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Unlearnable examples (UEs)—data modified with imperceptible perturbations to inhibit model training while preserving human usability—have emerged as a promising approach. However, existing UE methods assume unauthorized trainers have extensive exposure to UEs or that models are trained from scratch, which may not hold in practical scenarios. This paper investigates the effectiveness of UEs under the few-shot learning paradigm, pitching it against prompt learning (PL) models that leverage pretrained vision-language models (VLMs), like CLIP, capable of generalizing to new classes with minimal data. To address this, we introduce an adaptive UE framework to generate unlearnable examples that specifically target the PL process. In addition, we propose a novel UE countermeasure, $A^3$ , with cross-modal adversarial feature alignment, specifically designed to circumvent UEs under few-shot PL. Experimental evaluations on 7 datasets show that $A^3$ outperforms existing PL methods, achieving up to $33\%$ higher performance in learning from UEs. For example, in the scenario involving $\ell_{\infty}$ -bounded EM perturbations, $A^3$ has an average harmonic mean accuracy across 7 datasets of $82.43\%$ , compared to CoCoOp's baseline of $65.47\%$ . Our findings highlight the limitations of existing UEs against PL and lay the foundation for future data protection mechanisms. + +# 1. Introduction + +In the era of pervasive machine learning applications, protecting digital content from unauthorized use is an escalating concern. An emerging solution involves unlearnable ex + +amples (UEs) [9, 11, 29, 36, 40]. — data modified with imperceptible perturbations that prevent machine learning models from effectively learning and generalizing from it, while preserving its utility for human observers. Unlike traditional data poisoning attacks intended for malicious use, UEs serve content creators by providing a way to inhibit unauthorized model training. Beyond this, UEs can also be used to shed light on vulnerabilities and learning preferences [36] of deep learning models, and prevent unlawful use of personal features [24]. However, existing UE methods are primarily designed for models trained from scratch, and make strong assumptions where all or a large proportion of training data is used unknowingly by unauthorized trainers. These assumptions may not hold in the wilderness, for several reasons: (a) Creators may release limited data. (b) Unauthorized trainers may have limited exposure to the UEs: they may curate their training data from various sources and may only use a small fraction of the creator's data. (c) Trainers may leverage pretrained models to improve training efficiency, and to generalize well to new classes and contexts. + +In this paper, we found that recent advances in prompt learning (PL) with pretrained vision-language models (VLMs) can indeed challenge the robustness of UEs. VLMs use contrastive learning to align images and text features, enabling strong zero-shot and downstream tasks [15, 30, 32, 35]. PL further adapts CLIP by fine-tuning prompts instead of model weights, making it ideal for data-limited scenarios, and novel tasks and classes. This paper thus investigates a central question: Are UEs effective in protecting data against PL-enabled models? This question has profound implications from both the content creator's and the unauthorized trainer's perspectives. + +For content creators, understanding this question is crucial for several reasons: (a) To effectively prevent unauthorized usage, creators need to know the minimum amount of modified data required to maintain protection. (b) Content + +creators typically control and release a limited quantity of data, making it impractical to assume access to large datasets. This constraint naturally leads to a few-shot scenario, which is the focus of this study. + +For unauthorized trainers, PL represents an appealing tool to bypass UEs, as PL exploits the generalization strengths of VLMs: (a) The pretrained encoders of VLMs enables it to generalize well to novel classes, potentially circumventing perturbations that would normally deter training from scratch. (b) While existing methods to circumvent UEs typically involve adversarial training [19], or image augmentations [16, 25], which affect only the image seen by the model. PL may be able to enhance its robustness by incorporating text augmentations, offering a broader strategy to bypass unlearnability protections. + +To address these challenges, we propose an adaptive framework that targets UEs in the few-shot PL setting. The contributions of this paper are as follows: + +- We introduced a scenario designed to examine the effectiveness of UEs against prompt learning, particularly in a few-shot context where data availability is constrained. Beyond existing UE methods, we introduced an adaptive UE framework that incorporates PL-specific considerations for surrogate-based UEs, generating stronger UEs that are more effective against PL. +- We propose a novel method, $\mathrm{A}^3$ , which employs cross-modal adversarial augmented feature alignment to enhance PL's ability to generalize when learned from UEs. This method adversarially aligns diversely-augmented image and text augmentations to make PL robust against UEs. +- Experimental results demonstrate that $\mathrm{A}^3$ achieves significant performance gains over existing methods, proving more effective against other UE methods in few-shot scenarios, even when faced with larger perturbations, and partial poisoning. $\mathrm{A}^3$ also generalizes well to novel classes. + +This work offers new insights into the capabilities and limitations of UEs against PL, laying a foundation for more robust data protection strategies in the era of knowledge transfer with large pretrained models and multimodal machine learning. + +# 2. Related Work & Preliminaries + +# 2.1. Unlearnable Examples + +The primary goal of unlearnable examples [9, 11, 29, 33, 36, 40] is to safeguard the privacy and copyright of content providers by adding small, human-imperceptible perturbations to data. These perturbations prevent machine learning models from effectively generalizing to the data's original distribution. Unlike traditional data poisoning attacks [10], which aim to introduce backdoor patterns into a model, unlearnable examples are not intended for malicious purposes but solely to protect data from unauthorized use. + +Definition of Unlearnable Examples Consider a dataset with $N$ clean samples $\mathcal{D}_{\mathrm{clean}} = \{(x_i,y_i)\}_{i = 1}^N$ , where $\mathbf{x}_i\in \mathcal{X} = [0,1]^{C\times H\times W}$ and $y_{i}\in \mathcal{V} = \{1,\dots ,K\}$ represent the $i^{\mathrm{th}}$ input sample with $C$ channels and $H\times W$ spatial dimensions, and its corresponding true label. Each sample is drawn from a distribution $\mathcal{S}$ . The content provider aims to add small perturbations $\delta_{i}\in \mathcal{B}_{p}(\mathbf{x}_{i},\epsilon)$ to the clean samples in $\mathbf{x}_i\in \mathcal{D}_{\mathrm{clean}}$ to generate unlearnable examples $\mathcal{D}_{\mathrm{ue}}(\boldsymbol {\delta})\triangleq \{(\mathbf{x}_i + \boldsymbol {\delta}_i,y_i)\mid (\mathbf{x}_i,y_i)\in \mathcal{D}_{\mathrm{clean}}\}$ . The set $\mathcal{B}_p(\mathbf{x}_i,\epsilon)$ is: + +$$ +\mathcal {B} _ {p} \left(\mathbf {x} _ {i}, \epsilon\right) \triangleq \left\{\mathbf {d} \mid \| \mathbf {d} \| _ {p} \leq \epsilon , \mathbf {x} _ {i} + \mathbf {d} \in \mathcal {X} \right\}. \tag {1} +$$ + +It bounds the noise $\delta_{i}$ of each sample $\mathbf{x}_i$ within the $\epsilon$ -ball of $\ell_p$ -distance with respect to the sample, and the perturbed sample $\mathbf{x}_i + \delta_i$ remain within the input domain $\mathcal{X}$ . A small $\epsilon$ is crucial to ensure that the perturbations do not significantly alter the original content, thus preserving the data's utility, and typically $p \in \{0,2,\infty\}$ . + +When this perturbed dataset is used for training, the goal is for the resulting model to generalize poorly to the original distribution $S$ . The optimization for the noise can be formulated as the following bi-level optimization problem to solve for the bounded perturbations $\delta \triangleq \{\delta_i \in \mathcal{B}_p(\mathbf{x}_i, \epsilon)\}_{i=1}^N$ : + +$$ +\max _ {\delta} \mathbb {E} _ {\left(\mathbf {x} _ {i}, y _ {i}\right) \sim \mathcal {S}} \left[ \mathcal {L} \left(f _ {\boldsymbol {\theta} ^ {*} (\delta)} \left(\mathbf {x} _ {i}\right), y _ {i}\right) \right], \tag {2} +$$ + +where $f_{\theta}:\mathcal{X}\to \mathbb{R}^{K}$ denotes the model with parameters $\pmb{\theta}$ , $\mathcal{L}:\mathbb{R}^K\times \mathcal{V}\rightarrow \mathbb{R}$ is the loss function (typically cross-entropy), and $\pmb{\theta}^{\star}$ represents the model parameters optimized on the perturbed images: + +$$ +\boldsymbol {\theta} ^ {\star} (\boldsymbol {\delta}) = \operatorname {a r g m i n} _ {\boldsymbol {\theta}} \mathbb {E} _ {(\mathbf {x} _ {i}, y _ {i}) \sim \mathcal {D} _ {\text {c l e a n}}} [ \mathcal {L} (f _ {\boldsymbol {\theta}} (\mathbf {x} _ {i} + \boldsymbol {\delta} _ {i}), y _ {i}) ]. \tag {3} +$$ + +As the above problem is intractable, many works have proposed alternative methods to approximate the solution, commonly involving surrogate models: + +- Hypocritical perturbations (HYPO) [33] assumes a surrogate model $g_{\theta} : \mathcal{X} \to \mathbb{R}^{K}$ with pretrained weights $\theta$ learned on samples from $S$ , and directly finds the perturbations $\delta$ that makes the model easily produce correct predictions for $\mathcal{D}_{\mathrm{clean}}$ images. +- Error maximization (EM) [11] further considers a randomly-initialized surrogate $g_{\theta}$ , and optimizes the noise $\delta$ , and the surrogate model $g_{\theta}$ simultaneously. +- Robust error maximization (REM) [9] extends EM to optimize the surrogate $g_{\theta}$ under adversarial training [19], where the adversarial noise is also bounded within the $\epsilon$ -ball of $\ell_p$ -norm, and optimized via projected gradient descent (PGD) [19]. This helps to improve the effectiveness of the perturbations even under adversarial training. + +Interestingly, recent works have shown that unlearnable examples can also be curated without the need for optimization, where the perturbations form a linearly-separable subspace that can be learned easily by the model. This bias is so strong that it makes the underlying features less learnable by model training algorithms: + +- Linearly-separable perturbations (LSP) [40] generates random color patches as perturbations, and apply them to the images while ensuring the added noise is bounded within a small $\ell_2$ -distance from the original image. This simple method can enable strong unlearnable examples without the expensive optimization process and the need for surrogate models. +- Autoregressive Poisoning (AR) [29] Similar to LSP, AR prescribes a simple perturbation strategy which first fills all channels of the first 2 rows and columns of the image with Gaussian noise, then uses an autoregressive process to fill the remaining pixels with a $3 \times 3$ sliding window. It then re-scales the perturbations to be within the noise bound $\mathcal{B}_p(\mathbf{x}_i, \epsilon)$ , before adding them to the image $\mathbf{x}_i$ . +- One-pixel Shortcuts (OPS) [36] For each image belonging to a specific class, OPS searches for an optimal pixel and color value for the class, such that it results in the largest change in the pixel's color value for all perturbed images. This constitutes a simple $\ell_0$ -bounded perturbation where only one pixel is modified for each image. Surprisingly, when training models from scratch, OPS can generate even stronger unlearnable examples than EM with a 8/255 noise budget [25, 36]. It also resists even $\ell_{\{2,\infty\}}$ -bounded adversarial training, as the noise added by adversarial training cannot effectively perturb the pixel values for the erasure of $\ell_0$ -perturbations. + +As $\mathsf{A}^3$ considers the problem of learning from unlearnable examples from the perspective of few-shot learning with prompt learning (PL), we provide a framework that adapts the above methods to this setting, by making the surrogate models $g$ our prompt learners. It also shows that PL can be in a certain degree effective against unlearnable examples produced by these methods. + +# 2.2. Learning from Unlearnable Examples + +The emergence of unlearnable examples prompts investigation into the mechanisms that unauthorized trainers might exploit to extract useful features. + +Adversarial Training (AT) [2, 19] involves the generation of adversarial examples [4, 12, 41] specifically tailored to the model under training, which are in turn used to train the model to enhance the model's robustness. It also has been known to be an effective approach to improve the model generalization when trained on unlearnable examples [11]. However, adversarial training is known to be computationally expensive, and also affects the model's performance on clean data [38], especially when the sample size is small [5]. + +For this reason, Image Shortcut Squeezing (ISS) [16] introduces a suite of simple image processing methods can show surprising effectiveness in mitigating the impact of unlearnable examples, without the costs associated with adversarial training. Grayscale removes the color information from the training images, and JPEG Compression + +(JPEG) instead performs a lossy JPEG with high compression rate on the training images. However, it was recently discovered [26] that simple image processing is much less effective against adaptively-optimized unlearnable examples. Building upon this idea, UEraser [25] further proposes a stochastic augmentation pipeline with a wider range of transformations, and uses a simple adversarial augmentation to optimize models only on augmented images with the maximum loss. This allows the model to learn the underlying features without being affected by the easily learnable shortcuts in unlearnable examples. While all these methods have shown effectiveness against unlearnable examples, they consider the problem of training models from scratch rather than leveraging pretrained models. + +# 2.3. Prompt Learning + +Vision-language pretrained models (VLMs), such as CLIP [27] and ALIGN [13], represent a significant advancement in multi-modal learning. Trained on extensive image-text pair datasets, The VLM have two main components: an image encoder $f_{\mathrm{im}}: \mathcal{X} \to \mathbb{R}^d$ and a text encoder $f_{\mathrm{tx}}: \mathcal{W} \to \mathbb{R}^d$ , where $\mathcal{X}$ and $\mathcal{W}$ are the input image and text, respectively, and learn a shared embedding space $\mathbb{R}^d$ for images and texts. Image and text pairs that are semantically similar will have similar embeddings in this space, and vice versa. This makes them versatile for a wide range of downstream tasks, including image classification [27], captioning [1], retrieval [18], and providing guidance for image generation [7, 28]. Notably, VLMs show impressive zero-shot performance, where they can perform well on new tasks without task-specific training, showcasing their generalization capabilities. + +Prompt Engineering for VLMs seeks to use VLMs for image classification tasks by constructing class-specific text prompts, e.g., "a photo of a c1s" for the class c1s, and comparing the model's similarity scores between the features of these prompts and the target image. The class yielding the highest similarity score is selected as the predicted class for the image. Formally, prompt engineering creates $M$ text prompts, embedded as a tensor $\mathbf{V} = \{\mathbf{v}_m\}_{m=1}^M \in \mathbb{R}^{M \times T \times h}$ , where $\mathbf{v}_m$ denotes an embedded prompt prefix sequence of $T$ tokens. By appending each prefix $\mathbf{v}_i$ with $\mathbf{c}_k \in \mathbb{R}^h$ , the constant embedding vector of the $k^{\text{th}}$ class, the model can thus construct a holistic classifier $h_\phi: \mathcal{X} \to \mathbb{R}^K$ by averaging the similarity scores across all $M$ prompts, where $\phi = \{\theta, \mathbf{V}, \ldots\}$ denotes all parameters in $h_\phi$ , consisting of the pretrained CLIP weights $\pmb{\theta}$ , a manually-designed prompt embedding $\mathbf{V}$ , and other potential parameters used by the prompt learning algorithm. For the $k^{\text{th}}$ class, we can obtain its logit as follows: + +$$ +h _ {\phi} (\mathbf {x}) _ {k} = \frac {1}{M} \sum_ {m = 1} ^ {M} \operatorname {s i m} \left(f _ {\mathrm {i m}} (\mathbf {x}), f _ {\mathrm {t x}} \left(\left[ \mathbf {v} _ {m}, \mathbf {c} _ {k} \right]\right)\right). \tag {4} +$$ + +Here, sim denotes the similarity function used to compute the closeness between the image and text features, typically + +the cosine similarity. The $k^{\mathrm{th}}$ class probabilities can thus be computed using the softmax function, where $\tau$ is the softmax temperature and is usually set to 1: + +$$ +p (y = k \mid \mathbf {x}, \phi) = e ^ {h _ {\phi} (\mathbf {x}) _ {k} / \tau} / \sum_ {j = 1} ^ {K} e ^ {h _ {\phi} (x) _ {j} / \tau}. \quad (5) +$$ + +Prompt Learning (PL) While the above zero-shot method is effective for many tasks, it is limited by the quality of the manually-designed prompts and may require extensive labor and expert knowledge to construct. In contrast, PL aims to automatically learn the prompt embeddings $\mathbf{V}$ , and possibly other parameters in $\phi$ , by optimizing them during training. To improve downstream task performance, CoOp [43] learns the prompt embeddings $\mathbf{V}$ , show that even with few-shot examples, can generate better prompts than manual designs, and generalize well to unseen tasks. CoCoOp [42] builds upon CoOp by introducing a trainable meta-net to learn to generate prompt embeddings from the extracted image features, in order to improve the model's performance on unseen tasks. KgCoOp [39] further regularizes the prompt embeddings to be close to the initial handcrafted prompts, showing that by retaining proximity to the original prompts, unseen tasks can be generalized better. Finally, ProDA [17] uses Gaussian to model the prompt embedding distribution, and encourages orthogonality among the prompt embeddings. This paper presents the first work to highlight that prompt learning can be effective in learning useful features from unlearnable examples, even under few-shot scenarios. + +# 3. The $\mathbf{A}^3$ Method + +# 3.1. Adaptive UEs Targeting PL + +Surrogate-based methods (EM [11], REM [9], and HYPO [33]) for synthesizing UEs typically train models from scratch, and do not assume low data availability, which makes them an unsuitable choice for affecting the PL process of the pretrained CLIP model (Table 1). To address this limitation, we first introduce an adaptive approach for all methods that uses the PL process as the surrogate model. To make the UEs stronger, we also assume that the UEs are synthesized with the same PL method using the same pretrained CLIP model. We implemented adaptive-variations of EM, REM, and HYPO. As they are stronger UEs than the original methods, our experiments by default use these adaptive variants. Recall REM [9] in Section 2, we adapt its objective to PL, specifically CoCoOp [42] in this paper, by using the holistic classifier $h_{\phi}$ in (4) as the surrogate model. The REM objective to seek $\delta$ under PL is thus: + +$$ +\min _ {(\boldsymbol {\delta}, \mathbf {V}, \dots)} \max _ {\boldsymbol {\eta}} \mathbb {E} _ {(\mathbf {x} _ {i}, y _ {i}) \sim \mathcal {D} _ {\text {c l e a n}}} [ \mathcal {L} (h _ {\phi} (\mathbf {x} _ {i} + \boldsymbol {\delta} _ {i} + \boldsymbol {\eta}), y _ {i}) ], \tag {6} +$$ + +where $\pmb {\eta}\in \mathcal{B}_p(\mathbf{x}_i,\epsilon)$ is the $\epsilon$ -bounded $\ell_p$ -norm noise. + +In this adaptive context, EM [11] simplifies the above REM objective by removing the inner maximization over $\pmb{\eta}$ + +and $\eta = 0$ . Similarly, HYPO [33] further assumes that $\mathbf{V}$ is kept constant to its initial manual design, and searches for the perturbations $\delta$ directly. + +Surrogate-free methods such as LSP [40], AR [29] and OPS [36] do not rely on a surrogate model training process and directly prescribe the perturbations for a given set of clean examples. Therefore, they do not have an adaptive counterpart. In our experiments, we examine the performance of these methods by directly applying them to the training data used by the prompt learning process. + +# 3.2. An Overview of $\mathbf{A}^3$ + +Figure 1 provides an overview of $\mathrm{A}^3$ . The overall algorithm is in Algorithm 1 of Appendix A.3. $\mathrm{A}^3$ provides a pool of diverse image and text augmentation strategies $\mathcal{A}_{\mathrm{im}}$ and $\mathcal{A}_{\mathrm{tx}}$ . For each image-class training pair, it first samples $K_{\mathrm{im}}$ and $K_{\mathrm{tx}}$ different image and text augmentation strategies, and applies them to the image and text sample respectively. This results in $K_{\mathrm{im}} \times K_{\mathrm{tx}}$ distinct augmented pairs for each training sample. Following the prompt learning technique of CoCoOp [42], it then optimizes the prompt embeddings $\mathbf{V}$ and the meta-net weights $\psi$ to align the pair of augmented samples with the minimum similarity. Intuitively, training prompts with the most dissimilar augmented pairs of image and text features forces the model to learn from the underlying features rather than fixating on spurious correlations typically exploited by UEs. + +# 3.3. Augmentations for Image and Text Modalities + +Image Augmentations As noted by Qin et al. [26], the effectiveness of simple augmentation strategies, such as Grayscale and JPEG compression, is greatly diminished in the context of adaptively synthesized UEs. To address this, we follow the approach of UEraser [25], which proposes an extensive set of image augmentation strategies, including not only standard techniques (e.g., random cropping, rotation, etc.), and more complex strategies including fractal-based transformations [21], and TrivialAugment [20]. + +Text Augmentations Since CLIP models can leverage not only image features but also text embeddings, which makes it particularly effective in zero-shot classification tasks, and few-shot learning facilitated by PL algorithms. In our context of using PL as an effective defense against UEs, we also introduce a set of text augmentation strategies, which include techniques such as random token masking and reordering that operates in the discrete token space of the text input, and small random rotations of the text embeddings. + +For the details of the augmentation strategies used in $\mathrm{A}^3$ for both image and text, please refer to Appendix A.2. + +# 3.4. Cross-modal Adversarial Feature Alignment + +Given an image $\mathbf{x}$ and its corresponding label $y$ , we can use the above augmentation strategies to find $K_{\mathrm{im}}$ augmented + +![](images/55935ae4039ef7df53c264ca9a4b6db363a90b7a5a54779c9db26691094a1d0e.jpg) +Figure 1. An overview of $A^3$ . For each image-class training pair, $A^3$ respectively sample $K_{\mathrm{im}}$ and $K_{\mathrm{tx}}$ different image and text augmentation strategies ( $a_{\mathrm{im}} \sim \mathcal{A}_{\mathrm{im}}$ and $a_{\mathrm{tx}} \sim \mathcal{A}_{\mathrm{tx}}$ ). It then optimizes the prompt embeddings $\mathbf{V}$ and the meta-net $m_{\psi}$ for empirical risk minimization by aligning pairs of augmented samples with the minimum similarity (i.e., maximum loss) between the image and text features. + +images and $K_{\mathrm{tx}}$ text embeddings, by drawing from the sets of image $a_{\mathrm{im}} \sim \mathcal{A}_{\mathrm{im}}$ and text $a_{\mathrm{tx}} \sim \mathcal{A}_{\mathrm{tx}}$ augmentation strategies, and applying them to the image and text embeddings respectively, forming a set of augmented images $\tilde{\mathbf{x}} \triangleq \{\tilde{\mathbf{x}}_i\}_{i=1}^{K_{\mathrm{im}}}$ and a set of text embeddings $\tilde{\mathbf{t}} \triangleq \{\tilde{\mathbf{t}}_j\}_{j=1}^{K_{\mathrm{tx}}}$ : + +$$ +\tilde {\mathbf {x}} _ {i} = a _ {\mathrm {i m}} (\mathbf {x}), \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad a _ {\mathrm {i m}} \sim \mathcal {A} _ {\mathrm {i m}}, \text {f o r} i \in [ 1, \dots , K _ {\mathrm {i m}} ], +$$ + +$$ +\tilde {\mathbf {t}} _ {j} = a _ {\mathrm {t x}} \left(\left[ \mathbf {v} _ {j \bmod M}, \mathbf {c} _ {y} \right]\right), a _ {\mathrm {t x}} \sim \mathcal {A} _ {\mathrm {t x}}, \quad \text {f o r} j \in [ 1, \dots , K _ {\mathrm {t x}} ], \tag {7} +$$ + +Here, we note that the text embedding before augmentation $[\mathbf{v}_{j\mathrm{mod}M},\mathbf{c}_y]$ is a concatenation of the prompt embedding $\mathbf{v}_{j\mathrm{mod}M}$ and the class embedding $\mathbf{c}_y$ . Recall that $M$ is the number of prompt embeddings, and the modulus operation $j\mathrm{mod}M$ is to ensure that the prompt embedding is selected cyclically, if $K_{\mathrm{tx}}$ exceeds $M$ . + +Using the augmented samples, we can compute the similarity between the image and text features for each pair of augmented samples, assuming $S(\tilde{\mathbf{x}},\tilde{\mathbf{t}})\in [-1,1]^{K_{\mathrm{im}}\times K_{\mathrm{tx}}}$ is the (cosine) similarity matrix containing the similarity between each image-text pair of augmented samples. Namely, for the $\tilde{\mathbf{x}}_i$ and $\tilde{\mathbf{t}}_j$ pair, we have: + +$$ +\mathcal {S} (\tilde {\mathbf {x}}, \tilde {\mathbf {t}}) _ {i j} = \operatorname {s i m} \left(f _ {\mathrm {i m}} \left(\tilde {\mathbf {x}} _ {i}\right), f _ {\mathrm {t x}} \left(\tilde {\mathbf {t}} _ {j}\right)\right), \tag {8} +$$ + +and we optimize the trainable weights in $\phi$ by maximizing the similarity alignment between the least similar image and text augmented features. Putting it all together, we have the following min-max problem, which can be optimized using mini-batch stochastic gradient descent (SGD): + +$$ +\min _ {\phi} \mathbb {E} _ {(\mathbf {x}, y) \sim \mathcal {D} _ {\mathrm {u e}}} \left[ \max _ {(i, j)} \mathcal {L} \left(\mathcal {S} (\tilde {\mathbf {x}}, \tilde {\mathbf {t}}) _ {i j}, y\right) \right], \tag {9} +$$ + +where $\mathcal{L}$ is the softmax cross-entropy loss, and $\mathcal{D}_{\mathrm{ue}}$ is the set of unlearnable training examples. + +# 3.5. More Augmentation Diversity with Meta-Net + +To further enhance the diversity of the augmented samples, we introduce a meta-net $m_{\psi}:\mathbb{R}^d\to \mathbb{R}^{M\times (T - 1)\times h}$ with trainable weights $\psi$ , which is a small neural network that learns to predict prompt embeddings $\mathbf{V}$ from $f_{\mathrm{im}}(\tilde{\mathbf{x}})$ , i.e., the feature extracted from an augmented image by the image encoder. This allows us to generate more diverse augmented text embeddings in addition to the text augmentation strategies. While this can yield $K_{\mathrm{im}}\times K_{\mathrm{tx}}$ different augmented prompt features, with the computational cost of CLIP's feature extraction, we only use the meta-net for a random augmented image for each augmented text embedding. Using the meta-net, the similarity matrix in (8) thus becomes: + +$$ +\mathcal {S} (\tilde {\mathbf {x}}, \tilde {\mathbf {t}}) _ {i j} = \operatorname {s i m} \left(\mathbf {p} _ {i}, \mathbf {q} _ {j}\right), +$$ + +where $\mathbf{p}_i = f_{\mathrm{im}}(\tilde{\mathbf{x}}_i)$ (10) + +$$ +\mathbf {q} _ {j} = f _ {\mathrm {t x}} \left(\tilde {\mathbf {t}} _ {j} + m _ {\psi} \left(\mathbf {p} _ {k}\right)\right), k \sim \mathcal {U} \{1, K _ {\mathrm {i m}} \}. +$$ + +# 4. Experiments + +Datasets For the main experiments, We evaluate $A^3$ under 7 datasets, including ImageNet [6] Caltech-101 [8], Oxford Flowers-102 [22], Food-101 [3], Oxford-Pets [23], and UCF-101 [31]. These datasets cover various recognition tasks, including classification of generic objects, fine-grained classification, and action recognition. We also proportionally resized and cropped all images to $224 \times 224$ , the input size for the image encoder $f_{\mathrm{im}}$ . + +Models In our experiments, unless otherwise specified, we use either the ViT-B/16 or ResNet-50 as the backbone for the image encoder $f_{\mathrm{im}}$ , and the text encoder $f_{\mathrm{tx}}$ is a Transformer-based model [34]. All pretrained models are obtained from the official CLIP repository [27]. + +Evaluation For all experiments in this section, unless otherwise specified, we consider a common few-shot learning setup with $S$ labeled training examples per class, i.e., $S$ -shot learning, where $S = 16$ by default. We used a context length $T$ of 4, and $M = 1$ number of prompt embeddings. For all surrogate-based attacks we optimized perturbations $\delta$ for 15 epochs with the cosine annealing scheduler and a learning rate 0.002. For learning, we adopted the SGD optimizer with a momentum of 0.9 and a weight decay of $5 \times 10^{-4}$ . We consider the following dataset split protocols: + +- Standard We used the standard train-test splits from [42, 43] to ensure reproducibility. In this setting, all classes are included in the training phase, where each class contains $S$ labeled examples. +- Base-to-Novel To better evaluate the model's generalization ability in few-shot scenarios, we also followed [42] to divide each datasets into two equal and non-overlapping groups of classes, where the first group (base) is used for training the prompt learning model and validation, and the second group (novel) which contains unseen classes is also used for performance testing. For this protocol, we reported the test accuracies on the base classes $\alpha_{\mathrm{b}}$ , the novel classes $\alpha_{\mathrm{n}}$ , and also their harmonic mean $\alpha_{\mathrm{h}} = 2 / (\alpha_{\mathrm{b}}^{-1} + \alpha_{\mathrm{n}}^{-1})$ . + +Unlearnable Example Methods Different methods consider distinct perturbation types and perturbation budgets: + +- Surrogate-based methods such as EM [11], REM [9], and HYPO [33], consider $\ell_{\infty}$ -bounded perturbations, with a perturbation budget of $8/255$ . As these methods require surrogate models, we used Section 3.1 to adapt them to the prompt learning setting. +- LSP [40] and AR [29] both use the $\ell_2$ -norm perturbations, but their perturbation budgets are different due to their original setups. LSP assumes a perturbation budget of 1.30, while AR uses 1.00. +- OPS [36] is model-agnostic, and uses the $\ell_0$ -norm perturbations with a perturbation budget of 1 by default. + +For additional details regarding the experimental setup, please refer to Appendix B. We will now present the results and main findings of our experiments below. Appendix C provides additional results including sensitivity analysis of the hyperparameters, and more adaptive variants. + +# 4.1. Prompt Learning under UEs + +Prompt learning generalizes well to existing UEs. Table 1 compares EM-0 and EM, where EM-0 synthesizes UEs by training ResNet-18 surrogate models from scratch on the Caltech-101 dataset, and EM adapts the EM method to prompt learning using Section 3.1. Notably, we found that UE methods that can effectively thwart [26] supervised learning of small models (e.g., ResNet-18) on small datasets (e.g., CIFAR-10 [14]) are much less effective when transferred to CLIP-based prompt learning algorithms. + +Prompt learning generalizes better with increasing number of shots $S$ . Table 1 also shows that the performance of all prompt learning algorithms increases with the number of shots $S$ , even when all shots are UEs. This trend can be observed across all UE methods, but the adaptive EM method consistently suppresses the performance gains from increasing $S$ the most. + +CoCoOp and ProDA show increased robustness against UEs, while KgCoOp is the most fragile in Table 1. We speculate that this is because the meta-net used in CoCoOp may be able to absorb the shortcut present in the UEs, and ProDA models the Gaussian distribution of prompt embeddings, making it more robust to input-side perturbations. While trained on clean data, KgCoOp [42] exhibits the best performance, as shown in the "Clean" row of Table 1. However, it is notably prone to UEs, showing the largest performance drop when UEs are introduced, especially when using the adaptive EM method. This suggests that KgCoOp, guided by the regularization to be in close proximity to the initial manual prompts, cannot effectively evade crafted UEs by EM based on the initial prompts. Because of the robustness of CoCoOp under our default number of shots ( $S = 16$ ), we chose it as the baseline algorithm for the subsequent experiments. + +Without proper defenses, it is better off not learning from UEs. It is interesting to note that usually, the performance of CoCoOp when trained with UEs is worse than the zero-shot performance. This suggests that UEs can indeed be harmful to the model's performance. This behavior can be observed in Tables 1 and 2. + +# 4.2. Prompt Learning with $\mathbf{A}^3$ + +$\mathbf{A}^3$ is very effective (up to $33\%$ better than CoCoOp) in mitigating UEs. In Table 2, we observe that $\mathrm{A}^3$ consistently outperforms CoCoOp across all datasets, producing $15\%$ to $33\%$ higher $\alpha_{\mathrm{h}}$ than CoCoOp for surrogate-based methods (EM, REM, HYPO), and $6\%$ to $30\%$ higher for surrogate-free methods (LSP, AR, OPS). + +The image and text augmentations in $\mathbf{A}^3$ are both crucial for its effectiveness. Table 3 performs an ablation study on the individual contributions of image and text augmentations. We note that using either image-only or text-only augmentations can improve the model's performance, but the combination of both is the most effective, giving large accuracy gains over CoCoOp. + +Simple augmentation strategies fall short of $\mathbf{A}^3$ 's performance. We also highlight in Table 3 that applying simple augmentation strategies such as Grayscale and JPEG compression on CoCoOp can certainly gain improvement over the CoCoOp baseline. However, they are still outperformed by $\mathbf{A}^3$ , sometimes with a large margin ( $\geq 25\%$ ). + +A large arsenal of image augmentation strategies also fall short of $\mathrm{A}^3$ 's performance. Table 3 also shows that while + +Table 1. Test accuracies $(\%)$ of prompt learning algorithms on an unlearnability-poisoned Caltech-101 dataset under varying number of shots $S$ . Note that "EM-0" is the original EM [11] method, and "EM" is our adaptive variant (Section 3.1). The image encoder of the CLIP model is ResNet-50, and the zero-shot accuracy is $86.00\%$ . We also report the average accuracy across unlearnability methods (the "Avg." rows) and prompt learning algorithms (the "Avg." column). We highlight the best prompt learning algorithm against each unlearnability method in bold, and underline the strongest unlearnability methods for each prompt learning algorithm. + +
SMethodCoOpCoCoOpProDAKgCoOpAvg.
