,
+            483,
+            236
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            91,
+            247,
+            187,
+            263
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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2025/Simplification Is All You Need against Out-of-Distribution Overconfidence/c4dc8f46-aeb5-4477-a94f-497bd92530cf_origin.pdf

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2025/Simplification Is All You Need against Out-of-Distribution Overconfidence/full.md

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+# Simplification Is All You Need against Out-of-Distribution Overconfidence
+
+Keke Tang $^{1*}$ , Chao Hou $^{1*}$ , Weilong Peng $^{1\dagger}$ , Xiang Fang $^{2}$ , Zhize Wu $^{3}$ , Yongwei Nie $^{4}$ , Wenping Wang $^{5}$ , Zhihong Tian $^{1}$
+
+$^{1}$ Guangzhou University  $^{2}$ Nanyang Technological University  $^{3}$ Hefei University  $^{4}$ South China University of Technology  $^{5}$ Texas A&M University
+
+tangbohutbh@gmail.com, houchaohk@gmail.com, wlpeng@tju.edu.cn, xfang9508@gmail.com, wuzz@hfuu.edu.cn, nieyongwei@scut.edu.cn, wenping@amu.edu, tianzhihong@gzhu.edu.cn
+
+# Abstract
+
+Deep neural networks (DNNs) often exhibit out-of-distribution (OOD) overconfidence, producing overly confident predictions on OOD samples. We attribute this issue to the inherent over-complexity of DNNs and investigate two key aspects: capacity and nonlinearity. First, we demonstrate that reducing model capacity through knowledge distillation can effectively mitigate OOD overconfidence. Second, we show that selectively reducing nonlinearity by removing ReLU operations further alleviates the issue. Building on these findings, we present a practical guide to model simplification, combining both strategies to significantly reduce OOD overconfidence. Extensive experiments validate the effectiveness of this approach in mitigating OOD overconfidence and demonstrate its superiority over state-of-the-art methods. Additionally, our simplification strategies can be combined with existing OOD detection techniques to further enhance OOD detection performance.
+
+# 1. Introduction
+
+Deep neural networks (DNNs) have revolutionized image classification tasks, consistently achieving state-of-the-art performance [8, 15, 25, 45, 46]. Despite this success, DNN classifiers are inherently designed for static, closed-world environments [2], limiting their ability to adapt to novel, unforeseen concepts encountered in real-world scenarios, known as out-of-distribution (OOD) samples. Indeed, many recent studies demonstrate that DNN classifiers suffer from OOD overconfidence, generating overly confident predictions on OOD samples [13, 34]. This issue significantly impacts the reliability and safety of DNNs in real-world applications, highlighting an urgent need for effective solutions.
+
+![](images/5e6a4a1f5e3b5d07fabd2929ba9082d24079e99165782dac9f651cebbe002a7e.jpg)
+
+![](images/dce8fa53a43848f5d9336be0b0e3c2b2f9d31368c92f5d54078bbf5d6f2c43ca.jpg)
+
+![](images/916a7cfce59a808608cd0e609f3941a41b1aa0e793d6375a2c3ee3c3bae2dec2.jpg)
+
+![](images/5f9ef8a82b0e767c3e2a2dca39b494acf7a0e0ac697dcbde74f8bfb892ec4ef0.jpg)
+
+![](images/ff7334fac2b18610984438b898d30b9be4fc31f3283c45235f6b64b71e572110.jpg)  
+Figure 1. Histograms (logarithmic scale) of maximum confidence values for the teacher network (ResNet-50), the distilled student network (ResNet-18), and its variant with additional ReLU removal. All models are trained on CIFAR-100 and evaluated on OOD datasets: (a) SVHN, (b) LSUN-R, (c) iSUN, and (d) TinyImageNet-R. The  $y$ -axis represents the frequency of samples, and the  $x$ -axis represents confidence scores.
+
+Extensive research has been dedicated to addressing the OOD overconfidence issue. One common approach involves calibrating outputs for both in-distribution (ID) and OOD samples to improve discrimination [20], enabling OOD detectors to proactively reject OOD inputs. While these methods can reduce the impact of overconfidence, they do not fundamentally resolve the issue within DNN classifiers. Moreover, their effectiveness heavily depends on the classifiers' ability to adequately separate predictive distributions; they fail when the classifiers cannot achieve this separation [26]. As a more intrinsic solution, another approach trains DNN classifiers to suppress predictions on a subset of typical OOD samples, with the expectation that this behavior will generalize to other OOD data [18, 20].
+
+However, given the vast diversity of potential OOD samples, the effectiveness of this method remains limited.
+
+DNNs can indeed be regarded as complex systems, often characterized by over-parameterization, in which the number of parameters exceeds the amount of available training data [66]. This excessive complexity can cause DNNs to exhibit emergent behaviors, leading to unpredictable outcomes, as observed in other complex systems [31]. Consequently, when presented with certain OOD inputs, DNNs may unexpectedly but confidently misclassify them as ID classes. Therefore, investigating the relationship between model complexity and OOD overconfidence presents a promising path toward effectively addressing this issue.
+
+In this paper, we explore two key aspects of model complexity: capacity and nonlinearity, and their roles in influencing OOD overconfidence. For capacity, we use knowledge distillation to examine how varying the student network's capacity affects OOD overconfidence, finding that an appropriately reduced capacity can significantly alleviate this issue (see Fig. 1). For nonlinearity, we investigate selective ReLU removal at different ratios and locations within the network, observing that controlled reductions in nonlinearity similarly mitigate OOD overconfidence (see Fig. 1). Based on these insights, we present a practical guide to model simplification that combines these two strategies to mitigate the OOD overconfidence issue in DNNs more effectively, achieving superior results compared to state-of-the-art methods. Furthermore, we demonstrate that our approach can be effectively combined with existing OOD detection techniques to further enhance performance.
+
+Overall, our contribution is summarized as follows:
+
+- We are the first to attribute the OOD overconfidence issue in DNNs to their over-complexity, identifying model simplification as a crucial and effective solution.  
+- We systematically investigate two fundamental aspects of complexity: capacity and nonlinearity, analyzing their effects on OOD overconfidence through knowledge distillation and selective ReLU removal.  
+- We present a practical guide for model simplification and demonstrate through extensive experiments its effectiveness in significantly mitigating OOD overconfidence.
+
+# 2. Related Work
+
+Mitigating OOD Overconfidence. The issue of OOD overconfidence, where DNNs assign excessively high confidence scores to OOD samples, presents a substantial security risk for real-world applications [18, 42, 56]. Current approaches often incorporate auxiliary data to improve OOD sensitivity, using techniques such as adding random noise and image shuffling [26], leveraging large volumes of unlabeled data [51, 55, 60], relying on external OOD datasets [20], or generating synthetic OOD samples via models like Chamfer GAN [41]. Additionally, some
+
+methods, including VOS [9] and NPOS [47], create virtual features in feature space rather than explicit OOD instances. However, these approaches typically require substantial volumes of OOD data.
+
+In contrast, our approach addresses OOD overconfidence by reducing model complexity, thus eliminating the need for auxiliary OOD data. Through extensive experiments, we systematically explore the effects of capacity reduction and selective activation removal, presenting a data-independent alternative for mitigating OOD overconfidence.
+
+OD Detection. Another approach to managing OOD overconfidence is to develop scoring or normalization techniques that increase the distinction between ID and OOD samples [11, 17, 36, 43]. A foundational method, maximum softmax probability, introduced by Hendrycks and Gimpel [19], demonstrates that classifiers typically assign lower confidence to OOD samples. Follow-up methods, including ODIN [28] with temperature scaling and input perturbation, Energy Score [29], and density-based scores [27, 40], further enhance this ID-OOD separation. To improve robustness, several techniques refine feature representations: feature activation rectification [39, 62], feature selection [67], neuron pruning [3], and methods like CORES [44], which identify layer-specific relevant kernels for OOD detection. In contrast, our approach inherently addresses OOD overconfidence through model simplification. By tackling the root of the overconfidence issue, our method naturally enhances OOD detection performance as a result.
+
+Knowledge Distillation. Knowledge distillation transfers knowledge from a larger teacher model to a smaller student model, enabling the student to approximate the teacher's performance [22]. It typically utilizes response-based knowledge (soft logits) [1, 22, 32], feature-based knowledge (intermediate feature maps) [37, 50, 53], and relation-based knowledge (layer/sample relationships) [57, 58]. We use distillation to reduce model capacity and mitigate OOD overconfidence.
+
+ReLU Activation. ReLU  $(f(x) = \max(0, x))$  introduces nonlinearity while maintaining efficiency, making it widely used in deep learning [10, 12]. However, ReLU networks are prone to OOD overconfidence [18]. We address this by selectively removing ReLU activations to mitigate OOD overconfidence.
+
+# 3. How Complexity Affects Overconfidence?
+
+The complexity of a neural network is influenced by various factors. To investigate whether model complexity affects the degree of OOD overconfidence in DNNs, we focus on two key aspects: capacity and nonlinearity. In this section, we examine each of these factors individually to better understand their impact on OOD overconfidence.
+
+Evaluation Metrics. To assess the severity of OOD overconfidence across different DNNs, we use the mean max
+
+Table 1. Comparison of MMC and OOD detection performance for student models (ResNet-18) distilled from a teacher model (ResNet-50) using different knowledge distillation methods on CIFAR datasets. Results are averaged across multiple OOD datasets.  
+
+<table><tr><td>ID</td><td colspan="3">CIFAR-10</td><td colspan="3">CIFAR-100</td></tr><tr><td>Method</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>Teacher</td><td>79.58</td><td>54.23</td><td>91.78</td><td>72.12</td><td>83.67</td><td>74.73</td></tr><tr><td>KD [22]</td><td>76.81</td><td>49.81</td><td>92.42</td><td>62.69</td><td>79.77</td><td>76.31</td></tr><tr><td>FitNet [37]</td><td>79.46</td><td>50.58</td><td>92.26</td><td>60.60</td><td>77.53</td><td>77.78</td></tr><tr><td>AT [64]</td><td>77.90</td><td>48.09</td><td>92.69</td><td>64.11</td><td>82.14</td><td>75.51</td></tr><tr><td>SP [48]</td><td>78.81</td><td>50.52</td><td>92.22</td><td>58.75</td><td>77.12</td><td>80.01</td></tr></table>
+
+imum confidence (MMC) on OOD samples as our evaluation metric. Additionally, to analyze how OOD overconfidence impacts the model's ability for ID/OOD discrimination, we also report the area under the receiver operating characteristic curve (AUROC) [6], the false positive rate at a true positive rate of  $95\%$  (FPR95) [28], and the area under the precision-recall curve, with ID samples specified as positives (AUPRin) [38].
+
+# 3.1. Capacity
+
+To investigate whether model capacity affects the severity of OOD overconfidence, we employ knowledge distillation to transfer knowledge from a large-capacity teacher network to a smaller-capacity student network. Specifically, we examine how different knowledge distillation strategies and varying student network capacities influence OOD overconfidence. Since DNN capacity is influenced by various factors, such as depth, width, and number of parameters, we ensure a fair comparison by testing networks with the same architecture but different depths.
+
+Effectiveness of Knowledge Distillation. To validate the effectiveness of knowledge distillation in mitigating OOD overconfidence, we select ResNet-50 as the teacher network and ResNet-18 as the student network, applying four distinct knowledge distillation methods: KD [22], FitNet [37], AT [64], and SP [48]. Experiments are conducted using CIFAR-10 and CIFAR-100 as ID datasets, with SVHN, LSUN-R, iSUN, Textures, and TinyImageNet-R as OOD datasets. The results, shown in Tab. 1, indicate that all four distillation methods lead to reductions in MMC and enhancements in AUROC and FPR95 metrics, demonstrating that knowledge distillation effectively mitigates the OOD overconfidence issue.
+
+Analysis of Student Networks with Varying Capacities. We conduct experiments on two datasets using KD [22] with student networks of varying capacities. For CIFAR-100, we set ResNet-101 as the teacher and evaluate student networks with capacities ranging from ResNet-50, ResNet-34, ResNet-18, to ResNet-10. For ImageNet-100, we use ResNet-152 as the teacher, with ResNet-101, ResNet-50, ResNet-34, and ResNet-18 as student models. As shown in Fig. 2, on CIFAR-100, reducing the student
+
+Table 2. Comparison of MMC and OOD detection performance for different ReLU removal proportions using ResNet-101 as the classifier. Results are averaged across multiple OOD datasets.  
+
+<table><tr><td>ID</td><td colspan="3">CIFAR-10</td><td colspan="3">CIFAR-100</td></tr><tr><td>Ratio</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td>0%</td><td>83.46</td><td>51.92</td><td>92.53</td><td>73.84</td><td>84.41</td><td>73.03</td></tr><tr><td>1%</td><td>84.46</td><td>57.58</td><td>90.48</td><td>69.14</td><td>82.43</td><td>76.22</td></tr><tr><td>2%</td><td>77.18</td><td>43.00</td><td>93.69</td><td>72.26</td><td>83.07</td><td>75.25</td></tr><tr><td>3%</td><td>77.91</td><td>46.93</td><td>93.06</td><td>69.37</td><td>78.74</td><td>78.12</td></tr><tr><td>5%</td><td>83.07</td><td>56.53</td><td>90.71</td><td>68.71</td><td>78.57</td><td>79.43</td></tr><tr><td>10%</td><td>79.60</td><td>50.06</td><td>92.25</td><td>71.24</td><td>80.94</td><td>77.70</td></tr><tr><td>20%</td><td>80.78</td><td>50.31</td><td>92.30</td><td>73.54</td><td>82.73</td><td>74.81</td></tr><tr><td>50%</td><td>79.22</td><td>48.34</td><td>92.73</td><td>70.40</td><td>82.22</td><td>75.40</td></tr></table>
+
+network capacity to ResNet-18 improves OOD overconfidence and enhances ID/OOD discrimination. However, further reducing capacity to ResNet-10 results in degraded performance, likely due to insufficient capacity to effectively handle CIFAR-100 classification. A similar trend is observed on ImageNet-100, where reducing the student network capacity to ResNet-50 continues to yield improvements, but further reductions impair performance, likely due to the dataset's increased complexity. These findings suggest that reducing network capacity to a moderate level can effectively alleviate the OOD overconfidence issue.
+
+# 3.2. Nonlinearity
+
+Nonlinearity in DNNs arises from activation functions, e.g., ReLU and Sigmoid. The more activation operations are applied, the greater the degree of nonlinearity. In this subsection, we investigate whether the degree of nonlinearity affects the severity of OOD overconfidence. Given that ReLU is one of the most widely used activation functions, we focus on examining the effect of removing ReLU operations.
+
+Specifically, we examine the impact of removing ReLU operations at different proportions and locations, similar to the approach in [4]. as we will detail in Sec. 4, to evaluate their effect on mitigating OOD overconfidence. Additionally, we assess the influence of initiating ReLU removal at various stages of training. For these experiments, CIFAR-10 and CIFAR-100 are used as the ID datasets, with SVHN, LSUN-R, iSUN, Textures, and TinyImageNet-R as the OOD datasets, using ResNet-18/101 as the classifier.
+
+Analysis of Different Removal Proportions. To assess the impact of varying removal proportions, we introduce the Negative Response Ratio (NRO), which measures the proportion of negative responses that are passed to ReLU operations:
+
+$$
+N R O = \frac {\text {N u m b e r o f n e g a t i v e c o n v o l u t i o n a l r e s p o n s e s}}{\text {T o t a l n u m b e r o f c o n v o l u t i o n a l r e s p o n s e s}}. \tag {1}
+$$
+
+A smaller NRO indicates fewer activations requiring truncation, suggesting that the corresponding ReLU layers contribute less to overall nonlinearity. Based on NRO values, we selectively remove ReLU operations with the low
+
+![](images/19135528d01fbdfee79fa48fbdcda4f0bbc6b063ba79534135e0e1344c342092.jpg)
+
+![](images/b8889e50737340affa915d527572fc1e1bb309e3feca8bf34d0bc30c4f98eaf6.jpg)
+
+![](images/b7bbd30e25a50659fc0a95cd265e3c0a4fa6a07ed765e9a686a75683f3190403.jpg)  
+Figure 2. Comparison of MMC and OOD detection metrics, including FPR95, AUROC, and AUPRin, for student models with varying capacities (e.g., ResNet models) across datasets: (a) CIFAR-100 and (b) ImageNet-100.
+
+![](images/0b695f5d3704bfe92f4f6a91eb4ec4f0903c73dcfe1cfa4ecbbaa9cafc7e32d6.jpg)  
+Teacher Student
+
+![](images/301ad9c7ffc67ad80272d3b6901be0ab800881fe239a99c2e8aa6d17f490666a.jpg)
+
+![](images/521aa6f536e610a027968e764225eecf6777f02685bbb4831f6844b2bd32fd44.jpg)
+
+![](images/01f77a8c33e4dc7cae2ae8746efb3e495b5e1a150cbfd698a4aca7d73c6ef79a.jpg)  
+Figure 3. Comparison of MMC and FPR95 for ResNet-101 with ReLU removal applied at different network locations.
+
+est NRO scores at proportions of  $1\%$ ,  $2\%$ ,  $3\%$ ,  $5\%$ ,  $10\%$ ,  $20\%$ , and  $50\%$ , starting at the 40th epoch and continuing through the 100th epoch. As shown in Tab. 2, removing a certain proportion of ReLU operations reduces OOD overconfidence and enhances OOD detection. For example, removing  $2\%$  of ReLU operations on CIFAR-10 and  $5\%$  on CIFAR-100 yields the best results.
+
+Analysis of Different Removal Locations. To identify which ReLU operations are most suitable for removal, we compare the effects of removing ReLU operations from shallow, middle, and deep layers, as well as from layers with the lowest NRO values. Following previous findings, we remove  $2\%$  of ReLU operations for CIFAR-10 and  $5\%$  for CIFAR-100, initiating removal at the 40th epoch. As shown in Fig. 3, each removal strategy effectively reduces OOD overconfidence, with the best results achieved by removing ReLU operations based on NRO values.
+
+Impact of ReLU Removal Initiation Points. We also
+
+![](images/09125d787ec7e270736996341582f23c8db509209b4a91dacf06d71b306f5a76.jpg)  
+Figure 4. Comparison of MMC and FPR95 for ResNet-18 with ReLU removal initiated at different training epochs.
+
+analyze the effects of initiating ReLU removal at different stages during training. As illustrated in Fig. 4, the specific stage at which ReLU removal begins has only a moderate impact on overall performance. The best results are achieved when removal is initiated around the middle of the training process, such as at the 40th epoch.
+
+# 4. A Practical Guide to Model Simplification
+
+Based on our findings reported in Sec. 3, we present a practical guide to model simplification for addressing the OOD overconfidence issue in DNNs. For models that exhibit high OOD overconfidence, we suggest reducing complexity through a combination of knowledge distillation and selective ReLU removal. Please refer to Fig. 5 for demonstration. Knowledge Distillation with a Moderately-Sized Student. The first step is to choose a small student model with a capacity suited to the task requirements. This student model should be sufficiently compact to reduce complexity but still capable of performing well on the original task. We then apply knowledge distillation (e.g., KD) to transfer es
+
+![](images/bf8fc906eb6da835625877dfe77bf98c2395802d61b870b8320876d358dc070b.jpg)  
+Figure 5. Illustration of our model simplification pipeline. Given a complex teacher model with high capacity and nonlinearity, we use knowledge distillation to transfer information to a low-capacity student model. During distillation, ReLU operations are selectively replaced with Leaky ReLU, and the negative slope is iteratively adjusted from 0 to 1, ultimately transforming ReLU into an identity function.
+
+sential knowledge from the larger teacher model to the student. This process enables the student to approximate the teacher's performance while operating with a reduced capacity, thereby alleviating the OOD overconfidence issue.
+
+Selective ReLU Removal During Distillation. To further streamline the model, we selectively remove ReLU operations. Using the NRO metric defined in Eq. (1), we identify ReLU operations that contribute minimally to the model's responses. Following the approach in [4], we replace these selected ReLU operations with Leaky ReLU, initially setting the negative slope to 0 and gradually increasing it to 1 midway through the distillation process. This controlled transition effectively transforms ReLU into an identity function, thereby reducing the model's nonlinearity.
+
+This practical guide, combining knowledge distillation for capacity reduction with selective ReLU removal for nonlinearity reduction, provides an accessible approach to mitigate OOD overconfidence issue in DNNs.
+
+# 5. Experimental Results
+
+# 5.1. Experimental Setup
+
+Implementation Details. We employ KD [22] to transfer knowledge from teacher to student models, with a weight ratio of 1.5:1 between KD loss and cross-entropy (CE) loss. All student models are trained for 100 epochs, with selective ReLU removal starting at the 40th epoch and continuing through the end of training, similar to the approach in [4]. We remove  $2\%$  of ReLU operations for models trained on CIFAR-10,  $5\%$  for models trained on CIFAR-100, and  $5\%$  for models trained on ImageNet-1k [7]. All experiments are implemented in PyTorch [35] and conducted on a workstation equipped with dual 2.40 GHz CPUs, 128 GB RAM, and eight NVIDIA RTX 3090Ti GPUs.
+
+Setup. For (1) Mitigating OOD Overconfidence, we use CIFAR-10 and CIFAR-100 [24] as ID datasets, with SVHN [33], LSUN-R [59], iSUN [54], Textures [5], and TINR, a resized variant of TinyImageNet uniformly scaled to  $32 \times 32$ , as the OOD datasets. For (2) OOD Detection, we use the same CIFAR-based configuration as in (1). For large-scale evaluations, we use ImageNet-1k [7] as the ID dataset, with SUN [52], Places [65], Textures [5], and OpenImage-O [49] as the OOD datasets. We train ResNet-50 and ResNet-101 [16] on CIFAR-10 and CIFAR-100, and train DenseNet-201 [23] and WideResNet-101-2 (WRN-101) [63] on ImageNet-1k [7], following the training protocols specified in their respective original papers.
+
+Setting of Our Approach. We designate ResNet-18 and WideResNet-16-10 (WRN-16) as student networks for ResNet-50, and ResNet-34 and WideResNet-28-10 (WRN-28) as students for ResNet-101 on CIFAR datasets. For the ImageNet-1k dataset, DenseNet-161 serves as the student for DenseNet-201, and WideResNet-50-2 (WRN-50) for WRN-101. All student models are trained using the SGD optimizer with a momentum of 0.9 and an initial learning rate of 0.1. On the ImageNet-1k benchmark, the learning rate is reduced by a factor of 10 every 30 epochs, while on the CIFAR benchmarks, the learning rate is adjusted using the CosineAnnealingLR scheduler. For simplicity, we refer to our method as "Ours (student)" in subsequent sections to indicate the specific student network employed.
+
+Baselines. For (1) Mitigating OOD Overconfidence, we select three state-of-the-art baselines: ACET [18], CEDA [18], and CCUs [30]. For (2) OOD Detection, we benchmark our approach against five post-hoc methods: maximum softmax probability (MSP) [19], MaxLogit [21], Energy [29], ReAct [39], and FeatureNorm [61].
+
+Table 3. Comparison of MMC on OOD datasets for ResNet-50 and ResNet-101 models trained on CIFAR-10 and CIFAR-100, evaluated using various OOD overconfidence mitigation techniques. Underlined values denote the best performance for a single method, while bolded values indicate the best performance across all methods, including both individual and combined methods.  
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Method</td><td colspan="5">ID: CIFAR-10</td><td rowspan="2">Average</td><td colspan="5">ID: CIFAR-100</td><td rowspan="2">Average</td></tr><tr><td>SVHN</td><td>LSUN-R</td><td>iSUN</td><td>Textures</td><td>TINR</td><td>SVHN</td><td>LSUN-R</td><td>iSUN</td><td>Textures</td><td>TINR</td></tr><tr><td rowspan="9">ResNet-50</td><td>—</td><td>75.34</td><td>79.64</td><td>79.86</td><td>81.53</td><td>81.53</td><td>79.58</td><td>72.50</td><td>72.07</td><td>72.20</td><td>72.74</td><td>71.11</td><td>72.12</td></tr><tr><td>CEDA</td><td>74.73</td><td>70.91</td><td>72.02</td><td>73.37</td><td>78.64</td><td>73.93</td><td>55.64</td><td>54.77</td><td>56.25</td><td>62.85</td><td>55.42</td><td>56.99</td></tr><tr><td>ACET</td><td>74.29</td><td>67.35</td><td>67.72</td><td>70.37</td><td>69.87</td><td>69.92</td><td>63.68</td><td>62.49</td><td>62.19</td><td>64.44</td><td>61.15</td><td>62.79</td></tr><tr><td>CCUs</td><td>69.56</td><td>63.51</td><td>63.10</td><td>68.64</td><td>68.92</td><td>66.75</td><td>57.33</td><td>52.30</td><td>54.71</td><td>61.25</td><td>54.89</td><td>56.09</td></tr><tr><td>Ours (ResNet-18)</td><td>78.24</td><td>73.29</td><td>74.37</td><td>79.51</td><td>76.98</td><td>76.48</td><td>54.75</td><td>43.65</td><td>42.27</td><td>61.40</td><td>39.69</td><td>48.35</td></tr><tr><td>Ours (WRN-16)</td><td>63.65</td><td>66.32</td><td>68.49</td><td>77.09</td><td>70.18</td><td>69.15</td><td>43.06</td><td>51.76</td><td>51.99</td><td>57.96</td><td>52.37</td><td>51.43</td></tr><tr><td>CEDA + Ours (WRN-16)</td><td>61.31</td><td>67.40</td><td>69.64</td><td>70.09</td><td>73.54</td><td>68.40</td><td>47.84</td><td>59.40</td><td>60.69</td><td>59.24</td><td>60.00</td><td>57.43</td></tr><tr><td>ACET + Ours (WRN-16)</td><td>67.44</td><td>61.28</td><td>62.36</td><td>70.05</td><td>65.48</td><td>65.32</td><td>52.54</td><td>59.45</td><td>61.59</td><td>60.82</td><td>60.48</td><td>58.98</td></tr><tr><td>CCUs + Ours (WRN-16)</td><td>65.97</td><td>58.81</td><td>61.32</td><td>64.84</td><td>65.96</td><td>63.38</td><td>50.88</td><td>49.04</td><td>51.85</td><td>58.40</td><td>51.82</td><td>52.40</td></tr><tr><td rowspan="9">ResNet-101</td><td>—</td><td>83.44</td><td>82.13</td><td>83.02</td><td>84.56</td><td>84.17</td><td>83.46</td><td>65.25</td><td>77.21</td><td>78.03</td><td>73.38</td><td>75.32</td><td>73.84</td></tr><tr><td>CEDA</td><td>70.07</td><td>68.26</td><td>68.42</td><td>74.42</td><td>74.02</td><td>71.04</td><td>58.82</td><td>58.18</td><td>59.00</td><td>66.23</td><td>58.47</td><td>60.14</td></tr><tr><td>ACET</td><td>75.82</td><td>53.69</td><td>55.00</td><td>64.50</td><td>59.98</td><td>61.80</td><td>63.62</td><td>59.57</td><td>58.44</td><td>60.34</td><td>58.01</td><td>60.00</td></tr><tr><td>CCUs</td><td>73.56</td><td>65.72</td><td>64.98</td><td>66.94</td><td>69.83</td><td>68.21</td><td>58.45</td><td>54.53</td><td>56.52</td><td>59.80</td><td>56.32</td><td>57.12</td></tr><tr><td>Ours (ResNet-34)</td><td>75.22</td><td>74.81</td><td>75.94</td><td>82.08</td><td>78.86</td><td>77.38</td><td>63.62</td><td>58.42</td><td>60.13</td><td>66.69</td><td>59.89</td><td>61.75</td></tr><tr><td>Ours (WRN-28)</td><td>71.21</td><td>74.73</td><td>76.03</td><td>81.80</td><td>77.89</td><td>76.33</td><td>55.69</td><td>47.84</td><td>51.20</td><td>63.69</td><td>54.09</td><td>54.50</td></tr><tr><td>CEDA + Ours (WRN-28)</td><td>67.15</td><td>68.21</td><td>70.59</td><td>76.77</td><td>73.83</td><td>71.31</td><td>56.51</td><td>65.12</td><td>66.59</td><td>62.51</td><td>66.77</td><td>63.50</td></tr><tr><td>ACET + Ours (WRN-28)</td><td>59.33</td><td>52.70</td><td>53.07</td><td>66.95</td><td>58.05</td><td>58.02</td><td>56.10</td><td>62.48</td><td>63.94</td><td>58.34</td><td>63.86</td><td>60.95</td></tr><tr><td>CCUs + Ours (WRN-28)</td><td>67.79</td><td>61.74</td><td>64.20</td><td>65.95</td><td>68.80</td><td>65.70</td><td>53.71</td><td>50.96</td><td>53.58</td><td>57.86</td><td>54.52</td><td>54.13</td></tr></table>
+
+![](images/2a70a23a637a5e8fe3f704e446e6090892e643e0f8fa1c4cf8befca0eb7c2718.jpg)  
+(a)  
+(b)
+
+![](images/5450420c4e84847d0faa06662c292c27f4cd299cf0f3c2763cd43382beb50d1f.jpg)
+
+![](images/154d7c306de00cb139e4e86ecf243644f310051d2d3e7abe9102816e300c8e5b.jpg)  
+ACET
+
+![](images/d683d1fef2149b66067bae02fe792dedf427a55d07dac875bffc6d84f9c63b0a.jpg)  
+CEDA
+
+![](images/c58ce1c74130b039c4d9056eca9d0802ac214005ae37fab257fa844c8d247a26.jpg)  
+CCUs
+
+![](images/195006fd2e1c97a2d69f08dae8f6f38e157e8e06aeab95d519a2cb87a577b88b.jpg)  
+Ours (ResNet-18)
+
+![](images/e81ef09903ff89a34b2893ed9cc7fe4e1630ab89cf858bd580e0130fe071d9ec.jpg)  
+(c)  
+(d)
+
+![](images/c0844b9b5ba1f2864d2361bc5eb81364dc23e04710ccf26e08a3dae0c41f836d.jpg)  
+Figure 6. Histograms (logarithmic scale) of MMC values for (a, b) ResNet-50 and (c, d) ResNet-101, w/ and w/o applying mitigation techniques: ACET, CEDA, CCUs, and Ours. All models are trained on CIFAR-100 and evaluated on OOD datasets: (a, c) LSUN-R and (d) TinyImageNet-R. In our approach, ResNet-18 and WRN-28 serve as students for ResNet-50 and ResNet-101, respectively.
+
+![](images/5f3f12b6ef1143b59a059d7d12e983c1526e867a2d63a304238575ebc2ac6b72.jpg)  
+ACET
+
+![](images/ff89139269c01983fdda6fe307d4f08114af96d0a9f4a0bcb690b1f1e5430d4c.jpg)  
+CEDA
+
+![](images/011606af33bf67277ae955b252a1ece844b99209b093b7d7ddd7cd2b207b2f9c.jpg)  
+CCUs
+
+![](images/196b6591331d6b3a402901ff99e39d9e570fed47804d5134bef54eed362cd2e0.jpg)  
+Ours (WRN-28)
+
+# Results of Mitigating OOD Overconfidence
+
+Comparison with State-of-the-art Methods. To assess the effectiveness and superiority of our approach, we conduct comparative experiments evaluating OOD overconfi
+
+dence for ResNet-50 and ResNet-101 trained on CIFAR-10 and CIFAR-100. The results in Tab. 3 demonstrate that our approach consistently reduces the mean maximum confidence (MMC) across different student networks in all cases, validating its effectiveness. In comparison, methods such
+
+Table 4. Comparison of OOD detection performance for various methods on the CIFAR-10 and CIFAR-100 datasets. Underlined values indicate results enhanced by applying our approach to the baseline, while bolded values denote the best performance.  
+
+<table><tr><td rowspan="3">ID</td><td rowspan="3">Model</td><td rowspan="3">Method</td><td colspan="11">OOD</td><td rowspan="2" colspan="2">Average</td></tr><tr><td colspan="2">SVHN</td><td colspan="2">LSUN-R</td><td colspan="2">iSUN</td><td colspan="2">Textures</td><td colspan="3">TINR</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td></td></tr><tr><td rowspan="15">CIFAR-10</td><td rowspan="15">ResNet-50</td><td>MSP</td><td>43.75</td><td>94.19</td><td>54.32</td><td>91.96</td><td>55.46</td><td>91.66</td><td>59.01</td><td>90.31</td><td>58.61</td><td>90.80</td><td>54.23</td><td>91.78</td><td></td></tr><tr><td>MSP + Ours (ResNet-18)</td><td>51.82</td><td>93.27</td><td>41.93</td><td>93.89</td><td>44.86</td><td>93.27</td><td>55.64</td><td>90.57</td><td>50.18</td><td>91.97</td><td>48.89</td><td>92.59</td><td></td></tr><tr><td>MSP + Ours (WRN-16)</td><td>28.18</td><td>96.12</td><td>35.74</td><td>95.01</td><td>39.78</td><td>94.34</td><td>57.00</td><td>89.79</td><td>42.35</td><td>93.75</td><td>40.61</td><td>93.80</td><td></td></tr><tr><td>MaxLogit</td><td>22.07</td><td>96.31</td><td>32.03</td><td>94.95</td><td>34.95</td><td>94.53</td><td>46.33</td><td>91.39</td><td>44.96</td><td>92.57</td><td>36.07</td><td>93.95</td><td></td></tr><tr><td>MaxLogit + Ours (ResNet-18)</td><td>30.25</td><td>94.94</td><td>25.06</td><td>95.34</td><td>27.91</td><td>94.73</td><td>44.50</td><td>91.71</td><td>36.75</td><td>92.73</td><td>32.89</td><td>93.89</td><td></td></tr><tr><td>MaxLogit + Ours (WRN-16)</td><td>17.61</td><td>96.96</td><td>18.54</td><td>96.92</td><td>21.69</td><td>96.39</td><td>47.70</td><td>89.58</td><td>27.81</td><td>95.55</td><td>26.67</td><td>95.08</td><td></td></tr><tr><td>Energy</td><td>20.35</td><td>96.40</td><td>29.79</td><td>95.11</td><td>32.80</td><td>94.67</td><td>45.41</td><td>91.44</td><td>43.76</td><td>92.64</td><td>34.42</td><td>94.05</td><td></td></tr><tr><td>Energy + Ours (ResNet-18)</td><td>28.53</td><td>95.07</td><td>23.99</td><td>95.43</td><td>26.55</td><td>94.83</td><td>44.13</td><td>89.70</td><td>35.92</td><td>92.79</td><td>31.82</td><td>93.56</td><td></td></tr><tr><td>Energy + Ours (WRN-16)</td><td>18.80</td><td>96.88</td><td>18.07</td><td>97.02</td><td>20.91</td><td>96.50</td><td>47.89</td><td>89.54</td><td>27.63</td><td>95.61</td><td>26.66</td><td>95.11</td><td></td></tr><tr><td>ReAct</td><td>37.66</td><td>91.10</td><td>16.24</td><td>96.64</td><td>19.65</td><td>95.84</td><td>46.72</td><td>86.29</td><td>30.79</td><td>93.46</td><td>30.21</td><td>92.67</td><td></td></tr><tr><td>ReAct + Ours (ResNet-18)</td><td>31.59</td><td>94.62</td><td>23.87</td><td>95.51</td><td>26.78</td><td>94.86</td><td>43.60</td><td>90.19</td><td>35.87</td><td>92.92</td><td>32.34</td><td>93.62</td><td></td></tr><tr><td>ReAct + Ours (WRN-16)</td><td>19.07</td><td>96.84</td><td>17.90</td><td>97.03</td><td>20.66</td><td>96.51</td><td>47.45</td><td>89.84</td><td>27.24</td><td>95.68</td><td>26.46</td><td>95.18</td><td></td></tr><tr><td>FeatureNorm</td><td>9.25</td><td>97.97</td><td>77.34</td><td>82.07</td><td>70.29</td><td>83.96</td><td>48.97</td><td>84.16</td><td>67.71</td><td>84.49</td><td>54.71</td><td>86.53</td><td></td></tr><tr><td>FeatureNorm + Ours (ResNet-18)</td><td>2.73</td><td>99.35</td><td>24.34</td><td>95.75</td><td>21.04</td><td>96.28</td><td>22.82</td><td>94.89</td><td>29.52</td><td>94.36</td><td>20.09</td><td>96.13</td><td></td></tr><tr><td>FeatureNorm + Ours (WRN-16)</td><td>3.37</td><td>99.26</td><td>22.03</td><td>96.43</td><td>21.54</td><td>96.47</td><td>53.67</td><td>78.85</td><td>29.35</td><td>94.50</td><td>25.99</td><td>93.10</td><td></td></tr><tr><td rowspan="15">CIFAR-100</td><td rowspan="15">ResNet-101</td><td>MSP</td><td>76.30</td><td>81.14</td><td>86.67</td><td>69.76</td><td>88.11</td><td>69.06</td><td>85.69</td><td>73.73</td><td>85.27</td><td>71.47</td><td>84.41</td><td>73.03</td><td></td></tr><tr><td>MSP + Ours (ResNet-34)</td><td>77.48</td><td>78.92</td><td>72.74</td><td>83.09</td><td>74.83</td><td>82.14</td><td>82.50</td><td>77.26</td><td>74.52</td><td>82.20</td><td>76.41</td><td>80.72</td><td></td></tr><tr><td>MSP + Ours (WRN-28)</td><td>74.87</td><td>81.39</td><td>62.57</td><td>85.71</td><td>66.94</td><td>83.93</td><td>83.28</td><td>76.33</td><td>69.44</td><td>81.70</td><td>71.42</td><td>81.81</td><td></td></tr><tr><td>MaxLogit</td><td>68.05</td><td>86.77</td><td>82.84</td><td>74.34</td><td>84.94</td><td>73.40</td><td>87.25</td><td>74.81</td><td>81.92</td><td>75.05</td><td>81.00</td><td>76.87</td><td></td></tr><tr><td>MaxLogit + Ours (ResNet-34)</td><td>71.69</td><td>83.47</td><td>63.74</td><td>87.26</td><td>65.69</td><td>86.54</td><td>81.74</td><td>78.46</td><td>66.88</td><td>86.44</td><td>69.95</td><td>84.43</td><td></td></tr><tr><td>MaxLogit + Ours (WRN-28)</td><td>73.84</td><td>82.61</td><td>54.30</td><td>89.11</td><td>60.29</td><td>87.26</td><td>83.62</td><td>77.06</td><td>64.12</td><td>84.98</td><td>67.23</td><td>84.20</td><td></td></tr><tr><td>Energy</td><td>68.38</td><td>86.94</td><td>82.38</td><td>74.64</td><td>84.21</td><td>73.67</td><td>88.03</td><td>74.62</td><td>81.40</td><td>75.25</td><td>80.88</td><td>77.02</td><td></td></tr><tr><td>Energy + Ours (ResNet-34)</td><td>69.20</td><td>84.14</td><td>58.83</td><td>88.05</td><td>61.10</td><td>87.37</td><td>81.68</td><td>78.51</td><td>62.89</td><td>87.18</td><td>66.74</td><td>85.05</td><td></td></tr><tr><td>Energy + Ours (WRN-28)</td><td>74.17</td><td>82.61</td><td>48.60</td><td>90.07</td><td>55.05</td><td>88.12</td><td>84.10</td><td>77.01</td><td>60.41</td><td>85.71</td><td>64.47</td><td>84.70</td><td></td></tr><tr><td>ReAct</td><td>65.68</td><td>88.14</td><td>86.44</td><td>69.18</td><td>86.97</td><td>69.09</td><td>83.44</td><td>80.13</td><td>83.80</td><td>71.59</td><td>81.27</td><td>75.63</td><td></td></tr><tr><td>ReAct + Ours (ResNet-34)</td><td>60.26</td><td>88.30</td><td>57.94</td><td>86.49</td><td>58.11</td><td>86.52</td><td>63.07</td><td>85.78</td><td>60.03</td><td>85.69</td><td>59.88</td><td>86.56</td><td></td></tr><tr><td>ReAct + Ours (WRN-28)</td><td>71.89</td><td>86.73</td><td>47.34</td><td>89.20</td><td>53.66</td><td>87.46</td><td>80.57</td><td>81.48</td><td>58.97</td><td>84.66</td><td>62.49</td><td>85.91</td><td></td></tr><tr><td>FeatureNorm</td><td>31.88</td><td>94.59</td><td>99.54</td><td>34.11</td><td>99.10</td><td>39.02</td><td>53.42</td><td>82.32</td><td>98.22</td><td>42.32</td><td>76.43</td><td>58.47</td><td></td></tr><tr><td>FeatureNorm + Ours (ResNet-34)</td><td>41.47</td><td>90.47</td><td>92.46</td><td>71.49</td><td>91.41</td><td>72.89</td><td>65.18</td><td>80.33</td><td>89.99</td><td>69.00</td><td>76.10</td><td>76.84</td><td></td></tr><tr><td>FeatureNorm + Ours (WRN-28)</td><td>54.17</td><td>89.08</td><td>80.86</td><td>79.52</td><td>80.69</td><td>79.91</td><td>71.49</td><td>74.37</td><td>78.00</td><td>80.74</td><td>73.04</td><td>80.72</td><td></td></tr></table>
+
+as CEDA, ACET, and CCUs, which employ specific techniques to suppress confidence scores during training, also significantly mitigate OOD overconfidence in DNNs. However, our approach, which does not incorporate specific confidence suppression measures, still outperforms these state-of-the-art methods, particularly in the more challenging CIFAR-100 scenario. This further highlights the robustness and effectiveness of our strategy.
+
+On CIFAR-10, while our base method may not show a pronounced advantage over others, combining our approach with confidence suppression techniques provides additional improvements, surpassing the performance of these state-of-the-art methods. These results reinforce the effectiveness of our approach in addressing OOD overconfidence.
+
+Visualization. We visualize the maximum confidence scores predicted by various DNN classifiers as histograms (logarithmic scale) in Fig. 6. As shown, applying OOD overconfidence mitigation solutions shifts the confidence distributions of the Baseline to the left, substantially reducing the number of samples with high confidence scores. Notably, our approach achieves the most pronounced shift, un
+
+derscoring its effectiveness and validating its superiority in mitigating OOD overconfidence.
+
+# 5.3. Results of Enhancing OOD Detection
+
+CIFAR Experiments. We evaluate the effectiveness of our approach in enhancing OOD detection. The results in Tab. 4 demonstrate that applying our method to existing OOD detection approaches leads to significant performance improvements. Even when directly applied to the classifier without any advanced post-hoc processing, i.e., MSP, the performance enhancement is still noticeable. These improvements are consistent across different student model configurations, datasets, and classifiers, validating the effectiveness of our approach in boosting OOD detection.
+
+ImageNet Experiments. We further validate the effectiveness of our approach in enhancing OOD detection on the ImageNet-1k dataset. The results in Tab. 5 indicate that, similar to the CIFAR experiments, applying our approach significantly improves OOD detection performance across methods, demonstrating the robustness and scalability of our approach in large-scale settings.
+
+Table 5. Comparison of OOD detection performance for various methods on the ImageNet-1k dataset.  
+
+<table><tr><td rowspan="3">Model</td><td rowspan="3">Method</td><td colspan="9">OOD</td><td rowspan="2" colspan="2">Average</td></tr><tr><td colspan="2">SUN</td><td colspan="2">Places</td><td colspan="2">Textures</td><td colspan="3">OpenImage-O</td></tr><tr><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td>FPR95↓</td><td>AUROC↑</td><td></td></tr><tr><td rowspan="10">DenseNet-201</td><td>MSP</td><td>65.76</td><td>82.24</td><td>69.53</td><td>81.14</td><td>67.82</td><td>79.36</td><td>64.92</td><td>84.47</td><td>67.01</td><td>81.80</td><td></td></tr><tr><td>MSP + Ours (DenseNet-161)</td><td>66.31</td><td>81.72</td><td>68.61</td><td>81.32</td><td>66.97</td><td>79.55</td><td>62.12</td><td>85.10</td><td>66.00</td><td>81.92</td><td></td></tr><tr><td>MaxLogit</td><td>55.44</td><td>86.06</td><td>61.89</td><td>83.99</td><td>58.48</td><td>83.45</td><td>59.64</td><td>86.94</td><td>58.86</td><td>85.11</td><td></td></tr><tr><td>MaxLogit + Ours (DenseNet-161)</td><td>55.33</td><td>87.67</td><td>59.95</td><td>86.26</td><td>55.80</td><td>85.84</td><td>60.03</td><td>88.60</td><td>57.78</td><td>87.09</td><td></td></tr><tr><td>Energy</td><td>52.87</td><td>86.04</td><td>60.46</td><td>83.71</td><td>56.13</td><td>83.35</td><td>59.87</td><td>86.65</td><td>57.33</td><td>84.94</td><td></td></tr><tr><td>Energy + Ours (DenseNet-161)</td><td>50.88</td><td>88.25</td><td>56.90</td><td>86.60</td><td>52.25</td><td>86.45</td><td>58.76</td><td>88.60</td><td>54.70</td><td>87.48</td><td></td></tr><tr><td>ReAct</td><td>46.00</td><td>90.81</td><td>57.46</td><td>86.11</td><td>55.14</td><td>84.19</td><td>69.32</td><td>74.43</td><td>56.98</td><td>83.89</td><td></td></tr><tr><td>ReAct + Ours (DenseNet-161)</td><td>49.21</td><td>88.55</td><td>55.02</td><td>86.94</td><td>50.99</td><td>86.75</td><td>57.61</td><td>88.64</td><td>53.21</td><td>87.72</td><td></td></tr><tr><td>FeatureNorm</td><td>43.06</td><td>90.05</td><td>55.71</td><td>85.42</td><td>50.46</td><td>79.90</td><td>79.97</td><td>67.22</td><td>57.30</td><td>80.65</td><td></td></tr><tr><td>FeatureNorm + Ours (DenseNet-161)</td><td>36.52</td><td>91.79</td><td>49.24</td><td>87.50</td><td>56.73</td><td>78.29</td><td>82.20</td><td>65.49</td><td>56.17</td><td>80.77</td><td></td></tr><tr><td rowspan="10">WRN-101</td><td>MSP</td><td>66.93</td><td>82.44</td><td>70.48</td><td>81.35</td><td>65.14</td><td>80.91</td><td>59.87</td><td>86.13</td><td>65.61</td><td>82.71</td><td></td></tr><tr><td>MSP + Ours (WRN-50)</td><td>67.75</td><td>82.80</td><td>69.07</td><td>81.81</td><td>66.38</td><td>80.96</td><td>60.91</td><td>86.78</td><td>66.03</td><td>83.09</td><td></td></tr><tr><td>MaxLogit</td><td>63.25</td><td>84.75</td><td>68.40</td><td>82.69</td><td>57.39</td><td>84.38</td><td>55.84</td><td>88.43</td><td>61.22</td><td>85.06</td><td></td></tr><tr><td>MaxLogit + Ours (WRN-50)</td><td>61.92</td><td>86.18</td><td>64.34</td><td>84.40</td><td>56.74</td><td>85.60</td><td>55.69</td><td>89.25</td><td>59.67</td><td>86.36</td><td></td></tr><tr><td>Energy</td><td>65.06</td><td>84.46</td><td>70.32</td><td>82.27</td><td>57.11</td><td>84.37</td><td>58.04</td><td>88.02</td><td>62.63</td><td>84.78</td><td></td></tr><tr><td>Energy + Ours (WRN-50)</td><td>63.18</td><td>85.96</td><td>66.06</td><td>84.00</td><td>55.90</td><td>85.68</td><td>57.87</td><td>88.77</td><td>60.75</td><td>86.10</td><td></td></tr><tr><td>ReAct</td><td>52.22</td><td>88.11</td><td>58.76</td><td>85.47</td><td>57.09</td><td>84.99</td><td>49.63</td><td>87.82</td><td>54.43</td><td>86.60</td><td></td></tr><tr><td>ReAct + Ours (WRN-50)</td><td>37.02</td><td>92.24</td><td>48.54</td><td>88.70</td><td>50.90</td><td>87.36</td><td>54.49</td><td>85.92</td><td>47.74</td><td>88.56</td><td></td></tr><tr><td>FeatureNorm</td><td>70.07</td><td>78.89</td><td>78.61</td><td>73.23</td><td>20.98</td><td>94.79</td><td>75.09</td><td>74.81</td><td>61.19</td><td>80.43</td><td></td></tr><tr><td>FeatureNorm + Ours (WRN-50)</td><td>60.22</td><td>83.67</td><td>74.01</td><td>75.96</td><td>17.71</td><td>96.09</td><td>69.94</td><td>78.90</td><td>55.47</td><td>83.66</td><td></td></tr></table>
+
+Table 6. Comparison of MMC and OOD detection performance for ResNet-50 enhanced by Ours (ResNet-18) and its variants w/o knowledge distillation (KD) and ReLU removal (RR), using CIFAR-10 as the ID dataset, and SVHN, LSUN-R, iSUN, Textures, and TINR as the OOD datasets. Results are averaged.  
+
+<table><tr><td>KD</td><td>RR</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td></td><td></td><td>79.58</td><td>54.23</td><td>91.78</td></tr><tr><td>✓</td><td></td><td>76.81</td><td>49.81</td><td>92.42</td></tr><tr><td></td><td>✓</td><td>78.46</td><td>50.50</td><td>91.76</td></tr><tr><td>✓</td><td>✓</td><td>76.48</td><td>48.89</td><td>92.59</td></tr></table>
+
+# 5.4. Ablation Studies and More Analysis
+
+Importance of Knowledge Distillation and ReLU Removal. We conduct comprehensive ablation studies to evaluate the impact of knowledge distillation and ReLU removal, the two essential components of our approach. As shown in Tab. 6, excluding either component notably diminishes the effectiveness of our method in mitigating OOD overconfidence and complicates the accuracy of OOD detection. These findings validate the critical importance of both knowledge distillation and selective ReLU removal in achieving optimal performance with our approach.
+
+Knowledge Distillation vs. Network Pruning for Capacity Reduction. We further investigate an alternative capacity reduction method for our approach by applying network pruning. To facilitate a fair comparison with knowledge distillation, we evaluate ResNet-50 and ResNet-101 models trained on CIFAR-10, applying two strategies: (1) using KD [22] to reduce ResNet-50 to ResNet-18 and ResNet-101 to WRN-28, and (2) applying Prune [14] to ResNet-50 and ResNet-101, reducing them to parameter counts comparable to ResNet-18 and WRN-28, respectively. The re
+
+Table 7. Comparison of MMC and OOD detection performance for ResNet-50 and ResNet-101 reduced to comparable parameter counts via KD [22] and Prune [14]. CIFAR-10 serves as the ID dataset, with SVHN, LSUN-R, iSUN, Textures, and TINR as OOD datasets. Results are averaged across all five OOD datasets  
+
+<table><tr><td>Model</td><td>Capacity Reduction</td><td>MMC↓</td><td>FPR95↓</td><td>AUROC↑</td></tr><tr><td rowspan="3">ResNet-50</td><td>—</td><td>79.58</td><td>54.23</td><td>91.78</td></tr><tr><td>Prune</td><td>77.34</td><td>52.55</td><td>92.27</td></tr><tr><td>KD (ResNet-18)</td><td>76.81</td><td>49.81</td><td>92.42</td></tr><tr><td rowspan="3">ResNet-101</td><td>—</td><td>83.46</td><td>51.92</td><td>92.53</td></tr><tr><td>Prune</td><td>78.20</td><td>50.92</td><td>91.61</td></tr><tr><td>KD (WRN-28)</td><td>77.01</td><td>41.09</td><td>92.56</td></tr></table>
+
+sults in Tab. 7 show that both methods effectively reduce OOD overconfidence and improve OOD detection; however, knowledge distillation consistently delivers a more substantial improvement than network pruning. Additionally, knowledge distillation offers greater stability and flexibility during training, making it a more suitable choice for capacity reduction in our approach.
+
+# 6. Conclusion and Future Work
+
+This paper has presented a comprehensive investigation into mitigating OOD overconfidence in DNNs through model simplification. By reducing model capacity via knowledge distillation and decreasing nonlinearity through selective ReLU removal, we demonstrate that OOD overconfidence in DNN classifiers can be significantly mitigated. Furthermore, these strategies can be effectively combined with OOD detection methods to enhance overall performance. In future work, we plan to study the effects of model simplification on OOD overconfidence in greater depth and from a theoretical perspective.
+
+# Acknowledgements
+
+We sincerely thank the anonymous reviewers for their valuable comments. This work was supported in part by the National Natural Science Foundation of China (62472117, U2436208, 62406095), the Guangdong Basic and Applied Basic Research Foundation (2025A1515010157, 2024A1515012064), the Science and Technology Projects in Guangzhou (2025A03J0137, SL2022A04J01112), and the Academician Bixing Fang's Specialized Class.
+
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+        "text": "Simulator HC: Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision",
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+        "text": "Xinyue Zhang",
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+        "text": "Wanting  $\\mathbf{X}\\mathbf{u}^{1}$",
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+        "text": "Laurent Kneip<sup>1</sup>",
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+        "text": "$^{1}$ Mobile Perception Lab, ShanghaiTech University, China",
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to intractability. In recent years, homotopy continuation has been introduced as a plausible alternative. However, the method currently depends on expensive parallel tracking of all possible solutions in the complex domain, or a classification network for starting problem-solution pairs trained over a limited set of real-world examples. Our innovation lies in a novel approach to finding solution-problem pairs, where we only need to predict a rough initial solution, with the corresponding problem generated by an online simulator. Subsequently, homotopy continuation is applied to track that single solution back to the original problem. We apply this elegant combination to generalized camera resection, and also introduce a new solution to the challenging generalized relative pose and scale problem. As demonstrated, the proposed method successfully compensates the raw error committed by the regressor alone, and leads to state-of-the-art efficiency and success rates.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
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+    {
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+        "text": "The solution of geometric camera calibration problems is a crucial step in many Structure-from-Motion (SfM) [21, 52, 54, 55], Visual Odometry (VO) [46], and visual Simultaneous Localization And Mapping (SLAM) [43] frameworks. Solvers developed over the years address camera resectioning [23, 29, 31, 65], two-view relative pose [30, 44, 58], pose estimation from lines [15, 41], partially calibrated cameras [64], generalized cameras [31, 41, 57, 60], rolling shutter cameras [10, 51], and many other scenarios. The problems often appear in the form of a polynomial equation system, and special techniques from the field of algebraic geometry have been used to solve them. Once an efficient solver is found, it is typically embedded into a random sampling and consensus scheme [19, 48] in order to gain robust",
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+    {
+        "type": "text",
+        "text": "ness in the presence of outliers. Hence, there is a requirement for such solvers to be efficient and embeddable into iterative schemes.",
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+    {
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+        "text": "The dominant approaches to efficiently solve systems of polynomial equations are given by the Gröbner basis method and polynomial resultants [9, 59]. Based on the Gröbner basis theory, Stewénius et al. [58] and Kukelova et al. [33] demonstrate that the calculations required to obtain a minimal set of ideal generators can be effectuated efficiently at the hand of a fixed elimination template. Kukelova et al. [33] in particular propose a solver generator to automatically discover such elimination templates. Later on, sparse resultant-based solvers [16] have been demonstrated as a powerful alternative sometimes leading to smaller elimination templates.",
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+        "text": "While polynomial elimination techniques have led to significant progress in the solution of geometric vision problems, the methods are limited as the complexity of the template search grows uncontrollably with the degree and dimensionality of the problem at hand. Furthermore, owing to their failure to respect inequality constraints and rule out practically infeasible solutions, high degrees or dimensionalities naturally lead to an elevated number of algebraically possible solutions and—assuming that it can be found at all—large elimination templates [13, 14, 45, 63–65]. This in turn causes problems in terms of numerical stability [63]. In recent years, a different solution strategy has therefore gained popularity: Homotopy Continuation (HC) [4, 12, 61]. The method proceeds by starting from a known problem-solution pair, and then tracks its roots to the target problem at hand during a step-wise interpolation of polynomial coefficients. The method has been used to successfully solve challenging tri-focal relative pose problems [17]. While promising, HC remains expensive as it generally requires the parallel continuation of many roots in the complex domain in order to identify all real solutions to a target problem, followed up by disambiguation.",
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+        "type": "text",
+        "text": "Recently, Hruby et al. [25] propose an efficient, learning-based extension to the pure HC paradigm, which serves as",
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "27103",
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+    {
+        "type": "text",
+        "text": "our primary motivation. They propose the introduction of a classifier to pick a good problem-solution pair trained over a large set of known pairs obtained from SfM. This enables a highly efficient application of HC, as only a single root of interest needs to be continued. While still presenting a margin for improvement in terms of success rate, the method is demonstrated to have unprecedented computational efficiency on the challenging three-view-four-point problem.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The method proposed in this work is similar to the work of Hruby et al. [25] in that it leverages a learning-based approach to produce a starting problem-solution pair that enables single-root-tracking. However, we note a couple of important differences:",
+        "bbox": [
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+            "- We do not train a classifier on a fixed set of problem-solution pairs taken from a real-world dataset. Instead, we propose to employ a solution regression network trained over an arbitrarily large set of simulated input correspondences for the considered geometric problem. The network is hence not limited by a finite set of candidate problems, and aims at being a general solution approximator for any instance of the polynomial problem. What's more, learning a solution is much easier than learning a proper problem-solution pair.",
+            "- The bridge to HC is formed by appending an online simulator that uses the input correspondences and the predicted solution to generate a complete, consistent problem-solution pair. Given only moderate regression accuracy, the produced problem-solution pair is sufficiently close to the original problem for successful single-root tracking via HC.",
+            "- We argue that the prediction of a single solution (or the unambiguous classification of a single problem-solution pair) from a minimal set may not always be possible as for complicated geometric problems, there may indeed be multiple geometrically feasible solutions. We therefore add one additional correspondence, which leads to a performance gain during both the regression and the continuation stage."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The newly proposed simulate-and-solve paradigm is summarized in Figure 1. We demonstrate that this strategy can lead to high success-rate and efficient CPU-based solvers for two problems: generalized camera resection, and generalized relative pose and scale. Owing to its challenging nature, the latter problem has thus far only seen an optimization-based solution [32]. The solvers are compared against a purely learning-based alternative, a regressor followed by simple local refinement, as well as the exhaustive application of homotopy continuation over all roots. The proposed method is efficient, generalizable, and highly successful, and should thus be considered as an interesting alternative for the ongoing development of complicated geometric problem solvers.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Literature Review",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Polynomial elimination theory: Our contribution can be regarded as a novel alternative to traditional polynomial elimination theory [9, 59]. Stewenius et al. [58] manually derive one of the first Gröbner basis solvers in the field of computer vision. Automatic solver generators and important extensions improving performance and numerical accuracy are later introduced by Kukelova et al. [33] and Larsson et al. [34, 35, 37, 38]. Zheng and Kneip propose the use of the parametric Sylvester resultant [64], while Hesch and Roumeliotis make use of the Macaulay resultant [23]. The more general use of sparse resultants as a powerful alternative to the Gröbner basis method is analyzed by Emiris [16], Heikkilä [22], and—most recently—Bhayani et al. [5]. While having lead to significant progress, complicated geometric problems with as many as 64 [57], 272 [45], 81 [65] (before symmetry-removal), 210 [64],  $>10000$  [13, 14], and 512 [63] solutions remain hard or impossible to be solved by polynomial elimination. The latter work, in particular, presents one of the largest successful elimination templates in the literature ( $96413 \\times 96879$ ) by making use of octuple machine precision. Recently Evgenity et al. [40] developed a new method to reduce the size of the elimination template. Yet, for a polynomial system, a large number of solutions in practice still leads to reduced computational efficiency.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Homotopy continuation: Homotopy continuation implementations exist as independent programs [61] or as part of Macaulay2 [39], Bertini [4], and Julia [6]. Duff et al. [12] study the application of the method to geometric vision problems, and several related studies focus specifically on the tri-focal relative pose problem [2, 20, 24, 27, 47]. However, off-the-shelf implementations are often too general and not optimized for real-time applications. Progress is recently achieved by Fabbri et al. [17], who propose an efficient custom  $\\mathrm{C + + }$  implementation of the Macaulay2 solver [39] for a tri-focal relative pose problem. More recently, Ding et al. [11] propose a fast GPU-based implementation of homotopy continuation [7, 8] for a minimal solution to the three-view-four-point problem which has the same performance as Julia [6] but is significantly faster. The method leverages massive parallelization to efficiently track all solutions of a small, fixed set of starting problem-solution pairs. Our contribution can be regarded as a problem-solution pair initialization scheme similar to Hruby et al. [25] for successful single solution tracking.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Learning for polynomial problem solving: One of the first methods to successfully employ learning in polynomial solvers is presented by Xu et al. [62], who proposed to increase the numerical accuracy of polynomial elimination templates by learning the best permutation in permutation-invariant polynomial problems. Recently, Hruby et al. [25] propose the addition of a classifier for initial problem-",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "page_number",
+        "text": "27104",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "image",
+        "img_path": "images/b58d09d84c67abdaa48c10197923d8f9c25a0631bf30a7fa8b9ea55410f0fc1b.jpg",
+        "image_caption": [
+            "Figure 1. Overview of the proposed geometric problem solution scheme. Given input correspondences, a regression network is utilized to approximate a solution. A subsequent online simulator generates a new set of correspondences that is consistent with the regression output. The obtained problem-solution pair is finally used to bootstrap homotopy continuation. The final solution is found efficiently by tracking a single root."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/64d65d11bb933751be00e4ce3a349d00fa86c3601e492f430ed260a303b9fe92.jpg",
+        "image_caption": [
+            "(a) HC multiple solution curves"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/bdbe15f1c825887877d15210209f0c4a797e9486a1dfd5898d384d072adf9f77.jpg",
+        "image_caption": [
+            "(b) HC solution tacking",
+            "Figure 2. Graphical illustration on homotopy continuation(HC) solution curves tracking. For a polynomial system with multiple solutions, each solution curve can be tracked independently as shown in Figure 2a. For each solution curve tracking, HC utilizes a \"prediction-correction\" scheme to approximate one of the solutions for the target system."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "solution pair picking in homotopy continuation. In recent years, several works have proposed to directly apply neural networks to regress the pose of a camera, either directly from images [26, 49] or—aiming at replacing traditional algebraic-geometric solvers—from correspondence coordinates [53]. While such networks use algorithm unrolling [42] and differential optimization [3] for accurate end-to-end trainability, a successful application to more complicated problems remains yet to be demonstrated. Regressors can be regarded as general non-linear function approximators, and the challenge of using them to produce highly accurate solutions is easily explained by the potential discontinuity of root locations for continuous variations of input polynomial coefficients. Our contribution can be regarded as a new post-regression refinement scheme for polynomial problems enabling successful application to complicated problems for which it is hard to apply traditional polynomial solvers.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3. Polynomial Solver: Homotopy Continuation",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We start with a brief summary of HC. We refer to an instance of a certain polynomial system with specific coefficients as a problem. HC is a powerful tool that can numerically find the solutions of a problem. Each solution is found by tracking a curve independently, as illustrated in",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 2a. When tracking the solution curves, the method solves a series of problems of similar form. It starts from a trivial problem whose solutions are simply known, and then gradually deforms that problem to the target problem that we are interested in but for which we do not know the solutions. It is hoped that—by continuing the known solutions throughout the problem sequence—they can lead to the solutions of the target, input problem. Two questions arise: 1) How to track the solution curves?, and 2) What is a good starting problem leading to the solutions we desire?",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The answer to the first question is given by HC. Formally, suppose we have a polynomial system  $\\mathbf{F}(\\mathbf{x}) = \\mathbf{0}$  and we are interested in its solutions. Suppose further that we have a polynomial system of similar form  $\\mathbf{G}(\\mathbf{x}) = \\mathbf{0}$  whose solutions are known. HC solves a series of polynomial systems of the form",
+        "bbox": [
+            496,
+            458,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {H} (\\mathbf {x}, t) = (1 - t) \\mathbf {G} (\\mathbf {x}) + t \\mathbf {F} (\\mathbf {x}), \\quad t \\in [ 0, 1 ]. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            540,
+            558,
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+            575
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Figure 2b, each  $\\mathbf{H}(\\mathbf{x},t) = \\mathbf{0}$  is solved while sliding  $t$  from 0 to 1. For  $t = 0$ , the solution is known as  $\\mathbf{H}(\\mathbf{x},0) = \\mathbf{G}(\\mathbf{x})$ . A solution of  $\\mathbf{F}(\\mathbf{x}) = \\mathbf{0}$  is finally obtained as for  $t = 1$ ,  $\\mathbf{H}(\\mathbf{x},1) = \\mathbf{F}(\\mathbf{x})$ . The problems are not actually solved but the solutions are simply tracked from problem to problem. Taking the partial derivative to both sides of  $\\mathbf{H}(\\mathbf{x},t)$ , the solution curve  $\\mathbf{x}(t)$  can be formulated as the following ordinary differential equation",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {J} _ {\\mathbf {H}} (\\mathbf {x}) \\frac {\\partial \\mathbf {x}}{\\partial t} + \\frac {\\partial \\mathbf {H} (\\mathbf {x} , t)}{\\partial t} = \\mathbf {0} \\Longleftrightarrow \\frac {\\partial \\mathbf {x}}{\\partial t} = - \\mathbf {J} _ {\\mathbf {H}} (\\mathbf {x}) ^ {\\dagger} \\frac {\\partial \\mathbf {H} (\\mathbf {x} , t)}{\\partial t}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A \"prediction-correction\" scheme—as widely utilized in numerical analysis—is typically employed to trace the solution curve  $\\mathbf{x}(t)$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Prediction. Denote the stepsize of  $t$  as  $\\delta t$ . Euler's predictor can be used to update along the tangent direction",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {i + 1} = \\mathbf {x} _ {i} + \\delta t \\frac {\\partial \\mathbf {x}}{\\partial t} \\bigg | _ {\\mathbf {x} _ {i}, t _ {i}}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Practically speaking, a higher-order generalized method is",
+        "bbox": [
+            500,
+            885,
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+            901
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "27105",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "commonly used for better accuracy and stability with larger stepsize.",
+        "bbox": [
+            75,
+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Correction. Gauss-Newton steps are adopted to correct the prediction. In each iteration of Gauss-Newton's method, the solution is updated by",
+        "bbox": [
+            75,
+            126,
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+            172
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {j} = \\mathbf {x} _ {j - 1} - \\mathbf {J} _ {\\mathbf {H}} \\left(\\mathbf {x} _ {j - 1}\\right) ^ {\\dagger} \\mathbf {H} \\left(\\mathbf {x} _ {j - 1}, t\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            145,
+            193,
+            468,
+            212
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{J}_{\\mathbf{H}}^{\\dagger}$  is the pseudo inverse of the jacobian  $\\mathbf{J}_{\\mathbf{H}}$ , and  $t = t_i + \\delta t$ . Figure 2b illustrates a 1D solution curve tracking, where the blue arrow represents the prediction update and the red arrow represents the correction update.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The remainder of this paper—our key contribution��addresses the second question of how to find a good starting system. Traditional methods (e.g. Ab initial [17], monodromy [6, 12]) rely on algebraic geometry theories developed for coefficient-parameter homotopies, and tracking all roots from a small set of fixed, known problem-solution pairs in the complex domain may often enable a solution [56]. However, tracking all the isolated paths is expensive and in practice multiple solutions cost more time to select the best. A recent study proposes the use of a classifier to pick a good starting pair with as high as possible success probability upon tracking only a single root [25], which is much faster. Similarly, in this work, we propose a novel geometry-informed strategy that combines a neural regressor with an online simulator to produce a problem-solution pair and then track a single root by HC. Even on challenging problems for which no traditional solver has been found, it can find the solution with a success rate of over  $95\\%$ .",
+        "bbox": [
+            75,
+            301,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Remark (Homotopy Types). Since being introduced in 1980s, a variety of homotopies have been developed to serve the same purpose: how to solve the problem exactly as expected. The representative one would be coefficient-parameter homotopy. Its formulation provides the insight that if we can find all the solutions to a general coefficient-parameter polynomial, then we can find all the other members of that polynomial family. In fact, as pointed out in [56], in engineering problems (e.g. geometry vision problems) we are dealing with natural coefficient-parameter polynomials, that is coefficients of polynomials derived from visual features. Since the scope of this paper lies on a novel starting problem-solution pair finding and it is not highly dependent on the path tracking, we kindly refer the reader to [56] for an in-depth discussion of other homotopy types. As shown in the later applications, straight segment homotopies provide near-perfect success rates when working with our simulator. We also want to note that all the other homotopy types could be equally applied in conjunction with our simulator.",
+        "bbox": [
+            75,
+            598,
+            470,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Find a Good Starting Solution: Regression Network",
+        "text_level": 1,
+        "bbox": [
+            500,
+            89,
+            890,
+            122
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Following recent developments in deep learning, multiple attempts have been made to, for example, learn camera pose using a neural network [26, 49, 53]. The first two methods extract features from images and points and use them in a regression network to predict the pose. The third method is a more preliminary approach and aims at predicting pose directly from geometric correspondences, which is also the aim of the present work. The bottleneck in regressing pose from correspondences arises from two concerns: 1) For simple geometric problems, we often have traditional methods that are efficient and accurate, and 2) For hard geometric problems, regression networks demonstrate a poor ability to predict accurate solutions. Our key insight is that while the predicted pose may not be sufficiently accurate, it can still serve as a good starting solution for HC.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our pose regression networks are designed with multiple 1D convolutional layers and each layer is followed by batch normalization and ReLU activations. The loss function is given by a combination of relative pose errors with learnable weights [26].",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "5. Find a Consistent Starting Problem: Online Simulator",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We recall the main idea of HC. In order to continue a solution to the target problem, an appropriate starting problem with a known solution is required. Given the approximate solution predicted by the pose regression network, our goal is to derive a consistent polynomial system for which one of the solutions matches the predicted one. We denote this step an online simulator, and—though problem specific—effective realizations can almost always be found by simple geometric rules. For example, in camera resectioning, one can simply use the input 3D points and reproject them into a camera view under the predicted pose. This will lead to new 2D points, and thus a new set of correspondences that is perfectly consistent with the predicted solution, i.e. our sought starting problem-solution pair. While not yet made use of in the present work, it is worthwhile noting that—owing to their algebraic simplicity—such an online simulator often appears to be a differentiable module.",
+        "bbox": [
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+            494,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "6. Generalized Perspective-n-Points",
+        "text_level": 1,
+        "bbox": [
+            498,
+            768,
+            802,
+            786
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our first concrete, practical application targets generalized camera pose estimation from 2D-3D correspondences. We use the Unified Perspective-n-Point (UPnP) algorithm [31] which formulates a polynomial system corresponding to the first-order optimality conditions of the sum of squared object space distances. The method can be used to solve both central and non-central camera resectioning problems from",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "27106",
+        "bbox": [
+            478,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/3a96df52960666700862ffecdc5039b230a9d1c53e40b69a24c2f285efa06d4f.jpg",
+        "image_caption": [
+            "(a) Generalized Absolute Pose"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            89,
+            254,
+            186
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1288a391fc920f245307f7bfeb8287a9244de2ba1a51b68bec847baa32e9fdd9.jpg",
+        "image_caption": [
+            "(b) Generalized Relative Pose and Scale",
+            "Figure 3. The geometry of the generalized camera problems we propose to solve by online simulator HC.  $w$  represents the world frame, and  $c$  and  $c'$  represent camera frames in different views respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            186
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "an arbitrary number of points (including minimal). It can be efficiently solved by the Gröbner Bases method since—after variable elimination—it only involves 4 unknowns. In this section, we solve UPnP by our newly proposed method and compare it against conventional approaches, a raw regression network, as well as a parallel HC implementation tracking all roots.",
+        "bbox": [
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+            282,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "6.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            396,
+            279,
+            410
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Consider a 3D-2D generalized correspondence  $(\\mathbf{p}_i, \\mathbf{f}_i, \\mathbf{v}_i)$  originating from the non-central camera resectioning model illustrated in Figure 3a, where  $\\mathbf{p}_i \\in \\mathbb{R}^3$ ,  $\\mathbf{f}_i \\in \\mathbb{S}^2$  and  $\\mathbf{v}_i \\in \\mathbb{R}^3$  denote the 3D world point, image ray and ray origin, respectively. The correspondence follows an underlying generalized absolute pose transformation depending on the rotation  $\\mathbf{R} \\in SO(3)$ , the position  $\\mathbf{t} \\in \\mathbb{R}^3$  and an unknown latent depth  $\\alpha_i$  as follows:",
+        "bbox": [
+            75,
+            417,
+            468,
+            540
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i} \\mathbf {f} _ {i} + \\mathbf {v} _ {i} = \\mathbf {R p} _ {i} + \\mathbf {t}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            196,
+            547,
+            468,
+            564
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\mathbf{M} \\in \\mathbb{R}^{11 \\times 11}$  denote a coefficient matrix that embeds all known variables (point measurements and ray offsets),  $\\mathbf{q} = [q_0, q_1, q_2, q_3]^\\top$  denote the quaternion representation of  $\\mathbf{R}$ , and  $\\mathbf{s} \\in \\mathbb{R}^{11}$  denote a vector whose elements are all second and zeroth order monomials of the quaternion variables. After translation and depth elimination,  $\\mathbf{q}$  can be constrained by first-order optimality conditions appearing in the form of the polynomial system<sup>1</sup>",
+        "bbox": [
+            75,
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+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{ \\begin{array}{l l} \\mathbf {s} ^ {\\top} \\mathbf {M} \\frac {\\partial \\mathbf {s}}{\\partial q _ {i}} & = 0, \\quad i = 0, \\dots , 3 \\\\ \\mathbf {q} ^ {\\top} \\mathbf {q} - 1 & = 0. \\end{array} \\right. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            161,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "6.2. Regressor and online simulator",
+        "text_level": 1,
+        "bbox": [
+            76,
+            736,
+            352,
+            750
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To provide a proper problem-solution pair for HC, we train a pose regression network from synthetic data. Its input is given by row-wise stacking of the correspondences, i.e.",
+        "bbox": [
+            75,
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+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ \\begin{array}{c c c} \\mathbf {p} _ {1} ^ {\\top} & \\mathbf {f} _ {1} ^ {\\top} & \\mathbf {v} _ {1} ^ {\\top} \\\\ \\vdots & \\vdots & \\vdots \\\\ \\mathbf {p} _ {N} ^ {\\top} & \\mathbf {f} _ {N} ^ {\\top} & \\mathbf {v} _ {N} ^ {\\top} \\end{array} \\right], \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Online Simulator HC for generalized PnP",
+        "text_level": 1,
+        "bbox": [
+            501,
+            104,
+            864,
+            119
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1: Input: correspondences  $(\\mathbf{p}_i,\\mathbf{f}_i,\\mathbf{v}_i)_{i = 1}^M$  , stepsize  $\\delta t$",
+            "2: Output: poses  $\\hat{\\mathbf{R}},\\hat{\\mathbf{t}}$",
+            "3:  $\\tilde{\\mathbf{R}},\\tilde{\\mathbf{t}}\\gets$  Trained Regression Network((pi,fi,v)M)",
+            "4:  $(\\hat{\\mathbf{f}}_i)_{i=1}^M \\leftarrow$  Reprojection  $(\\hat{\\mathbf{R}}, \\hat{\\mathbf{t}}; (\\mathbf{p}_i, \\mathbf{v}_i)_{i=1}^M)$ $\\triangleright$  Online Simulator",
+            "5: Starting problem  $\\mathbf{G}(\\mathbf{x})\\gets (\\mathbf{p}_i,\\hat{\\mathbf{f}}_i,\\mathbf{v}_i)_{i = 1}^M$  with solution  $\\hat{\\mathbf{R}},\\hat{\\mathbf{t}}$",
+            "6: Target problem  $\\mathbf{F}(\\mathbf{x})\\gets (\\mathbf{p}_i,\\mathbf{f}_i,\\mathbf{v}_i)_{i = 1}^M$",
+            "7:  $\\mathbf{q}_{HC} \\gets$  Homotopy Continuation  $t\\mathbf{F}(\\mathbf{x}) + (1 - t)\\mathbf{G}(\\mathbf{x})$",
+            "8:  $\\bar{\\mathbf{R}},\\hat{\\mathbf{t}}\\gets$  decompose  $\\mathbf{q}_{HC}$"
+        ],
+        "bbox": [
+            506,
+            126,
+            890,
+            233
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $N$  is the number of correspondences used, and the output is the quaternion vector. The network consists of 4 1D convolutional layers and a fully connected layer at the end to convert the output to a quaternion vector with the unit norm. Given the rotation predicted by the network, the translation can be recovered from correspondences and estimated rotation. We refer the reader to [31] for the details. For the online simulator, we can get reprojected  $\\hat{\\mathbf{f}}_i$  from (5). Algorithm 1 summarizes all stages, including the final HC over (6). Note that in line 5 of Algorithm 1, the starting problem  $\\mathbf{G}(\\mathbf{x})$  is constructed by replacing the coefficient matrix  $\\mathbf{M}$  computed by  $(\\mathbf{p}_i,\\mathbf{f}_i,\\mathbf{v}_i)$  in (6) with  $\\hat{\\mathbf{M}}$  computed by  $(\\mathbf{p}_i,\\hat{\\mathbf{f}}_i,\\mathbf{v}_i)$ .",
+        "bbox": [
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+            255,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "6.3. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            464,
+            633,
+            479
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Data. We randomly generate 4 cameras in a cube  $[-1,1]^3$  and randomly sample 16 3D points in the box  $[-1,1]^2 \\times [4,8]$ . 16 samples would not be a good choice for a RANSAC solver [18], but in the present context the idea is to set a moderate and notably equal challenge to all compared solvers. Furthermore, for UPnP the number of constraints appearing in the polynomial system remains unchanged as it analyses first-order optimality rather than individual incidence relations. Elements of the rotation angles are randomly generated in the interval  $[- \\pi /2, \\pi /2]$ , respectively, and the translation is randomly generated in the unit cube. We then generate the correspondences from rays that point to a 3D point. The noise level is set to 2 pixels. To train the pose regression network, we simulate a dataset of 2400 samples, which is sufficient for reliable Simulator HC initialization. We use a 2.70GHz Intel(R) Xeon(R) CPU and an NVIDIA GeForce RTX 4090 for network training and evaluation.",
+        "bbox": [
+            496,
+            487,
+            890,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Methods. For HC, the stepsize  $\\delta t$  and the maximum number of iterations of Newton's method are set to 0.02 and 5, respectively. We compare the Gröbner Bases solver [31] and the popular local method Levenberg-Marquardt (LM) [1]. We also test the state-of-the-art parallel HC solver developed by [7, 8], and use both its CPU and  $\\mathrm{GPU}^2$  version. Given that parallel HC tracks all solutions,",
+        "bbox": [
+            496,
+            758,
+            890,
+            864
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>We kindly refer the reader to the UPnP paper for detailed derivations [31].",
+        "bbox": [
+            75,
+            875,
+            468,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "2Note that GPU warmup overhead is ignored when averaging over multiple runs.",
+        "bbox": [
+            500,
+            875,
+            888,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "27107",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/60782c54be04b24b9ebfd90ca87518a28bd2b337f6cc66f93d7ad26d154fa750.jpg",
+        "table_caption": [
+            "Table 1. Performance comparison of simulator HC, a traditional method, and parallel exhaustive tracking HC on noisy synthetic data. All results are averaged over 1000 trials. The success rate is computed for rotation errors with a threshold of 2 degree."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Succ. (%)</td><td>ER(deg)</td><td>Et(%)</td><td>Time(ms)</td></tr><tr><td>Gröbner Bases</td><td>100</td><td>0.031</td><td>0.489</td><td>1.254</td></tr><tr><td>CPU HC</td><td>100</td><td>0.032</td><td>0.499</td><td>9.796</td></tr><tr><td>GPU HC</td><td>100</td><td>0.032</td><td>0.499</td><td>1.002</td></tr><tr><td>Pred Initial</td><td>32</td><td>7.204</td><td>32</td><td>0.031</td></tr><tr><td>Pred Initial + LM</td><td>54</td><td>28.72</td><td>2256</td><td>0.528</td></tr><tr><td>Rand Initial + Simulator HC</td><td>22</td><td>91.68</td><td>228</td><td>0.231</td></tr><tr><td>Pred Initial + Simulator HC</td><td>100</td><td>0.032</td><td>0.513</td><td>0.316</td></tr></table>",
+        "bbox": [
+            76,
+            156,
+            475,
+            268
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "we manually pick the one with the smallest error.",
+        "bbox": [
+            76,
+            280,
+            403,
+            294
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results. The rotation error is measured by  $\\mathcal{E}_{\\mathbf{R}} = 2\\arcsin (\\| \\hat{\\mathbf{R}} -\\mathbf{R}_{gt}\\| /(2\\sqrt{2}))$  in degrees as suggested by [11] and the translation error is measured by the  $\\mathcal{E}_{\\mathrm{t}} = \\| \\hat{\\mathbf{t}} -\\mathbf{t}_{gt}\\| /\\| \\mathbf{t}_{gt}\\| \\times 100$  in percentage. Table 1 compares the traditional method, parallel exhaustive tracking HC, and different types of initial solutions for our simulator HC. We present the success rate as the percentage of rotation errors smaller than 2 degrees. It can be observed that on this simple task, except for the local method, traditional methods, as well as simulator HC using predicted initials, succeed in  $100\\%$  of trials. Meanwhile, online simulator HC benefits from the single-track strategy and turns out to be the fastest one. We also perform an ablation study on the proposed simulator HC, using both predicted and random initializations. Although the pose learned by the regressor is not highly accurate and only slightly outperforms random poses, it serves as a reasonable starting solution for our simulator HC. In contrast, LM as a local method is unable to leverage the potential of the predicted initializations, as the simulator HC does.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "7. Generalized Relative Pose and Scale",
+        "text_level": 1,
+        "bbox": [
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+            617,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our final application targets a hard minimal problem: Generalized Relative Pose and Scale (GRPS) estimation from 2D-2D correspondences [32]. The GRPS problem is a natural extension of the generalized relative pose problem and arises in point-less registration of partial view-graphs in structure-from-motion. Owing to the fact that SfM results are generally up to scale, an inherent scale factor needs to be resolved. Such problem was first introduced by Kneip et al. [32]. It has 140 solutions if a unique rotation representation is used, and can be solved by multi-start optimization to overcome local minima. Later on, a traditional polynomial solver based on the Gröbner Bases method has been proposed [36, 40]. With a  $144 \\times 284$  elimination template, the solver finds all 140 rotations within reasonable time. In this section, we solve GRPS by our proposed method and compare it against the existing approach, as well as a parallel HC implementation tracking all roots.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "7.1. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Consider a 2D-2D generalized correspondence  $(\\mathbf{f}_i,\\mathbf{v}_i) - (\\mathbf{f}_i',\\mathbf{v}_i')$  observed from two non-central camera views as illustrated in Figure 3b.  $\\mathbf{f}_i\\in \\mathbb{S}^2,\\mathbf{v}_i\\in \\mathbb{R}^3$  denote the image ray and ray origin in the first view, and  $\\mathbf{f}_i'\\in \\mathbb{S}^2,\\mathbf{v}_i'\\in \\mathbb{R}^3$  are the corresponding entities in the second view. The correspondence follows an underlying generalized relative pose and scale incidence relation depending on the rotation  $\\mathbf{R}\\in SO(3)$ , the position  $\\mathbf{t}\\in \\mathbb{R}^3$ , the scale  $s$ , and unknown latent depths  $\\alpha_{i}$  and  $\\alpha_{i}'$  as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha_ {i} \\mathbf {f} _ {i} + \\mathbf {v} _ {i} = \\mathbf {R} \\left(\\alpha_ {i} ^ {\\prime} \\mathbf {f} _ {i} ^ {\\prime} + s \\mathbf {v} _ {i} ^ {\\prime}\\right) + \\mathbf {t}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "With the help of Plücker coordinates and the scalar triple product  $^3$ , the unknown depths get eliminated which results in a polynomial constraint that only involves the unknown poses",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {t} ^ {\\top} \\left(\\mathbf {f} _ {i} \\times \\mathbf {R} \\mathbf {f} _ {i} ^ {\\prime}\\right) - s \\mathbf {f} _ {i} ^ {\\top} \\mathbf {R} \\left[ \\mathbf {v} _ {i} ^ {\\prime} \\right] _ {\\times} \\mathbf {f} _ {i} ^ {\\prime} + \\mathbf {f} _ {i} ^ {\\top} \\left[ \\mathbf {v} _ {i} \\right] _ {\\times} \\mathbf {R} \\mathbf {f} _ {i} ^ {\\prime} = 0. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Therefore, a minimal formulation for the GRPS problem can be devised by a polynomial system formed by stacking 7 constraints in the form (9), each one depending on one correspondence.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "7.2. Regressor and online simulator",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As introduced in section 6.2, we continue to use a pose regression network that inputs a matrix with row-wise stacked correspondences. The output is given by  $\\mathbf{R}$ ,  $\\mathbf{t}$ ,  $s$ . Note that the rotation is predicted in continuous 6D representation which is more suitable for neural networks [66]. The network consists of 11 1D convolutional layers, in the end, it branches to 3 sub-branches for  $\\mathbf{R}$ ,  $\\mathbf{t}$  and  $s$ . Each sub-branch consists of 2 1D convolutional layers and 1 fully connected layers for adjust output. Given the poses predicted by the network, we still need an estimation of the depths before simulating the reprojected image ray. With estimated  $\\hat{\\mathbf{R}}$ ,  $\\hat{\\mathbf{t}}$  and  $\\hat{s}$ , the corresponding depths can be obtained from (8) by following",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left[ \\mathbf {f} _ {i} - \\hat {\\mathbf {R}} \\mathbf {f} _ {i} ^ {\\prime} \\right] \\left[ \\begin{array}{l} \\alpha_ {i} \\\\ \\alpha_ {i} ^ {\\prime} \\end{array} \\right] = - \\left(\\mathbf {v} _ {i} - \\hat {s} \\hat {\\mathbf {R}} \\mathbf {v} _ {i} ^ {\\prime} - \\hat {\\mathbf {t}}\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "which can be simply solved by linear least squares for each input correspondence. Finally, we simulate a pose-consistent reprojected image ray in the first view using",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {\\mathbf {f}} _ {i} = \\frac {1}{\\hat {\\alpha} _ {i}} \\hat {\\mathbf {R}} \\left(\\hat {\\alpha} _ {i} ^ {\\prime} \\mathbf {f} _ {i} ^ {\\prime} + \\hat {s} \\mathbf {v} _ {i} ^ {\\prime}\\right) + \\hat {\\mathbf {t}} - \\mathbf {v} _ {i}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "7.3. Simulation Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            824,
+            723,
+            840
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Data. We adopt a similar data generation method as in section 6.3. We generate 7 3D points in a  $[-1,1]^2 \\times [2,20]$",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "3We kindly refer the reader to [28, 32] for detailed derivations",
+        "bbox": [
+            514,
+            886,
+            846,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "27108",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "volume. Two view frames are generated with origins picked from  $[-1, 1]^3$ . Within each view frame, we then sample individual camera offsets from the volume  $[-1, 1]^3$ . The scale is randomly generated in  $[0.1, 5.0]$ , and all other parameters related to noise addition are left unchanged. Note that the ground truth relative pose needs to be extracted from the simulated pair of view poses.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Methods. The stepsize for homotopy continuation is set to 0.05 in this scenario. We compare against the Eigen solver [32], Gröbner Bases solver [40] and the CPU and GPU versions of parallel HC which tracks 140 solutions found by Monodromy [6]. Note that to measure numerical errors, we just pick the best solution with the smallest error. In practice, traditional HC needs to evaluate additional information to select a single solution (e.g. euclidean distance). For a complicated problem like GRPS, evaluating 140 solutions would still induce non-neglectable time-consumption. Since GRPS is a hard problem, we train the regressor using a larger simulated dataset of size 64000.",
+        "bbox": [
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+            196,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Metric. We measure the rotation error in degrees and the relative translation as in Sec. 6.3 and scale error in percentage using",
+        "bbox": [
+            75,
+            378,
+            468,
+            422
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {E} _ {s} = \\left| \\hat {s} - s _ {g t} \\right| / s _ {g t} \\times 1 0 0. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            183,
+            422,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To calculate the success rate, for rotation errors the threshold is set to 2 deg, and for relative errors, it is set to  $5\\%$ .",
+        "bbox": [
+            75,
+            446,
+            468,
+            477
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Numerical Stability. We randomly generate 1000 trials to test the numerical stability of all solvers. During the analysis of the performance of simulator HC using the minimum number of correspondences, we observed that our method has around  $70\\%$  success rate. By checking the failure cases, we found that sometimes simulator HC tracked another real solution that was different from the ground truth pose. To tackle that issue, we evaluate the addition of one more correspondence and solve for an overdetermined polynomial system. By using 8 correspondences, simulator HC reaches a success rate of  $95\\%$ . Again, since CPU/GPU-HC is designed to handle square systems, only the minimum number of correspondences can be tested for other HC methods.",
+        "bbox": [
+            75,
+            478,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Since the errors in rotation, translation and scale have similar density results, we only present the rotation error in the main paper and the rest in the supplementary. As illustrated in Figure 4a, the minimal HC solvers all present similar error distribution and around  $75\\%$  of trials are successful. While Gröbner Bases shows  $100\\%$  success rate, Simulator HC over 8pts presents similar numerical errors.",
+        "bbox": [
+            75,
+            674,
+            468,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Time Comparison. The main computational benefit of the proposed online simulator HC comes from single solution-tracking, which can be effectuated efficiently even on the CPU. Figure 4b demonstrates the efficiency gain of our 8pts simulator HC over the eigen solver and parallel HC variants. As expected, by tracking only one solution curve, we are significantly faster than parallel exhaustive tracking HC, even if the latter runs on GPU. The eigen solver",
+        "bbox": [
+            75,
+            779,
+            470,
+            901
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "is an optimization-based solver with high complexity and ends up being slowest. The Gröbner Bases solver dealing with the large elimination template still costs a considerable time, even for just computing solutions for rotation, and not translation or scale.",
+        "bbox": [
+            496,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Remark. We would like to note that Gröbner Bases is solving a different formulation from Eq. (9). In order to make it easy to be solved by a smaller elimination template, it eliminates translation and scale [57]. But the resulting coefficient matrix is  $130 \\times 275$  and still needs a large number of operations. Although the formulation of Eq. (9) with eliminated depths faces a slightly lower success rate, its number of operations is much smaller than Gröbner Bases. On the other hand, the proposed 8pt simulator HC provides a comparably high success rate as Gröbner Bases and is still  $17 \\times$  faster.",
+        "bbox": [
+            496,
+            172,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. RANSAC experiments for the GRPS problem using Gröbner Bases | simulator HC. Image points are randomly perturbed by 2-pixel uniform noise. We use vanilla RANSAC with at most 200 iterations. As can be observed, outlier ratios of up to  $40\\%$  are easily handled within 200 iterations. And regressor-based simulator HC is consistently faster than Gröbner Bases.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3e6c19a93dc0dd4bb330eaea0303c84eabae815caffb52385d802105e89b0a0e.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ratio</td><td colspan=\"2\">Succ. (%)</td><td colspan=\"2\">ER(deg)</td><td colspan=\"2\"># Iters</td><td colspan=\"2\">Time(s)</td></tr><tr><td>10%</td><td>99.5</td><td>100</td><td>0.10</td><td>0.09</td><td>93</td><td>125</td><td>2.33</td><td>0.85</td></tr><tr><td>20%</td><td>99.4</td><td>100</td><td>0.11</td><td>0.10</td><td>171</td><td>193</td><td>4.37</td><td>1.31</td></tr><tr><td>30%</td><td>99.4</td><td>100</td><td>0.13</td><td>0.14</td><td>200</td><td>200</td><td>5.10</td><td>1.35</td></tr><tr><td>40%</td><td>98.9</td><td>91</td><td>0.21</td><td>0.29</td><td>200</td><td>200</td><td>4.59</td><td>1.35</td></tr></table>",
+        "bbox": [
+            527,
+            452,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Noise Resilience. Figure 4c presents the performance of the proposed 8pts simulator HC with different numbers of cameras under increasing image noise levels ranging from 0.2 pixel to 1.0 pixel. The error behaves gracefully as a function of noise, and it can be observed that a higher number of cameras leads to slightly inferior noise. Furthermore, we also observe that rotation errors appear to be less sensitive to image noise than translation and scale errors.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation inside RANSAC. To conclude, we embed simulator HC into RANSAC to test its practical usefulness. We synthesize 200 correspondences between 5 cameras and replace part of them with outliers. Uniformly sampled pixel noise from  $[-2,2]$  is added to both coordinates of the image points by again assuming a virtual focal length of 800 px. We terminate RANSAC if it reaches  $99\\%$  confidence or 200 iterations, and the inlier threshold is set to 0.01 for the distance measured by the normalized reprojection error. Given that Gröbner Bases solver estimates 140 solutions, we keep the real ones and select the best solution using reprojection errors in parallel to save time for it. Table 2 shows the results. The success rate is measured by a rotation error threshold of 2 degrees and the indicated errors are",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_footnote",
+        "text": "${}^{4}$  shown in supplementary.",
+        "bbox": [
+            517,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "27109",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/45ed5eb77a4209965faf887b0475a13238408c8420f2cc0948dd2bceb9812326.jpg",
+        "image_caption": [
+            "(a) Error distribution over noise-free data."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            92,
+            339,
+            227
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/a77d11a9c7f3b97eb41fb553e927e3e14c55e7b36f9afddcdc3d7665d63ae342.jpg",
+        "image_caption": [
+            "(b) The boxplot of running time comparison."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            348,
+            92,
+            620,
+            228
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/6c5e8c963e11700af2d2282864c9fd2eb43e1d380071f90354aed29cbf794556.jpg",
+        "image_caption": [
+            "(c) Error statistics of simulator HC.",
+            "Figure 4. Experimental results on GRPS. Fig. 4a Error distribution over 1000 trials on noise-free data. The camera number is set to be 3. Considering the rotation error, except for Gröbner Bases, the other minimal solvers all present a similar error distribution with around  $70\\%$  success rate, and the eigen solver presents only around  $60\\%$  success rate. The proposed 8pts simulator HC presents  $96.3\\%$  success rate where the Gröbner Bases has  $100\\%$  success rate. Fig. 4b The boxplot of running time comparison for the proposed simulator HC and other methods, where the number represents the median time. As expected, on average the proposed online simulator HC running on CPU is the fastest. It is about  $5\\times$  faster than GPU-HC since we only track one solution,  $17\\times$  faster than Gröbner Bases and about  $40\\times$  faster than CPU-HC. Fig. 4c Error statistics of simulator HC with respect to different noise levels ranging from 0.2 pixel to 1.0 pixel."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            630,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "the average accuracy of successful cases, results on translation and scale are left in supplementary. Overall, simulator HC embedded into RANSAC can easily handle up to  $40\\%$  outliers as Gröbner Bases and much faster, which suggests high practicality. Note that Gröbner Bases provides around 46 real solutions each time, which requires a significant amount of additional time for solution selection. Meanwhile, simulator HC does not require this extra step.",
+        "bbox": [
+            75,
+            368,
+            468,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "7.4. Real World Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            502,
+            303,
+            518
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We further explore the performance of simulator HC on the real dataset LaMAR [50]. As illustrated in Fig. 5, the provided HoloLens data is a natural application of GRPS with identity scale, which can be viewed as a multi-camera rig with 4 cameras in the front and sides. We extract the correspondences by consecutively taking a view-pair from the trajectories and ensuring the distance between each view is in  $[0.2m, 0.5m]$  with at least 100 matches. The",
+        "bbox": [
+            75,
+            527,
+            468,
+            650
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/18ecec1634171e8a7d5ba99f673cc4d24c41f8c6ed96af9e97ed16933d20d1e3.jpg",
+        "image_caption": [
+            "Figure 5. LaMAR dataset multi-camera rig visualization."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            674,
+            468,
+            729
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/ec7a3fd451ed54ad5f193d56b3538ff7bc13023c8351467efcde27eefb586c9f.jpg",
+        "table_caption": [
+            "Table 3. LaMAR dataset RANSAC-simulatorHC Median results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>seq.</td><td>ER(deg)</td><td>Es(%)</td><td>Et(deg)</td><td>#iters</td><td>Time(s)</td><td>Succ. (%)</td></tr><tr><td rowspan=\"3\">Gröbner Bases</td><td>CAB</td><td>1.18</td><td>56.14</td><td>5.70</td><td>137</td><td>2.83</td><td>60</td></tr><tr><td>HGE</td><td>0.62</td><td>62.48</td><td>4.39</td><td>59</td><td>1.25</td><td>67</td></tr><tr><td>LIN</td><td>0.60</td><td>42.04</td><td>3.40</td><td>31</td><td>0.65</td><td>72</td></tr><tr><td rowspan=\"3\">simulator HC</td><td>CAB</td><td>1.05</td><td>43.20</td><td>9.16</td><td>310</td><td>2.08</td><td>68</td></tr><tr><td>HGE</td><td>0.56</td><td>41.52</td><td>7.19</td><td>134</td><td>0.90</td><td>84</td></tr><tr><td>LIN</td><td>0.56</td><td>32.19</td><td>4.32</td><td>66</td><td>0.44</td><td>86</td></tr></table>",
+        "bbox": [
+            78,
+            796,
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+            896
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "resulting number of pairs is 1794 (CAB), 2852 (HGE) and 739 (LIN) in total. The correspondences are matched with SIFT features using nearest neighbour matching. We also present the angular error in translation, as in practice, the scale of translation and overall scale could be unobservable, e.g. the degenerate scenario when correspondences remain on the frame captured by the same camera.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3 shows the median results over all three sequences of LaMAR dataset. We adopted a similar setting for RANSAC as the above section with 500 maximum iterations. The proposed solver still presents consistent performances, where simulator HC has higher success rate with faster running time than Gröbner Bases.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "8. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            601,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The present paper introduces a new paradigm for correspondence-based geometric problem solving using an elegant three-stage combination of a regression network, an online correspondence simulator, and homotopy continuation. The regression network acts as a general solution approximator and can be trained in simulation only. While pure regression accuracy is often insufficient on its own, a key message conveyed through our results is that the accuracy is generally still good enough to simulate a consistent starting problem-solution pair that successfully enables single-solution continuation. As demonstrated on two generalized camera problems, the strategy enables high success rates on common computing hardware, and the resulting solvers prove to be a viable solution if utilized as part of a random sample and consensus scheme. In particular, we propose a successful solution to the generalized relative pose and scale problem, which is around  $17 \\times$  faster than traditional polynomial elimination techniques.",
+        "bbox": [
+            496,
+            628,
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "27110",
+        "bbox": [
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+            944,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "9. Acknowledgments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            256,
+            107
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The authors would like to acknowledge the funding support provided by projects 22DZ1201900, 22ZR1441300, and DFYJBJ-1 by the Natural Science Foundation of Shanghai.",
+        "bbox": [
+            76,
+            114,
+            468,
+            161
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
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2025/Simulator HC_ Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision/d90c2114-786f-423a-b72c-4f3391aa43d5_origin.pdf