2EM-078.2380.4581.9177.8679.61
EM61.7864.1365.0559.2662.56
OPS74.4076.9175.7573.1075.04
AR80.6381.8380.7479.8980.77
Avg.73.7675.8375.8672.5374.50
4EM-083.2985.1986.0280.8383.83
EM68.4170.4570.1464.9168.48
OPS78.8080.8880.1578.0779.48
AR82.5483.7084.4182.6683.33
Avg.78.2680.0680.1876.6278.78
8EM-086.1889.4490.6485.4287.92
EM70.5072.2873.0367.0770.72
OPS80.7483.3582.6379.3181.51
AR85.8188.4188.5083.7786.62
Avg.80.8183.3783.7078.8981.69
16EM-090.7690.8590.4889.6090.42
EM71.4272.8372.1069.3471.42
OPS82.4084.0984.4380.0282.74
AR88.6390.7490.0886.4688.98
Avg.83.3084.6384.2781.3683.39
16Clean91.2091.7091.6091.8091.58
+ +UEraser [25] is the most effective strategy to learn from UEs among all tested existing methods, the performance of UEraser is still inferior to $\mathrm{A}^3$ , particularly on HYPO, LSP and AR, with increased perturbation budgets. To preserve image semantics while maximizing augmentation diversity, such image augmentation strategies are often designed with a balance between the two. This trade-off choice may limit the ability to suppress UE perturbations in images. While this is also true for $\mathrm{A}^3$ , but the additional text augmentation strategies of $\mathrm{A}^3$ can help to work around this limitation. + +Adversarial training (AT) may not be the most effective defense against UEs. As the settings of AT in Table 3 assume $\ell_{\infty}$ -bounded perturbations with $\epsilon = 8 / 255$ , it notably struggles against large $\ell_{\infty}$ perturbation budgets ( $\epsilon = 16 / 255$ ), and other types of perturbation norm-bounds ( $\ell_{2}$ and $\ell_{0}$ ), as it is not designed to handle them. There may also be an intricate balance between accuracy and robustness [38], which could result in a seesaw effect in the performance as the perturbation budget increases. + +Increasing the number of shots $S$ improves $\mathbf{A}^3$ 's performance. In Table 4, we found that while CoCoOp's performance metrics continue to improve with increasing $S$ , it never surpassed the performance of zero-shot CLIP. This echoes the findings in Table 1. On the other hand, $\mathbf{A}^3$ im + +Table 2. Base-to-novel prompt learning accuracies (\%) for CoCoOp and $\mathrm{A}^3$ trained with unlearnable examples under $\ell_{\infty}$ -bounded attacks. Rows with "+" indicate when $\mathrm{A}^3$ is applied. $\alpha_{\mathrm{b}}$ refers to the model accuracy on poisoned data, while $\alpha_{\mathrm{n}}$ refers to the model accuracy on novel classes, excluding the poisoned classes. We also report the harmonic mean $\alpha_{\mathrm{h}} = 2 / (\alpha_{\mathrm{b}}^{-1} + \alpha_{\mathrm{n}}^{-1})$ . For the "Δ" column, we report the test accuracy drop for the CoCoOp baseline from the clean training setting, and accuracy gain for $\mathrm{A}^3$ over CoCoOp. The backbone is VIT-B/16. + +
ImNetCaltechPetsFlowersFoodSUNUCFAvg.Δ
Zero-Shot [27]
αb67.5092.6087.4067.9082.9064.8066.1075.60
αn60.2087.4083.7060.8075.5056.9059.5069.14
αh63.6489.0085.5264.8079.0560.6062.8172.20
Baseline (CoCoOp [42])
αb75.2596.3094.3592.8690.1878.3880.5386.84
αn69.4393.2396.8870.1790.8074.7273.2881.22
αh72.3994.7495.5879.7490.3476.2876.6183.67
+αb76.0397.9594.0692.4190.6877.5980.2587.00
+αn70.4793.8093.1870.2991.2974.8371.8980.82
+αh73.0995.7393.6379.7490.9876.1475.8883.60
EM [11] (l∞, ε = 8/255)
αb56.4780.6878.4474.4079.9358.9063.7170.36-16.48
αn43.2774.9076.3851.6678.1553.3352.0961.40-19.82
αh48.7777.5477.4061.0379.0456.0157.3865.31-18.36
+αb73.4895.4993.7191.8489.3877.6579.3485.8215.46
+αn67.8593.0793.5368.0888.0073.1771.6979.3017.90
+αh70.4194.3493.7478.2088.8775.1875.1282.2716.96
REM [9] (l∞, ε = 8/255)
αb43.5162.6364.6061.9860.2148.2950.5355.94-30.90
αn30.4954.7760.1246.6458.0844.3041.9848.05-33.16
αh35.7458.3962.2553.1759.0646.1846.0251.54-32.12
+αb72.7694.5293.2891.0088.0676.9478.4685.0029.06
+αn66.4292.1691.9466.7487.3471.9871.2278.2630.21
+αh69.3793.6992.7476.7387.5474.4374.9481.3529.80
HYPO [33] (l∞, ε = 8/255)
αb40.0858.5959.8357.3356.5044.1147.6652.01-34.83
αn30.6454.8257.1144.7656.9041.2543.5847.01-34.21
αh34.6856.5758.4650.3056.5542.4745.4549.21-34.46
+αb71.8094.2893.5990.7588.5577.6778.9285.0833.07
+αn65.2990.3792.0165.2584.9370.0469.8576.8229.81
+αh68.3992.1393.0576.2086.6973.7374.4380.6631.45
LSP [40] (l2, ε = 1.30)
αb49.7268.4965.9963.3361.8850.6951.4758.80-28.04
αn36.0456.2963.3550.6259.4146.2048.8851.54-29.67
αh41.7961.8464.4756.1860.5348.4350.0454.75-28.91
+αb72.5394.9794.0291.2988.6477.0478.1785.2426.44
+αn67.3792.4493.8067.5287.4072.2171.1178.8427.30
+αh69.9793.7494.2777.0987.7774.4774.5481.6926.94
AR [29] (l2, ε = 1.00)
αb42.3361.7360.5859.0157.2046.2349.0653.73-33.11
αn31.6756.4258.0844.5455.9643.3042.6947.52-33.69
αh36.2959.0059.2750.6356.5244.7445.6750.30-33.37
+αb71.6894.3892.5590.8287.7776.6777.5884.4930.76
+αn66.0991.5991.6766.0686.2571.1970.8677.6730.15
+αh68.7492.9892.1078.4087.0073.9374.2181.0530.75
OPS [36] (l0, ε = 1)
αb68.2888.6086.2081.5985.6565.6068.9877.84-9.00
αn54.5080.2180.8358.7079.0660.4960.3267.73-13.49
αh60.5784.0583.4568.2882.2462.8964.3972.37-11.40
+αb73.0895.1093.3991.5089.5676.9778.1383.967.55
+αn67.2092.6393.8868.0388.0172.6471.2879.1011.37
+αh70.0693.8693.6378.0588.8774.6974.5081.429.68
+ +Table 3. Clean test accuracies (\%) on Caltech-101 datasets (16-shots, standard protocol). "UEr" means UEraser. Baseline and compared methods are adapted to CoCoOp [42]. Image encoder backbone is ResNet-50. "Text" and "Image" refer to the augmented modalities, "Full" includes both. + +
BaselineGrayJPEGATUErTextImageFull
EM8/25575.5374.2879.2182.8490.3784.6992.5194.28
16/25559.3660.9664.5877.0388.7982.4590.4091.86
REM8/25552.3363.7170.2278.9690.7386.8992.3293.88
16/25537.9759.5466.7874.1086.9683.3389.3590.25
HYPO8/25547.3650.0264.5678.8987.7484.0791.4793.21
16/25527.1834.6759.1172.2682.4879.2786.0989.33
LSP1.3043.2364.7080.0181.5890.6683.3792.8394.02
1.7425.4142.5868.3076.2983.0580.7787.2491.62
AR1.0050.1853.2481.4076.7390.1284.9691.6393.41
1.3032.6535.5769.2664.2282.8981.1786.6190.06
OPS186.1786.5289.7383.1688.6189.9390.5093.86
473.2473.3480.2369.5980.1281.3784.0787.10
+ +Table 4. Base-to-novel metrics for different number of shots $S \in \{ 0,2,4,8,{16}\}$ . The image encoder backbone is ResNet-50. + +
SCaltechFoodImageNet
A3-+-+-+
0αb86.778.162.7
αn78.474.952.8
αh82.676.457.2
2αb69.3488.5166.1184.3444.0466.04
αn61.7883.4560.2981.7730.960.03
αh65.3485.9163.0783.0436.3262.89
4αb76.0991.2375.2187.8150.4368.1
αn67.5187.9366.1986.1536.6162.9
αh71.5489.5570.4186.9742.4265.4
8αb77.8692.8975.8588.0351.6569.01
αn70.1989.1170.0986.4439.2264.58
αh73.8390.9672.8687.2344.5866.72
16αb77.5293.3676.6788.5253.7271.08
αn72.4391.0273.3487.7640.7464.95
αh74.8992.1874.9788.1446.3467.88
+ +![](images/3e63b6b5e9254872d7c39ebffcb88b9b4640ae4b812eb8255b8919a5c846b150.jpg) +αoriginal αunlearn 01 αtest αtrain + +![](images/cd91b39d42053d417575a3e791bbf2c683504123f56e5f0e61be118cd4fe24c9.jpg) + +![](images/0e966e46ae20f2d8b7aafbc0fd37033660a7ccc32b79ee38a6907e2f24abd3a5.jpg) +(a) $\mathrm{EM} + \mathrm{CoCoOp}$ +(c) $\mathrm{REM} + \mathrm{CoCoOp}$ + +![](images/13a94f1e41a87b7f18ea40d518aa2cd3057bf3ccb934147e291bfc18ae11ba04.jpg) +(b) $\mathrm{EM} + \mathrm{A}^3$ +(d) $\mathrm{REM} + \mathrm{A}^3$ + +![](images/81616334ed89d10775a3865fa15e1d3ed0af05dedecca17cf98b084e1cdb7d74.jpg) + +![](images/a6ad827e2de157735f90f2d0d34f9bc8deb05ba662f5c66c99a57b3fa52a03e9.jpg) +(f) $\mathrm{AR} + \mathrm{A}^3$ + +![](images/2a809476949a81417905ada8d5f012a84bf314fba9e658888963850b1dcbf5e6.jpg) +(e) $\mathrm{AR} + \mathrm{CoCoOp}$ +(g) $\mathrm{LSP} + \mathrm{CoCoOp}$ +Figure 2. CoCoOp vs. A3 under partial poisoning with rates $R \in \{\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, 1\}$ (x-axis, %). Accuracy metrics (y-axis, %): $\alpha_{\text{unlearn}} = \text{UEs}$ in the training set; $\alpha_{\text{original}} = \text{original clean images of the UEs}$ ; $\alpha_{\text{test}} = \text{clean images in the test set}$ ; $\alpha_{\text{train}} = \text{clean images in the training set}$ . The image encoder backbone is ResNet-50. + +![](images/9c16c1e3695b1908ad6ede841fafda072772a77904d57be754a7105f372b4987.jpg) +(h) $\mathrm{LSP} + \mathrm{A}^3$ + +proves notably with increasing $S$ , where CoCoOp falls behind while $A^3$ leads by a large margin. + +With partially poisoned datasets, $\mathbf{A}^3$ learns the underlying features while CoCoOp likely does not. In practice, model trainers may curate datasets from a variety of sources, + +and only a portion of the data may contain UE perturbations. Training on such partially poisoned datasets typically result in minimal performance loss over the clean dataset, and is not indicative of the model's ability to learn the underlying features of the UEs. In Figure 2, we thus investigate whether CoCoOp and $\mathbf{A}^3$ can learn such features when trained on partially poisoned datasets. It evaluates the accuracy metrics of the unlearnable part ( $\alpha_{\mathrm{unlearn}}$ ), the original images of the unlearnable part ( $\alpha_{\mathrm{original}}$ , i.e., before perturbation), the samples from the test set ( $\alpha_{\mathrm{test}}$ ), and the clean part of the train set ( $\alpha_{\mathrm{train}}$ ). Importantly, if the model can learn the underlying features, then the $\alpha_{\mathrm{original}}$ should be close to $\alpha_{\mathrm{train}}$ , otherwise, it should be close to $\alpha_{\mathrm{test}}$ . It is evident that CoCoOp actually struggles to learn useful features from the UEs, as $\alpha_{\mathrm{original}}$ closely tracks $\alpha_{\mathrm{test}}$ , while $\alpha_{\mathrm{unlearn}}$ is higher than $\alpha_{\mathrm{train}}$ . This suggests that CoCoOp is likely overfitting to the UE perturbations, even more so than the clean training data. In contrast, $\mathbf{A}^3$ shows that $\alpha_{\mathrm{original}}$ follows $\alpha_{\mathrm{train}}$ closely, and $\alpha_{\mathrm{unlearn}}$ is close to $\alpha_{\mathrm{test}}$ , hinting that $\mathbf{A}^3$ is learning the underlying features instead of the UE-crafted perturbations. + +# 5. Conclusion + +First, PLs' generalization combined with $A^3$ make them challenging adversaries for traditional UEs. Second, Augmenting PL with diverse image and text perturbations significantly improves their resilience against UEs, pointing to the need for multimodal considerations in both UEs and countermeasures. Third, compared to simpler augmentations or adversarial training, $A^3$ 's cross-modal feature alignment proved especially effective in mitigating PL's adaptation to UEs than preexisting learning methods. Finally, we emphasize the need for adaptive, multimodal approaches in UEs and open pathways toward more sophisticated protections against unauthorized training in an era of large multimodal and pretrained models. + +# Acknowledgment + +This work is supported in part by National Natural Science Foundation of China (62376263, 62372443 and 62271496), Guangdong Basic and Applied Basic Research Foundation (2023B1515130002), Natural Science Foundation of Guangdong (2024A1515030209 and 2024A1515011970), Shenzhen Science and Technology Innovation Commission (JCYJ20230807140507015 and JCYJ20220531100804009), and Yu-Liang Lu's Project Team Development Funding (KY23A102). 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The existing adapters struggle to keep pace with these models, requiring extensive retraining. This paper proposes a novel adapter transfer framework, A4A (Adapter for Adapter), which uses an all-for-all mapping approach to seamlessly transfer attention-based adapters across different model architectures (e.g., U-Net to transformer). The framework consists of Coupling Space Projection and Upgraded Space Mapping. During Coupling Space Projection, all attention features of the pretrained adapter are aggregated to fully capture the coupling relationship before being projected into a unified space. The unified space maintains coupling features in a consistent dimension, effectively and efficiently addressing feature scale discrepancies arising from the base model's architecture. In the Upgraded Space Mapping Module, randomly initialized learnable features are introduced to connect the unified and upgraded spaces by integrating reference features via the attention mechanism. The learned features are adaptively injected into the upgrade model through the Alignment module, which bridges the discrepancies between the models using the all-for-all mapping. Experimental results on personalized image generation tasks demonstrate that A4A outperforms previous methods in transferring adapters while being the first to achieve adapter transfer across model architectures. + +# 1. Introduction + +Recent advancements in large-scale text-to-image diffusion models [5, 11, 23, 26] have significantly improved their ability to generate high-quality, realistic images based on user-friendly textual prompts. Building on these generative capabilities, numerous adapters have been developed upon these pretrained models to further endow them with new control conditions, such as pose and human identity control, + +thereby fostering the growth of downstream real-world applications like personalized image creation. As pretrained models rapidly evolve, with increasing parameters (e.g., from SD1.5's 860M to SDXL's 2600M) and developing architectures (e.g., from the convolution U-Net [27] to the transformer [22]), the original adapters built on base models require substantial resources for retraining and significant effort for redesign to accommodate upgraded models. This leads to a lag in adapter development compared to the progression of upgraded models1. Therefore, the adapter transfer task, i.e., effectively and efficiently transferring existing adapters from base models to upgraded models to leverage the strong control capabilities of the original well-developed adapters and the superior generative abilities of the upgraded models, has become an increasingly important and urgent requirement in both academia and industry. + +Given the substantial potential benefits of adapter transfer, several prior studies have been conducted in this field. For instance, Ctrl-Adapter [19] has been proposed to transfer the ControlNet [41] architecture by fusing the output of the zero-convolution from the pretrained ControlNet into the corresponding layer in the upgraded model. Concurrently, X-Adapter [25] has been explored for mapping the latent from the base model's decoder block and adding them to the corresponding location within the upgraded model's decoder. In summary, existing adapter transfer methods primarily focus on addition-based adapters (i.e., the control conditions are injected into the pretrained models by simple addition, typically, ControlNet), through a layer-by-layer mapping, i.e., the output of each layer in the base model's adapters are mapped to the semantically equivalent layer in the upgraded model. + +However, in this study, we argue that the existing layer-by-layer mapping fails to fully exploit the coupling between original adapters and base models to effectively bridge the + +discrepancies between base models and upgraded models. Here, coupling refers to the already well-trained compatibility between the original adapters and base models, while differences refer to the architectural discrepancies between base models and upgraded models. The reason behind this is that the original adapters and base models function as an integrated whole, and the layer-by-layer mapping disrupts this holistic consistency by isolating the output of each layer. Consequently, during the subsequent mapping to the upgraded models, this overall consistency cannot be effectively utilized. As a result, existing adapter transfer methods suffer from limited transfer scopes. On the one hand, they can only transfer addition-based adapters (typically, ControlNet) but fail to generalize to the attention-based adapters, which are more widely used. This is technically more challenging because attention-based adapters (i.e. the control conditions are injected into pretrained models by attention mechanisms) involve more complex interactions and dependencies across different layers of the model. On the other hand, these methods are limited to transferring between similar pretrained model architectures (e.g., from a U-Net model to another U-Net model) but fail when transferring from a U-Net model to a transformer model. This limitation is particularly critical, as the latest state-of-the-art pretrained text-to-image models [1, 6] are predominantly transformer-based, while the current most mature adapters remain developed on the U-Net architecture. + +To address this challenge, we propose a novel adapter transfer framework, A4A (Adapter for Adapter), which utilizes an innovative all-for-all mapping approach to seamlessly transfer the intrinsic coupling between all layers of the original adapters and base models to all layers of the upgraded models, thereby enabling the transfer of more difficult and widely used attention-based adapters and facilitating cross-architecture model transfers. Specifically, A4A achieves all-for-all mapping through the Coupling Space Projection and Upgraded Space Mapping. In the Coupling Space Projection phase, all attention features of the pretrained adapter are collected, capturing the complete coupling relationship between the adapter and the base model, and then projected into a unified space. The coupling relationship treats the features of all layers of the adapter as a unified whole, conveying a continuous representation of the new control conditions throughout the generation process, distinguishing it from isolated layer mappings. Upgraded space refers to the coupled feature space that corresponds to the upgraded model, where we randomly initialize learnable attention features to transfer the coupling relationship from the base model to the upgraded model. By integrating the reference features through the attention mechanism and aligning them with the upgraded architecture, the learnable features bridge the discrepancies between the models. + +The contributions of this work are as follows: + +1. To alleviate the limited transfer scopes, we introduce a novel all-for-all mapping approach that enables the transfer of attention-based adapters and facilitates cross-architecture model transfers. +2. A4A projects the adapter's complete features into the unified coupling space and bridges it with the upgraded space by fusing these features with randomly initialized learnable features through the attention mechanism. +3. Experiments in various types of personalized image creation demonstrate that A4A is an effective attention-based adapter transfer approach for cross-architecture models, achieving better performance than the pretrained adapter from the upgraded model with minimal training costs. + +# 2. Related work + +# 2.1. Latent Diffusion Models + +Recent diffusion-based text-to-image models [11, 23, 26, 29] have received wide acclaim for their outstanding image fidelity and diversity. Ho et al. [11] introduce the denoising diffusion process into generation models in the seminal work DDPM. Diffusion models learn the generation process through iterative denoising steps. Latent Diffusion Model (LDM) [26] proposed to perform the diffusion process in the latent space of a Variational Autoencoder [31]. Under the LDM architecture, two primary backbone models are employed: the convolutional U-Net [27] and the transformer [22]. While these models share a similar generation process, there are significant differences between the two models. The most notable example of U-Net models is the StableDiffusion [23, 26] series, excluding SDv3.0 [6], which consists of the symmetric encoder and decoder. The encoder is composed of multiple blocks of diverse dimensions, interconnected by down-sampling layers. Each block incorporates several attention layers [32] to fuse latents and conditions. Another series of models [4, 6, 9, 28] adopts DiT blocks [22] for denoising. The transformer model has been widely used in recent video generation tasks [20], where it has achieved state-of-the-art results. After patchification, the resulting features are progressively processed through a series of DiT blocks. In the DiT blocks, the features are scaled and shifted using AdaLN, maintaining the same dimension, which distinguishes them from U-Net-based models. Transformer-based models, with their flexible structure and impressive generative capabilities, have garnered significant attention due to their great potential. + +# 2.2. Adapters for Text-to-Image Diffusion Models + +Given the inefficiencies of fine-tuning large pretrained models, an alternative strategy is to utilize adapters, which introduce a limited number of trainable parameters while keeping the pretrained model frozen. Due to their flexibility and + +greater efficiency compared to fine-tuning, adapters have gained significant interest. By designing conditional modules, an adapter can introduce new control conditions, such as personalized characters, objects, layouts, and style information, to a pretrained text-to-image model. Downstream tasks for these adapters include personalized character generation (ID customization) [7, 34, 40, 42, 44], personalized object generation (IP customization) [2, 7, 13, 21, 30, 36, 37, 40, 42], attribute and layout control [3, 16, 18, 35, 38, 43], and stylization [10, 39]. As discussed in Sec. 1, these adapters can be categorized into two main types: attention-based and addition-based. In the addition-based adapter (typically, ControlNet [41]), the encoded new conditions are directly added to the output of the sub-blocks of the generation model. In contrast, the attention-based adapter processes the encoded conditions through attention layers, modifying the original attention values based on both the new conditions and the text prompts. Attention-based adapters [7, 10, 30, 34, 36-40, 42-44] have received widespread attention due to their efficient and precise condition control capabilities, dominating the field of adapters. + +# 2.3. Adapter Transferring + +The rapid evolution and diverse architectures of text-to-image generation models place constraints on transferring the aforementioned adapters. Consequently, to accommodate new models, adapters often require retraining from scratch on these pretrained diffusion models. X-Adapter [25] designates models equipped with the well-trained adapter as base models, with the upgraded version referred to as the upgraded model. It establishes manual connections between decoder blocks of the same dimensions in both the base and upgraded models. Specifically, the decoder of SD1.5 and SDXL consists of blocks with dimensions 1280, 640, and 320. X-Adapter [25] maps the output of the base model's blocks to the corresponding blocks of identical dimensions in the upgraded model. As a result, X-Adapter is specifically suited for SD-series models and faces challenges when transferring to transformer-based models [4, 6, 9, 22, 28]. Ctrl-Adapter [19] aims to transfer the addition-based adapter, ControlNet [41], for video generation models or upgraded image generation models. It connects the output of the zero-convolutional layers of both models through mappers to transfer the ControlNet. + +# 3. Method + +We propose a novel framework for transferring well-trained adapters from the base model to the upgraded model with architectural discrepancies, specifically U-Net model and transformer model. For the sake of brevity, we define PTA as the Pre-Trained Adapter. Specifically, pretrained refers to the version that has been officially published. Additionally, we denote $M_{base}$ and $M_{up}$ as the previously mentioned + +base model and upgraded model. A4A first projects the extracted attention features into the unified coupling to maintain the coupling relationship between PTAs and $M_{base}$ . Then, the coupling space is mapped to the upgraded space, where learnable features integrate the reference coupling features with attention layers. These learned features are then adaptively aligned with $M_{up}$ through the Alignment component. + +# 3.1. Preliminaries + +Before presenting our method, we introduce the diffusion model with various backbones. The Latent Diffusion Model (LDM), which perform noise addition and denoising in the latent space $z$ of the VAE encoder, is the most prominent open-source community for text-to-image generation. The objective of training LDMs is: + +$$ +\min _ {\theta} \mathcal {L} _ {L D M} = \mathbb {E} _ {z, \epsilon \sim \mathcal {N} (0, I), t} | | \epsilon - \epsilon_ {\theta} (z _ {t}, t, E _ {t} (y _ {t})) | | _ {2} ^ {2}, \tag {1} +$$ + +where $t$ is uniformly sampled from the time steps $\{1, \dots, T\}$ , $y_{t}$ denotes the conditional text prompt, and $E_{t}$ represents the text encoder. The parameterized denoising network denoted as $\epsilon_{\theta}$ , may take the form of either a U-Net model or a transformer model. The U-Net architecture consists of blocks with varying dimensions. Each U-Net block includes down-sampling or up-sampling layers along with attention layers. The transformer model primarily consists of multiple DiT blocks grounded on the transformer architecture. Since our method aims to transfer the widely used attention-based adapters, we define the cross-attention process and its associated signals as follows: + +$$ +\boldsymbol {q} = \boldsymbol {W} ^ {q} \cdot \boldsymbol {i}, \quad \boldsymbol {k} = \boldsymbol {W} ^ {k} \cdot \boldsymbol {c}, \quad a n d \quad \boldsymbol {v} = \boldsymbol {W} ^ {v} \cdot \boldsymbol {c} \tag {2} +$$ + +where $i$ denotes the latents of the image, and $c$ signifies the embeddings of the condition, such as the text prompt in the original model. Additionally, $W$ represents the weights for attention projection. Attention is conducted as follows: + +$$ +\operatorname {A t t e n t i o n} (\boldsymbol {q}, \boldsymbol {k}, \boldsymbol {v}) = \operatorname {S o f t m a x} \left(\frac {\boldsymbol {q} \cdot \boldsymbol {k} ^ {T}}{\sqrt {d}}\right) \boldsymbol {v} \tag {3} +$$ + +where $d$ represents the dimensions of $\pmb{k}$ and $\pmb{v}$ . Through cross-attention, the image latents and condition embeddings are comprehensively integrated. + +# 3.2. Coupling Space Projection + +Condition Encoder of PTA. For new control conditions $y_{n}$ beyond the original text prompt, adapters typically incorporate a condition encoder as illustrated in Fig. 1. We denote $E_{n}$ to distinguish it from the original text encoder $E_{t}$ of the pretrained large-scale T2I models: + +$$ +\boldsymbol {c} _ {n} = E _ {n} \left(y _ {n}\right), \tag {4} +$$ + +![](images/a86d0fff88187fdbf456d2a9bebc8d42078a61a7a43735c068e5321b344f0df4.jpg) +Figure 1. The illustration of the Adapter for Adapter (A4A) framework. Both the base model and the upgraded model are kept frozen. (a) Coupling Space Projection: The pretrained Adapter, consisting of the condition encoder and attention layers (highlighted in pink), is loaded. The adapter features $k_{i}$ and $v_{i}$ are projected into a unified coupling space, reshaping them as $K$ and $V$ . (b) Upgraded Space Mapping: Randomly initialized learnable upgraded features, $\bar{K}$ and $\bar{V}$ , are concatenated with $K$ and $V$ as references. The learning process of $\bar{K}$ and $\bar{V}$ bridges the discrepancy between the base model and the upgraded model. These features are then aligned with the original cross-attention layers of the upgraded model through Alignment, which can be a U-Net or Transformer model. Best viewed in color. + +where $c_{n}$ denotes the new condition embeddings. Taking IP-Adapter [40] as an example, the Image Encoder external to the original generation model serves as the condition encoder. And we directly integrate the pretrained condition encoder $E_{n}$ from the adapter to efficiently transfer the well-trained adapter to the upgraded model. + +Attention Layers of PTA. As illustrated in Fig. 1, the encoded new condition embeddings $c_{n}$ are processed through the attention mechanism coupling with the base model. We explicitly depict the attention layers associated with the pretrained adapter in the figure, denoting the weights of the $i$ -th attention layer of the adapter as $W_{A,i}$ , distinguishing them from the original attention weights $W$ in the base model. Subscript $A$ represents the adapter, and $i$ represents the $i$ -th adapter attention layer. For instance, the fine-tuned cross-attention layers in the Decoupled Cross-Attention module of IP-Adapter [40] exemplify this. $c_{n}$ are sequentially fed into the aforementioned adapter's attention layers $W_{A,i}$ : + +$$ +\boldsymbol {k} _ {i} = \boldsymbol {W} _ {A, i} ^ {k} \left(\boldsymbol {c} _ {n}\right), \quad \boldsymbol {k} _ {i} \in \mathbb {R} ^ {N \times d _ {i}}, \tag {5} +$$ + +$$ +\boldsymbol {v} _ {i} = \boldsymbol {W} _ {A, i} ^ {v} \left(\boldsymbol {c} _ {n}\right), \quad \boldsymbol {v} _ {i} \in \mathbb {R} ^ {N \times d _ {i}}, \tag {6} +$$ + +where $d_{i}$ is the dimension of the feature, and $\mathbf{N}$ denotes the number of tokens for feature $k_{i}$ and $\boldsymbol{v}_{i}$ . To extract the attention features from $\boldsymbol{c}_{n}$ , we employ the attention layers of the adapter rather than utilizing the entire base model. + +Projection onto the Coupling Space. The features obtained from multiple layers form a sequence of length $l$ , $[k_1, k_2, \dots, k_l]$ and $[v_1, v_2, \dots, v_l]$ , where $l$ represents the number of attention layers of PTA. The dimensions $d_i$ of the features vary, as shown in Fig. 1. To achieve the all-for-all mapping for the attention-based adapter from $M_{base}$ to $M_{up}$ , the features of all cross-attention layers need to be + +projected into a unified coupling space $S_{co}$ which is defined by the smallest common multiple $d_{scm}$ of all dimensions $d_{i}$ : + +$$ +\boldsymbol {K} = \operatorname {P r o j} ([ \boldsymbol {k} _ {1}, \boldsymbol {k} _ {2}, \dots , \boldsymbol {k} _ {l} ]), \quad \boldsymbol {K} \in \mathbb {R} ^ {l \times N \times d _ {s c m}}, \quad (7) +$$ + +$$ +\pmb {V} = \mathrm {P r o j} ([ \pmb {v} _ {1}, \pmb {v} _ {2}, \dots , \pmb {v} _ {l} ]), \quad \pmb {V} \in \mathbb {R} ^ {l \times N \times d _ {s c m}}. \quad (8) +$$ + +The projection module consists of several linear layers designed to map dimensions $d_{i}$ to $d_{scm}$ . After the sequences are projected to $S_{co}$ , they are reshaped into matrices $K$ , and $V$ . Mapping to $S_{co}$ defined by $d_{scm}$ strikes the best balance between efficiency and effectiveness. Sec. 7.3 in the supplementary material demonstrates this through experiments. It reduces computational complexity by aligning features to a common dimension, avoiding the overhead of larger spaces. At the same time, it maintains sufficient representational capacity, preventing the loss of important information, which can happen with smaller spaces. This ensures effective feature alignment without excessive resource usage, making it an optimal choice for both computational efficiency and model performance. + +# 3.3. Upgraded Space Mapping + +Similarly, we define the number of the cross-attention layers in the upgraded model as $\bar{l}$ , and the space for upgraded models as $S_{up}$ . To transfer the unified adapter features to the upgraded space, inspired by BLIP-2 [17], we randomly initialize two learnable parameters $\bar{K} \in \mathbb{R}^{\bar{l} \times N \times d_{\text{scm}}}$ and $\bar{V} \in \mathbb{R}^{\bar{l} \times N \times d_{\text{scm}}}$ . Given that the attention layer is effective for integrating features, we adopt this architecture to learn the aforementioned parameters. Consider the learning of $\bar{K}$ as an example. To enhance the robustness, we first + +normalize $\bar{\pmb{K}}$ and $\pmb{K}$ using layer normalization. And then, the following operation is performed: + +$$ +\begin{array}{l} \bar {\boldsymbol {K}} = \operatorname {F F N} \left[ \boldsymbol {W} ^ {o u t} \cdot \text {A t t e n t i o n} \left(\bar {\boldsymbol {K}} \boldsymbol {W} _ {1} ^ {k}, \right. \right. \tag {9} \\ [ \boldsymbol {K}, \bar {\boldsymbol {K}} ] W _ {2} ^ {k}, [ \boldsymbol {K}, \bar {\boldsymbol {K}} ] W _ {3} ^ {k}) ]. \\ \end{array} +$$ + +where $[\pmb{K},\bar{\pmb{K}} ]$ denotes the concatenation of $\pmb{K}$ and $\bar{\pmb{K}}$ along dimension $N$ . The projection weights $\pmb{W}_1^k,\pmb{W}_2^k,\pmb{W}_3^k\in \mathbb{R}^{d_{scm}\times d_{in}}$ map $\bar{\pmb{K}}$ and $\pmb{K}$ , respectively, to the intermediate space with dimension $d_{in}$ . Following the processing of features using the Attention as described in Eq. (3), they are subsequently transformed back to the original space via the $\pmb{W}^{out}$ . The Feed Forward Network (FFN) is composed of layers arranged sequentially, including layer normalization, linear transformations, GELU activation, and additional linear layers. The aforementioned process of Eq. (9) is iterated $\mathbf{R}$ times, with $\mathbf{R}$ serving as a hyperparameter. The learning process of $\bar{\pmb{V}}$ is similar to $\bar{\pmb{K}}$ : + +$$ +\bar {\boldsymbol {V}} = \operatorname {F F N} \left[ \boldsymbol {W} ^ {\text {o u t}} \cdot \text {A t t e n t i o n} \left(\bar {\boldsymbol {V}} \boldsymbol {W} _ {1} ^ {v}, \right. \right. \\ \left. [ \boldsymbol {V}, \bar {\boldsymbol {V}} ] \boldsymbol {W} _ {2} ^ {v}, [ \boldsymbol {V}, \bar {\boldsymbol {V}} ] \boldsymbol {W} _ {3} ^ {v}) \right]. \tag {10} +$$ + +We clarify that two distinct modules with an identical structure are responsible for learning $\bar{K}$ and $\bar{V}$ , respectively. Throughout this process, the learnable features $\bar{\bar{K}}$ and $\bar{V}$ are seamlessly integrated with the adapter features $K$ and $V$ of the PTA, effectively bridging the unified coupling space to the upgraded space. + +Alignment with the Upgraded Model. The learned features in the upgraded space should be aligned with the attention layers of $M_{up}$ to fully leverage the adapter's capabilities. Specifically, we first fetch the dimensions $\bar{d}_i$ of the cross-attention layers within the original upgraded model. Then, we employ the linear layer to align the $i$ -th row of the matrix $\bar{\mathbf{K}}$ to $\bar{d}_i$ dimensions through Alignment, which we denote as $\bar{k}_i$ : + +$$ +[ \bar {\boldsymbol {k}} _ {1}, \dots , \bar {\boldsymbol {k}} _ {\bar {l}} ] = \operatorname {A l i g n} (\bar {\boldsymbol {K}}). \tag {11} +$$ + +Similarly, the identical operation is applied to the $\bar{\mathbf{V}}$ matrix in order to derive the vector $\bar{\pmb{v}}_i$ : + +$$ +[ \bar {\boldsymbol {v}} _ {1}, \dots , \bar {\boldsymbol {v}} _ {\bar {l}} ] = \operatorname {A l i g n} (\bar {\boldsymbol {V}}). \tag {12} +$$ + +For the $i$ -th cross-attention layer, let $\pmb{q}_i^{up}$ , $\pmb{k}_i^{up}$ , and $\pmb{v}_i^{up}$ be the original features. The extracted features, $\bar{\pmb{k}}_i$ and $\bar{\pmb{v}}_i$ , are combined through linear weighting and summation with the prior values of the upgraded model using Attention Eq. (3): + +$$ +\begin{array}{l} \bar {\boldsymbol {Z}} = \operatorname {A t t e n t i o n} \left(\boldsymbol {q} _ {i} ^ {u p}, \boldsymbol {k} _ {i} ^ {u p}, \boldsymbol {v} _ {i} ^ {u p}\right) + \tag {13} \\ \lambda \text {A t t e n t i o n} \left(\boldsymbol {q} _ {i} ^ {u p}, \bar {\boldsymbol {k}} _ {i}, \bar {\boldsymbol {v}} _ {i}\right). \\ \end{array} +$$ + +The result of Eq. (13), $\bar{Z}$ , serves as the output for the $i$ -th cross-attention layer and will be forwarded to the next layer of the upgraded model. The parameter $\lambda$ serves as a balancing factor, fixed at 1.0 during training and subsequently adjusted for downstream tasks during inference. + +# 3.4. Optimization Loss Function + +To optimize the A4A framework, we employ the loss function $\mathcal{L}_{LDM}$ of the upgraded model $M_{up}$ as defined in Equation Eq. (1): + +$$ +\mathcal {L} _ {L D M} = \mathbb {E} _ {z, \epsilon \sim \mathcal {N} (0, I), t} \| \epsilon - \epsilon_ {\theta} ^ {u p} \left(z _ {t}, t, c ^ {u p}\right) \| _ {2} ^ {2}, \tag {14} +$$ + +The condition $c^{up}$ includes the original text prompt $y_{t}$ and new control conditions $y_{n}$ . The upgraded model $\epsilon_{\theta}^{up}$ acquires new control conditions and capabilities by injecting learned adapter features. + +The base model and upgraded model remain frozen. The loss function is exclusively used to update the A4A module, which consists of the network with learnable features and the PTA for fine-tuning. To optimize model training, given the varying numbers of parameters in each trainable module, we adopt an asynchronous training strategy. Specifically, for training the projection in $S_{co}$ and alignment in $S_{up}$ , a learning rate of $1 \times 10^{-5}$ is employed to avoid overfitting, while a learning rate of $1 \times 10^{-4}$ is applied to the other components. If the pretrained adapter is fine-tuned, a smaller learning rate of $1 \times 10^{-6}$ is used to effectively retain PTA's conditional encoding capabilities. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. In our study, we utilize the CelebAMask-HQ dataset [15], which consists of approximately 20,000 high-quality facial images, each with a resolution of $1024 \times 1024$ pixels, and the OpenImages dataset [14], which offers a diverse collection of images featuring a wide range of clearly identifiable objects. We employ the BLIP-2 model [17] to generate captions for the aforementioned datasets, which serve as text prompts paired with the images. For validation, we randomly select 100 images from CelebAMask-HQ, ensuring they are distinct from those in the training set, and generate four images for each reference image. + +Implementation Details. We implement A4A using SD1.5 [26] as the base model, and SDXL [23] and Pixart-Alpha (XL) [4] as the upgraded models. Both SDXL and Pixart-Alpha are significantly larger text-to-image models compared to SD1.5, and we use them as upgraded models for the U-Net and transformer architectures, respectively. In this paper, we utilize the IP-Adapter [40] as our pretrained adapter. The IP-Adapter series has recently demonstrated remarkable capabilities, garnering significant interest for its ability to enhance personalization in generative models. Its performance across a variety of tasks highlights its increasing potential to advance text-to-image generation. Due to variations in GPU types across compared methods and the absence of comprehensive GPU hour reports, we use Sample Count (SC), which represents the number of samples processed up to a specific time point, as a metric + +![](images/66b93cd27e2503d438b30bfa123b5769814d45f9d50523f09cd82bea5f899aa3.jpg) +Figure 2. The visualization of personalized human generation using SDXL with U-Net architecture as the upgraded model. A4A(ours) compares with the previous work X-Adapter and pretrained adapter from the upgraded model (PTA-UM). + +![](images/9ce9673e3ffcd9fd32f55633093dce31a2d23a1288de851c5e4c5d47441de51a.jpg) +Figure 3. The visualization of personalized object generation using SDXL with U-Net architecture as the upgraded model. A4A(ours) compares with the previous work X-Adapter and pretrained adapter from the upgraded model (PTA-UM). + +for evaluating training costs and efficiency. For example, the officially published PTA has an SC of 64M (i.e., the PTA is trained with 8 V100 GPUs for 1M steps with a batch size of 8 per GPU). The terms in the following charts are defined as: (1) A4A (ours): transferring the PTA from the base model to the upgraded model using our method A4A; (2) X-Adapter: transferring the PTA using the published X-Adapter [25] checkpoint; (3) PTA-UM: the officially published pretrained adapter from the upgraded model. + +Evaluation Metrics. To verify the effectiveness and effi + +ciency of our method, we evaluate A4A on two tasks: personalized human generation (ID customization) and personalized object generation (IP customization). For ID customization, we utilize IDentity Alignment scores (IDA) to measure the similarity between generated and reference facial features, alongside the OMG method [12]. Specifically, we employ the Antelopev2 model from the InsightFace library [8] to detect faces and extract facial embeddings from both reference and generated images. For IP customization, we extract image embeddings using pretrained CLIP + +# A4A(ours) + +Photo of a man/woman standing in a garden, dressed in casual clothing, dressed in casual clothing + +![](images/fe64143bd4cf19a61c1bf3199a22b1d70b415ba7436a7f604f6aa56a82aa538b.jpg) + +![](images/7cbebc0524ffe155f0ad73ec4d8ecaf31faee6c9492bb38ad5ee3223746d5a13.jpg) + +![](images/47ac2fc31e6a7d274633709f46eda1e61a85864123096e5ec72d3fa992b45b5b.jpg) + +![](images/f3980b481ad7f811b9edbfb4db3d972ef35f68e0d8074f2b15b4ad6cbd0330fb.jpg) +Figure 4. The visualization of transferring the IP-Adapter from SD1.5 (U-Net architecture) to Pixart-Alpha (Transformer architecture). The middle line, framed in orange, serves as the reference for comparison. The left side shows the A4A effect, which closely resembles the reference, while the right side (IP-Adapter*) displays the results of training IP-Adapter from scratch. + +![](images/8f7780d3c305c94afee09681906fd201028bf1dd539e67ff149a9b2f836f12cd.jpg) + +![](images/a1041bd4031e5f914ab1d88e8219f1e2c2444a34b4fcaa721a492d8addd44746.jpg) + +![](images/83158e4f5833c57823086f319547980fdf46aba07f0b41f5b6e9a324039fc58c.jpg) + +![](images/337e5402090e1bbfd29065a07a30ca3b9b53cb40e8f89e1bbd30d525117e5a58.jpg) + +![](images/7c531b3162fde19d76daede2e22a3e8be96995b3a1790e2b383e8ef6e3c15251.jpg) + +![](images/16528312b9c32bd01ab2a8f9b83c5bed68a88e60f9c21df5e58aaa5feb0d3df2.jpg) + +![](images/4b72913cfc36aad22e8606f661f048f5b333a606e398c6ee29790df710b5a8b4.jpg) + +![](images/af99a3e34f50e28b99e049bc0a3f27ba947b4b200d5f87b2ef7e203bb92bf519.jpg) + +![](images/57ae4f7e95072d572b606bb37c9f5f6a14a0dc165cb0830d7edfeab86e59d2a4.jpg) +Text Prompt + +![](images/61d26fa82a7bb677a72b24b19ad76424bc57ba2a107e45ecbfd3bcfaafcb8239.jpg) + +![](images/848236a53755e1139544513f3d308a4305297bcda1f6f10336ca8cbcd9ca02f7.jpg) + +![](images/ae32af3ce002090ac247c4c2d85168234bc82d85ca77bd6053d2fbd1a25003e5.jpg) + +![](images/c7bc67cba504b80415a83eee1f1a51e7e2f5d6ef8950e1d978c7e39bfc1f22b1.jpg) + +![](images/5bc2b7e4ea6ee70730c32a70883a7d7d20f799edb14bd29fd180c609dd7bf10c.jpg) + +![](images/5fb976c3468f42757a85f83aa4eca62f05cc02e23375216a8f167825dda78ce2.jpg) + +![](images/a2283328ee278da6f9fba1185c9d3a8d7829de61d95a5a08045866e2e02d252e.jpg) + +# IP-Adapter\* + +Photo of a man/woman standing in a garden, dressed in casual clothing, dressed in casual clothing + +![](images/962e45ecfd2217bb41ba0a074ccdef3c37c8c0136df0fae9dcd51d9bad7d0de9.jpg) + +![](images/959c47cf92a3b815ce1eb45301729c6de4eedf17943a5249b17aaf16d2d7bb73.jpg) + +![](images/fdba5f17f5d669645cd571225b302c820053f927e6bf0ff0efe5b08c90a39b6d.jpg) + +![](images/6e44ce8e6807b350b95d84a69ae27961cdec95add122ba0a5be6afb69f5efa02.jpg) + +![](images/3e7d6088f62cdd2d630e57fd4eda834eac73b2b2fc292729dab221070bc55960.jpg) + +![](images/a25eb9338a194802f6bf62585c6c47b963d3c8212afc35a53caf27593f4eabd4.jpg) + +![](images/53512d3eae80263c154286529562d1c7bfc6e7d3016850b84a731822613a82cc.jpg) + +![](images/79f36e8373c041b56e98430c85e0e398b5791190220a2d660decdd554635447d.jpg) + +![](images/20bcbc720f725f45c4fdc3a1f29bd471a6bbcbcd51a9460863ffd252192a1dac.jpg) + +![](images/128dbbaf9f45590515898394dc2828d87dbc506efaa05e4fa0279c7ad9cc5c68.jpg) + +![](images/37f8a1f3a2e0e035f59c33aec3b06ab7a3c6a4afeb366f6d6b7038b88bb12ca3.jpg) + +![](images/079969bf3c7337de7a2f70e422babc77e6788101ecb5c08954fd16130ca45eea.jpg) + +![](images/55081e8dd368ae1851a919b8f7d61a0dbf81c0a74aa4f2d73f79c8620cdd262d.jpg) + +![](images/e51493f7821e830e5deca317a74b0dae8367f4398fe4c3ed78b7114f2b73bd39.jpg) + +![](images/21b4bfc819dbbaa88e276dcbdde80a291423726dc2c681a93e83bcdc22838a8a.jpg) + +![](images/4a1e99966750ed40efee9a98d7b465d20557986942b83b8fcb7631d2cf81ac04.jpg) + +model [24] and report the embedding similarity between generated and reference images, referred to as the CLIP-score. In the graph, we use the previously defined SC as the horizontal axis to represent the training process. + +# 4.2. Transferring to the U-Net model + +We use SDXL as the upgraded model and compare our results with the officially published PTA-UM [40] (represented by the green star in Fig. 5). To facilitate comparison, we extend a horizontal line from this point to represent the performance of PTA-UM, rather than the actual training curve. As illustrated in Fig. 5, transferring the PTA using A4A achieves an IDA comparable to that of the PTA-UM at approximately $\mathrm{SC}0.5\mathrm{M}^2$ . Furthermore, as shown in Fig. 2, the lines "A4A (ours)" and "PTA-UM" demonstrate that A4A not only preserves the intellectual property of the characters but also maintains the editing capabilities of the upgraded model with minimal training cost. + +For personalized object generation (IP customization), as shown in Fig. 6, transferring the PTA using A4A achieves a CLIP-score comparable to that of PTA-UM at approximately 2.5M SC, compared to 64M SC for PTA-UM. As illustrated in Fig. 3, the lines labeled "A4A (ours)" and "PTA-UM" demonstrate that control ability, as guided by the text prompt, is also preserved. When the attention-based adapter is transferred to the upgraded U-Net model, A4A ef + +![](images/aa1bc97f37480ed25043a456cef3b14af810c985f912776542fd091739d160a3.jpg) +Figure 5. The graph shows the IDA of ID preservation when transferring to SDXL, compared to the pretrained adapter from SDXL (PTA-UM). The horizontal axis is in units of M. + +![](images/c93ac3380b00ea9ed059918b0e1a147a89f8ee44b8013b744a536d2b44511e41.jpg) +Figure 6. The graph shows the CLIP-score of personalized object generation when transferring to SDXL, compared to PTA-UM. The horizontal axis is in units of M. + +fectively retains and transfers the adapter's capabilities with minimal training cost. The data of the quantitative indica + +tors corresponding to the line chart are shown in Tab. 1. + +# 4.3. Transferring to Transformer model + +We use Pixart-Alpha [4] with the transformer architecture as the upgraded model. Given the absence of a corresponding published version of the IP-Adapter for Pixart-Alpha, we train it from scratch using the CelebAMask-HQ dataset as our baseline, represented by the orange line labeled "IP-Adapter*" in Fig. 7 and Fig. 4. As illustrated in Fig. 7, employing A4A to transfer pretrained adapters to transformer models offers a significant advantage over training adapters directly on the transformer models. It is worth noting that our work is the first to transfer the adapter from the U-Net model to the transformer model, achieving strong results. Fig. 4 presents a visualization comparing our method with training the IP-Adapter from scratch, both at 30k steps with a batch size of 8. The images generated by A4A show significant facial similarity to the reference image, while the image on the right does not yield comparable results. + +![](images/576d606fe6975be35450003a2984ee536f2e2db225ca61a8629aba5825bef934.jpg) +Figure 7. The IDA of transferring the pretrained IP-Adapter from SD1.5 to Pixart-Alpha using A4A (red line with dots), compared to training the IP-Adapter from scratch (orange line with stars). The horizontal axis is in units of K. Best viewed in color. + +# 4.4. Ablation Study + +In the previous section, we adopted the A4A paradigm, which includes training our modules, namely Coupling Space Projection and Upgraded Space Mapping, along with fine-tuning the PTA. To demonstrate that fine-tuning is not the core driving force of our method, we conducted the following experiment. As shown, the two curves are very close, with the fine-tuning paradigm showing only a slight improvement over the non-fine-tuning version. + +We present experiments on the hyperparameter settings of the learning rates for each component in Sec. 7. It is worth mentioning that, since Projection and Alignment have similar numbers of parameters, we group them together. The ablation study of the two core modules is presented in Sec. 8, which demonstrates that our design achieves a satisfactory transfer effect with an efficient structure. + +![](images/973239fcf626e413ae96724f8697f9c406221073a8f100f655bb295998e01bc3.jpg) +Figure 8. The yellow line labeled "A4A(ours w/fine-tuning)" represents training A4A without fine-tuning the PTA, while the red line represents the full A4A approach with fine-tuning the PTA. + +
PTA: IP-AdapterIDA↑CLIP-score↑
X-Adapter0.0620.7894
PTA-UM0.45310.9124
A4A(ours)0.51270.9154
+ +Table 1. The evaluation metrics for IP customization (CLIP-score) and ID customization (IDA) are presented. Using SDXL as the upgraded model and IP-Adapter as the pretrained adapter, A4A (ours) is compared with the transfer method X-Adapter and the pretrained adapter from the upgraded model (PTA-UM). + +# 4.5. Comparison with X-Adapter + +The previous work X-Adapter [25] is designed specifically for transferring adapters from U-Net models. To demonstrate the effectiveness of A4A, we also compare it with X-Adapter. As shown in Tab. 1, our method achieves better results in generation using the transferred adapter for both IP and ID customization. The visualizations in Figure 2 and Fig. 3, particularly the row labeled "X-Adapter", further substantiate this when compared to the adjacent rows. It is also worth noting that our method requires only the adapter for training and inference, without the need for denoising using the base model as in X-Adapter, which makes it more efficient. + +# 5. Conclusion + +We propose A4A (Adapter for Adapter), a novel framework designed to address the challenges of transferring pretrained adapters across rapidly evolving model architectures. By employing an all-for-all mapping approach, A4A seamlessly transfers attention-based adapters from U-Net to transformer models without the need for extensive retraining. The framework's two key components, Coupling Space Projection and Upgraded Space Mapping, enable effective bridging of adapter features with upgraded model structures. Our experimental results demonstrate that A4A preserves both the generative power of upgraded models and the controllability of the original adapters. This work offers a scalable solution for cross-architecture adapter transfer. + +# 6. Acknowledgment + +This research is supported by Artificial Intelligence National Science and Technology Major Project 2023ZD0121200, and National Natural Science Foundation of China under Grant 62222212 and 623B2094. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023. 2 +[2] Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Jiaming Song, Qinsheng Zhang, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, et al. ediff-i: Text-to-image diffusion models with an ensemble of expert denoisers. arXiv preprint arXiv:2211.01324, 2022. 3 +[3] Marco Bellagente, Manuel Brack, Hannah Teufel, Felix Friedrich, Björn Deiseroth, Constantin Eichenberg, Andrew M Dai, Robert Baldock, Souradeep Nanda, Koen Oostermeijer, et al. 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(Left) CLIP's anomaly unawareness: Category-level image-text alignment in pre-training leads to CLIP's vague distinctions in anomaly/normal semantics and inaccurate patch-text alignment. (Middle) Our two-stage adaptation strategy: In Stage1, anomaly and normal text features are disentangled as anchors in text space; in Stage2, patch-level visual features are trained to align to these anchors, forming Anomaly-Aware CLIP. (Right) Generalizable anomaly awareness: Our method enables CLIP with generalizable anomaly awareness for both known and unseen classes. + +![](images/405427f90a30740df75eebe906d8559fa16b9540f06778b3baeee3d49ac5bb62.jpg) +Stage1: Disentangling Anomaly-Aware Text Anchors +(Middle) + +![](images/199d6c14ef078069f92c1d73c20758998ba76787d4d6aa8c8ad9f11f37685ab5.jpg) +Stage2: Aligning Patch Features According to Text Anchors + +![](images/f86c1c21560c68444a6a9dbb56d8d95195a458263ac431a206d76551bc0659ef.jpg) +Features from our Anomaly-Aware CLIP +(Right) + +# Abstract + +Anomaly detection (AD) identifies outliers for applications like defect and lesion detection. While CLIP shows promise for zero-shot AD tasks due to its strong generalization capabilities, its inherent Anomaly-Unawareness leads to limited discrimination between normal and abnormal features. To address this problem, we propose Anomaly-Aware CLIP (AA-CLIP), which enhances CLIP's anomaly discrimination ability in both text and visual spaces while preserving its generalization capability. AA-CLIP is achieved through a straightforward yet effective two-stage approach: it first creates anomaly-aware text anchors to differentiate normal and abnormal semantics clearly, then aligns patch-level visual features with these anchors for precise anomaly localization. This two-stage strategy, with the help of residual adapters, gradually adapts CLIP in a controlled man + +ner, achieving effective AD while maintaining CLIP's class knowledge. Extensive experiments validate AA-CLIP as a resource-efficient solution for zero-shot AD tasks, achieving state-of-the-art results in industrial and medical applications. The code is available at https://github.com/Mwxinnn/AA-CLIP. + +# 1. Introduction + +Anomaly detection (AD) involves modeling the distribution of a dataset to identify outliers, such as defects in industrial products [2] or lesions in medical images [13]. Despite that previous AD frameworks [10, 11, 15, 23, 31, 58] effectively detect anomalies when sufficient labeled data is available for specific classes, their high resource demands often limit their generalization ability to novel and rare classes. This limitation is particularly challenging in real-world scenarios where collecting comprehensive labeled datasets for AD is often infeasible, necessitating the exploration of low-shot + +learning and transfer learning approaches. + +Contrastive Language-Image Pretraining (CLIP) model has emerged as a promising solution, demonstrating remarkable generalization capabilities across various zero-shot tasks [24-26, 42]. Building upon CLIP's success, several recent studies have adapted CLIP for few/zero-shot AD tasks by utilizing anomaly-related