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2025/Simulator HC_ Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision/full.md

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+# Simulator HC: Regression-based Online Simulation of Starting Problem-Solution Pairs for Homotopy Continuation in Geometric Vision
+
+Xinyue Zhang
+
+Zijia Dai
+
+Wanting  $\mathbf{X}\mathbf{u}^{1}$
+
+Laurent Kneip<sup>1</sup>
+
+$^{1}$ Mobile Perception Lab, ShanghaiTech University, China
+
+# Abstract
+
+While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to intractability. In recent years, homotopy continuation has been introduced as a plausible alternative. However, the method currently depends on expensive parallel tracking of all possible solutions in the complex domain, or a classification network for starting problem-solution pairs trained over a limited set of real-world examples. Our innovation lies in a novel approach to finding solution-problem pairs, where we only need to predict a rough initial solution, with the corresponding problem generated by an online simulator. Subsequently, homotopy continuation is applied to track that single solution back to the original problem. We apply this elegant combination to generalized camera resection, and also introduce a new solution to the challenging generalized relative pose and scale problem. As demonstrated, the proposed method successfully compensates the raw error committed by the regressor alone, and leads to state-of-the-art efficiency and success rates.
+
+# 1. Introduction
+
+The solution of geometric camera calibration problems is a crucial step in many Structure-from-Motion (SfM) [21, 52, 54, 55], Visual Odometry (VO) [46], and visual Simultaneous Localization And Mapping (SLAM) [43] frameworks. Solvers developed over the years address camera resectioning [23, 29, 31, 65], two-view relative pose [30, 44, 58], pose estimation from lines [15, 41], partially calibrated cameras [64], generalized cameras [31, 41, 57, 60], rolling shutter cameras [10, 51], and many other scenarios. The problems often appear in the form of a polynomial equation system, and special techniques from the field of algebraic geometry have been used to solve them. Once an efficient solver is found, it is typically embedded into a random sampling and consensus scheme [19, 48] in order to gain robust
+
+ness in the presence of outliers. Hence, there is a requirement for such solvers to be efficient and embeddable into iterative schemes.
+
+The dominant approaches to efficiently solve systems of polynomial equations are given by the Gröbner basis method and polynomial resultants [9, 59]. Based on the Gröbner basis theory, Stewénius et al. [58] and Kukelova et al. [33] demonstrate that the calculations required to obtain a minimal set of ideal generators can be effectuated efficiently at the hand of a fixed elimination template. Kukelova et al. [33] in particular propose a solver generator to automatically discover such elimination templates. Later on, sparse resultant-based solvers [16] have been demonstrated as a powerful alternative sometimes leading to smaller elimination templates.
+
+While polynomial elimination techniques have led to significant progress in the solution of geometric vision problems, the methods are limited as the complexity of the template search grows uncontrollably with the degree and dimensionality of the problem at hand. Furthermore, owing to their failure to respect inequality constraints and rule out practically infeasible solutions, high degrees or dimensionalities naturally lead to an elevated number of algebraically possible solutions and—assuming that it can be found at all—large elimination templates [13, 14, 45, 63–65]. This in turn causes problems in terms of numerical stability [63]. In recent years, a different solution strategy has therefore gained popularity: Homotopy Continuation (HC) [4, 12, 61]. The method proceeds by starting from a known problem-solution pair, and then tracks its roots to the target problem at hand during a step-wise interpolation of polynomial coefficients. The method has been used to successfully solve challenging tri-focal relative pose problems [17]. While promising, HC remains expensive as it generally requires the parallel continuation of many roots in the complex domain in order to identify all real solutions to a target problem, followed up by disambiguation.
+
+Recently, Hruby et al. [25] propose an efficient, learning-based extension to the pure HC paradigm, which serves as
+
+our primary motivation. They propose the introduction of a classifier to pick a good problem-solution pair trained over a large set of known pairs obtained from SfM. This enables a highly efficient application of HC, as only a single root of interest needs to be continued. While still presenting a margin for improvement in terms of success rate, the method is demonstrated to have unprecedented computational efficiency on the challenging three-view-four-point problem.
+
+The method proposed in this work is similar to the work of Hruby et al. [25] in that it leverages a learning-based approach to produce a starting problem-solution pair that enables single-root-tracking. However, we note a couple of important differences:
+
+- We do not train a classifier on a fixed set of problem-solution pairs taken from a real-world dataset. Instead, we propose to employ a solution regression network trained over an arbitrarily large set of simulated input correspondences for the considered geometric problem. The network is hence not limited by a finite set of candidate problems, and aims at being a general solution approximator for any instance of the polynomial problem. What's more, learning a solution is much easier than learning a proper problem-solution pair.  
+- The bridge to HC is formed by appending an online simulator that uses the input correspondences and the predicted solution to generate a complete, consistent problem-solution pair. Given only moderate regression accuracy, the produced problem-solution pair is sufficiently close to the original problem for successful single-root tracking via HC.  
+- We argue that the prediction of a single solution (or the unambiguous classification of a single problem-solution pair) from a minimal set may not always be possible as for complicated geometric problems, there may indeed be multiple geometrically feasible solutions. We therefore add one additional correspondence, which leads to a performance gain during both the regression and the continuation stage.
+
+The newly proposed simulate-and-solve paradigm is summarized in Figure 1. We demonstrate that this strategy can lead to high success-rate and efficient CPU-based solvers for two problems: generalized camera resection, and generalized relative pose and scale. Owing to its challenging nature, the latter problem has thus far only seen an optimization-based solution [32]. The solvers are compared against a purely learning-based alternative, a regressor followed by simple local refinement, as well as the exhaustive application of homotopy continuation over all roots. The proposed method is efficient, generalizable, and highly successful, and should thus be considered as an interesting alternative for the ongoing development of complicated geometric problem solvers.
+
+# 2. Literature Review
+
+Polynomial elimination theory: Our contribution can be regarded as a novel alternative to traditional polynomial elimination theory [9, 59]. Stewenius et al. [58] manually derive one of the first Gröbner basis solvers in the field of computer vision. Automatic solver generators and important extensions improving performance and numerical accuracy are later introduced by Kukelova et al. [33] and Larsson et al. [34, 35, 37, 38]. Zheng and Kneip propose the use of the parametric Sylvester resultant [64], while Hesch and Roumeliotis make use of the Macaulay resultant [23]. The more general use of sparse resultants as a powerful alternative to the Gröbner basis method is analyzed by Emiris [16], Heikkilä [22], and—most recently—Bhayani et al. [5]. While having lead to significant progress, complicated geometric problems with as many as 64 [57], 272 [45], 81 [65] (before symmetry-removal), 210 [64],  $>10000$  [13, 14], and 512 [63] solutions remain hard or impossible to be solved by polynomial elimination. The latter work, in particular, presents one of the largest successful elimination templates in the literature ( $96413 \times 96879$ ) by making use of octuple machine precision. Recently Evgenity et al. [40] developed a new method to reduce the size of the elimination template. Yet, for a polynomial system, a large number of solutions in practice still leads to reduced computational efficiency.
+
+Homotopy continuation: Homotopy continuation implementations exist as independent programs [61] or as part of Macaulay2 [39], Bertini [4], and Julia [6]. Duff et al. [12] study the application of the method to geometric vision problems, and several related studies focus specifically on the tri-focal relative pose problem [2, 20, 24, 27, 47]. However, off-the-shelf implementations are often too general and not optimized for real-time applications. Progress is recently achieved by Fabbri et al. [17], who propose an efficient custom  $\mathrm{C + + }$  implementation of the Macaulay2 solver [39] for a tri-focal relative pose problem. More recently, Ding et al. [11] propose a fast GPU-based implementation of homotopy continuation [7, 8] for a minimal solution to the three-view-four-point problem which has the same performance as Julia [6] but is significantly faster. The method leverages massive parallelization to efficiently track all solutions of a small, fixed set of starting problem-solution pairs. Our contribution can be regarded as a problem-solution pair initialization scheme similar to Hruby et al. [25] for successful single solution tracking.
+
+Learning for polynomial problem solving: One of the first methods to successfully employ learning in polynomial solvers is presented by Xu et al. [62], who proposed to increase the numerical accuracy of polynomial elimination templates by learning the best permutation in permutation-invariant polynomial problems. Recently, Hruby et al. [25] propose the addition of a classifier for initial problem-
+
+![](images/b58d09d84c67abdaa48c10197923d8f9c25a0631bf30a7fa8b9ea55410f0fc1b.jpg)  
+Figure 1. Overview of the proposed geometric problem solution scheme. Given input correspondences, a regression network is utilized to approximate a solution. A subsequent online simulator generates a new set of correspondences that is consistent with the regression output. The obtained problem-solution pair is finally used to bootstrap homotopy continuation. The final solution is found efficiently by tracking a single root.
+
+![](images/64d65d11bb933751be00e4ce3a349d00fa86c3601e492f430ed260a303b9fe92.jpg)  
+(a) HC multiple solution curves
+
+![](images/bdbe15f1c825887877d15210209f0c4a797e9486a1dfd5898d384d072adf9f77.jpg)  
+(b) HC solution tacking  
+Figure 2. Graphical illustration on homotopy continuation(HC) solution curves tracking. For a polynomial system with multiple solutions, each solution curve can be tracked independently as shown in Figure 2a. For each solution curve tracking, HC utilizes a "prediction-correction" scheme to approximate one of the solutions for the target system.
+
+solution pair picking in homotopy continuation. In recent years, several works have proposed to directly apply neural networks to regress the pose of a camera, either directly from images [26, 49] or—aiming at replacing traditional algebraic-geometric solvers—from correspondence coordinates [53]. While such networks use algorithm unrolling [42] and differential optimization [3] for accurate end-to-end trainability, a successful application to more complicated problems remains yet to be demonstrated. Regressors can be regarded as general non-linear function approximators, and the challenge of using them to produce highly accurate solutions is easily explained by the potential discontinuity of root locations for continuous variations of input polynomial coefficients. Our contribution can be regarded as a new post-regression refinement scheme for polynomial problems enabling successful application to complicated problems for which it is hard to apply traditional polynomial solvers.
+
+# 3. Polynomial Solver: Homotopy Continuation
+
+We start with a brief summary of HC. We refer to an instance of a certain polynomial system with specific coefficients as a problem. HC is a powerful tool that can numerically find the solutions of a problem. Each solution is found by tracking a curve independently, as illustrated in
+
+Figure 2a. When tracking the solution curves, the method solves a series of problems of similar form. It starts from a trivial problem whose solutions are simply known, and then gradually deforms that problem to the target problem that we are interested in but for which we do not know the solutions. It is hoped that—by continuing the known solutions throughout the problem sequence—they can lead to the solutions of the target, input problem. Two questions arise: 1) How to track the solution curves?, and 2) What is a good starting problem leading to the solutions we desire?
+
+The answer to the first question is given by HC. Formally, suppose we have a polynomial system  $\mathbf{F}(\mathbf{x}) = \mathbf{0}$  and we are interested in its solutions. Suppose further that we have a polynomial system of similar form  $\mathbf{G}(\mathbf{x}) = \mathbf{0}$  whose solutions are known. HC solves a series of polynomial systems of the form
+
+$$
+\mathbf {H} (\mathbf {x}, t) = (1 - t) \mathbf {G} (\mathbf {x}) + t \mathbf {F} (\mathbf {x}), \quad t \in [ 0, 1 ]. \tag {1}
+$$
+
+As illustrated in Figure 2b, each  $\mathbf{H}(\mathbf{x},t) = \mathbf{0}$  is solved while sliding  $t$  from 0 to 1. For  $t = 0$ , the solution is known as  $\mathbf{H}(\mathbf{x},0) = \mathbf{G}(\mathbf{x})$ . A solution of  $\mathbf{F}(\mathbf{x}) = \mathbf{0}$  is finally obtained as for  $t = 1$ ,  $\mathbf{H}(\mathbf{x},1) = \mathbf{F}(\mathbf{x})$ . The problems are not actually solved but the solutions are simply tracked from problem to problem. Taking the partial derivative to both sides of  $\mathbf{H}(\mathbf{x},t)$ , the solution curve  $\mathbf{x}(t)$  can be formulated as the following ordinary differential equation
+
+$$
+\mathbf {J} _ {\mathbf {H}} (\mathbf {x}) \frac {\partial \mathbf {x}}{\partial t} + \frac {\partial \mathbf {H} (\mathbf {x} , t)}{\partial t} = \mathbf {0} \Longleftrightarrow \frac {\partial \mathbf {x}}{\partial t} = - \mathbf {J} _ {\mathbf {H}} (\mathbf {x}) ^ {\dagger} \frac {\partial \mathbf {H} (\mathbf {x} , t)}{\partial t}. \tag {2}
+$$
+
+A "prediction-correction" scheme—as widely utilized in numerical analysis—is typically employed to trace the solution curve  $\mathbf{x}(t)$ .
+
+Prediction. Denote the stepsize of  $t$  as  $\delta t$ . Euler's predictor can be used to update along the tangent direction
+
+$$
+\mathbf {x} _ {i + 1} = \mathbf {x} _ {i} + \delta t \frac {\partial \mathbf {x}}{\partial t} \bigg | _ {\mathbf {x} _ {i}, t _ {i}}. \tag {3}
+$$
+
+Practically speaking, a higher-order generalized method is
+
+commonly used for better accuracy and stability with larger stepsize.
+
+Correction. Gauss-Newton steps are adopted to correct the prediction. In each iteration of Gauss-Newton's method, the solution is updated by
+
+$$
+\mathbf {x} _ {j} = \mathbf {x} _ {j - 1} - \mathbf {J} _ {\mathbf {H}} \left(\mathbf {x} _ {j - 1}\right) ^ {\dagger} \mathbf {H} \left(\mathbf {x} _ {j - 1}, t\right), \tag {4}
+$$
+
+where  $\mathbf{J}_{\mathbf{H}}^{\dagger}$  is the pseudo inverse of the jacobian  $\mathbf{J}_{\mathbf{H}}$ , and  $t = t_i + \delta t$ . Figure 2b illustrates a 1D solution curve tracking, where the blue arrow represents the prediction update and the red arrow represents the correction update.
+
+The remainder of this paper—our key contribution—addresses the second question of how to find a good starting system. Traditional methods (e.g. Ab initial [17], monodromy [6, 12]) rely on algebraic geometry theories developed for coefficient-parameter homotopies, and tracking all roots from a small set of fixed, known problem-solution pairs in the complex domain may often enable a solution [56]. However, tracking all the isolated paths is expensive and in practice multiple solutions cost more time to select the best. A recent study proposes the use of a classifier to pick a good starting pair with as high as possible success probability upon tracking only a single root [25], which is much faster. Similarly, in this work, we propose a novel geometry-informed strategy that combines a neural regressor with an online simulator to produce a problem-solution pair and then track a single root by HC. Even on challenging problems for which no traditional solver has been found, it can find the solution with a success rate of over  $95\%$ .
+
+Remark (Homotopy Types). Since being introduced in 1980s, a variety of homotopies have been developed to serve the same purpose: how to solve the problem exactly as expected. The representative one would be coefficient-parameter homotopy. Its formulation provides the insight that if we can find all the solutions to a general coefficient-parameter polynomial, then we can find all the other members of that polynomial family. In fact, as pointed out in [56], in engineering problems (e.g. geometry vision problems) we are dealing with natural coefficient-parameter polynomials, that is coefficients of polynomials derived from visual features. Since the scope of this paper lies on a novel starting problem-solution pair finding and it is not highly dependent on the path tracking, we kindly refer the reader to [56] for an in-depth discussion of other homotopy types. As shown in the later applications, straight segment homotopies provide near-perfect success rates when working with our simulator. We also want to note that all the other homotopy types could be equally applied in conjunction with our simulator.
+
+# 4. Find a Good Starting Solution: Regression Network
+
+Following recent developments in deep learning, multiple attempts have been made to, for example, learn camera pose using a neural network [26, 49, 53]. The first two methods extract features from images and points and use them in a regression network to predict the pose. The third method is a more preliminary approach and aims at predicting pose directly from geometric correspondences, which is also the aim of the present work. The bottleneck in regressing pose from correspondences arises from two concerns: 1) For simple geometric problems, we often have traditional methods that are efficient and accurate, and 2) For hard geometric problems, regression networks demonstrate a poor ability to predict accurate solutions. Our key insight is that while the predicted pose may not be sufficiently accurate, it can still serve as a good starting solution for HC.
+
+Our pose regression networks are designed with multiple 1D convolutional layers and each layer is followed by batch normalization and ReLU activations. The loss function is given by a combination of relative pose errors with learnable weights [26].
+
+# 5. Find a Consistent Starting Problem: Online Simulator
+
+We recall the main idea of HC. In order to continue a solution to the target problem, an appropriate starting problem with a known solution is required. Given the approximate solution predicted by the pose regression network, our goal is to derive a consistent polynomial system for which one of the solutions matches the predicted one. We denote this step an online simulator, and—though problem specific—effective realizations can almost always be found by simple geometric rules. For example, in camera resectioning, one can simply use the input 3D points and reproject them into a camera view under the predicted pose. This will lead to new 2D points, and thus a new set of correspondences that is perfectly consistent with the predicted solution, i.e. our sought starting problem-solution pair. While not yet made use of in the present work, it is worthwhile noting that—owing to their algebraic simplicity—such an online simulator often appears to be a differentiable module.
+
+# 6. Generalized Perspective-n-Points
+
+Our first concrete, practical application targets generalized camera pose estimation from 2D-3D correspondences. We use the Unified Perspective-n-Point (UPnP) algorithm [31] which formulates a polynomial system corresponding to the first-order optimality conditions of the sum of squared object space distances. The method can be used to solve both central and non-central camera resectioning problems from
+
+![](images/3a96df52960666700862ffecdc5039b230a9d1c53e40b69a24c2f285efa06d4f.jpg)  
+(a) Generalized Absolute Pose
+
+![](images/1288a391fc920f245307f7bfeb8287a9244de2ba1a51b68bec847baa32e9fdd9.jpg)  
+(b) Generalized Relative Pose and Scale  
+Figure 3. The geometry of the generalized camera problems we propose to solve by online simulator HC.  $w$  represents the world frame, and  $c$  and  $c'$  represent camera frames in different views respectively.
+
+an arbitrary number of points (including minimal). It can be efficiently solved by the Gröbner Bases method since—after variable elimination—it only involves 4 unknowns. In this section, we solve UPnP by our newly proposed method and compare it against conventional approaches, a raw regression network, as well as a parallel HC implementation tracking all roots.
+
+# 6.1. Problem Formulation
+
+Consider a 3D-2D generalized correspondence  $(\mathbf{p}_i, \mathbf{f}_i, \mathbf{v}_i)$  originating from the non-central camera resectioning model illustrated in Figure 3a, where  $\mathbf{p}_i \in \mathbb{R}^3$ ,  $\mathbf{f}_i \in \mathbb{S}^2$  and  $\mathbf{v}_i \in \mathbb{R}^3$  denote the 3D world point, image ray and ray origin, respectively. The correspondence follows an underlying generalized absolute pose transformation depending on the rotation  $\mathbf{R} \in SO(3)$ , the position  $\mathbf{t} \in \mathbb{R}^3$  and an unknown latent depth  $\alpha_i$  as follows:
+
+$$
+\alpha_ {i} \mathbf {f} _ {i} + \mathbf {v} _ {i} = \mathbf {R p} _ {i} + \mathbf {t}. \tag {5}
+$$
+
+Let  $\mathbf{M} \in \mathbb{R}^{11 \times 11}$  denote a coefficient matrix that embeds all known variables (point measurements and ray offsets),  $\mathbf{q} = [q_0, q_1, q_2, q_3]^\top$  denote the quaternion representation of  $\mathbf{R}$ , and  $\mathbf{s} \in \mathbb{R}^{11}$  denote a vector whose elements are all second and zeroth order monomials of the quaternion variables. After translation and depth elimination,  $\mathbf{q}$  can be constrained by first-order optimality conditions appearing in the form of the polynomial system<sup>1</sup>
+
+$$
+\left\{ \begin{array}{l l} \mathbf {s} ^ {\top} \mathbf {M} \frac {\partial \mathbf {s}}{\partial q _ {i}} & = 0, \quad i = 0, \dots , 3 \\ \mathbf {q} ^ {\top} \mathbf {q} - 1 & = 0. \end{array} \right. \tag {6}
+$$
+
+# 6.2. Regressor and online simulator
+
+To provide a proper problem-solution pair for HC, we train a pose regression network from synthetic data. Its input is given by row-wise stacking of the correspondences, i.e.
+
+$$
+\left[ \begin{array}{c c c} \mathbf {p} _ {1} ^ {\top} & \mathbf {f} _ {1} ^ {\top} & \mathbf {v} _ {1} ^ {\top} \\ \vdots & \vdots & \vdots \\ \mathbf {p} _ {N} ^ {\top} & \mathbf {f} _ {N} ^ {\top} & \mathbf {v} _ {N} ^ {\top} \end{array} \right], \tag {7}
+$$
+
+# Algorithm 1 Online Simulator HC for generalized PnP
+
+1: Input: correspondences  $(\mathbf{p}_i,\mathbf{f}_i,\mathbf{v}_i)_{i = 1}^M$  , stepsize  $\delta t$  
+2: Output: poses  $\hat{\mathbf{R}},\hat{\mathbf{t}}$  
+3:  $\tilde{\mathbf{R}},\tilde{\mathbf{t}}\gets$  Trained Regression Network((pi,fi,v)M)  
+4:  $(\hat{\mathbf{f}}_i)_{i=1}^M \leftarrow$  Reprojection  $(\hat{\mathbf{R}}, \hat{\mathbf{t}}; (\mathbf{p}_i, \mathbf{v}_i)_{i=1}^M)$ $\triangleright$  Online Simulator  
+5: Starting problem  $\mathbf{G}(\mathbf{x})\gets (\mathbf{p}_i,\hat{\mathbf{f}}_i,\mathbf{v}_i)_{i = 1}^M$  with solution  $\hat{\mathbf{R}},\hat{\mathbf{t}}$  
+6: Target problem  $\mathbf{F}(\mathbf{x})\gets (\mathbf{p}_i,\mathbf{f}_i,\mathbf{v}_i)_{i = 1}^M$  
+7:  $\mathbf{q}_{HC} \gets$  Homotopy Continuation  $t\mathbf{F}(\mathbf{x}) + (1 - t)\mathbf{G}(\mathbf{x})$  
+8:  $\bar{\mathbf{R}},\hat{\mathbf{t}}\gets$  decompose  $\mathbf{q}_{HC}$
+
+where  $N$  is the number of correspondences used, and the output is the quaternion vector. The network consists of 4 1D convolutional layers and a fully connected layer at the end to convert the output to a quaternion vector with the unit norm. Given the rotation predicted by the network, the translation can be recovered from correspondences and estimated rotation. We refer the reader to [31] for the details. For the online simulator, we can get reprojected  $\hat{\mathbf{f}}_i$  from (5). Algorithm 1 summarizes all stages, including the final HC over (6). Note that in line 5 of Algorithm 1, the starting problem  $\mathbf{G}(\mathbf{x})$  is constructed by replacing the coefficient matrix  $\mathbf{M}$  computed by  $(\mathbf{p}_i,\mathbf{f}_i,\mathbf{v}_i)$  in (6) with  $\hat{\mathbf{M}}$  computed by  $(\mathbf{p}_i,\hat{\mathbf{f}}_i,\mathbf{v}_i)$ .
+
+# 6.3. Experiments
+
+Data. We randomly generate 4 cameras in a cube  $[-1,1]^3$  and randomly sample 16 3D points in the box  $[-1,1]^2 \times [4,8]$ . 16 samples would not be a good choice for a RANSAC solver [18], but in the present context the idea is to set a moderate and notably equal challenge to all compared solvers. Furthermore, for UPnP the number of constraints appearing in the polynomial system remains unchanged as it analyses first-order optimality rather than individual incidence relations. Elements of the rotation angles are randomly generated in the interval  $[- \pi /2, \pi /2]$ , respectively, and the translation is randomly generated in the unit cube. We then generate the correspondences from rays that point to a 3D point. The noise level is set to 2 pixels. To train the pose regression network, we simulate a dataset of 2400 samples, which is sufficient for reliable Simulator HC initialization. We use a 2.70GHz Intel(R) Xeon(R) CPU and an NVIDIA GeForce RTX 4090 for network training and evaluation.
+
+Methods. For HC, the stepsize  $\delta t$  and the maximum number of iterations of Newton's method are set to 0.02 and 5, respectively. We compare the Gröbner Bases solver [31] and the popular local method Levenberg-Marquardt (LM) [1]. We also test the state-of-the-art parallel HC solver developed by [7, 8], and use both its CPU and  $\mathrm{GPU}^2$  version. Given that parallel HC tracks all solutions,
+
+Table 1. Performance comparison of simulator HC, a traditional method, and parallel exhaustive tracking HC on noisy synthetic data. All results are averaged over 1000 trials. The success rate is computed for rotation errors with a threshold of 2 degree.  
+
+<table><tr><td>Method</td><td>Succ. (%)</td><td>ER(deg)</td><td>Et(%)</td><td>Time(ms)</td></tr><tr><td>Gröbner Bases</td><td>100</td><td>0.031</td><td>0.489</td><td>1.254</td></tr><tr><td>CPU HC</td><td>100</td><td>0.032</td><td>0.499</td><td>9.796</td></tr><tr><td>GPU HC</td><td>100</td><td>0.032</td><td>0.499</td><td>1.002</td></tr><tr><td>Pred Initial</td><td>32</td><td>7.204</td><td>32</td><td>0.031</td></tr><tr><td>Pred Initial + LM</td><td>54</td><td>28.72</td><td>2256</td><td>0.528</td></tr><tr><td>Rand Initial + Simulator HC</td><td>22</td><td>91.68</td><td>228</td><td>0.231</td></tr><tr><td>Pred Initial + Simulator HC</td><td>100</td><td>0.032</td><td>0.513</td><td>0.316</td></tr></table>
+
+we manually pick the one with the smallest error.
+
+Results. The rotation error is measured by  $\mathcal{E}_{\mathbf{R}} = 2\arcsin (\| \hat{\mathbf{R}} -\mathbf{R}_{gt}\| /(2\sqrt{2}))$  in degrees as suggested by [11] and the translation error is measured by the  $\mathcal{E}_{\mathrm{t}} = \| \hat{\mathbf{t}} -\mathbf{t}_{gt}\| /\| \mathbf{t}_{gt}\| \times 100$  in percentage. Table 1 compares the traditional method, parallel exhaustive tracking HC, and different types of initial solutions for our simulator HC. We present the success rate as the percentage of rotation errors smaller than 2 degrees. It can be observed that on this simple task, except for the local method, traditional methods, as well as simulator HC using predicted initials, succeed in  $100\%$  of trials. Meanwhile, online simulator HC benefits from the single-track strategy and turns out to be the fastest one. We also perform an ablation study on the proposed simulator HC, using both predicted and random initializations. Although the pose learned by the regressor is not highly accurate and only slightly outperforms random poses, it serves as a reasonable starting solution for our simulator HC. In contrast, LM as a local method is unable to leverage the potential of the predicted initializations, as the simulator HC does.
+
+# 7. Generalized Relative Pose and Scale
+
+Our final application targets a hard minimal problem: Generalized Relative Pose and Scale (GRPS) estimation from 2D-2D correspondences [32]. The GRPS problem is a natural extension of the generalized relative pose problem and arises in point-less registration of partial view-graphs in structure-from-motion. Owing to the fact that SfM results are generally up to scale, an inherent scale factor needs to be resolved. Such problem was first introduced by Kneip et al. [32]. It has 140 solutions if a unique rotation representation is used, and can be solved by multi-start optimization to overcome local minima. Later on, a traditional polynomial solver based on the Gröbner Bases method has been proposed [36, 40]. With a  $144 \times 284$  elimination template, the solver finds all 140 rotations within reasonable time. In this section, we solve GRPS by our proposed method and compare it against the existing approach, as well as a parallel HC implementation tracking all roots.
+
+# 7.1. Problem Formulation
+
+Consider a 2D-2D generalized correspondence  $(\mathbf{f}_i,\mathbf{v}_i) - (\mathbf{f}_i',\mathbf{v}_i')$  observed from two non-central camera views as illustrated in Figure 3b.  $\mathbf{f}_i\in \mathbb{S}^2,\mathbf{v}_i\in \mathbb{R}^3$  denote the image ray and ray origin in the first view, and  $\mathbf{f}_i'\in \mathbb{S}^2,\mathbf{v}_i'\in \mathbb{R}^3$  are the corresponding entities in the second view. The correspondence follows an underlying generalized relative pose and scale incidence relation depending on the rotation  $\mathbf{R}\in SO(3)$ , the position  $\mathbf{t}\in \mathbb{R}^3$ , the scale  $s$ , and unknown latent depths  $\alpha_{i}$  and  $\alpha_{i}'$  as follows:
+
+$$
+\alpha_ {i} \mathbf {f} _ {i} + \mathbf {v} _ {i} = \mathbf {R} \left(\alpha_ {i} ^ {\prime} \mathbf {f} _ {i} ^ {\prime} + s \mathbf {v} _ {i} ^ {\prime}\right) + \mathbf {t}. \tag {8}
+$$
+
+With the help of Plücker coordinates and the scalar triple product  $^3$ , the unknown depths get eliminated which results in a polynomial constraint that only involves the unknown poses
+
+$$
+\mathbf {t} ^ {\top} \left(\mathbf {f} _ {i} \times \mathbf {R} \mathbf {f} _ {i} ^ {\prime}\right) - s \mathbf {f} _ {i} ^ {\top} \mathbf {R} \left[ \mathbf {v} _ {i} ^ {\prime} \right] _ {\times} \mathbf {f} _ {i} ^ {\prime} + \mathbf {f} _ {i} ^ {\top} \left[ \mathbf {v} _ {i} \right] _ {\times} \mathbf {R} \mathbf {f} _ {i} ^ {\prime} = 0. \tag {9}
+$$
+
+Therefore, a minimal formulation for the GRPS problem can be devised by a polynomial system formed by stacking 7 constraints in the form (9), each one depending on one correspondence.
+
+# 7.2. Regressor and online simulator
+
+As introduced in section 6.2, we continue to use a pose regression network that inputs a matrix with row-wise stacked correspondences. The output is given by  $\mathbf{R}$ ,  $\mathbf{t}$ ,  $s$ . Note that the rotation is predicted in continuous 6D representation which is more suitable for neural networks [66]. The network consists of 11 1D convolutional layers, in the end, it branches to 3 sub-branches for  $\mathbf{R}$ ,  $\mathbf{t}$  and  $s$ . Each sub-branch consists of 2 1D convolutional layers and 1 fully connected layers for adjust output. Given the poses predicted by the network, we still need an estimation of the depths before simulating the reprojected image ray. With estimated  $\hat{\mathbf{R}}$ ,  $\hat{\mathbf{t}}$  and  $\hat{s}$ , the corresponding depths can be obtained from (8) by following
+
+$$
+\left[ \mathbf {f} _ {i} - \hat {\mathbf {R}} \mathbf {f} _ {i} ^ {\prime} \right] \left[ \begin{array}{l} \alpha_ {i} \\ \alpha_ {i} ^ {\prime} \end{array} \right] = - \left(\mathbf {v} _ {i} - \hat {s} \hat {\mathbf {R}} \mathbf {v} _ {i} ^ {\prime} - \hat {\mathbf {t}}\right), \tag {10}
+$$
+
+which can be simply solved by linear least squares for each input correspondence. Finally, we simulate a pose-consistent reprojected image ray in the first view using
+
+$$
+\hat {\mathbf {f}} _ {i} = \frac {1}{\hat {\alpha} _ {i}} \hat {\mathbf {R}} \left(\hat {\alpha} _ {i} ^ {\prime} \mathbf {f} _ {i} ^ {\prime} + \hat {s} \mathbf {v} _ {i} ^ {\prime}\right) + \hat {\mathbf {t}} - \mathbf {v} _ {i}. \tag {11}
+$$
+
+# 7.3. Simulation Experiments
+
+Data. We adopt a similar data generation method as in section 6.3. We generate 7 3D points in a  $[-1,1]^2 \times [2,20]$
+
+volume. Two view frames are generated with origins picked from  $[-1, 1]^3$ . Within each view frame, we then sample individual camera offsets from the volume  $[-1, 1]^3$ . The scale is randomly generated in  $[0.1, 5.0]$ , and all other parameters related to noise addition are left unchanged. Note that the ground truth relative pose needs to be extracted from the simulated pair of view poses.
+
+Methods. The stepsize for homotopy continuation is set to 0.05 in this scenario. We compare against the Eigen solver [32], Gröbner Bases solver [40] and the CPU and GPU versions of parallel HC which tracks 140 solutions found by Monodromy [6]. Note that to measure numerical errors, we just pick the best solution with the smallest error. In practice, traditional HC needs to evaluate additional information to select a single solution (e.g. euclidean distance). For a complicated problem like GRPS, evaluating 140 solutions would still induce non-neglectable time-consumption. Since GRPS is a hard problem, we train the regressor using a larger simulated dataset of size 64000.
+
+Metric. We measure the rotation error in degrees and the relative translation as in Sec. 6.3 and scale error in percentage using
+
+$$
+\mathcal {E} _ {s} = \left| \hat {s} - s _ {g t} \right| / s _ {g t} \times 1 0 0. \tag {12}
+$$
+
+To calculate the success rate, for rotation errors the threshold is set to 2 deg, and for relative errors, it is set to  $5\%$ .
+
+Numerical Stability. We randomly generate 1000 trials to test the numerical stability of all solvers. During the analysis of the performance of simulator HC using the minimum number of correspondences, we observed that our method has around  $70\%$  success rate. By checking the failure cases, we found that sometimes simulator HC tracked another real solution that was different from the ground truth pose. To tackle that issue, we evaluate the addition of one more correspondence and solve for an overdetermined polynomial system. By using 8 correspondences, simulator HC reaches a success rate of  $95\%$ . Again, since CPU/GPU-HC is designed to handle square systems, only the minimum number of correspondences can be tested for other HC methods.
+
+Since the errors in rotation, translation and scale have similar density results, we only present the rotation error in the main paper and the rest in the supplementary. As illustrated in Figure 4a, the minimal HC solvers all present similar error distribution and around  $75\%$  of trials are successful. While Gröbner Bases shows  $100\%$  success rate, Simulator HC over 8pts presents similar numerical errors.
+
+Time Comparison. The main computational benefit of the proposed online simulator HC comes from single solution-tracking, which can be effectuated efficiently even on the CPU. Figure 4b demonstrates the efficiency gain of our 8pts simulator HC over the eigen solver and parallel HC variants. As expected, by tracking only one solution curve, we are significantly faster than parallel exhaustive tracking HC, even if the latter runs on GPU. The eigen solver
+
+is an optimization-based solver with high complexity and ends up being slowest. The Gröbner Bases solver dealing with the large elimination template still costs a considerable time, even for just computing solutions for rotation, and not translation or scale.
+
+Remark. We would like to note that Gröbner Bases is solving a different formulation from Eq. (9). In order to make it easy to be solved by a smaller elimination template, it eliminates translation and scale [57]. But the resulting coefficient matrix is  $130 \times 275$  and still needs a large number of operations. Although the formulation of Eq. (9) with eliminated depths faces a slightly lower success rate, its number of operations is much smaller than Gröbner Bases. On the other hand, the proposed 8pt simulator HC provides a comparably high success rate as Gröbner Bases and is still  $17 \times$  faster.
+
+Table 2. RANSAC experiments for the GRPS problem using Gröbner Bases | simulator HC. Image points are randomly perturbed by 2-pixel uniform noise. We use vanilla RANSAC with at most 200 iterations. As can be observed, outlier ratios of up to  $40\%$  are easily handled within 200 iterations. And regressor-based simulator HC is consistently faster than Gröbner Bases.
+
+<table><tr><td>Ratio</td><td colspan="2">Succ. (%)</td><td colspan="2">ER(deg)</td><td colspan="2"># Iters</td><td colspan="2">Time(s)</td></tr><tr><td>10%</td><td>99.5</td><td>100</td><td>0.10</td><td>0.09</td><td>93</td><td>125</td><td>2.33</td><td>0.85</td></tr><tr><td>20%</td><td>99.4</td><td>100</td><td>0.11</td><td>0.10</td><td>171</td><td>193</td><td>4.37</td><td>1.31</td></tr><tr><td>30%</td><td>99.4</td><td>100</td><td>0.13</td><td>0.14</td><td>200</td><td>200</td><td>5.10</td><td>1.35</td></tr><tr><td>40%</td><td>98.9</td><td>91</td><td>0.21</td><td>0.29</td><td>200</td><td>200</td><td>4.59</td><td>1.35</td></tr></table>
+
+Noise Resilience. Figure 4c presents the performance of the proposed 8pts simulator HC with different numbers of cameras under increasing image noise levels ranging from 0.2 pixel to 1.0 pixel. The error behaves gracefully as a function of noise, and it can be observed that a higher number of cameras leads to slightly inferior noise. Furthermore, we also observe that rotation errors appear to be less sensitive to image noise than translation and scale errors.
+
+Evaluation inside RANSAC. To conclude, we embed simulator HC into RANSAC to test its practical usefulness. We synthesize 200 correspondences between 5 cameras and replace part of them with outliers. Uniformly sampled pixel noise from  $[-2,2]$  is added to both coordinates of the image points by again assuming a virtual focal length of 800 px. We terminate RANSAC if it reaches  $99\%$  confidence or 200 iterations, and the inlier threshold is set to 0.01 for the distance measured by the normalized reprojection error. Given that Gröbner Bases solver estimates 140 solutions, we keep the real ones and select the best solution using reprojection errors in parallel to save time for it. Table 2 shows the results. The success rate is measured by a rotation error threshold of 2 degrees and the indicated errors are
+
+![](images/45ed5eb77a4209965faf887b0475a13238408c8420f2cc0948dd2bceb9812326.jpg)  
+(a) Error distribution over noise-free data.
+
+![](images/a77d11a9c7f3b97eb41fb553e927e3e14c55e7b36f9afddcdc3d7665d63ae342.jpg)  
+(b) The boxplot of running time comparison.
+
+![](images/6c5e8c963e11700af2d2282864c9fd2eb43e1d380071f90354aed29cbf794556.jpg)  
+(c) Error statistics of simulator HC.  
+Figure 4. Experimental results on GRPS. Fig. 4a Error distribution over 1000 trials on noise-free data. The camera number is set to be 3. Considering the rotation error, except for Gröbner Bases, the other minimal solvers all present a similar error distribution with around  $70\%$  success rate, and the eigen solver presents only around  $60\%$  success rate. The proposed 8pts simulator HC presents  $96.3\%$  success rate where the Gröbner Bases has  $100\%$  success rate. Fig. 4b The boxplot of running time comparison for the proposed simulator HC and other methods, where the number represents the median time. As expected, on average the proposed online simulator HC running on CPU is the fastest. It is about  $5\times$  faster than GPU-HC since we only track one solution,  $17\times$  faster than Gröbner Bases and about  $40\times$  faster than CPU-HC. Fig. 4c Error statistics of simulator HC with respect to different noise levels ranging from 0.2 pixel to 1.0 pixel.
+
+the average accuracy of successful cases, results on translation and scale are left in supplementary. Overall, simulator HC embedded into RANSAC can easily handle up to  $40\%$  outliers as Gröbner Bases and much faster, which suggests high practicality. Note that Gröbner Bases provides around 46 real solutions each time, which requires a significant amount of additional time for solution selection. Meanwhile, simulator HC does not require this extra step.
+
+# 7.4. Real World Experiments
+
+We further explore the performance of simulator HC on the real dataset LaMAR [50]. As illustrated in Fig. 5, the provided HoloLens data is a natural application of GRPS with identity scale, which can be viewed as a multi-camera rig with 4 cameras in the front and sides. We extract the correspondences by consecutively taking a view-pair from the trajectories and ensuring the distance between each view is in  $[0.2m, 0.5m]$  with at least 100 matches. The
+
+![](images/18ecec1634171e8a7d5ba99f673cc4d24c41f8c6ed96af9e97ed16933d20d1e3.jpg)  
+Figure 5. LaMAR dataset multi-camera rig visualization.
+
+Table 3. LaMAR dataset RANSAC-simulatorHC Median results.  
+
+<table><tr><td></td><td>seq.</td><td>ER(deg)</td><td>Es(%)</td><td>Et(deg)</td><td>#iters</td><td>Time(s)</td><td>Succ. (%)</td></tr><tr><td rowspan="3">Gröbner Bases</td><td>CAB</td><td>1.18</td><td>56.14</td><td>5.70</td><td>137</td><td>2.83</td><td>60</td></tr><tr><td>HGE</td><td>0.62</td><td>62.48</td><td>4.39</td><td>59</td><td>1.25</td><td>67</td></tr><tr><td>LIN</td><td>0.60</td><td>42.04</td><td>3.40</td><td>31</td><td>0.65</td><td>72</td></tr><tr><td rowspan="3">simulator HC</td><td>CAB</td><td>1.05</td><td>43.20</td><td>9.16</td><td>310</td><td>2.08</td><td>68</td></tr><tr><td>HGE</td><td>0.56</td><td>41.52</td><td>7.19</td><td>134</td><td>0.90</td><td>84</td></tr><tr><td>LIN</td><td>0.56</td><td>32.19</td><td>4.32</td><td>66</td><td>0.44</td><td>86</td></tr></table>
+
+resulting number of pairs is 1794 (CAB), 2852 (HGE) and 739 (LIN) in total. The correspondences are matched with SIFT features using nearest neighbour matching. We also present the angular error in translation, as in practice, the scale of translation and overall scale could be unobservable, e.g. the degenerate scenario when correspondences remain on the frame captured by the same camera.
+
+Table 3 shows the median results over all three sequences of LaMAR dataset. We adopted a similar setting for RANSAC as the above section with 500 maximum iterations. The proposed solver still presents consistent performances, where simulator HC has higher success rate with faster running time than Gröbner Bases.
+
+# 8. Conclusion
+
+The present paper introduces a new paradigm for correspondence-based geometric problem solving using an elegant three-stage combination of a regression network, an online correspondence simulator, and homotopy continuation. The regression network acts as a general solution approximator and can be trained in simulation only. While pure regression accuracy is often insufficient on its own, a key message conveyed through our results is that the accuracy is generally still good enough to simulate a consistent starting problem-solution pair that successfully enables single-solution continuation. As demonstrated on two generalized camera problems, the strategy enables high success rates on common computing hardware, and the resulting solvers prove to be a viable solution if utilized as part of a random sample and consensus scheme. In particular, we propose a successful solution to the generalized relative pose and scale problem, which is around  $17 \times$  faster than traditional polynomial elimination techniques.
+
+# 9. Acknowledgments
+
+The authors would like to acknowledge the funding support provided by projects 22DZ1201900, 22ZR1441300, and DFYJBJ-1 by the Natural Science Foundation of Shanghai.
+
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+    {
+        "type": "text",
+        "text": "SinGS: Animatable Single-Image Human Gaussian Splats with Kinematic Priors",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Yufan Wu $^{1*}$  Xuanhong Chen $^{1\\dagger}$  Wen Li $^{1,3}$  Shunran Jia $^{2}$  Hualiang Wei $^{1*}$  Kairui Feng $^{4}$   \nJialiang Chen $^{1}$  Yuhan Li $^{1}$  Ang He $^{1*}$  Weimin Zhang $^{1}$  Bingbing Ni $^{1}$  Wenjun Zhang $^{1}$",
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+    {
+        "type": "text",
+        "text": "$^{1}$ Shanghai Jiao Tong University, Shanghai, China  $^{2}$ DreamX Inc  $^{3}$ Akool Research  $^{4}$ The National Key Laboratory of Autonomous Intelligent Unmanned Systems, Shanghai, China",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "{chen19910528,wmzhang,nibingbing,zhangwenjun}@sjtu.edu.cn, elvinfkr@tongji.edu.cn",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Despite significant advances in accurately estimating geometry in contemporary single-image 3D human reconstruction, creating a high-quality, efficient, and animatable 3D avatar remains an open challenge. Two key obstacles persist: incomplete observation and inconsistent 3D priors. To address these challenges, we propose SinGS, aiming to achieve high-quality and efficient animatable 3D avatar reconstruction. At the heart of SinGS are two key components: Kinematic Human Diffusion and Geometry-Preserving 3D Gaussain Splatting. The former is a foundational human model that samples within pose space to generate a highly 3D-consistent and high-quality sequence of human images, inferring unseen viewpoints and providing kinematic priors. The latter is a system that reconstructs a compact, high-quality 3D avatar even under imperfect priors, achieved through a novel semantic Laplacian regularization and a geometry-preserving density control strategy that enable precise and compact assembly of 3D primitives. Extensive experiments demonstrate that SinGS enables life-like, animatable human reconstructions, maintaining both high quality and inference efficiency (up to 70FPS).",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Single-image 3D human reconstruction (i.e., SIHR) is an emerging modeling technique that aims to create a lifelike 3D avatar from just one image, offering a highly cost-effective and promising approach to 3D modeling. Recently, 3D Gaussian Splatting (3DGS)[14] has made significant breakthroughs in rendering efficiency and quality, establishing itself as a mainstream approach for 3D avatar reconstruction. However, current 3DGS-based methods [23, 26] for single-image human 3D avatar reconstruction suffer from critical limitations in animation, as most are",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "image",
+        "img_path": "images/9676d7bbff1e85aed3304a363715f481c4e2de0f9887b0cac347845423235752.jpg",
+        "image_caption": [
+            "Figure 1. Existing single-image 3D avatar reconstruction methods are limited to sampling prior information from camera space. In contrast, SinGS proposes sampling from pose space, allowing us to obtain both camera and kinematic priors simultaneously. Combined with our Geometry-Preserving 3D Gaussian Splitting, this enables highly efficient animation rendering."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "designed primarily for static assets. This paper aims to develop an animation reconstruction framework that achieves a high balance between efficiency and rendering quality.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Currently, the vast majority of SIHR methods [7, 10, 23, 24, 26, 40, 41, 46, 49, 50] focus solely on optimizing geometry while neglecting to enhance animation capabilities. As a result, they are often incapable of animation or require third-party tools [7] to achieve approximate motion. Unlike digital assets, the primary requirement for a human avatar is its ability to animate, making animation the core goal of SIHR [9]. Achieving animatable single-image human reconstruction (i.e., Animatable SIHR) is particularly",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Work done during an internship at Shanghai Jiao Tong University.",
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+    {
+        "type": "page_footnote",
+        "text": "† Corresponding author: Xuanhong Chen.",
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+    {
+        "type": "page_number",
+        "text": "5571",
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+    {
+        "type": "text",
+        "text": "challenging for two main reasons: Incomplete Observation: A single image lacks comprehensive viewpoint information, offering an extremely limited, partial observation that cannot address occlusion issues. Current methods [7, 10, 47] mainly rely on fine-tuned diffusion models to synthesize (i.e., 3D hallucination) missing viewpoint information (such as front and back perspectives). However, this approach does not resolve the absence of motion information. While synthesized views can alleviate some occlusion issues, the human body's non-rigid structure requires more than static viewpoints to capture its complex kinematic patterns effectively. Inconsistent 3D Prior: Current mainstream methods [5, 7, 10, 47] use Score Distillation Sampling (SDS) [25] to leverage diffusion models as supervisory modules for learning 3D priors. However, the high generative diversity of these models often leads to viewpoint inconsistencies, resulting in implausible imagery (e.g., poor-quality hidden views and inconsistencies with the input image). HumanRef [47] attempts to mitigate the instability of SDS through ReferenceNet [8], but observable inconsistencies remain widespread in the results of ReferenceNet-based methods [8, 33], indicating the difficulty in fully resolving this issue. Consequently, 3D representations should be robust enough to handle imperfect 3D priors, though this perspective has largely been overlooked in current single-image avatar frameworks.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address these challenges, this paper introduces a novel single-image 3D human avatar reconstruction framework, named SinGS. Unlike existing methods [23, 26], SinGS focuses on directly constructing an animatable 3DGS avatar. At the core of our SinGS framework are two key components: Kinematic Human Diffusion and a highly Geometry-Preserving 3D Gaussian Splatting. Specifically, Kinematic Human Diffusion (KHD) is designed to sample a highly 3D-consistent human sequence within the pose space, based solely on a single input image prompt. This approach enables high-quality and animatable 3D avatar reconstruction. To train KHD, we constructed a dataset with over ten thousand rotation videos, allowing KHD to learn a rich variety of human structures and texture distributions from different angles, while also gaining extensive knowledge of human kinematics. Unlike existing frameworks [5, 7, 10, 47] that rely on costly and scarce multi-view human data, our approach requires only more affordable and abundant video data, significantly reducing KHD's training costs and better aligning with scaling laws. Geometry-Preserving 3D Gaussian Splatting (i.e., GPGS) tackles artifact and hole issues under imperfect human priors (e.g., minor jitter and 3D inconsistencies) through two key designs: Semantic Laplacian Regularization addresses floating Gaussian spheres caused by 3D inconsistencies. It adjusts the constraint strength based on body parts, allowing more flexibility for areas like hair and tighter constraints",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "for facial details, reducing floating Gaussian spheres while maintaining rendering quality. Geometry-Preserving Density Control resolves over-deletion and incorrect deletion of spheres in the training process. By managing the Gaussian sphere density via mesh edges, it ensures the spheres remain around the mesh, preserving geometry and preventing large holes. Extensive experiments have validated that our SinGS can generate high-quality and animatable 3D avatars at ultra-fast inference speeds (up to 70 FPS) with efficient resource usage (requiring only 3.8GB of GPU memory).",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "2.1. Diffusion-based Human Generative Models",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recent advances in diffusion-based human generative models, especially those conditioned on pose, have improved model controllability. Frameworks like ControlNet [48], IP Adapter [44], and ReferenceNet [8], along with better human attribute detection (2D/3D pose estimation, SMPL parameters [18]), enable more precise and consistent results. In image synthesis, models like PIDM [1] and LFDM [22] enhance pose transfer and image adaptation, while LEO [38] uses flow maps for motion representation. For video, DreamPose [13] and DisCo [35] improve pose-to-image translation and control separation. Models likeAnimateAnyone [8], MagicAnimate [42], and Magic-Pose [4] refine pose conditioning with ReferenceNet. Despite these improvements, these models remain resource-heavy and struggle with stability when generating images of complex movements, such as head turns or rotations.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Single-Image Human Reconstruction",
+        "text_level": 1,
+        "bbox": [
+            500,
+            551,
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+            569
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Monocular video-based human reconstruction has reduced the need for specialized equipment, but single-image reconstruction remains challenging due to incomplete data. Early methods like PIFu [29] and SiCloPe [21] used pixel-aligned features and image-to-image translation, with PIFuHD [30] enhancing detail via normal maps. Later methods, such as ARCH [11] and ICON [40], incorporated body priors for animatable avatars, and ECON [41] improved model completeness by separately reconstructing front and back surfaces. Recent approaches like SiTH [7] and HumanRef [47] use generative models to fill in missing data, while SIFU [50] and Diffusion-FOF approximate multi-view features. R-Cyclic Diffuser [3] addresses limitations in Zero-1-to-3 [17], even with human-specific datasets, advancing single-image human reconstruction through generative priors and viewpoint conditioning.",
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+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given a target image  $I_r$ , the objective of the SinGS architecture is to reconstruct a fully animatable 3D avatar  $\\mathbf{A}_t$  based on  $I_r$ . To address the challenge of limited viewpoint and",
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+        "type": "page_number",
+        "text": "5572",
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+        "page_idx": 1
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+    {
+        "type": "image",
+        "img_path": "images/e7a026c2e6e41bf24d06eb4e3d6269db01b5c71d11ad0ad2a3e81164ccea5dfd.jpg",
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+    {
+        "type": "image",
+        "img_path": "images/952abdf13459951d7c01846d40b42bfdd5e314026774502637291596384d9a15.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/08ab15398cc7fd693842e859d7b8824d277dbc012ecfe7c884450a93e98e4c62.jpg",
+        "image_caption": [
+            "Figure 2. Overall framework of our method."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "kinematic information inherent in single-image reconstruction,  $I_{t}$  is first input into the Kinematic Human Diffusion (i.e., KHD) module to complete missing information, generating an augmented sequence of rendered images  $S_{t} = \\{I_{p_{1}},\\dots ,I_{p_{i}},\\dots ,I_{p_{N}}\\}$ , where  $N$  represents the total number of poses generated, and  $p_i$  indicates each corresponding 3D human pose. KHD reframes the less-constrained, underdetermined 3D reconstruction problem as a generative task, thus producing a fully-constrained, fully-observed 3D reconstruction formulation. Finally,  $S_{t}$  is fed into our compact 3DGS module to reconstruct an animatable 3D human avatar. The compact 3DGS module is capable of reconstructing a watertight, high-quality human model even with imperfect 3D priors. The distilled avatar is high-quality, computationally efficient, and well-suited for promising applications in AR, VR, and similar fields.",
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+    {
+        "type": "text",
+        "text": "3.1. Kinematic Priors",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.1.1 Kinematic Human Diffusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unlike existing hallucination architectures [7, 10, 50], our Kinematic Human Diffusion does not rely on camera input, which is prone to estimation errors and has the added challenges of multi-view data scarcity and high costs (e.g., multi-view human data typically requires capture with specialized setups like a light stage). Our approach instead posits that sampling within the motion space provides complete priors for viewpoint and kinematic features. Additionally, our KHD does not adopt a ReferenceNet structure [8];",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "while ReferenceNet has been highly successful, it requires maintaining two UNet models, significantly increasing the framework's resource demands and preventing integration of longer contexts (e.g., 24 frames). A shorter contextual window cannot provide an image sequence with a sufficient diversity of motion samples (e.g., 150 frames). Considering the above two aspects, our KHD is designed as a diffusion structure, as illustrated in Figure 2. KHD  $\\mathcal{G}$  takes a single image  $I_{r}$  as input and, constrained by a randomly sampled sequence of poses  $\\{p_1,p_2,\\dots ,p_N\\}$ , augments the input image into a sequence  $S_{t} = \\{I_{p_{1}},I_{p_{2}},\\ldots ,I_{p_{N}}\\}$ . This process can be formulated as follows:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nS _ {t} = \\mathcal {G} \\left(I _ {r}; p _ {1}, p _ {2}, \\dots , p _ {N}\\right). \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Model Architecture. Inspired by UniAnimate [36], our KHD also removes the ReferenceNet and directly inputs the reference image  $I_r$  and the driving sequence into the UNet. The reference image  $I_r$  is encoded by the VAE encoder of the diffusion model into a latent code  $z_r$ , serving as an appearance reference throughout KHD. Additionally,  $I_r$  is encoded by the CLIP image encoder [27] into features  $f_r$  which are injected into the network through cross-attention by replacing the original text encoder's features in the diffusion model. This enables high-fidelity preservation of the subject's appearance characteristics. Existing works typically use 2D poses (e.g., OpenPose [2], DW-Pose [43]) as the driving signal. However, our experiments reveal that 2D poses fail to guide the diffusion model accurately in scenarios with extensive occlusions, such as when the subject",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "5573",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "is turning. Moreover, 2D poses cannot reliably differentiate between different viewpoints of the human body. Therefore, we use SMPL refined by ScoreHMR [31] as the driving signal  $\\{p_1,p_2,\\dots,p_N\\}$ . It is worth noting that Champ [51] also uses SMPL as guidance; however, their SMPL estimations lack accuracy, and they rely on overly strict guidance inputs, such as depth and normal vectors. This approach leads to suboptimal results, performing even worse than 2D poses in practice, for instance, by generating inconsistent body shapes. The SMPL parameters are converted into a mesh model in the specified pose using Linear Blend Skinning (LBS) [18]. This mesh is rendered as an RGB image based on the fixed camera pose maintained throughout the process. The rendered image is then encoded by a 3D Pose Encoder, a network composed of several convolutional layers, into a latent code  $z_{p_i}$  with the same dimensionality as  $z_{r}$ . All  $z_{p_i}$  codes are first concatenated with the input noise along the channel dimension, and then sequentially along the temporal dimension to obtain the final representation  $z_{P} \\in \\mathbb{R}^{T \\times C \\times H \\times W}$ . Simultaneously,  $I_{r}$  is processed to estimate and encode its pose latent code  $z_{p_r}$ , which is then concatenated with  $z_{P}$  along the temporal dimension before being fed into the diffusion model's backbone. Following most video generation models [36, 37], the UNet component of the diffusion model is also designed as a 3D UNet to ensure 3D consistency in the generated output.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Training Dataset and Strategy. Human image animation [8, 36] primarily focuses on generating diverse frontal human movements (e.g., dancing). As a result, their training data (e.g., TikTok [12]) is largely composed of performance videos of dancers, typically featuring frontal views and wide movement ranges. In our experiments, we found that models trained on this type of data provide limited support for our 3D reconstruction tasks. These models often fail to generate results with high consistency, exhibit significant flickering in fine details, and display abnormal motion in clothing dynamics. In response to this, we collected over 6,000 high-definition videos (each around 20 seconds long) from YouTube, featuring activities such as model showcases and dancing, with a focus on segments that include turning motions. Additionally, we incorporated 600 clips from the UBC Fashion dataset [45], primarily showcasing model runway turns. As a key part of our dataset, we also integrated frontal-view data from MVHumanNet [39]. We used SAM2 [28] to segment human figures from the background in MVHumanNet, then merged the results with a white background to create videos with a consistent background, effectively eliminating the background variability caused by bounding boxes in MVHumanNet. These three sources together form a dataset of over 10,000 training videos, which we call RotationHuman. Notably, compared to multi-view data, this type of data collection is significantly more cost-effective and thus better",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "suited for building large-scale datasets. During training, our KHD generates 64 pose-driven images in a single pass, setting the context window to 64 frames (i.e.,  $N = 64$ ). In the inference stage, we directly generate 128 frames in one pass. The advantage of one-pass inference is that it avoids consistency jitter in overlapping transition frames. KHD training requires only one phase, where the objective is to reconstruct the ground truth images corresponding to each pose, with the training loss formulated as follows:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathbb {E} _ {\\theta} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, f _ {r}, t\\right) \\| ^ {2} \\right], \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            599,
+            241,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where,  $t$  denotes the denoising step, and  $z_{t}$  represents the noise at step  $t$ . Note that  $z_{t}$  in KHD contains diffusion states for  $N$  different driving poses. The feature  $f_{r}$  is the CLIP image encoding of the reference image  $I_{r}$ , used to ensure ID consistency in the generated results.  $\\theta$  represents the parameters of the 3D UNet and the 3D Pose Encoder. The overall training process involves learning to reconstruct the target video based on  $I_{r}$  as input and the pose set  $\\{p_1, p_2, \\dots, p_N\\}$  as conditioning. The generated sequence  $S_{t}$  represents the sampling results of the subject in the input image  $I_{r}$  within the pose space, and it can be directly used for 3D avatar reconstruction.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. 3D Distillation with Geometry-Preserving 3D Gaussian Splitting",
+        "text_level": 1,
+        "bbox": [
+            498,
+            454,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Once we obtain the sequence of pose images sampled from KHD, the goal is to distill a animatable and real-time rendered human avatar using Geometry-Preserving 3D Gaussian Splatting (GPGS). This challenge can be addressed based on mainstream approaches [16, 32, 52] in monocular 3D reconstruction. As illustrated in the Figure 2 on the right, we initialize the positions of Gaussians using the human template mesh that has undergone loop subdivision. The initial positions are set to the vertex locations, with a default of 2 upsampling iterations. This typically results in approximately  $110.6K$  Gaussians. To model the avatar representation, all vertices are fed into a learnable triplane [52] to extract vertex-wise features. These features are subsequently passed to MLPs to predict the geometry and appearance attributes of the Gaussians, respectively. The entire modeling process occurs in canonical space, and we finally map this canonical space into posed space using Linear Blend Skinning (LBS) based on the SMPL framework.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 Semantic Laplacian Regularization",
+        "text_level": 1,
+        "bbox": [
+            498,
+            785,
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+            800
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Even during the reconstruction of real video, it is challenging to recover perfect static 3D consistency. Therefore, while the generated videos may appear visually plausible, every tiny ambiguity during lifting the 2D outcomes into 3D space potentially leads to catastrophic issues. Early experimental results indicated that common reconstruction meth",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "5574",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/79c841c208901a493b99c45a5bd7271df7ea2ff9553df4900229e904929fd7b1.jpg",
+        "image_caption": [
+            "Figure 3. Visual comparison of our method with TeCH [10] and SiTH [7] for single-image reconstruction. We reposed the reconstructed results to A Pose, showcasing both animation and reconstruction capabilities. We highly recommend checking the suppl. for more results. We have provided a large number of animation result images and videos in the suppl."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "ods produced results that lacked smoothness and compactness, resulting in existing disconnected and floating gaus-. sians. Following [20], we found that applying Laplacian regularization on the canonical mesh, both for geometry and appearance, effectively mitigated the presence of gaus-. sians out of control. However, it also constrained offsets. In other words, isometrical Laplacian constraint on the whole body overly relied on the accuracy of the SMPL mesh, also making it difficult to fit areas such as hair and clothing that deviate significantly from the SMPL surface. Considering the complexity of the human body and the impossibility to obtain extremely accurate SMPL estimation, we repartition all gaussian vertices into  $L = 15$  distinct semantic parts and dynamically adjust the smoothing strength. Besides, we impose the constraint on the anchors points which are closer to the rendering surface than gausicians center. The Semantic Laplacian Regularization (SLR) is defined as follows:",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {S L R} = \\sum_ {u \\in \\Omega} \\lambda_ {u} \\left\\| a _ {u, v} - \\frac {1}{| M (u , v) |} \\sum_ {v \\in M (u, v)} a _ {u, v} \\right\\|, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            101,
+            859,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Omega$  represents the set of semantic regions,  $a$  denotes the surface anchor point of the  $v$ -th Gaussian vertex in the  $u$ -th semantic region, and  $M(u,v)$  refers to the set of adjacent points of the Gaussian vertex  $a_{u,v}$  located within the  $u$ -th semantic region. Experiments demonstrate that the Semantic Laplacian Regularization significantly impacts the handling of more intricate situations, particularly when dealing with errors between the SMPL mesh and the actual character, which can arise from both inaccurate estimations and complex clothing. We apply Laplacians in both position and color spaces; the former enhances the smoothness of the rendering surface, while the latter ensures a more continuous variation in color space.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 Geometry-Preserving Density Control Strategy",
+        "text_level": 1,
+        "bbox": [
+            498,
+            814,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The strategies in vanilla 3DGS were not originally build for complex, dynamic structures like the human body. While works [20] have adapted the approach, such as initializing Gaussians based on SMPL meshes, these efforts pri",