descriptions to guide the detection of anomalous regions. Specifically, the vision encoder is trained to map anomaly images to visual features that align more closely with text features of abnormal descriptions than with those of normal descriptions [29, 30, 49, 60]. Further works [6, 7, 17, 41] have focused on enhancing CLIP's patch-level feature representations to achieve better alignment with text features, resulting in improved anomaly localization performance. + +These methods depend on text features that need to be anomaly-aware to effectively differentiate abnormalities. However, recent studies highlight CLIP's limitations in fine-grained semantic perception and reasoning [21, 22, 36, 38, 45, 46]. Upon exploring CLIP's texture features for AD, we observe that while CLIP's text encoder effectively captures object-level information, it struggles to reliably distinguish between normal and abnormal semantics. As shown in conceptual visualization Fig. 1(left) and sampled examples in Fig. 2, CLIP has the intrinsic Anomaly-Unawareness problem: the overlap of normal and abnormal texture features hampers the precision of text-guided anomaly detection. We argue that making CLIP anomaly-aware — by establishing clearer distinctions between normal and abnormal semantics in the text space — is essential for guiding the vision encoder to precisely detect and localize anomalies. + +This observation drives us to improve CLIP-based zero-shot AD through enhancing anomaly discrimination in text space, achieved with our method Anomaly-Aware CLIP (AA-CLIP) — a CLIP model with anomaly-aware information encoded. AA-CLIP is implemented through a novel two-stage adaptation approach. In the first stage, AA-CLIP adapts the text encoder with frozen visual encoder, creating "anchors" for anomaly-aware semantics within the text space for each trained class. As illustrated in Fig. 1(middle), each class's text features are disentangled to distinct anchors, with clear abnormality discrimination. Notably, this disentanglement also applies to novel, unseen classes, supporting effective zero-shot inference in AD tasks (refer to Fig. 1(right)). In the second stage, AA-CLIP aligns patch-level visual features with these specially adapted texture anchors, guiding CLIP's visual encoder to concentrate on anomaly-relevant regions. This two-stage approach ensures a focused and precise anomaly detection framework. + +Importantly, as CLIP is extensively trained on massive data, to preserve its pre-trained knowledge, we utilize simple-structured Residual Adapters in both stages. This design enables a controlled adaptation of CLIP while en + +hancing its capability to handle fine-grained AD tasks without sacrificing its generalization ability. + +Our extensive experiments in both industrial and medical domains demonstrate that our straightforward approach equips CLIP with improved zero-shot AD ability, even in data-limited scenarios. By training with a minimal sample — such as one normal sample and one anomaly sample (2-shot) per class — and testing across unseen datasets, our method achieves zero-shot performance comparable to other CLIP-based AD techniques. With only 64-shot of each class seen in the training set, our method reaches state-of-the-art (SOTA) results in cross-dataset zero-shot testing, validating our method's ability to maximize the CLIP's potential for AD with a minimal data requirement. + +Our contributions are summarized as follows: + +1. Anomaly-Aware CLIP with enhanced and generalizable anomaly-discriminative ability. We introduce AA-CLIP which is more sensitive to anomalies sequentially in text and visual spaces, encoding anomaly-aware information into the original CLIP. +2. Efficient adaptation using residual adapters. We implement simple residual adapters to boost zero-shot anomaly detection performance without compromising the model's generalization ability. +3. SOTA performance with high training efficiency. Our method achieves SOTA results across diverse datasets, showing robust anomaly detection capabilities even with limited training samples. + +# 2. Related Work + +Traditional Anomaly Detection in images involves modeling the normal data distribution to detect rare and diverse unexpected signals within visual data [44, 52, 53, 61]. Reconstruction-based [11, 16, 32, 33, 54, 56], augmentation-based [31, 44, 48, 55, 58] and discriminative [10, 15, 23, 31, 43, 61] methods are typically used to facilitate better modeling. Despite the huge progress of traditional anomaly detection methods, their effectiveness relies heavily on a well-modeled normal data distribution. Without sufficient normal data, their ability to accurately detect anomalies is significantly reduced. + +CLIP, trained on a vast amount of image-text data, leverages contrastive learning alongside powerful language models and visual feature encoders to capture robust concepts. This combination enables CLIP to achieve impressive zero-shot performance on image classification, as it can generalize well to new categories without requiring task-specific training [24-27, 42, 51]. More recently, numerous studies [9, 12, 35, 39] have explored ways to transfer the knowledge embedded in CLIP models to a variety of downstream tasks, yielding promising results in fields like image captioning, image-text retrieval, and image generation. These efforts demonstrate CLIP's versatility and potential to drive + +advancements across diverse applications. + +Despite the rapid advancements achieved by CLIP, numerous studies have highlighted persistent limitations in the features it extracts. While CLIP demonstrates strong generalization across various tasks, it often struggles to capture nuanced details and essential spatial relationships, which are crucial for tasks demanding precise boundary delineation and fine-grained feature extraction. This limitation results in suboptimal performance in downstream applications, especially that require high levels of detail, such as object detection, scene segmentation, or tasks in medical imaging [14, 29, 30, 37, 49, 50, 57, 60]. As a result, leveraging CLIP for fine-granular tasks frequently necessitates task-specific adaptations to bridge the gap between its generalized feature extraction and the precision required for specialized applications. + +CLIP-based Anomaly Detection There have been several efforts to leverage CLIP for AD tasks. One of the pioneering approaches, WinCLIP [19], proposes a method for extracting and aggregating visual features from multiple levels to align with text features, demonstrating the potential of CLIP in this context. Subsequent research investigates various adaptation methods to bridge the gap between natural domains and the AD domain, resulting in performance improvements. For instance, [7, 8, 18] focus on refining visual features by employing adapters to enhance patch-level visual representations. However, these approaches often rely on text embeddings from the original CLIP model as soft supervision and overlook a critical limitation of CLIP in AD: itsunclearness in distinguishing between anomalous and normal semantics, particularly within the text encoder, resulting in suboptimal performance. Other works have employed prompt-learning-based methods[5, 6, 41, 59], introducing learnable embeddings into the text encoder to better represent abnormality. However, the class information in CLIP can be damaged, potentially degrading generalization, especially in data-limited and zero-shot settings. + +Different from previous methods, we are the first to investigate CLIP's inherent limitation in capturing anomaly-aware information, specifically in differentiating between normal and anomalous semantics in text prompts. Rather than relying solely on the original anomaly-unaware text embeddings or unaltered feature spaces, our method is able to refine the embeddings to actively incorporate anomaly-discriminative representations. + +# 3. Method + +# 3.1. Overview + +# 3.1.1. Problem Formulation + +Zero-shot AD models are trained to identify anomalous samples whose categories may be unseen in the training dataset. Specifically, the model is expected to learn + +![](images/1f4b294e7d4def9bcc526a78197fc3385e97f3cb55a77e48738270adecb8c5f1.jpg) + +![](images/b75f5d93de627136e49c895ecdf83d74a7eab7e2e9f221c69e97c6c8bbd33721.jpg) + +"This is a [ ] carpet." + +
SemanticsSimilarityProbabilityτ=0.01
broken0.180.22
normal0.190.78
+ +"This is a [ ] zipper." + +
SemanticsSimilarityProbabilityτ=0.01
broken0.200.38
normal0.210.62
+ +![](images/467ee38e87dd5ff7fa4576a42be09710e9d3a22d802523419eec73f0820be9d3.jpg) +Figure 2. (Top) Examples illustrating CLIP's Anomaly Unawareness. Despite the obvious anomalies present in the images, image features have higher similarities to normal descriptions, rather than anomaly descriptions, mistakenly. This problem is enlarged with a low temperature $\tau$ . (Bottom) Text Feature Similarity Heatmap among Normal and Anomaly Descriptions: Original CLIP vs. After Text Adaptation. Red indicates high similarity. In original CLIP, normal features exhibit strong similarity with anomaly features, whereas text adaptation successfully separates them, clarifying the semantic distinctions between normal and anomaly descriptions. + +both normal and abnormal patterns that are shared across different classes given a training set $\mathcal{D}_{train}$ with normal or anomalous samples, in order to be capable of performing AD tasks on a series of different test datasets $\{\mathcal{D}_{test}^{1},\mathcal{D}_{test}^{2},\dots,\mathcal{D}_{test}^{n}\}$ , where each $\mathcal{D}_{test}^{i}$ is distinct from $\mathcal{D}_{train}$ . Image-level AD can be formally defined as a binary classification problem, where the model aims to classify samples $x\in \mathcal{D}$ as either normal ( $y = 0$ ) or anomalous ( $y = 1$ ). Anomaly segmentation extends this concept to pixel-level with mask $S$ , aiming to identify anomalous regions by highlighting pixels associated with anomalies. + +# 3.1.2. Current Challenges + +Anomaly Unawareness in CLIP: The CLIP-based AD method classifies visual features as "anomalies" if they exhibit greater similarities to anomaly prompt embeddings than to normal prompt embeddings, thus requiring well-defined boundaries between these two kinds of prompts. However, in real applications, CLIP's text embeddings often lack the clear separability needed to reliably distinguish between normal and anomaly classes. + +We observe that, despite the visible defects in example images from the MVTec-AD [2], their features exhibit higher cosine similarity with "normal" prompts than with correct "anomaly" descriptions (see Fig. 2 (top)), indicating CLIP's inaccurate semantic understanding. Without adap + +![](images/85d153d5a9c1ba27ae30deddc2e6b7643a16c6f2889c919f03a81988d171c738.jpg) +Figure 3. t-SNE Visualization of Text Features from Original CLIP vs. AA-CLIP. Each point represents a text feature encoded from a prompt. Original CLIP's normal and anomaly text features are intertwined, while our method effectively disentangles them. This disentanglement is generalizable to novel classes, validating the anomaly-awareness of our model. + +tation, there persists a high similarity between the normal and abnormal text embeddings of a single class, as shown in Fig. 2 (bottom), suggesting a potential entanglement of normal and anomaly semantics within text space. We term this limitation Anomaly Unawareness and attribute it to the training process of CLIP: it is primarily trained on general, non-anomalous datasets and lacks specific guidance on defect detection. Consequently, it is challenging to rely on original CLIP embeddings to detect subtle or context-specific anomalies. + +This issue remains evident across different categories in our t-SNE analysis: as shown in Fig. 3 (top), only subtle separations are observed within an object cluster, where text embeddings for both normal and abnormal semantics are intermixed. This entangled pattern may potentially lead to anomaly-unaware text-image alignment, which reinforces the necessity to adapt CLIP's to enhance its ability of anomaly-awareness. + +**Embedding Adaptation Dilemma:** Discussion above renders the adaptation of CLIP essential for effective AD. However, since CLIP's embeddings are already optimized through extensive pretraining, it could be susceptible to overfitting to new dataset during adaptation. Overfitting convergence leads to minimized intra-class distinctions in the training data, often at the expense of the feature separability for effective generalization to unseen data. + +To address this, a carefully controlled refinement is crucial to preserve CLIP's generalization capabilities while enhancing its sensitivity to anomalies. + +# 3.1.3. Overview of Our Solution + +Motivated by Sec. 3.1.2, we propose Anomaly-Aware CLIP (AA-CLIP) with improved anomaly awareness. As shown in Fig. 4, AA-CLIP is trained through a two-stage training strategy that sequentially adapts the semantic-rich text space and detail-focused visual space, with original CLIP parameters remaining frozen. In the first stage (see Fig. 4 (Top)), we incorporate Residual Adapters into the shallow layers of the text encoder, and the visual features from the fixed image encoder serve as a stable reference for optimization. A Disentangle Loss is proposed to enforce effective discrimination by ensuring independence between normal and anomaly embeddings. In the second stage, we integrate Residual Adapters into the shallow layers of the visual encoder to align patch-level features with the fixed, specially adapted texture features from the fixed text encoder (see in Fig. 4 (Bottom)). Ultimately, our AA-CLIP succeeds in equipping CLIP with anomaly awareness across seen and unseen classes, as shown in Fig. 3 (bottom). + +# 3.2. AA-CLIP with Two-Stage Adaptation Strategy + +# 3.2.1. Residual Adapter + +To preserve CLIP's pre-trained knowledge while enabling targeted adaptation, we introduce lightweight Residual Adapters in the shallow layers (up to layer $K$ ) of both text and vision encoders. + +The output feature $x^{i} \in \mathbb{R}^{N \times d}$ of CLIP's $i$ -th ( $i \leq K$ ) transformer layer is fed into the $i$ -th adapter, outputting adapted feature $x_{residual}^{i}$ , as shown in Eq. (1), + +$$ +x _ {\text {r e s i d u a l}} ^ {i} = \operatorname {N o r m} \left(\operatorname {A c t} \left(W ^ {i} x ^ {i}\right)\right), \tag {1} +$$ + +where $W^{i} \in \mathbb{R}^{d \times d}$ is the trainable linear weight of $i$ -th adapter, $Act(\cdot)$ is an activation function, and $Norm(\cdot)$ is a normalizing function. The original feature $x^{i}$ and the enhanced feature $x_{residual}^{i}$ are fused in a weighted manner, generating $x_{enhanced}^{i}$ , the input to the next transformer layer, as shown in Eq. (2), + +$$ +x _ {\text {e n h a n c e d}} ^ {i} = \lambda x _ {\text {r e s i d u a l}} ^ {i} + (1 - \lambda) x ^ {i}, \tag {2} +$$ + +where $\lambda$ is a hyper-parameter to control the residual ratio, adjusting the fusing degree of AD-specific knowledge for preserving the original CLIP's generalization ability and improved performance. + +# 3.2.2. Two-Stage Training Strategy + +Disentangling Anomaly-Aware Text Anchors: In the first stage, our objective is to learn anomaly-discriminative text anchors by adapting the text encoder while keeping the + +![](images/a4a610b1167236135a85d221e41e21c181b00e2ab31d2c098f0a54df24da772a.jpg) +Stage1: Disentangling Anomaly-Aware Text Anchors + +![](images/b1ece9f7bcb30903f6b874d348410a737150e0d213c2bd10ec011036cf8438ca.jpg) +Stage2: Aligning Patch Features According to Text Anchors +Figure 4. The Two-Stage Training Pipeline of Anomaly-Aware CLIP. In the first stage, the text encoder of AA-CLIP is trained to identify anomaly-related semantics, helped by a disentangle loss. In the second stage, patch features are aligned with these text anchors. Both stages are achieved by the integration of Residual Adapters into the shallow layers of CLIP's backbone. This controlled adaptation enables CLIP to effectively distinguish anomalies, which forms our Anomaly-Aware CLIP. + +image encoder fixed. We incorporate Residual Adapters into the first $K_{T}$ layers of the CLIP text encoder, as illustrated in Fig. 4 (Top), and set the final projector in the text encoder to be learnable to facilitate improved alignment. + +Using prompts designed to encapsulate both normal and anomalous semantics (as detailed in Appendix), text encoder generates corresponding high-level embeddings. The average embeddings of the normal and anomaly prompts serve as our initial text anchors, denoted as $T_{N}$ and $T_{A} \in \mathbb{R}^{d}$ , respectively. These anchors are refined by being aligned with visual features extracted from an enhanced CLIP visual encoder, as [28, 59]. Alignment is conducted at both image and patch levels to incorporate both global and local semantics. By calculating the cosine similarity between these anchors and the image features $V_{image} \in \mathbb{R}^{d}$ or patch features $V_{patch} \in \mathbb{R}^{N \times d}$ , as shown in Eq. (3), + +$$ +p _ {c l s} = \operatorname {C o s S i m} \left(V _ {\text {i m a g e}}, \left[ T _ {N}, T _ {A} \right]\right), \tag {3} +$$ + +$$ +p _ {s e g} ^ {o} = \operatorname {C o s S i m} (V _ {p a t c h}, [ T _ {N}, T _ {A} ]), +$$ + +where $[\cdot, \cdot]$ means concatenate operation, we obtain the classification prediction $p_{cls} \in \mathbb{R}^2$ and the segmentation prediction $p_{seg}^{o} \in \mathbb{R}^{N \times 2}$ . The segmentation prediction $p_{seg}^{o}$ is then reshaped and upsampled to $p_{seg} \in \mathbb{R}^{H \times W \times 2}$ to align + +with the height $H$ and width $W$ of segmentation mask $S$ . Following previous works [6, 7, 18, 59], we compute the classification loss $\mathcal{L}_{cls}$ and segmentation loss $\mathcal{L}_{seg}$ to optimize parameters, as specified in Eq. (4). Specifically, the classification loss is a binary cross-entropy that compares classification predictions with ground-truth labels $y$ , and the segmentation loss is a