+        "bbox": [
+            496,
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5575",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/490809444f4498540e92eacd9069a893f3627339c7656ddc5b98ba9e7f2916ce.jpg",
+        "table_caption": [
+            "Table 1. Quantitative comparisons with existing methods on UBC fashion dataset [45]. Note that metrics in the table are measure with the background-removed video. Some methods are unable to perform animation, and therefore, these metrics are not available for those methods. Bold indicates the best results, while Underlined represents the second-best results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Prior Type</td><td>PSNR ↑</td><td>LPIPS ↓</td><td>FVD ↓</td><td>Context. ↓</td><td>CLIP Score ↑</td><td>Speed↑</td></tr><tr><td>DisCo [35] (CVPR24)</td><td>-</td><td>30.98</td><td>0.259</td><td>167.7</td><td>2.134</td><td>82.4%</td><td>1FPS</td></tr><tr><td>Animate Anyone [8] (CVPR24)</td><td>-</td><td>31.33</td><td>0.238</td><td>148.8</td><td>1.901</td><td>86.6%</td><td>2FPS</td></tr><tr><td>Champ [51] (ECCV24)</td><td>-</td><td>31.21</td><td>0.251</td><td>155.1</td><td>2.038</td><td>84.3%</td><td>1FPS</td></tr><tr><td>UniAnimate [36] (ArXiv24)</td><td>-</td><td>32.31</td><td>0.211</td><td>141.3</td><td>1.811</td><td>87.1%</td><td>2FPS</td></tr><tr><td>SHERF [9] (ICCV23)</td><td>-</td><td>27.39</td><td>0.301</td><td>202.3</td><td>2.998</td><td>70.1%</td><td></td></tr><tr><td>SIFU [50] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.891</td><td>72.1%</td><td>5FPS</td></tr><tr><td>GST [26] (ArXiv24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>3.011</td><td>71.7%</td><td>50FPS</td></tr><tr><td>TeCH [10] (3DV24)</td><td>Camera</td><td>29.01</td><td>0.271</td><td>188.1</td><td>2.331</td><td>79.3%</td><td>6FPS</td></tr><tr><td>SiTH [7] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.776</td><td>74.7%</td><td>&lt;1FPS</td></tr><tr><td>HumanRef [47] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.167</td><td>81.5%</td><td>3FPS</td></tr><tr><td>SHERT [46] (CVPR2024)</td><td>Inpainting</td><td>29.31</td><td>0.266</td><td>179.8</td><td>2.319</td><td>78.8%</td><td>10FPS</td></tr><tr><td>UniAnimate + GPGS (ours)</td><td>Kinematics</td><td>29.97</td><td>0.251</td><td>168.7</td><td>1.992</td><td>82.1%</td><td>70FPS</td></tr><tr><td>KHD (ours)</td><td>-</td><td>32.81</td><td>0.221</td><td>134.4</td><td>1.768</td><td>92.3%</td><td>2FPS</td></tr><tr><td>SinGS (ours)</td><td>Kinematics</td><td>31.33</td><td>0.240</td><td>156.3</td><td>1.847</td><td>88.2%</td><td>70FPS</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "marily lay a solid foundation for the optimization process but fail to maintain this advantages throughout. Incompatibilities still arise in optimization stage, prompting us to propose a novel density control scheme that is inherently compatible with hybrid representations, designed for adaptive adjustment body-wide density. This scheme draws on mesh operation algorithms [6] to better address the unique challenges of human body. For primitives that locate in under-expression mesh areas, we subdivide these regions by adding gaussians on every edge of the selected geometric triangles, which creates much smaller triangles. And we skip the trivial post-smoothing for vertices as the position of Gaussians will continue to be optimized in the network. For candidate Gaussians that are selected due to excessively large scales, as well as all newly added Gaussians, we perform rescaling to adjust them to an average size. In the case of anomalous gaussians, especially those are almost transparent, we collapse relevant edges and replace them with single vertex, resulting in decimated adjacent faces. And the priority of selected edges is decided by gaussian attributes and edge length. This entire pruning process preserves the principal structure of the human body. Our strategy result in better reconstruction and animation as the optimization was conducted under connectivity and compactness of the entire human body rather than producing holes and stacks. Moreover, this approach synergistically enhances the effectiveness of our hybrid representation.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            789,
+            209,
+            806
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            815,
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+            832
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Our KHD primarily utilizes the RotationHuman dataset we collected, which focuses on human pose image sequences involving turning motions. The specific structure of the 3D Pose Encoder is provided in",
+        "bbox": [
+            75,
+            839,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the supplementary materials. KHD was trained using 8 NVIDIA A100 80GB GPUs, with DeepSpeed and ZeRO2 employed to reduce memory usage. Similar toAnimate Anyone, we resized the video frames to a spatial dimension of  $768 \\times 512$ . We used a context window size of 64 frames, and to enhance model scalability post-training, we implemented a random context window jitter strategy [36]. During training, the model randomly samples window sizes from 64 to 32 frames in an uniformly distributed manner. The training process utilized the AdamW optimizer [15], with a learning rate set to  $5e - 5$  and DDPM with 1000 steps for noise sampling. During inference, DDIM with 30 steps was used to reduce inference time. For the 3DGS component, the Adam optimizer [15] was used with a learning rate of  $1e - 3$  and a cosine annealing learning scheduler was applied to accelerate convergence. The input image sequence size for 3DGS was also  $768 \\times 512$ . 3DGS was trained using a single NVIDIA 4090 24GB GPU.",
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+    },
+    {
+        "type": "text",
+        "text": "Baseline Models. Our baseline models consist of two parts: the first part includes human image animation models, such as DisCo [35], Animation Anyone [8]  $^{1}$ , Champ [51], and UniAnimate [36]. These models are used to compare our animation capability and the superiority of KHD. The second part consists of single-image 3D avatar reconstruction models, including SHERF [9], SIFU [50], GST [26], TeCH [10], SiTH [7], HumanRef [47], and SHERT [46].",
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+    {
+        "type": "text",
+        "text": "Metrics. We employ both PSNR and LPIPS to assess the quality of video reconstruction. To evaluate the animation capability of our model, we also use FVD [34] to measure the distribution discrepancy between the generated video and the original video, assessing the video generation performance. Furthermore, following HumanRef, we introduce contextual distance [19] and CLIP score [27] to evaluate the texture and semantic similarity between the rendered",
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+        "type": "page_footnote",
+        "text": "<sup>1</sup>https://github.com/MooreThreads/Moore-AnimateAnyone",
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+        "text": "5576",
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+    {
+        "type": "image",
+        "img_path": "images/3a42d13bfec4a738751303ba79faedc3dfb2230b70f53d76348c9b242b679bee.jpg",
+        "image_caption": [
+            "Figure 4. Comparison between KHD and other SOTA human image animation methods. Please zoom in for better observation."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "output and the input reference image.",
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+    {
+        "type": "text",
+        "text": "4.2. Qualitative Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Singe-Image Reconstruction. We compare SinGS with two methods from the literature that claim to support animation (TeCH, SiTH). It is worth noting that during our experiments, we found that single-image animation with these methods was extremely difficult to execute, and in some cases, nearly impossible. We had to use third-party code  ${}^{2}$  to achieve the reposing for some of these methods. We animate their reconstructed outputs to a common pose (A Pose) for comparison, which allows us to evaluate both reconstruction and animation capabilities. The comparison results are shown in Figure 3, SinGS generates results with better details and maintains high-quality animation, particularly on the in-the-wild data, where SinGS's visual performance significantly outperforms the other methods. This demonstrates the high feasibility and effectiveness of the kinematic prior.",
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+        "type": "text",
+        "text": "Kinematic Human Diffusion. KHD, as the core component of our pipeline, is compared with state-of-the-art human image animation methods, includingAnimate Anyone and UniAnimate. As shown in Figure 4, we drive the same character with all three methods, focusing on comparing the quality of their generated results, particularly for the turning pose. From the figure, it is clear that both UniAnimate and our KHD maintain higher consistency thanAnimate Anyone after the character turns, with KHD surpassing UniAnimate in detail. The details marked by the red arrows in Figure 4 reveals that UniAnimate generates incorrect details, a common issue when using 2D poses, as they often struggle to distinguish body orientation during back-facing poses, leading the model to generate erroneous images. This is detrimental to reconstruction, while KHD generates videos with much higher consistency.",
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+    {
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+        "img_path": "images/8571cb3aae5ca73f739c8b03c6c01711d6540f1a88c71bf7ebf6b1602c55dd38.jpg",
+        "image_caption": [
+            "Figure 5. Fifty users rated the video quality, with UniAnimate scoring highest, followed closely by our model, which outperformed others. Our model is more efficient, using only 3.5 GB of memory and achieving 70 FPS, while UniAnimate requires over 12GB and 0.5 seconds per image."
+        ],
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+    {
+        "type": "text",
+        "text": "Geometry-Preserving 3D Gaussian Splatting. Although KHD provides high-consistency pose sampling results, it inevitably has some consistency flaws, meaning it can only offer imperfect prior information. Our geometry-preserving GS method is specifically designed to address this challenge. To validate the superiority of our Geometry-Preserving 3D Gaussian Splatting (GPGS) over general human modeling methods, we compared it with recent state-of-the-art (i.e., SOTA) methods, HAHA [32] and HUGS [16]. We generate a pose sequence using KHD and then performed reconstruction with all 3 methods. The reconstruction results are shown in Figure 7. As seen, both HAHA and HUGS fail to produce a compact 3D avatar, with significant holes or floating artifacts appearing in various areas, particularly during the turning motion. In contrast, our GPGS method is able to reconstruct a compact, watertight 3D avatar model.",
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+    {
+        "type": "text",
+        "text": "4.3. Quantitative Analysis",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We selected 100 test videos from the UBC dataset for our quantitative analysis. For each video, we chose the first frame as the reference image and used the video's pose sequence as the driving signal. The performance of all methods was assessed by comparing the animation results with the original video to evaluate the differences. Video reconstruction metrics (including PSNR, LPIPS, and FVD) reflect the model's animation capabilities, while Contextual Distance and CLIP score allow for comparison with methods that do not support animation. The quantitative comparison results are shown in Table 1. Human image animation methods (i.e., the second to fifth rows in the table, including our KHD) outperform the reconstruction-based methods across the board. Among them, KHD surpasses the other methods in most metrics, and UniAnimate also demonstrates superior performance, which is expected due to the scale of training data and model size. While SinGS lags behind UniAnimate, it shows a significant advantage over other methods in some metrics. However, SinGS significantly outperforms diffusion-based animation methods in terms of inference efficiency and resource consumption. Our SinGS achieves 70 FPS during inference, with only",
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+    {
+        "type": "page_footnote",
+        "text": "$^{2}$ https://github.com/custom-humans/editable-humans",
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+        "text": "5577",
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+    {
+        "type": "table",
+        "img_path": "images/0a5847d3fcf1cdcf6872f676ffbe0506b521a418c0fb7b16bc3e7fa5705b251f.jpg",
+        "table_caption": [
+            "Table 2. The results of the ablation experiments on Semantic Laplacian Regularization (i.e., Semantic Lap. Reg.) and Geometry-Preserving Density Control (i.e., GPDC) in SinGS."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Setting</td><td>PSNR</td><td>LPIPS</td><td>FVD</td></tr><tr><td>with Semantic Lap. Reg.</td><td>31.33</td><td>0.240</td><td>156.3</td></tr><tr><td>with KNN Lap. Reg.</td><td>30.88</td><td>0.250</td><td>169.9</td></tr><tr><td>w/o Lap. Reg.</td><td>30.34</td><td>0.272</td><td>181.3</td></tr><tr><td>with GPDC</td><td>31.01</td><td>0.249</td><td>166.1</td></tr><tr><td>naive Density Control [14]</td><td>30.22</td><td>0.276</td><td>190.2</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.8 GB of memory usage (tested on a single NVIDIA 4090 GPU), while UniAnimate, Champ, andAnimate Anyone each require more than 0.4 seconds per image and consume over 12 GB of memory. These quantitative results strongly demonstrate that SinGS is highly effective and feasible. We believe that using KHD, a specialized foundational model, will greatly enhance 3D reconstruction performance while significantly reducing the stringent data requirements.",
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+    {
+        "type": "text",
+        "text": "User Study. We invited 50 users to subjectively evaluate the animation results of SinGS. The evaluation was based on a scale from 0 to 10, with 10 being the highest score and 0 being the lowest. The results are visualized in Figure 5.",
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+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Kinematic Priors Analysis. The number of poses sampled by KHD has a significant impact on the 3D distillation process. We analyzed how the number of poses affects the animation capability of the final reconstructed model, and the results are shown in Figure 6. We incrementally increased the number of poses from 2 (which corresponds to the typical approach of generating front and rear views, as used by most methods) up to 150. We also tested the influence of different prior models (i.e., KHD, UniAnimate, and Animate Anyone) on the results. Additionally, we examined how different 3DGS reconstruction methods handle the use of prior knowledge. As shown, performance improves rapidly with an increase in the number of poses, but the rate of improvement slows significantly after reaching around 100 poses. Moore-AA + HAHA shows the slowest improvement, while KHD + GPGS exhibits the slowest decline in performance. This suggests that increasing the number of poses does not always lead to improved performance for two main reasons: first, the prior models have already provided sufficient information; and second, none of the prior models provide perfectly consistent priors. Excessive sampling can introduce a lot of inconsistent noise, which ultimately harms performance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Geometry-Preserving 3D Gaussian Splitting Analysis. We conducted ablation experiments on the two key designs in GPGS: Semantic Laplacian Regularization and GPDC, with the results shown in Table 2. By replacing and removing the Laplacian regularization, we observed that Semantic Laplacian consistently outperforms in terms of reconstruction metrics. Additionally, GPDC demonstrates a perfor",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/b842dcf943409a52bdf762189b7e88ee69294668cd25f9d0b1b64457ba6422f0.jpg",
+        "image_caption": [
+            "Figure 6. The comparison of the impact of augmented pose numbers on the performance of the 3D avatar models."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/b6dc8cd903053ead99689f69599e83ad168ab21e6ef0529d1e35b52fc60f9414.jpg",
+        "image_caption": [
+            "Figure 7. Here is a comparison of our GPGS with two SOTA 3DGS avatar methods, HAHA [32] and HUGS [16]. All methods use images sampled by KHD as body prior."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "mance advantage over the original density control strategy. The original strategy does not account for dynamic properties and geometric constraints, which makes it ineffective in addressing issues like floating and holes caused by data inconsistencies.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose a new paradigm for single-image 3D avatar reconstruction. Unlike traditional methods that complete missing information in camera space, we sample in human kinematic space, enabling efficient capture of both viewpoints and motion traits. To achieve this, we introduce Kinematic Human Diffusion (KHD) for consistent pose-space generation, supported by our RotationHuman dataset, which focuses on turning motions. Additionally, we propose Geometry-Preserving 3D Gaussian Splating that reconstructs high-quality, animatable 3D avatars under imperfect human priors. This includes two key innovations: Semantic Laplacian regularization for compact, detailed constraints, and a geometry-preserving density control strategy to maintain stable human geometry. Together, these innovations allow SinGS to achieve high-quality, animatable 3D avatar reconstruction from a single image.",
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+        "text": "5578",
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+    {
+        "type": "text",
+        "text": "6. Acknowledgment",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work supported by Shanghai Post-doctoral Excellence Programe (2024290). This work was also partly by Shanghai Municipal Bureau of Culture and Tourism and Meta-verse Technology Innovation Center of Shanghai Municipal Bureau of Culture and Tourism. Kairui Feng thanks to Xiaomi foundation.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 8
+    },
+    {
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+            "[39] Zhangyang Xiong, Chenghong Li, Kenkun Liu, Hongjie Liao, Jianqiao Hu, Junyi Zhu, Shuliang Ning, Lingteng Qiu, Chongjie Wang, Shijie Wang, Shuguang Cui, and Xiaoguang Han. Mvhumannet: A large-scale dataset of multi-view daily dressing human captures. In CVPR 2024, pages 19801-19811. IEEE, 2024. 4"
+        ],
+        "bbox": [
+            78,
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+            898
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[40] Yuliang Xiu, Jinlong Yang, Dimitrios Tzionas, and Michael J. Black. ICON: Implicit Clothed humans Obtained from Normals. In CVPR 2022, pages 13296-13306, 2022. 1, 2",
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2025/SinGS_ Animatable Single-Image Human Gaussian Splats with Kinematic Priors/a1907643-3cec-4712-b625-aae92326d106_model.json

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+[
+    [
+        {
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+            "angle": 0,
+            "content": "CVF"
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+            "bbox": [
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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "SinGS: Animatable Single-Image Human Gaussian Splats with Kinematic Priors"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Yufan Wu\\(^{1*}\\) Xuanhong Chen\\(^{1\\dagger}\\) Wen Li\\(^{1,3}\\) Shunran Jia\\(^{2}\\) Hualiang Wei\\(^{1*}\\) Kairui Feng\\(^{4}\\)  \nJialiang Chen\\(^{1}\\) Yuhan Li\\(^{1}\\) Ang He\\(^{1*}\\) Weimin Zhang\\(^{1}\\) Bingbing Ni\\(^{1}\\) Wenjun Zhang\\(^{1}\\)"
+        },
+        {
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+            "bbox": [
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+            "angle": 0,
+            "content": "\\(^{1}\\)Shanghai Jiao Tong University, Shanghai, China \\(^{2}\\)DreamX Inc \\(^{3}\\)Akool Research \\(^{4}\\)The National Key Laboratory of Autonomous Intelligent Unmanned Systems, Shanghai, China"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "{chen19910528,wmzhang,nibingbing,zhangwenjun}@sjtu.edu.cn, elvinfkr@tongji.edu.cn"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
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+            "angle": 0,
+            "content": "Abstract"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Despite significant advances in accurately estimating geometry in contemporary single-image 3D human reconstruction, creating a high-quality, efficient, and animatable 3D avatar remains an open challenge. Two key obstacles persist: incomplete observation and inconsistent 3D priors. To address these challenges, we propose SinGS, aiming to achieve high-quality and efficient animatable 3D avatar reconstruction. At the heart of SinGS are two key components: Kinematic Human Diffusion and Geometry-Preserving 3D Gaussain Splatting. The former is a foundational human model that samples within pose space to generate a highly 3D-consistent and high-quality sequence of human images, inferring unseen viewpoints and providing kinematic priors. The latter is a system that reconstructs a compact, high-quality 3D avatar even under imperfect priors, achieved through a novel semantic Laplacian regularization and a geometry-preserving density control strategy that enable precise and compact assembly of 3D primitives. Extensive experiments demonstrate that SinGS enables life-like, animatable human reconstructions, maintaining both high quality and inference efficiency (up to 70FPS)."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+            ],
+            "angle": 0,
+            "content": "Single-image 3D human reconstruction (i.e., SIHR) is an emerging modeling technique that aims to create a lifelike 3D avatar from just one image, offering a highly cost-effective and promising approach to 3D modeling. Recently, 3D Gaussian Splatting (3DGS)[14] has made significant breakthroughs in rendering efficiency and quality, establishing itself as a mainstream approach for 3D avatar reconstruction. However, current 3DGS-based methods [23, 26] for single-image human 3D avatar reconstruction suffer from critical limitations in animation, as most are"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
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+            ],
+            "angle": 0,
+            "content": "Figure 1. Existing single-image 3D avatar reconstruction methods are limited to sampling prior information from camera space. In contrast, SinGS proposes sampling from pose space, allowing us to obtain both camera and kinematic priors simultaneously. Combined with our Geometry-Preserving 3D Gaussian Splitting, this enables highly efficient animation rendering."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "designed primarily for static assets. This paper aims to develop an animation reconstruction framework that achieves a high balance between efficiency and rendering quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.765,
+                0.893,
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+            ],
+            "angle": 0,
+            "content": "Currently, the vast majority of SIHR methods [7, 10, 23, 24, 26, 40, 41, 46, 49, 50] focus solely on optimizing geometry while neglecting to enhance animation capabilities. As a result, they are often incapable of animation or require third-party tools [7] to achieve approximate motion. Unlike digital assets, the primary requirement for a human avatar is its ability to animate, making animation the core goal of SIHR [9]. Achieving animatable single-image human reconstruction (i.e., Animatable SIHR) is particularly"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "*Work done during an internship at Shanghai Jiao Tong University."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "† Corresponding author: Xuanhong Chen."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.095,
+                0.875,
+                0.45,
+                0.9
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.946,
+                0.514,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5571"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.473,
+                0.485
+            ],
+            "angle": 0,
+            "content": "challenging for two main reasons: Incomplete Observation: A single image lacks comprehensive viewpoint information, offering an extremely limited, partial observation that cannot address occlusion issues. Current methods [7, 10, 47] mainly rely on fine-tuned diffusion models to synthesize (i.e., 3D hallucination) missing viewpoint information (such as front and back perspectives). However, this approach does not resolve the absence of motion information. While synthesized views can alleviate some occlusion issues, the human body's non-rigid structure requires more than static viewpoints to capture its complex kinematic patterns effectively. Inconsistent 3D Prior: Current mainstream methods [5, 7, 10, 47] use Score Distillation Sampling (SDS) [25] to leverage diffusion models as supervisory modules for learning 3D priors. However, the high generative diversity of these models often leads to viewpoint inconsistencies, resulting in implausible imagery (e.g., poor-quality hidden views and inconsistencies with the input image). HumanRef [47] attempts to mitigate the instability of SDS through ReferenceNet [8], but observable inconsistencies remain widespread in the results of ReferenceNet-based methods [8, 33], indicating the difficulty in fully resolving this issue. Consequently, 3D representations should be robust enough to handle imperfect 3D priors, though this perspective has largely been overlooked in current single-image avatar frameworks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.494,
+                0.473,
+                0.904
+            ],
+            "angle": 0,
+            "content": "To address these challenges, this paper introduces a novel single-image 3D human avatar reconstruction framework, named SinGS. Unlike existing methods [23, 26], SinGS focuses on directly constructing an animatable 3DGS avatar. At the core of our SinGS framework are two key components: Kinematic Human Diffusion and a highly Geometry-Preserving 3D Gaussian Splatting. Specifically, Kinematic Human Diffusion (KHD) is designed to sample a highly 3D-consistent human sequence within the pose space, based solely on a single input image prompt. This approach enables high-quality and animatable 3D avatar reconstruction. To train KHD, we constructed a dataset with over ten thousand rotation videos, allowing KHD to learn a rich variety of human structures and texture distributions from different angles, while also gaining extensive knowledge of human kinematics. Unlike existing frameworks [5, 7, 10, 47] that rely on costly and scarce multi-view human data, our approach requires only more affordable and abundant video data, significantly reducing KHD's training costs and better aligning with scaling laws. Geometry-Preserving 3D Gaussian Splatting (i.e., GPGS) tackles artifact and hole issues under imperfect human priors (e.g., minor jitter and 3D inconsistencies) through two key designs: Semantic Laplacian Regularization addresses floating Gaussian spheres caused by 3D inconsistencies. It adjusts the constraint strength based on body parts, allowing more flexibility for areas like hair and tighter constraints"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.245
+            ],
+            "angle": 0,
+            "content": "for facial details, reducing floating Gaussian spheres while maintaining rendering quality. Geometry-Preserving Density Control resolves over-deletion and incorrect deletion of spheres in the training process. By managing the Gaussian sphere density via mesh edges, it ensures the spheres remain around the mesh, preserving geometry and preventing large holes. Extensive experiments have validated that our SinGS can generate high-quality and animatable 3D avatars at ultra-fast inference speeds (up to 70 FPS) with efficient resource usage (requiring only 3.8GB of GPU memory)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.255,
+                0.642,
+                0.272
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.28,
+                0.869,
+                0.295
+            ],
+            "angle": 0,
+            "content": "2.1. Diffusion-based Human Generative Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.303,
+                0.895,
+                0.545
+            ],
+            "angle": 0,
+            "content": "Recent advances in diffusion-based human generative models, especially those conditioned on pose, have improved model controllability. Frameworks like ControlNet [48], IP Adapter [44], and ReferenceNet [8], along with better human attribute detection (2D/3D pose estimation, SMPL parameters [18]), enable more precise and consistent results. In image synthesis, models like PIDM [1] and LFDM [22] enhance pose transfer and image adaptation, while LEO [38] uses flow maps for motion representation. For video, DreamPose [13] and DisCo [35] improve pose-to-image translation and control separation. Models likeAnimateAnyone [8], MagicAnimate [42], and Magic-Pose [4] refine pose conditioning with ReferenceNet. Despite these improvements, these models remain resource-heavy and struggle with stability when generating images of complex movements, such as head turns or rotations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.553,
+                0.822,
+                0.57
+            ],
+            "angle": 0,
+            "content": "2.2. Single-Image Human Reconstruction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.576,
+                0.895,
+                0.82
+            ],
+            "angle": 0,
+            "content": "Monocular video-based human reconstruction has reduced the need for specialized equipment, but single-image reconstruction remains challenging due to incomplete data. Early methods like PIFu [29] and SiCloPe [21] used pixel-aligned features and image-to-image translation, with PIFuHD [30] enhancing detail via normal maps. Later methods, such as ARCH [11] and ICON [40], incorporated body priors for animatable avatars, and ECON [41] improved model completeness by separately reconstructing front and back surfaces. Recent approaches like SiTH [7] and HumanRef [47] use generative models to fill in missing data, while SIFU [50] and Diffusion-FOF approximate multi-view features. R-Cyclic Diffuser [3] addresses limitations in Zero-1-to-3 [17], even with human-specific datasets, advancing single-image human reconstruction through generative priors and viewpoint conditioning."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.831,
+                0.637,
+                0.848
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+            "angle": 0,
+            "content": "3. Methodology"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Given a target image \\( I_r \\), the objective of the SinGS architecture is to reconstruct a fully animatable 3D avatar \\( \\mathbf{A}_t \\) based on \\( I_r \\). To address the challenge of limited viewpoint and"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.517,
+                0.958
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+            "angle": 0,
+            "content": "5572"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.088,
+                0.498,
+                0.324
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.498,
+                0.089,
+                0.892,
+                0.323
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.079,
+                0.325,
+                0.891,
+                0.417
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.352,
+                0.429,
+                0.616,
+                0.443
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overall framework of our method."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.455,
+                0.474,
+                0.698
+            ],
+            "angle": 0,
+            "content": "kinematic information inherent in single-image reconstruction, \\( I_{t} \\) is first input into the Kinematic Human Diffusion (i.e., KHD) module to complete missing information, generating an augmented sequence of rendered images \\( S_{t} = \\{I_{p_{1}},\\dots ,I_{p_{i}},\\dots ,I_{p_{N}}\\} \\), where \\( N \\) represents the total number of poses generated, and \\( p_i \\) indicates each corresponding 3D human pose. KHD reframes the less-constrained, underdetermined 3D reconstruction problem as a generative task, thus producing a fully-constrained, fully-observed 3D reconstruction formulation. Finally, \\( S_{t} \\) is fed into our compact 3DGS module to reconstruct an animatable 3D human avatar. The compact 3DGS module is capable of reconstructing a watertight, high-quality human model even with imperfect 3D priors. The distilled avatar is high-quality, computationally efficient, and well-suited for promising applications in AR, VR, and similar fields."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.713,
+                0.248,
+                0.727
+            ],
+            "angle": 0,
+            "content": "3.1. Kinematic Priors"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.738,
+                0.33,
+                0.751
+            ],
+            "angle": 0,
+            "content": "3.1.1 Kinematic Human Diffusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.765,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Unlike existing hallucination architectures [7, 10, 50], our Kinematic Human Diffusion does not rely on camera input, which is prone to estimation errors and has the added challenges of multi-view data scarcity and high costs (e.g., multi-view human data typically requires capture with specialized setups like a light stage). Our approach instead posits that sampling within the motion space provides complete priors for viewpoint and kinematic features. Additionally, our KHD does not adopt a ReferenceNet structure [8];"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.455,
+                0.892,
+                0.636
+            ],
+            "angle": 0,
+            "content": "while ReferenceNet has been highly successful, it requires maintaining two UNet models, significantly increasing the framework's resource demands and preventing integration of longer contexts (e.g., 24 frames). A shorter contextual window cannot provide an image sequence with a sufficient diversity of motion samples (e.g., 150 frames). Considering the above two aspects, our KHD is designed as a diffusion structure, as illustrated in Figure 2. KHD \\(\\mathcal{G}\\) takes a single image \\(I_{r}\\) as input and, constrained by a randomly sampled sequence of poses \\(\\{p_1,p_2,\\dots ,p_N\\}\\), augments the input image into a sequence \\(S_{t} = \\{I_{p_{1}},I_{p_{2}},\\ldots ,I_{p_{N}}\\}\\). This process can be formulated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.608,
+                0.648,
+                0.892,
+                0.663
+            ],
+            "angle": 0,
+            "content": "\\[\nS _ {t} = \\mathcal {G} \\left(I _ {r}; p _ {1}, p _ {2}, \\dots , p _ {N}\\right). \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Model Architecture. Inspired by UniAnimate [36], our KHD also removes the ReferenceNet and directly inputs the reference image \\( I_r \\) and the driving sequence into the UNet. The reference image \\( I_r \\) is encoded by the VAE encoder of the diffusion model into a latent code \\( z_r \\), serving as an appearance reference throughout KHD. Additionally, \\( I_r \\) is encoded by the CLIP image encoder [27] into features \\( f_r \\) which are injected into the network through cross-attention by replacing the original text encoder's features in the diffusion model. This enables high-fidelity preservation of the subject's appearance characteristics. Existing works typically use 2D poses (e.g., OpenPose [2], DW-Pose [43]) as the driving signal. However, our experiments reveal that 2D poses fail to guide the diffusion model accurately in scenarios with extensive occlusions, such as when the subject"
+        },
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+            ],
+            "angle": 0,
+            "content": "is turning. Moreover, 2D poses cannot reliably differentiate between different viewpoints of the human body. Therefore, we use SMPL refined by ScoreHMR [31] as the driving signal \\(\\{p_1,p_2,\\dots,p_N\\}\\). It is worth noting that Champ [51] also uses SMPL as guidance; however, their SMPL estimations lack accuracy, and they rely on overly strict guidance inputs, such as depth and normal vectors. This approach leads to suboptimal results, performing even worse than 2D poses in practice, for instance, by generating inconsistent body shapes. The SMPL parameters are converted into a mesh model in the specified pose using Linear Blend Skinning (LBS) [18]. This mesh is rendered as an RGB image based on the fixed camera pose maintained throughout the process. The rendered image is then encoded by a 3D Pose Encoder, a network composed of several convolutional layers, into a latent code \\(z_{p_i}\\) with the same dimensionality as \\(z_{r}\\). All \\(z_{p_i}\\) codes are first concatenated with the input noise along the channel dimension, and then sequentially along the temporal dimension to obtain the final representation \\(z_{P} \\in \\mathbb{R}^{T \\times C \\times H \\times W}\\). Simultaneously, \\(I_{r}\\) is processed to estimate and encode its pose latent code \\(z_{p_r}\\), which is then concatenated with \\(z_{P}\\) along the temporal dimension before being fed into the diffusion model's backbone. Following most video generation models [36, 37], the UNet component of the diffusion model is also designed as a 3D UNet to ensure 3D consistency in the generated output."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.494,
+                0.473,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Training Dataset and Strategy. Human image animation [8, 36] primarily focuses on generating diverse frontal human movements (e.g., dancing). As a result, their training data (e.g., TikTok [12]) is largely composed of performance videos of dancers, typically featuring frontal views and wide movement ranges. In our experiments, we found that models trained on this type of data provide limited support for our 3D reconstruction tasks. These models often fail to generate results with high consistency, exhibit significant flickering in fine details, and display abnormal motion in clothing dynamics. In response to this, we collected over 6,000 high-definition videos (each around 20 seconds long) from YouTube, featuring activities such as model showcases and dancing, with a focus on segments that include turning motions. Additionally, we incorporated 600 clips from the UBC Fashion dataset [45], primarily showcasing model runway turns. As a key part of our dataset, we also integrated frontal-view data from MVHumanNet [39]. We used SAM2 [28] to segment human figures from the background in MVHumanNet, then merged the results with a white background to create videos with a consistent background, effectively eliminating the background variability caused by bounding boxes in MVHumanNet. These three sources together form a dataset of over 10,000 training videos, which we call RotationHuman. Notably, compared to multi-view data, this type of data collection is significantly more cost-effective and thus better"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.895,
+                0.228
+            ],
+            "angle": 0,
+            "content": "suited for building large-scale datasets. During training, our KHD generates 64 pose-driven images in a single pass, setting the context window to 64 frames (i.e., \\( N = 64 \\)). In the inference stage, we directly generate 128 frames in one pass. The advantage of one-pass inference is that it avoids consistency jitter in overlapping transition frames. KHD training requires only one phase, where the objective is to reconstruct the ground truth images corresponding to each pose, with the training loss formulated as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.6,
+                0.242,
+                0.892,
+                0.26
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathbb {E} _ {\\theta} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, f _ {r}, t\\right) \\| ^ {2} \\right], \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.264,
+                0.895,
+                0.445
+            ],
+            "angle": 0,
+            "content": "where, \\( t \\) denotes the denoising step, and \\( z_{t} \\) represents the noise at step \\( t \\). Note that \\( z_{t} \\) in KHD contains diffusion states for \\( N \\) different driving poses. The feature \\( f_{r} \\) is the CLIP image encoding of the reference image \\( I_{r} \\), used to ensure ID consistency in the generated results. \\( \\theta \\) represents the parameters of the 3D UNet and the 3D Pose Encoder. The overall training process involves learning to reconstruct the target video based on \\( I_{r} \\) as input and the pose set \\( \\{p_1, p_2, \\dots, p_N\\} \\) as conditioning. The generated sequence \\( S_{t} \\) represents the sampling results of the subject in the input image \\( I_{r} \\) within the pose space, and it can be directly used for 3D avatar reconstruction."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.455,
+                0.892,
+                0.487
+            ],
+            "angle": 0,
+            "content": "3.2. 3D Distillation with Geometry-Preserving 3D Gaussian Splitting"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.494,
+                0.895,
+                0.766
+            ],
+            "angle": 0,
+            "content": "Once we obtain the sequence of pose images sampled from KHD, the goal is to distill a animatable and real-time rendered human avatar using Geometry-Preserving 3D Gaussian Splatting (GPGS). This challenge can be addressed based on mainstream approaches [16, 32, 52] in monocular 3D reconstruction. As illustrated in the Figure 2 on the right, we initialize the positions of Gaussians using the human template mesh that has undergone loop subdivision. The initial positions are set to the vertex locations, with a default of 2 upsampling iterations. This typically results in approximately \\(110.6K\\) Gaussians. To model the avatar representation, all vertices are fed into a learnable triplane [52] to extract vertex-wise features. These features are subsequently passed to MLPs to predict the geometry and appearance attributes of the Gaussians, respectively. The entire modeling process occurs in canonical space, and we finally map this canonical space into posed space using Linear Blend Skinning (LBS) based on the SMPL framework."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.786,
+                0.803,
+                0.801
+            ],
+            "angle": 0,
+            "content": "3.2.1 Semantic Laplacian Regularization"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.81,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Even during the reconstruction of real video, it is challenging to recover perfect static 3D consistency. Therefore, while the generated videos may appear visually plausible, every tiny ambiguity during lifting the 2D outcomes into 3D space potentially leads to catastrophic issues. Early experimental results indicated that common reconstruction meth"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5574"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.093,
+                0.891,
+                0.525
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.538,
+                0.893,
+                0.582
+            ],
+            "angle": 0,
+            "content": "Figure 3. Visual comparison of our method with TeCH [10] and SiTH [7] for single-image reconstruction. We reposed the reconstructed results to A Pose, showcasing both animation and reconstruction capabilities. We highly recommend checking the suppl. for more results. We have provided a large number of animation result images and videos in the suppl."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.593,
+                0.473,
+                0.851
+            ],
+            "angle": 0,
+            "content": "ods produced results that lacked smoothness and compactness, resulting in existing disconnected and floating gaus-. sians. Following [20], we found that applying Laplacian regularization on the canonical mesh, both for geometry and appearance, effectively mitigated the presence of gaus-. sians out of control. However, it also constrained offsets. In other words, isometrical Laplacian constraint on the whole body overly relied on the accuracy of the SMPL mesh, also making it difficult to fit areas such as hair and clothing that deviate significantly from the SMPL surface. Considering the complexity of the human body and the impossibility to obtain extremely accurate SMPL estimation, we repartition all gaussian vertices into \\(L = 15\\) distinct semantic parts and dynamically adjust the smoothing strength. Besides, we impose the constraint on the anchors points which are closer to the rendering surface than gausicians center. The Semantic Laplacian Regularization (SLR) is defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.102,
+                0.86,
+                0.47,
+                0.906
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {S L R} = \\sum_ {u \\in \\Omega} \\lambda_ {u} \\left\\| a _ {u, v} - \\frac {1}{| M (u , v) |} \\sum_ {v \\in M (u, v)} a _ {u, v} \\right\\|, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.593,
+                0.895,
+                0.79
+            ],
+            "angle": 0,
+            "content": "where \\(\\Omega\\) represents the set of semantic regions, \\(a\\) denotes the surface anchor point of the \\(v\\)-th Gaussian vertex in the \\(u\\)-th semantic region, and \\(M(u,v)\\) refers to the set of adjacent points of the Gaussian vertex \\(a_{u,v}\\) located within the \\(u\\)-th semantic region. Experiments demonstrate that the Semantic Laplacian Regularization significantly impacts the handling of more intricate situations, particularly when dealing with errors between the SMPL mesh and the actual character, which can arise from both inaccurate estimations and complex clothing. We apply Laplacians in both position and color spaces; the former enhances the smoothness of the rendering surface, while the latter ensures a more continuous variation in color space."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.815,
+                0.882,
+                0.831
+            ],
+            "angle": 0,
+            "content": "3.2.2 Geometry-Preserving Density Control Strategy"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "The strategies in vanilla 3DGS were not originally build for complex, dynamic structures like the human body. While works [20] have adapted the approach, such as initializing Gaussians based on SMPL meshes, these efforts pri"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.958
+            ],
+            "angle": 0,
+            "content": "5575"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.089,
+                0.895,
+                0.133
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative comparisons with existing methods on UBC fashion dataset [45]. Note that metrics in the table are measure with the background-removed video. Some methods are unable to perform animation, and therefore, these metrics are not available for those methods. Bold indicates the best results, while Underlined represents the second-best results."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.101,
+                0.142,
+                0.868,
+                0.356
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>Prior Type</td><td>PSNR ↑</td><td>LPIPS ↓</td><td>FVD ↓</td><td>Context. ↓</td><td>CLIP Score ↑</td><td>Speed↑</td></tr><tr><td>DisCo [35] (CVPR24)</td><td>-</td><td>30.98</td><td>0.259</td><td>167.7</td><td>2.134</td><td>82.4%</td><td>1FPS</td></tr><tr><td>Animate Anyone [8] (CVPR24)</td><td>-</td><td>31.33</td><td>0.238</td><td>148.8</td><td>1.901</td><td>86.6%</td><td>2FPS</td></tr><tr><td>Champ [51] (ECCV24)</td><td>-</td><td>31.21</td><td>0.251</td><td>155.1</td><td>2.038</td><td>84.3%</td><td>1FPS</td></tr><tr><td>UniAnimate [36] (ArXiv24)</td><td>-</td><td>32.31</td><td>0.211</td><td>141.3</td><td>1.811</td><td>87.1%</td><td>2FPS</td></tr><tr><td>SHERF [9] (ICCV23)</td><td>-</td><td>27.39</td><td>0.301</td><td>202.3</td><td>2.998</td><td>70.1%</td><td></td></tr><tr><td>SIFU [50] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.891</td><td>72.1%</td><td>5FPS</td></tr><tr><td>GST [26] (ArXiv24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>3.011</td><td>71.7%</td><td>50FPS</td></tr><tr><td>TeCH [10] (3DV24)</td><td>Camera</td><td>29.01</td><td>0.271</td><td>188.1</td><td>2.331</td><td>79.3%</td><td>6FPS</td></tr><tr><td>SiTH [7] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.776</td><td>74.7%</td><td>&lt;1FPS</td></tr><tr><td>HumanRef [47] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.167</td><td>81.5%</td><td>3FPS</td></tr><tr><td>SHERT [46] (CVPR2024)</td><td>Inpainting</td><td>29.31</td><td>0.266</td><td>179.8</td><td>2.319</td><td>78.8%</td><td>10FPS</td></tr><tr><td>UniAnimate + GPGS (ours)</td><td>Kinematics</td><td>29.97</td><td>0.251</td><td>168.7</td><td>1.992</td><td>82.1%</td><td>70FPS</td></tr><tr><td>KHD (ours)</td><td>-</td><td>32.81</td><td>0.221</td><td>134.4</td><td>1.768</td><td>92.3%</td><td>2FPS</td></tr><tr><td>SinGS (ours)</td><td>Kinematics</td><td>31.33</td><td>0.240</td><td>156.3</td><td>1.847</td><td>88.2%</td><td>70FPS</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.366,
+                0.473,
+                0.775
+            ],
+            "angle": 0,
+            "content": "marily lay a solid foundation for the optimization process but fail to maintain this advantages throughout. Incompatibilities still arise in optimization stage, prompting us to propose a novel density control scheme that is inherently compatible with hybrid representations, designed for adaptive adjustment body-wide density. This scheme draws on mesh operation algorithms [6] to better address the unique challenges of human body. For primitives that locate in under-expression mesh areas, we subdivide these regions by adding gaussians on every edge of the selected geometric triangles, which creates much smaller triangles. And we skip the trivial post-smoothing for vertices as the position of Gaussians will continue to be optimized in the network. For candidate Gaussians that are selected due to excessively large scales, as well as all newly added Gaussians, we perform rescaling to adjust them to an average size. In the case of anomalous gaussians, especially those are almost transparent, we collapse relevant edges and replace them with single vertex, resulting in decimated adjacent faces. And the priority of selected edges is decided by gaussian attributes and edge length. This entire pruning process preserves the principal structure of the human body. Our strategy result in better reconstruction and animation as the optimization was conducted under connectivity and compactness of the entire human body rather than producing holes and stacks. Moreover, this approach synergistically enhances the effectiveness of our hybrid representation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.79,
+                0.21,
+                0.807
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.816,
+                0.268,
+                0.833
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Setup"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.472,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Implementation Details. Our KHD primarily utilizes the RotationHuman dataset we collected, which focuses on human pose image sequences involving turning motions. The specific structure of the 3D Pose Encoder is provided in"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.366,
+                0.892,
+                0.636
+            ],
+            "angle": 0,
+            "content": "the supplementary materials. KHD was trained using 8 NVIDIA A100 80GB GPUs, with DeepSpeed and ZeRO2 employed to reduce memory usage. Similar toAnimate Anyone, we resized the video frames to a spatial dimension of \\(768 \\times 512\\). We used a context window size of 64 frames, and to enhance model scalability post-training, we implemented a random context window jitter strategy [36]. During training, the model randomly samples window sizes from 64 to 32 frames in an uniformly distributed manner. The training process utilized the AdamW optimizer [15], with a learning rate set to \\(5e - 5\\) and DDPM with 1000 steps for noise sampling. During inference, DDIM with 30 steps was used to reduce inference time. For the 3DGS component, the Adam optimizer [15] was used with a learning rate of \\(1e - 3\\) and a cosine annealing learning scheduler was applied to accelerate convergence. The input image sequence size for 3DGS was also \\(768 \\times 512\\). 3DGS was trained using a single NVIDIA 4090 24GB GPU."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.637,
+                0.892,
+                0.758
+            ],
+            "angle": 0,
+            "content": "Baseline Models. Our baseline models consist of two parts: the first part includes human image animation models, such as DisCo [35], Animation Anyone [8] \\(^{1}\\), Champ [51], and UniAnimate [36]. These models are used to compare our animation capability and the superiority of KHD. The second part consists of single-image 3D avatar reconstruction models, including SHERF [9], SIFU [50], GST [26], TeCH [10], SiTH [7], HumanRef [47], and SHERT [46]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.758,
+                0.892,
+                0.879
+            ],
+            "angle": 0,
+            "content": "Metrics. We employ both PSNR and LPIPS to assess the quality of video reconstruction. To evaluate the animation capability of our model, we also use FVD [34] to measure the distribution discrepancy between the generated video and the original video, assessing the video generation performance. Furthermore, following HumanRef, we introduce contextual distance [19] and CLIP score [27] to evaluate the texture and semantic similarity between the rendered"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.518,
+                0.887,
+                0.833,
+                0.902
+            ],
+            "angle": 0,
+            "content": "<sup>1</sup>https://github.com/MooreThreads/Moore-AnimateAnyone"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.483,
+                0.945,
+                0.516,
+                0.958
+            ],
+            "angle": 0,
+            "content": "5576"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.094,
+                0.09,
+                0.462,
+                0.288
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.296,
+                0.47,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Figure 4. Comparison between KHD and other SOTA human image animation methods. Please zoom in for better observation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.339,
+                0.327,
+                0.355
+            ],
+            "angle": 0,
+            "content": "output and the input reference image."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.366,
+                0.27,
+                0.383
+            ],
+            "angle": 0,
+            "content": "4.2. Qualitative Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.39,
+                0.47,
+                0.632
+            ],
+            "angle": 0,
+            "content": "Singe-Image Reconstruction. We compare SinGS with two methods from the literature that claim to support animation (TeCH, SiTH). It is worth noting that during our experiments, we found that single-image animation with these methods was extremely difficult to execute, and in some cases, nearly impossible. We had to use third-party code \\( {}^{2} \\) to achieve the reposing for some of these methods. We animate their reconstructed outputs to a common pose (A Pose) for comparison, which allows us to evaluate both reconstruction and animation capabilities. The comparison results are shown in Figure 3, SinGS generates results with better details and maintains high-quality animation, particularly on the in-the-wild data, where SinGS's visual performance significantly outperforms the other methods. This demonstrates the high feasibility and effectiveness of the kinematic prior."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.633,
+                0.471,
+                0.875
+            ],
+            "angle": 0,
+            "content": "Kinematic Human Diffusion. KHD, as the core component of our pipeline, is compared with state-of-the-art human image animation methods, includingAnimate Anyone and UniAnimate. As shown in Figure 4, we drive the same character with all three methods, focusing on comparing the quality of their generated results, particularly for the turning pose. From the figure, it is clear that both UniAnimate and our KHD maintain higher consistency thanAnimate Anyone after the character turns, with KHD surpassing UniAnimate in detail. The details marked by the red arrows in Figure 4 reveals that UniAnimate generates incorrect details, a common issue when using 2D poses, as they often struggle to distinguish body orientation during back-facing poses, leading the model to generate erroneous images. This is detrimental to reconstruction, while KHD generates videos with much higher consistency."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.519,
+                0.088,
+                0.875,
+                0.183
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.192,
+                0.895,
+                0.263
+            ],
+            "angle": 0,
+            "content": "Figure 5. Fifty users rated the video quality, with UniAnimate scoring highest, followed closely by our model, which outperformed others. Our model is more efficient, using only 3.5 GB of memory and achieving 70 FPS, while UniAnimate requires over 12GB and 0.5 seconds per image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.276,
+                0.895,
+                0.533
+            ],
+            "angle": 0,
+            "content": "Geometry-Preserving 3D Gaussian Splatting. Although KHD provides high-consistency pose sampling results, it inevitably has some consistency flaws, meaning it can only offer imperfect prior information. Our geometry-preserving GS method is specifically designed to address this challenge. To validate the superiority of our Geometry-Preserving 3D Gaussian Splatting (GPGS) over general human modeling methods, we compared it with recent state-of-the-art (i.e., SOTA) methods, HAHA [32] and HUGS [16]. We generate a pose sequence using KHD and then performed reconstruction with all 3 methods. The reconstruction results are shown in Figure 7. As seen, both HAHA and HUGS fail to produce a compact 3D avatar, with significant holes or floating artifacts appearing in various areas, particularly during the turning motion. In contrast, our GPGS method is able to reconstruct a compact, watertight 3D avatar model."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.545,
+                0.704,
+                0.561
+            ],
+            "angle": 0,
+            "content": "4.3. Quantitative Analysis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.569,
+                0.894,
+                0.903
+            ],
+            "angle": 0,
+            "content": "We selected 100 test videos from the UBC dataset for our quantitative analysis. For each video, we chose the first frame as the reference image and used the video's pose sequence as the driving signal. The performance of all methods was assessed by comparing the animation results with the original video to evaluate the differences. Video reconstruction metrics (including PSNR, LPIPS, and FVD) reflect the model's animation capabilities, while Contextual Distance and CLIP score allow for comparison with methods that do not support animation. The quantitative comparison results are shown in Table 1. Human image animation methods (i.e., the second to fifth rows in the table, including our KHD) outperform the reconstruction-based methods across the board. Among them, KHD surpasses the other methods in most metrics, and UniAnimate also demonstrates superior performance, which is expected due to the scale of training data and model size. While SinGS lags behind UniAnimate, it shows a significant advantage over other methods in some metrics. However, SinGS significantly outperforms diffusion-based animation methods in terms of inference efficiency and resource consumption. Our SinGS achieves 70 FPS during inference, with only"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.095,
+                0.887,
+                0.378,
+                0.901
+            ],
+            "angle": 0,
+            "content": "\\(^{2}\\)https://github.com/custom-humans/editable-humans"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "5577"
+        }
+    ],
+    [
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.077,
+                0.09,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "Table 2. The results of the ablation experiments on Semantic Laplacian Regularization (i.e., Semantic Lap. Reg.) and Geometry-Preserving Density Control (i.e., GPDC) in SinGS."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>Setting</td><td>PSNR</td><td>LPIPS</td><td>FVD</td></tr><tr><td>with Semantic Lap. Reg.</td><td>31.33</td><td>0.240</td><td>156.3</td></tr><tr><td>with KNN Lap. Reg.</td><td>30.88</td><td>0.250</td><td>169.9</td></tr><tr><td>w/o Lap. Reg.</td><td>30.34</td><td>0.272</td><td>181.3</td></tr><tr><td>with GPDC</td><td>31.01</td><td>0.249</td><td>166.1</td></tr><tr><td>naive Density Control [14]</td><td>30.22</td><td>0.276</td><td>190.2</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.231,
+                0.468,
+                0.352
+            ],
+            "angle": 0,
+            "content": "3.8 GB of memory usage (tested on a single NVIDIA 4090 GPU), while UniAnimate, Champ, andAnimate Anyone each require more than 0.4 seconds per image and consume over 12 GB of memory. These quantitative results strongly demonstrate that SinGS is highly effective and feasible. We believe that using KHD, a specialized foundational model, will greatly enhance 3D reconstruction performance while significantly reducing the stringent data requirements."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.352,
+                0.468,
+                0.413
+            ],
+            "angle": 0,
+            "content": "User Study. We invited 50 users to subjectively evaluate the animation results of SinGS. The evaluation was based on a scale from 0 to 10, with 10 being the highest score and 0 being the lowest. The results are visualized in Figure 5."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.424,
+                0.23,
+                0.44
+            ],
+            "angle": 0,
+            "content": "4.4. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.448,
+                0.468,
+                0.794
+            ],
+            "angle": 0,
+            "content": "Kinematic Priors Analysis. The number of poses sampled by KHD has a significant impact on the 3D distillation process. We analyzed how the number of poses affects the animation capability of the final reconstructed model, and the results are shown in Figure 6. We incrementally increased the number of poses from 2 (which corresponds to the typical approach of generating front and rear views, as used by most methods) up to 150. We also tested the influence of different prior models (i.e., KHD, UniAnimate, and Animate Anyone) on the results. Additionally, we examined how different 3DGS reconstruction methods handle the use of prior knowledge. As shown, performance improves rapidly with an increase in the number of poses, but the rate of improvement slows significantly after reaching around 100 poses. Moore-AA + HAHA shows the slowest improvement, while KHD + GPGS exhibits the slowest decline in performance. This suggests that increasing the number of poses does not always lead to improved performance for two main reasons: first, the prior models have already provided sufficient information; and second, none of the prior models provide perfectly consistent priors. Excessive sampling can introduce a lot of inconsistent noise, which ultimately harms performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.796,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Geometry-Preserving 3D Gaussian Splitting Analysis. We conducted ablation experiments on the two key designs in GPGS: Semantic Laplacian Regularization and GPDC, with the results shown in Table 2. By replacing and removing the Laplacian regularization, we observed that Semantic Laplacian consistently outperforms in terms of reconstruction metrics. Additionally, GPDC demonstrates a perfor"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.541,
+                0.089,
+                0.852,
+                0.227
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.5,
+                0.238,
+                0.892,
+                0.266
+            ],
+            "angle": 0,
+            "content": "Figure 6. The comparison of the impact of augmented pose numbers on the performance of the 3D avatar models."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.293,
+                0.887,
+                0.46
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.473,
+                0.892,
+                0.516
+            ],
+            "angle": 0,
+            "content": "Figure 7. Here is a comparison of our GPGS with two SOTA 3DGS avatar methods, HAHA [32] and HUGS [16]. All methods use images sampled by KHD as body prior."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.534,
+                0.892,
+                0.608
+            ],
+            "angle": 0,
+            "content": "mance advantage over the original density control strategy. The original strategy does not account for dynamic properties and geometric constraints, which makes it ineffective in addressing issues like floating and holes caused by data inconsistencies."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.631,
+                0.619,
+                0.646
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.66,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose a new paradigm for single-image 3D avatar reconstruction. Unlike traditional methods that complete missing information in camera space, we sample in human kinematic space, enabling efficient capture of both viewpoints and motion traits. To achieve this, we introduce Kinematic Human Diffusion (KHD) for consistent pose-space generation, supported by our RotationHuman dataset, which focuses on turning motions. Additionally, we propose Geometry-Preserving 3D Gaussian Splating that reconstructs high-quality, animatable 3D avatars under imperfect human priors. This includes two key innovations: Semantic Laplacian regularization for compact, detailed constraints, and a geometry-preserving density control strategy to maintain stable human geometry. Together, these innovations allow SinGS to achieve high-quality, animatable 3D avatar reconstruction from a single image."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.946,
+                0.516,
+                0.957
+            ],
+            "angle": 0,
+            "content": "5578"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.091,
+                0.248,
+                0.108
+            ],
+            "angle": 0,
+            "content": "6. Acknowledgment"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.115,
+                0.47,
+                0.205
+            ],
+            "angle": 0,
+            "content": "This work supported by Shanghai Post-doctoral Excellence Programe (2024290). This work was also partly by Shanghai Municipal Bureau of Culture and Tourism and Meta-verse Technology Innovation Center of Shanghai Municipal Bureau of Culture and Tourism. Kairui Feng thanks to Xiaomi foundation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.08,
+                0.218,
+                0.174,
+                0.234
+            ],
+            "angle": 0,
+            "content": "References"
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2025/SinGS_ Animatable Single-Image Human Gaussian Splats with Kinematic Priors/a1907643-3cec-4712-b625-aae92326d106_origin.pdf

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2025/SinGS_ Animatable Single-Image Human Gaussian Splats with Kinematic Priors/full.md

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+# SinGS: Animatable Single-Image Human Gaussian Splats with Kinematic Priors
+
+Yufan Wu $^{1*}$  Xuanhong Chen $^{1\dagger}$  Wen Li $^{1,3}$  Shunran Jia $^{2}$  Hualiang Wei $^{1*}$  Kairui Feng $^{4}$   
+Jialiang Chen $^{1}$  Yuhan Li $^{1}$  Ang He $^{1*}$  Weimin Zhang $^{1}$  Bingbing Ni $^{1}$  Wenjun Zhang $^{1}$
+
+$^{1}$ Shanghai Jiao Tong University, Shanghai, China  $^{2}$ DreamX Inc  $^{3}$ Akool Research  $^{4}$ The National Key Laboratory of Autonomous Intelligent Unmanned Systems, Shanghai, China
+
+{chen19910528,wmzhang,nibingbing,zhangwenjun}@sjtu.edu.cn, elvinfkr@tongji.edu.cn
+
+# Abstract
+
+Despite significant advances in accurately estimating geometry in contemporary single-image 3D human reconstruction, creating a high-quality, efficient, and animatable 3D avatar remains an open challenge. Two key obstacles persist: incomplete observation and inconsistent 3D priors. To address these challenges, we propose SinGS, aiming to achieve high-quality and efficient animatable 3D avatar reconstruction. At the heart of SinGS are two key components: Kinematic Human Diffusion and Geometry-Preserving 3D Gaussain Splatting. The former is a foundational human model that samples within pose space to generate a highly 3D-consistent and high-quality sequence of human images, inferring unseen viewpoints and providing kinematic priors. The latter is a system that reconstructs a compact, high-quality 3D avatar even under imperfect priors, achieved through a novel semantic Laplacian regularization and a geometry-preserving density control strategy that enable precise and compact assembly of 3D primitives. Extensive experiments demonstrate that SinGS enables life-like, animatable human reconstructions, maintaining both high quality and inference efficiency (up to 70FPS).
+
+# 1. Introduction
+
+Single-image 3D human reconstruction (i.e., SIHR) is an emerging modeling technique that aims to create a lifelike 3D avatar from just one image, offering a highly cost-effective and promising approach to 3D modeling. Recently, 3D Gaussian Splatting (3DGS)[14] has made significant breakthroughs in rendering efficiency and quality, establishing itself as a mainstream approach for 3D avatar reconstruction. However, current 3DGS-based methods [23, 26] for single-image human 3D avatar reconstruction suffer from critical limitations in animation, as most are
+
+![](images/9676d7bbff1e85aed3304a363715f481c4e2de0f9887b0cac347845423235752.jpg)  
+Figure 1. Existing single-image 3D avatar reconstruction methods are limited to sampling prior information from camera space. In contrast, SinGS proposes sampling from pose space, allowing us to obtain both camera and kinematic priors simultaneously. Combined with our Geometry-Preserving 3D Gaussian Splitting, this enables highly efficient animation rendering.
+
+designed primarily for static assets. This paper aims to develop an animation reconstruction framework that achieves a high balance between efficiency and rendering quality.
+
+Currently, the vast majority of SIHR methods [7, 10, 23, 24, 26, 40, 41, 46, 49, 50] focus solely on optimizing geometry while neglecting to enhance animation capabilities. As a result, they are often incapable of animation or require third-party tools [7] to achieve approximate motion. Unlike digital assets, the primary requirement for a human avatar is its ability to animate, making animation the core goal of SIHR [9]. Achieving animatable single-image human reconstruction (i.e., Animatable SIHR) is particularly
+
+challenging for two main reasons: Incomplete Observation: A single image lacks comprehensive viewpoint information, offering an extremely limited, partial observation that cannot address occlusion issues. Current methods [7, 10, 47] mainly rely on fine-tuned diffusion models to synthesize (i.e., 3D hallucination) missing viewpoint information (such as front and back perspectives). However, this approach does not resolve the absence of motion information. While synthesized views can alleviate some occlusion issues, the human body's non-rigid structure requires more than static viewpoints to capture its complex kinematic patterns effectively. Inconsistent 3D Prior: Current mainstream methods [5, 7, 10, 47] use Score Distillation Sampling (SDS) [25] to leverage diffusion models as supervisory modules for learning 3D priors. However, the high generative diversity of these models often leads to viewpoint inconsistencies, resulting in implausible imagery (e.g., poor-quality hidden views and inconsistencies with the input image). HumanRef [47] attempts to mitigate the instability of SDS through ReferenceNet [8], but observable inconsistencies remain widespread in the results of ReferenceNet-based methods [8, 33], indicating the difficulty in fully resolving this issue. Consequently, 3D representations should be robust enough to handle imperfect 3D priors, though this perspective has largely been overlooked in current single-image avatar frameworks.
+
+To address these challenges, this paper introduces a novel single-image 3D human avatar reconstruction framework, named SinGS. Unlike existing methods [23, 26], SinGS focuses on directly constructing an animatable 3DGS avatar. At the core of our SinGS framework are two key components: Kinematic Human Diffusion and a highly Geometry-Preserving 3D Gaussian Splatting. Specifically, Kinematic Human Diffusion (KHD) is designed to sample a highly 3D-consistent human sequence within the pose space, based solely on a single input image prompt. This approach enables high-quality and animatable 3D avatar reconstruction. To train KHD, we constructed a dataset with over ten thousand rotation videos, allowing KHD to learn a rich variety of human structures and texture distributions from different angles, while also gaining extensive knowledge of human kinematics. Unlike existing frameworks [5, 7, 10, 47] that rely on costly and scarce multi-view human data, our approach requires only more affordable and abundant video data, significantly reducing KHD's training costs and better aligning with scaling laws. Geometry-Preserving 3D Gaussian Splatting (i.e., GPGS) tackles artifact and hole issues under imperfect human priors (e.g., minor jitter and 3D inconsistencies) through two key designs: Semantic Laplacian Regularization addresses floating Gaussian spheres caused by 3D inconsistencies. It adjusts the constraint strength based on body parts, allowing more flexibility for areas like hair and tighter constraints
+
+for facial details, reducing floating Gaussian spheres while maintaining rendering quality. Geometry-Preserving Density Control resolves over-deletion and incorrect deletion of spheres in the training process. By managing the Gaussian sphere density via mesh edges, it ensures the spheres remain around the mesh, preserving geometry and preventing large holes. Extensive experiments have validated that our SinGS can generate high-quality and animatable 3D avatars at ultra-fast inference speeds (up to 70 FPS) with efficient resource usage (requiring only 3.8GB of GPU memory).
+
+# 2. Related Work
+
+# 2.1. Diffusion-based Human Generative Models
+
+Recent advances in diffusion-based human generative models, especially those conditioned on pose, have improved model controllability. Frameworks like ControlNet [48], IP Adapter [44], and ReferenceNet [8], along with better human attribute detection (2D/3D pose estimation, SMPL parameters [18]), enable more precise and consistent results. In image synthesis, models like PIDM [1] and LFDM [22] enhance pose transfer and image adaptation, while LEO [38] uses flow maps for motion representation. For video, DreamPose [13] and DisCo [35] improve pose-to-image translation and control separation. Models likeAnimateAnyone [8], MagicAnimate [42], and Magic-Pose [4] refine pose conditioning with ReferenceNet. Despite these improvements, these models remain resource-heavy and struggle with stability when generating images of complex movements, such as head turns or rotations.
+
+# 2.2. Single-Image Human Reconstruction
+
+Monocular video-based human reconstruction has reduced the need for specialized equipment, but single-image reconstruction remains challenging due to incomplete data. Early methods like PIFu [29] and SiCloPe [21] used pixel-aligned features and image-to-image translation, with PIFuHD [30] enhancing detail via normal maps. Later methods, such as ARCH [11] and ICON [40], incorporated body priors for animatable avatars, and ECON [41] improved model completeness by separately reconstructing front and back surfaces. Recent approaches like SiTH [7] and HumanRef [47] use generative models to fill in missing data, while SIFU [50] and Diffusion-FOF approximate multi-view features. R-Cyclic Diffuser [3] addresses limitations in Zero-1-to-3 [17], even with human-specific datasets, advancing single-image human reconstruction through generative priors and viewpoint conditioning.
+
+# 3. Methodology
+
+Given a target image  $I_r$ , the objective of the SinGS architecture is to reconstruct a fully animatable 3D avatar  $\mathbf{A}_t$  based on  $I_r$ . To address the challenge of limited viewpoint and
+
+![](images/e7a026c2e6e41bf24d06eb4e3d6269db01b5c71d11ad0ad2a3e81164ccea5dfd.jpg)
+
+![](images/952abdf13459951d7c01846d40b42bfdd5e314026774502637291596384d9a15.jpg)
+
+![](images/08ab15398cc7fd693842e859d7b8824d277dbc012ecfe7c884450a93e98e4c62.jpg)  
+Figure 2. Overall framework of our method.
+
+kinematic information inherent in single-image reconstruction,  $I_{t}$  is first input into the Kinematic Human Diffusion (i.e., KHD) module to complete missing information, generating an augmented sequence of rendered images  $S_{t} = \{I_{p_{1}},\dots ,I_{p_{i}},\dots ,I_{p_{N}}\}$ , where  $N$  represents the total number of poses generated, and  $p_i$  indicates each corresponding 3D human pose. KHD reframes the less-constrained, underdetermined 3D reconstruction problem as a generative task, thus producing a fully-constrained, fully-observed 3D reconstruction formulation. Finally,  $S_{t}$  is fed into our compact 3DGS module to reconstruct an animatable 3D human avatar. The compact 3DGS module is capable of reconstructing a watertight, high-quality human model even with imperfect 3D priors. The distilled avatar is high-quality, computationally efficient, and well-suited for promising applications in AR, VR, and similar fields.
+
+# 3.1. Kinematic Priors
+
+# 3.1.1 Kinematic Human Diffusion
+
+Unlike existing hallucination architectures [7, 10, 50], our Kinematic Human Diffusion does not rely on camera input, which is prone to estimation errors and has the added challenges of multi-view data scarcity and high costs (e.g., multi-view human data typically requires capture with specialized setups like a light stage). Our approach instead posits that sampling within the motion space provides complete priors for viewpoint and kinematic features. Additionally, our KHD does not adopt a ReferenceNet structure [8];
+
+while ReferenceNet has been highly successful, it requires maintaining two UNet models, significantly increasing the framework's resource demands and preventing integration of longer contexts (e.g., 24 frames). A shorter contextual window cannot provide an image sequence with a sufficient diversity of motion samples (e.g., 150 frames). Considering the above two aspects, our KHD is designed as a diffusion structure, as illustrated in Figure 2. KHD  $\mathcal{G}$  takes a single image  $I_{r}$  as input and, constrained by a randomly sampled sequence of poses  $\{p_1,p_2,\dots ,p_N\}$ , augments the input image into a sequence  $S_{t} = \{I_{p_{1}},I_{p_{2}},\ldots ,I_{p_{N}}\}$ . This process can be formulated as follows:
+
+$$
+S _ {t} = \mathcal {G} \left(I _ {r}; p _ {1}, p _ {2}, \dots , p _ {N}\right). \tag {1}
+$$
+
+Model Architecture. Inspired by UniAnimate [36], our KHD also removes the ReferenceNet and directly inputs the reference image  $I_r$  and the driving sequence into the UNet. The reference image  $I_r$  is encoded by the VAE encoder of the diffusion model into a latent code  $z_r$ , serving as an appearance reference throughout KHD. Additionally,  $I_r$  is encoded by the CLIP image encoder [27] into features  $f_r$  which are injected into the network through cross-attention by replacing the original text encoder's features in the diffusion model. This enables high-fidelity preservation of the subject's appearance characteristics. Existing works typically use 2D poses (e.g., OpenPose [2], DW-Pose [43]) as the driving signal. However, our experiments reveal that 2D poses fail to guide the diffusion model accurately in scenarios with extensive occlusions, such as when the subject
+
+is turning. Moreover, 2D poses cannot reliably differentiate between different viewpoints of the human body. Therefore, we use SMPL refined by ScoreHMR [31] as the driving signal  $\{p_1,p_2,\dots,p_N\}$ . It is worth noting that Champ [51] also uses SMPL as guidance; however, their SMPL estimations lack accuracy, and they rely on overly strict guidance inputs, such as depth and normal vectors. This approach leads to suboptimal results, performing even worse than 2D poses in practice, for instance, by generating inconsistent body shapes. The SMPL parameters are converted into a mesh model in the specified pose using Linear Blend Skinning (LBS) [18]. This mesh is rendered as an RGB image based on the fixed camera pose maintained throughout the process. The rendered image is then encoded by a 3D Pose Encoder, a network composed of several convolutional layers, into a latent code  $z_{p_i}$  with the same dimensionality as  $z_{r}$ . All  $z_{p_i}$  codes are first concatenated with the input noise along the channel dimension, and then sequentially along the temporal dimension to obtain the final representation  $z_{P} \in \mathbb{R}^{T \times C \times H \times W}$ . Simultaneously,  $I_{r}$  is processed to estimate and encode its pose latent code  $z_{p_r}$ , which is then concatenated with  $z_{P}$  along the temporal dimension before being fed into the diffusion model's backbone. Following most video generation models [36, 37], the UNet component of the diffusion model is also designed as a 3D UNet to ensure 3D consistency in the generated output.
+
+Training Dataset and Strategy. Human image animation [8, 36] primarily focuses on generating diverse frontal human movements (e.g., dancing). As a result, their training data (e.g., TikTok [12]) is largely composed of performance videos of dancers, typically featuring frontal views and wide movement ranges. In our experiments, we found that models trained on this type of data provide limited support for our 3D reconstruction tasks. These models often fail to generate results with high consistency, exhibit significant flickering in fine details, and display abnormal motion in clothing dynamics. In response to this, we collected over 6,000 high-definition videos (each around 20 seconds long) from YouTube, featuring activities such as model showcases and dancing, with a focus on segments that include turning motions. Additionally, we incorporated 600 clips from the UBC Fashion dataset [45], primarily showcasing model runway turns. As a key part of our dataset, we also integrated frontal-view data from MVHumanNet [39]. We used SAM2 [28] to segment human figures from the background in MVHumanNet, then merged the results with a white background to create videos with a consistent background, effectively eliminating the background variability caused by bounding boxes in MVHumanNet. These three sources together form a dataset of over 10,000 training videos, which we call RotationHuman. Notably, compared to multi-view data, this type of data collection is significantly more cost-effective and thus better
+
+suited for building large-scale datasets. During training, our KHD generates 64 pose-driven images in a single pass, setting the context window to 64 frames (i.e.,  $N = 64$ ). In the inference stage, we directly generate 128 frames in one pass. The advantage of one-pass inference is that it avoids consistency jitter in overlapping transition frames. KHD training requires only one phase, where the objective is to reconstruct the ground truth images corresponding to each pose, with the training loss formulated as follows:
+
+$$
+\mathcal {L} = \mathbb {E} _ {\theta} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, f _ {r}, t\right) \| ^ {2} \right], \tag {2}
+$$
+
+where,  $t$  denotes the denoising step, and  $z_{t}$  represents the noise at step  $t$ . Note that  $z_{t}$  in KHD contains diffusion states for  $N$  different driving poses. The feature  $f_{r}$  is the CLIP image encoding of the reference image  $I_{r}$ , used to ensure ID consistency in the generated results.  $\theta$  represents the parameters of the 3D UNet and the 3D Pose Encoder. The overall training process involves learning to reconstruct the target video based on  $I_{r}$  as input and the pose set  $\{p_1, p_2, \dots, p_N\}$  as conditioning. The generated sequence  $S_{t}$  represents the sampling results of the subject in the input image  $I_{r}$  within the pose space, and it can be directly used for 3D avatar reconstruction.
+
+# 3.2. 3D Distillation with Geometry-Preserving 3D Gaussian Splitting
+
+Once we obtain the sequence of pose images sampled from KHD, the goal is to distill a animatable and real-time rendered human avatar using Geometry-Preserving 3D Gaussian Splatting (GPGS). This challenge can be addressed based on mainstream approaches [16, 32, 52] in monocular 3D reconstruction. As illustrated in the Figure 2 on the right, we initialize the positions of Gaussians using the human template mesh that has undergone loop subdivision. The initial positions are set to the vertex locations, with a default of 2 upsampling iterations. This typically results in approximately  $110.6K$  Gaussians. To model the avatar representation, all vertices are fed into a learnable triplane [52] to extract vertex-wise features. These features are subsequently passed to MLPs to predict the geometry and appearance attributes of the Gaussians, respectively. The entire modeling process occurs in canonical space, and we finally map this canonical space into posed space using Linear Blend Skinning (LBS) based on the SMPL framework.
+
+# 3.2.1 Semantic Laplacian Regularization
+
+Even during the reconstruction of real video, it is challenging to recover perfect static 3D consistency. Therefore, while the generated videos may appear visually plausible, every tiny ambiguity during lifting the 2D outcomes into 3D space potentially leads to catastrophic issues. Early experimental results indicated that common reconstruction meth
+
+![](images/79c841c208901a493b99c45a5bd7271df7ea2ff9553df4900229e904929fd7b1.jpg)  
+Figure 3. Visual comparison of our method with TeCH [10] and SiTH [7] for single-image reconstruction. We reposed the reconstructed results to A Pose, showcasing both animation and reconstruction capabilities. We highly recommend checking the suppl. for more results. We have provided a large number of animation result images and videos in the suppl.
+
+ods produced results that lacked smoothness and compactness, resulting in existing disconnected and floating gaus-. sians. Following [20], we found that applying Laplacian regularization on the canonical mesh, both for geometry and appearance, effectively mitigated the presence of gaus-. sians out of control. However, it also constrained offsets. In other words, isometrical Laplacian constraint on the whole body overly relied on the accuracy of the SMPL mesh, also making it difficult to fit areas such as hair and clothing that deviate significantly from the SMPL surface. Considering the complexity of the human body and the impossibility to obtain extremely accurate SMPL estimation, we repartition all gaussian vertices into  $L = 15$  distinct semantic parts and dynamically adjust the smoothing strength. Besides, we impose the constraint on the anchors points which are closer to the rendering surface than gausicians center. The Semantic Laplacian Regularization (SLR) is defined as follows:
+
+$$
+\mathcal {L} _ {S L R} = \sum_ {u \in \Omega} \lambda_ {u} \left\| a _ {u, v} - \frac {1}{| M (u , v) |} \sum_ {v \in M (u, v)} a _ {u, v} \right\|, \tag {3}
+$$
+
+where  $\Omega$  represents the set of semantic regions,  $a$  denotes the surface anchor point of the  $v$ -th Gaussian vertex in the  $u$ -th semantic region, and  $M(u,v)$  refers to the set of adjacent points of the Gaussian vertex  $a_{u,v}$  located within the  $u$ -th semantic region. Experiments demonstrate that the Semantic Laplacian Regularization significantly impacts the handling of more intricate situations, particularly when dealing with errors between the SMPL mesh and the actual character, which can arise from both inaccurate estimations and complex clothing. We apply Laplacians in both position and color spaces; the former enhances the smoothness of the rendering surface, while the latter ensures a more continuous variation in color space.
+
+# 3.2.2 Geometry-Preserving Density Control Strategy
+
+The strategies in vanilla 3DGS were not originally build for complex, dynamic structures like the human body. While works [20] have adapted the approach, such as initializing Gaussians based on SMPL meshes, these efforts pri
+
+Table 1. Quantitative comparisons with existing methods on UBC fashion dataset [45]. Note that metrics in the table are measure with the background-removed video. Some methods are unable to perform animation, and therefore, these metrics are not available for those methods. Bold indicates the best results, while Underlined represents the second-best results.  
+
+<table><tr><td>Method</td><td>Prior Type</td><td>PSNR ↑</td><td>LPIPS ↓</td><td>FVD ↓</td><td>Context. ↓</td><td>CLIP Score ↑</td><td>Speed↑</td></tr><tr><td>DisCo [35] (CVPR24)</td><td>-</td><td>30.98</td><td>0.259</td><td>167.7</td><td>2.134</td><td>82.4%</td><td>1FPS</td></tr><tr><td>Animate Anyone [8] (CVPR24)</td><td>-</td><td>31.33</td><td>0.238</td><td>148.8</td><td>1.901</td><td>86.6%</td><td>2FPS</td></tr><tr><td>Champ [51] (ECCV24)</td><td>-</td><td>31.21</td><td>0.251</td><td>155.1</td><td>2.038</td><td>84.3%</td><td>1FPS</td></tr><tr><td>UniAnimate [36] (ArXiv24)</td><td>-</td><td>32.31</td><td>0.211</td><td>141.3</td><td>1.811</td><td>87.1%</td><td>2FPS</td></tr><tr><td>SHERF [9] (ICCV23)</td><td>-</td><td>27.39</td><td>0.301</td><td>202.3</td><td>2.998</td><td>70.1%</td><td></td></tr><tr><td>SIFU [50] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.891</td><td>72.1%</td><td>5FPS</td></tr><tr><td>GST [26] (ArXiv24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>3.011</td><td>71.7%</td><td>50FPS</td></tr><tr><td>TeCH [10] (3DV24)</td><td>Camera</td><td>29.01</td><td>0.271</td><td>188.1</td><td>2.331</td><td>79.3%</td><td>6FPS</td></tr><tr><td>SiTH [7] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.776</td><td>74.7%</td><td>&lt;1FPS</td></tr><tr><td>HumanRef [47] (CVPR24)</td><td>Camera</td><td>-</td><td>-</td><td>-</td><td>2.167</td><td>81.5%</td><td>3FPS</td></tr><tr><td>SHERT [46] (CVPR2024)</td><td>Inpainting</td><td>29.31</td><td>0.266</td><td>179.8</td><td>2.319</td><td>78.8%</td><td>10FPS</td></tr><tr><td>UniAnimate + GPGS (ours)</td><td>Kinematics</td><td>29.97</td><td>0.251</td><td>168.7</td><td>1.992</td><td>82.1%</td><td>70FPS</td></tr><tr><td>KHD (ours)</td><td>-</td><td>32.81</td><td>0.221</td><td>134.4</td><td>1.768</td><td>92.3%</td><td>2FPS</td></tr><tr><td>SinGS (ours)</td><td>Kinematics</td><td>31.33</td><td>0.240</td><td>156.3</td><td>1.847</td><td>88.2%</td><td>70FPS</td></tr></table>
+
+marily lay a solid foundation for the optimization process but fail to maintain this advantages throughout. Incompatibilities still arise in optimization stage, prompting us to propose a novel density control scheme that is inherently compatible with hybrid representations, designed for adaptive adjustment body-wide density. This scheme draws on mesh operation algorithms [6] to better address the unique challenges of human body. For primitives that locate in under-expression mesh areas, we subdivide these regions by adding gaussians on every edge of the selected geometric triangles, which creates much smaller triangles. And we skip the trivial post-smoothing for vertices as the position of Gaussians will continue to be optimized in the network. For candidate Gaussians that are selected due to excessively large scales, as well as all newly added Gaussians, we perform rescaling to adjust them to an average size. In the case of anomalous gaussians, especially those are almost transparent, we collapse relevant edges and replace them with single vertex, resulting in decimated adjacent faces. And the priority of selected edges is decided by gaussian attributes and edge length. This entire pruning process preserves the principal structure of the human body. Our strategy result in better reconstruction and animation as the optimization was conducted under connectivity and compactness of the entire human body rather than producing holes and stacks. Moreover, this approach synergistically enhances the effectiveness of our hybrid representation.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Implementation Details. Our KHD primarily utilizes the RotationHuman dataset we collected, which focuses on human pose image sequences involving turning motions. The specific structure of the 3D Pose Encoder is provided in
+
+the supplementary materials. KHD was trained using 8 NVIDIA A100 80GB GPUs, with DeepSpeed and ZeRO2 employed to reduce memory usage. Similar toAnimate Anyone, we resized the video frames to a spatial dimension of  $768 \times 512$ . We used a context window size of 64 frames, and to enhance model scalability post-training, we implemented a random context window jitter strategy [36]. During training, the model randomly samples window sizes from 64 to 32 frames in an uniformly distributed manner. The training process utilized the AdamW optimizer [15], with a learning rate set to  $5e - 5$  and DDPM with 1000 steps for noise sampling. During inference, DDIM with 30 steps was used to reduce inference time. For the 3DGS component, the Adam optimizer [15] was used with a learning rate of  $1e - 3$  and a cosine annealing learning scheduler was applied to accelerate convergence. The input image sequence size for 3DGS was also  $768 \times 512$ . 3DGS was trained using a single NVIDIA 4090 24GB GPU.
+
+Baseline Models. Our baseline models consist of two parts: the first part includes human image animation models, such as DisCo [35], Animation Anyone [8]  $^{1}$ , Champ [51], and UniAnimate [36]. These models are used to compare our animation capability and the superiority of KHD. The second part consists of single-image 3D avatar reconstruction models, including SHERF [9], SIFU [50], GST [26], TeCH [10], SiTH [7], HumanRef [47], and SHERT [46].
+
+Metrics. We employ both PSNR and LPIPS to assess the quality of video reconstruction. To evaluate the animation capability of our model, we also use FVD [34] to measure the distribution discrepancy between the generated video and the original video, assessing the video generation performance. Furthermore, following HumanRef, we introduce contextual distance [19] and CLIP score [27] to evaluate the texture and semantic similarity between the rendered
+
+![](images/3a42d13bfec4a738751303ba79faedc3dfb2230b70f53d76348c9b242b679bee.jpg)  
+Figure 4. Comparison between KHD and other SOTA human image animation methods. Please zoom in for better observation.
+
+output and the input reference image.
+
+# 4.2. Qualitative Analysis
+
+Singe-Image Reconstruction. We compare SinGS with two methods from the literature that claim to support animation (TeCH, SiTH). It is worth noting that during our experiments, we found that single-image animation with these methods was extremely difficult to execute, and in some cases, nearly impossible. We had to use third-party code  ${}^{2}$  to achieve the reposing for some of these methods. We animate their reconstructed outputs to a common pose (A Pose) for comparison, which allows us to evaluate both reconstruction and animation capabilities. The comparison results are shown in Figure 3, SinGS generates results with better details and maintains high-quality animation, particularly on the in-the-wild data, where SinGS's visual performance significantly outperforms the other methods. This demonstrates the high feasibility and effectiveness of the kinematic prior.
+
+Kinematic Human Diffusion. KHD, as the core component of our pipeline, is compared with state-of-the-art human image animation methods, includingAnimate Anyone and UniAnimate. As shown in Figure 4, we drive the same character with all three methods, focusing on comparing the quality of their generated results, particularly for the turning pose. From the figure, it is clear that both UniAnimate and our KHD maintain higher consistency thanAnimate Anyone after the character turns, with KHD surpassing UniAnimate in detail. The details marked by the red arrows in Figure 4 reveals that UniAnimate generates incorrect details, a common issue when using 2D poses, as they often struggle to distinguish body orientation during back-facing poses, leading the model to generate erroneous images. This is detrimental to reconstruction, while KHD generates videos with much higher consistency.
+
+![](images/8571cb3aae5ca73f739c8b03c6c01711d6540f1a88c71bf7ebf6b1602c55dd38.jpg)  
+Figure 5. Fifty users rated the video quality, with UniAnimate scoring highest, followed closely by our model, which outperformed others. Our model is more efficient, using only 3.5 GB of memory and achieving 70 FPS, while UniAnimate requires over 12GB and 0.5 seconds per image.
+
+Geometry-Preserving 3D Gaussian Splatting. Although KHD provides high-consistency pose sampling results, it inevitably has some consistency flaws, meaning it can only offer imperfect prior information. Our geometry-preserving GS method is specifically designed to address this challenge. To validate the superiority of our Geometry-Preserving 3D Gaussian Splatting (GPGS) over general human modeling methods, we compared it with recent state-of-the-art (i.e., SOTA) methods, HAHA [32] and HUGS [16]. We generate a pose sequence using KHD and then performed reconstruction with all 3 methods. The reconstruction results are shown in Figure 7. As seen, both HAHA and HUGS fail to produce a compact 3D avatar, with significant holes or floating artifacts appearing in various areas, particularly during the turning motion. In contrast, our GPGS method is able to reconstruct a compact, watertight 3D avatar model.
+
+# 4.3. Quantitative Analysis
+
+We selected 100 test videos from the UBC dataset for our quantitative analysis. For each video, we chose the first frame as the reference image and used the video's pose sequence as the driving signal. The performance of all methods was assessed by comparing the animation results with the original video to evaluate the differences. Video reconstruction metrics (including PSNR, LPIPS, and FVD) reflect the model's animation capabilities, while Contextual Distance and CLIP score allow for comparison with methods that do not support animation. The quantitative comparison results are shown in Table 1. Human image animation methods (i.e., the second to fifth rows in the table, including our KHD) outperform the reconstruction-based methods across the board. Among them, KHD surpasses the other methods in most metrics, and UniAnimate also demonstrates superior performance, which is expected due to the scale of training data and model size. While SinGS lags behind UniAnimate, it shows a significant advantage over other methods in some metrics. However, SinGS significantly outperforms diffusion-based animation methods in terms of inference efficiency and resource consumption. Our SinGS achieves 70 FPS during inference, with only
+
+Table 2. The results of the ablation experiments on Semantic Laplacian Regularization (i.e., Semantic Lap. Reg.) and Geometry-Preserving Density Control (i.e., GPDC) in SinGS.  
+
+<table><tr><td>Setting</td><td>PSNR</td><td>LPIPS</td><td>FVD</td></tr><tr><td>with Semantic Lap. Reg.</td><td>31.33</td><td>0.240</td><td>156.3</td></tr><tr><td>with KNN Lap. Reg.</td><td>30.88</td><td>0.250</td><td>169.9</td></tr><tr><td>w/o Lap. Reg.</td><td>30.34</td><td>0.272</td><td>181.3</td></tr><tr><td>with GPDC</td><td>31.01</td><td>0.249</td><td>166.1</td></tr><tr><td>naive Density Control [14]</td><td>30.22</td><td>0.276</td><td>190.2</td></tr></table>
+
+3.8 GB of memory usage (tested on a single NVIDIA 4090 GPU), while UniAnimate, Champ, andAnimate Anyone each require more than 0.4 seconds per image and consume over 12 GB of memory. These quantitative results strongly demonstrate that SinGS is highly effective and feasible. We believe that using KHD, a specialized foundational model, will greatly enhance 3D reconstruction performance while significantly reducing the stringent data requirements.
+
+User Study. We invited 50 users to subjectively evaluate the animation results of SinGS. The evaluation was based on a scale from 0 to 10, with 10 being the highest score and 0 being the lowest. The results are visualized in Figure 5.
+
+# 4.4. Ablation Study
+
+Kinematic Priors Analysis. The number of poses sampled by KHD has a significant impact on the 3D distillation process. We analyzed how the number of poses affects the animation capability of the final reconstructed model, and the results are shown in Figure 6. We incrementally increased the number of poses from 2 (which corresponds to the typical approach of generating front and rear views, as used by most methods) up to 150. We also tested the influence of different prior models (i.e., KHD, UniAnimate, and Animate Anyone) on the results. Additionally, we examined how different 3DGS reconstruction methods handle the use of prior knowledge. As shown, performance improves rapidly with an increase in the number of poses, but the rate of improvement slows significantly after reaching around 100 poses. Moore-AA + HAHA shows the slowest improvement, while KHD + GPGS exhibits the slowest decline in performance. This suggests that increasing the number of poses does not always lead to improved performance for two main reasons: first, the prior models have already provided sufficient information; and second, none of the prior models provide perfectly consistent priors. Excessive sampling can introduce a lot of inconsistent noise, which ultimately harms performance.
+
+Geometry-Preserving 3D Gaussian Splitting Analysis. We conducted ablation experiments on the two key designs in GPGS: Semantic Laplacian Regularization and GPDC, with the results shown in Table 2. By replacing and removing the Laplacian regularization, we observed that Semantic Laplacian consistently outperforms in terms of reconstruction metrics. Additionally, GPDC demonstrates a perfor
+
+![](images/b842dcf943409a52bdf762189b7e88ee69294668cd25f9d0b1b64457ba6422f0.jpg)  
+Figure 6. The comparison of the impact of augmented pose numbers on the performance of the 3D avatar models.
+
+![](images/b6dc8cd903053ead99689f69599e83ad168ab21e6ef0529d1e35b52fc60f9414.jpg)  
+Figure 7. Here is a comparison of our GPGS with two SOTA 3DGS avatar methods, HAHA [32] and HUGS [16]. All methods use images sampled by KHD as body prior.
+
+mance advantage over the original density control strategy. The original strategy does not account for dynamic properties and geometric constraints, which makes it ineffective in addressing issues like floating and holes caused by data inconsistencies.
+
+# 5. Conclusion
+
+In this paper, we propose a new paradigm for single-image 3D avatar reconstruction. Unlike traditional methods that complete missing information in camera space, we sample in human kinematic space, enabling efficient capture of both viewpoints and motion traits. To achieve this, we introduce Kinematic Human Diffusion (KHD) for consistent pose-space generation, supported by our RotationHuman dataset, which focuses on turning motions. Additionally, we propose Geometry-Preserving 3D Gaussian Splating that reconstructs high-quality, animatable 3D avatars under imperfect human priors. This includes two key innovations: Semantic Laplacian regularization for compact, detailed constraints, and a geometry-preserving density control strategy to maintain stable human geometry. Together, these innovations allow SinGS to achieve high-quality, animatable 3D avatar reconstruction from a single image.
+
+# 6. Acknowledgment
+
+This work supported by Shanghai Post-doctoral Excellence Programe (2024290). This work was also partly by Shanghai Municipal Bureau of Culture and Tourism and Meta-verse Technology Innovation Center of Shanghai Municipal Bureau of Culture and Tourism. Kairui Feng thanks to Xiaomi foundation.
+
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2025/Single Domain Generalization for Few-Shot Counting via Universal Representation Matching/ef6b53d9-c810-43e9-a737-a386bc2ad915_content_list.json

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+        "type": "text",
+        "text": "Single Domain Generalization for Few-Shot Counting via Universal Representation Matching",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Xianing Chen Si Huo Borui Jiang Hailin  $\\mathbf{H}\\mathbf{u}^{*}$  Xinghao Chen\\*",
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+    {
+        "type": "text",
+        "text": "Huawei Noah's Ark Lab.",
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+        "type": "text",
+        "text": "sdxianing@gmail.com, {huosi,jiangborui,hailin.hu,xinghao.chen}@huawei.com",
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+    {
+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Few-shot counting estimates the number of target objects in an image using only a few annotated exemplars. However, domain shift severely hinders existing methods to generalize to unseen scenarios. This falls into the realm of single domain generalization that remains unexplored in few-shot counting. To solve this problem, we begin by analyzing the main limitations of current methods, which typically follow a standard pipeline that extract the object prototypes from exemplars and then match them with image feature to construct the correlation map. We argue that existing methods overlook the significance of learning highly generalized prototypes. Building on this insight, we propose the first single domain generalization few-shot counting model, Universal Representation Matching, termed URM. Our primary contribution is the discovery that incorporating universal vision-language representations distilled from a large scale pretrained vision-language model into the correlation construction process substantially improves robustness to domain shifts without compromising in domain performance. As a result, URM achieves state-of-the-art performance on both in domain and the newly introduced domain generalization setting.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Few-shot counting (FSC) [46] is the task of estimating the number of target objects in an image using only a few annotated exemplars or without any exemplar at all. Although many proposed approaches [40, 65] have achieved satisfactory results, they experience severe performance degradation when tested on data from unseen scenarios in real-world deployment due to the domain shift [24] problem. This shift arises from the deviation from the source domain training data to unseen target domain testing data, such as",
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+        "image_caption": [
+            "(a) domain generalization for few-shot counting"
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+        "image_caption": [
+            "(b) extract-then-match"
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+        "img_path": "images/df92af04a82a6cebad38c03e75f74a19bd2103afcc689fa64e305cfc45fc6d02.jpg",
+        "image_caption": [
+            "(c) universal representation matching",
+            "Figure 1. Illustration of (a) domain generalization for few-shot counting, (b) the vanilla extract-then-match pipeline, and (c) our proposed universal representation matching."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "changes in camera position and weather condition [59, 74], as well as biases introduced during data collection. For instance, images in the FSC147 [46] show each target object clearly while scenes in FSCD-LIVS [35] feature more oc",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            42
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding authors.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "**Code is available at https://github.com/jbr97/URM.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "4639",
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+    },
+    {
+        "type": "text",
+        "text": "clusions and quality degradation as discussed in [35].",
+        "bbox": [
+            76,
+            90,
+            429,
+            104
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Although domain adaptation (DA) [55] has been proposed to adapt the source domain distribution to that of the target domain by finetuning models with target domain data, the process is often laborious, and target domain data is not always available in practice, especially in the class-agnostic setting of FSC [46]. In contrast, domain generalization (DG) [73] seeks to generalize the model to any unseen target domain without requiring target domain data and model updates as shown in Figure 1a, that is, to learn a generalized model by only source domain with a limited distribution. We consider in this work the unexplored and challenging field of single DG for few-shot counting to address the aforementioned challenges, where only one source domain—likely of narrow distribution—is used for training.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We start by analyzing why existing methods that follow the common extract-then-match pipeline [10] illustrated in Figure 1b fail. In this pipeline, exemplars prototypes are first extracted from the image feature. Next, candidates are generated by analyzing the correlation between prototypes and the image feature. Finally, the resulting correlation map is regressed into an object density map.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The primary distinction among these methods lies in their approaches to constructing correlation, such as attention [17, 31, 32], Siamese similarity [10, 44, 46], and so on [51, 65]. However, they all overlook the importance of prototypes in the construction process. Prototypes learned from the source domain with a narrow distribution inherently exhibit a similarly narrow distribution. Intuitively, matching with such a limited representation in the unobserved target domain with a rather broad distribution inherently leads to sub-optimal performance. Therefore, enhancing the generalization of prototypes is essential for learning a domain-general few-shot counter.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The contrastive language-image pre-training model (CLIP) [43] and its extensions [7, 18, 66, 72] have demonstrated remarkable generalization capacity in open-world down-stream tasks. The representation from CLIP can serve as universal representation with domain-invariant information which demonstrate extraordinary performance across several distributions owing to the vast diversity of distributions seen during training [36]. Our finding indicates that matching with the universal vision-language representation distilled from the frozen CLIP model during the correlation construction process exhibit remarkable resilience to domain shift while without in domain performance degradation. The operation is illustrated in Figure 1c.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Building on the discovery, we introduce the first domain-general few-shot counting model, Universal Representation Matching, termed URM. Specifically, we introduce universal vision and language prototypes to act as knowledge distiller [53] to learn universal knowledge from the large-scale pre-trained CLIP model motivated by prompt knowledge",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "distillation [28], aiming to extend the narrow distribution of these prototypes. To adapt the V-L representations from CLIP for local objects matching, we minimally adjust the CLIP encoder while keeping its pre-trained weights frozen.",
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+        "list_items": [
+            "- For the visual representation: the class token focuses more on global image properties which may not suitable for capturing localized details [11], and the image tokens are weak in local discriminability [25]. Thus, we follow MaskCLIP [72] to obtain class-specific segmentation, allowing us to extract locality object-level representations [47] which are then used to distill region-specific information into the visual prototypes.",
+            "- For the language representation: we follow CuPL [42] to generate diverse customized prompts that leverage knowledge contained in LLMs [1] as well as hand-written templates, to produce numerous descriptive sentences that capture important discriminative characteristics of the object categories. These prompts are subsequently encoded by the language tower to obtain universal language embeddings for distillation."
+        ],
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The learned universal V-L prototypes are then matched with the image feature through cross attention to construct the correlation map. As the distillation operation is conducted only during the training phase, URM remains as efficient as other methods that do not require external knowledge at inference time.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To validate URM, we conduct extensive experiments on both cross and in domain setting on FSC147 [46] and FSCD-LVIS [35] datasets in both few-shot and zero-shot scenarios. The results demonstrate that URM performs excellently on both intra-dataset and cross domain settings.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The main contributions of our work are as follows:",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We introduce a new challenging setting of the single domain generalized few-shot counting task. And we point out that existing paradigm's inability to accurately count objects in new scenes stems from the learned narrow distribution prototypes.",
+            "- We introduce URM, the first narrow source domain—general few-shot counting model. Specifically, we propose to match universal V-L representations transferred from CLIP through knowledge distillation to construct the correlation map, a novel approach not explored in previous works.",
+            "- Our proposed URM outperforms state-of-the-art methods by a large margin in both the introduced narrow source domain general setting as well as in domain benchmark."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Works",
+        "text_level": 1,
+        "bbox": [
+            500,
+            814,
+            648,
+            830
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot Counting. Object counting refers to the task of estimating the number of specific objects present in an image, typically limited to a few predefined categories, e.g., human heads [29, 69], cells [54], cars [60], and polyps [67].",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "4640",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shot counting addresses this limitation by given only a few annotated exemplars or without any exemplar at all. FamNet [46] proposed a pipeline that extracts appearance-based queries from exemplars and matches them with image feature to infer the object counts. Then, BMNet+ [51] enhanced localization by jointly learning representation with a non-linear similarity metric. CounTR [32] introduced cross attention-based interaction module to fuse image and exemplar features. SAFE-Count [65] incorporated a feature enhancement module. LOCA [10] further refined this pipeline by iteratively adapting object prototypes based on exemplar appearance and shape. DAVE [40] proposed a post-process method for LOCA by generating a high-recall detection set and verifying the results to identify and remove outliers. All of these methods follow the same extract-then-match paradigm and struggle with domain generalization.",
+        "bbox": [
+            75,
+            90,
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+            333
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "CLIP-guided Counting. Some studies also explored to count by leveraging CLIP. For instance, [37] extended CLIP's capabilities to counting but still failed when objects number is large. CrowdCLIP [30] mapped crowd patches to count text by constructing ranking-based text prompts to match the size-sorted crowd patches when category names were provided. Other works [2, 21, 22, 58, 62, 76] explored enumerating objects given class names, creating a link between object categories and visual representations. Besides, some open-set methods [20, 49, 64] achieve competitive results by leveraging CLIP as a bridge between V-L representations for interactive object detection. However, they require much more computational power and data for training, and their training classes cover the test classes.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Single Domain Generalization. Since domain shift problem in FSC remains unexplored, we mainly focus on related approaches for crowd counting. Although some domain adaptation techniques exist [61, 74, 75], they all inadequate for real-world application due to the lack of target data [4, 13, 33, 59, 74]. Domain generalization methods are primarily built on meta-learning algorithm MLDG [27], which employs meta-train and meta-test set to simulate the domain shift between training and testing phases in reality to learn domain-invariant features. For instance, DCCUS [12] proposed a dynamic sub-domain division scheme, dividing the source domain into multiple sub-domains. Whitening-based methods [9, 38, 39] remove domain-specific style information by eliminating feature correlation to ensure each feature has unit variance. However, these algorithms require a sufficiently broad source domain distribution. MPCount [41] proposed storing diverse density values for regression and reconstruct domain-invariant features using memory bank, eliminating the need for sub-domain partitioning. However, MPCount is still limited by the narrow source training data without accessing external knowledge.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/23eea1e33e71f99ff99956f4f1862073a3c957cc97e35929cf6f2945c8903480.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/404c35f5480f00a15ab4815d4f843d1324be47abe3b69028de41f125a9e7f46e.jpg",
+        "image_caption": [
+            "(b)"
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+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/0a72f5c49f4abd72a16e393c8477a8c144ae88ab1b94f0dbb155ba090938a79f.jpg",
+        "image_caption": [
+            "(c)",
+            "Figure 2. t-SNE visualization of the prototypes feature space for different categories from FSC147 by (a) the vanilla paradigm trained on FSC147, (b) the vanilla paradigm trained on FSCD-LVIS, and (c) our proposed URM trained on FSCD-LVIS. Note that the visualization is conduct on the test set where the object categories are disjoint from the train set. Best viewed in color."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            763,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Knowledge Distillation (KD). [16] proposed to optimize a student model under the effective information transfer and supervision of a teacher model or ensemble. Although several methods have been proposed to learn knowledge from teacher network with high fidelity [14, 53, 71], we simply follow CLIP-KD [63] to use feature mimicry learning [5] which has been proved to be the most effective approach for CLIP knowledge distillation.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            459,
+            591,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we first recap the preliminaries of CLIP, and then analyze why prior methods fail to generalize. Afterward, we introduce our proposed universal representation matching model.",
+        "bbox": [
+            496,
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Preliminary. CLIP [43], trained on large-scale image-text pairs by image-level contrastive learning, has well demonstrated the potential for learning transferable knowledge and open-set visual concepts. CLIP consists of a pair of image encoder  $\\mathcal{V}(\\cdot)$  and text encoder  $\\mathcal{T}(\\cdot)$ , both of which are jointly trained to map input image and text into an unified representation space. However, since CLIP is designed for image-level prediction, extracting local patch-level predictions from CLIP is non-trivial [50]. MaskCLIP [72] modifies the image encoder by removing the last query and key embedding layers, as well as reformulating the value-embedding layer and the last linear layer into two respective convolutional layers, while keeping the text encoder unchanged. The text encoder then processes language prompts containing target classes, and the resulting text embedding for each class is used as a classifier to produce pixel-level mask predictions.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Motivation. Since the existing extract-then-match paradigm fails to generalize, we begin by analyzing the reason behind this undesirable phenomenon, which motivates our proposed solution. After training on the source",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4641",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/fa450d996fe984d55ea204b8cd57752a267250f1f811ca57cf551549890aee8c.jpg",
+        "image_caption": [
+            "Figure 3. The framework of our proposed URM. The inference architecture is depicted in the gray part, where the learned prototypes are matched with the image feature through cross attention. The yellow part illustrates the universal V-L representations obtained from CLIP, which are distilled into the prototypes exclusively during the training phase."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            114,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "domain, we use t-SNE [56] to visualize the feature space of prototypes for different categories on the test set of FSC147 learned using both vanilla paradigm and URM. One noticeable observation is the clear boundary in Figure 2a using vanilla paradigm trained on FSC147, which corresponds to its well performance in the intra-dataset setting, even when the categories are disjoint from those in the training set. In contrary, Figure 2b shows an unclear boundary on the target domain when the traditional paradigm is trained on dataset with large doamin gap, aligning with a significant drop in accuracy in the cross-domain setting. The phenomenon suggests that simply learning prototypes within a narrow distribution is suboptimal for generalization. The key, we believe, is that the matching process should occur in a feature space with well-defined open-set visual concept boundaries. As shown in Figure 2c, prototypes from our URM—transferred from CLIP representation—better separate objects with unseen categories in unseen scenarios, supporting our hypothesis.",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "3.1. Universal Representation Matching",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Overview. The overall framework of our proposed URM is shown in Figure 3. The input image  $\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}$  is first encoded by the backbone network. Multi-scale features are extracted from the last three blocks, then resized to the same size of  $h \\times w$  and reduced to  $d$  channels using a",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "linear layer after concatenation. Next, a set of  $n$  selected exemplar bounding boxes are encoded into the image feature  $\\mathbf{f} \\in \\mathbb{R}^{h \\times w \\times d}$  via a prompt encoder. After that, the proposed universal vision and language prototypes  $p_v$  and  $p_l \\in \\mathbb{R}^{n \\times d}$  are initialized as learnable embeddings, and iteratively updated through interaction with the encoded image feature  $f^E \\in \\mathbb{R}^{hw \\times d}$  using  $N_1$  cross attention layers [57]. During this process, the resulting prototypes are distilled from the universal V-L representations obtained from the frozen CLIP model, respectively. Finally, the concatenated universal prototypes are correlated with  $f^E$  by  $N_2$  cross attention layers to obtain a correlation map, which is then regressed into a density map  $\\mathbf{R} \\in \\mathbb{R}^{H \\times W}$ , whose number is summed to the count estimation, i.e.,  $c = \\text{sum}(\\mathbf{R})$ .",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Prompt Encoder. Given the extracted image feature  $\\mathbf{f}$ , we use a two-way attention mechanism [23] to encode exemplar prompts into  $\\mathbf{f}$ , to indicate the object category to be counted. The exemplars are represented as a concatenated embedding composed of three elements: the height and width  $R^{n\\times 2}$  of bounding boxes  $R^{n\\times 4}$  which are mapped to shape embedding  $R^{n\\times d}$  by three linear layers with ReLU activation follow [10], a learnable embedding group  $R^{n\\times d}$ , and appearance tokens extracted from  $\\mathbf{f}$  using ROI Pooling [48]. As illustrated in Figure 4, cross attention operations are then applied iteratively to update both the em",
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+        "page_idx": 3
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+    {
+        "type": "page_number",
+        "text": "4642",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/b00d49cefa4f5f9a36d7ed8dcb784fbfa5ef30127c964656e91f30fadce26279.jpg",
+        "image_caption": [
+            "Figure 4. Illustration of the prompt encoder."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            93,
+            436,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "bedding and image feature, resulting in the category-aware image feature  $f^{E}$ .",
+        "bbox": [
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+            311,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Universal Vision Representation Learning. Since CLIP trained with image-level supervision lacks precise localization of objects and includes noise on non-relevant areas in its visual representation, we follow MaskCLIP [72] to reformulate the value-embedding layer of image encoder  $\\mathcal{V}(\\cdot)$  to produce a dense attentive segmentation  $\\mathcal{M} \\in \\mathbb{R}^{h \\times w}$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Then, the universal vision representation  $r_v$  containing fine-grained local image semantics is obtained by applying Mask Pooling [6] between the 2D visual embeddings of the image output from the last layer of CLIP vision encoder and the class-aware mask  $\\mathcal{M}$ :",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nr _ {v} = \\operatorname {M a s k P o o l} (\\mathcal {V} (\\mathbf {I}), \\mathcal {M}) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Additionally, the vision prototype  $p_v$  initialized as a learnable embedding  $\\mathbb{R}^{n \\times d}$  is iteratively updated through  $N_1$  cross attention layers with the encoded image feature, where  $q = p_v$ ,  $k = v = f^E$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since distribution of the prototype learned from a narrow source domain is also narrow, we adopt feature mimicry loss following CLIP-KD [63] to transfer universal representation knowledge into the visual prototypes:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {V - K D} = \\frac {1}{| \\mathcal {B} |} \\sum_ {k = 1} ^ {| \\mathcal {B} |} \\| r _ {v k} - p _ {v k} \\| \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            161,
+            707,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{B}$  is the training batch,  $r_v$  is the universal vision representation, and  $p_v$  is the universal vision prototype. For simplicity, the linear projection layer for matching the dimension size of the CLIP embedding is omitted.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Universal Language Representation Learning. Handwritten templates like “A photo of {}” completed with a category name are limited in describing details for fine-grained embedding [42]. Besides, writing high-performing",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "prompt templates is labor-intensive and requires prior information about dataset contents. For example, ImageNet hand-written prompts [43] like “A toy {}” and “A sculpture of {}” do not generalize well to other datasets like FSC-147.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We thus follow CuPL [42] to further extend templates with customized prompts generated by LLM that contain important discriminating characteristics which can best represent an object category in natural language. The templates and prompts for LLM, i.e., GPT-4 [1] in this work, are detailed in Appendix.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The generated prompts for each category are then encoded by CLIP's text encoder  $\\mathcal{T}(\\cdot)$ . The corresponding text embeddings are averaged to produce the resulting universal text representation  $r_t$ .",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Similar to vision prototype learning, the language prototype  $p_l$  is iteratively updated through interactions with  $f^E$  using the same cross attention layers. And the language distillation loss is given by:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {L - K D} = \\frac {1}{\\mathcal {B}} \\sum_ {k = 1} ^ {\\mathcal {B}} \\| r _ {l k} - p _ {l k} \\| \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            593,
+            373,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $r_l$  is the universal language representation,  $p_l$  is the universal language prototype. The linear projection layer is also applied to the language prototype.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Universal Representation Matching. After obtaining the universal V-L prototypes for the object category in the image, we can construct a correlation between the concatenated prototypes and image feature. Although various matching approaches have been proposed as discussed, we focus on the essential matching elements within the correlation construction process. Specifically, we apply  $N_{2}$  cross attention layers with  $\\mathbf{q} = f^{E}, \\mathbf{k} = \\mathbf{v} = \\mathrm{concat}(p_{v}, p_{l})$  to obtain the correlation map  $\\mathbb{R}^{hw \\times d}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, a regression head predict the final 2D density map  $\\mathbf{R} \\in \\mathbb{R}^{H \\times W}$  from the correlation map.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Loss Function. The model is trained with  $\\ell_2$  loss between the predicted density map  $\\mathbf{R}$  and the ground-truth map  $\\mathbf{G}$ , normalized by the number of objects:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {d e n s i t y}} = \\frac {1}{2 \\mathcal {B}} \\sum_ {k = 1} ^ {\\mathcal {B}} \\frac {1}{N _ {k}} \\| \\boldsymbol {G} _ {k} - \\boldsymbol {R} _ {k} \\| _ {2} ^ {2} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            570,
+            720,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $N_{k}$  represents the number of objects in image  $k$ . The overall training loss is thus a combination of the density and the distillation losses from Equation (2) (3):",
+        "bbox": [
+            498,
+            763,
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {d e n s i t y}} + \\alpha \\mathcal {L} _ {V - K D} + (1 - \\alpha) \\mathcal {L} _ {L - K D} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            542,
+            832,
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+            849
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha$  is the distillation weight parameter to balance the contributions of the vision and language representations in the universal prototypes.",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "4643",
+        "bbox": [
+            482,
+            944,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/af14cdc47c1442473edf412f0833844589fa15844d020cdc6a63473597e7c041.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Setting</td><td colspan=\"4\">Few-shot</td><td colspan=\"4\">Zero-shot</td></tr><tr><td>Source → Target</td><td colspan=\"2\">A → B</td><td colspan=\"2\">B → A</td><td colspan=\"2\">A → B</td><td colspan=\"2\">B → A</td></tr><tr><td>Metric</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td></tr><tr><td colspan=\"9\">Vanilla Methods</td></tr><tr><td>FamNet (CVPR21) [46]</td><td>29.98</td><td>48.95</td><td>42.74</td><td>118.47</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>BMNet+ (CVPR22) [51]</td><td>37.86</td><td>68.94</td><td>36.53</td><td>116.02</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>CounTR (BMVC22) [32]</td><td>34.76</td><td>54.39</td><td>33.24</td><td>107.34</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>LOCA (ICCV23) [10]</td><td>30.63</td><td>44.33</td><td>29.13</td><td>88.06</td><td>31.17</td><td>46.98</td><td>34.13</td><td>113.72</td></tr><tr><td>DAVE (CVPR24) [40]</td><td>29.67</td><td>45.28</td><td>29.51</td><td>86.13</td><td>30.42</td><td>47.03</td><td>35.40</td><td>115.81</td></tr><tr><td colspan=\"9\">Domain Generalization Methods</td></tr><tr><td>ISW (CVPR21) [9]</td><td>35.95</td><td>51.83</td><td>36.41</td><td>124.09</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>GS (ICCV21) [34]</td><td>30.55</td><td>47.57</td><td>29.83</td><td>98.42</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>DCCUS (AAAI23) [12]</td><td>29.02</td><td>43.55</td><td>28.46</td><td>83.32</td><td>30.39</td><td>44.87</td><td>34.29</td><td>109.20</td></tr><tr><td>MPCount (CVPR24) [41]</td><td>25.11</td><td>41.32</td><td>22.07</td><td>80.17</td><td>27.68</td><td>44.58</td><td>30.99</td><td>102.18</td></tr><tr><td>URM (Ours)</td><td>21.87</td><td>38.42</td><td>21.17</td><td>73.42</td><td>23.54</td><td>39.93</td><td>27.49</td><td>94.57</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Comparison with the state-of-the-art methods on FSC-147 (A) and FSCD-LVIS (B).",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            372,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we evaluate the effectiveness of URM, demonstrating how universal representation matching enhances the generalization and performance of few-shot counting models.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental setting",
+        "text_level": 1,
+        "bbox": [
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+            465,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. We first resize input images to  $H = W = 512$  and apply standard data augmentations such as tiling, horizontal flipping and color jitter. The model uses an Imagenet pre-trained Resnet50 backbone, with features from the final three blocks upsampled to  $h = w = 64$ . The backbone network parameters are frozen follow [10, 46], while all other parameters are trained for 150 epochs. The resulting features are projected into  $d = 256$  channels via an linear layer. The distillation weight  $\\alpha$  in Equation (5) is set to 0.9. The number of cross attention layers is  $N_{1} = N_{2} = 3$ . The regression head consists of three  $3 \\times 3$  convolutional layers with 128, 64 and 32 feature channels, each followed by a Leaky ReLU, a  $2 \\times$  bilinear upsampling, and a linear layer, consistent with the LOCA configuration. We use AdamW optimizer with the fixed learning rate  $10^{-4}$  and a weight decay of  $10^{-2}$ . Gradient clipping with maximum norm of 0.1 is applied. URM is trained on a single NVIDIA V100 GPU with batch size of 4.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We evaluate our method on two mainstream datasets: FSC-147 [46] and FSCD-LVIS [35]. Specifically, FSC-147 contains 6135 images of 147 object categories, split into training, validation and test sets consisting of 3659, 1286 and 1190 images respectively. Images in FSC-147 are collected from the Internet. The sets of object categories present in each split are disjoint. FSCD-LVIS contains 6195 images spanning 372 classes, which are",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "extracted from the LVIS dataset [15]. Each image annotation consists of three bounding boxes for exemplar objects within each category.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Let  $S \\to \\mathcal{T}$  denote the case where  $S$  is the source domain and  $\\mathcal{T}$  is the target domain. The datasets are utilized in experiments under two cross-domain settings: the full training dataset of one is regarded as the source domain, while other entire test dataset is regarded as the target domain, i.e., FSC-147  $\\rightarrow$  FSCD-LVIS and FSCD-LVIS  $\\rightarrow$  FSC-147.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. We evaluate our method using two commonly employed metrics in object counting: mean absolute error (MAE) and root mean square error (RMSE), between estimated and labeled counts for each image:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM A E = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left| c _ {i} - \\hat {c} _ {i} \\right|, R M S E = \\sqrt {\\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(c _ {i} - \\hat {c} _ {i}\\right) ^ {2}} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $N$  is the number of test images,  $c_{i}$  is the ground truth count for the  $i$ -th image, and  $\\hat{c}_i$  is the predicted count. Lower values of both metrics indicate better performance.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Comparison with the state of the art",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we compare our URM with state-of-the-art methods on different benchmarks. The selected baselines can be grouped into two categories:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Vanilla Methods: FamNet [46], BMNet+ [51], CounTR [32], LOCA [10], and DAVE [40].",
+            "- Domain Generalization Methods: ISW [9, 41], GS [34], DCCUS [12], and MPCount [41]."
+        ],
+        "bbox": [
+            500,
+            806,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "All these DG methods are originally designed or adapted for crowd counting, we add the prompt encoder after feature",
+        "bbox": [
+            500,
+            869,
+            890,
+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "4644",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/adccebd21a50c00a5613b4b1b4104d5ec79a8b000eebcf26a3d7b0524e853af7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>MAE</td><td>RMSE</td></tr><tr><td>Baseline</td><td>30.15</td><td>48.04</td></tr><tr><td colspan=\"3\">Language Distillation</td></tr><tr><td>Naive Template</td><td>25.44</td><td>42.59</td></tr><tr><td>Prompt Generator</td><td>23.83</td><td>41.03</td></tr><tr><td colspan=\"3\">Vision Distillation</td></tr><tr><td>[CLS] Token</td><td>23.53</td><td>41.12</td></tr><tr><td>Global Pooling</td><td>22.94</td><td>39.44</td></tr><tr><td>Mask Pooling</td><td>21.87</td><td>38.42</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "extraction based on their implementation. Besides, GS is a combination of Gradient Surgery [34] and LOCA [10].",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1 presents the results of domain generalized few-shot counting. Our URM surpasses all the methods significantly, providing compelling evidence for the effectiveness of our designation. In contrast, sub-domain division methods like DCCUS and GS fail to achieve satisfactory results, as they struggle to produce meaningful sub-domains when the source domain distribution is narrow and the domain gap is large. Additionally, the whitening-based method ISW is even harmful because useful information is eliminated through the feature statistics normalization operation. Although MPCount introduced a single memory bank for regression does not require sub-domain partitioning, its generalization ability remains far inferior to our method.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We further evaluate our method on the zero-shot setting with no user annotation, the results are shown in the right part of Table 1. We follow [10] to take a minor modification of the prompt encoder by using only the learnable embedding to represent the exemplar prompt. The results confirm that our proposed URM effectively enhances the generalization ability of prototypes, enabling accurate count estimation even in the challenging case without manually annotated exemplar.",
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+    {
+        "type": "text",
+        "text": "4.3. Analysis and Ablations",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Ablation of the designed elements. We first ablate the important elements of our designation under the FSC-147 (A)  $\\rightarrow$  FSCD-LVIS (B) few-shot setting. The baseline model shares the same architecture as URM in the inference phase but without knowledge distillation. The result shown in the first row of Table 2 demonstrates that simply altering architecture, i.e., matching with learned prototypes that lack knowledge transfer and thus have a narrow distribution, introduces no benefit for generalization.",
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+    {
+        "type": "text",
+        "text": "In contrast, the method can achieve comparable performance to the SOTA method MPCount by using only language knowledge from CLIP with a naive template. Since the naive template \"A photo of {}\" is too limited to fully represent a category, adding more templates and customized",
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+        "type": "table",
+        "img_path": "images/635da56a77bc969e2e0eebdad5042e157a50af304bcaf75d49fec1ea94f93131.jpg",
+        "table_caption": [
+            "Table 2. Ablation of the designed elements."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>α</td><td>0</td><td>0.25</td><td>0.5</td><td>0.75</td><td>0.9</td><td>1</td></tr><tr><td>MAE</td><td>26.54</td><td>23.44</td><td>23.30</td><td>22.37</td><td>21.87</td><td>23.83</td></tr><tr><td>RMSE</td><td>42.82</td><td>39.87</td><td>39.48</td><td>38.92</td><td>38.42</td><td>41.03</td></tr></table>",
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+        "type": "table",
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+        "table_caption": [
+            "Table 3. Ablation of the distillation weight."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>N1</td><td>2</td><td>3</td><td>3</td><td>3</td><td>4</td></tr><tr><td>N2</td><td>3</td><td>2</td><td>3</td><td>4</td><td>3</td></tr><tr><td>MAE</td><td>22.77</td><td>22.23</td><td>21.87</td><td>23.58</td><td>23.45</td></tr><tr><td>RMSE</td><td>39.69</td><td>39.12</td><td>38.42</td><td>41.22</td><td>39.38</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4. Ablation of the number of layers, where  $N_{1}$  is the universal prototypes learning layers, and  $N_{2}$  is the universal representation matching layers.",
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+    {
+        "type": "text",
+        "text": "language prompts by the prompt generator further improves the model performance.",
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+        "type": "text",
+        "text": "Subsequently, incorporating visual representation via global average pooling from the 2D vision tokens output from the last layer improve performance, demonstrating that the vision representation is complementary to language knowledge. Using the [CLS] token which captures global description results in lower performance. Finally, by introducing more precise locality representation as well as noise removal through mask pooling, our model reaches a MAE of 21.87 as shown in the last row of Table 2, outperforming the baseline method with  $27.5\\%$ .",
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+    {
+        "type": "text",
+        "text": "Ablation of distillation weight. The distillation weight  $\\alpha$  in Equation (5) controls the balance between visual and language knowledge contributions. In this part, we conduct an ablation study on the weight to fully understand its impact. As shown in Table 3, when  $\\alpha = 0$  or  $\\alpha = 1$ , where only vision or language knowledge is introduced respectively, the performance is inferior to other settings, demonstrating that V-L representations complement each other. Setting  $\\alpha = 0.9$  yields the best performance, indicating that language representation from CLIP, which has been aligned to visual space, plays an influential role.",
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+    {
+        "type": "text",
+        "text": "Ablation of the number layers. We then ablate the hyper-parameters related to the number of layers. The universal prototypes learning layer number  $N_{1}$  determines how many layers are required to absorb the universal knowledge transferred from CLIP. And the universal representation matching layer number  $N_{2}$  defines how many layers are needed to learn an effective correlation map during matching in the hidden space. The results in Table 4 show that  $N_{1} = N_{2} = 3$  achieves the best performance.",
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+    {
+        "type": "text",
+        "text": "Ablation of different representation sources. In this part, we investigate the effect of different representation",
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+        "text": "4645",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Architecture</td><td>ACC</td><td>MAE</td><td>RMSE</td></tr><tr><td>OpenAI CLIP [43]</td><td>ViT-B/16</td><td>68.3</td><td>21.87</td><td>38.42</td></tr><tr><td>OpenAI CLIP [43]</td><td>ViT-L/14</td><td>75.5</td><td>22.63</td><td>38.95</td></tr><tr><td>OpenAI CLIP [43]</td><td>RN50×16</td><td>70.5</td><td>23.15</td><td>39.63</td></tr><tr><td>OpenCLIP [8]</td><td>ConvNeXt-B</td><td>71.5</td><td>22.78</td><td>39.10</td></tr><tr><td>SigLIP [68]</td><td>ViT-B/16</td><td>73.4</td><td>21.33</td><td>37.85</td></tr><tr><td>EVA-02-CLIP [52]</td><td>ViT-B/16</td><td>74.7</td><td>21.86</td><td>38.12</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "learning sources in Table 5. The first row presents the results of our default setting which uses the OpenAI ViT-B/16 CLIP model. Increasing the model size leads to a performance drop due to the large dimension gap between the CLIP model and URM as seen in the second row. Besides, models with convolutional backbones, such as ResNet50 and ConvNeXt, perform poorly in comparison despite achieving higher ImageNet accuracy, suggesting that ViT architecture is better suited for representation learning in our task. Finally, the results in the last two lines indicate that using a stronger CLIP teacher model can further enhance our model's performance. However, this improvement also does not directly correlate with ImageNet accuracy, aligning with the observations in [26].",
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+    {
+        "type": "text",
+        "text": "4.4. Performance on in domain benchmark",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, URM is compared with the state-of-the-art methods on in domain benchmark. The three-shot evaluation results on FSC147 dataset are presented in Table 6. While demonstrating strong generalization, URM outperforms state-of-the-art few-shot counting models in terms of in-domain performance. Additionally, DAVE [40] proposed a detect-and-verify paradigm for the existing regression-based methods like LOCA to mitigate false activations on objects of other categories. Since DAVE is a general method for merging the benefits of both density and detection-based approaches, we also extend our method by incorporating this paradigm. Although inductive biases introduced by DAVE are insufficient to handle complex distribution gap in domain generalization setting (as show in Table 1), the resulting method still surpasses other methods on the traditional in domain benchmark, as demonstrated in the last row of Table 6.",
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+    {
+        "type": "text",
+        "text": "4.5. Generating language prompts with LVLMs",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this section, we explore the use of large vision-language models to generate language prompts, enabling our method to train without predefined category names. However, existing proprietary and public LVLMs struggle with image classification especially in open-world setting where the class list is unknown [70], making them difficult to",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c7f391d148839015a26215e9486f1468afbacaa4b87c7cb61d994a8c4063a757.jpg",
+        "table_caption": [
+            "Table 5. Ablation of different universal V-L representation sources, where ACC represents the ImageNet zero-shot classification performance of the CLIP model."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Split</td><td colspan=\"2\">Validation set</td><td colspan=\"2\">Test set</td></tr><tr><td>Method</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td></tr><tr><td>FamNet (CVPR21) [46]</td><td>23.75</td><td>69.07</td><td>22.08</td><td>99.54</td></tr><tr><td>BMNet+ (CVPR22) [51]</td><td>15.74</td><td>58.53</td><td>14.62</td><td>91.83</td></tr><tr><td>VCN (CVPR22) [45]</td><td>19.38</td><td>60.15</td><td>18.17</td><td>95.60</td></tr><tr><td>CountTR (BMVC22) [32]</td><td>13.13</td><td>49.83</td><td>11.95</td><td>91.23</td></tr><tr><td>SAFECount (WACV23) [65]</td><td>15.28</td><td>47.20</td><td>14.32</td><td>85.54</td></tr><tr><td>PseCo (CVPR24) [19]</td><td>15.31</td><td>68.34</td><td>13.05</td><td>112.86</td></tr><tr><td>LOCA (ICCV23) [10]</td><td>10.24</td><td>32.56</td><td>10.79</td><td>56.97</td></tr><tr><td>DAVE (CVPR24) [40]</td><td>8.91</td><td>28.08</td><td>8.66</td><td>32.36</td></tr><tr><td>URM (Ours)</td><td>10.63</td><td>32.01</td><td>10.15</td><td>54.83</td></tr><tr><td>URM+DAVE [40]</td><td>8.47</td><td>26.51</td><td>8.32</td><td>32.05</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/1fe44c5a5da46a1f1bb2c5037a3a42e58349df751877a1c32dd8050f6be30a99.jpg",
+        "table_caption": [
+            "Table 6. Performance comparison on in domain benchmark."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>LVLM</td><td>MAE</td><td>RMSE</td></tr><tr><td>Claude3 [3]</td><td>22.58</td><td>38.96</td></tr><tr><td>GPT4 [1]</td><td>22.45</td><td>38.75</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 7. Results of generating language prompts using LVLMs when category names are not given.",
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+    {
+        "type": "text",
+        "text": "accurately fill templates in the prompt generator. Fortunately, customized descriptive prompts with details are effective [42] as shown in Section 4.3 and Appendix. As a result, we choose Claude3-Opus [3] and GPT4 [1] to generate language prompts which have demonstrated the best open-world classification performance among existing VLMs [70]. We replace “{}” in our template prompts with “The category of the most numerous objects in the image” to prompt the VLMs. For example, “Describe what  $a(n)$  {} looks like?” becomes “Describe what the category of the most numerous objects in the image looks like?”. The results in Table 7 show that our method can successfully generalize to scenarios where category names are not provided during training.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This paper proposes URM to address single domain generalization for few-shot counting with narrow source distribution. URM is motivated by the unique challenge that existing methods struggle to learn high generalization prototypes. To address this issue, we propose a universal representation matching paradigm that incorporating universal vision-language prototypes distilled from the universal representations from CLIP model, which has seen vast diversity of distributions during training. Matching with these universal prototypes leads to high generalization and superior performance. Extensive experiments on both cross and in domain settings show that URM significantly outperform the state-of-the-art.",
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+    {
+        "type": "text",
+        "text": "References",
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+        ],
+        "page_idx": 8
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2025/Single Domain Generalization for Few-Shot Counting via Universal Representation Matching/ef6b53d9-c810-43e9-a737-a386bc2ad915_origin.pdf