combination of dice loss and focal loss applied to segmentation predictions and the anomaly segmentation mask $S$ . + +$$ +\mathcal {L} _ {c l s} = \operatorname {B C E} (p _ {c l s}, y), +$$ + +$$ +\mathcal {L} _ {\text {s e g}} = \operatorname {D i c e} \left(p _ {\text {s e g}}, S\right) + \operatorname {F o c a l} \left(p _ {\text {s e g}}, S\right), \tag {4} +$$ + +$$ +\mathcal {L} _ {\text {a l i g n}} = \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {s e g}}. +$$ + +To enhance the separation between normal and anomaly text embeddings, we introduce a Disentangle Loss encouraging orthogonality between $T_{N}$ and $T_{A}$ to minimize correlation, as in Eq. (5): + +$$ +\mathcal {L} _ {\text {d i s}} = | < T _ {N}, T _ {A} > | ^ {2}. \tag {5} +$$ + +The Disentangle Loss $\mathcal{L}_{dis}$ is incorporated into the alignment loss $\mathcal{L}_{\text {align }}$ as a regularization term, weighted by a factor $\gamma$ , which forms the total loss, as in Eq. (6): + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {a l i g n}} + \gamma \mathcal {L} _ {\text {d i s}}. \tag {6} +$$ + +In this stage, the distinction between normal and anomaly semantics is embedded into CLIP's text encoder while its original object-recognition capability is preserved. Figure 3 indicates that this ability of anomaly-awareness is robust and generalizable to novel classes. + +Aligning Patch Features According to Text Anchors: Anomaly-aware semantic anchors can facilitate the adaptation of patch features, thereby improving the effectiveness and generalizability of anomaly localization. To achieve alignment between patch features and anchors from the previous stage, we introduce trainable Residual Adapters within the initial $K_{I}$ layers of the CLIP visual encoder. + +Features with multi-granularities are utilized to enhance segmentation [7, 19, 59]. Specifically, as shown in Fig. 4 (bottom), the intermediate output feature $F^i$ are extracted from four distinct granularities. These multi-granularity features are then projected to align with the channel of text anchors via a trainable projector $Proj_i(\cdot)$ , yielding $V_{patch}^i$ at four distinct levels of granularity. The aggregated output $V_{patch}$ is computed by summing individual $V_{patch}^i$ outputs, as in Eq. (7): + +$$ +\begin{array}{l} V _ {p a t c h} ^ {i} = \operatorname {P r o j} _ {i} \left(F ^ {i}\right), i \in \{1, 2, 3, 4 \} \\ V _ {p a t c h} = \sum_ {i = 1} ^ {4} V _ {p a t c h} ^ {i}. \tag {7} \\ \end{array} +$$ + +The cosine similarity scores between the aggregated $V_{patch}$ and the text anchors are calculated to generate patch-level predictions as Eq. (3), resulting in the prediction maps. + +During training, alignment is guided by the loss function defined in Eq. (4), facilitating both global and local alignment. During inference, anomaly prediction maps and corresponding anomaly scores are derived by comparing the similarity scores of visual features against normal and anomaly text embeddings. + +# 4. Experiments + +# 4.1. Experiment Setups + +Datasets We evaluate our model on 11 widely used benchmarks, as previous AD works [6, 7, 18, 19, 59], with distinct foreground objects spanning a variety of modalities, including photography, endoscopy, CT, MRI, and OCT. For the industrial domain, we use MVtec AD [2], VisA [62], BTAD [34] and MPDD [20]. For medical domain, we use brain MRI, liver CT and retina OCT from BMAD [1], and four different colon polyp detection datasets with different views (CVC-ClinicDB [4], CVC-ColonDB [3], Kvasir-SEG [40] and CVC-300 [47]). Each dataset has both image-level labels and pixel-level masks for evaluation. + +We train our model on a real-world industrial AD dataset - VisA [62] - in which objects are different from other datasets. Results of VisA are obtained using MVtec-AD as + +the training dataset. To demonstrate adaptation efficiency, we conduct training under various data levels: 2-shot per class, 16-shot per class, 64-shot per class, and full-shot. The corresponding number of samples are randomly selected from each class, while maintaining a consistent 1:1 ratio between normal and anomaly samples. + +Metrics Following [6, 7, 10, 11, 18, 19, 43, 55], we use the Area Under the Receiver Operating Characteristic Curve (AUROC) as the metric. We compute AUROC at both the image and pixel levels to comprehensively assess the model's effectiveness in detecting and localizing anomalies. Implementation Details Following [6, 7, 41, 59], we use OpenCLIP with the ViT-L/14 architecture as the backbone, and input images are resized to $518 \times 518$ . All parameters of CLIP remain frozen. We set $\lambda$ to 0.1, $K_{T}$ to 3, $K_{I}$ to 6, and $\gamma$ to 0.1. For multi-level feature extraction, we utilize outputs from the 6-th, 12-th, 18-th, and 24-th layers of the visual encoder to compose the overall output. For the first stage, we train the model for 5 epochs with a learning rate of $1 \times 10^{-5}$ . For the second stage, we continue training for 20 epochs, adjusting the learning rate to $5 \times 10^{-4}$ . Parameters are updated by Adam optimizers. All experiments are conducted on a single NVIDIA GeForce RTX 3090 GPU. More details are available in Appendix. + +# 4.2. Comparison with SOTA Methods + +We compare our method against CLIP and several recent SOTA models. Among them, WinCLIP [19], VAND [7] and MVFA-AD [18] use original CLIP text encoder, and AnomalyCLIP [59] and AdaCLIP [6] incorporate learnable prompts. To ensure a fair comparison, we re-train models that are originally trained on different datasets to match the dataset settings of other approaches (detailed in Appendix). + +Quantitative results are presented in Tab. 1 and Tab. 2. Although adapting only the patch feature with original text embeddings has made progress in AD, the superior performance of AA-CLIP highlights its effective disentanglement of anomaly-discriminative semantics, leading to further progress. Notably, even in data-limited situations, our method consistently demonstrates top performance. At the pixel level, with only 2 shots per class used for training, our method achieves improved average zero-shot performance compared to previous methods. With the full dataset, we set a new pixel-level SOTA with an AUROC of $93.4\%$ . At the image level, our method is competitive with just 2 shots for training and establishes a new SOTA of $83.1\%$ with 64 shots per class. + +Unlike previous methods, our approach does not rely heavily on data resources to achieve top-tier performance. Comparison under different levels of data available, as shown in Fig. 5, reveals that our approach consistently outperforms other methods in general. Even with limited data, our model reaches competitive results, while other methods + +
DomainDatasetCLIP*WinCLIP*VAND*MVFA-ADAnomalyCLIP*AdaCLIPOurs
OpenCLIPCVPR 2023CVPRw 2023CVPR 2024ICLR2024ECCV2024-
Available training shots--fullfullfullfull21664full
IndustrialBTAD30.632.891.190.193.390.892.894.496.597.0
MPDD62.195.294.994.596.296.696.396.596.396.7
MVTec-AD38.485.187.684.991.189.991.091.291.691.9
VisA46.679.694.293.495.495.593.493.894.095.5
MedicalBrain MRI68.386.094.595.696.293.996.396.496.595.5
Liver CT90.596.295.696.893.994.597.397.797.797.8
Retina OCT21.380.688.590.992.688.594.295.194.495.5
ColonDB49.551.278.278.482.980.083.983.584.784.0
ClinicDB47.570.385.183.985.085.989.287.687.889.9
Kvasir44.669.780.381.981.986.482.184.685.287.2
CVC-30049.9-92.882.695.492.996.097.496.096.4
Average49.974.789.388.591.390.492.092.692.893.4
+ +Table 1. Pixel-level AUROC of zero-shot AD methods in Industrial and Medical domains. Method sources and the number of shots used for training are noted. Results of methods with * are copied from the papers or inferred from official weight. Best results are highlighted as first, second and third. + +
DomainDatasetCLIP&VAND*WinCLIP*MVFA-ADAnomalyCLIP*AdaCLIPOurs
OpenCLIPCVPR 2023CVPR 2024ICLR2024ECCV2024-
Available training shots--fullfullfull21664full
IndustrialBTAD73.668.294.385.390.988.090.994.794.8
MPDD73.063.670.973.772.163.678.375.775.1
MVTec-AD86.191.886.690.990.085.989.792.090.5
VisA66.478.076.582.184.378.484.084.184.6
MedicalBrain MRI58.866.570.983.380.284.380.483.480.2
Liver CT54.764.263.061.664.269.468.169.269.7
Retina OCT65.642.577.375.782.777.481.082.982.7
Average68.367.877.178.480.678.181.883.182.5
+ +display signs of underfitting. As data increases, our method maintains its lead, establishing a new SOTA at both pixel and image levels. + +# 4.3. Visualization + +To illustrate the alignment intuitively, we present visualization examples in Fig. 6 with original configuration for previous works. Although previous methods with can detect anomalous regions, our AA-CLIP demonstrates fewer false-negative predictions in both industrial and medical domains, accurately highlighting the correct anomaly regions. + +# 4.4. Ablations Analysis + +We conduct thorough ablation experiments of our refinement of both visual and text space, as shown in Tab. 3 and Fig. 7. The second row in Tab. 3, which mirrors the structure of VAND [7], serves as our baseline. + +Image Space: As shown in Tab. 3 line “2,” inserting the vallina linear adapter into transformer layers results in a significant decline in zero-shot performance, indicating the + +Table 2. Image-level AUROC of zero-shot AD methods in Industrial and Medical domains. Method sources and the number of shots used for training are noted. Results of methods with * are copied from the papers or inferred from official weight. Best results are highlighted as first, second and third. + +
MethodAvg. AUROC
Pixel-LevelImage-Level
CLIP50.369.3
Image1. + Linear Proj. (VAND [7])88.969.3
2. + Adapter48.9(-40.0)53.4(-15.9)
3. + Residual Adapter91.3(+2.4)80.7(+11.4)
Text4. + Residual Adapter92.1(+3.2)82.6(+13.3)
5. + Disentangle Loss92.7(+3.8)83.3(+14.0)
+ +Table 3. Ablation Study of Our Training Strategy with VisA-Trained 64-Shot Setup. Our contributions are bold. While VAND uses linear projectors to improve AD performance, incorporating Residual Adapters further refines patch feature adaptation. Moreover, integrating our Disentangle Loss yields the best overall results. + +damage of the original generalization ability of CLIP. Incorporating our Residual Adapters mitigates this issue (shown in line "3"). enhancing performance while preserving original information stored in CLIP. + +Text Space: The last two rows in Tab. 3 highlight the impact of our approach in equipping CLIP's encoder with + +![](images/7ed1b930e4e1be716f6dffd2599518a4b01f6650e935501bb949bd4c8306b1b1.jpg) +Figure 5. Average Results (Top) and Results on BTAD (Bottom) of Different methods Trained on 2-, 16-, 64-shot per Class and Full Data of VisA. Our method shows high fitting efficiency, achieving strong results across all data scales. + +![](images/4bd703a8e390087c44ea087922519b276bf75f577a1ad93c32da10a282ef7e44.jpg) + +![](images/54bc6d0e000fbbc5adb9f62b15ea2babb5449548126f172d62748e47bc6428f7.jpg) +Figure 6. Visualization of Anomaly Localization Results of Original CLIP [42], AnomalyCLIP [59], VAND [7] and our AA-CLIP. Compared to previous methods, AA-CLIP demonstrates more reliable prediction capabilities in localizing anomaly. + +anomaly-aware semantics. Line "4." validates that, with AA-CLIP, the model's ability to discriminate anomalies further improves, as the AA-CLIP's text encoder provides a more precise semantic foundation. Adding Disentangle Loss leads to an additional improvement (shown in Line "5"), especially at image-level, validating the necessity of independence between normal and anomaly anchors. These results underscore the crucial role of text space refinement in improved anomaly localization and classification. + +Two-Stage Training: To validate the necessity of two-stage training, we adapt both text and image encoders together within one stage (also adopted by AdaCLIP). As shown + +![](images/b940ce809bb20f102d5ab0c763d469f6ba1df9bd728863b2e2e5aa8edcb03ef5.jpg) +Figure 7. Visualization of Text Space from One-Stage Training and from AdaCLIP. During one-stage training, class information collapses easily, leading to damaged zero-shot performance. + +in Fig. 7, one-stage model can easily exaggerate anomaly semantics and forget class information embedded in CLIP, damaging the model's generalization ability. The two-stage training strategy allows controlled adaptation, preserving CLIP's class-relevant knowledge in one end while adapting the other, as shown in Fig. 3. + +# 5. Conclusion and Discussion + +To our knowledge, this is the first work to explicitly analyze the intrinsic Anomaly Unawareness problem in CLIP. To tackle this issue, we propose a simple yet effective two-stage training strategy to embed anomaly-aware information into CLIP, enabling clear disentanglement of anomaly representations across both seen and novel classes. By leveraging residual adapters, our method preserves CLIP's strong generalization ability, achieving outstanding zero-shot performance across multiple datasets. + +Our adapted AA-CLIP, developed through this two-stage adaptation strategy, reveals the potential of refining CLIP's feature space for improved performance in downstream applications. Beyond addressing anomaly unawareness, our work also provides a potential foundation for tackling other "unawareness" issues within CLIP. 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Performance comparison of HBox-supervised orientated detectors. (a) Top: A coarse horizontal bounding box (C-HBox) $(②)$ and its corresponding rotated bounding box (RBox) $(①)$ . Bottom: A tight horizontal bounding box (T-HBox)( $(2)$ ) and its corresponding RBox $(①)$ . (b) Our ABBSPO is capable of accurately detecting both orientations and scales for GT C-HBoxes and T-HBoxes. (c) Average Precision $\left(\mathrm{AP}_{50}\right)$ for H2RBox [42], H2RBox-v2 [48], and our ABBSPO. $3-\mathrm{AP}_{50}$ represents the mean $\mathrm{AP}_{50}$ for three complex shaped objects: (i) DIOR: 'airplane', 'expressway service area', and 'overpass' and (ii) DOTA: 'plane', 'swimming pool', and 'helicopter'. + +![](images/abbe6ce2f4ccfae50e61911adbfc36c43a0599bc320175b91a448662945033d5.jpg) + +![](images/d935d857a5b65cffbee17d0414115fdc61d65805e5ef4c398351ff5540f95a21.jpg) + +![](images/8bd69b0bee5866f4cba10b95e82ac4c8cc5b57f2cd8ba8783c90a33616727935.jpg) + +![](images/e955c6c9f48296b82376f41da38d1df88096b41e872664228316cfcd675731db.jpg) + +![](images/949e5f4d898a521f3773f2cdc29482ebb42f4bc6bc2189ba275e0d71a3b33682.jpg) + +![](images/a5b098d46dbb0f780bcd7fc46372d3c5816887a0ef6a2fc8e0c422f150b54626.jpg) +H2RBox H2RBox-v2 ABBSPO) Performance overview 3-AP50 AP50 + +# Abstract + +Weakly supervised Oriented Object Detection (WS-OOD) has gained attention as a cost-effective alternative to fully supervised methods, providing efficiency and high accuracy. Among weakly supervised approaches, horizontal bounding box (HBox) supervised OOD stands out for its ability to directly leverage existing HBox annotations while achieving the highest accuracy under weak supervision settings. This paper introduces adaptive bounding box scaling and symmetry-prior-based orientation prediction, called ABBSPO that is a framework for WS-OOD. Our ABB- + +SPO addresses the limitations of previous HBox-supervised OOD methods, which compare ground truth (GT) HBoxes directly with predicted RBoxes' minimum circumscribed rectangles, often leading to inaccuracies. To overcome this, we propose: (i) Adaptive Bounding Box Scaling (ABBS) that appropriately scales the GT HBoxes to optimize for the size of each predicted RBox, ensuring more accurate prediction for RBoxes' scales; and (ii) a Symmetric Prior Angle (SPA) loss that uses the inherent symmetry of aerial objects for self-supervised learning, addressing the issue in previous methods where learning fails if they consistently make incorrect predictions for all three augmented views (original, rotated, and flipped). Extensive experimental results demonstrate that our ABBsPO achieves state-of-the-art results, outperforming existing methods. + +# 1. Introduction + +Object detection often leverages supervised learning with ground truth horizontal bounding box labels (GT HBoxes) to locate the objects of interest. However, the usage of GT HBoxes limits the precise localization of the objects with their orientations and tight surrounding boundaries, especially for objects such as airplanes and ships of various orientations in aerial images. To handle object detection as an oriented object detection problem, more precise rotated bounding box labels (GT RBoxes) are required, which is very costly to generate [49]. So, to mitigate this challenge, previous methods [17, 23, 42, 47-49] have explored weakly supervised oriented object detection (OOD) that utilizes less expensive forms of annotations, such as image-level, point and HBox annotations. Among these, the use of HBoxes is the most popular due to their widespread availability in existing public datasets [4, 9, 12, 21, 30, 31] to predict the RBoxes for objects of interest. So, this approach can detour the costly process of generating GT RBoxes. + +The previous weakly supervised (WS) learning of OOD [22, 27, 42, 48] utilizes GT HBoxes in the forms of coarse HBoxes, called GT C-HBoxes, as supervision to compare with the HBoxes derived as the minimum circumscribed rectangles from the predicted RBoxes by their OOD models. As shown in the upper figure of Fig. 1-(a), the GT C-HBoxes are defined as coarse horizontal bounding boxes that loosely encompass the boundaries of objects (not tightly bounded). The GT HBoxes of the DOTA [29] dataset are in the forms of C-HBoxes which are derived as the minimum circumscribed horizontal bounding boxes of their GT RBoxes. However, when the previous OOD methods [42, 48] are supervised with the other GT HBoxes that are in the form of tight HBoxes, called GT T-HBoxes (e.g. DIOR dataset [13]), as shown in the bottom figure of Fig. 1-(a), we found that their performances are significantly degraded because GT T-HBoxes tend to have different scales, compared to those of GT C-HBoxes (see Fig. 