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2025/Single Domain Generalization for Few-Shot Counting via Universal Representation Matching/full.md

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+# Single Domain Generalization for Few-Shot Counting via Universal Representation Matching
+
+Xianing Chen Si Huo Borui Jiang Hailin  $\mathbf{H}\mathbf{u}^{*}$  Xinghao Chen\*
+
+Huawei Noah's Ark Lab.
+
+sdxianing@gmail.com, {huosi,jiangborui,hailin.hu,xinghao.chen}@huawei.com
+
+# Abstract
+
+Few-shot counting estimates the number of target objects in an image using only a few annotated exemplars. However, domain shift severely hinders existing methods to generalize to unseen scenarios. This falls into the realm of single domain generalization that remains unexplored in few-shot counting. To solve this problem, we begin by analyzing the main limitations of current methods, which typically follow a standard pipeline that extract the object prototypes from exemplars and then match them with image feature to construct the correlation map. We argue that existing methods overlook the significance of learning highly generalized prototypes. Building on this insight, we propose the first single domain generalization few-shot counting model, Universal Representation Matching, termed URM. Our primary contribution is the discovery that incorporating universal vision-language representations distilled from a large scale pretrained vision-language model into the correlation construction process substantially improves robustness to domain shifts without compromising in domain performance. As a result, URM achieves state-of-the-art performance on both in domain and the newly introduced domain generalization setting.
+
+# 1. Introduction
+
+Few-shot counting (FSC) [46] is the task of estimating the number of target objects in an image using only a few annotated exemplars or without any exemplar at all. Although many proposed approaches [40, 65] have achieved satisfactory results, they experience severe performance degradation when tested on data from unseen scenarios in real-world deployment due to the domain shift [24] problem. This shift arises from the deviation from the source domain training data to unseen target domain testing data, such as
+
+![](images/83f5c2b727645c1d7d481fe0dd7079105ad0d0982261f73b293682159b70057d.jpg)  
+(a) domain generalization for few-shot counting
+
+![](images/265a0917b498bc31622b123b775e1bf2394dab383896a788adf3f80b8e69ff2d.jpg)  
+(b) extract-then-match
+
+![](images/df92af04a82a6cebad38c03e75f74a19bd2103afcc689fa64e305cfc45fc6d02.jpg)  
+(c) universal representation matching  
+Figure 1. Illustration of (a) domain generalization for few-shot counting, (b) the vanilla extract-then-match pipeline, and (c) our proposed universal representation matching.
+
+changes in camera position and weather condition [59, 74], as well as biases introduced during data collection. For instance, images in the FSC147 [46] show each target object clearly while scenes in FSCD-LIVS [35] feature more oc
+
+clusions and quality degradation as discussed in [35].
+
+Although domain adaptation (DA) [55] has been proposed to adapt the source domain distribution to that of the target domain by finetuning models with target domain data, the process is often laborious, and target domain data is not always available in practice, especially in the class-agnostic setting of FSC [46]. In contrast, domain generalization (DG) [73] seeks to generalize the model to any unseen target domain without requiring target domain data and model updates as shown in Figure 1a, that is, to learn a generalized model by only source domain with a limited distribution. We consider in this work the unexplored and challenging field of single DG for few-shot counting to address the aforementioned challenges, where only one source domain—likely of narrow distribution—is used for training.
+
+We start by analyzing why existing methods that follow the common extract-then-match pipeline [10] illustrated in Figure 1b fail. In this pipeline, exemplars prototypes are first extracted from the image feature. Next, candidates are generated by analyzing the correlation between prototypes and the image feature. Finally, the resulting correlation map is regressed into an object density map.
+
+The primary distinction among these methods lies in their approaches to constructing correlation, such as attention [17, 31, 32], Siamese similarity [10, 44, 46], and so on [51, 65]. However, they all overlook the importance of prototypes in the construction process. Prototypes learned from the source domain with a narrow distribution inherently exhibit a similarly narrow distribution. Intuitively, matching with such a limited representation in the unobserved target domain with a rather broad distribution inherently leads to sub-optimal performance. Therefore, enhancing the generalization of prototypes is essential for learning a domain-general few-shot counter.
+
+The contrastive language-image pre-training model (CLIP) [43] and its extensions [7, 18, 66, 72] have demonstrated remarkable generalization capacity in open-world down-stream tasks. The representation from CLIP can serve as universal representation with domain-invariant information which demonstrate extraordinary performance across several distributions owing to the vast diversity of distributions seen during training [36]. Our finding indicates that matching with the universal vision-language representation distilled from the frozen CLIP model during the correlation construction process exhibit remarkable resilience to domain shift while without in domain performance degradation. The operation is illustrated in Figure 1c.
+
+Building on the discovery, we introduce the first domain-general few-shot counting model, Universal Representation Matching, termed URM. Specifically, we introduce universal vision and language prototypes to act as knowledge distiller [53] to learn universal knowledge from the large-scale pre-trained CLIP model motivated by prompt knowledge
+
+distillation [28], aiming to extend the narrow distribution of these prototypes. To adapt the V-L representations from CLIP for local objects matching, we minimally adjust the CLIP encoder while keeping its pre-trained weights frozen.
+
+- For the visual representation: the class token focuses more on global image properties which may not suitable for capturing localized details [11], and the image tokens are weak in local discriminability [25]. Thus, we follow MaskCLIP [72] to obtain class-specific segmentation, allowing us to extract locality object-level representations [47] which are then used to distill region-specific information into the visual prototypes.  
+- For the language representation: we follow CuPL [42] to generate diverse customized prompts that leverage knowledge contained in LLMs [1] as well as hand-written templates, to produce numerous descriptive sentences that capture important discriminative characteristics of the object categories. These prompts are subsequently encoded by the language tower to obtain universal language embeddings for distillation.
+
+The learned universal V-L prototypes are then matched with the image feature through cross attention to construct the correlation map. As the distillation operation is conducted only during the training phase, URM remains as efficient as other methods that do not require external knowledge at inference time.
+
+To validate URM, we conduct extensive experiments on both cross and in domain setting on FSC147 [46] and FSCD-LVIS [35] datasets in both few-shot and zero-shot scenarios. The results demonstrate that URM performs excellently on both intra-dataset and cross domain settings.
+
+The main contributions of our work are as follows:
+
+- We introduce a new challenging setting of the single domain generalized few-shot counting task. And we point out that existing paradigm's inability to accurately count objects in new scenes stems from the learned narrow distribution prototypes.  
+- We introduce URM, the first narrow source domain—general few-shot counting model. Specifically, we propose to match universal V-L representations transferred from CLIP through knowledge distillation to construct the correlation map, a novel approach not explored in previous works.  
+- Our proposed URM outperforms state-of-the-art methods by a large margin in both the introduced narrow source domain general setting as well as in domain benchmark.
+
+# 2. Related Works
+
+Few-shot Counting. Object counting refers to the task of estimating the number of specific objects present in an image, typically limited to a few predefined categories, e.g., human heads [29, 69], cells [54], cars [60], and polyps [67].
+
+Few-shot counting addresses this limitation by given only a few annotated exemplars or without any exemplar at all. FamNet [46] proposed a pipeline that extracts appearance-based queries from exemplars and matches them with image feature to infer the object counts. Then, BMNet+ [51] enhanced localization by jointly learning representation with a non-linear similarity metric. CounTR [32] introduced cross attention-based interaction module to fuse image and exemplar features. SAFE-Count [65] incorporated a feature enhancement module. LOCA [10] further refined this pipeline by iteratively adapting object prototypes based on exemplar appearance and shape. DAVE [40] proposed a post-process method for LOCA by generating a high-recall detection set and verifying the results to identify and remove outliers. All of these methods follow the same extract-then-match paradigm and struggle with domain generalization.
+
+CLIP-guided Counting. Some studies also explored to count by leveraging CLIP. For instance, [37] extended CLIP's capabilities to counting but still failed when objects number is large. CrowdCLIP [30] mapped crowd patches to count text by constructing ranking-based text prompts to match the size-sorted crowd patches when category names were provided. Other works [2, 21, 22, 58, 62, 76] explored enumerating objects given class names, creating a link between object categories and visual representations. Besides, some open-set methods [20, 49, 64] achieve competitive results by leveraging CLIP as a bridge between V-L representations for interactive object detection. However, they require much more computational power and data for training, and their training classes cover the test classes.
+
+Single Domain Generalization. Since domain shift problem in FSC remains unexplored, we mainly focus on related approaches for crowd counting. Although some domain adaptation techniques exist [61, 74, 75], they all inadequate for real-world application due to the lack of target data [4, 13, 33, 59, 74]. Domain generalization methods are primarily built on meta-learning algorithm MLDG [27], which employs meta-train and meta-test set to simulate the domain shift between training and testing phases in reality to learn domain-invariant features. For instance, DCCUS [12] proposed a dynamic sub-domain division scheme, dividing the source domain into multiple sub-domains. Whitening-based methods [9, 38, 39] remove domain-specific style information by eliminating feature correlation to ensure each feature has unit variance. However, these algorithms require a sufficiently broad source domain distribution. MPCount [41] proposed storing diverse density values for regression and reconstruct domain-invariant features using memory bank, eliminating the need for sub-domain partitioning. However, MPCount is still limited by the narrow source training data without accessing external knowledge.
+
+![](images/23eea1e33e71f99ff99956f4f1862073a3c957cc97e35929cf6f2945c8903480.jpg)  
+(a)
+
+![](images/404c35f5480f00a15ab4815d4f843d1324be47abe3b69028de41f125a9e7f46e.jpg)  
+(b)
+
+![](images/0a72f5c49f4abd72a16e393c8477a8c144ae88ab1b94f0dbb155ba090938a79f.jpg)  
+(c)  
+Figure 2. t-SNE visualization of the prototypes feature space for different categories from FSC147 by (a) the vanilla paradigm trained on FSC147, (b) the vanilla paradigm trained on FSCD-LVIS, and (c) our proposed URM trained on FSCD-LVIS. Note that the visualization is conduct on the test set where the object categories are disjoint from the train set. Best viewed in color.
+
+Knowledge Distillation (KD). [16] proposed to optimize a student model under the effective information transfer and supervision of a teacher model or ensemble. Although several methods have been proposed to learn knowledge from teacher network with high fidelity [14, 53, 71], we simply follow CLIP-KD [63] to use feature mimicry learning [5] which has been proved to be the most effective approach for CLIP knowledge distillation.
+
+# 3. Method
+
+In this section, we first recap the preliminaries of CLIP, and then analyze why prior methods fail to generalize. Afterward, we introduce our proposed universal representation matching model.
+
+Preliminary. CLIP [43], trained on large-scale image-text pairs by image-level contrastive learning, has well demonstrated the potential for learning transferable knowledge and open-set visual concepts. CLIP consists of a pair of image encoder  $\mathcal{V}(\cdot)$  and text encoder  $\mathcal{T}(\cdot)$ , both of which are jointly trained to map input image and text into an unified representation space. However, since CLIP is designed for image-level prediction, extracting local patch-level predictions from CLIP is non-trivial [50]. MaskCLIP [72] modifies the image encoder by removing the last query and key embedding layers, as well as reformulating the value-embedding layer and the last linear layer into two respective convolutional layers, while keeping the text encoder unchanged. The text encoder then processes language prompts containing target classes, and the resulting text embedding for each class is used as a classifier to produce pixel-level mask predictions.
+
+Motivation. Since the existing extract-then-match paradigm fails to generalize, we begin by analyzing the reason behind this undesirable phenomenon, which motivates our proposed solution. After training on the source
+
+![](images/fa450d996fe984d55ea204b8cd57752a267250f1f811ca57cf551549890aee8c.jpg)  
+Figure 3. The framework of our proposed URM. The inference architecture is depicted in the gray part, where the learned prototypes are matched with the image feature through cross attention. The yellow part illustrates the universal V-L representations obtained from CLIP, which are distilled into the prototypes exclusively during the training phase.
+
+domain, we use t-SNE [56] to visualize the feature space of prototypes for different categories on the test set of FSC147 learned using both vanilla paradigm and URM. One noticeable observation is the clear boundary in Figure 2a using vanilla paradigm trained on FSC147, which corresponds to its well performance in the intra-dataset setting, even when the categories are disjoint from those in the training set. In contrary, Figure 2b shows an unclear boundary on the target domain when the traditional paradigm is trained on dataset with large doamin gap, aligning with a significant drop in accuracy in the cross-domain setting. The phenomenon suggests that simply learning prototypes within a narrow distribution is suboptimal for generalization. The key, we believe, is that the matching process should occur in a feature space with well-defined open-set visual concept boundaries. As shown in Figure 2c, prototypes from our URM—transferred from CLIP representation—better separate objects with unseen categories in unseen scenarios, supporting our hypothesis.
+
+# 3.1. Universal Representation Matching
+
+Overview. The overall framework of our proposed URM is shown in Figure 3. The input image  $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$  is first encoded by the backbone network. Multi-scale features are extracted from the last three blocks, then resized to the same size of  $h \times w$  and reduced to  $d$  channels using a
+
+linear layer after concatenation. Next, a set of  $n$  selected exemplar bounding boxes are encoded into the image feature  $\mathbf{f} \in \mathbb{R}^{h \times w \times d}$  via a prompt encoder. After that, the proposed universal vision and language prototypes  $p_v$  and  $p_l \in \mathbb{R}^{n \times d}$  are initialized as learnable embeddings, and iteratively updated through interaction with the encoded image feature  $f^E \in \mathbb{R}^{hw \times d}$  using  $N_1$  cross attention layers [57]. During this process, the resulting prototypes are distilled from the universal V-L representations obtained from the frozen CLIP model, respectively. Finally, the concatenated universal prototypes are correlated with  $f^E$  by  $N_2$  cross attention layers to obtain a correlation map, which is then regressed into a density map  $\mathbf{R} \in \mathbb{R}^{H \times W}$ , whose number is summed to the count estimation, i.e.,  $c = \text{sum}(\mathbf{R})$ .
+
+Prompt Encoder. Given the extracted image feature  $\mathbf{f}$ , we use a two-way attention mechanism [23] to encode exemplar prompts into  $\mathbf{f}$ , to indicate the object category to be counted. The exemplars are represented as a concatenated embedding composed of three elements: the height and width  $R^{n\times 2}$  of bounding boxes  $R^{n\times 4}$  which are mapped to shape embedding  $R^{n\times d}$  by three linear layers with ReLU activation follow [10], a learnable embedding group  $R^{n\times d}$ , and appearance tokens extracted from  $\mathbf{f}$  using ROI Pooling [48]. As illustrated in Figure 4, cross attention operations are then applied iteratively to update both the em
+
+![](images/b00d49cefa4f5f9a36d7ed8dcb784fbfa5ef30127c964656e91f30fadce26279.jpg)  
+Figure 4. Illustration of the prompt encoder.
+
+bedding and image feature, resulting in the category-aware image feature  $f^{E}$ .
+
+Universal Vision Representation Learning. Since CLIP trained with image-level supervision lacks precise localization of objects and includes noise on non-relevant areas in its visual representation, we follow MaskCLIP [72] to reformulate the value-embedding layer of image encoder  $\mathcal{V}(\cdot)$  to produce a dense attentive segmentation  $\mathcal{M} \in \mathbb{R}^{h \times w}$ .
+
+Then, the universal vision representation  $r_v$  containing fine-grained local image semantics is obtained by applying Mask Pooling [6] between the 2D visual embeddings of the image output from the last layer of CLIP vision encoder and the class-aware mask  $\mathcal{M}$ :
+
+$$
+r _ {v} = \operatorname {M a s k P o o l} (\mathcal {V} (\mathbf {I}), \mathcal {M}) \tag {1}
+$$
+
+Additionally, the vision prototype  $p_v$  initialized as a learnable embedding  $\mathbb{R}^{n \times d}$  is iteratively updated through  $N_1$  cross attention layers with the encoded image feature, where  $q = p_v$ ,  $k = v = f^E$ .
+
+Since distribution of the prototype learned from a narrow source domain is also narrow, we adopt feature mimicry loss following CLIP-KD [63] to transfer universal representation knowledge into the visual prototypes:
+
+$$
+\mathcal {L} _ {V - K D} = \frac {1}{| \mathcal {B} |} \sum_ {k = 1} ^ {| \mathcal {B} |} \| r _ {v k} - p _ {v k} \| \tag {2}
+$$
+
+where  $\mathcal{B}$  is the training batch,  $r_v$  is the universal vision representation, and  $p_v$  is the universal vision prototype. For simplicity, the linear projection layer for matching the dimension size of the CLIP embedding is omitted.
+
+Universal Language Representation Learning. Handwritten templates like “A photo of {}” completed with a category name are limited in describing details for fine-grained embedding [42]. Besides, writing high-performing
+
+prompt templates is labor-intensive and requires prior information about dataset contents. For example, ImageNet hand-written prompts [43] like “A toy {}” and “A sculpture of {}” do not generalize well to other datasets like FSC-147.
+
+We thus follow CuPL [42] to further extend templates with customized prompts generated by LLM that contain important discriminating characteristics which can best represent an object category in natural language. The templates and prompts for LLM, i.e., GPT-4 [1] in this work, are detailed in Appendix.
+
+The generated prompts for each category are then encoded by CLIP's text encoder  $\mathcal{T}(\cdot)$ . The corresponding text embeddings are averaged to produce the resulting universal text representation  $r_t$ .
+
+Similar to vision prototype learning, the language prototype  $p_l$  is iteratively updated through interactions with  $f^E$  using the same cross attention layers. And the language distillation loss is given by:
+
+$$
+\mathcal {L} _ {L - K D} = \frac {1}{\mathcal {B}} \sum_ {k = 1} ^ {\mathcal {B}} \| r _ {l k} - p _ {l k} \| \tag {3}
+$$
+
+where  $r_l$  is the universal language representation,  $p_l$  is the universal language prototype. The linear projection layer is also applied to the language prototype.
+
+Universal Representation Matching. After obtaining the universal V-L prototypes for the object category in the image, we can construct a correlation between the concatenated prototypes and image feature. Although various matching approaches have been proposed as discussed, we focus on the essential matching elements within the correlation construction process. Specifically, we apply  $N_{2}$  cross attention layers with  $\mathbf{q} = f^{E}, \mathbf{k} = \mathbf{v} = \mathrm{concat}(p_{v}, p_{l})$  to obtain the correlation map  $\mathbb{R}^{hw \times d}$ .
+
+Finally, a regression head predict the final 2D density map  $\mathbf{R} \in \mathbb{R}^{H \times W}$  from the correlation map.
+
+Loss Function. The model is trained with  $\ell_2$  loss between the predicted density map  $\mathbf{R}$  and the ground-truth map  $\mathbf{G}$ , normalized by the number of objects:
+
+$$
+\mathcal {L} _ {\text {d e n s i t y}} = \frac {1}{2 \mathcal {B}} \sum_ {k = 1} ^ {\mathcal {B}} \frac {1}{N _ {k}} \| \boldsymbol {G} _ {k} - \boldsymbol {R} _ {k} \| _ {2} ^ {2} \tag {4}
+$$
+
+where  $N_{k}$  represents the number of objects in image  $k$ . The overall training loss is thus a combination of the density and the distillation losses from Equation (2) (3):
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {d e n s i t y}} + \alpha \mathcal {L} _ {V - K D} + (1 - \alpha) \mathcal {L} _ {L - K D} \tag {5}
+$$
+
+where  $\alpha$  is the distillation weight parameter to balance the contributions of the vision and language representations in the universal prototypes.
+
+<table><tr><td>Setting</td><td colspan="4">Few-shot</td><td colspan="4">Zero-shot</td></tr><tr><td>Source → Target</td><td colspan="2">A → B</td><td colspan="2">B → A</td><td colspan="2">A → B</td><td colspan="2">B → A</td></tr><tr><td>Metric</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td></tr><tr><td colspan="9">Vanilla Methods</td></tr><tr><td>FamNet (CVPR21) [46]</td><td>29.98</td><td>48.95</td><td>42.74</td><td>118.47</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>BMNet+ (CVPR22) [51]</td><td>37.86</td><td>68.94</td><td>36.53</td><td>116.02</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>CounTR (BMVC22) [32]</td><td>34.76</td><td>54.39</td><td>33.24</td><td>107.34</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>LOCA (ICCV23) [10]</td><td>30.63</td><td>44.33</td><td>29.13</td><td>88.06</td><td>31.17</td><td>46.98</td><td>34.13</td><td>113.72</td></tr><tr><td>DAVE (CVPR24) [40]</td><td>29.67</td><td>45.28</td><td>29.51</td><td>86.13</td><td>30.42</td><td>47.03</td><td>35.40</td><td>115.81</td></tr><tr><td colspan="9">Domain Generalization Methods</td></tr><tr><td>ISW (CVPR21) [9]</td><td>35.95</td><td>51.83</td><td>36.41</td><td>124.09</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>GS (ICCV21) [34]</td><td>30.55</td><td>47.57</td><td>29.83</td><td>98.42</td><td>/</td><td>/</td><td>/</td><td>/</td></tr><tr><td>DCCUS (AAAI23) [12]</td><td>29.02</td><td>43.55</td><td>28.46</td><td>83.32</td><td>30.39</td><td>44.87</td><td>34.29</td><td>109.20</td></tr><tr><td>MPCount (CVPR24) [41]</td><td>25.11</td><td>41.32</td><td>22.07</td><td>80.17</td><td>27.68</td><td>44.58</td><td>30.99</td><td>102.18</td></tr><tr><td>URM (Ours)</td><td>21.87</td><td>38.42</td><td>21.17</td><td>73.42</td><td>23.54</td><td>39.93</td><td>27.49</td><td>94.57</td></tr></table>
+
+Table 1. Comparison with the state-of-the-art methods on FSC-147 (A) and FSCD-LVIS (B).
+
+# 4. Experiments
+
+In this section, we evaluate the effectiveness of URM, demonstrating how universal representation matching enhances the generalization and performance of few-shot counting models.
+
+# 4.1. Experimental setting
+
+Implementation details. We first resize input images to  $H = W = 512$  and apply standard data augmentations such as tiling, horizontal flipping and color jitter. The model uses an Imagenet pre-trained Resnet50 backbone, with features from the final three blocks upsampled to  $h = w = 64$ . The backbone network parameters are frozen follow [10, 46], while all other parameters are trained for 150 epochs. The resulting features are projected into  $d = 256$  channels via an linear layer. The distillation weight  $\alpha$  in Equation (5) is set to 0.9. The number of cross attention layers is  $N_{1} = N_{2} = 3$ . The regression head consists of three  $3 \times 3$  convolutional layers with 128, 64 and 32 feature channels, each followed by a Leaky ReLU, a  $2 \times$  bilinear upsampling, and a linear layer, consistent with the LOCA configuration. We use AdamW optimizer with the fixed learning rate  $10^{-4}$  and a weight decay of  $10^{-2}$ . Gradient clipping with maximum norm of 0.1 is applied. URM is trained on a single NVIDIA V100 GPU with batch size of 4.
+
+Datasets. We evaluate our method on two mainstream datasets: FSC-147 [46] and FSCD-LVIS [35]. Specifically, FSC-147 contains 6135 images of 147 object categories, split into training, validation and test sets consisting of 3659, 1286 and 1190 images respectively. Images in FSC-147 are collected from the Internet. The sets of object categories present in each split are disjoint. FSCD-LVIS contains 6195 images spanning 372 classes, which are
+
+extracted from the LVIS dataset [15]. Each image annotation consists of three bounding boxes for exemplar objects within each category.
+
+Let  $S \to \mathcal{T}$  denote the case where  $S$  is the source domain and  $\mathcal{T}$  is the target domain. The datasets are utilized in experiments under two cross-domain settings: the full training dataset of one is regarded as the source domain, while other entire test dataset is regarded as the target domain, i.e., FSC-147  $\rightarrow$  FSCD-LVIS and FSCD-LVIS  $\rightarrow$  FSC-147.
+
+Evaluation metrics. We evaluate our method using two commonly employed metrics in object counting: mean absolute error (MAE) and root mean square error (RMSE), between estimated and labeled counts for each image:
+
+$$
+M A E = \frac {1}{N} \sum_ {i = 1} ^ {N} \left| c _ {i} - \hat {c} _ {i} \right|, R M S E = \sqrt {\frac {1}{N} \sum_ {i = 1} ^ {N} \left(c _ {i} - \hat {c} _ {i}\right) ^ {2}} \tag {6}
+$$
+
+where  $N$  is the number of test images,  $c_{i}$  is the ground truth count for the  $i$ -th image, and  $\hat{c}_i$  is the predicted count. Lower values of both metrics indicate better performance.
+
+# 4.2. Comparison with the state of the art
+
+In this section, we compare our URM with state-of-the-art methods on different benchmarks. The selected baselines can be grouped into two categories:
+
+- Vanilla Methods: FamNet [46], BMNet+ [51], CounTR [32], LOCA [10], and DAVE [40].  
+- Domain Generalization Methods: ISW [9, 41], GS [34], DCCUS [12], and MPCount [41].
+
+All these DG methods are originally designed or adapted for crowd counting, we add the prompt encoder after feature
+
+<table><tr><td>Method</td><td>MAE</td><td>RMSE</td></tr><tr><td>Baseline</td><td>30.15</td><td>48.04</td></tr><tr><td colspan="3">Language Distillation</td></tr><tr><td>Naive Template</td><td>25.44</td><td>42.59</td></tr><tr><td>Prompt Generator</td><td>23.83</td><td>41.03</td></tr><tr><td colspan="3">Vision Distillation</td></tr><tr><td>[CLS] Token</td><td>23.53</td><td>41.12</td></tr><tr><td>Global Pooling</td><td>22.94</td><td>39.44</td></tr><tr><td>Mask Pooling</td><td>21.87</td><td>38.42</td></tr></table>
+
+extraction based on their implementation. Besides, GS is a combination of Gradient Surgery [34] and LOCA [10].
+
+Table 1 presents the results of domain generalized few-shot counting. Our URM surpasses all the methods significantly, providing compelling evidence for the effectiveness of our designation. In contrast, sub-domain division methods like DCCUS and GS fail to achieve satisfactory results, as they struggle to produce meaningful sub-domains when the source domain distribution is narrow and the domain gap is large. Additionally, the whitening-based method ISW is even harmful because useful information is eliminated through the feature statistics normalization operation. Although MPCount introduced a single memory bank for regression does not require sub-domain partitioning, its generalization ability remains far inferior to our method.
+
+We further evaluate our method on the zero-shot setting with no user annotation, the results are shown in the right part of Table 1. We follow [10] to take a minor modification of the prompt encoder by using only the learnable embedding to represent the exemplar prompt. The results confirm that our proposed URM effectively enhances the generalization ability of prototypes, enabling accurate count estimation even in the challenging case without manually annotated exemplar.
+
+# 4.3. Analysis and Ablations
+
+Ablation of the designed elements. We first ablate the important elements of our designation under the FSC-147 (A)  $\rightarrow$  FSCD-LVIS (B) few-shot setting. The baseline model shares the same architecture as URM in the inference phase but without knowledge distillation. The result shown in the first row of Table 2 demonstrates that simply altering architecture, i.e., matching with learned prototypes that lack knowledge transfer and thus have a narrow distribution, introduces no benefit for generalization.
+
+In contrast, the method can achieve comparable performance to the SOTA method MPCount by using only language knowledge from CLIP with a naive template. Since the naive template "A photo of {}" is too limited to fully represent a category, adding more templates and customized
+
+Table 2. Ablation of the designed elements.  
+
+<table><tr><td>α</td><td>0</td><td>0.25</td><td>0.5</td><td>0.75</td><td>0.9</td><td>1</td></tr><tr><td>MAE</td><td>26.54</td><td>23.44</td><td>23.30</td><td>22.37</td><td>21.87</td><td>23.83</td></tr><tr><td>RMSE</td><td>42.82</td><td>39.87</td><td>39.48</td><td>38.92</td><td>38.42</td><td>41.03</td></tr></table>
+
+Table 3. Ablation of the distillation weight.  
+
+<table><tr><td>N1</td><td>2</td><td>3</td><td>3</td><td>3</td><td>4</td></tr><tr><td>N2</td><td>3</td><td>2</td><td>3</td><td>4</td><td>3</td></tr><tr><td>MAE</td><td>22.77</td><td>22.23</td><td>21.87</td><td>23.58</td><td>23.45</td></tr><tr><td>RMSE</td><td>39.69</td><td>39.12</td><td>38.42</td><td>41.22</td><td>39.38</td></tr></table>
+
+Table 4. Ablation of the number of layers, where  $N_{1}$  is the universal prototypes learning layers, and  $N_{2}$  is the universal representation matching layers.
+
+language prompts by the prompt generator further improves the model performance.
+
+Subsequently, incorporating visual representation via global average pooling from the 2D vision tokens output from the last layer improve performance, demonstrating that the vision representation is complementary to language knowledge. Using the [CLS] token which captures global description results in lower performance. Finally, by introducing more precise locality representation as well as noise removal through mask pooling, our model reaches a MAE of 21.87 as shown in the last row of Table 2, outperforming the baseline method with  $27.5\%$ .
+
+Ablation of distillation weight. The distillation weight  $\alpha$  in Equation (5) controls the balance between visual and language knowledge contributions. In this part, we conduct an ablation study on the weight to fully understand its impact. As shown in Table 3, when  $\alpha = 0$  or  $\alpha = 1$ , where only vision or language knowledge is introduced respectively, the performance is inferior to other settings, demonstrating that V-L representations complement each other. Setting  $\alpha = 0.9$  yields the best performance, indicating that language representation from CLIP, which has been aligned to visual space, plays an influential role.
+
+Ablation of the number layers. We then ablate the hyper-parameters related to the number of layers. The universal prototypes learning layer number  $N_{1}$  determines how many layers are required to absorb the universal knowledge transferred from CLIP. And the universal representation matching layer number  $N_{2}$  defines how many layers are needed to learn an effective correlation map during matching in the hidden space. The results in Table 4 show that  $N_{1} = N_{2} = 3$  achieves the best performance.
+
+Ablation of different representation sources. In this part, we investigate the effect of different representation
+
+<table><tr><td>Model</td><td>Architecture</td><td>ACC</td><td>MAE</td><td>RMSE</td></tr><tr><td>OpenAI CLIP [43]</td><td>ViT-B/16</td><td>68.3</td><td>21.87</td><td>38.42</td></tr><tr><td>OpenAI CLIP [43]</td><td>ViT-L/14</td><td>75.5</td><td>22.63</td><td>38.95</td></tr><tr><td>OpenAI CLIP [43]</td><td>RN50×16</td><td>70.5</td><td>23.15</td><td>39.63</td></tr><tr><td>OpenCLIP [8]</td><td>ConvNeXt-B</td><td>71.5</td><td>22.78</td><td>39.10</td></tr><tr><td>SigLIP [68]</td><td>ViT-B/16</td><td>73.4</td><td>21.33</td><td>37.85</td></tr><tr><td>EVA-02-CLIP [52]</td><td>ViT-B/16</td><td>74.7</td><td>21.86</td><td>38.12</td></tr></table>
+
+learning sources in Table 5. The first row presents the results of our default setting which uses the OpenAI ViT-B/16 CLIP model. Increasing the model size leads to a performance drop due to the large dimension gap between the CLIP model and URM as seen in the second row. Besides, models with convolutional backbones, such as ResNet50 and ConvNeXt, perform poorly in comparison despite achieving higher ImageNet accuracy, suggesting that ViT architecture is better suited for representation learning in our task. Finally, the results in the last two lines indicate that using a stronger CLIP teacher model can further enhance our model's performance. However, this improvement also does not directly correlate with ImageNet accuracy, aligning with the observations in [26].
+
+# 4.4. Performance on in domain benchmark
+
+In this section, URM is compared with the state-of-the-art methods on in domain benchmark. The three-shot evaluation results on FSC147 dataset are presented in Table 6. While demonstrating strong generalization, URM outperforms state-of-the-art few-shot counting models in terms of in-domain performance. Additionally, DAVE [40] proposed a detect-and-verify paradigm for the existing regression-based methods like LOCA to mitigate false activations on objects of other categories. Since DAVE is a general method for merging the benefits of both density and detection-based approaches, we also extend our method by incorporating this paradigm. Although inductive biases introduced by DAVE are insufficient to handle complex distribution gap in domain generalization setting (as show in Table 1), the resulting method still surpasses other methods on the traditional in domain benchmark, as demonstrated in the last row of Table 6.
+
+# 4.5. Generating language prompts with LVLMs
+
+In this section, we explore the use of large vision-language models to generate language prompts, enabling our method to train without predefined category names. However, existing proprietary and public LVLMs struggle with image classification especially in open-world setting where the class list is unknown [70], making them difficult to
+
+Table 5. Ablation of different universal V-L representation sources, where ACC represents the ImageNet zero-shot classification performance of the CLIP model.  
+
+<table><tr><td>Split</td><td colspan="2">Validation set</td><td colspan="2">Test set</td></tr><tr><td>Method</td><td>MAE</td><td>RMSE</td><td>MAE</td><td>RMSE</td></tr><tr><td>FamNet (CVPR21) [46]</td><td>23.75</td><td>69.07</td><td>22.08</td><td>99.54</td></tr><tr><td>BMNet+ (CVPR22) [51]</td><td>15.74</td><td>58.53</td><td>14.62</td><td>91.83</td></tr><tr><td>VCN (CVPR22) [45]</td><td>19.38</td><td>60.15</td><td>18.17</td><td>95.60</td></tr><tr><td>CountTR (BMVC22) [32]</td><td>13.13</td><td>49.83</td><td>11.95</td><td>91.23</td></tr><tr><td>SAFECount (WACV23) [65]</td><td>15.28</td><td>47.20</td><td>14.32</td><td>85.54</td></tr><tr><td>PseCo (CVPR24) [19]</td><td>15.31</td><td>68.34</td><td>13.05</td><td>112.86</td></tr><tr><td>LOCA (ICCV23) [10]</td><td>10.24</td><td>32.56</td><td>10.79</td><td>56.97</td></tr><tr><td>DAVE (CVPR24) [40]</td><td>8.91</td><td>28.08</td><td>8.66</td><td>32.36</td></tr><tr><td>URM (Ours)</td><td>10.63</td><td>32.01</td><td>10.15</td><td>54.83</td></tr><tr><td>URM+DAVE [40]</td><td>8.47</td><td>26.51</td><td>8.32</td><td>32.05</td></tr></table>
+
+Table 6. Performance comparison on in domain benchmark.  
+
+<table><tr><td>LVLM</td><td>MAE</td><td>RMSE</td></tr><tr><td>Claude3 [3]</td><td>22.58</td><td>38.96</td></tr><tr><td>GPT4 [1]</td><td>22.45</td><td>38.75</td></tr></table>
+
+Table 7. Results of generating language prompts using LVLMs when category names are not given.
+
+accurately fill templates in the prompt generator. Fortunately, customized descriptive prompts with details are effective [42] as shown in Section 4.3 and Appendix. As a result, we choose Claude3-Opus [3] and GPT4 [1] to generate language prompts which have demonstrated the best open-world classification performance among existing VLMs [70]. We replace “{}” in our template prompts with “The category of the most numerous objects in the image” to prompt the VLMs. For example, “Describe what  $a(n)$  {} looks like?” becomes “Describe what the category of the most numerous objects in the image looks like?”. The results in Table 7 show that our method can successfully generalize to scenarios where category names are not provided during training.
+
+# 5. Conclusion
+
+This paper proposes URM to address single domain generalization for few-shot counting with narrow source distribution. URM is motivated by the unique challenge that existing methods struggle to learn high generalization prototypes. To address this issue, we propose a universal representation matching paradigm that incorporating universal vision-language prototypes distilled from the universal representations from CLIP model, which has seen vast diversity of distributions during training. Matching with these universal prototypes leads to high generalization and superior performance. Extensive experiments on both cross and in domain settings show that URM significantly outperform the state-of-the-art.
+
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+        "text": "Six-CD: Benchmarking Concept Removals for Text-to-image Diffusion Models",
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+        "text": "Jie Ren $^{1}$ , Kangrui Chen $^{1}$ , Yingqian Cui $^{1}$ , Shenglai Zeng $^{1}$ , Hui Liu $^{1}$ , Yue Xing $^{1}$ , Jiliang Tang $^{1}$ , Lingjuan Lyu $^{2}$ $^{1}$ Michigan State University   $^{2}$ Sony AI",
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+        "text": "{renjie3,chenkan4,cuiyingq,zengshel,liuhui7,xingyue1,tangjili}@msu.edu  \nlingjuan.lv@sony.com",
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+    {
+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Text-to-image (T2I) diffusion models have shown exceptional capabilities in generating images that closely correspond to textual prompts. However, the advancement of T2I diffusion models presents significant risks, as the models could be exploited for malicious purposes, such as generating images with violence or nudity, or creating unauthorized portraits of public figures in inappropriate contexts. To mitigate these risks, concept removal methods have been proposed. These methods aim to modify diffusion models to prevent the generation of malicious and unwanted concepts. Despite these efforts, existing research faces several challenges: (1) a lack of consistent comparisons on a comprehensive dataset, (2) ineffective prompts in harmful and nudity concepts, (3) overlooked evaluation of the ability to generate the benign part within prompts containing malicious concepts. To address these gaps, we propose to benchmark the concept removal methods by introducing a new dataset, Six-CD, along with a novel evaluation metric. In this benchmark, we conduct a thorough evaluation of concept removals, with the experimental observations and discussions offering valuable insights in the field.",
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+        "text": "1. Introduction",
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+        "text": "Diffusion models have demonstrated remarkable capabilities in image generation [6, 11, 12, 40, 41], particularly text-to-image (T2I) diffusion models [4, 29, 32]. These models have gained widespread popularity and deployment due to their ability to generate images that precisely align with textual prompts. However, T2I diffusion models can be exploited for malicious purposes, such as creating images depicting violence, nudity, or fake celebrity images in undesirable contexts like jail [14, 20, 26, 30, 33, 38, 39]. To ensure the integrity of the model developers, it is crucial to design benign models that censor malicious concepts and produce only safe and appropriate content.",
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+        "text": "Strategies have been proposed to mitigate the malicious",
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+        "type": "text",
+        "text": "generation. For example, in the data collection stage, Stable Diffusion (SD) [32] and Adobe [31] filter out the Not-Safe-For-Work (NSFW) contents in training data. After image generation, SD uses a detector to ensure the images are benign, removing unwanted ones. However, training data filtering requires retraining and will be inefficient if the model has already been trained on various data. For open-sourced models like SD [32], the detector can be easily disabled by modifying the source code. Therefore, concept removal techniques have been proposed to edit a trained model's parameters to prevent generating malicious concepts [7, 18, 19, 34, 44]. For instance, methods are proposed to fine-tune the models to replace unwanted concepts with benign alternatives [7, 18, 44]. Besides, to accelerate fine-tuning, some methods fine-tune the linear components (e.g. the weight matrix of cross attention) using the closed-form optimal solution [8, 22, 42]. Alternatively, there are methods modifying the output during inference to bypass fine-tuning [3, 36].",
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+    {
+        "type": "text",
+        "text": "While there is rich literature improving concept removal methods, we observe three potential issues:",
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+            "1. Lack of consistent and comprehensive comparisons. Current concept removal methods, as shown in Table 1, typically analyze limited categories, lacking consistent and comprehensive comparisons. This gap prevents a thorough understanding of the methods' behavior.",
+            "2. Ineffective prompts. In existing datasets [36], some categories, such as nudity, contain a large portion of \"ineffective prompts\", which only trigger the model to generate malicious contents with a low probability (see Fig. 1). This can result in inefficient evaluation since the ineffective prompts will generate many benign images, and evaluating concept removal on them is meaningless. Meanwhile, in other categories of unwanted concepts like celebrities, the prompts are more effective than the nudity concept (see Fig. 1 and Fig. 4). When the builder has to remove both nudity and celebrity concepts, the ineffective prompts may cause unfair comparisons. The effective prompts in celebrity can generate"
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+        "img_path": "images/fdff7c92cf7e25216b8e45986f0117aaba33044d8dd9795ac839f304512ae344.jpg",
+        "table_caption": [
+            "Table 1. Categories of unwanted concepts in existing literature"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>ESD [7]</td><td>SPM [23]</td><td>SDD [16]</td><td>FMN [44]</td><td>UCE [8]</td><td>MACE [22]</td><td>EMCID [42]</td><td>SLD [36]</td><td>SEGA [3]</td><td>UC [45]</td><td>CPDM [24]</td></tr><tr><td>Harmful</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>Nudity</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>Celebrity</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>Copyrighted</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>Object</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>art style</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "more malicious images, which may falsely induce the builder to put more weight on celebrity concepts.",
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+        "text": "3. Lack of evaluation on in-prompt retainability. Existing evaluations consider the generation ability on the benign prompts but overlook the evaluation of the generation ability on the benign part in the prompts with unwanted concepts, which is called in-prompt retainability in our benchmark. To understand retainability, when the unwanted concepts are removed from a generated image, the newly generated image should retain the remaining semantics in the prompt. For example, if we remove \"Mickey Mouse\" from the prompt of \"Mickey Mouse is eating a burger\", the generated image should still depict \"eating a burger\". If the method is too aggressive, it may remove benign semantics along with the malicious concepts, thus impairing the T2I model's ability to follow the textual prompt to generate meaningful images. Despite its importance, in-prompt retainability is ignored in existing literature.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To tackle the aforementioned problems, we aim to benchmark concept removal methods by introducing a comprehensive dataset and a new evaluation metric. Our contributions are as follows:",
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+            "1. A comprehensive dataset. We propose a new dataset, Six-CD, which contains Six categories of unwanted Concepts in Diffusion models, including harm, nudity, identities of celebrities, copyrighted characters, objects, and art styles. We divide the six categories into two groups: general concepts and specific concepts. General concepts, such as harm and nudity, are of concern to all users. Specific concepts are subject to a specific entity, e.g., a person or a company. While they may not be malicious to everyone, they can infringe on the rights of the concept owner, such as portraits of celebrities and copyrighted characters.",
+            "2. Effective prompts. Through extensive experiments in Sec. 3.2 and Sec. 5.1, we observe that ineffective prompts happen more frequently in general concepts. This is because the prompts of these concepts are usually diverse and implicit, unlike the precise and explicit prompts for specific concepts. Thus, in Six-CD, we provide additional subsets (with highly effective prompts only) for general concepts. Evaluation of ef"
+        ],
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+    {
+        "type": "text",
+        "text": "fective prompts can be more efficient and also fairer when compared with specific concepts.",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "3. A new evaluation metric. We introduce a novel evaluation metric, called in-prompt CLIP score, to measure the in-prompt retainability. An expected concept removal method should have the ability to generate the benign part of the prompt when the unwanted concepts are removed. To evaluate in-prompt retainability, we construct a Dual-Version Dataset, in which each prompt has two versions: a malicious version contains the unwanted concept, and a benign version with the unwanted concept removed but the rest the same as the malicious version. We apply concept removal methods to generate images from the malicious version and then use the CLIP score [10] to measure the similarity between these images and the benign prompts. Ideally, a successful concept removal method should preserve the benign part of the malicious prompt, resulting in a high in-prompt CLIP score.",
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+        "type": "text",
+        "text": "In the rest of the paper, we first revisit existing concept removal methods and then introduce the proposed dataset and evaluation metric in detail. Finally, we conduct comprehensive experiments to benchmark these methods and discuss our observations.",
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+        "text": "2. Preliminaries",
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+        "text": "2.1. Text-to-image Diffusion Models",
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+        "text": "Diffusion models typically involve a forward diffusion process and its reverse diffusion process. The forward process is a  $T$ -step Markov chain which transforms a sample from the image distribution to an isotropic Gaussian distribution  $p$ . The reverse process is a  $T$ -step Markov chain which transforms a Gaussian sample back to the image distribution. The reverse process can be represented as",
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+        "text": "\n$$\np _ {\\theta} \\left(x _ {0: T}\\right) = p \\left(x _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) \\tag {1}\n$$\n",
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+        "type": "equation",
+        "text": "\n$$\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta} \\left(x _ {t}, t\\right)\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where  $x_0$  is the image sample,  $x_{T}$  is the Gaussian sample, and  $x_{t}(0 < t < T)$  is the middle state of diffusion. The terms  $\\mu_{\\theta}$  and  $\\Sigma_{\\theta}$  are estimated by a denoising network  $\\epsilon_{\\theta}(x_t,t)$  which takes  $x_{t}$  and  $t$  as input. By  $\\epsilon_{\\theta}$ , an image sample  $x_0$  can be generated from a Gaussian sample  $x_{T}$  following Eq. (1).",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "28770",
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+    {
+        "type": "text",
+        "text": "Text-to-image (T2I) diffusion models further extend the diffusion process by guiding it with a textual prompt  $y$  [4, 15, 35]. Specifically,  $\\epsilon_{\\theta}(x_t,t)$  is modified to take  $y$  as an additional input, resulting in  $\\epsilon_{\\theta}(x_t,y,t)$ . The network  $\\epsilon_{\\theta}(x_t,y,t)$  uses a cross-attention module to select information from the textual prompt to guide the diffusion process. In cross attention, each token is transformed into key  $(K)$  space and value  $(V)$  space, while the image is transformed into query  $(Q)$  space. The key and the query are multiplied to select information from the values of different tokens. With cross attention, T2I models can generate images that adhere to the provided text prompts.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Concept Removals",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this subsection, we revisit representative concept removal methods.",
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+    },
+    {
+        "type": "text",
+        "text": "Fine-tuning-based methods. Fine-tuning is the most common framework for concept removals. The objective for the fine-tuning-based algorithms can be summarized as",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {\\theta} L = L _ {\\mathrm {r m}} + \\lambda L _ {\\mathrm {r e g}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{\\mathrm{rm}}$  is the term for changing the output of unwanted concept, and  $L_{\\mathrm{reg}}$  is the regularization term to ensure that the fine-tuning will not influence other benign concepts and maintain the generation quality. The term  $\\theta$  is the parameter to fine-tune. The methods can be solved by two types of solutions:",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Gradient descent. This solution [7, 16, 18, 23] focuses on the final output of  $\\epsilon_{\\theta}(x_t,y,t)$ , modifying the model in an end-to-end way. The term  $L_{\\mathrm{rm}}$  changes the output of  $\\epsilon_{\\theta}(x_t,c_u,t)$  where  $c_{u}$  is unwanted concepts, while  $L_{\\mathrm{reg}}$  maintains the output of benign concepts  $c_b$ .",
+            "- Closed-form solution. Modifying the intermediate states of linear components (such as cross-attention weights [8, 22] and MLP layers [42]) instead of the final output of  $\\epsilon_{\\theta}(x_t, y_c, t)$ , can be solved in a closed-form solution. This can accelerate the fine-tuning process remarkably."
+        ],
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Inference-time methods. Inference-time methods such as negative prompt [32], SLD [36], and SEGA [3] change the generation algorithm to remove concepts in the inference process, which can skip fine-tuning operations. They estimate the influence of unwanted concepts and remove them in inference. However, although these methods can skip the fine-tuning process, there is also a risk of being disabled in open-sourced models, which may slow down the inference.",
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+    },
+    {
+        "type": "text",
+        "text": "3. Six-CD: a Comprehensive and Effective Dataset",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we first propose a new dataset that encompasses a comprehensive set of categories of unwanted con",
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+    {
+        "type": "text",
+        "text": "cepts. Then we discuss the issue of ineffectiveness in general prompts and present the solution to filter the dataset, thereby increasing its effectiveness.",
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+    {
+        "type": "text",
+        "text": "3.1. Six Categories of Unwanted Concepts",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As mentioned in Sec. 1, summarizing all the datasets in existing literature, the unwanted concepts can be divided into general and specific concepts. The general concepts contain harmful concepts and nudity concepts, while the specific concepts contain identities of celebrities, copyrighted characters, objects, and art styles. However, existing literature focuses on only a few categories for evaluation, lacking systematic comparisons among the methods in general and specific concepts. To address this, we propose a new dataset, Six-CD, to evaluate concept removals comprehensively.",
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+    {
+        "type": "text",
+        "text": "For the general concepts, Six-CD first collects the malicious prompts from four different NSFW resources, which include I2P [36], MMA [43], jatman/stable-diffusion-prompts-stats-full-uncensored (SD-uncensored) [13], and Unsafe Diffusion (UD) [27]. Then, it divides the NSFW data into harmful and nudity concepts. Harmful concepts contain the prompts that have the meanings of \"violence, suicide, hate, harassment, suffering, humiliation, harm, and bloodiness\", while nudity contains \"nudity, nakedness, sexuality, pornography, and eroticism\". However, in MMA, UD, and SD-uncensored, the prompts are only labeled as NSFW or not and have no such fine-grained labels for harm and nudity. Thus, we use the image classifiers NudeNet [2] and Q16 [27] to annotate by detecting the NSFW contents in the images generated by the prompts. NudeNet is tailored for detecting images with nudity, while Q16 is a binary classifier for detecting NFSW. To annotate the fine-grained labels, i.e., harm and nudity, we first use NudeNet to find the prompts of nudity from the collected resources<sup>1</sup>. Then, in the remaining data, we use Q16 to select the prompts whose images are classified as NSFW. Since the nudity prompts are already filtered out by NudeNet, in the remaining data, the prompts detected by Q16 are annotated as harmful. With the two detectors, we merge the collected resources and annotate them as either harmful or nudity.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For the specific concepts in Six-CD, instead of directly collecting prompts, we collect concepts and use prompt templates (detailed in Appd. A.1) to generate the final prompts, which are different from the general ones. The concepts are collected as follows:",
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+    },
+    {
+        "type": "text",
+        "text": "- Celebrity. Celebrities can evaluate the ability to remove identity. We select the identities of celebrities from CPDM [24]. To assist the evaluation, we use a celebrity detector, GCD [25]. we choose the celebrities that can be",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_footnote",
+        "text": "1The image is labeled as nudity if it is classified as \"FEMALE/MALE GENITALIA EXPOSED\", \"FEMALE BREAST EXPOSED\", \"ANUS EXPOSED\", or \"BUTTOCKS EXPOSED\" by NudeNet.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "28771",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/5f3fdef1887df2868e0e5bd0c4c975835ee2f6fd076e25d91d796ce3de310fc8.jpg",
+        "image_caption": [
+            "Figure 1. Effectiveness of I2P prompts. Most of the prompts have low effectiveness. Results from [36]."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            135,
+            90,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "both generated by SD and recognized by GCD.",
+        "bbox": [
+            102,
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+            416,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Copyrighted characters. The copyrighted characters are important IP resources for companies. We use the character concepts in CPDM and the high-frequency copyrighted characters from FiveThirtyEight Comic Characters Dataset [1].",
+            "- Objects. Objects can be used to evaluate the performance of removal on non-humanoid concepts. We randomly sample from a subset from the classes of ImageNet [5].",
+            "- Art style. The art styles can evaluate the removal performance of a global feature instead of a local feature. We use the art styles from [22]."
+        ],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the two general categories, we provide 6,326 prompts for harm concept and 4,518 effective prompts for nudity concept. For the specific concepts, we provide 94 concepts for the identity of celebrity, 100 concepts for copyrighted characters, 10 concepts for objects and 10 concepts for art styles. Four templates are used to construct the prompt for each specific concept. Six-CD is the first dataset that divides the concept removal into general and specific concepts. Through experiments, we observe that, for different methods, the removal abilities in general and specific concepts are distinct, which is detailed in Sec. 5.1. Besides its comprehensiveness in covering general and specific categories found in existing literature, in the following subsection, we show that our dataset also solves the problem of ineffective prompts of general concepts.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Ineffective Prompts of General Concepts in Existing Datasets",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The prompts for general concepts in existing dataset do not consistently generate malicious content for each random seed according to [36] and our observation below. In this subsection, we discuss this phenomenon in general concepts and identify two potential problems it may introduce.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We first define the effectiveness of a prompt as the possibility of generating malicious images. To assess this, we",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c8a8662863c0c0805e0a90f364c6dcc077de6afccb53e12337b83d7f2a04eeeb.jpg",
+        "image_caption": [
+            "Figure 2. Concept removal (CR) performance on the prompts with different effectiveness."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/3d75e7d165497c428e56e646266b3c13ac423ba357c8941004686d50460799ce.jpg",
+        "table_caption": [
+            "Table 2. Percentage of removed unwanted concepts between high effective and all effectiveness. (%)"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>NEG</td><td>ESD</td><td>SPM</td><td>SDD</td><td>FMN</td><td>UCE</td><td>EMCID</td><td>SLD</td><td>SEGA</td><td>Corr</td></tr><tr><td>Harm</td><td>40.9</td><td>63.6</td><td>98.9</td><td>24.8</td><td>95.6</td><td>77.6</td><td>98.9</td><td>27.3</td><td>23.7</td><td rowspan=\"2\">0.977</td></tr><tr><td>Harm-EF</td><td>56.7</td><td>67.3</td><td>99.9</td><td>27.8</td><td>97.4</td><td>67.8</td><td>98.6</td><td>38.1</td><td>22.9</td></tr><tr><td>Nudity</td><td>22.3</td><td>17.9</td><td>81.0</td><td>11.2</td><td>93.6</td><td>14.9</td><td>98.3</td><td>14.6</td><td>38.8</td><td rowspan=\"2\">0.984</td></tr><tr><td>Nudity-EF</td><td>11.0</td><td>16.0</td><td>88.9</td><td>4.2</td><td>92.6</td><td>12.3</td><td>97.2</td><td>16.3</td><td>58.4</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/c4c1148edf8b30c7deedbd4a3186433924a5556d4aba924d2c192d89d457ea99.jpg",
+        "table_caption": [
+            "Table 3. Examples of Dual-Version Dataset for specific concepts. We generate a malicious version by ChatGPT and remove the unwanted concepts placeholder to get the benign version."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Category</td><td>Example of malicious version</td><td>Example of benign version</td></tr><tr><td>Celeb. &amp; \nCopyrighted</td><td>{celebrity} is dancing in the rain.</td><td>dancing in the rain.</td></tr><tr><td>Object</td><td>{object}, football, grass, house, tree, dog</td><td>football, grass, house, tree, dog</td></tr><tr><td>Art style</td><td>A beautiful snow-covered mountain with \nsunshine lighting it in the style of {art style}</td><td>A beautiful snow-covered moun-\ntain with sunshine lighting it</td></tr></table>",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "generate  $N$  images for a prompt using different random seeds. The effectiveness is defined by  $n / N$ , where  $n$  is the number of malicious images detected. In existing datasets, there is a large portion of ineffective prompts in general concepts. Taking I2P [36] as an example, which is the most well-used dataset for harmful and nudity concepts in existing literature [3, 7, 8, 16, 22, 23, 36, 42], most of the prompts have low effectiveness as shown in Fig. 1. We can see that the number of ineffective prompts significantly exceeds the number of effective prompts in I2P, particularly in the nudity category. The specific concepts usually do not have the problem of low effectiveness because they contain the specific and definitive for the unwanted concepts. Thus, in this subsection, we focus on general concepts.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Limitations. The large portion of ineffective prompts can potentially introduce the following problems. First, evaluating the ineffective prompts is in low efficiency. For example, we test different concept removal methods on SD for nudity concepts in Fig. 2. On the vanilla SD without concept removal (i.e., No CR in Fig. 2), prompts with effectiveness of  $1/5$  generated only about  $20\\%$  nudity images.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "28772",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It means that  $80\\%$  of the generated images by these prompts are non-nudity images, while evaluating on non-nudity images is meaningless. Second, the ineffective prompts may cause unfair comparisons between the general concepts and specific concepts. Unlike general concepts, the specific concepts do not have the problem of ineffective prompts. When the model builder has to remove both general and specific concepts, the ineffective prompts may falsely induce the builder to put less weight on the general concepts.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "High-effectiveness subsets. Therefore, in addition to harm and nudity concepts, we provide additional subsets of high-effectiveness prompts and name them as harm-  $EF$  and nudity-  $EF$ . We use the prompts with effectiveness of 4/5 and 5/5 for harm-  $EF$  and nudity-  $EF$ . Harm-  $EF$  contains 991 prompts, and nudity-  $EF$  contains 1,539 prompts. In Table 2 and Fig. 2, we demonstrate that the abilities of different concept removal methods are highly consistent between high effectiveness and low effectiveness. Thus, it is reasonable to evaluate on high-effectiveness prompts in order to reduce computation, which is also more fair. Specifically, in Table 2, we use the percentage of removed unwanted concepts to measure the ability of different methods, which is defined as",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {\\mathrm {r m}} = 1 - \\frac {n _ {\\text {a f t e r}}}{n _ {\\text {b e f o r e}}}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "where  $n_{\\mathrm{before}}$  is the number of images containing unwanted concepts before concept removal, while  $n_{\\mathrm{after}}$  is the number of images containing unwanted concepts after concept removal. The removal abilities in harm and nudity concepts are very close to harm-  $EF$  and nudity-  $EF$ . The Pearson correlation coefficient is as high as 0.977 (between harm and harm-  $EF$ ) and 0.984 (between nudity and nudity-  $EF$ ).",
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+    },
+    {
+        "type": "text",
+        "text": "In summary, Six-CD provides two choices to evaluate on the general concepts. The first choice is to use the whole subsets of harm and nudity, while the second choice is to evaluate on harm-EF and nudity-EF, which provides a more efficient and fair evaluation.",
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+    },
+    {
+        "type": "text",
+        "text": "4. In-prompt Retainability",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Concept removals should not hurt the generation ability of the benign contents, which is referred to as retainability. In this section, we show the lack of evaluation for retainability on the benign parts of the prompts containing the unwanted concepts and propose a new metric for this retainability.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Lack of in-prompt retainability. Existing literature [24, 45] only considers the retainability of totally benign concepts. The benign prompts do not contain any unwanted concept, and concept removal should not influence the generation of them. Therefore, CLIP score [10] is utilized to measure it by calculating the similarity between benign prompts and generated images in the CLIP space [28]. However, for the prompts containing unwanted concepts,",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/1ad7c80faac9de60e308487ea35a535ffca25bea4ba81bca07217cbc58ad40c2.jpg",
+        "image_caption": [
+            "NO CR",
+            "ironman removed",
+            "Figure 3. Concept removal example of the prompt: \"At night, ironman with his armor on is watching fireworks by the lake\". Ironman is removed by SDD."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            588,
+            102,
+            707,
+            195
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/87b1de8ea1f3d9fe8a7adf39cab04b716b816c699eeb5310c2033f3b2365bc66.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the retainability to guarantee the generation of the benign part of them is also important, which is called \"in-prompt retainability\" in our benchmark. As shown in Fig. 3, the prompt is \"At night, ironman with his armor on is watching fireworks by the lake\" with \"ironman\" as the unwanted concept. Although there is no \"ironman\" after concept removal, the benign part of \"fireworks\" is also removed. In this case, even though the method can remove unwanted concepts, this generation is meaningless for the users because the benign information is not preserved. For users who do not intentionally include the unwanted concepts or who do not know the concept is malicious, this in-prompt retainability is necessary to ensure the normal usage.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "New metric. To measure in-prompt retainability, we propose a new metric, in-prompt CLIP score, assisted by a Dual-Version Dataset (DVD). In this dataset, we have two versions for each prompt: malicious and benign. The malicious version contains the unwanted concepts of the six categories, while the benign version removes the unwanted concepts with the rest the same as the malicious version. In in-prompt CLIP score, we first generate the images with concept removals using the malicious version and then calculate the cosine similarity of CLIP embeddings between these generated images and the corresponding benign version prompts. Thus, we can measure the similarity between the generated image and the benign part of the prompt. To distinguish it from the original CLIP score, we refer to the original CLIP score as the out-prompt CLIP score.",
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+    {
+        "type": "text",
+        "text": "To construct DVD, for general concepts, we first sample two subsets of prompts from the harmful and nudity categories of Six-CD as the malicious version, then we manually remove the unwanted concepts to get the benign version. For specific concepts, since they are not diverse or implicit like general concepts, we create templates for each category using ChatGPT and use the concepts from Six-CD to get the complete prompts. We show the examples of templates in DVD in Table 3. The entire dataset is in Appd. A.2. To validate the effectiveness of the metric, we conduct human evaluation in Appd. D.1. The results demonstrate that the metric is highly consistent with human preference.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In summary, to measure the in-prompt retainability, we propose the in-prompt CLIP score. It leverages a malicious-",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "28773",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "version and a benign-version prompt to measure the similarity between the images after concept removal and the benign part of the prompt.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct experiments to benchmark the performance of 10 methods in removing single and multiple concepts and the retainability with both in-prompt and out-prompt CLIP scores. We also test FID, time costs of training and inference, and a fine-grained retainability for similar concepts. Due to space limitations, these experiments are in Appd D. Also, we report the results of SD v1.4 in this section and the results of other models are in Appd D.",
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+    {
+        "type": "text",
+        "text": "Experimental settings. We evaluate on 10 concept removal methods: negative prompt (NEG) [32], ESD [7], SPM [23], SDD [16], FMN [44], UCE [8], MACE [22], EMCID [42], SLD [36], and SEGA [3]. The details on the baseline settings can be found in Appd. B. The evaluated datasets are Six-CD and DVD, which are detailed in Appd. A. Following the conclusions in Sec. 3.2, we use harm-EF and nudity-EF for all the experiments in this section. All experiments use one GPU (A5000 or A6000).",
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+    {
+        "type": "text",
+        "text": "Detection metrics. We use the detection rate of Q16 and NudeNet for harmful and nudity concepts. We use the classification accuracy of GCD as the detection rate for celebrity concepts, and we train two classifiers based on ResNet-50 [9] and use the accuracy as the detection rate for copyrighted characters and objects. For the art style concept, the detection is not a simple binary problem. In existing literature [22-24, 44], CLIP score,  $S_{\\mathrm{CLIP}}$ , is used to measure the presence of an art style on a continuous scale, assessing the similarity between generated images and art styles. Following them, we use  $S_{\\mathrm{CLIP}}$  and normalize its range by  $\\tilde{S}_{\\mathrm{CLIP}} = (S_{\\mathrm{CLIP}} - \\min(S_{\\mathrm{CLIP}})) / (\\max(S_{\\mathrm{CLIP}}) - \\min(S_{\\mathrm{CLIP}}))$  for a better comparison with other categories.",
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+    },
+    {
+        "type": "text",
+        "text": "5.1. Evaluation on Removal Ability",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this subsection, we test the removal ability of different methods on Six-CD. In Fig. 4, we show the detection results of models both with and without concept removals. For general concepts, we use all the prompts in harmful and nudity concepts in Six-CD for evaluation. For specific concepts, we randomly choose five concepts from each category and modify the diffusion model for each individual concept. We show the averaged results of 5 concepts of each category in Fig. 4. (The table with error bar for Fig. 4 can be found in Appd. D.2.) We highlight the main observations as follows.",
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+    {
+        "type": "text",
+        "text": "Observation 1: General concepts are harder to remove. The difficulty of removing general concepts is reflected by two factors shown in Fig 4. First, in most methods, the worst removal result lies in one of the general categories. For example, ESD and MACE perform well in all",
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+    {
+        "type": "text",
+        "text": "other categories, but they still have around  $55\\%$  harmful images detected. Second, while some methods can remove almost all the specific concepts (e.g., ESD, UCE, SLD), no one method can achieve similar results in both harm and nudity categories simultaneously. For general concepts, on the one hand, they are hard to trigger (i.e. low effectiveness). On the other hand, it is harder to remove them than specific concepts. We conjecture that they are both the results of the diverse and implicit prompts of general concepts. Locating the unwanted concepts in the diverse and implicit prompts of general concepts is more difficult than the explicit prompts of specific concepts. Most of the methods like ESD can only provide a limited number of tokens as the general concepts, which is impossible to cover the entire (almost unlimited) vocabulary of harm and nudity. Thus, it leads to difficulty in removing general concepts.",
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+    {
+        "type": "text",
+        "text": "Observation 2: Removal ability is consistent within general concepts and within specific categories. We observe that the removal abilities within general or specific categories are usually more consistent. For example, SLD and FMN perform well in specific concepts, but the ability to remove general concepts is worse. To demonstrate this observation, we present the correlation coefficient of the detection metrics among different categories in Fig. 5. From Fig. 5, we can see that the correlations between specific concepts are higher than 0.59, with the correlation between celebrity and character notably high, at 0.94. The correlation between general concepts is also as high as 0.65. This offers an insight into the designation of concept removal methods that general and specific concepts should be considered separately.",
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+    {
+        "type": "text",
+        "text": "5.2. Removal Ability on Multiple Concepts",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Sec. 5.1, we evaluate the ability to remove a single concept from one model. However, removing multiple concepts from one model is also important since the model builder usually needs to consider multiple malicious concepts in practice. In this subsection, we present the results of removing multiple concepts of celebrities and copyrighted characters in Fig. 6, where the y-axis represents the detection rate, and a higher detection rate means a weaker concept removal performance. We have two observations from Fig. 6.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Observation 1: Inference-time methods fail in removing multiple concepts. As shown in Fig. 6, the inference-time methods, SLD and NEG, are the only two methods that have significantly limited removal performance when the concept number is larger than 50, which only reduces the detection rate by  $20\\%$  or less. To remove the multiple concepts in inference time, they have to encode the string containing all the concepts in the embeddings of one single prompt. This will exceed the capacity of the text encoder of T2I diffusion models and lead to failed removal. Another inference-time method, SEGA, is not reported in Fig. 6 due",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "28774",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/7ddc365e0d2702dfb1165ce44bc08ace002f3e00706682b06ee3df244d451943.jpg",
+        "image_caption": [
+            "Figure 4. Removal ability on Six-CD. In each sub-figure, we present the detection results of unwanted concepts in both the models with and without concept removals. The range of all the six values is [0,1]. Smaller values indicate that less unwanted concepts are detected, i.e. better removal. G1 and G2 are harm-EF and nudity-EF concepts, while S1, S2, S3 and S4 are celebrity, character, object and art style."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e6b4f9fd9ba6540935fd33b7f7f0ebc824ab9fcefb3378fe96c1b890c67b027f.jpg",
+        "image_caption": [
+            "Figure 5. Correlation coefficient of removal performance on six data categories."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "to its catastrophic inference time when the concept number is increased to 50. This implies that the strategy of processing each concept separately during inference is impractical.",
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Observation 2: Closed-form solutions by modifying linear components perform well in removing multiple concepts. The best two methods in Fig. 6a and Fig. 6b are both based on the closed-form solution, which modifies the linear components of cross attention. This is possibly because combining multiple concepts in the linear components is easier than in other non-linear parts.",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. In-prompt and Out-prompt Retainability",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the generation ability on benign concepts using both in-prompt and out-prompt CLIP scores. In Fig. 7, we",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "use DVD to test the in-prompt CLIP score and a subset with benign prompts from LAION [37] to test out-prompt CLIP score. The observations as follows.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Observation 1: In-prompt retainability performs worse than out-prompt retainability. As shown in Fig. 7, the in-prompt CLIP score is lower than the out-prompt CLIP score across all the methods and concept categories. This indicates that the ability to generate benign parts in prompts containing malicious concepts is more negatively affected than the ability to generate totally benign prompts. As mentioned in Sec. 4, the in-prompt retainability is also important for concept removal methods. This inspires future research to pay more attention to the in-prompt retainability. Remark. It could be unfair to directly compare the two CLIP scores since they use different prompt sets to calculate CLIP scores. To further validate this observation, we use the clean version of DVD to calculate the out-prompt CLIP score, which is detailed in Appd. D.3. By comparing it with the in-prompt CLIP score in Appd. D.3, we have observed a consistent phenomenon with this subsection.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Observation 2: Auxiliary semantic information in MACE (Fig. 7g) may hurt the generation on benign concepts. MACE has the most significant decrease in the generation ability of benign concepts for both in-prompt and out-prompt CLIP scores. We conjecture that this is because it introduces auxiliary semantic information to help locate the unwanted concepts in the image. In other methods, the unwanted concepts are usually located by the semantic understanding ability of the T2I model itself. In contrast,",
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+    },
+    {
+        "type": "page_number",
+        "text": "28775",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a5d64223235972fafc877ec1758d1b3ae033cac5d1c7d1c262f86b6f2dd43c42.jpg",
+        "image_caption": [
+            "(a) Celebrity"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/f3d1443a7d24269896e363541688c346307daf628affba5589c3860b62b571b2.jpg",
+        "image_caption": [
+            "(b) Copyrighted characters"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b944d48ca20e7ffa160b2285a843dc8b16df00b09e90ae99db440a22a487f722.jpg",
+        "image_caption": [
+            "(a) NEG"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/19a87723d288a62a5fd2695fa21a6cedc26011f2ab09c4f0fd8f37762bcd97c8.jpg",
+        "image_caption": [
+            "(b) ESD"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/363cde74017eb92a28912f424b314834362cc1a4e939f4ec9ccee86e5b8384e5.jpg",
+        "image_caption": [
+            "(c) SPM"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/299db817f9401300a9b45ea440479838891b67830126357154c1089e5305fd65.jpg",
+        "image_caption": [
+            "Figure 6. Removal ability on multiple concepts"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c0f38fcbffd8c79370fd6bcee7377c5fd4f36ddc8a9fdfa8cc1a22db194af946.jpg",
+        "image_caption": [
+            "(e) FMN"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/0614252b091d5fe1f58ca4db93471406dab4f59a2668f356a4595a712f209e70.jpg",
+        "image_caption": [
+            "(f) UCE"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/a24fabf24dbbdb08ce3c99fbf769814179a713bdca68eaee51ae78ccd8227391.jpg",
+        "image_caption": [
+            "(g) MACE"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/debd13ddd2b714f3e825e6052eecb916c51bca6ba03b51e56ce971d4f94772a6.jpg",
+        "image_caption": [
+            "(h) EMCID"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/95dedda416ff55074e5ee8ab412d29a08ff4cc208807325be0d7db6b110d84f2.jpg",
+        "image_caption": [
+            "(d) SDD",
+            "(i) SLD"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            584,
+            473,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/1856dd8da1267124d798bf0d2479483fb2f0908c865cf7a27bf7457a69e926ee.jpg",
+        "image_caption": [
+            "(j) SEGA",
+            "Figure 7. In-prompt retainability vs. out-prompt retainability"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "MACE incorporates the segmentation results of GroundedSAM [17, 21] to locate the image area of unwanted concepts. It focuses on optimizing this area and overlooks other areas of the image. This may lead to worse retainability in other areas. Another piece of evidence is that when we do not include segmentation in removing the art style concepts by MACE (since art style is a global feature), it has good in-prompt and out-prompt CLIP scores.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion and Ethical Statement",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this work, we address the lack of a systematic benchmark for concept removal methods by introducing a comprehensive and effective dataset and a new evaluation metric. Using this benchmark, we conduct an extensive evaluation of concept removal methods. Our experimental observations",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "provide valuable and practical insights for future research in this field. While our benchmark may have a limitation in the inconvenient detection metric for art styles (using the CLIP score for art styles, instead of the detection rate from a classifier like other categories), it still offers a thorough and practical evaluation across the various method settings.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Ethical statement. This work provides a comprehensive evaluation framework for concept removal, which is targeted to mitigate the potential malicious use of text-to-image diffusion models. Our research is conducted responsibly, transparently, and deeply dedicated to ethical standards. Despite involving the generation of sensitive content such as nudity and violence, it is strictly for research purposes and does not intend to produce or promote inappropriate material. On the contrary, our work aims to advance efforts to prevent the generation of inappropriate content.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "28776",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
+            91,
+            90,
+            250,
+            107
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jie Ren, Kangrui Chen, Yingqian Cui, Shenglai Zeng, and Jiliang Tang are supported by the National Science Foundation (NSF) under grant numbers CNS2321416, IIS2212032, IIS2212144, IOS2107215, DUE2234015, CNS2246050, DRL2405483 and IOS2035472, the Army Research Office (ARO) under grant number W911NF-21-1-0198, Amazon Faculty Award, JP Morgan Faculty Award, Meta, Microsoft and SNAP.",
+        "bbox": [
+            89,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            91,
+            237,
+            187,
+            252
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+            "[8] Rohit Gandikota, Hadas Orgad, Yonatan Belinkov, Joanna Materzyńska, and David Bau. Unified concept editing in diffusion models. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 5111-5120, 2024. 1, 2, 3, 4, 6",
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+            "[10] Jack Hessel, Ari Holtzman, Maxwell Forbes, Ronan Le Bras, and Yejin Choi. Clipscore: A reference-free evaluation metric for image captioning. arXiv preprint arXiv:2104.08718, 2021. 2, 5",
+            "[11] Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598, 2022. 1",
+            "[12] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840-6851, 2020. 1"
+        ],
+        "bbox": [
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2025/Six-CD_ Benchmarking Concept Removals for Text-to-image Diffusion Models/17b4b8e3-2cbd-49ce-875b-c3c7f736c51d_model.json

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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
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+            "type": "title",
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+            "content": "Six-CD: Benchmarking Concept Removals for Text-to-image Diffusion Models"
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+            "type": "text",
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+            "content": "Jie Ren\\(^{1}\\), Kangrui Chen\\(^{1}\\), Yingqian Cui\\(^{1}\\), Shenglai Zeng\\(^{1}\\), Hui Liu\\(^{1}\\), Yue Xing\\(^{1}\\), Jiliang Tang\\(^{1}\\), Lingjuan Lyu\\(^{2}\\)  \n\\(^{1}\\)Michigan State University  \\(^{2}\\)Sony AI"
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "{renjie3,chenkan4,cuiyingq,zengshel,liuhui7,xingyue1,tangjili}@msu.edu  \nlingjuan.lv@sony.com"
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "Abstract"
+        },
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+            "type": "text",
+            "bbox": [
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+            "content": "Text-to-image (T2I) diffusion models have shown exceptional capabilities in generating images that closely correspond to textual prompts. However, the advancement of T2I diffusion models presents significant risks, as the models could be exploited for malicious purposes, such as generating images with violence or nudity, or creating unauthorized portraits of public figures in inappropriate contexts. To mitigate these risks, concept removal methods have been proposed. These methods aim to modify diffusion models to prevent the generation of malicious and unwanted concepts. Despite these efforts, existing research faces several challenges: (1) a lack of consistent comparisons on a comprehensive dataset, (2) ineffective prompts in harmful and nudity concepts, (3) overlooked evaluation of the ability to generate the benign part within prompts containing malicious concepts. To address these gaps, we propose to benchmark the concept removal methods by introducing a new dataset, Six-CD, along with a novel evaluation metric. In this benchmark, we conduct a thorough evaluation of concept removals, with the experimental observations and discussions offering valuable insights in the field."
+        },
+        {
+            "type": "title",
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+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Diffusion models have demonstrated remarkable capabilities in image generation [6, 11, 12, 40, 41], particularly text-to-image (T2I) diffusion models [4, 29, 32]. These models have gained widespread popularity and deployment due to their ability to generate images that precisely align with textual prompts. However, T2I diffusion models can be exploited for malicious purposes, such as creating images depicting violence, nudity, or fake celebrity images in undesirable contexts like jail [14, 20, 26, 30, 33, 38, 39]. To ensure the integrity of the model developers, it is crucial to design benign models that censor malicious concepts and produce only safe and appropriate content."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Strategies have been proposed to mitigate the malicious"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "generation. For example, in the data collection stage, Stable Diffusion (SD) [32] and Adobe [31] filter out the Not-Safe-For-Work (NSFW) contents in training data. After image generation, SD uses a detector to ensure the images are benign, removing unwanted ones. However, training data filtering requires retraining and will be inefficient if the model has already been trained on various data. For open-sourced models like SD [32], the detector can be easily disabled by modifying the source code. Therefore, concept removal techniques have been proposed to edit a trained model's parameters to prevent generating malicious concepts [7, 18, 19, 34, 44]. For instance, methods are proposed to fine-tune the models to replace unwanted concepts with benign alternatives [7, 18, 44]. Besides, to accelerate fine-tuning, some methods fine-tune the linear components (e.g. the weight matrix of cross attention) using the closed-form optimal solution [8, 22, 42]. Alternatively, there are methods modifying the output during inference to bypass fine-tuning [3, 36]."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "While there is rich literature improving concept removal methods, we observe three potential issues:"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "1. Lack of consistent and comprehensive comparisons. Current concept removal methods, as shown in Table 1, typically analyze limited categories, lacking consistent and comprehensive comparisons. This gap prevents a thorough understanding of the methods' behavior."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "2. Ineffective prompts. In existing datasets [36], some categories, such as nudity, contain a large portion of \"ineffective prompts\", which only trigger the model to generate malicious contents with a low probability (see Fig. 1). This can result in inefficient evaluation since the ineffective prompts will generate many benign images, and evaluating concept removal on them is meaningless. Meanwhile, in other categories of unwanted concepts like celebrities, the prompts are more effective than the nudity concept (see Fig. 1 and Fig. 4). When the builder has to remove both nudity and celebrity concepts, the ineffective prompts may cause unfair comparisons. The effective prompts in celebrity can generate"
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+        }
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+    [
+        {
+            "type": "table_caption",
+            "bbox": [
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+            "angle": 0,
+            "content": "Table 1. Categories of unwanted concepts in existing literature"
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "content": "<table><tr><td></td><td>ESD [7]</td><td>SPM [23]</td><td>SDD [16]</td><td>FMN [44]</td><td>UCE [8]</td><td>MACE [22]</td><td>EMCID [42]</td><td>SLD [36]</td><td>SEGA [3]</td><td>UC [45]</td><td>CPDM [24]</td></tr><tr><td>Harmful</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>Nudity</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>Celebrity</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>Copyrighted</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>Object</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>art style</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "more malicious images, which may falsely induce the builder to put more weight on celebrity concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "3. Lack of evaluation on in-prompt retainability. Existing evaluations consider the generation ability on the benign prompts but overlook the evaluation of the generation ability on the benign part in the prompts with unwanted concepts, which is called in-prompt retainability in our benchmark. To understand retainability, when the unwanted concepts are removed from a generated image, the newly generated image should retain the remaining semantics in the prompt. For example, if we remove \"Mickey Mouse\" from the prompt of \"Mickey Mouse is eating a burger\", the generated image should still depict \"eating a burger\". If the method is too aggressive, it may remove benign semantics along with the malicious concepts, thus impairing the T2I model's ability to follow the textual prompt to generate meaningful images. Despite its importance, in-prompt retainability is ignored in existing literature."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
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+            "angle": 0,
+            "content": "To tackle the aforementioned problems, we aim to benchmark concept removal methods by introducing a comprehensive dataset and a new evaluation metric. Our contributions are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.099,
+                0.599,
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+            "content": "1. A comprehensive dataset. We propose a new dataset, Six-CD, which contains Six categories of unwanted Concepts in Diffusion models, including harm, nudity, identities of celebrities, copyrighted characters, objects, and art styles. We divide the six categories into two groups: general concepts and specific concepts. General concepts, such as harm and nudity, are of concern to all users. Specific concepts are subject to a specific entity, e.g., a person or a company. While they may not be malicious to everyone, they can infringe on the rights of the concept owner, such as portraits of celebrities and copyrighted characters."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+                0.781,
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+            ],
+            "angle": 0,
+            "content": "2. Effective prompts. Through extensive experiments in Sec. 3.2 and Sec. 5.1, we observe that ineffective prompts happen more frequently in general concepts. This is because the prompts of these concepts are usually diverse and implicit, unlike the precise and explicit prompts for specific concepts. Thus, in Six-CD, we provide additional subsets (with highly effective prompts only) for general concepts. Evaluation of ef"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.098,
+                0.599,
+                0.483,
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+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.54,
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+            "angle": 0,
+            "content": "fective prompts can be more efficient and also fairer when compared with specific concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.521,
+                0.268,
+                0.907,
+                0.522
+            ],
+            "angle": 0,
+            "content": "3. A new evaluation metric. We introduce a novel evaluation metric, called in-prompt CLIP score, to measure the in-prompt retainability. An expected concept removal method should have the ability to generate the benign part of the prompt when the unwanted concepts are removed. To evaluate in-prompt retainability, we construct a Dual-Version Dataset, in which each prompt has two versions: a malicious version contains the unwanted concept, and a benign version with the unwanted concept removed but the rest the same as the malicious version. We apply concept removal methods to generate images from the malicious version and then use the CLIP score [10] to measure the similarity between these images and the benign prompts. Ideally, a successful concept removal method should preserve the benign part of the malicious prompt, resulting in a high in-prompt CLIP score."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.522,
+                0.906,
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+            ],
+            "angle": 0,
+            "content": "In the rest of the paper, we first revisit existing concept removal methods and then introduce the proposed dataset and evaluation metric in detail. Finally, we conduct comprehensive experiments to benchmark these methods and discuss our observations."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
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+            "angle": 0,
+            "content": "2. Preliminaries"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.633,
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+            "angle": 0,
+            "content": "2.1. Text-to-image Diffusion Models"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.655,
+                0.906,
+                0.761
+            ],
+            "angle": 0,
+            "content": "Diffusion models typically involve a forward diffusion process and its reverse diffusion process. The forward process is a \\(T\\)-step Markov chain which transforms a sample from the image distribution to an isotropic Gaussian distribution \\(p\\). The reverse process is a \\(T\\)-step Markov chain which transforms a Gaussian sample back to the image distribution. The reverse process can be represented as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.565,
+                0.766,
+                0.905,
+                0.786
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {\\theta} \\left(x _ {0: T}\\right) = p \\left(x _ {T}\\right) \\prod_ {t = 1} ^ {T} p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) \\tag {1}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.536,
+                0.787,
+                0.905,
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+            "angle": 0,
+            "content": "\\[\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) = \\mathcal {N} \\left(x _ {t - 1}; \\mu_ {\\theta} \\left(x _ {t}, t\\right), \\Sigma_ {\\theta} \\left(x _ {t}, t\\right)\\right), \\tag {2}\n\\]"
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+            "type": "text",
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+            ],
+            "angle": 0,
+            "content": "where \\( x_0 \\) is the image sample, \\( x_{T} \\) is the Gaussian sample, and \\( x_{t}(0 < t < T) \\) is the middle state of diffusion. The terms \\( \\mu_{\\theta} \\) and \\( \\Sigma_{\\theta} \\) are estimated by a denoising network \\( \\epsilon_{\\theta}(x_t,t) \\) which takes \\( x_{t} \\) and \\( t \\) as input. By \\( \\epsilon_{\\theta} \\), an image sample \\( x_0 \\) can be generated from a Gaussian sample \\( x_{T} \\) following Eq. (1)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28770"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.273
+            ],
+            "angle": 0,
+            "content": "Text-to-image (T2I) diffusion models further extend the diffusion process by guiding it with a textual prompt \\( y \\) [4, 15, 35]. Specifically, \\( \\epsilon_{\\theta}(x_t,t) \\) is modified to take \\( y \\) as an additional input, resulting in \\( \\epsilon_{\\theta}(x_t,y,t) \\). The network \\( \\epsilon_{\\theta}(x_t,y,t) \\) uses a cross-attention module to select information from the textual prompt to guide the diffusion process. In cross attention, each token is transformed into key \\( (K) \\) space and value \\( (V) \\) space, while the image is transformed into query \\( (Q) \\) space. The key and the query are multiplied to select information from the values of different tokens. With cross attention, T2I models can generate images that adhere to the provided text prompts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.282,
+                0.273,
+                0.297
+            ],
+            "angle": 0,
+            "content": "2.2. Concept Removals"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.303,
+                0.483,
+                0.334
+            ],
+            "angle": 0,
+            "content": "In this subsection, we revisit representative concept removal methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.334,
+                0.484,
+                0.38
+            ],
+            "angle": 0,
+            "content": "Fine-tuning-based methods. Fine-tuning is the most common framework for concept removals. The objective for the fine-tuning-based algorithms can be summarized as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.21,
+                0.404,
+                0.483,
+                0.425
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {\\theta} L = L _ {\\mathrm {r m}} + \\lambda L _ {\\mathrm {r e g}}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.434,
+                0.484,
+                0.524
+            ],
+            "angle": 0,
+            "content": "where \\( L_{\\mathrm{rm}} \\) is the term for changing the output of unwanted concept, and \\( L_{\\mathrm{reg}} \\) is the regularization term to ensure that the fine-tuning will not influence other benign concepts and maintain the generation quality. The term \\( \\theta \\) is the parameter to fine-tune. The methods can be solved by two types of solutions:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.526,
+                0.483,
+                0.602
+            ],
+            "angle": 0,
+            "content": "- Gradient descent. This solution [7, 16, 18, 23] focuses on the final output of \\(\\epsilon_{\\theta}(x_t,y,t)\\), modifying the model in an end-to-end way. The term \\(L_{\\mathrm{rm}}\\) changes the output of \\(\\epsilon_{\\theta}(x_t,c_u,t)\\) where \\(c_{u}\\) is unwanted concepts, while \\(L_{\\mathrm{reg}}\\) maintains the output of benign concepts \\(c_b\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.602,
+                0.483,
+                0.678
+            ],
+            "angle": 0,
+            "content": "- Closed-form solution. Modifying the intermediate states of linear components (such as cross-attention weights [8, 22] and MLP layers [42]) instead of the final output of \\(\\epsilon_{\\theta}(x_t, y_c, t)\\), can be solved in a closed-form solution. This can accelerate the fine-tuning process remarkably."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.091,
+                0.526,
+                0.483,
+                0.678
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.68,
+                0.483,
+                0.814
+            ],
+            "angle": 0,
+            "content": "Inference-time methods. Inference-time methods such as negative prompt [32], SLD [36], and SEGA [3] change the generation algorithm to remove concepts in the inference process, which can skip fine-tuning operations. They estimate the influence of unwanted concepts and remove them in inference. However, although these methods can skip the fine-tuning process, there is also a risk of being disabled in open-sourced models, which may slow down the inference."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.827,
+                0.483,
+                0.861
+            ],
+            "angle": 0,
+            "content": "3. Six-CD: a Comprehensive and Effective Dataset"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.871,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In this section, we first propose a new dataset that encompasses a comprehensive set of categories of unwanted con"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.092,
+                0.905,
+                0.138
+            ],
+            "angle": 0,
+            "content": "cepts. Then we discuss the issue of ineffectiveness in general prompts and present the solution to filter the dataset, thereby increasing its effectiveness."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.148,
+                0.84,
+                0.166
+            ],
+            "angle": 0,
+            "content": "3.1. Six Categories of Unwanted Concepts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.171,
+                0.905,
+                0.337
+            ],
+            "angle": 0,
+            "content": "As mentioned in Sec. 1, summarizing all the datasets in existing literature, the unwanted concepts can be divided into general and specific concepts. The general concepts contain harmful concepts and nudity concepts, while the specific concepts contain identities of celebrities, copyrighted characters, objects, and art styles. However, existing literature focuses on only a few categories for evaluation, lacking systematic comparisons among the methods in general and specific concepts. To address this, we propose a new dataset, Six-CD, to evaluate concept removals comprehensively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.338,
+                0.905,
+                0.715
+            ],
+            "angle": 0,
+            "content": "For the general concepts, Six-CD first collects the malicious prompts from four different NSFW resources, which include I2P [36], MMA [43], jatman/stable-diffusion-prompts-stats-full-uncensored (SD-uncensored) [13], and Unsafe Diffusion (UD) [27]. Then, it divides the NSFW data into harmful and nudity concepts. Harmful concepts contain the prompts that have the meanings of \"violence, suicide, hate, harassment, suffering, humiliation, harm, and bloodiness\", while nudity contains \"nudity, nakedness, sexuality, pornography, and eroticism\". However, in MMA, UD, and SD-uncensored, the prompts are only labeled as NSFW or not and have no such fine-grained labels for harm and nudity. Thus, we use the image classifiers NudeNet [2] and Q16 [27] to annotate by detecting the NSFW contents in the images generated by the prompts. NudeNet is tailored for detecting images with nudity, while Q16 is a binary classifier for detecting NFSW. To annotate the fine-grained labels, i.e., harm and nudity, we first use NudeNet to find the prompts of nudity from the collected resources<sup>1</sup>. Then, in the remaining data, we use Q16 to select the prompts whose images are classified as NSFW. Since the nudity prompts are already filtered out by NudeNet, in the remaining data, the prompts detected by Q16 are annotated as harmful. With the two detectors, we merge the collected resources and annotate them as either harmful or nudity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.716,
+                0.905,
+                0.79
+            ],
+            "angle": 0,
+            "content": "For the specific concepts in Six-CD, instead of directly collecting prompts, we collect concepts and use prompt templates (detailed in Appd. A.1) to generate the final prompts, which are different from the general ones. The concepts are collected as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.513,
+                0.792,
+                0.905,
+                0.853
+            ],
+            "angle": 0,
+            "content": "- Celebrity. Celebrities can evaluate the ability to remove identity. We select the identities of celebrities from CPDM [24]. To assist the evaluation, we use a celebrity detector, GCD [25]. we choose the celebrities that can be"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.512,
+                0.863,
+                0.905,
+                0.901
+            ],
+            "angle": 0,
+            "content": "1The image is labeled as nudity if it is classified as \"FEMALE/MALE GENITALIA EXPOSED\", \"FEMALE BREAST EXPOSED\", \"ANUS EXPOSED\", or \"BUTTOCKS EXPOSED\" by NudeNet."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28771"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.137,
+                0.092,
+                0.442,
+                0.266
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.282,
+                0.486,
+                0.311
+            ],
+            "angle": 0,
+            "content": "Figure 1. Effectiveness of I2P prompts. Most of the prompts have low effectiveness. Results from [36]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.104,
+                0.337,
+                0.418,
+                0.352
+            ],
+            "angle": 0,
+            "content": "both generated by SD and recognized by GCD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.353,
+                0.483,
+                0.427
+            ],
+            "angle": 0,
+            "content": "- Copyrighted characters. The copyrighted characters are important IP resources for companies. We use the character concepts in CPDM and the high-frequency copyrighted characters from FiveThirtyEight Comic Characters Dataset [1]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.428,
+                0.483,
+                0.473
+            ],
+            "angle": 0,
+            "content": "- Objects. Objects can be used to evaluate the performance of removal on non-humanoid concepts. We randomly sample from a subset from the classes of ImageNet [5]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.091,
+                0.473,
+                0.483,
+                0.519
+            ],
+            "angle": 0,
+            "content": "- Art style. The art styles can evaluate the removal performance of a global feature instead of a local feature. We use the art styles from [22]."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.091,
+                0.353,
+                0.483,
+                0.519
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.52,
+                0.486,
+                0.746
+            ],
+            "angle": 0,
+            "content": "For the two general categories, we provide 6,326 prompts for harm concept and 4,518 effective prompts for nudity concept. For the specific concepts, we provide 94 concepts for the identity of celebrity, 100 concepts for copyrighted characters, 10 concepts for objects and 10 concepts for art styles. Four templates are used to construct the prompt for each specific concept. Six-CD is the first dataset that divides the concept removal into general and specific concepts. Through experiments, we observe that, for different methods, the removal abilities in general and specific concepts are distinct, which is detailed in Sec. 5.1. Besides its comprehensiveness in covering general and specific categories found in existing literature, in the following subsection, we show that our dataset also solves the problem of ineffective prompts of general concepts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.757,
+                0.483,
+                0.789
+            ],
+            "angle": 0,
+            "content": "3.2. Ineffective Prompts of General Concepts in Existing Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.795,
+                0.483,
+                0.87
+            ],
+            "angle": 0,
+            "content": "The prompts for general concepts in existing dataset do not consistently generate malicious content for each random seed according to [36] and our observation below. In this subsection, we discuss this phenomenon in general concepts and identify two potential problems it may introduce."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.871,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We first define the effectiveness of a prompt as the possibility of generating malicious images. To assess this, we"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.557,
+                0.092,
+                0.865,
+                0.268
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.511,
+                0.282,
+                0.907,
+                0.31
+            ],
+            "angle": 0,
+            "content": "Figure 2. Concept removal (CR) performance on the prompts with different effectiveness."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.326,
+                0.907,
+                0.354
+            ],
+            "angle": 0,
+            "content": "Table 2. Percentage of removed unwanted concepts between high effective and all effectiveness. (%)"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.517,
+                0.365,
+                0.905,
+                0.426
+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>NEG</td><td>ESD</td><td>SPM</td><td>SDD</td><td>FMN</td><td>UCE</td><td>EMCID</td><td>SLD</td><td>SEGA</td><td>Corr</td></tr><tr><td>Harm</td><td>40.9</td><td>63.6</td><td>98.9</td><td>24.8</td><td>95.6</td><td>77.6</td><td>98.9</td><td>27.3</td><td>23.7</td><td rowspan=\"2\">0.977</td></tr><tr><td>Harm-EF</td><td>56.7</td><td>67.3</td><td>99.9</td><td>27.8</td><td>97.4</td><td>67.8</td><td>98.6</td><td>38.1</td><td>22.9</td></tr><tr><td>Nudity</td><td>22.3</td><td>17.9</td><td>81.0</td><td>11.2</td><td>93.6</td><td>14.9</td><td>98.3</td><td>14.6</td><td>38.8</td><td rowspan=\"2\">0.984</td></tr><tr><td>Nudity-EF</td><td>11.0</td><td>16.0</td><td>88.9</td><td>4.2</td><td>92.6</td><td>12.3</td><td>97.2</td><td>16.3</td><td>58.4</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.513,
+                0.434,
+                0.907,
+                0.476
+            ],
+            "angle": 0,
+            "content": "Table 3. Examples of Dual-Version Dataset for specific concepts. We generate a malicious version by ChatGPT and remove the unwanted concepts placeholder to get the benign version."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.517,
+                0.486,
+                0.905,
+                0.561
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Category</td><td>Example of malicious version</td><td>Example of benign version</td></tr><tr><td>Celeb. &amp; \nCopyrighted</td><td>{celebrity} is dancing in the rain.</td><td>dancing in the rain.</td></tr><tr><td>Object</td><td>{object}, football, grass, house, tree, dog</td><td>football, grass, house, tree, dog</td></tr><tr><td>Art style</td><td>A beautiful snow-covered mountain with \nsunshine lighting it in the style of {art style}</td><td>A beautiful snow-covered moun-\ntain with sunshine lighting it</td></tr></table>"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.582,
+                0.907,
+                0.794
+            ],
+            "angle": 0,
+            "content": "generate \\(N\\) images for a prompt using different random seeds. The effectiveness is defined by \\(n / N\\), where \\(n\\) is the number of malicious images detected. In existing datasets, there is a large portion of ineffective prompts in general concepts. Taking I2P [36] as an example, which is the most well-used dataset for harmful and nudity concepts in existing literature [3, 7, 8, 16, 22, 23, 36, 42], most of the prompts have low effectiveness as shown in Fig. 1. We can see that the number of ineffective prompts significantly exceeds the number of effective prompts in I2P, particularly in the nudity category. The specific concepts usually do not have the problem of low effectiveness because they contain the specific and definitive for the unwanted concepts. Thus, in this subsection, we focus on general concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.511,
+                0.796,
+                0.909,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Limitations. The large portion of ineffective prompts can potentially introduce the following problems. First, evaluating the ineffective prompts is in low efficiency. For example, we test different concept removal methods on SD for nudity concepts in Fig. 2. On the vanilla SD without concept removal (i.e., No CR in Fig. 2), prompts with effectiveness of \\(1/5\\) generated only about \\(20\\%\\) nudity images."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.958
+            ],
+            "angle": 0,
+            "content": "28772"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.482,
+                0.227
+            ],
+            "angle": 0,
+            "content": "It means that \\(80\\%\\) of the generated images by these prompts are non-nudity images, while evaluating on non-nudity images is meaningless. Second, the ineffective prompts may cause unfair comparisons between the general concepts and specific concepts. Unlike general concepts, the specific concepts do not have the problem of ineffective prompts. When the model builder has to remove both general and specific concepts, the ineffective prompts may falsely induce the builder to put less weight on the general concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.093,
+                0.228,
+                0.485,
+                0.438
+            ],
+            "angle": 0,
+            "content": "High-effectiveness subsets. Therefore, in addition to harm and nudity concepts, we provide additional subsets of high-effectiveness prompts and name them as harm- \\(EF\\) and nudity- \\(EF\\). We use the prompts with effectiveness of 4/5 and 5/5 for harm- \\(EF\\) and nudity- \\(EF\\). Harm- \\(EF\\) contains 991 prompts, and nudity- \\(EF\\) contains 1,539 prompts. In Table 2 and Fig. 2, we demonstrate that the abilities of different concept removal methods are highly consistent between high effectiveness and low effectiveness. Thus, it is reasonable to evaluate on high-effectiveness prompts in order to reduce computation, which is also more fair. Specifically, in Table 2, we use the percentage of removed unwanted concepts to measure the ability of different methods, which is defined as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.223,
+                0.447,
+                0.483,
+                0.475
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {\\mathrm {r m}} = 1 - \\frac {n _ {\\text {a f t e r}}}{n _ {\\text {b e f o r e}}}, \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.485,
+                0.483,
+                0.59
+            ],
+            "angle": 0,
+            "content": "where \\( n_{\\mathrm{before}} \\) is the number of images containing unwanted concepts before concept removal, while \\( n_{\\mathrm{after}} \\) is the number of images containing unwanted concepts after concept removal. The removal abilities in harm and nudity concepts are very close to harm- \\( EF \\) and nudity- \\( EF \\). The Pearson correlation coefficient is as high as 0.977 (between harm and harm- \\( EF \\)) and 0.984 (between nudity and nudity- \\( EF \\))."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.59,
+                0.483,
+                0.665
+            ],
+            "angle": 0,
+            "content": "In summary, Six-CD provides two choices to evaluate on the general concepts. The first choice is to use the whole subsets of harm and nudity, while the second choice is to evaluate on harm-EF and nudity-EF, which provides a more efficient and fair evaluation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.68,
+                0.317,
+                0.697
+            ],
+            "angle": 0,
+            "content": "4. In-prompt Retainability"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.705,
+                0.483,
+                0.78
+            ],
+            "angle": 0,
+            "content": "Concept removals should not hurt the generation ability of the benign contents, which is referred to as retainability. In this section, we show the lack of evaluation for retainability on the benign parts of the prompts containing the unwanted concepts and propose a new metric for this retainability."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.781,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Lack of in-prompt retainability. Existing literature [24, 45] only considers the retainability of totally benign concepts. The benign prompts do not contain any unwanted concept, and concept removal should not influence the generation of them. Therefore, CLIP score [10] is utilized to measure it by calculating the similarity between benign prompts and generated images in the CLIP space [28]. However, for the prompts containing unwanted concepts,"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.626,
+                0.09,
+                0.673,
+                0.101
+            ],
+            "angle": 0,
+            "content": "NO CR"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.709,
+                0.09,
+                0.834,
+                0.102
+            ],
+            "angle": 0,
+            "content": "ironman removed"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.589,
+                0.103,
+                0.709,
+                0.196
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.712,
+                0.103,
+                0.832,
+                0.196
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.513,
+                0.207,
+                0.905,
+                0.249
+            ],
+            "angle": 0,
+            "content": "Figure 3. Concept removal example of the prompt: \"At night, ironman with his armor on is watching fireworks by the lake\". Ironman is removed by SDD."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.267,
+                0.907,
+                0.463
+            ],
+            "angle": 0,
+            "content": "the retainability to guarantee the generation of the benign part of them is also important, which is called \"in-prompt retainability\" in our benchmark. As shown in Fig. 3, the prompt is \"At night, ironman with his armor on is watching fireworks by the lake\" with \"ironman\" as the unwanted concept. Although there is no \"ironman\" after concept removal, the benign part of \"fireworks\" is also removed. In this case, even though the method can remove unwanted concepts, this generation is meaningless for the users because the benign information is not preserved. For users who do not intentionally include the unwanted concepts or who do not know the concept is malicious, this in-prompt retainability is necessary to ensure the normal usage."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.464,
+                0.906,
+                0.689
+            ],
+            "angle": 0,
+            "content": "New metric. To measure in-prompt retainability, we propose a new metric, in-prompt CLIP score, assisted by a Dual-Version Dataset (DVD). In this dataset, we have two versions for each prompt: malicious and benign. The malicious version contains the unwanted concepts of the six categories, while the benign version removes the unwanted concepts with the rest the same as the malicious version. In in-prompt CLIP score, we first generate the images with concept removals using the malicious version and then calculate the cosine similarity of CLIP embeddings between these generated images and the corresponding benign version prompts. Thus, we can measure the similarity between the generated image and the benign part of the prompt. To distinguish it from the original CLIP score, we refer to the original CLIP score as the out-prompt CLIP score."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.69,
+                0.906,
+                0.871
+            ],
+            "angle": 0,
+            "content": "To construct DVD, for general concepts, we first sample two subsets of prompts from the harmful and nudity categories of Six-CD as the malicious version, then we manually remove the unwanted concepts to get the benign version. For specific concepts, since they are not diverse or implicit like general concepts, we create templates for each category using ChatGPT and use the concepts from Six-CD to get the complete prompts. We show the examples of templates in DVD in Table 3. The entire dataset is in Appd. A.2. To validate the effectiveness of the metric, we conduct human evaluation in Appd. D.1. The results demonstrate that the metric is highly consistent with human preference."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.871,
+                0.905,
+                0.902
+            ],
+            "angle": 0,
+            "content": "In summary, to measure the in-prompt retainability, we propose the in-prompt CLIP score. It leverages a malicious-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28773"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.092,
+                0.486,
+                0.138
+            ],
+            "angle": 0,
+            "content": "version and a benign-version prompt to measure the similarity between the images after concept removal and the benign part of the prompt."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.15,
+                0.226,
+                0.168
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.175,
+                0.483,
+                0.297
+            ],
+            "angle": 0,
+            "content": "In this section, we conduct experiments to benchmark the performance of 10 methods in removing single and multiple concepts and the retainability with both in-prompt and out-prompt CLIP scores. We also test FID, time costs of training and inference, and a fine-grained retainability for similar concepts. Due to space limitations, these experiments are in Appd D. Also, we report the results of SD v1.4 in this section and the results of other models are in Appd D."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.297,
+                0.483,
+                0.432
+            ],
+            "angle": 0,
+            "content": "Experimental settings. We evaluate on 10 concept removal methods: negative prompt (NEG) [32], ESD [7], SPM [23], SDD [16], FMN [44], UCE [8], MACE [22], EMCID [42], SLD [36], and SEGA [3]. The details on the baseline settings can be found in Appd. B. The evaluated datasets are Six-CD and DVD, which are detailed in Appd. A. Following the conclusions in Sec. 3.2, we use harm-EF and nudity-EF for all the experiments in this section. All experiments use one GPU (A5000 or A6000)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.433,
+                0.483,
+                0.629
+            ],
+            "angle": 0,
+            "content": "Detection metrics. We use the detection rate of Q16 and NudeNet for harmful and nudity concepts. We use the classification accuracy of GCD as the detection rate for celebrity concepts, and we train two classifiers based on ResNet-50 [9] and use the accuracy as the detection rate for copyrighted characters and objects. For the art style concept, the detection is not a simple binary problem. In existing literature [22-24, 44], CLIP score, \\( S_{\\mathrm{CLIP}} \\), is used to measure the presence of an art style on a continuous scale, assessing the similarity between generated images and art styles. Following them, we use \\( S_{\\mathrm{CLIP}} \\) and normalize its range by \\( \\tilde{S}_{\\mathrm{CLIP}} = (S_{\\mathrm{CLIP}} - \\min(S_{\\mathrm{CLIP}})) / (\\max(S_{\\mathrm{CLIP}}) - \\min(S_{\\mathrm{CLIP}})) \\) for a better comparison with other categories."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.638,
+                0.365,
+                0.654
+            ],
+            "angle": 0,
+            "content": "5.1. Evaluation on Removal Ability"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.66,
+                0.483,
+                0.824
+            ],
+            "angle": 0,
+            "content": "In this subsection, we test the removal ability of different methods on Six-CD. In Fig. 4, we show the detection results of models both with and without concept removals. For general concepts, we use all the prompts in harmful and nudity concepts in Six-CD for evaluation. For specific concepts, we randomly choose five concepts from each category and modify the diffusion model for each individual concept. We show the averaged results of 5 concepts of each category in Fig. 4. (The table with error bar for Fig. 4 can be found in Appd. D.2.) We highlight the main observations as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.826,
+                0.483,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Observation 1: General concepts are harder to remove. The difficulty of removing general concepts is reflected by two factors shown in Fig 4. First, in most methods, the worst removal result lies in one of the general categories. For example, ESD and MACE perform well in all"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.092,
+                0.905,
+                0.333
+            ],
+            "angle": 0,
+            "content": "other categories, but they still have around \\(55\\%\\) harmful images detected. Second, while some methods can remove almost all the specific concepts (e.g., ESD, UCE, SLD), no one method can achieve similar results in both harm and nudity categories simultaneously. For general concepts, on the one hand, they are hard to trigger (i.e. low effectiveness). On the other hand, it is harder to remove them than specific concepts. We conjecture that they are both the results of the diverse and implicit prompts of general concepts. Locating the unwanted concepts in the diverse and implicit prompts of general concepts is more difficult than the explicit prompts of specific concepts. Most of the methods like ESD can only provide a limited number of tokens as the general concepts, which is impossible to cover the entire (almost unlimited) vocabulary of harm and nudity. Thus, it leads to difficulty in removing general concepts."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.335,
+                0.905,
+                0.562
+            ],
+            "angle": 0,
+            "content": "Observation 2: Removal ability is consistent within general concepts and within specific categories. We observe that the removal abilities within general or specific categories are usually more consistent. For example, SLD and FMN perform well in specific concepts, but the ability to remove general concepts is worse. To demonstrate this observation, we present the correlation coefficient of the detection metrics among different categories in Fig. 5. From Fig. 5, we can see that the correlations between specific concepts are higher than 0.59, with the correlation between celebrity and character notably high, at 0.94. The correlation between general concepts is also as high as 0.65. This offers an insight into the designation of concept removal methods that general and specific concepts should be considered separately."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.513,
+                0.575,
+                0.844,
+                0.59
+            ],
+            "angle": 0,
+            "content": "5.2. Removal Ability on Multiple Concepts"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.598,
+                0.905,
+                0.734
+            ],
+            "angle": 0,
+            "content": "In Sec. 5.1, we evaluate the ability to remove a single concept from one model. However, removing multiple concepts from one model is also important since the model builder usually needs to consider multiple malicious concepts in practice. In this subsection, we present the results of removing multiple concepts of celebrities and copyrighted characters in Fig. 6, where the y-axis represents the detection rate, and a higher detection rate means a weaker concept removal performance. We have two observations from Fig. 6."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.735,
+                0.905,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Observation 1: Inference-time methods fail in removing multiple concepts. As shown in Fig. 6, the inference-time methods, SLD and NEG, are the only two methods that have significantly limited removal performance when the concept number is larger than 50, which only reduces the detection rate by \\(20\\%\\) or less. To remove the multiple concepts in inference time, they have to encode the string containing all the concepts in the embeddings of one single prompt. This will exceed the capacity of the text encoder of T2I diffusion models and lead to failed removal. Another inference-time method, SEGA, is not reported in Fig. 6 due"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28774"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.101,
+                0.08,
+                0.898,
+                0.371
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.089,
+                0.38,
+                0.908,
+                0.424
+            ],
+            "angle": 0,
+            "content": "Figure 4. Removal ability on Six-CD. In each sub-figure, we present the detection results of unwanted concepts in both the models with and without concept removals. The range of all the six values is [0,1]. Smaller values indicate that less unwanted concepts are detected, i.e. better removal. G1 and G2 are harm-EF and nudity-EF concepts, while S1, S2, S3 and S4 are celebrity, character, object and art style."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.137,
+                0.44,
+                0.428,
+                0.626
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.09,
+                0.642,
+                0.483,
+                0.671
+            ],
+            "angle": 0,
+            "content": "Figure 5. Correlation coefficient of removal performance on six data categories."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.688,
+                0.483,
+                0.734
+            ],
+            "angle": 0,
+            "content": "to its catastrophic inference time when the concept number is increased to 50. This implies that the strategy of processing each concept separately during inference is impractical."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.734,
+                0.483,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Observation 2: Closed-form solutions by modifying linear components perform well in removing multiple concepts. The best two methods in Fig. 6a and Fig. 6b are both based on the closed-form solution, which modifies the linear components of cross attention. This is possibly because combining multiple concepts in the linear components is easier than in other non-linear parts."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.091,
+                0.849,
+                0.443,
+                0.866
+            ],
+            "angle": 0,
+            "content": "5.3. In-prompt and Out-prompt Retainability"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.871,
+                0.483,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We evaluate the generation ability on benign concepts using both in-prompt and out-prompt CLIP scores. In Fig. 7, we"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.449,
+                0.907,
+                0.494
+            ],
+            "angle": 0,
+            "content": "use DVD to test the in-prompt CLIP score and a subset with benign prompts from LAION [37] to test out-prompt CLIP score. The observations as follows."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.501,
+                0.908,
+                0.759
+            ],
+            "angle": 0,
+            "content": "Observation 1: In-prompt retainability performs worse than out-prompt retainability. As shown in Fig. 7, the in-prompt CLIP score is lower than the out-prompt CLIP score across all the methods and concept categories. This indicates that the ability to generate benign parts in prompts containing malicious concepts is more negatively affected than the ability to generate totally benign prompts. As mentioned in Sec. 4, the in-prompt retainability is also important for concept removal methods. This inspires future research to pay more attention to the in-prompt retainability. Remark. It could be unfair to directly compare the two CLIP scores since they use different prompt sets to calculate CLIP scores. To further validate this observation, we use the clean version of DVD to calculate the out-prompt CLIP score, which is detailed in Appd. D.3. By comparing it with the in-prompt CLIP score in Appd. D.3, we have observed a consistent phenomenon with this subsection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.765,
+                0.909,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Observation 2: Auxiliary semantic information in MACE (Fig. 7g) may hurt the generation on benign concepts. MACE has the most significant decrease in the generation ability of benign concepts for both in-prompt and out-prompt CLIP scores. We conjecture that this is because it introduces auxiliary semantic information to help locate the unwanted concepts in the image. In other methods, the unwanted concepts are usually located by the semantic understanding ability of the T2I model itself. In contrast,"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28775"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.147,
+                0.092,
+                0.443,
+                0.26
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.26,
+                0.267,
+                0.33,
+                0.279
+            ],
+            "angle": 0,
+            "content": "(a) Celebrity"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.465,
+                0.092,
+                0.85,
+                0.26
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.543,
+                0.267,
+                0.685,
+                0.279
+            ],
+            "angle": 0,
+            "content": "(b) Copyrighted characters"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.357,
+                0.287,
+                0.642,
+                0.302
+            ],
+            "angle": 0,
+            "content": "Figure 6. Removal ability on multiple concepts"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.094,
+                0.314,
+                0.249,
+                0.459
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.149,
+                0.461,
+                0.195,
+                0.471
+            ],
+            "angle": 0,
+            "content": "(a) NEG"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.257,
+                0.314,
+                0.413,
+                0.459
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.313,
+                0.461,
+                0.358,
+                0.471
+            ],
+            "angle": 0,
+            "content": "(b) ESD"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.422,
+                0.315,
+                0.576,
+                0.459
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.476,
+                0.461,
+                0.522,
+                0.471
+            ],
+            "angle": 0,
+            "content": "(c) SPM"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.585,
+                0.313,
+                0.74,
+                0.459
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.64,
+                0.461,
+                0.686,
+                0.471
+            ],
+            "angle": 0,
+            "content": "(d) SDD"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.749,
+                0.334,
+                0.904,
+                0.459
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.803,
+                0.461,
+                0.851,
+                0.471
+            ],
+            "angle": 0,
+            "content": "(e) FMN"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.094,
+                0.474,
+                0.248,
+                0.597
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.15,
+                0.6,
+                0.193,
+                0.611
+            ],
+            "angle": 0,
+            "content": "(f) UCE"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.257,
+                0.474,
+                0.413,
+                0.598
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.307,
+                0.6,
+                0.364,
+                0.612
+            ],
+            "angle": 0,
+            "content": "(g) MACE"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.422,
+                0.474,
+                0.576,
+                0.598
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.468,
+                0.6,
+                0.531,
+                0.611
+            ],
+            "angle": 0,
+            "content": "(h) EMCID"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.585,
+                0.474,
+                0.74,
+                0.598
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.642,
+                0.6,
+                0.684,
+                0.611
+            ],
+            "angle": 0,
+            "content": "(i) SLD"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.749,
+                0.474,
+                0.904,
+                0.598
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.801,
+                0.6,
+                0.853,
+                0.611
+            ],
+            "angle": 0,
+            "content": "(j) SEGA"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.316,
+                0.624,
+                0.68,
+                0.639
+            ],
+            "angle": 0,
+            "content": "Figure 7. In-prompt retainability vs. out-prompt retainability"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.089,
+                0.655,
+                0.483,
+                0.777
+            ],
+            "angle": 0,
+            "content": "MACE incorporates the segmentation results of GroundedSAM [17, 21] to locate the image area of unwanted concepts. It focuses on optimizing this area and overlooks other areas of the image. This may lead to worse retainability in other areas. Another piece of evidence is that when we do not include segmentation in removing the art style concepts by MACE (since art style is a global feature), it has good in-prompt and out-prompt CLIP scores."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.09,
+                0.798,
+                0.401,
+                0.813
+            ],
+            "angle": 0,
+            "content": "6. Conclusion and Ethical Statement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.825,
+                0.484,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In this work, we address the lack of a systematic benchmark for concept removal methods by introducing a comprehensive and effective dataset and a new evaluation metric. Using this benchmark, we conduct an extensive evaluation of concept removal methods. Our experimental observations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.656,
+                0.907,
+                0.746
+            ],
+            "angle": 0,
+            "content": "provide valuable and practical insights for future research in this field. While our benchmark may have a limitation in the inconvenient detection metric for art styles (using the CLIP score for art styles, instead of the detection rate from a classifier like other categories), it still offers a thorough and practical evaluation across the various method settings."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.512,
+                0.75,
+                0.909,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Ethical statement. This work provides a comprehensive evaluation framework for concept removal, which is targeted to mitigate the potential malicious use of text-to-image diffusion models. Our research is conducted responsibly, transparently, and deeply dedicated to ethical standards. Despite involving the generation of sensitive content such as nudity and violence, it is strictly for research purposes and does not intend to produce or promote inappropriate material. On the contrary, our work aims to advance efforts to prevent the generation of inappropriate content."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.479,
+                0.945,
+                0.521,
+                0.957
+            ],
+            "angle": 0,
+            "content": "28776"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.092,
+                0.091,
+                0.251,
+                0.108
+            ],
+            "angle": 0,
+            "content": "Acknowledgement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.09,
+                0.114,
+                0.484,
+                0.226
+            ],
+            "angle": 0,
+            "content": "Jie Ren, Kangrui Chen, Yingqian Cui, Shenglai Zeng, and Jiliang Tang are supported by the National Science Foundation (NSF) under grant numbers CNS2321416, IIS2212032, IIS2212144, IOS2107215, DUE2234015, CNS2246050, DRL2405483 and IOS2035472, the Army Research Office (ARO) under grant number W911NF-21-1-0198, Amazon Faculty Award, JP Morgan Faculty Award, Meta, Microsoft and SNAP."
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2025/Six-CD_ Benchmarking Concept Removals for Text-to-image Diffusion Models/17b4b8e3-2cbd-49ce-875b-c3c7f736c51d_origin.pdf

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2025/Six-CD_ Benchmarking Concept Removals for Text-to-image Diffusion Models/full.md

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+# Six-CD: Benchmarking Concept Removals for Text-to-image Diffusion Models
+
+Jie Ren $^{1}$ , Kangrui Chen $^{1}$ , Yingqian Cui $^{1}$ , Shenglai Zeng $^{1}$ , Hui Liu $^{1}$ , Yue Xing $^{1}$ , Jiliang Tang $^{1}$ , Lingjuan Lyu $^{2}$ $^{1}$ Michigan State University   $^{2}$ Sony AI
+
+{renjie3,chenkan4,cuiyingq,zengshel,liuhui7,xingyue1,tangjili}@msu.edu  
+lingjuan.lv@sony.com
+
+# Abstract
+
+Text-to-image (T2I) diffusion models have shown exceptional capabilities in generating images that closely correspond to textual prompts. However, the advancement of T2I diffusion models presents significant risks, as the models could be exploited for malicious purposes, such as generating images with violence or nudity, or creating unauthorized portraits of public figures in inappropriate contexts. To mitigate these risks, concept removal methods have been proposed. These methods aim to modify diffusion models to prevent the generation of malicious and unwanted concepts. Despite these efforts, existing research faces several challenges: (1) a lack of consistent comparisons on a comprehensive dataset, (2) ineffective prompts in harmful and nudity concepts, (3) overlooked evaluation of the ability to generate the benign part within prompts containing malicious concepts. To address these gaps, we propose to benchmark the concept removal methods by introducing a new dataset, Six-CD, along with a novel evaluation metric. In this benchmark, we conduct a thorough evaluation of concept removals, with the experimental observations and discussions offering valuable insights in the field.
+
+# 1. Introduction
+
+Diffusion models have demonstrated remarkable capabilities in image generation [6, 11, 12, 40, 41], particularly text-to-image (T2I) diffusion models [4, 29, 32]. These models have gained widespread popularity and deployment due to their ability to generate images that precisely align with textual prompts. However, T2I diffusion models can be exploited for malicious purposes, such as creating images depicting violence, nudity, or fake celebrity images in undesirable contexts like jail [14, 20, 26, 30, 33, 38, 39]. To ensure the integrity of the model developers, it is crucial to design benign models that censor malicious concepts and produce only safe and appropriate content.
+
+Strategies have been proposed to mitigate the malicious
+
+generation. For example, in the data collection stage, Stable Diffusion (SD) [32] and Adobe [31] filter out the Not-Safe-For-Work (NSFW) contents in training data. After image generation, SD uses a detector to ensure the images are benign, removing unwanted ones. However, training data filtering requires retraining and will be inefficient if the model has already been trained on various data. For open-sourced models like SD [32], the detector can be easily disabled by modifying the source code. Therefore, concept removal techniques have been proposed to edit a trained model's parameters to prevent generating malicious concepts [7, 18, 19, 34, 44]. For instance, methods are proposed to fine-tune the models to replace unwanted concepts with benign alternatives [7, 18, 44]. Besides, to accelerate fine-tuning, some methods fine-tune the linear components (e.g. the weight matrix of cross attention) using the closed-form optimal solution [8, 22, 42]. Alternatively, there are methods modifying the output during inference to bypass fine-tuning [3, 36].
+
+While there is rich literature improving concept removal methods, we observe three potential issues:
+
+1. Lack of consistent and comprehensive comparisons. Current concept removal methods, as shown in Table 1, typically analyze limited categories, lacking consistent and comprehensive comparisons. This gap prevents a thorough understanding of the methods' behavior.  
+2. Ineffective prompts. In existing datasets [36], some categories, such as nudity, contain a large portion of "ineffective prompts", which only trigger the model to generate malicious contents with a low probability (see Fig. 1). This can result in inefficient evaluation since the ineffective prompts will generate many benign images, and evaluating concept removal on them is meaningless. Meanwhile, in other categories of unwanted concepts like celebrities, the prompts are more effective than the nudity concept (see Fig. 1 and Fig. 4). When the builder has to remove both nudity and celebrity concepts, the ineffective prompts may cause unfair comparisons. The effective prompts in celebrity can generate
+
+Table 1. Categories of unwanted concepts in existing literature  
+
+<table><tr><td></td><td>ESD [7]</td><td>SPM [23]</td><td>SDD [16]</td><td>FMN [44]</td><td>UCE [8]</td><td>MACE [22]</td><td>EMCID [42]</td><td>SLD [36]</td><td>SEGA [3]</td><td>UC [45]</td><td>CPDM [24]</td></tr><tr><td>Harmful</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>Nudity</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>Celebrity</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>Copyrighted</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>Object</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>art style</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td></tr></table>
+
+more malicious images, which may falsely induce the builder to put more weight on celebrity concepts.
+
+3. Lack of evaluation on in-prompt retainability. Existing evaluations consider the generation ability on the benign prompts but overlook the evaluation of the generation ability on the benign part in the prompts with unwanted concepts, which is called in-prompt retainability in our benchmark. To understand retainability, when the unwanted concepts are removed from a generated image, the newly generated image should retain the remaining semantics in the prompt. For example, if we remove "Mickey Mouse" from the prompt of "Mickey Mouse is eating a burger", the generated image should still depict "eating a burger". If the method is too aggressive, it may remove benign semantics along with the malicious concepts, thus impairing the T2I model's ability to follow the textual prompt to generate meaningful images. Despite its importance, in-prompt retainability is ignored in existing literature.
+
+To tackle the aforementioned problems, we aim to benchmark concept removal methods by introducing a comprehensive dataset and a new evaluation metric. Our contributions are as follows:
+
+1. A comprehensive dataset. We propose a new dataset, Six-CD, which contains Six categories of unwanted Concepts in Diffusion models, including harm, nudity, identities of celebrities, copyrighted characters, objects, and art styles. We divide the six categories into two groups: general concepts and specific concepts. General concepts, such as harm and nudity, are of concern to all users. Specific concepts are subject to a specific entity, e.g., a person or a company. While they may not be malicious to everyone, they can infringe on the rights of the concept owner, such as portraits of celebrities and copyrighted characters.  
+2. Effective prompts. Through extensive experiments in Sec. 3.2 and Sec. 5.1, we observe that ineffective prompts happen more frequently in general concepts. This is because the prompts of these concepts are usually diverse and implicit, unlike the precise and explicit prompts for specific concepts. Thus, in Six-CD, we provide additional subsets (with highly effective prompts only) for general concepts. Evaluation of ef
+
+fective prompts can be more efficient and also fairer when compared with specific concepts.
+
+3. A new evaluation metric. We introduce a novel evaluation metric, called in-prompt CLIP score, to measure the in-prompt retainability. An expected concept removal method should have the ability to generate the benign part of the prompt when the unwanted concepts are removed. To evaluate in-prompt retainability, we construct a Dual-Version Dataset, in which each prompt has two versions: a malicious version contains the unwanted concept, and a benign version with the unwanted concept removed but the rest the same as the malicious version. We apply concept removal methods to generate images from the malicious version and then use the CLIP score [10] to measure the similarity between these images and the benign prompts. Ideally, a successful concept removal method should preserve the benign part of the malicious prompt, resulting in a high in-prompt CLIP score.
+
+In the rest of the paper, we first revisit existing concept removal methods and then introduce the proposed dataset and evaluation metric in detail. Finally, we conduct comprehensive experiments to benchmark these methods and discuss our observations.
+
+# 2. Preliminaries
+
+# 2.1. Text-to-image Diffusion Models
+
+Diffusion models typically involve a forward diffusion process and its reverse diffusion process. The forward process is a  $T$ -step Markov chain which transforms a sample from the image distribution to an isotropic Gaussian distribution  $p$ . The reverse process is a  $T$ -step Markov chain which transforms a Gaussian sample back to the image distribution. The reverse process can be represented as
+
+$$
+p _ {\theta} \left(x _ {0: T}\right) = p \left(x _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) \tag {1}
+$$
+
+$$
+p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) = \mathcal {N} \left(x _ {t - 1}; \mu_ {\theta} \left(x _ {t}, t\right), \Sigma_ {\theta} \left(x _ {t}, t\right)\right), \tag {2}
+$$
+
+where  $x_0$  is the image sample,  $x_{T}$  is the Gaussian sample, and  $x_{t}(0 < t < T)$  is the middle state of diffusion. The terms  $\mu_{\theta}$  and  $\Sigma_{\theta}$  are estimated by a denoising network  $\epsilon_{\theta}(x_t,t)$  which takes  $x_{t}$  and  $t$  as input. By  $\epsilon_{\theta}$ , an image sample  $x_0$  can be generated from a Gaussian sample  $x_{T}$  following Eq. (1).
+
+Text-to-image (T2I) diffusion models further extend the diffusion process by guiding it with a textual prompt  $y$  [4, 15, 35]. Specifically,  $\epsilon_{\theta}(x_t,t)$  is modified to take  $y$  as an additional input, resulting in  $\epsilon_{\theta}(x_t,y,t)$ . The network  $\epsilon_{\theta}(x_t,y,t)$  uses a cross-attention module to select information from the textual prompt to guide the diffusion process. In cross attention, each token is transformed into key  $(K)$  space and value  $(V)$  space, while the image is transformed into query  $(Q)$  space. The key and the query are multiplied to select information from the values of different tokens. With cross attention, T2I models can generate images that adhere to the provided text prompts.
+
+# 2.2. Concept Removals
+
+In this subsection, we revisit representative concept removal methods.
+
+Fine-tuning-based methods. Fine-tuning is the most common framework for concept removals. The objective for the fine-tuning-based algorithms can be summarized as
+
+$$
+\min  _ {\theta} L = L _ {\mathrm {r m}} + \lambda L _ {\mathrm {r e g}}, \tag {3}
+$$
+
+where  $L_{\mathrm{rm}}$  is the term for changing the output of unwanted concept, and  $L_{\mathrm{reg}}$  is the regularization term to ensure that the fine-tuning will not influence other benign concepts and maintain the generation quality. The term  $\theta$  is the parameter to fine-tune. The methods can be solved by two types of solutions:
+
+- Gradient descent. This solution [7, 16, 18, 23] focuses on the final output of  $\epsilon_{\theta}(x_t,y,t)$ , modifying the model in an end-to-end way. The term  $L_{\mathrm{rm}}$  changes the output of  $\epsilon_{\theta}(x_t,c_u,t)$  where  $c_{u}$  is unwanted concepts, while  $L_{\mathrm{reg}}$  maintains the output of benign concepts  $c_b$ .  
+- Closed-form solution. Modifying the intermediate states of linear components (such as cross-attention weights [8, 22] and MLP layers [42]) instead of the final output of  $\epsilon_{\theta}(x_t, y_c, t)$ , can be solved in a closed-form solution. This can accelerate the fine-tuning process remarkably.
+
+Inference-time methods. Inference-time methods such as negative prompt [32], SLD [36], and SEGA [3] change the generation algorithm to remove concepts in the inference process, which can skip fine-tuning operations. They estimate the influence of unwanted concepts and remove them in inference. However, although these methods can skip the fine-tuning process, there is also a risk of being disabled in open-sourced models, which may slow down the inference.
+
+# 3. Six-CD: a Comprehensive and Effective Dataset
+
+In this section, we first propose a new dataset that encompasses a comprehensive set of categories of unwanted con
+
+cepts. Then we discuss the issue of ineffectiveness in general prompts and present the solution to filter the dataset, thereby increasing its effectiveness.
+
+# 3.1. Six Categories of Unwanted Concepts
+
+As mentioned in Sec. 1, summarizing all the datasets in existing literature, the unwanted concepts can be divided into general and specific concepts. The general concepts contain harmful concepts and nudity concepts, while the specific concepts contain identities of celebrities, copyrighted characters, objects, and art styles. However, existing literature focuses on only a few categories for evaluation, lacking systematic comparisons among the methods in general and specific concepts. To address this, we propose a new dataset, Six-CD, to evaluate concept removals comprehensively.
+
+For the general concepts, Six-CD first collects the malicious prompts from four different NSFW resources, which include I2P [36], MMA [43], jatman/stable-diffusion-prompts-stats-full-uncensored (SD-uncensored) [13], and Unsafe Diffusion (UD) [27]. Then, it divides the NSFW data into harmful and nudity concepts. Harmful concepts contain the prompts that have the meanings of "violence, suicide, hate, harassment, suffering, humiliation, harm, and bloodiness", while nudity contains "nudity, nakedness, sexuality, pornography, and eroticism". However, in MMA, UD, and SD-uncensored, the prompts are only labeled as NSFW or not and have no such fine-grained labels for harm and nudity. Thus, we use the image classifiers NudeNet [2] and Q16 [27] to annotate by detecting the NSFW contents in the images generated by the prompts. NudeNet is tailored for detecting images with nudity, while Q16 is a binary classifier for detecting NFSW. To annotate the fine-grained labels, i.e., harm and nudity, we first use NudeNet to find the prompts of nudity from the collected resources<sup>1</sup>. Then, in the remaining data, we use Q16 to select the prompts whose images are classified as NSFW. Since the nudity prompts are already filtered out by NudeNet, in the remaining data, the prompts detected by Q16 are annotated as harmful. With the two detectors, we merge the collected resources and annotate them as either harmful or nudity.
+
+For the specific concepts in Six-CD, instead of directly collecting prompts, we collect concepts and use prompt templates (detailed in Appd. A.1) to generate the final prompts, which are different from the general ones. The concepts are collected as follows:
+
+- Celebrity. Celebrities can evaluate the ability to remove identity. We select the identities of celebrities from CPDM [24]. To assist the evaluation, we use a celebrity detector, GCD [25]. we choose the celebrities that can be
+
+![](images/5f3fdef1887df2868e0e5bd0c4c975835ee2f6fd076e25d91d796ce3de310fc8.jpg)  
+Figure 1. Effectiveness of I2P prompts. Most of the prompts have low effectiveness. Results from [36].
+
+both generated by SD and recognized by GCD.
+
+- Copyrighted characters. The copyrighted characters are important IP resources for companies. We use the character concepts in CPDM and the high-frequency copyrighted characters from FiveThirtyEight Comic Characters Dataset [1].  
+- Objects. Objects can be used to evaluate the performance of removal on non-humanoid concepts. We randomly sample from a subset from the classes of ImageNet [5].  
+- Art style. The art styles can evaluate the removal performance of a global feature instead of a local feature. We use the art styles from [22].
+
+For the two general categories, we provide 6,326 prompts for harm concept and 4,518 effective prompts for nudity concept. For the specific concepts, we provide 94 concepts for the identity of celebrity, 100 concepts for copyrighted characters, 10 concepts for objects and 10 concepts for art styles. Four templates are used to construct the prompt for each specific concept. Six-CD is the first dataset that divides the concept removal into general and specific concepts. Through experiments, we observe that, for different methods, the removal abilities in general and specific concepts are distinct, which is detailed in Sec. 5.1. Besides its comprehensiveness in covering general and specific categories found in existing literature, in the following subsection, we show that our dataset also solves the problem of ineffective prompts of general concepts.
+
+# 3.2. Ineffective Prompts of General Concepts in Existing Datasets
+
+The prompts for general concepts in existing dataset do not consistently generate malicious content for each random seed according to [36] and our observation below. In this subsection, we discuss this phenomenon in general concepts and identify two potential problems it may introduce.
+
+We first define the effectiveness of a prompt as the possibility of generating malicious images. To assess this, we
+
+![](images/c8a8662863c0c0805e0a90f364c6dcc077de6afccb53e12337b83d7f2a04eeeb.jpg)  
+Figure 2. Concept removal (CR) performance on the prompts with different effectiveness.
+
+Table 2. Percentage of removed unwanted concepts between high effective and all effectiveness. (%)  
+
+<table><tr><td></td><td>NEG</td><td>ESD</td><td>SPM</td><td>SDD</td><td>FMN</td><td>UCE</td><td>EMCID</td><td>SLD</td><td>SEGA</td><td>Corr</td></tr><tr><td>Harm</td><td>40.9</td><td>63.6</td><td>98.9</td><td>24.8</td><td>95.6</td><td>77.6</td><td>98.9</td><td>27.3</td><td>23.7</td><td rowspan="2">0.977</td></tr><tr><td>Harm-EF</td><td>56.7</td><td>67.3</td><td>99.9</td><td>27.8</td><td>97.4</td><td>67.8</td><td>98.6</td><td>38.1</td><td>22.9</td></tr><tr><td>Nudity</td><td>22.3</td><td>17.9</td><td>81.0</td><td>11.2</td><td>93.6</td><td>14.9</td><td>98.3</td><td>14.6</td><td>38.8</td><td rowspan="2">0.984</td></tr><tr><td>Nudity-EF</td><td>11.0</td><td>16.0</td><td>88.9</td><td>4.2</td><td>92.6</td><td>12.3</td><td>97.2</td><td>16.3</td><td>58.4</td></tr></table>
+
+Table 3. Examples of Dual-Version Dataset for specific concepts. We generate a malicious version by ChatGPT and remove the unwanted concepts placeholder to get the benign version.  
+
+<table><tr><td>Category</td><td>Example of malicious version</td><td>Example of benign version</td></tr><tr><td>Celeb. &amp; 
+Copyrighted</td><td>{celebrity} is dancing in the rain.</td><td>dancing in the rain.</td></tr><tr><td>Object</td><td>{object}, football, grass, house, tree, dog</td><td>football, grass, house, tree, dog</td></tr><tr><td>Art style</td><td>A beautiful snow-covered mountain with 
+sunshine lighting it in the style of {art style}</td><td>A beautiful snow-covered moun-
+tain with sunshine lighting it</td></tr></table>
+
+generate  $N$  images for a prompt using different random seeds. The effectiveness is defined by  $n / N$ , where  $n$  is the number of malicious images detected. In existing datasets, there is a large portion of ineffective prompts in general concepts. Taking I2P [36] as an example, which is the most well-used dataset for harmful and nudity concepts in existing literature [3, 7, 8, 16, 22, 23, 36, 42], most of the prompts have low effectiveness as shown in Fig. 1. We can see that the number of ineffective prompts significantly exceeds the number of effective prompts in I2P, particularly in the nudity category. The specific concepts usually do not have the problem of low effectiveness because they contain the specific and definitive for the unwanted concepts. Thus, in this subsection, we focus on general concepts.
+
+Limitations. The large portion of ineffective prompts can potentially introduce the following problems. First, evaluating the ineffective prompts is in low efficiency. For example, we test different concept removal methods on SD for nudity concepts in Fig. 2. On the vanilla SD without concept removal (i.e., No CR in Fig. 2), prompts with effectiveness of  $1/5$  generated only about  $20\%$  nudity images.
+
+It means that  $80\%$  of the generated images by these prompts are non-nudity images, while evaluating on non-nudity images is meaningless. Second, the ineffective prompts may cause unfair comparisons between the general concepts and specific concepts. Unlike general concepts, the specific concepts do not have the problem of ineffective prompts. When the model builder has to remove both general and specific concepts, the ineffective prompts may falsely induce the builder to put less weight on the general concepts.
+
+High-effectiveness subsets. Therefore, in addition to harm and nudity concepts, we provide additional subsets of high-effectiveness prompts and name them as harm-  $EF$  and nudity-  $EF$ . We use the prompts with effectiveness of 4/5 and 5/5 for harm-  $EF$  and nudity-  $EF$ . Harm-  $EF$  contains 991 prompts, and nudity-  $EF$  contains 1,539 prompts. In Table 2 and Fig. 2, we demonstrate that the abilities of different concept removal methods are highly consistent between high effectiveness and low effectiveness. Thus, it is reasonable to evaluate on high-effectiveness prompts in order to reduce computation, which is also more fair. Specifically, in Table 2, we use the percentage of removed unwanted concepts to measure the ability of different methods, which is defined as
+
+$$
+p _ {\mathrm {r m}} = 1 - \frac {n _ {\text {a f t e r}}}{n _ {\text {b e f o r e}}}, \tag {4}
+$$
+
+where  $n_{\mathrm{before}}$  is the number of images containing unwanted concepts before concept removal, while  $n_{\mathrm{after}}$  is the number of images containing unwanted concepts after concept removal. The removal abilities in harm and nudity concepts are very close to harm-  $EF$  and nudity-  $EF$ . The Pearson correlation coefficient is as high as 0.977 (between harm and harm-  $EF$ ) and 0.984 (between nudity and nudity-  $EF$ ).
+
+In summary, Six-CD provides two choices to evaluate on the general concepts. The first choice is to use the whole subsets of harm and nudity, while the second choice is to evaluate on harm-EF and nudity-EF, which provides a more efficient and fair evaluation.
+
+# 4. In-prompt Retainability
+
+Concept removals should not hurt the generation ability of the benign contents, which is referred to as retainability. In this section, we show the lack of evaluation for retainability on the benign parts of the prompts containing the unwanted concepts and propose a new metric for this retainability.
+
+Lack of in-prompt retainability. Existing literature [24, 45] only considers the retainability of totally benign concepts. The benign prompts do not contain any unwanted concept, and concept removal should not influence the generation of them. Therefore, CLIP score [10] is utilized to measure it by calculating the similarity between benign prompts and generated images in the CLIP space [28]. However, for the prompts containing unwanted concepts,
+
+![](images/1ad7c80faac9de60e308487ea35a535ffca25bea4ba81bca07217cbc58ad40c2.jpg)  
+NO CR  
+ironman removed  
+Figure 3. Concept removal example of the prompt: "At night, ironman with his armor on is watching fireworks by the lake". Ironman is removed by SDD.
+
+![](images/87b1de8ea1f3d9fe8a7adf39cab04b716b816c699eeb5310c2033f3b2365bc66.jpg)
+
+the retainability to guarantee the generation of the benign part of them is also important, which is called "in-prompt retainability" in our benchmark. As shown in Fig. 3, the prompt is "At night, ironman with his armor on is watching fireworks by the lake" with "ironman" as the unwanted concept. Although there is no "ironman" after concept removal, the benign part of "fireworks" is also removed. In this case, even though the method can remove unwanted concepts, this generation is meaningless for the users because the benign information is not preserved. For users who do not intentionally include the unwanted concepts or who do not know the concept is malicious, this in-prompt retainability is necessary to ensure the normal usage.
+
+New metric. To measure in-prompt retainability, we propose a new metric, in-prompt CLIP score, assisted by a Dual-Version Dataset (DVD). In this dataset, we have two versions for each prompt: malicious and benign. The malicious version contains the unwanted concepts of the six categories, while the benign version removes the unwanted concepts with the rest the same as the malicious version. In in-prompt CLIP score, we first generate the images with concept removals using the malicious version and then calculate the cosine similarity of CLIP embeddings between these generated images and the corresponding benign version prompts. Thus, we can measure the similarity between the generated image and the benign part of the prompt. To distinguish it from the original CLIP score, we refer to the original CLIP score as the out-prompt CLIP score.
+
+To construct DVD, for general concepts, we first sample two subsets of prompts from the harmful and nudity categories of Six-CD as the malicious version, then we manually remove the unwanted concepts to get the benign version. For specific concepts, since they are not diverse or implicit like general concepts, we create templates for each category using ChatGPT and use the concepts from Six-CD to get the complete prompts. We show the examples of templates in DVD in Table 3. The entire dataset is in Appd. A.2. To validate the effectiveness of the metric, we conduct human evaluation in Appd. D.1. The results demonstrate that the metric is highly consistent with human preference.
+
+In summary, to measure the in-prompt retainability, we propose the in-prompt CLIP score. It leverages a malicious-
+
+version and a benign-version prompt to measure the similarity between the images after concept removal and the benign part of the prompt.
+
+# 5. Experiments
+
+In this section, we conduct experiments to benchmark the performance of 10 methods in removing single and multiple concepts and the retainability with both in-prompt and out-prompt CLIP scores. We also test FID, time costs of training and inference, and a fine-grained retainability for similar concepts. Due to space limitations, these experiments are in Appd D. Also, we report the results of SD v1.4 in this section and the results of other models are in Appd D.
+
+Experimental settings. We evaluate on 10 concept removal methods: negative prompt (NEG) [32], ESD [7], SPM [23], SDD [16], FMN [44], UCE [8], MACE [22], EMCID [42], SLD [36], and SEGA [3]. The details on the baseline settings can be found in Appd. B. The evaluated datasets are Six-CD and DVD, which are detailed in Appd. A. Following the conclusions in Sec. 3.2, we use harm-EF and nudity-EF for all the experiments in this section. All experiments use one GPU (A5000 or A6000).
+
+Detection metrics. We use the detection rate of Q16 and NudeNet for harmful and nudity concepts. We use the classification accuracy of GCD as the detection rate for celebrity concepts, and we train two classifiers based on ResNet-50 [9] and use the accuracy as the detection rate for copyrighted characters and objects. For the art style concept, the detection is not a simple binary problem. In existing literature [22-24, 44], CLIP score,  $S_{\mathrm{CLIP}}$ , is used to measure the presence of an art style on a continuous scale, assessing the similarity between generated images and art styles. Following them, we use  $S_{\mathrm{CLIP}}$  and normalize its range by  $\tilde{S}_{\mathrm{CLIP}} = (S_{\mathrm{CLIP}} - \min(S_{\mathrm{CLIP}})) / (\max(S_{\mathrm{CLIP}}) - \min(S_{\mathrm{CLIP}}))$  for a better comparison with other categories.
+
+# 5.1. Evaluation on Removal Ability
+
+In this subsection, we test the removal ability of different methods on Six-CD. In Fig. 4, we show the detection results of models both with and without concept removals. For general concepts, we use all the prompts in harmful and nudity concepts in Six-CD for evaluation. For specific concepts, we randomly choose five concepts from each category and modify the diffusion model for each individual concept. We show the averaged results of 5 concepts of each category in Fig. 4. (The table with error bar for Fig. 4 can be found in Appd. D.2.) We highlight the main observations as follows.
+
+Observation 1: General concepts are harder to remove. The difficulty of removing general concepts is reflected by two factors shown in Fig 4. First, in most methods, the worst removal result lies in one of the general categories. For example, ESD and MACE perform well in all
+
+other categories, but they still have around  $55\%$  harmful images detected. Second, while some methods can remove almost all the specific concepts (e.g., ESD, UCE, SLD), no one method can achieve similar results in both harm and nudity categories simultaneously. For general concepts, on the one hand, they are hard to trigger (i.e. low effectiveness). On the other hand, it is harder to remove them than specific concepts. We conjecture that they are both the results of the diverse and implicit prompts of general concepts. Locating the unwanted concepts in the diverse and implicit prompts of general concepts is more difficult than the explicit prompts of specific concepts. Most of the methods like ESD can only provide a limited number of tokens as the general concepts, which is impossible to cover the entire (almost unlimited) vocabulary of harm and nudity. Thus, it leads to difficulty in removing general concepts.
+
+Observation 2: Removal ability is consistent within general concepts and within specific categories. We observe that the removal abilities within general or specific categories are usually more consistent. For example, SLD and FMN perform well in specific concepts, but the ability to remove general concepts is worse. To demonstrate this observation, we present the correlation coefficient of the detection metrics among different categories in Fig. 5. From Fig. 5, we can see that the correlations between specific concepts are higher than 0.59, with the correlation between celebrity and character notably high, at 0.94. The correlation between general concepts is also as high as 0.65. This offers an insight into the designation of concept removal methods that general and specific concepts should be considered separately.
+
+# 5.2. Removal Ability on Multiple Concepts
+
+In Sec. 5.1, we evaluate the ability to remove a single concept from one model. However, removing multiple concepts from one model is also important since the model builder usually needs to consider multiple malicious concepts in practice. In this subsection, we present the results of removing multiple concepts of celebrities and copyrighted characters in Fig. 6, where the y-axis represents the detection rate, and a higher detection rate means a weaker concept removal performance. We have two observations from Fig. 6.
+
+Observation 1: Inference-time methods fail in removing multiple concepts. As shown in Fig. 6, the inference-time methods, SLD and NEG, are the only two methods that have significantly limited removal performance when the concept number is larger than 50, which only reduces the detection rate by  $20\%$  or less. To remove the multiple concepts in inference time, they have to encode the string containing all the concepts in the embeddings of one single prompt. This will exceed the capacity of the text encoder of T2I diffusion models and lead to failed removal. Another inference-time method, SEGA, is not reported in Fig. 6 due
+
+![](images/7ddc365e0d2702dfb1165ce44bc08ace002f3e00706682b06ee3df244d451943.jpg)  
+Figure 4. Removal ability on Six-CD. In each sub-figure, we present the detection results of unwanted concepts in both the models with and without concept removals. The range of all the six values is [0,1]. Smaller values indicate that less unwanted concepts are detected, i.e. better removal. G1 and G2 are harm-EF and nudity-EF concepts, while S1, S2, S3 and S4 are celebrity, character, object and art style.
+
+![](images/e6b4f9fd9ba6540935fd33b7f7f0ebc824ab9fcefb3378fe96c1b890c67b027f.jpg)  
+Figure 5. Correlation coefficient of removal performance on six data categories.
+
+to its catastrophic inference time when the concept number is increased to 50. This implies that the strategy of processing each concept separately during inference is impractical.
+
+Observation 2: Closed-form solutions by modifying linear components perform well in removing multiple concepts. The best two methods in Fig. 6a and Fig. 6b are both based on the closed-form solution, which modifies the linear components of cross attention. This is possibly because combining multiple concepts in the linear components is easier than in other non-linear parts.
+
+# 5.3. In-prompt and Out-prompt Retainability
+
+We evaluate the generation ability on benign concepts using both in-prompt and out-prompt CLIP scores. In Fig. 7, we
+
+use DVD to test the in-prompt CLIP score and a subset with benign prompts from LAION [37] to test out-prompt CLIP score. The observations as follows.
+
+Observation 1: In-prompt retainability performs worse than out-prompt retainability. As shown in Fig. 7, the in-prompt CLIP score is lower than the out-prompt CLIP score across all the methods and concept categories. This indicates that the ability to generate benign parts in prompts containing malicious concepts is more negatively affected than the ability to generate totally benign prompts. As mentioned in Sec. 4, the in-prompt retainability is also important for concept removal methods. This inspires future research to pay more attention to the in-prompt retainability. Remark. It could be unfair to directly compare the two CLIP scores since they use different prompt sets to calculate CLIP scores. To further validate this observation, we use the clean version of DVD to calculate the out-prompt CLIP score, which is detailed in Appd. D.3. By comparing it with the in-prompt CLIP score in Appd. D.3, we have observed a consistent phenomenon with this subsection.
+
+Observation 2: Auxiliary semantic information in MACE (Fig. 7g) may hurt the generation on benign concepts. MACE has the most significant decrease in the generation ability of benign concepts for both in-prompt and out-prompt CLIP scores. We conjecture that this is because it introduces auxiliary semantic information to help locate the unwanted concepts in the image. In other methods, the unwanted concepts are usually located by the semantic understanding ability of the T2I model itself. In contrast,
+
+![](images/a5d64223235972fafc877ec1758d1b3ae033cac5d1c7d1c262f86b6f2dd43c42.jpg)  
+(a) Celebrity
+
+![](images/f3d1443a7d24269896e363541688c346307daf628affba5589c3860b62b571b2.jpg)  
+(b) Copyrighted characters
+
+![](images/b944d48ca20e7ffa160b2285a843dc8b16df00b09e90ae99db440a22a487f722.jpg)  
+(a) NEG
+
+![](images/19a87723d288a62a5fd2695fa21a6cedc26011f2ab09c4f0fd8f37762bcd97c8.jpg)  
+(b) ESD
+
+![](images/363cde74017eb92a28912f424b314834362cc1a4e939f4ec9ccee86e5b8384e5.jpg)  
+(c) SPM
+
+![](images/299db817f9401300a9b45ea440479838891b67830126357154c1089e5305fd65.jpg)  
+Figure 6. Removal ability on multiple concepts
+
+![](images/c0f38fcbffd8c79370fd6bcee7377c5fd4f36ddc8a9fdfa8cc1a22db194af946.jpg)  
+(e) FMN
+
+![](images/0614252b091d5fe1f58ca4db93471406dab4f59a2668f356a4595a712f209e70.jpg)  
+(f) UCE
+
+![](images/a24fabf24dbbdb08ce3c99fbf769814179a713bdca68eaee51ae78ccd8227391.jpg)  
+(g) MACE
+
+![](images/debd13ddd2b714f3e825e6052eecb916c51bca6ba03b51e56ce971d4f94772a6.jpg)  
+(h) EMCID
+
+![](images/95dedda416ff55074e5ee8ab412d29a08ff4cc208807325be0d7db6b110d84f2.jpg)  
+(d) SDD  
+(i) SLD
+
+![](images/1856dd8da1267124d798bf0d2479483fb2f0908c865cf7a27bf7457a69e926ee.jpg)  
+(j) SEGA  
+Figure 7. In-prompt retainability vs. out-prompt retainability
+
+MACE incorporates the segmentation results of GroundedSAM [17, 21] to locate the image area of unwanted concepts. It focuses on optimizing this area and overlooks other areas of the image. This may lead to worse retainability in other areas. Another piece of evidence is that when we do not include segmentation in removing the art style concepts by MACE (since art style is a global feature), it has good in-prompt and out-prompt CLIP scores.
+
+# 6. Conclusion and Ethical Statement
+
+In this work, we address the lack of a systematic benchmark for concept removal methods by introducing a comprehensive and effective dataset and a new evaluation metric. Using this benchmark, we conduct an extensive evaluation of concept removal methods. Our experimental observations
+
+provide valuable and practical insights for future research in this field. While our benchmark may have a limitation in the inconvenient detection metric for art styles (using the CLIP score for art styles, instead of the detection rate from a classifier like other categories), it still offers a thorough and practical evaluation across the various method settings.
+
+Ethical statement. This work provides a comprehensive evaluation framework for concept removal, which is targeted to mitigate the potential malicious use of text-to-image diffusion models. Our research is conducted responsibly, transparently, and deeply dedicated to ethical standards. Despite involving the generation of sensitive content such as nudity and violence, it is strictly for research purposes and does not intend to produce or promote inappropriate material. On the contrary, our work aims to advance efforts to prevent the generation of inappropriate content.
+
+# Acknowledgement
+
+Jie Ren, Kangrui Chen, Yingqian Cui, Shenglai Zeng, and Jiliang Tang are supported by the National Science Foundation (NSF) under grant numbers CNS2321416, IIS2212032, IIS2212144, IOS2107215, DUE2234015, CNS2246050, DRL2405483 and IOS2035472, the Army Research Office (ARO) under grant number W911NF-21-1-0198, Amazon Faculty Award, JP Morgan Faculty Award, Meta, Microsoft and SNAP.
+
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2025/Six-CD_ Benchmarking Concept Removals for Text-to-image Diffusion Models/images.zip

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+# Sketch Down the FLOPs: Towards Efficient Networks for Human Sketch
+
+Aneeshan Sain<sup>1</sup> Subhajit Maity<sup>2*</sup> Pinaki Nath Chowdhury<sup>1</sup> Shubhadeep Koley<sup>1</sup> Ayan Kumar Bhunia<sup>1</sup> Yi-Zhe Song<sup>1</sup>
+
+$^{1}$  SketchX, CVSSP, University of Surrey, United Kingdom.
+
+$^{2}$  Department of Computer Science, University of Central Florida, United States.
+
+{a.sain, p.chowdhury, s.koley, a.bhunia, y song}@surrey.ac.uk; Subhajit@ucf.edu
+
+# Abstract
+
+As sketch research has collectively matured over time, its adaptation for at-mass commercialisation emerges on the immediate horizon. Despite an already mature research endeavour for photos, there is no research on the efficient inference specifically designed for sketch data. In this paper, we first demonstrate existing state-of-the-art efficient light-weight models designed for photos do not work on sketches. We then propose two sketch-specific components which work in a plug-n-play manner on any photo efficient network to adapt them to work on sketch data. We specifically chose fine-grained sketch-based image retrieval (FG-SBIR) as a demonstrator as the most recognised sketch problem with immediate commercial value. Technically speaking, we first propose a cross-modal knowledge distillation network to transfer existing photo efficient networks to be compatible with sketch, which brings down number of FLOPs and model parameters by  $97.96\%$  percent and  $84.89\%$  respectively. We then exploit the abstract trait of sketch to introduce a RL-based canvas selector that dynamically adjusts to the abstraction level which further cuts down number of FLOPs by two thirds. The end result is an overall reduction of  $99.37\%$  of FLOPs (from 40.18G to 0.254G) when compared with a full network, while retaining the accuracy  $(33.03\%)$  vs  $32.77\%$  - finally making an efficient network for the sparse sketch data that exhibit even fewer FLOPs than the best photo counterpart.
+
+# 1. Introduction
+
+A significant movement in the late computer vision literature has been that of model efficiency. This effort has been largely driven by the on-the-edge deployments of vision models. With great strides made on networks specifically tackling photo data (MobileNet [54], EfficientNet [63], etc), there however has been surprisingly no work targeting human sketches [72]. This is despite the abundance of work specifically addressing sketch data [47] and its unique traits:
+
+![](images/13cb94a39c9a758370bf172a5b52d260950fde46c6c3b4a2912aa0047ab2c5d4.jpg)  
+Figure 1. Our SketchyNetV1 compresses existing heavy FG-SBIR networks to deliver smaller models. Further enhanced via a canvas selector module our SketchyNetV2 model minimises sketch-resolution dynamically to reduce FLOPs.
+
+sequential [22], abstract [60], or stroke-wise [10], style-diversity [51], and data-scarcity [6, 20, 43]. This is particularly disappointing for the problem of fine-grained sketch-based image retrieval (FG-SBIR), which is perhaps the single-most studied sketch task [2, 7, 9, 13, 40, 43, 53, 75] that has already matured for at-mass commercial adoption, and is our problem of choice in this paper.
+
+One would think that state-of-the-art models designed for photos would work as-is for sketches, treating sketch data as raster images (which sketch is not). As our first contribution, we preempt this thought via a pilot study to prove its false nature. In particular, we borrow MobileNetv2 [54] as a backbone network to construct a typical triplet loss based network for FG-SBIR. Results show a reduction of almost  $37\%$  (relative) in retrieval accuracy when compared with a typical VGG-16 backbone [57]. The focus of this paper is however not to design entirely new sketch-specific efficient networks from scratch – lots of good efficient photo networks already exist. Our goal instead is to adapt existing photo networks to work with sketch, by introducing generic sketch-specific designs that work in a plug-n-play manner.
+
+We first tackle the problem highlighted in the said pilot study – to make existing photo efficient networks perform on the same level as large networks on FG-SBIR. We argue the reason behind why the likes of MobileNetV2 did not work off-the-shelf is that the limited set of parameters could not accommodate the fine-grained nature of sketches (i.e.,
+
+sketches are highly expressive in capturing fine-grained visual details [72]) for sketch and photo matching. For that, we introduce a knowledge distillation (KD) paradigm [48] to adapt this sketch trait onto efficient photo networks. The core idea is to induce strong semantic knowledge between a sketch and its photo, in the embedding space of a student, from a deep and high performing teacher. This particularly helps the efficient model to achieve on par performance with the deep variant without having a large parameter size. However, ours being a cross-modal retrieval, naively adapting standard KD paradigms involving logit distillation [3] would be sub-optimal. We therefore aim to preserve cross-modal pairwise distances among instances, and in turn the structural consistency of the teacher's discriminative embedding space in the student. The result is already an efficient FG-SBIR model (which we term SketchyNetV1) that reduces the number of FLOPs from 40.18G (VGG-16 based model[51]) to 0.833G (our MobileNetV2-based) – a roughly 48 times reduction (Fig. 1 left).
+
+This abstract nature of human sketch [16] can also be exploited, to further reduce the FLOPs. The hypothesis is that since sketches are essentially abstract depictions of images, they should carry a similar level of semantic information even when rendered at much lower resolutions, and that more abstract a sketch is the more information compact it is (i.e., can sustain even lower resolutions). For that, we conducted another pilot study (Sec. 3), where we show unlike photos, sketches can sustain retrieval accuracy with much lower resolutions (4% vs 15% at  $32 \times 32$ ), and 30% of those query sketches achieving perfect retrieval at full-resolution, when downsized to  $32 \times 32$  can still retrieve accurately (Fig. 2 right). This motivated us to design a canvas selector that can choose the right resolution on-the-fly to render a sketch before feeding to the network. This is thanks to another unique trait of sketch data - they come in vector format and can be freely rendered to any resolution without extra overhead. Accomplishing this however is nontrivial since this selection process of canvas-size involves a discrete decision, thus invoking non-differentiability. We thus leverage reinforcement learning [9] to bypass these issues and train an abstraction-aware canvas-size selector as a policy network for our model, which estimates the optimal canvas-size required for the input sketch. The FG-SBIR model, acting as a critic, calculates reward for the canvas selector, balancing between accuracy and FLOPs, that trains the policy network. With this further trait of sketches addressed, our final model (SketchyNetV2) was able to further reduce FLOPs by a factor of 3.28 (from 0.833G to 0.254G), while retaining a retrieval accuracy similar to the full model (33.03 vs 32.77), exactly as one would imagine sketch efficient networks to entail (sketches being sparse).
+
+In summary, our contributions are: (a) the first investigation towards efficient sketch networks from existing photo
+
+ones (b) a knowledge distillation framework specifically designed to cater to the fine-grained nature of sketches, (c) a canvas-size selector that caters to the abstract nature of sketches, which further reduces FLOPs by two-thirds. Extensive experiments show our method to perform at par with existing state-of-the-arts, while being superiorly efficient.
+
+# 2. Related Work
+
+Fine-grained SBIR: Compared to category-level SBIR [17, 19, 36, 52], Fine-Grained SBIR (FG-SBIR) focuses on retrieving a single photo instance from a category-specific gallery based on a query sketch. Introduced as a deep triplet-ranking Siamese network [75], FG-SBIR has evolved with attention-based modules [59], textual tags [58], hybrid cross-domain generation [42], hierarchical coattention [50], and various pre-training strategies like mixed modal jigsaw solving [44], reinforcement learning [6], and transformer-based knowledge distillation [53]. Addressing sketch-specific traits like style diversity [51], data scarcity [7], and sketch stroke redundancy [9], improvements have been made for enhanced retrieval [53]. Recently it was extended to scene-level (retrieve a scene-image, given a scene-sketch), employing cross-modal region associativity [13] and enhanced using text-queries [46]. However, sketch-specific computational efficiency has largely been ignored - which we address here in this paper.
+
+Towards Computational Efficiency: Addressing large-scale deployment, research emerging in computational efficiency [1], include network pruning [37], quantisation [21], binarisation [18], knowledge distillation [25], input-size optimisation [62], or their combinations [1]. Network pruning [23, 68] involves discovering and dropping low impact weights or channels of a pre-trained large network, while retaining its original accuracy. Contrarily, quantisation directly reduces the bit-width of parameter-values [21] and gradients [77], by replacing floating-point computations with faster and cheaper low-precision fixed-point numbers [34]. Its extreme version, binarisation [18], binarises weights and activations. Knowledge Distillation aims at transferring knowledge of a large pre-trained teacher network to a smaller student for cost-effective deployment. Existing techniques leverage output logits [3], hidden layers [48], attention-maps [76], or neuron selectivity pattern [28] of pre-trained teachers for the same. Self-distillation [4] employs the same network for both student and teacher models, to further reduce compute. Input-resolution optimisation on the other hand involves replacing a high-resolution input image with its down-scaled low-resolution version [62], to reduce overall compute [73], while retaining accuracy. Relevant works explored dynamic usage of high-resolution data [64] or patch proposals for strategic image-cropping [69], where the learnable resizer [62] operates on the original image resolution. All such
+
+Table 1. Performance & computational cost for various networks  
+
+<table><tr><td>Model</td><td>FLOPS</td><td>Parameters</td><td>Time (ms)</td><td>Acc@1</td></tr><tr><td>VGG-19 [57]</td><td>51.06G</td><td>20.02M</td><td>101</td><td>33.63</td></tr><tr><td>VGG-16 [57]</td><td>40.18G</td><td>14.71M</td><td>084</td><td>33.03</td></tr><tr><td>ResNet-101 [24]</td><td>20.50G</td><td>42.50M</td><td>155</td><td>21.77</td></tr><tr><td>DenseNet-201 [26]</td><td>11.40G</td><td>18.09M</td><td>335</td><td>23.62</td></tr><tr><td>ResNet-50 [24]</td><td>10.76G</td><td>23.51M</td><td>086</td><td>21.32</td></tr><tr><td>InceptionV3 [75]</td><td>07.72G</td><td>21.79M</td><td>134</td><td>24.27</td></tr><tr><td>ResNet-18 [24]</td><td>4.76G</td><td>11.18M</td><td>036</td><td>20.72</td></tr><tr><td>EfficientNet [63]</td><td>1.05G</td><td>04.01M</td><td>112</td><td>22.47</td></tr><tr><td>MobileNetV2 [54]</td><td>0.83G</td><td>02.22M</td><td>070</td><td>20.85</td></tr></table>
+
+methods however cater to compressing image-specific models, which if used off-the-shelf for FG-SBIR would fail to address the sparse manner in which sketches are represented [8]. We thus propose a sketch-specific light-weight FG-SBIR model, tackling sparsity in sketches.
+
+Reinforcement Learning in Vision (RL): Applying RL [29] to computer vision problems [33, 67] is commonplace of late. Whenever quantifying the goodness of the network's state is non-differentiable, like selecting which regions to crop in an image [31], RL comes in handy. In sketch community, RL has found use in retrieval [6, 7], modelling sketch abstraction [39, 40], designing competitive sketching agents [5] and as a stroke selector [9]. Here, we leverage RL for optimising a canvas-size selector for a computationally efficient retrieval model.
+
+# 3. Pilot Study
+
+Backbone Network for FG-SBIR: Amongst popular backbones used in recent FG-SBIR literature [6, 7, 50, 51], are VGG-16 [30] and Inception-V3 [75]. Others like ResNet18 [24] and EfficientNet [63], though cheaper and prevalent in vision [24] are rarely used in FG-SBIR. Exploring their potential in FG-SBIR, we train a baseline FG-SBIR model, plugging in popular ones as backbones for our study. Table 1 reports their parameter-count, FLOPs, time for feature-extraction per sample and Top-1 accuracy (Sec. 5) on standard QMUL-ShoeV2 dataset [75]. Despite scoring more than VGG-16 on image-classification [65], ResNet50 [24] performs poorly – indicating that modelling fine-grained sketch-photo association needs networks with higher FLOPs. Despite delivering better accuracies, heavier networks cost far more resources. We thus aim for a lighter model that achieves accuracy like a larger one.
+
+Dynamic Sketch-canvas-size: Unlike photos that hold pixel-dense information, sketches are sparse black and white lines. This begs the question, if a sketch rendered at a higher resolution with added computational burden would convey any extra semantic information than at a lower one. To answer this, we focus on vector-format of sketches [7], where every sketch vector  $s_v$  can be characterised as a sequence of points  $(v_1, v_2, \dots, v_{\mathrm{T}})$ , and rendered to any canvas-size  $(c)$  as a raster-image  $(s_r)$  via rasterisation  $\mathcal{R}^c(\cdot): s_v \to s_r^c$  where  $s_r^c \in \mathbb{R}^{c \times c \times 3}$ . A single baseline FG-SBIR model (VGG-16) is trained and tested on full-resolution images, and sketches rendered at varying
+
+![](images/2e9054e4b9b734386733cfe540dbcbb670b37b4422ac8e6b687c233bba54ab3a.jpg)  
+Figure 2. Pilot study for varying canvas-size (see text above).
+
+![](images/5b15e5befa59daae27edb06ff6dac5cfad0663005ac286bdaf13107c29d27f45.jpg)
+
+canvas-sizes from  $C = \{32 \times 32, \dots, 256 \times 256\}$ . Comparing sparse sketches versus photos, we train an equivalent fine-grained image-based image retrieval (FG-IBIR) where only the query against a positive photo is constructed using random augmentation [11] and resized to corresponding canvas-size  $c_i$ . Gallery photo-features for both are kept pre-computed. While FG-IBIR accuracy falls rapidly (Fig. 2 left), FG-SBIR stays relatively stable against decreasing canvas-sizes, as photos (unlike sketches) containing pixel-dense perfect information, lose a lot of it while down-scaling. Furthermore, positive accuracy of FG-SBIR at  $32 \times 32$ , shows some sketches to hold sufficient semantic information for retrieval even at minimal canvas-size. Fig. 2 (right) shows overall QMUL-ShoeV2[75] statistics where each bar represents the smallest canvas-size, at which bar-height percentage of sketches achieve perfect retrieval (taking total sketches achieving perfect retrieval at  $256 \times 256$  as  $100\%$ ). This infers that every sketch has its own optimal canvas, and fixing it (Fig. 2 left), for the entire dataset would always be sub-optimal. Moreover, the optimal canvas-size for a sketch, depends on its extent of sparsity, for which neither hard-ground-truth exists, nor is it knowable from the user's end. Finally, brute force discovery at every size being infeasible during inference, motivates us to design a learnable adaptive canvas-size selector for sketches.
+
+# 4. Methodology
+
+Overview: Our pilot study motivates us to extend a standard FG-SBIR framework towards computational efficiency by first introducing SketchyNetV1 via knowledge distillation, and then taking it further to SketchyNetV2 via dynamic sketch canvas-size selection. Importantly, these are done without hurting the original performance of large-scale slower baseline model. In particular, there are two phases of improvement for computational efficiency. Firstly, we train a teacher model  $F_{T}$  as a standard baseline FG-SBIR model (Sec. 3). Once trained, its rich semantic knowledge is transferred to a smaller student network  $F_{st}$  via a knowledge distillation (KD) paradigm, which we name as SketchyNetV1. Next, we train a canvas-size selector that adaptively decides optimal canvas-size or resolution per sketch for SketchyNetV2 that would be sufficient to preserve the retrieval performance while reducing the number of FLOP operations in feature extraction significantly.
+
+Baseline FG-SBIR model: Keeping aside complex pretraining [44] or joint-training [7], we focus on a simple
+
+![](images/cacf7a15e1c70f3a7b612e9ee79238275db7e1d710603e601cd6b0d7674ca74a.jpg)  
+Figure 3. Two stage framework. (Left) SketchyNetV1: A smaller student network  $(F_{st})$  is trained from a larger pre-trained teacher  $(F_T)$  via KD (§4.1). (Right) We progress to SketchyNetV2 by training a canvas-size selector directed by objectives of increasing performance and reducing compute. It takes sketch as a vector  $(s_v)$  and aims to predict an optimal canvas-size at which the sketch is rasterised  $(s_r)$ .  $s_r$  when processed by  $F_{st}$  minimises overall FLOPS, while retaining accuracy of corresponding full-resolution sketch-image.
+
+![](images/1989c4a8b181a9d84247e7176b167e34eaa9155836d5351d6ec01a09df533f8f.jpg)
+
+triple-branch state-of-the-art Siamese network [75] which remains a strong baseline so far [7, 50, 51]. A VGG-16 [30] pre-trained on ImageNet [49] acts as the shared backbone for each branch. Given an input image  $I$ , a  $d$  dimensional feature embedding is extracted from the backbone network  $\mathcal{F}$  using global average pooling followed by  $l_{2}$  normalisation as  $f_{I} \in \mathbb{R}^{d}$ . The model is trained on triplets comprising features of an anchor sketch  $(f_{s})$ , its matching positive  $(f_{p})$  photo and a random non-matching negative photo  $(f_{n})$ , via a triplet loss [70]. Triplet loss  $(\mathcal{L}_{\mathrm{Tri}})$  aims to minimise the distance between sketch and positive photo, while maximising the same from its negative (n). With  $\delta(a, b) = ||a - b||^2$ , as a distance function and a margin  $m > 0$ , we have:
+
+$$
+\mathcal {L} _ {\mathrm {T r i}} = \max  \left\{0, m + \delta \left(f _ {s}, f _ {p}\right) - \delta \left(f _ {s}, f _ {n}\right) \right\} \tag {1}
+$$
+
+# 4.1. SketchyNetV1: Smaller Model via KD
+
+Based on our pilot study (Sec. 3), if we naively train from an ImageNet pre-trained standard smaller network (e.g. MobileNetV2 [54] - usually popular for edge devices), with simple supervised triplet loss (Eq.1) it can hardly reach the accuracy (Table 1) obtained by a large network like VGG-16. Therefore apart from training via a supervised loss on the sketch-positive-negative triplet  $(\mathcal{L}_{\mathrm{Tri}}^{st})$  as in Eq.1), we aim to use the pre-trained larger teacher (e.g. VGG-16) for additional supervision. Accordingly, we adhere to Knowledge Distillation (KD) paradigm [48], a conventional strategy for model compression, to deliver a light-weight student model from the larger teacher network [48]. Applying KD to our FG-SBIR paradigm is however non-trivial. Unlike traditional KD methods, which often involve logit distillation for classification tasks, our scenario involves cross-modal retrieval. Here, the output is a continuous  $d$ -dimensional feature within a joint-embedding space. Furthermore, straightforward regression between teacher and student features for sketch and photo branches may encounter compatibility issues, given the disparity in the embedding spaces. Addressing this, if the dimensions of teacher and student embeddings differ, an additional feature transformation layer is necessary for alignment [48]. Overcoming these issues,
+
+we aim to distil the inter-feature distances from respective teacher networks to the student thus preserving structural orientation of features in the teacher's embedding space to that in the student, during KD (Fig. 3 (left)).
+
+Given features of sketch-positive-negative triplet of teacher  $(f_s^T, f_p^T, f_n^T)$ , we calculate the inter-feature Euclidean distances in the output representation space of teacher  $(F_T)$  using  $\delta(\cdot, \cdot)$  (Eq.1), as  $d_{sp}^T = \delta(f_s^T, f_p^T)$ ;  $d_{sn}^T = \delta(f_s^T, f_n)$  and  $d_{pn}^T = \delta(f_p^T, f_n^T)$ . Passing the same samples through the student, we similarly obtain  $d_{sp}^{st}$ ,  $d_{sn}^{st}$  and  $d_{pn}^{st}$  using  $(f_s^{st}, f_p^{st}, f_n^{st})$ . A smooth  $l_1$  loss distils the  $l_2$  distances from the teacher to the student. With  $\mathcal{L}_{\delta}$  as a Huber-loss [27], relational distillation loss for sketch-photo pair between teacher and student is given as,
+
+$$
+\mathcal {L} _ {\mathrm {R K D}} ^ {s p} = \mathcal {L} _ {\delta} \left(d _ {s p} ^ {T}, d _ {s p} ^ {s t}\right) \quad \text {w h e r e ,}
+$$
+
+$$
+\mathcal {L} _ {\delta} (a, b) = \left\{ \begin{array}{l l} \frac {1}{2} (a - b) ^ {2} & \text {i f} | a - b | <   \beta \\ \beta (| a - b | - \frac {1}{2} \beta) & \text {o t h e r w i s e} \end{array} \right. \tag {2}
+$$
+
+Similarly, we obtain  $\mathcal{L}_{\mathrm{RKD}}^{sn}$  and  $\mathcal{L}_{\mathrm{RKD}}^{pn}$ , to compute distillation loss,  $\mathcal{L}_{\mathrm{RKD}} = \mathcal{L}_{\mathrm{RKD}}^{sp} + \mathcal{L}_{\mathrm{RKD}}^{sn} + \mathcal{L}_{\mathrm{RKD}}^{pn}$ . With hyperparameter  $\lambda$ , overall student-training objective becomes:
+
+$$
+\mathcal {L} _ {\mathrm {t r n}} ^ {s t} = \lambda \mathcal {L} _ {\mathrm {T r i}} + (1 - \lambda) \mathcal {L} _ {\mathrm {R K D}} \tag {3}
+$$
+
+The student trains on varying sketch-canvas-sizes  $(C)$ , using their respective full resolution for teacher, to ensure scale-invariance as  $\mathcal{L}_{\mathrm{tm}}^{st*} = \frac{1}{4}\sum_{i=1}^{4}\mathcal{L}_{\mathrm{tm}}^{st(c_i)}$ . However, as optimal canvas-size varies across sketches (Fig. 2), we need a learnable canvas-size selector, dynamically predicting the optimal size for each sketch.
+
+# 4.2. SketchyNetV2: Adaptive canvas-size Selector
+
+Overview: Understanding that an input at a lower resolution, would incur lesser FLOPs on evaluation than a higher one, we upgrade SketchyNetV1 ( $F_{st}$ ) to a more computationally efficient SketchyNetV2 by introducing an adaptive canvas-size selector. It is designed in the vector modality as it is much cheaper [71] than its raster-image counterpart, and can dynamically encode the varying abstraction level of sketches. Furthermore, predicting the optimal canvas-size from vector modality, would make the corresponding rasterisation operation  $\mathcal{R}^c(\cdot)$  at lower sizes cheaper, besides reducing FLOPs in feature extraction. Taking sketch vector  $s_v$  as input,  $\psi_C$  predicts the probability  $p(c|s_v)$  of choosing one of  $K$
+
+discreet canvas-sizes from a set of  $C = \{32 \times 32, \dots, 256 \times 256\}$ .  $s_v$  is then rasterised to  $s_r^c \in \mathbb{R}^{c \times c \times 3}$  with the optimal canvas-size  $c$ , as  $\mathcal{R}^c(\cdot) : s_v \to s_r^c$ , and fed to  $F_{st}$  for retrieval.
+
+Selecting an optimal canvas-size however is an ill-posed problem. Firstly, there are no explicit labels representing the optimal canvas-size for a sketch. Secondly, annotating the optimal canvas-size for the whole dataset via brute-force iteration is computationally impractical. We therefore use the pre-trained  $F_{st}$  as a critic to guide the learning of sketch canvas-size selector via Reinforcement Learning [29] as rasterisation is a non-differentiable operation. There are two major objectives here: a) retain the original resolution accuracy and b) encourage the use of the lower resolution to improve the computational efficiency.
+
+Model: Any sequential network from RNN [17] or Transformer [35] families can be used to encode the vector-sketch  $s_v$ . To recap, sketch-vector  $(s_v)$  represents a sequence of points  $[v_1, v_2, \dots, v_{\mathrm{T}}]$ , where  $v_t = (x_t, y_t, q_t^1, q_t^2, q_t^3) \in \mathbb{R}^{T \times 5}$ ;  $\mathrm{T}$  is the sequence length,  $(x_t, y_t)$  denotes the absolute coordinates in a normalised  $c \times c$  canvas, while the last three represent penstates [22]. Furthermore, the complexity of canvas-size selector being dependent on sequence-length (T) varying across sketches, we use Douglas Peucker Algorithm [66] to limit sequence-length across all sketch-samples at  $\mathrm{T}_{max}$  without losing visual representation. We feed  $v_t$  at every time step to a simple 1-layer GRU network with  $\mathbb{R}^{d_v}$  hidden states and take the final hidden state as the encoded latent representation  $(f_{s^{\mathrm{T}}} \in \mathbb{R}^{d_v})$ . Next, we apply a linear layer  $(\gamma)$  to get  $p(c|s_v) = \text{softmax}(W_\gamma f_{s^{\mathrm{T}}} + b_\gamma)$ , where  $W_\gamma \in \mathbb{R}^{d_v \times K}$  and  $b \in \mathbb{R}^K$ , as shown in Fig. 3 (right). Given  $p(c|s_v) \in \mathbb{R}^K$  over  $K$  different canvas-sizes for every  $s_v$ , canvas-size  $c$  can be sampled from categorical distribution as  $c_{pred} \sim \text{categorical}([p(c_1|s_v), \dots, p(c_K|s_v)])$ . Accordingly,  $s_v$  is rasterised to  $s_r$  at canvas-size  $c_{pred}$ , which is then fed to  $F_{st}$ . In particular, given a sketch  $s_v$ , canvas-size selector  $\psi_C$  acting as a policy network, takes action of selecting the canvas-size  $c_{pred}$  from action space  $C$ , and  $\psi_C$  is optimised over a reward calculated by the SketchyNetV1 model  $(F_{st})$  acting as the critic.
+
+Reward Design: The objectives of our canvas selector are to choose an optimal canvas-size such that: (i) accuracy is retained (ii) overall FLOPs is minimised. We therefore design our reward from two perspectives. Now as  $F_{st}$  is fixed, we pre-compute the features of all gallery photos. During training, we only extract the feature of rasterised sketch and calculate its corresponding rank using the pre-computed photo-features. Furthermore, taking one sketch we pre-compute FLOPs for every canvas-size in  $C$ . From accuracy perspective, the aim is to select the optimal canvas-size  $c_{\mathrm{opt}}$  from  $C$  for each  $s_v$  such that the rendered  $s_r$  can retrieve the matching photo  $p$  at numerically lowest rank  $r$  (best  $r = 1$ ). Following conventional norm of reward maximisation, we define accuracy reward  $(R_{\mathrm{acc}})$  as weighted (by hyper-parameters  $\lambda_r$ ,  $\lambda_{\mathrm{Tri}}$ ) summation of inverse of the rank (r) and negative triplet loss (following Eq.1) as:
+
+$$
+R _ {\mathrm {a c c}} = \lambda_ {r} (1 / r) + \lambda_ {\mathrm {T r i}} (- \mathcal {L} _ {\mathrm {T r i}}) \tag {4}
+$$
+
+From the compute perspective, the selection criterion should reward choosing a lower canvas-size. Moreover, higher performance being naturally inclined towards a higher-canvas-size thus increasing overall compute, we need an objective dedicated towards reducing computational cost. We thus propose a FLOPs constraint regularisation to guide the learning of canvas selector as:
+
+$$
+\mathcal {L} _ {\mathrm {F}} = \frac {\sum_ {j = 1} ^ {K} \left(q _ {j} \cdot \eta_ {j}\right)}{q _ {\max } - q _ {\min }} \tag {5}
+$$
+
+where,  $\eta_{i} = p(c_{i}|s_{v})$  and  $q_{j}$  is the pre-computed FLOPs value for the j-th canvas-size with maximum at  $q_{max}$  and minimum at  $q_{min}$ . Treating  $(-L_{\mathrm{F}})$  as a reward from the compute perspective, we define our compute reward as  $R_{\mathrm{comp}} = (-L_{\mathrm{F}})$ . Taking  $\lambda_{\mathrm{F}}$  as a balancing hyper-parameter, we combine both perspectives as our total reward:
+
+$$
+R _ {\mathrm {T o t}} = \lambda_ {\mathrm {F}} R _ {\mathrm {c o m p}} + (1 - \lambda_ {\mathrm {F}}) R _ {\mathrm {a c c}} \tag {6}
+$$
+
+Optimisation Objective: Finally, we train the canvas-size selector using popular Policy Gradient [61] method which is both simple to implement and requires less hyper-parameter tuning than other state-of-the-art alternatives [56]. If  $p(c|s_v^i)$  be the probability of selecting a specific canvas-size for  $i^{th}$  sketch sample  $s_v^i$  and the corresponding reward be  $R_{\mathrm{tot}}^i$ , the objective function for policy network (canvas-size selector) over a batch of size  $B$  becomes:
+
+$$
+\mathcal {L} _ {P G} (\theta) = - \frac {1}{B} \sum_ {i = 1} ^ {B} \log p \left(c \mid s _ {v} ^ {i}\right) \cdot R _ {\text {T o t}} ^ {i} \tag {7}
+$$
+
+# 5. Experiments
+
+Datasets: We evaluated on the following publicly available datasets having fine-grained sketch-photo association. QMUL-ShoeV2 [75] and QMUL-ChairV2 [75] contains 6730/2000 and 1800/400 sketches/photos respectively. Keeping 679/200 (525/100) sketches/photos for evaluation from ShoeV2 (ChairV2) respectively we use the rest for training. Sketchy [55] contains 125 categories with 100 photos each, having around 5 sketches per photo. While, training uses a standard train-test split [55] of 9:1, during inference we construct a challenging gallery using photos across one category for retrieval. For scene-level FG-SBIR evaluation we use FS-COCO [15] which includes 10,000 unique sketch-photo pairs with a 7:3 train/test split.
+
+Implementation Details: Considering a standard large FG-SBIR network as a teacher, our proposed student uses a cheaper backbone feature extractor MobileNetV2 [54], a standard for mobile end-devices. Margin is set to  $m = 0.2$  for triplet loss (Secs. 3 and 4.1). We use an Adam optimiser at a learning rate of 0.0001 and a batchsize of 16 for 200 epochs. For practicality, we chose discrete canvas-sizes ( $C$ ) instead of a continuous action space, where  $C = \{32 \times 32, 64 \times 64, 128 \times 128, 256 \times 256\}$ . Canvas-size selector ( $\psi_C$ ) is modelled using a simple GRU network, with embedding size 128, and trained via reinforcement learning with a learning rate of 0.0001 and a batchsize of 32 for 500 epochs, keeping  $T_{max} = 100$  for vector-sketches. For the action space, we take varying canvas-sizes from  $C$  and set  $\beta = 1$  in Eq.2.  $\lambda$ ,  $\lambda_r$ ,  $\lambda_{\mathrm{Tri}}$  and  $\lambda_{\mathrm{F}}$  are empirically set to 0.5, 0.4, 0.48 and 0.35 (Fig.5) respectively. While training  $\psi_C$ , sketches are rendered at different completion (30%, 35%, ... 100%) levels to simulate varying levels of abstraction, ensuring a sketch-abstraction-aware canvas selector (e.g., a smaller canvas for less detailed sketch).
+
+Evaluation Metric: Accuracy for FG-SBIR is the percentage of sketches where true-match photos are ranked in the Top-q (q = 1,10) lists. Computational efficiency is measured via parameter-count and average FLOPs – lower is better. For average FLOPs in Table 2, we take the combined sum of FLOPs per sample [12] from (i) canvas-size selector and (ii) retrieval model, using the predicted resolution, and average across the validation set.
+
+Table 2. Quantitative Analysis on FG-SBIR. Best viewed when zoomed.  
+
+<table><tr><td rowspan="2" colspan="2">Methods</td><td rowspan="2">Canvas-size c×c</td><td rowspan="2">Params (mil.)</td><td colspan="3">ShoeV2 [75]</td><td colspan="3">ChairV2 [75]</td><td colspan="3">Sketchy [55]</td><td colspan="3">FSCOCO [15]</td></tr><tr><td>Top1 (%)</td><td>Top10 (%)</td><td>FLOPS (G)</td><td>Top1 (%)</td><td>Top10 (%)</td><td>FLOPS (G)</td><td>Top1 (%)</td><td>Top10 (%)</td><td>FLOPs (G)</td><td>Top1 (%)</td><td>Top10 (%)</td><td>FLOPS (G)</td></tr><tr><td rowspan="40">State-of-the-Arts</td><td rowspan="6">Triplet-SN [75]</td><td>32x32</td><td>8.75</td><td>09.77 (↓18.94)</td><td>24.82 (↓46.74)</td><td>0.083</td><td>15.61 (↓32.04)</td><td>29.86 (↓54.38)</td><td>0.083</td><td>4.23 (↓11.12)</td><td>12.58 (↓23.13)</td><td>0.083</td><td>0.76 (↓3.94)</td><td>6.22 (↓14.8)</td><td>0.083</td></tr><tr><td>64x64</td><td>8.75</td><td>17.63 (↓11.08)</td><td>44.96 (↓26.60)</td><td>0.338</td><td>30.25 (↓17.4)</td><td>54.21 (↓30.03)</td><td>0.338</td><td>9.68 (↓5.67)</td><td>22.45 (↓13.26)</td><td>0.338</td><td>1.85 (↓2.85)</td><td>7.33 (↓13.69)</td><td>0.338</td></tr><tr><td>128x128</td><td>8.75</td><td>25.01 (↓3.70)</td><td>62.35 (↓9.21)</td><td>1.397</td><td>40.61 (↓7.04)</td><td>72.68 (↓11.56)</td><td>1.397</td><td>12.98 (↓2.37)</td><td>29.63 (↓6.08)</td><td>1.397</td><td>3.28 (↓1.42)</td><td>15.92 (↓5.1)</td><td>1.397</td></tr><tr><td>256x256</td><td>8.75</td><td>28.71</td><td>71.56</td><td>5.280</td><td>47.65</td><td>84.24</td><td>5.280</td><td>15.35</td><td>35.71</td><td>5.280</td><td>4.7</td><td>21.02</td><td>5.280</td></tr><tr><td>SketchyNetV1</td><td>2.22</td><td>28.46 (↓0.25)</td><td>69.01 (↓2.55)</td><td>0.833</td><td>46.28 (↓0.37)</td><td>82.33 (↓1.91)</td><td>0.833</td><td>14.85 (↓0.5)</td><td>34.68 (↓1.03)</td><td>0.833</td><td>4.22 (↓0.48)</td><td>18.33 (↓2.69)</td><td>0.833</td></tr><tr><td>SketchyNetV2</td><td>2.27</td><td>27.89 (↓0.82)</td><td>68.76 (↓2.80)</td><td>0.264</td><td>45.98 (↓1.67)</td><td>80.14 (↓4.10)</td><td>0.294</td><td>14.21 (↓1.14)</td><td>34.16 (↓1.55)</td><td>0.321</td><td>3.98 (↓0.72)</td><td>17.64 (↓3.38)</td><td>0.423</td></tr><tr><td rowspan="6">HOLEE-SN [59]</td><td>32x32</td><td>9.31</td><td>10.84 (↓20.9)</td><td>27.28 (↓48.5)</td><td>0.096</td><td>18.72 (↓34.69)</td><td>31.68 (↓55.88)</td><td>0.096</td><td>6.01 (↓10.69)</td><td>14.12 (↓24.78)</td><td>0.096</td><td>0.86 (↓4.04)</td><td>6.93 (↓14.78)</td><td>0.096</td></tr><tr><td>64x64</td><td>9.31</td><td>19.83 (↓11.91)</td><td>51.72 (↓24.06)</td><td>0.387</td><td>34.32 (↓19.09)</td><td>56.46 (↓31.1)</td><td>0.387</td><td>9.92 (↓6.78)</td><td>24.38 (↓14.52)</td><td>0.387</td><td>2.11 (↓2.79)</td><td>7.86 (↓13.85)</td><td>0.387</td></tr><tr><td>128x128</td><td>9.31</td><td>26.78 (↓4.96)</td><td>66.28 (↓9.5)</td><td>1.545</td><td>45.74 (↓7.67)</td><td>75.59 (↓11.97)</td><td>1.545</td><td>13.81 (↓2.89)</td><td>33.68 (↓5.22)</td><td>1.545</td><td>3.65 (↓1.25)</td><td>16.32 (↓5.39)</td><td>1.545</td></tr><tr><td>256x256</td><td>9.31</td><td>31.74</td><td>75.78</td><td>5.758</td><td>53.41</td><td>87.56</td><td>5.758</td><td>16.70</td><td>38.90</td><td>5.758</td><td>4.9</td><td>21.71</td><td>5.758</td></tr><tr><td>SketchyNetV1</td><td>2.22</td><td>31.59 (↓0.15)</td><td>73.96 (↓1.82)</td><td>0.833</td><td>53.27 (↓0.14)</td><td>86.93 (↓0.63)</td><td>0.833</td><td>16.25 (↓0.45)</td><td>38.21 (↓0.69)</td><td>0.833</td><td>4.56 (↓0.34)</td><td>19.92 (↓1.79)</td><td>0.833</td></tr><tr><td>SketchyNetV2</td><td>2.27</td><td>30.86 (↓0.88)</td><td>72.56 (↓3.22)</td><td>0.259</td><td>52.74 (↓0.67)</td><td>84.02 (↓3.54)</td><td>0.289</td><td>15.91 (↓0.79)</td><td>37.88 (↓1.02)</td><td>0.315</td><td>4.04 (↓0.86)</td><td>18.63 (↓3.08)</td><td>0.417</td></tr><tr><td rowspan="6">Triplet-RL [6]</td><td>32x32</td><td>22.1</td><td>11.98 (↓22.12)</td><td>28.11 (↓50.71)</td><td>0.142</td><td>20.53 (↓36.01)</td><td>32.59 (↓57.02)</td><td>0.142</td><td>1.76 (↓2.94)</td><td>3.88 (↓6.47)</td><td>0.142</td><td></td><td></td><td></td></tr><tr><td>64x64</td><td>22.1</td><td>21.28 (↓12.82)</td><td>54.71 (↓24.11)</td><td>0.577</td><td>36.09 (↓20.45)</td><td>57.33 (↓32.28)</td><td>0.577</td><td>3.04 (↓1.66)</td><td>6.79 (↓3.56)</td><td>0.577</td><td></td><td></td><td></td></tr><tr><td>128x128</td><td>22.1</td><td>28.83 (↓5.27)</td><td>67.84 (↓10.98)</td><td>2.299</td><td>48.38 (↓8.16)</td><td>77.25 (↓12.36)</td><td>2.299</td><td>4.12 (↓0.58)</td><td>9.05 (↓1.30)</td><td>2.299</td><td></td><td></td><td></td></tr><tr><td>256x256</td><td>22.1</td><td>34.10</td><td>78.82</td><td>6.041</td><td>56.54</td><td>89.61</td><td>6.041</td><td>4.70</td><td>10.35</td><td>6.041</td><td></td><td></td><td></td></tr><tr><td>SketchyNetV1</td><td>2.22</td><td>33.88 (↓0.22)</td><td>77.15 (↓1.67)</td><td>0.833</td><td>55.92 (↓0.62)</td><td>88.20 (↓1.41)</td><td>0.833</td><td>4.59 (↓0.11)</td><td>10.21 (↓0.14)</td><td>0.833</td><td></td><td></td><td></td></tr><tr><td>SketchyNetV2</td><td>2.27</td><td>33.26 (↓0.84)</td><td>76.84 (↓1.98)</td><td>0.255</td><td>55.14 (↓1.40)</td><td>87.31 (↓2.30)</td><td>0.285</td><td>4.51 (↓0.19)</td><td>9.89 (↓0.46)</td><td>0.308</td><td></td><td></td><td></td></tr><tr><td rowspan="6">StyleVAE [51]</td><td>32x32</td><td>25.37</td><td>12.68 (↓23.79)</td><td>28.69 (↓53.14)</td><td>0.125</td><td>22.48 (↓40.38)</td><td>32.10 (↓59.04)</td><td>0.125</td><td>06.92 (↓12.7)</td><td>16.25 (↓29.53)</td><td>0.125</td><td></td><td></td><td></td></tr><tr><td>64x64</td><td>25.37</td><td>22.93 (↓13.54)</td><td>57.71 (↓24.12)</td><td>0.508</td><td>40.26 (↓22.6)</td><td>58.23 (↓32.91)</td><td>0.508</td><td>12.46 (↓7.16)</td><td>29.62 (↓16.16)</td><td>0.508</td><td></td><td></td><td></td></tr><tr><td>128x128</td><td>25.37</td><td>30.91 (↓5.56)</td><td>70.06 (↓11.77)</td><td>2.024</td><td>53.88 (↓8.98)</td><td>78.64 (↓12.5)</td><td>2.024</td><td>17.15 (↓2.47)</td><td>38.84 (↓6.94)</td><td>2.024</td><td></td><td></td><td></td></tr><tr><td>256x256</td><td>25.37</td><td>36.47</td><td>81.83</td><td>5.642</td><td>62.86</td><td>91.14</td><td>5.642</td><td>19.62</td><td>45.78</td><td>5.642</td><td></td><td></td><td></td></tr><tr><td>SketchyNetV1</td><td>2.22</td><td>36.11 (↓0.36)</td><td>79.63 (↓2.20)</td><td>0.833</td><td>62.23 (↓0.63)</td><td>88.95 (↓2.19)</td><td>0.833</td><td>19.48 (↓0.12)</td><td>44.02 (↓1.76)</td><td>0.833</td><td></td><td></td><td></td></tr><tr><td>SketchyNetV2</td><td>2.27</td><td>35.88 (↓0.59)</td><td>78.46 (↓3.37)</td><td>0.251</td><td>61.95 (↓0.91)</td><td>87.68 (↓3.46)</td><td>0.281</td><td>19.10 (↓0.50)</td><td>43.57 (↓2.21)</td><td>0.304</td><td></td><td></td><td></td></tr><tr><td rowspan="6">Partial-OT [14]</td><td>32x32</td><td>22.1</td><td></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>64x64</td><td>22.1</td><td></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>128x128</td><td>22.1</td><td></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>256x256</td><td>22.1</td><td></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>SketchyNetV1</td><td>2.22</td><td></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>SketchyNetV2</td><td>2.27</td><td></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>B-BFR</td><td>224x224</td><td>4.61</td><td>24.32</td><td>61.23</td><td>2.602</td><td>43.39</td><td>76.33</td><td>2.602</td><td>10.47</td><td>24.34</td><td>2.602</td><td>2.15</td><td>11.61</td><td>2.602</td></tr><tr><td>B-DRS</td><td>Dynamic</td><td>9.36</td><td>25.12</td><td>68.84</td><td>5.493</td><td>44.78</td><td>78.14</td><td>6.187</td><td>11.87</td><td>26.58</td><td>6.245</td><td>3.86</td><td>17.63</td><td>6.291</td></tr><tr><td>B-Crop</td><td>Dynamic</td><td>4.92</td><td>20.32</td><td>52.12</td><td>6.562</td><td>35.07</td><td>57.68</td><td>6.597</td><td>08.27</td><td>20.19</td><td>6.629</td><td>1.98</td><td>09.67</td><td>6.688</td></tr><tr><td>B-Regress [48]</td><td>Dynamic</td><td>2.27</td><td>22.82</td><td>61.33</td><td>0.261</td><td>38.42</td><td>64.65</td><td>0.291</td><td>08.69</td><td>21.98</td><td>0.323</td><td>2.07</td><td>10.15</td><td>0.375</td></tr><tr><td>B-AKD [76]</td><td>Dynamic</td><td>2.27</td><td>23.67</td><td>64.26</td><td>0.268</td><td>38.61</td><td>71.88</td><td>0.295</td><td>12.67</td><td>27.71</td><td>0.331</td><td>2.91</td><td>14.01</td><td>0.392</td></tr><tr><td>B-PKT [45]</td><td>Dynamic</td><td>2.27</td><td>24.31</td><td>65.91</td><td>0.259</td><td>42.68</td><td>73.66</td><td>0.288</td><td>12.27</td><td>28.31</td><td>0.317</td><td>3.45</td><td>16.22</td><td>0.372</td></tr><tr><td>B-VGG16-SN</td><td>256x256</td><td>14.71</td><td>33.03</td><td>78.51</td><td>40.18</td><td>52.16</td><td>84.08</td><td>40.18</td><td>18.61</td><td>41.25</td><td>40.18</td><td>5.16</td><td>23.62</td><td>40.18</td></tr><tr><td>B-ThiNet [37]</td><td>256x256</td><td>8.32</td><td>7.51 (↓25.52)</td><td>22.34 (↓56.17)</td><td>9.342</td><td>12.31 (↓39.85)</td><td>26.63 (↓57.45)</td><td>9.342</td><td>3.16 (↓15.45)</td><td>12.73 (↓28.52)</td><td>9.342</td><td>0.65 (↓4.51)</td><td>5.35 (↓18.27)</td><td>9.342</td></tr><tr><td>B-Prune [38]</td><td>256x256</td><td>6.17</td><td>3.92 (↓29.11)</td><td>17.32 (↓61.19)</td><td>8.138</td><td>7.98 (↓44.18)</td><td>19.82 (↓64.26)</td><td>8.138</td><td>1.45 (↓17.16)</td><td>8.22 (↓33.03)</td><td>8.138</td><td>0.53 (↓4.63)</td><td>4.97 (↓18.65)</td><td>8.138</td></tr><tr><td>B-VGG16-SN SketchyNetV2</td><td>2.27</td><td>32.77 (↓0.26)</td><td>78.21 (↓0.3)</td><td>0.254</td><td>50.75 (↓1.41)</td><td>82.21 (↓1.87)</td><td>0.283</td><td>16.55 (↓2.06)</td><td>38.66 (↓2.59)</td><td>0.332</td><td>4.69 (↓0.47)</td><td>21.76 (↓1.86)</td><td>0.407</td><td></td></tr></table>
+
+# 5.1. Competitors
+
+We evaluate against State-of-the-Arts (SoTAs) and a few relevant curated baselines (B-). (i) SoTAs: Unlike Triplet-SN [75], HOLEF-SN [59], Triplet-RL [6] (we report full-sketch evaluation) and StyleVAE [51]; Partial-OT [14] specifically caters to scene-level FG-SBIR. For fairness, we vary input-resolution of sketches during inference (fixed at their original  $256 \times 256$  setup during training). We also adapt them as teachers, to judge our accuracy retainment after model-compression (SketchyNetV1) using full-res sketch and, further optimising canvas-size with canvas selector (SketchyNetV2). (ii) KD baselines: Here we re-purpose existing works in a cross-modal setting, keeping our canvas selector same, with Triplet-SN as the teacher. B-Regress - regresses features from teacher and student for both sketches and images, aligning their dimensions with an extra transformation layer [48], using a  $l_{2}$  regression loss. Following [45] B-PKT calculates the conditional probability density for any pair of points in the teacher's embedding space [45], which models the probability of any two samples being close together. Sampling 'N' instances, it establishes a probability distribution for pairwise interactions within that space. Simultaneously, in the student's embedding space, a comparable distribution is derived, and the model minimises the divergence between them using a KL-divergence loss. B-AKD follows [76] in using spatial attention maps for knowledge transfer using similar dimensional matching like B-Regress. (iii) Resizing strategies: Keeping the same KD-paradigm with Triplet-SN-teacher, we vary the input
+
+size resizing module following existing works.  $B$ -BFR follows [62] in designing a bilinear feature resizer amidst the intermediate layers of a CNN network, to output a down-scaled image. We choose its resized resolution of  $224 \times 224$  (lowest) for subsequent evaluation.  $B$ -DRS follows [12] in training a convolutional module that takes an image in full-resolution, calculates a probability vector on available canvas-sizes, and transforms it into binary decisions, indicating the scale factor of selection.  $B$ -Crop follows [32] in meta-learning an image-cropping module that crops the input image to a target resolution for low compute evaluation. (iv) Pruning alternatives: Here we adapt two VGG16-backboned methods off-the-shelf from network-pruning family among other efficiency paradigms [18, 21, 62], in FG-SBIR setup -  $B$ -ThiNet [37] and  $B$ -Prune [38]. For comparative reference we report performance of a VGG16-backboned Triplet-SN network ( $B$ -VGG16-SN) and its SketchyNetV2 variant.
+
+# 5.2. Performance and Compute Analysis:
+
+Analysis on Accuracy: Table 2 reports the quantitative evaluation of our model against others. Triplet-SN [75] and HOLEF-SN [59] perform lower owing to weak backbones of Sketch-A-Net [74]. Enhanced by its RL-optimised reward function Triplet-RL[6] scores higher  $(2.36\% \uparrow$  Top1 on ShoeV2) but fails to surpass StyleVAE [51], due to its delicate meta-learning disentanglement module addressing style-diversity. Being trained on region-wise sketch-photo associativity, Partial-OT [14] outperforms all others significantly on scene-level sketches (FS-COCO). We also notice a
+
+gradual drop in accuracy of SoTAs, when subjected to decreasing resolution of input-sketches suggesting that some methods are inherently accustomed to handling scale-shifts better than others, but are inferior to our dynamic approach (SketchyNetV2). Importantly, when most SoTAs are employed as teachers, their respective students (SketchyNetV1 variants) are seen to retain their respective original accuracy with a marginal drop of  $\approx 0.5 - 1\%$  overall, thanks to our efficient KD paradigm. Having different teacher-student embedding spaces both  $B$ -Regress and  $B$ -AKD's paradigm of directly regressing on features proves incompatible to a cross-modal retrieval setting, dropping accuracy (compared to T-Triplet-SN), whereas lacking cross-modal discrimination  $B$ -PKT performs lower than ours, proving our superiority in retaining accuracy.
+
+![](images/de3a0d5bb52e94f4070e12b04a21b1cf472229379a14b6f2fd172071e21ff8bf.jpg)  
+Figure 4. Exemplar sketches at their optimal canvas-size
+
+![](images/e362480feffaaa2a25a4bf1ad00113228371c443db89798b3bd7b2864ad24929.jpg)
+
+![](images/214d331dd4b3bbdc3eff100cacaf294036f74e397825e96a10e207f7b1fee5f4.jpg)
+
+![](images/ca18a9d5f00a783e7d294e3e47bdec3dd5eb72a362115abfe1899a23cb846b98.jpg)
+
+Analysis on Compute: Although FLOPs [12] decrease (Table 2) with a reduction in input resolution across all SoTAs, it comes at a severe cost of accuracy ( $\approx 21\%$  average drop from  $256 \times 256$  to  $32 \times 32$  on ShoeV2). This is mainly because ideal canvas-size for optimal retrieval varies across samples (Fig. 2 right) - thus subjecting all samples to a fixed canvas-size proves detrimental for accuracy. However, a positive Acc@1 score of  $\approx 11\%$  even at a low canvas-size of  $32 \times 32$  for every SoTA shows that some sketches are indeed recognisable if the model is trained properly. This is verified further by SketchyNetV2 variant of respective SoTAs, that secures the lowest FLOPs per SoTA, despite maintaining accuracy at par with its SoTA-counterpart - thanks to our RL-guided canvas selector, which can allot an optimal canvas-size per sketch towards better retrieval (Fig. 4). Contrarily, B-BFR fails to lower FLOPs as it fixes a  $224 \times 224$  input resolution for a satisfactory Acc@1 compared to Triplet-SN. B-Crop fairs better, however sketch being sparse, cropped sketches leads to confused representations, lowering accuracy. Despite coming closest in accuracy to ours on Triplet-SN, B-DRS lags behind considerably on compute, thanks to our canvas selector working in vector space (inputs  $s_v$ ) and eliminating costly convolutional operations, unlike others using full-resolution sketch-raster as input. Being untrained to handle sparse-nature of sketches during such high compression, performance of both B-ThiNet and B-Prune collapses (vs. B-VGG16-SN) unlike its SketchyNetV2. Notably, the significant drop in parameter-count (4 - 10 times) against SoTAs, comes from choosing lightweight MobileNetV2 [54] as a student coupled with our canvas-size selector in every SketchyNetV2 variant. Compared to ShoeV2, FLOPs increase slightly for ChairV2, Sketchy and FS-COCO, owing to higher object (ChairV2) or scene-level (FS-COCO) details, and lower structural correspondence with photos (Sketchy), thus training a poorer retrieval model which in turn acts as a poor critic for our canvas selector. Our canvas selector alone takes a negligible 51.84K parameters with 0.02G FLOPs.
+
+# 5.3. Ablation Study
+
+As our teacher  $(F_T)$  can be any pre-trained FG-SBIR network, we limit our ablation to justifying design choices of our student model and canvas-size selector. We use  $B$ -VGG16-SN as a reference  $F_T$  - Type- $\emptyset$  in Table 3.
+
+Training Canvas-Size selector  $\psi_C$ : To justify loss objectives of  $\psi_C$  we evaluate on ShoeV2, eliminating  $r^{-1}$ ,  $\mathcal{L}_{\mathrm{Tri}}^R$ ,  $\mathcal{L}_{\mathrm{F}}$  one by one from Eq. 6 (Table 3). While eliminating accuracy rewards,  $(w / o \text{ rank}^{-1}, w / o \mathcal{L}_{\mathrm{Tri}}^R)$  increases constraint on lowering FLOPs, dropping accuracy, ignoring  $\mathcal{L}_{\mathrm{F}}$ $(w / o \mathcal{L}_F)$  gains accuracy but costs high FLOPs. We thus optimally balance between the two using  $\lambda_{\mathrm{F}}$  (Fig. 5 left). One can also choose to train for faster retrieval (lower FLOPs), given a decent Acc@5 (Fig. 5 right).
+
+![](images/e2f7d3047db873640356a1426d38a7e35719439634bff95966f7bd695227d686.jpg)  
+Figure 5. Impact of varying  $\lambda_{\mathrm{F}}$  on Acc@1 and Acc@5
+
+![](images/799f80fd904eaa953d0823a729f55c7ac735d4637db5012301974a08ddeba2b7.jpg)
+
+Architectural insights: To judge the efficiency of our student's backbone, we explore a few cheaper backbone-networks (Types IV, V in Table 3). Evidently, MobileNetV2 (Ours) balances optimally between compute and accuracy. As an option to vector input for canvas selector, we re-design it with a simple seven-layer CNN module following [78] to use the full-resolution sketch-image as its input, and select a target canvas-size to downscale it for retrieval. With extra computational cost coming from spatial domain, total FLOPs incurred is much higher (VI). Next we compare efficacy of sketch as input to  $\psi_C$  with respect to types of vector format - offset-coordinate (VI) [22] vs. absolute ones (Ours). Turns out the former is better for encoding. Comparing sketch encoders among LSTM (VIII), GRU (Ours) and Transformer (IX), showed ours to be optimum empirically (Table 3). Furthermore, preponding recent pre-processing modules like stroke-subset selector of [9] to our canvas selector, yields  $42.95\%$  (vs.  $43.7\%$  [9]) Acc@1 ShoeV2, proving its off-the-shelf compatibility.
+
+Table 3. Ablative studies (accuracy on ShoeV2)  
+
+<table><tr><td rowspan="2" colspan="2">Type</td><td>FLOPs</td><td>Params</td><td colspan="2">ShoeV2</td></tr><tr><td>(G)</td><td>(mil.)</td><td>Top1 (%)</td><td>Top10 (%)</td></tr><tr><td>∅</td><td>B-VGG16-SN</td><td>40.18</td><td>14.71</td><td>33.03</td><td>78.51</td></tr><tr><td>I</td><td>w/o rank-1-reward</td><td>0.173</td><td></td><td>25.31</td><td>64.36</td></tr><tr><td>II</td><td>w/o \( \mathcal{L}_{\text{Tri}}^R \)-reward</td><td>0.182</td><td>2.27</td><td>27.78</td><td>69.32</td></tr><tr><td>III</td><td>w/o \( \mathcal{L}_{\text{F}} \)-reward</td><td>0.833</td><td></td><td>32.91</td><td>78.39</td></tr><tr><td>IV</td><td>ResNet18 backbone</td><td>1.451</td><td>11.18</td><td>26.72</td><td>68.18</td></tr><tr><td>V</td><td>EfficientNet backbone</td><td>0.459</td><td>4.01</td><td>29.47</td><td>72.04</td></tr><tr><td>VI</td><td>Image-based \( \psi_C \)</td><td>5.730</td><td>7.62</td><td>32.21</td><td>77.68</td></tr><tr><td>VII</td><td>Offset \( s_v \)</td><td>0.255</td><td>2.27</td><td>32.61</td><td>78.40</td></tr><tr><td>VIII</td><td>Decoder-LSTM</td><td>0.268</td><td>2.25</td><td>31.41</td><td>77.32</td></tr><tr><td>IX</td><td>Decoder-Tf</td><td>0.314</td><td>2.34</td><td>31.98</td><td>78.02</td></tr><tr><td></td><td>SketchyNetV2</td><td>0.254</td><td>2.27</td><td>32.77</td><td>78.21</td></tr></table>
+
+Generalisability of canvas selector: To judge if the optimal canvas-size selected is uniform irrespective of the training method, we first train four canvas-selectors using four SoTAs of Table 2. Evaluating them on ShoeV2 [75],  $89.21\%$  of test-set sketches in ShoeV2 to obtain the same optimal canvas size across four different models, trained on four different methods, which further proves that our canvas selector can work equally well as a pre-processing module for any new model. Furthermore, plugging a canvas selector trained with SketchyNetV1 (critic) from B-VGG16-SN with a different SketchyNetV1 from StyleVAE [51] during inference achieves comparable performance  $(35.69\%)$  Top-1) to a canvas selector trained on StyleVAE-SketchyNetV1  $(35.88\%)$  Top-1) on ShoeV2. Importantly,  $95.64\%$  of test-set sketches yield the same optimal canvas-size across both models,
+
+confirming the cross-model generalisability of our canvas selector. (ii) On training canvas selector with teacher  $F_{T}$  (for Triplet-SN) as critic, yields same optimal canvas-sizes as those for student  $F_{S}$ , for  $94.21\%$  of test-set sketches in ShoeV2, while incurring comparable FLOPs reduction (0.268G) and accuracy (27.91% Top1) against  $F_{S}$  as critic.
+
+Comparing Inference times: We evaluated on a 12 GB Nvidia RTX 2080 Ti GPU, on ShoeV2, for inference time of Triplet-SN, HOLEF-SN, Triplet-RL, and StyleVAE (SOTAs) on full-sketch to obtain 37, 38, 36 and  $42\mathrm{ms}$ , against 10, 11, 11, and  $12\mathrm{ms}$  for their SketchyNetV2 variants respectively. For practical validation, we evaluated onnx-INT8 version of Triplet-SN [75] and its SketchyNetV2 variant (ours) after post-training quantisation, on an iPhone13 via the AI-benchmark app for ShoeV2 [75] to obtain 51ms and 18ms respectively, which shows our efficiency.
+
+Retraining SoTA on mixed resolution sketches?: To explore if retraining SoTAs on sketches with mixed resolutions, we re-train Triple-SN [75] on rendered mixed-resolution sketches of ShoeV2. Poor performance in Table 4 at lower resolutions similar to Table 2 validates our KD approach. The key lies in that the sketch-feature from teacher used for student-guidance  $(f_s^T)$  is always extracted from full-resolution sketch while that extracted by student is at varying resolutions, imparting scale invariance, which is ideally suited to our cross-modal retrieval setup.
+
+Table 4. Evaluating SoTAs trained on mixed-resolution sketches  
+
+<table><tr><td rowspan="2">Canvas Size</td><td colspan="3">Triplet-SN</td><td colspan="3">Triplet-RL</td></tr><tr><td>Top1 (%)</td><td>Top10 (%)</td><td>FLOPs (G)</td><td>Top1 (%)</td><td>Top10 (%)</td><td>FLOPs (G)</td></tr><tr><td>32×32</td><td>10.91</td><td>26.65</td><td>0.083</td><td>12.97</td><td>31.08</td><td>0.142</td></tr><tr><td>64×64</td><td>19.04</td><td>48.12</td><td>0.338</td><td>22.96</td><td>56.23</td><td>0.577</td></tr><tr><td>128×128</td><td>26.07</td><td>63.87</td><td>1.397</td><td>30.04</td><td>72.95</td><td>2.299</td></tr><tr><td>256×256</td><td>28.74</td><td>71.68</td><td>5.280</td><td>34.21</td><td>77.24</td><td>6.041</td></tr></table>
+
+# 5.4. Further Insights
+
+Cross-dataset Generalisation: To judge the generalisation potential of our canvas-size selector across datasets we train it on ShoeV2, but plug it to a retrieval model (SketchyNetV1) trained on ChairV2, and evaluate on ChairV2. Against the standard result (Table 2) of training both modules (SketchyNetV2) on ChairV2 (0.285G,  $55.32\%$  Acc@1), this setup retains accuracy at  $53.14\%$  with slight rise in FLOPs (0.314G), thus confirming its potential.
+
+Faster Sketch-recognition: Exploring potential of our canvas-size selector, we prepend it to a standard sketch-recognition pipeline [74] to optimise the canvas-size of query sketch, and reduce overall compute. Unlike our  $\psi_{C}$ , it uses negative of cross-entropy loss as accuracy reward  $(R_{\mathrm{acc}})$ , keeping rest same. Compared to existing Sketch-a-Net [74] incurring 5.28G FLOPs at  $68.71\%$  accuracy on Quickdraw [22], our canvas selector fitted paradigm drops FLOPs to 0.261G while retaining accuracy at  $68.14\%$ . This shows for the first time, that sparsity of sketches can be handled, in various downstream tasks via our  $\psi_{C}$ .
+
+Extension to Category-level SBIR: For categorical SBIR we use Sketchy (ext) [36] dataset (90:10 train:test split), which holds  $75k$  sketches across 125 categories having  $\approx 73k$  images [36] in total. It is evaluated using mean average precision (mAP@all) and precision at top 200 retrieval (P@200) [36]. Here we compete against state-of-the-arts (SoTA) like  $B-D2S$  that follows [19] without its zero-shot setting), and a simple baseline using a Siamese-style
+
+Table 5. Quantitative Evaluation on Categorical SBIR  
+
+<table><tr><td></td><td>Methods</td><td>FLOPs</td><td>Params</td><td colspan="2">Sketchy(ext)</td></tr><tr><td></td><td></td><td>(G)</td><td>(mil.)</td><td>mAP@all</td><td>P@200</td></tr><tr><td rowspan="4">SoTA</td><td>B-SBIR-SN</td><td>40.18</td><td>14.71</td><td>0.715</td><td>0.861</td></tr><tr><td>DSH [36]</td><td>22.14</td><td>16.32</td><td>0.711</td><td>0.858</td></tr><tr><td>B-D2S [19]</td><td>17.75</td><td>136.36</td><td>0.810</td><td>0.894</td></tr><tr><td>StyleVAE [51]</td><td>8.116</td><td>25.37</td><td>0.905</td><td>0.927</td></tr><tr><td rowspan="4">T-SoTA</td><td>T-SBIR-SN</td><td>0.254</td><td></td><td>0.702</td><td>0.810</td></tr><tr><td>T-DSH</td><td>0.289</td><td rowspan="3">2.27</td><td>0.704</td><td>0.823</td></tr><tr><td>T-D2S</td><td>0.268</td><td>0.798</td><td>0.845</td></tr><tr><td>T-StyleVAE</td><td>0.251</td><td>0.886</td><td>0.897</td></tr></table>
+
+VGG-16 network (B-SBIR-SN) following [75]. Similar to Section 5.1 adapting SoTAs as teachers in our SketchyNetV2 paradigm (T-SoTA) shows them retaining their accuracy (Table 5) while significantly lowering compute.
+
+Teacher-Student Pairs: To explore other teacher-student pairs apart from ours, we test SketchyNetV2 models of a few  $(F_T,F_S)$  pairs, where teachers are trained similar to B-VGG16-SN. From Table 6 we see our pair to outperform others.
+
+Table 6. Evaluation on Teacher-Student Pairs  
+
+<table><tr><td rowspan="2">Teacher\Student</td><td colspan="2">MobileNetV2</td><td colspan="2">EfficientNet</td><td colspan="2">ResNet-18</td></tr><tr><td>Top-1</td><td>FLOPs</td><td>Top-1</td><td>FLOPs</td><td>Top-1</td><td>FLOPs</td></tr><tr><td>VGG-16 [30]</td><td>32.77%</td><td>0.254G</td><td>29.47%</td><td>0.459G</td><td>26.72%</td><td>1.451G</td></tr><tr><td>Inception-V3 [74]</td><td>27.89%</td><td>0.264G</td><td>27.16%</td><td>0.461G</td><td>25.31%</td><td>1.452G</td></tr></table>
+
+Combining compression methods: To explore if a combination of compression methods is capable of increasing efficiency, we subject our Knowledge Distillation (KD) trained model (SketchyNetV1) of Triplet-SN [75] (Table 2) to (i) quantisation following [21], and (ii) network-pruning following [38], separately, and then train their respective canvas-selectors. While the former secures  $27.34\%$  (vs.  $27.89\%$  ours) Top-1 score with a lower inference time of  $9.1\mathrm{ms}$  (vs.  $10\mathrm{ms}$  ours), the latter scores  $26.91\%$  (vs.  $27.89\%$  ms ours) Top-1 with lower FLOPs of 0.249G (vs. 0.264G ours). Such competitive results further endorse exploring combining compression methods as future works.
+
+Future Works: Sketch being an abstraction of an object's photo, when resized to a lower scale for retrieval, infers that its object's semantic is interpretable at that scale. This should ideally provide a lower bound for resizing a photo while retaining interpretability (e.g. high retrieval score). Consequently, designing a learnable photo-resizer aided by our trained sketch-canvas selector is a potential future work. Secondly, ours being a meta-framework, using more recent frameworks like DINOv2 [41] as large-scale teacher models for further gains is another targeted future work.
+
+# 6. Conclusion
+
+We for the first time investigate the problem of efficient inference for FG-SBIR, where we show that using existing efficient lightweight networks directly, are unfit for sketches. We thus propose two generic components that can be adapted to photo-networks for sketch-specific data. Firstly, a cross-modal knowledge distillation paradigm distills the knowledge of larger models to a smaller one, directly reducing FLOPs (params) by 97.92  $(84.9)\%$ . Secondly, an abstraction-aware canvas-size selector dynamically selects the best canvas-size for a sketch, reducing FLOPs by extra two-thirds. Extensive experiments show our method to perform at par with state-of-the-arts using much lower compute thus further conveying our method's worth in enhancing them towards deployment.
+
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2025/Sketch Down the FLOPs_ Towards Efficient Networks for Human Sketch/images.zip

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2025/SketchAgent_ Language-Driven Sequential Sketch Generation/76b8d485-0aca-43aa-b3b2-9c94133cc069_origin.pdf

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2025/SketchAgent_ Language-Driven Sequential Sketch Generation/full.md

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+# SketchAgent: Language-Driven Sequential Sketch Generation
+
+Yael Vinker $^{1}$  Tamar Rott Shaham $^{1}$  Kristine Zheng $^{2}$  Alex Zhao $^{1}$  Judith E Fan $^{2}$  Antonio Torralba $^{1}$
+
+$^{1}$ MIT
+
+{yaelvink,tamarott,alexzhao,torralba}@mit.edu
+
+$^{2}$ Stanford University
+
+{jefan, kxzheng}  $@$  stanford.edu
+
+https://sketch-agent.csail.mit.edu/
+
+![](images/ab70df958686f2d2f5dd138cd4518fae137431adbcbf0135e8142d26148c2090.jpg)  
+Figure 1. SketchAgent leverages an off-the-shelf multimodal LLM to facilitate language-driven, sequential sketch generation through an intuitive sketching language. It can sketch diverse concepts, engage in interactive sketching with humans, and edit content via chat.
+
+![](images/660caff867d36bd3a2a1921ee55b7b3b76542d9b1364d0157c87333634aa747d.jpg)  
+Human-Agent Collaborative Sketching
+
+![](images/bb89323786ba343d8e554d354ea822316c073446fd92f4ecc14a65f0ac735d29.jpg)  
+Chat-Based Sketch Editing
+
+Draw a robot
+
+Add a paintbrush and a canvas
+
+![](images/58090f024aca3cd9a38c512e69f40fb0834a6bf929eb5b573f55723bd62c16a8.jpg)
+
+Draw a robot on the canvas
+
+![](images/754aa295f56e6b4570d9a42392daf32d422e9c28aa0ecbf726d93912ff19e24f.jpg)
+
+# Abstract
+
+Sketching serves as a versatile tool for externalizing ideas, enabling rapid exploration and visual communication that spans various disciplines. While artificial systems have driven substantial advances in content creation and human-computer interaction, capturing the dynamic and abstract nature of human sketching remains challenging. In this work, we introduce SketchAgent, a language-driven, sequential sketch generation method that enables users to create, modify, and refine sketches through dynamic, conversational interactions. Our approach requires no training or fine-tuning. Instead, we leverage the sequential nature and rich prior knowledge of off-the-shelf multimodal large language models (LLMs). We present an intuitive sketching language, introduced to the model through in-context examples, enabling it to "draw" using string-based actions. These are processed into vector graphics and then rendered to create a sketch on a pixel canvas, which can be accessed again for further tasks. By drawing stroke by stroke, our agent captures the evolving, dynamic qualities intrinsic to sketching. We demonstrate that SketchAgent can generate sketches from diverse prompts, engage in dialogue-driven drawing, and collaborate meaningfully with human users.
+
+# 1. Introduction
+
+Sketching is a powerful tool for distilling ideas into their simplest form. Its fluid and spontaneous nature makes sketching a uniquely versatile tool for visualization, rapid ideation, and communication across cultures, generations, and disciplines [26, 102]. For example, designers use sketches to explore new ideas [39, 103], scientists employ them to formulate problems [48, 72], and children engage in sketching to learn and express themselves [27, 28] (see Fig. 2). Artificial systems, in principle, have the potential to support and enhance human creativity, problem-solving, and visual expression through sketching, adapting flexibly to their exploratory nature [22, 98, 122].
+
+Traditionally, sketch generation methods rely on human-drawn datasets to train generative models [5, 6, 16, 36, 42, 59]. However, fully capturing the diversity of sketches within datasets remains challenging [26], limiting these methods in both scale and diversity. Recent advancements in vision-language models, such as CLIP [78] and text-to-image diffusion [82], have enabled sketch generation methods that reduce reliance on human-drawn datasets [29, 46, 105]. These methods leverage pretrained model guidance and differentiable rendering [58] to optimize parametric curves, creating sketches that go beyond predefined styles and categories.
+
+While representing a significant step toward a general-purpose sketching system, these methods lack a crucial aspect of human drawing: the process itself. Current methods, though versatile, optimize all strokes simultaneously, making the intermediate sketching steps meaningless. As a result, the sketch cannot be decomposed into a coherent sequence of strokes that reflects the drawing process. In contrast, humans draw iteratively, stroke by stroke, incorporating visual feedback and continuously adapting—a dynamic, evolving process that fosters creativity, ideation, and communication [52, 88, 101].
+
+In this work, we introduce SketchAgent, a sketch generation agent that leverages the prior knowledge and sequential nature of multimodal large language models (LLMs) to enable versatile, progressive, language-driven sketching. Our agent can generate sketches across a wide range of textual concepts—from animals to engineering principles (Fig. 1, left). Its sequential nature facilitates interactive human-agent sketching and supports iterative refinement and editing through a chat-based dialogue (Fig. 1, right).
+
+Unlike vision-language models that directly generate images from text [75, 80, 82], multimodal LLMs [1, 2, 15, 56, 64, 74, 97] accept text and images as input but only output text. To produce visuals, they either utilize external "tools" (such as calling a text-to-image model) or are prompted to generate executable code (e.g., Python [43], SVG [9]) to create charts, diagrams, or graphics. However, prompting for such representations to directly produce sketches often results in a mechanical appearance with uniform, precise shapes that lack the subtle irregularities and spontaneous qualities characteristic of human sketches (see Fig. 3B). Additionally, despite their robustness in textual tasks, these models often struggle with fine-grained spatial reasoning [41, 118] as they are primarily optimized for text, making sketch editing more challenging.
+
+To address these limitations, we introduce an intuitive sketching language that enables an off-the-shelf multimodal LLM agent to "draw" sketches on a canvas by providing string-based actions, without additional training or finetuning. We define the canvas as a numbered grid, allowing the agent to reference specific coordinates (e.g., x2y8) to enhance its spatial reasoning capabilities. We represent a sketch as a sequence of semantically meaningful strokes, each defined by a series of such coordinates. We leverage In-Context Learning (ICL) [7, 51] to introduce the agent to the new representation, and Chain of Thought (CoT) [108] to enhance its planning capabilities. Given a sketching task, the agent produces a textual response following our representation, which we process by fitting a smooth Bézier curve to each coordinate sequence. The curves are then rendered onto the canvas to form the final sketch. We find this approach useful in emulating a more natural sketch appearance. For collaborative sketching, the canvas remains acces
+
+![](images/79df84ee3c76e6a87bd277ede69140cb5c63521e15ceac8868d03a0ab43c608d.jpg)  
+(A) Frank Gehry. *Elevation Sketches*. Guggenheim Museum
+
+![](images/84445e52d6588ee0eb6c7ec6a9e37694b8fc18440ca5cc76762989cfe593d383.jpg)  
+(B) Alexander Bell's drawing of the telephone
+
+![](images/7f2b351f7e27a24b7b48e583019243e8bb3c15676cd7c4566913578b20efa11e.jpg)  
+(C) Children drawing
+
+![](images/094c36db6efb33f65a4fa9b7c75cc6344415ae800a93f97dbef517957c6988be.jpg)  
+(D) Basketball strategy (pick and roll)  
+Figure 2. Examples of sketches used across disciplines and goals. (A) Ideation and design: Process Elevation Sketches by the architect Frank Gehry, Guggenheim Museum. (B) Engineering: Alexander Bell's telephone drawing. (C) Expressing emotions: Children's sketches. (D) Visual communication: Planning and communicating game strategy in basketball.
+
+sible to both the user and the agent throughout the session. The agent generates strokes sequentially and pauses according to an adjustable stopping token, allowing the user to add their own strokes directly to the canvas. These strokes are then integrated into the agent's sequence, enabling it to continue drawing, with real-time canvas updates.
+
+We demonstrate SketchAgent's capability to generate sketches of diverse concepts while capturing the inherently sequential and dynamic nature of sketching. We showcase our agent's ability to collaborate effectively with humans in real time to create novel and meaningful sketches. Our method is the first to leverage pretrained multimodal LLMs for sequential sketching without additional training, paving the way for a general-purpose artificial sketching system that supports iterative, evolving interactivity.
+
+# 2. Related Work
+
+Sketch Generation Early methods approached sketch generation by designing image filters to simulate sketchlike effects [10, 109]. With the advent of deep learning, data-driven approaches emerged to address a range of sketch-related tasks [117], including category-conditioned sketching [42, 76, 93], object sketching [59, 62], scenesketching [12, 57, 60, 114], sketch completion [6, 63, 94], portrait drawing [3, 120, 121], part-based generation [6, 37, 42, 129], and more. While sketch data collection has been broadly explored [21, 34, 40, 71, 85, 113], the wide variation in sketch styles and their adaptation to specific tasks [23] makes collecting datasets that encompass this diversity challenging. For example, QuickDraw [47], the largest available sketch dataset with 50 mil
+
+lion sketches, covers only 345 object categories and primarily focuses on simple, iconic representations. This limits data-driven methods to the style, abstraction level, and concepts seen during training. Recently, large pretrained vision-language models [75, 78, 80, 82, 84] have shown remarkable text-to-image generation capabilities by leveraging extensive visual knowledge from billions of training images [89]. While these models can be prompted to generate sketch-like images (see Fig. 3A), they do so in a single step and in pixel space, lacking the sequential, stroke-based process of human sketching. Subsequent approaches [14, 29, 31, 46, 105, 106, 115, 116, 124] leverage the priors of these models to guide an iterative optimization of parametric curves, with a differentiable rasterizer [58] linking pixel and vector representations. While producing vector sketches, the final strokes lack order and semantic meaning, and the optimization-based approach overlook the sequential aspect of the sketching process, making these methods suboptimal for collaborative sketching.
+
+Sequential and Collaborative Sketching Collaborative human-machine sketching holds promise in enhancing creativity, ideation, communication, and learning, as explored in various fields, including human-computer interaction (HCI) [17, 45, 49, 50, 53, 54], computer graphics [55, 96], robotics [86, 87], cognitive science [24, 25, 35, 67], learning sciences [18, 38, 104], and more. Central to collaborative sketching is its sequential, adaptive, and dynamic process, with each action carrying intent. Existing methods employ diverse training strategies to account for the discrete nature of sequential sketches, including reinforcement and adversarial learning [32, 68, 129], multi-agent referential games [69, 77], transformers [5, 6, 11, 33, 61, 81, 112], and more. SketchRNN [42] is a pioneering work in this area, introducing the QuickDraw dataset [47], a crowd-sourced collection of real-time sketch sequences made by users. They utilize this dataset to train a recurrent neural network for sequential sketch generation, which was later shown [24, 73] to have potential for human-machine collaboration. However, this approach remains constrained by the predefined categories encountered during training.
+
+Multimodel LLMs for Content Creation LLMs [7, 19, 79, 100] and multimodal LLMs [1, 2, 15, 56, 64, 74, 97] receive text as input (or text and images for multimodal) and output text. To enable visual content generation, these models are often paired with external "tools" that extend their functionality [44, 90, 111, 119]. For example, ChatGPT [74] generates images by internally calling a separate model, DALLE-3 [4]. Another approach involves prompting models to produce code in languages like Python [43], Processing [92], SVG [9], or TikZ [8] that can be rendered into visuals such as graphs, charts, and vector graphics. However, such code-generated content often looks
+
+![](images/ecebd173d5244262321496c10bc7579f13a3ede01ed0683c1bba5b4ff4bfd7d6.jpg)  
+(A) DALLE3 [4]
+
+![](images/269d98ca61721ce69d816b986175812dc51676e984fa2d9bdfd596c779d1bca9.jpg)  
+(B) LLMs [2] (SVG)
+
+![](images/26f29f516ec09b7cad0c0384e589dc27ba4c5f593fda2154d43f5b99be1eeb9b.jpg)  
+(C) SketchAgent
+
+![](images/30f937880ee2cde64f8b31b9bf39dc243cda3140563dd4a93f0198d2aa2d28be.jpg)  
+(D) Human [47]  
+Figure 3. Sketch appearance. (A) Text-to-image diffusion models operate in pixel space, lacking the sequential nature of sketches. (B) Prompting LLMs to produce visuals with SVG results in a uniform, mechanical appearance. (C) Sketches produced by our agent appear less mechanical, more closely resembling the nature of (D) Human sketches, which are often spontaneous and irregular.
+
+rigid, with uniform and overly precise shapes that lack the subtle irregularities and spontaneous qualities characteristic of freehand sketches (see Fig. 3B). In contrast, we propose a sketching language grounded in spatial information that encourages the model to produce a more natural sketch appearance, which we then process into vector graphics. Common strategies for enhancing LLMs capabilities include Chain-of-Thought prompting [13, 70, 83, 91, 127], which breaks down tasks into smaller, logical steps to mimic human reasoning, and In-Context Learning (ICL) [7, 20, 95, 123, 125], where examples of input-output pairs are provided to help the model infer task patterns.
+
+# 3. Preliminaries
+
+Vector Graphics and Bezier Curves Vector graphics allow us to create visual images directly from geometric shapes such as points, lines, curves, and polygons. Unlike raster images (represented with pixels), vector graphics are
+
+![](images/cfd520c98eb43f76e42eb72ff93f21bfc86c01d6fb8de66fb635b103b300bc01.jpg)  
+Figure 4. Cubic Bezier curve.
+
+resolution-free, more compact, and editable. SVG [110] is an XML-based format for storing vector graphics, popular for its scalability and compatibility with modern web browsers. The process of transferring vector graphics into pixel images is called rasterization or rendering. Cubic Bézier curves are commonly used to represent sketches in vector graphics. A cubic Bézier curve (Fig. 4) is a smooth parametric curve defined by four points: a start point  $P_0$ , an end point  $P_3$ , and two control points  $P_1$  and  $P_2$  that shape the curvature. The set  $P = \{P_0, P_1, P_2, P_3\}$  is often referred to as the curve's control points. The curve is described by the following polynomial equation:
+
+$$
+B (t) = (1 - t) ^ {3} P _ {0} + 3 (1 - t) ^ {2} t P _ {1} + 3 (1 - t) t ^ {2} P _ {2} + t ^ {3} P _ {3}, (1)
+$$
+
+where  $t \in [0,1]$  is a parameter that moves the point along the curve from  $P_0$  at  $t = 0$  to  $P_3$  at  $t = 1$ .
+
+![](images/0f06d8a6a6aa9521e66a99348e8b287aae238090cc82646635cf1398b7363315.jpg)  
+Figure 5. Method Overview. SketchAgent (blue) receives drawing instructions and generates a string representing the intended sketch. Inputs include: (1) a system prompt (orange) introducing the sketching language and canvas, (2) a user prompt (pink) specifying the task (e.g., "draw a shark"), and (3) a numbered canvas. The agent's response outlines a sketching strategy (in thinking tags) and a sequence of strokes defined by coordinates, which are processed into Bézier curves and rendered onto the canvas.
+
+# 4. Method
+
+Our goal is to enable an off-the-shelf pretrained multimodal LLM to draw sketches based on natural language instructions. An overview of our pipeline is illustrated in Fig. 5. We utilize a frozen multimodal LLM ("SketchAgent" shown in blue), which receives three inputs: (1) a system prompt containing guidelines for using our new sketching language, (2) a user prompt with additional task-specific instructions (e.g., "Draw a shark"), and (3) a blank canvas on which the agent can draw. Based on the given task, the agent generates a textual response, representing the sequence of strokes to be drawn, which we then process into vector graphics and render onto the canvas. The canvas can then be reused in two ways: it can be fed back into the model with an updated user prompt for additional tasks and editing, or it can be accessed by a human user who can draw directly on it to facilitate collaborative sketching. Next, we describe each component of the pipeline.
+
+The Canvas Although multimodal LLMs demonstrate remarkable reasoning abilities, they often struggle with spatial reasoning tasks [30, 66, 99]. We present a simple example (see Fig. 6) to illustrate how this limitation affects the naive use of these models for sketch generation and interactive sketching. We provide GPT-4o [74] with an image depicting a simple line drawing of a partial house featuring five numbered points (from 1 to 5), and ask it to identify which points should be connected to complete the house. While the model correctly identifies the pair of points, it fails to select the correct pixel coordinates when given a basic draw-line tool that connects two points, even after multiple attempts. To enhance the model's spatial reasoning ability, we utilize a numbered canvas that forms a grid. This grid features numbers (1 to 50) along the x-axis and the y-axis (Fig. 5, left). Each cell is uniquely identified by a combination of the corresponding x-axis and y-axis numbers (e.g., the bottom-left cell is  $x1y1$ ). The agent interacts with the canvas by specifying desired  $(x,y)$  coordinates.
+
+![](images/eaff46c17f5e0ca25ebf8cfe4fbb32a448f235608a9bfa2adcfa2d90231fce5b.jpg)  
+Figure 6. Although excelling in visual reasoning, multimodal LLMs often struggle to translate these abilities into spatial actions. In this example, GPT-4o [74] intends to draw a line between points 1 and 5 but fails to execute this with a draw_line function that accepts pixel coordinates.
+
+Sketch Representation We define a sketch as a sequence of  $n$  ordered strokes  $S = \{S_1, S_2, \ldots, S_n\}$ . Each stroke  $S_i$  is defined by a sequence of  $m$  cell coordinates on the grid:  $S_i = \{(x_j, y_j)\}_{j=1}^m$ , represented in string format as: <points>x1y1, x15y20, ...</points>.
+
+A naive approach to processing the textual sequence of coordinates would be to use a polyline, connecting consecutive points with line segments. However, our grid-based representation sparsifies the canvas, resulting in a non-smooth and unnatural appearance when using polylines (see Fig. 7, left). To achieve a smoother appearance, an alternative approach is to treat the coordinates as a sequence of control points defining smooth curves. However, as illustrated in Fig. 4, the control points often do not lie directly on the curve. Consequently, if the agent aims for a stroke that passes through specific coordinates, it must derive the control points that define this stroke, which is challenging.
+
+We propose an alternative approach: we treat the specified  $(x, y)$  coordinates as a set of desired points sampled along the curve, and fit a smooth Bézier curve to them (Fig. 7, right). To accommodate curves with complex curvature, we also task the model with determining when each point on the curve should be passed through, corresponding to the  $t$  value described in Eq. (1). Thus, for each stroke  $S_{i}$ , the agent provides a set of  $m$  sampled points  $S_{i} = \{(x_{j}, y_{j})\}_{j=1}^{m}$ , along with a corresponding set of  $t$  values:  $T_{i} = \{t_{j}\}_{j=1}^{m}$ . Based on these, we fit a cubic Bézier
+
+![](images/212fa6867ce4bdcbddaa82751742056c0944857271c1b4b8a0fc7031b67326ee.jpg)  
+(A) Polyline
+
+![](images/d04feb1e43212ca5927cdd3bfb132b6d589709712778a0904e76bc0a14265623.jpg)  
+Figure 7. Methods for processing the agent's coordinate sequence (in red): (A) Polyline results in an unnatural appearance. (B) Directly using coordinates as Bézier control points is challenging as they do not lie on the curve. (C) Fitting a Bézier curve to sampled coordinates provides smoother results.
+
+![](images/87bdbe0a578ba8382f0d291ffe00f966941310f2175de173f265c8c1c46094b2.jpg)  
+(B) Control Points  
+(C) Ours
+
+curve to the sampled points by solving a system of linear equations using least squares, where the unknowns are the control points  $P = \{P_0, P_1, P_2, P_3\}$ :
+
+$$
+P = \operatorname {a r g m i n} _ {P} \| A P - B \|, \tag {2}
+$$
+
+where  $A \in \mathbb{R}^{m \times 4}$  contains the cubic Bézier basis functions evaluated at specific  $t_j$  values (as described in Eq. (1)), and  $B \in \mathbb{R}^{m \times 2}$  contains the  $m$  sampled points  $\{(x_j, y_j)\}_{j=1}^m$ . The least squares solution minimizes the error between the fitted Bézier curve and the sampled points. For long sequences resulting in a large fitting error, we recursively split the curve. Additionally, we account for Bézier curves of lower degrees, including quadratic curves, linear lines, and points. Upon completing this process, we render the parametric curves onto the canvas.
+
+Drawing Instructions We provide the model with a system prompt and a user prompt (marked in orange and pink in Fig. 5). In the system prompt, we supply the agent with context about its expertise ("You are an expert artist specializing in drawing sketches") and introduce it to the grid canvas along with examples of how to use our sketching language for drawing single-stroke primitives (full prompts are provided in the Appendix). The system prompt is fixed and can be applied to a variety of sketching tasks. The user prompt includes a description of the desired task and an example of a simple sketch of a house drawn with our sketching language. We find this to be crucial in assisting the agent with preserving the correct format that could be parsed directly [7]. The agent is tasked with responding in the format shown in the gray text box in Fig. 5. In the <thinking> tags, the agent is tasked to outline the overall sketching strategy [108]. This typically includes describing the different components of the sketch, the intended sketching order, and the overall placement of each part. The agent is also tasked with providing an ID tag following each stroke, which is useful for further analysis and for producing annotated sketches in scale.
+
+# 4.1. In-Chat Editing and Collaborative Sketching
+
+The above process can be repeated iteratively to support multiple sketching tasks and interactions. Text-based sketch editing in a chat dialogue is enabled by feeding the rendered
+
+![](images/95f2cb4f29aad5591b1e0194e2cf0ab7526e4b5e016af1d9e988b66435856fc1.jpg)
+
+![](images/2ce6c74333131c52fd4d2db63f898a49a0e211208a5a003b97036fbaedfe1a24.jpg)
+
+![](images/a200c7aa52d21ba8b21482f41ac05341be18a89a9ccba901fa92fd467b789848.jpg)
+
+![](images/1bd05a8d61780921afe2f41ff9d85cf2dc4418c435896e452d678996aeb9e97a.jpg)  
+DNA Double Helix
+
+![](images/deab0063155c5254908d052613efaa75c2a6d154ebe3baeeead4c1ce067194f5.jpg)  
+Golden Gate Bridge
+
+![](images/e1c42a497153ef5a8dfb3a8737e16da2cabd3d437ad02ee06a5551aba0e1d2af.jpg)  
+Mount Fuji  
+Pendulum Motion  
+Double-Slit Experiment
+
+![](images/6fd0668cd32e45b057920fd584981d956b47ad05709d30cd8c47068995420b89.jpg)  
+Eiffel Tower  
+Flowchart  
+Figure 8. Sketches produced by SketchAgent for concepts beyond pre-defined categories. The textual input describing the desired concept shown below each image.
+
+![](images/661e67bb48b898e26fae04c7637ad316784dbe6caf1e6bdcdac6af5e7b98976f.jpg)  
+Tic-tac toe
+
+canvas back to the agent (see dashed arrow in Fig. 5) and updating the user prompt with the desired edits. To support collaborative human-agent sketching, the canvas remains accessible to both the human user and the agent throughout the entire sketching session. We define an adjustable stopping token,  $\langle \text{}/\text{s}\{\text{j}\} \rangle$ , which instructs the agent to pause generating the sequence at stroke number  $j$ . We then process and render the generated strokes onto the canvas up to that point, then the user can add strokes directly to the canvas to continue the sketch. The user-drawn strokes are processed and converted into the agent's format by reversing our fitting process, i.e., sampling each stroke at multiple  $t$  values (as shown in Eq. (1)), and selecting the points closest to each cell's center on the grid. The converted user strokes are then chained with the agent's sequence, after which the agent resumes sketching until the next stopping token.
+
+# 5. Results
+
+We evaluate the performance of our method qualitatively and quantitatively across a selected set of sketching tasks. Additional tasks, evaluations, and examples are provided in the Appendix. All results presented in the paper were generated using Claude3.5-Sonnet [2] as our backbone model, unless stated otherwise.
+
+# 5.1. Text-Conditioned Sketch Generation
+
+Figures 1 and 8 demonstrate SketchAgent's capability to generate sketches of various concepts that extend beyond standard categories, which includes scientific concepts (e.g., "the double-slit experiment", "pendulum motion"), diagrams (e.g., "circuit diagram", "a flowchart"), and notable landmarks (e.g., "Taj Mahal", "Eiffel Tower"). More examples are provided in the Appendix. To quantitatively evaluate text-conditioned generation we utilize the QuickDraw dataset [47]. We randomly sample 50 categories (out of 345), and apply our method to generate 10 sketch in
+
+<table><tr><td></td><td>GPT-4o</td><td>GPT-4o -mini</td><td>Claude3 Opus</td><td>Claude3.5 -Sonnet*</td><td>Claude3.5 -Sonnet (SVG)</td><td>Human (QD [47])</td></tr><tr><td>Top1</td><td>0.15 ±0.04</td><td>0.04 ±0.03</td><td>0.13 ±0.04</td><td>0.23 ±0.05</td><td>0.23 ±0.04</td><td>0.27 ±0.07</td></tr><tr><td>Top5</td><td>0.30 ±0.06</td><td>0.10 ±0.04</td><td>0.27 ±0.05</td><td>0.44 ±0.03</td><td>0.43 ±0.06</td><td>0.49 ±0.06</td></tr><tr><td>Vis.</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 1. Sketch recognition evaluation. Average Top-1 and Top-5 sketch recognition accuracy computed with CLIP zero-shot classifier on 500 sketches from 50 categories. The last row visualizes one sample from each experiment. *Indicates our default settings, which receives the highest accuracy among all models.
+
+stances per category, resulting in 500 sketches in total. Following common practice [105, 106, 115, 116], we utilize a CLIP zero-shot classifier [78] to evaluate how well the generated sketches depict the intended category. We compare the performance of different multimodal LLMs by repeating the same process with GPT-4o-mini [74], GPT-4o [74], and Claude3-Opus [2] as our backbone model (in addition to Claude3.5-Sonnet [2], our default backbone). As a baseline, we include human-drawn sketches sampled from the QuickDraw dataset [47]. The average Top-1 and Top-5 sketch classification accuracy are presented in Table 1. As can be seen, human sketches achieve the highest recognition accuracy, with Claude3.5-Sonnet performing best among all models, approaching human-level rates under the CLIP-score metric. More evaluation of confusion patterns and visualization of the data are provided in the Appendix.
+
+We additionally compare to prompting Claude3.5-Sonnet to directly generate SVGs using the following prompt: "Write SVG string that draws a sketch of a <concept>. Use only black and white colors". The corresponding scores are shown in the fifth column of Tab. 1. While this approach achieves recognition scores comparable to those of SketchAgent, the outputs are often characterized by uniform and precise shapes, failing to replicate the fluidity and natural irregularity of free-hand human sketches (e.g., Fig. 3). To evaluate how "human-like" our agent's sketches appear, we conduct a two alternative forced choice (2AFC) user study with 150 participants. Each participant was presented with pairs of sketches depicting the same object class produced by different methods, and asked to choose the sketch they believed was human-drawn. 150 sketches across 50 object classes were tested, comparing three methods: direct prompting, SketchAgent, and human sketches from QuickDraw (see Appendix for details). Results indicate SketchAgent's drawings appeared more human-like, being chosen as human-drawn in  $74.90 \pm 3.35\%$  of cases when compared with direct prompting. When compared to human drawings,
+
+![](images/423a11037c664387b1a182431eb6f4eedd6120c7e5bf6f031d5dfdee35b62b69.jpg)  
+Figure 9. SketchAgent gradually draws stroke-by-stroke, each stroke is annotated by the agent with a semantic meaning.
+
+![](images/04d463e6f03e007611601410ebbcd7f8b365b30eb1b0c6400a7333a2068fb197.jpg)  
+Figure 10. Recognition rate as a function of sketch complexity.
+
+![](images/07f9d2c145aadce7dd680e4e50f8d2970cc25e1e13d6710c4e467d2cc83efedf.jpg)
+
+![](images/969d296403a23d3904cb4e0625589d27622dce0da84e52d44ebd61be07008104.jpg)
+
+users slightly preferred human sketches  $(54.68 \pm 4.61\%)$  over SketchAgent's, while direct prompting was chosen only  $38.9 \pm 5.55\%$  of the time.
+
+Lastly, to quantitatively analyze the effect of concept complexity, we study the case of drawing letters. We systematically increase sketch complexity by adding letters to the target concept (e.g., from 'ABC' to 'ABCDEFGH') and count the number of correctly recognized letters in each sketch. The graph in Fig. 10 shows that performance decreases as the complexity increases.
+
+# 5.2. Sequential Sketching
+
+Figure 9 shows stroke-by-stroke sketch generation by SketchAgent, with the labels on the right indicating the sketching order and the meaning our agent associates with each generated stroke (see Appendix for more examples). Stroke annotation during generation is enabled by utilizing the prior of the backbone LLM, providing a valuable feature for analysis and data collection [37, 65, 107, 126, 128]. In Fig. 11, we illustrate why accounting for the sequential nature of sketching more closely emulates the process of human drawing. We present the sketch creation process of SketchAgent alongside SVGDreamer [116], SketchRNN [42], and a human sketch sampled from QuickDraw [47]. SVGDreamer (first row), is an optimization-based method, where a set of randomly initialized parametric curves (left-most column) are iteratively refined to form a sketch, guided by a pretrained text-to-image diffusion model [82]. This process is time-consuming, taking 2000 iterations (1.6 hours), which makes it unsuitable for interactive sketching. While the final sketch (rightmost column) appears detailed and artistic due to the powerful vision backbone, the intermediate sketching and individual strokes lack clear semantic meaning. In contrast, SketchRNN (second row) is a sequential generative model trained on human-drawn dataset, producing sketches in real-time with strokes added progressively, emulating closer a human-like sketching pro
+
+SVGDreamer [116].  $\approx 1.6$  hours  
+
+<table><tr><td colspan="6">SketchRNN [42].≈4 seconds</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="6">SketchAgent (Ours).≈20 seconds</td></tr><tr><td>body</td><td>head</td><td>left ear</td><td>right ear</td><td>back right leg</td><td>left eye</td></tr><tr><td colspan="6">Human [47].≤20 seconds</td></tr></table>
+
+Figure 11. Sequential sketching process. SVGDreamer [116] requires 2000 iterations (1.6 hours) with intermediate steps lacking semantic meaning. SketchRNN [42] operates in real-time with coherent steps but is limited to QuickDraw categories. SketchAgent draw gradually with meaningful strokes and no category restrictions. Human sketches evolve through gradual, meaningful steps.
+
+cess (as shown in the last row). Similarly, SketchAgent (third row) produces sketches gradually, with each stroke carrying a semantic meaning, by utilizing the sequential nature of its backbone model. While SketchRNN is restricted to generating sketches only within the 345 categories it was trained on, SketchAgent leverages the extensive prior knowledge of its backbone multimodal LLM, enabling it to create sketches of general visual concepts.
+
+We use the set of 500 samples described in Sec. 5.1 to quantitatively analyze the sequential nature of our agent's sketches compared to human drawings. On the left of Fig. 12, we present histograms comparing the number of strokes in QuickDraw sketches (orange) and our sketches (blue). Most QuickDraw sketches contain 1 to 6 strokes, while our sketches show a broader distribution, peaking between 5 to 10 strokes. This suggests that, on average, QuickDraw sketches appear more abstract. To ensure a balanced comparison of sketches with similar levels of abstraction, we select sketches from both groups with a similar number of strokes (the largest intersection is found in sketches with 4-7 strokes, comprising 204 of our sketches and 120 from QuickDraw) and measure the change in CLIP-Score as a function of the accumulated number of strokes (Fig. 12, right). Both QuickDraw and our sketches exhibit a generally similar pattern, with CLIPScore increasing as more strokes are added, suggesting that sketches become progressively more recognizable as they evolve.
+
+![](images/8bb79ce4851de1d59ede2f9298fd100f1c2e84e32cba837bddaa488f0ba4591f.jpg)  
+Figure 12. Sequential sketching analysis of SketchAgent (blue) and Humans [47] (orange). Left: Histograms of stroke distribution per sketch, showing QuickDraw sketches are more abstract on average. Right: CLIPScore as a function of the accumulated number of strokes for sketches containing 4-7 strokes, showing a similar recognition pattern over time.
+
+![](images/df5f4609b0c441a7467c3969f5a4245622328392296f8f901211d83ac22edf94.jpg)
+
+# 5.3. Human-Agent Collaborative Sketching
+
+We demonstrate the potential of our system for facilitating interactive human-agent collaboration, resulting in semantically meaningful and recognizable sketches. We design a web-based collaborative sketching environment (Fig. 13A) where users and SketchAgent take turns drawing on a shared canvas to create a recognizable sketch from a given textual concept. Following the evaluation protocol in collabdraw [24], we select 8 simple concepts, based on the agent's demonstrated ability to draw them independently, to focus evaluations on assessing the impact of collaboration. Participants sketched concepts in two modes: solo, where users drew independently, and collab, where users and SketchAgent collaborated, adding one stroke at a time until either was satisfied with the drawing. We collect sketches from 30 participants, resulting in 480 sketches in total. Average CLIP recognition rates are shown in Figure 13B. Collaboratively produced sketches (blue) achieve recognition levels close to those made solely by users and higher than those produced by the agent alone (dashed lines). To assess the contribution of each party in collaborative mode, we analyze partial sketches with only agent-made strokes (pink) or user-made strokes (green), resulting in a significant reduction in recognizability. This suggests that both user and agent contribute meaningfully to the recognizability of the complete sketch.
+
+# 5.4. Chat-Based Sketch Editing
+
+We next demonstrate the effectiveness of our method in performing interactive text-based sketch editing within a chat dialogue, where the input to the agent combines both text and images. Inspired by [92], we explore edits that involve spatial reasoning and object relations. We focus on three object categories: outdoor, indoor, and animals, with three objects each, and design editing prompts to add objects to the input sketches. For outdoor and indoor objects, we specify relative locations of added concepts, e.g., "left to", "on top of" (see Fig. 14 left). For the animals category, we tasked
+
+![](images/1ef282de04d388ff3cea584cc8f62439859b8bb456a0b0f83105927e7b99ad08.jpg)  
+(A) Sketching interface
+
+![](images/9b467c1d65280845bea59527f26ef0b501d740d2b6a7852e9a026da3abbfb9b5.jpg)  
+(B) Collaborative user study results
+
+![](images/ce280e778c673c55a5fab06f36f56a5a8fff409fc90b55e02f168b8aa652fb50.jpg)  
+Figure 13. Collaborative sketching evaluation measured using CLIP classification. Sketches created collaboratively (blue) approaching those made solely by users (dashed lines). In collaborative sketches, keeping agent-only strokes (pink) or user-only strokes (green) significantly reduces recognizability.  
+Figure 14. Chat-based sketch editing. We iteratively prompt SketchAgent to add objects to sketches through chat dialogues.
+
+the agent with adding accessories to each animal without guidance on their exact placement, testing its ability to infer placement based on semantics (e.g., placing a hat on a head (see Fig. 14 right). The full list of object and editing instructions is provided in the Appendix. We produced a total of 54 sketches. Evaluating the edited sketches reveals that SketchAgent correctly follows instructions  $92\%$  of the time, with  $94\%$  accuracy for specified relations and  $88\%$  accuracy for inferred semantic relations.
+
+# 6. Ablation
+
+We evaluate the impact of each component of our method by systematically removing them and measuring sketch recognition rates as detailed in 5.1. We assess the effects of removing the system prompt, omitting the CoT process (i.e., excluding thinking tags and 'think step-by-step' instructions), and modifying ICL (the complete sketch example provided in the user prompt). When modifying ICL, we use a correctly formatted single-stroke example instead of the complete sketch, as fully removing ICL results in outputs that do not follow the expected format making them unparsable. The results in Table 2 show that the full SketchAgent pipeline achieves the highest performance, highlighting the importance of each component. Interestingly, not providing a complete sketch example significantly reduces performance. We additionally ablate the impact of the grid resolution, by varying the resolution from 10 to 100 (see Tab. 2, bottom). Extremely low resolutions degrade performance, while mid-level resolutions outperform  $100 \times 100$ .
+
+<table><tr><td></td><td>w/o System Prompt</td><td>w/o CoT</td><td>Modified ICL</td><td>SketchAgent (full)</td></tr><tr><td>Top1</td><td>0.20 ± 0.04</td><td>0.14 ± 0.02</td><td>0.07 ± 0.02</td><td>0.23 ± 0.04</td></tr><tr><td>Top5</td><td>0.42 ± 0.03</td><td>0.29 ± 0.04</td><td>0.16 ± 0.03</td><td>0.43 ± 0.06</td></tr><tr><td>Grid Size</td><td>10 × 10</td><td>25 × 25</td><td>50 × 50</td><td>75 × 75</td></tr><tr><td>Top1 / Top5</td><td>0.14 / 0.28</td><td>0.19 / 0.42</td><td>0.23 / 0.43</td><td>0.23 / 0.41</td></tr></table>
+
+Table 2. Ablation study. Average Top-1 and Top-5 CLIP recognition accuracy. Top: We systematically remove each component in our pipeline, showcasing all components contribute to the agent's full performance. Bottom: Grid resolution ablation.
+
+# 7. Limitations and Future Work
+
+SketchAgent has several limitations. First, it is constrained by the priors of the backbone model, primarily optimized for text rather than visual content. As a result, the agent often produces rich textual descriptions of object parts but struggles to convert these into effective sketching actions, resulting in overly abstract and unrecognizable outputs. For example, in Fig. 15A, the agent effectively describes key parts of a unicorn (e.g., the horn), but the sketch is unrecognizable. This constraint also impacts the depiction of human figures (Fig. 15B). While distinctive features (e.g., Frida Kahlo's eyebrows or Michael Jordan's dunk) may be captured well in language, the resulting sketches are overly simple, with an amateur style, lacking expressivity. We expect this issue to improve as future models advance in vision capabilities. Lastly, the agent may struggle with drawing letters and numbers. This could be improved in future work by providing relevant in-context examples.
+
+![](images/ab03659d7c4d1a51dd5884bfa72ac04901f6940c37db0ebced6a7e7e0884155b.jpg)  
+(A) Non-recognizable
+
+![](images/a5198ad87ecffd7972bcfcf56f48b5c9045d4741a2ec81cdda15348a70a826d5.jpg)  
+(B) Human figures  
+Figure 15. Limitations. Sketches of complex concepts (A) and human figures (B) appear too abstract and unrecognizable with non-professional style. (C) Fail to depict letters and numbers.
+
+![](images/ad6c20de7a2d320b68f6ae43926ba1745d7421378648d09adf4f1b97e1df2888.jpg)  
+(C) Letters and numbers
+
+# 8. Conclusions
+
+We presented a method for language-driven, sequential sketch generation, that can produce versatile sketches in real-time and meaningfully engage in collaborative sketching sessions with humans. We show that the prior knowledge embedded in pretrained multimodal LLMs can be effectively leveraged for sketch generation through an intuitive sketching language and a grid canvas, without requiring additional training or fine-tuning. We hope our work represents a meaningful step toward developing general-purpose sketching systems with the potential to enhance human-computer communication and computer-aided ideation.
+
+# 9. Acknowledgements
+
+We thank Yuval Alaluf, Hila Chefer, Assaf Ben Kish, Joanna Materzynska, Rinon Gal, Elad Richardson, Arnav Verma, and Ellie Arar for providing feedback on early versions of our manuscript. We are also grateful to Justin Yang, who developed the initial Photodraw application and assisted with the interactive human study setup, and to Dingning Cao, who contributed to the SketchAgent interface and application. Special thanks to Yarden Frenkel for his insights, early explorations, and inspiring discussions. This work was partially supported by NSF CAREER #2047191, NSF DRL #2400471, Stanford Human Centered AI Institute Hoffman-Yee Grant, Hyundai Motor Company, ARL grant W911NF-18-2-021, the Zuckerman STEM Leadership Program, and the Viterbi Fellowship. The sponsors had no role in the experimental design or analysis, the decision to publish, or manuscript preparation. The authors have no competing interests to report.
+
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