1-(c)). As shown in Fig. 1-(b), this causes the previous methods to predict either RBoxes with accurate orientations but inaccurate scales smaller than the sizes of their corresponding objects, or the RBoxes with inaccurate (close to horizontal) orientations but somewhat accurate scales (almost the same as HBoxes). + +To overcome the above limitations of the previous WS-OOD methods, we propose an adaptive bounding box scaling and symmetry-prior-based orientation prediction, called as ABBSPO, as a WS-OOD framework that can be effectively trained with either GT C-HBoxes or GT T-Hboxes for aerial images. For this, (i) a novel Adaptive Bounding Box Scaling (ABBS) module is designed to have the flexibility of adjusting the GT HBoxes for each object into random sizes and then selecting the optimal scaled GT HBoxes that allow it to encompass the predicted RBoxes. Note that + +the previous methods are not possible to have such flexibility for the adjustment of GT HBoxes; (ii) An angle learning module is proposed in a self-supervised manner that utilizes the symmetric priors of the objects that open appear in top-down views of aerial images. As shown in Figs 1-(b) and (c), Our proposed method predicts accurate orientation and surrounding boxes of objects for both cases of using GT C-HBoxes and GT T-HBoxes, outperforming the previous methods in angle accuracy and localization in terms of average precision (AP). Our contributions are summarized as: + +- To the best of our knowledge, our work is the first to address the limitations of previous weakly supervised OOD learning methods with T-HBoxes as GT. To overcome this, we propose a novel weakly supervised OOD method that can be effectively trained with T-HBoxes or C-HBoxes that can be cheaply annotated as GT; +- The adaptive bounding box scaling (ABBS) module is proposed to flexibly adjust the HBox (GT) for each object toward an appropriately scaled HBox. This allows part of the predicted RBoxes to place outside the T-HBox (GT), yielding precise RBox prediction; +- A symmetric prior angle (SPA) loss is presented to enhance the orientation prediction accuracy by leveraging the symmetric priors of the objects in aerial images; +- Our method significantly outperforms the state-of-the-art OOD methods using weakly supervised learning with HBoxes (GT) for aerial datasets. + +# 2. Related Work + +# 2.1. RBox-supervised Oriented Object Detection + +Oriented Object Detection (OOD) has gained significant attention, leading to extensive research in RBox-supervised methods (using GT RBoxes) such as Rotated RetinaNet [20], Rotated FCOS [24], $\mathrm{R}^3\mathrm{Det}$ [37], ROI Transformer [6], ReDet [8], and $\mathrm{S}^2\mathrm{A}$ -Net [7]. Rotated FCOS [24] improves OOD performance by introducing center-ness, which assigns weights to samples based on their proposal locations, thereby emphasizing well-positioned proposals. OrientedRepPoints methods [3, 14, 43], in contrast, utilize flexible receptive fields to extract key object points. However, a common challenge in RBox-supervised OOD methods is the boundary discontinuity problem that arises from the definition and prediction of angle parameters $(\theta)$ [33, 34]. To address this, several methods modified the ways of defining the RBox representations, such as Gaussian distributions [25, 26, 35, 36, 38-41], thereby avoiding straightforward regression of angle parameters. On the other hand, in weakly supervised learning, the boundary discontinuity issue does not arise thanks to the absence of direct RBox supervision, allowing for more stable angle predictions without the need for complex mitigation strategies. + +![](images/9058721b81e8835b11068c548c9030cde9f80c85472d688e79cb7a9fc205dd43.jpg) + +![](images/3b91cfd3d439130d68778ce5b060bd3e80c614824624b643e61de1a383877e2f.jpg) +Figure 2. Overall pipeline of our ABBsPO framework. Our ABBsPO leverages weakly supervised learning from HBox annotations to accurately predict RBoxes. The framework incorporates the Orientation Learning Branch (OLB) for precise angle estimation, using the Symmetric Prior Angle (SPA) loss, and the Scale Learning Branch (SLB) for optimal scale adjustment via the Adaptive Bounding Box Scaling (ABBS) module. The framework supports both C-HBox and T-HBox ground truths, ensuring robust and accurate predictions. + +![](images/55d9e3d1694b0495f9e982e4c5a131893a68faaf37d1a22e07983bd4262d8421.jpg) + +# 2.2. Weakly-supervised Orientd Object Detection + +Weakly supervised OOD methods learn to predict RBoxes without directly utilizing GT RBoxes. The approaches in this domain are primarily categorized based on the types of labels they employ: image-based [23], point-based [17, 47], and HBox-based [42, 48]. + +Image-based supervision. WSODet [23], aims to generate pseudo-RBoxes without explicit localization supervision, thus encountering significant limitations when relying solely on image labels, especially for the scenes with numerous and diverse object types. + +Point-based supervision. By leveraging one representative point at the center location as a label for each object, point label-based methods offer the advantage of being cost-effective [1, 2, 11, 16, 19, 44]. PointOBB [17] estimates angles from geometric relationships across original, rotated, and flipped views, and determines scales by analyzing proposal distributions between original and scaled input images. PointOBB-v2 [18] improves single point supervision by refining pseudo-label generation, leading to enhanced efficiency and accuracy. Point2RBox [47] employed fundamental patterns as priors to guide the regression of RBoxes. Point-based methods are cost-effective and straightforward, but still struggle with limited supervision. + +HBox-based supervision. As annotating HBoxes is more + +straightforward than RBoxes, the HBox-supervised OOD has gained increasing attention in recent studies. H2RBox [42] utilized rotated views from the original view and provided self-supervision of object orientations without requiring the GT angles. H2RBox-v2 [48] expanded the use of geometric relationships between views by adding flipped views. These methods learn to predict RBoxes by converting minimum circumscribed HBoxes that encompass the predicted RBoxes to directly compare IoU with the GT HBoxes, thereby enabling HBox-supervised OOD. However, these methods only guarantee performance when trained with GT C-HBoxes that are derived from GT RBoxes. These methods struggle to learn precise OOD when being trained with GT T-HBoxes, because of the significant gap between the GT T-HBoxes and the HBoxes derived from predicted RBoxes. To address the issue, we propose an ABBS module to effectively handle both types of GTs (C-HBoxes and T-HBoxes). + +# 3. Method + +# 3.1. Overall Pipeline + +Weakly supervised OOD aims to predict RBoxes using less expensive annotations such as HBoxes. Existing methods such as H2RBox [42] and its improved version H2RBox-v2 [48] have laid the foundation for directly predicting RBoxes from HBoxes. Our proposed pipeline builds upon the H2RBox-v2 [48] framework to effectively enable weakly + +supervised OOD from either C-HBoxes or T-Boxes. Figure 2 depicts the conceptual framework of our weakly supervised OOD method. Given an input image $\mathrm{I}_{\mathrm{ori}}$ and its rotated and flipped version $\mathrm{I}_{\mathrm{rot}}$ and $\mathrm{I}_{\mathrm{flp}}$ , our proposed pipeline obtains the RBox for each input view ( $\mathrm{I}_{\mathrm{ori}}$ , $\mathrm{I}_{\mathrm{rot}}$ , $\mathrm{I}_{\mathrm{flp}}$ ), including the center position $(x,y)$ , size $(w,h)$ , angle $(\theta)$ , class scores $(p)$ , and the center-ness $(cn)$ . To classify each detected object, we follow FCOS [24] by supervising both the classification $(p)$ and the center-ness $(cn)$ . The angle $(\theta)$ prediction is obtained by using the method proposed in PSC [46]. Our contribution mainly lies in the supervision for localization, consisting of two branches: a scale learning branch (SLB) and an orientation learning branch (OLB). + +In the SLB, the adaptive bounding box scaling (ABBS) module addresses the relationships between GT HBoxes and predicted RBoxes. This ABBS module provides proper minimum circumscribed rectangle for the accurately predicted RBoxes, by adaptively scaling the HBoxes based on a predefined scale range. The OLB guides accurate prediction of object orientation by utilizing three input views $(\mathrm{I}_{\mathrm{ori}},\mathrm{I}_{\mathrm{rot}},\mathrm{I}_{\mathrm{flp}})$ , following H2RBox-v2 [48]. Additionally, the OLB utilizes these orientation predictions for our symmetric prior angle (SPA) loss, which leverages the inherent left-right symmetry of objects in aerial images. The SPA loss enforces to further adjust the orientations of the predicted RBoxes to be aligned with the orientations of the symmetric objects such as airplanes, ships, ground track fields etc. + +# 3.2. Adaptive Bounding Box Scaling Module + +In Fig. 2, 'Scale Learning Branch' illustrates the conceptual process of our adaptive bounding box scaling module (ABBS) module. In HBox-supervised OOD learning, the predicted RBoxes $(RB^{\mathrm{pred}})$ must be compared with the GT HBoxes $(HB^{\mathrm{gt}})$ . Since they cannot be directly compared, $RB^{\mathrm{pred}}$ is first converted to $HB^{\mathrm{pred}}$ , defined as the minimum circumscribed HBox of $RB^{\mathrm{pred}}$ as: + +$$ +H B ^ {\text {p r e d}} = M C R (R B ^ {\text {p r e d}}), \tag {1} +$$ + +where $MCR(\cdot)$ is an operator converting $RB$ to the minimum circumscribed $HB$ , allowing $HB^{\mathrm{pred}}$ to be compared with $HB^{\mathrm{gt}}$ . $HB^{\mathrm{pred}}$ and $RB^{\mathrm{pred}}$ are given by: + +$$ +R B ^ {\text {p r e d}} = \left[ x _ {r b} ^ {\text {p r e d}}, y _ {r b} ^ {\text {p r e d}}, w _ {r b} ^ {\text {p r e d}}, h _ {r b} ^ {\text {p r e d}}, \theta_ {r b} ^ {\text {p r e d}} \right], \tag {2} +$$ + +$$ +H B ^ {\text {p r e d}} = \left[ x _ {h b} ^ {\text {p r e d}}, y _ {h b} ^ {\text {p r e d}}, w _ {h b} ^ {\text {p r e d}}, h _ {h b} ^ {\text {p r e d}} \right], +$$ + +where $(x_{rb}^{\mathrm{pred}},y_{rb}^{\mathrm{pred}})$ and $(x_{hb}^{\mathrm{pred}},y_{hb}^{\mathrm{pred}})$ are the centers of $RB^{\mathrm{pred}}$ and $HB^{\mathrm{pred}}$ , respectively. The width $w$ and height $h$ of $HB^{\mathrm{pred}}$ can be computed as: + +$$ +w _ {h b} ^ {\text {p r e d}} = w _ {r b} ^ {\text {p r e d}} \left| \cos \theta_ {r b} ^ {\text {p r e d}} \right| + h _ {r b} ^ {\text {p r e d}} \left| \sin \theta_ {r b} ^ {\text {p r e d}} \right|, \tag {3} +$$ + +$$ +h _ {h b} ^ {\text {p r e d}} = w _ {r b} ^ {\text {p r e d}} | \sin \theta_ {r b} ^ {\text {p r e d}} | + h _ {r b} ^ {\text {p r e d}} | \cos \theta_ {r b} ^ {\text {p r e d}} |. +$$ + +If $RB^{\mathrm{opt}}$ is defined as the tightly surrounding object boundary RBox with the precise orientation, then we have + +![](images/0f0e3f67749295fd52092e18a0c6894c7b925e01576410d11a332bc47f5de4d9.jpg) +(a) + +![](images/325bb1fc626aaefc2c05d0140a6886eacafedfc82231735440732d56a2dee2c6.jpg) +(b) + +![](images/5c549cac7a8d8f46a869cf8c9dfc6cfb6146911f9a57937bfa47698c6a67e05b.jpg) +(c) + +![](images/11ae87346cdf7ff7e0c88c472005c62c18768baf3a886fa74174d5159e1b3c45.jpg) +(d) + +![](images/c71e66550e76ebe42e0f7ba49bef5c0a389b45ee411cfcf5cca25d30fde80b8f.jpg) +(e) + +![](images/d75f200c7a4f589524d78653290a80f31a6c6d2a6006a1a73ed76d29a5d60139.jpg) +(f) +Figure 3. Analysis of scale adjustment function $(f(\cdot))$ based on the shape and angle of objects. (a) rectangular shape, (b) rounded rectangular shape, (c) complex shape, (d) horizontal orientation, (e) slightly tilted orientation, (f) diagonal orientation. The cyan solid box, green solid box and red dotted box represent GT T-HBox, RBox and adjusted GT HBox, respectively. + +$HB^{\mathrm{opt}} = MCR(RB^{\mathrm{opt}})$ for the 'Predicted RBox Projection Process' block in the SLB of Fig. 2. When the size of $HB^{\mathrm{gt}}$ is larger or smaller than that of $HB^{\mathrm{opt}}$ , the model needs to adaptively adjust and find the optimal scale within a predefined range of scale variations. We propose an ABBS module that estimates $RB^{\mathrm{opt}}$ by adaptively adjusting the scale of $HB^{\mathrm{gt}}$ . Notably, even if $RB^{\mathrm{pred}}$ is accurately estimated, its $HB^{\mathrm{pred}}$ may not overlap well with $HB^{\mathrm{gt}}$ , leading to a low Intersection over Union (IoU) value. Enforcing $HB^{\mathrm{pred}}$ to match $HB^{\mathrm{gt}}$ can cause a misalignment with $RB^{\mathrm{pred}}$ because $HB^{\mathrm{gt}}$ may not be ideal in estimating $RB^{\mathrm{opt}}$ . To address this, our ABBS module adaptively scales and adjusts $HB^{\mathrm{gt}}$ in the context of $RB^{\mathrm{pred}}$ , rather than forcing $HB^{\mathrm{pred}}$ to match $HB^{\mathrm{gt}}$ . + +For the detailed explanation of our ABBS module, we first define a set of scaled versions of $HB^{\mathrm{gt}}$ for the 'Scaled GT HBoxes Generation Process' in the SLB of Fig. 2 as: + +$$ +\mathbf {H B} _ {\mathrm {s}} ^ {\mathrm {g t}} = \left\{H B _ {\mathrm {s}, 1} ^ {\mathrm {g t}}, H B _ {\mathrm {s}, 2} ^ {\mathrm {g t}}, \dots , H B _ {\mathrm {s}, \mathrm {K}} ^ {\mathrm {g t}} \right\}, \tag {4} +$$ + +where $HB_{s,k}^{\mathrm{gt}}$ is the k-th scaled version of $HB^{\mathrm{gt}}$ and $\mathbf{K}$ is the total number of scaled variations of $HB^{\mathrm{gt}}$ . $\mathbf{HB}_{\mathbf{S}}^{\mathrm{gt}}$ is determined as the combinations of angle-adjusted width and height scale factors, $\{s_{adj,i}^{w}\}_{i=1}^{N_s}$ and $\{s_{adj,j}^{h}\}_{j=1}^{N_s}$ , that are transformed from basic width and height scale factors, $\{s_i^{w}\}_{i=1}^{N_s}$ and $\{s_j^{h}\}_{j=1}^{N_s}$ by considering angle prediction. Basic scale factors are uniformly spaced in a predefined scale range as: + +$$ +S _ {w} = \left\{s _ {1} ^ {w}, s _ {2} ^ {w}, \dots , s _ {N _ {s}} ^ {w} \right\}, S _ {h} = \left\{s _ {1} ^ {h}, s _ {2} ^ {h}, \dots , s _ {N _ {s}} ^ {h} \right\}, \tag {5} +$$ + +where $S_w$ and $S_h$ are the sets of basic width and height scale factors, respectively. $s_i^w$ and $s_i^h$ are calculated as: + +$$ +s _ {i} ^ {w} = s _ {1} ^ {w} + \left(s _ {N _ {s}} ^ {w} - s _ {1} ^ {w}\right) / \left(N _ {s} - 1\right) \cdot (i - 1), +$$ + +$$ +s _ {j} ^ {h} = s _ {1} ^ {h} + \left(s _ {N _ {s}} ^ {h} - s _ {1} ^ {h}\right) / \left(N _ {s} - 1\right) \cdot (j - 1), \tag {6} +$$ + +where $s_{N_s}^w = s_{N_s}^h$ is the predefined largest basic scale factor for both width and height of $HB^{\mathrm{gt}}$ , and $N_{s}$ is the number of uniform quantization for the both range $[s_1^w..s_{N_s}^w]$ and $[s_1^h..s_{N_s}^h]$ . In order to generate $HB_{s,i}^{\mathrm{gt}}$ , we transform the basic width and height scale factors, $\{s_i^w\}_{i=1}^{N_s}$ and $\{s_j^h\}_{j=1}^{N_s}$ , into angle-adjusted width and height scale factors, $\{s_{adj,i}^w\}_{i=1}^{N_s}$ and $\{s_{adj,j}^h\}_{j=1}^{N_s}$ , using the predicted angle $\theta^{\mathrm{pred}}$ through the scale adjustment function $f$ : + +$$ +s _ {a d j, i} ^ {w} = f \left(\theta_ {r b} ^ {\text {p r e d}}, s _ {i} ^ {w}\right), s _ {a d j, j} ^ {h} = f \left(\theta_ {r b} ^ {\text {p r e d}}, s _ {j} ^ {h}\right). \tag {7} +$$ + +To define $f(\cdot)$ , it's essential to consider the object types and rotation angles. Fig. 3 shows the effect of scale adjustments on T-HBoxes for three object types: (i) For rectangular objects like tennis courts (Fig. 3-(a)), the adjusted T-HBox (red dotted box) aligns precisely with the GT T-HBox (cyan solid box) and tightly circumscribes the optimal RBox (green solid box); (ii) For rounded rectangular objects (Fig. 3-(b)), the optimal RBox slightly exceeds the GT T-HBox; (iii) Complex shapes like airplanes (Fig. 3-(c)) show a larger discrepancy, with parts of the optimal RBox lying outside the GT T-HBox. Furthermore, scale adjustments also depend on rotation angles: (i) Fig. 3-(d) for a vertically (or horizontally) aligned airplane, the GT T-HBox and optimal RBox are identical; (ii) For Fig. 3-(e) with a small rotation angle, they differ slightly; (iii) For Fig. 3-(f) with a larger angle, the difference is more pronounced. Therefore, to take the object's shape types and orientation degrees into account for the scale adjustment for the widths and heights of T-HBoxes, $f(\cdot)$ in Eq. 7 is defined as: + +$$ +f (\theta , s) = \left\{ \begin{array}{l l} \frac {4}{\pi} (s - 1) \cdot \theta + 1, & \text {i f} 0 \leq \theta < \frac {\pi}{4}, \\ \frac {4}{\pi} (1 - s) \cdot \theta + (2 s - 1), & \text {i f} \frac {\pi}{4} \leq \theta < \frac {\pi}{2}, \end{array} \right. \tag {8} +$$ + +where the angle range is set to $\theta \in [0,\pi /2)$ due to the periodicity of the angle. According to $f(\cdot)$ and Eq. 7, $HB_{s,k}^{\mathrm{gt}}$ in $\mathbf{HB}_s^{\mathrm{gt}}$ can be expressed as: + +$$ +H B _ {s, k} ^ {\mathrm {g t}} = \left[ x ^ {\mathrm {g t}}, y ^ {\mathrm {g t}}, w ^ {\mathrm {g t}} \cdot s _ {a d j, i} ^ {w}, h ^ {\mathrm {g t}} \cdot s _ {a d j, j} ^ {h} \right], \tag {9} +$$ + +where $(x^{\mathrm{gt}},y^{\mathrm{gt}})$ is the center point, and $w^{\mathrm{gt}}$ and $h^{\mathrm{gt}}$ are width and height of $HB^{\mathrm{gt}}$ . As shown in the 'IoU Calculation' and 'Optimal Scale Learning' blocks in the SLB of Fig. 2, $HB^{\mathrm{opt}}$ among $\{HB_{s,k}^{\mathrm{gt}}\}_{k=1}^{K}$ can be determined which minimizes the IoU loss for all proposals by an ABBS loss as: + +$$ +\mathcal {L} _ {\mathrm {a s}} = \frac {1}{N _ {p}} \sum_ {l = 1} ^ {N _ {p}} \min _ {s _ {i} ^ {w} \in S _ {w}, \atop s _ {j} ^ {h} \in S _ {h}} \mathcal {L} _ {\mathrm {I o U}} \left(H B _ {l} ^ {\text {p r e d}}, H B _ {s, k} ^ {\text {g t}, l} \left(s _ {i} ^ {w}, s _ {j} ^ {h}\right)\right), \tag {10} +$$ + +where $N_{p}$ is the total number of proposals for input I. $HB_{l}^{\mathrm{pred}}$ is $HB^{\mathrm{pred}}$ for $l$ -th proposal, and $HB_{s,k}^{\mathrm{gt},l}(s_i^w,s_j^h)$ is $k$ -th scaled $HB^{\mathrm{gt}}$ , as $HB_{s,k}^{\mathrm{gt}}$ , whose width and height are scaled for $l$ -th proposal according to Eq. 7 to Eq. 9. Finally, by adding a regularization term using the IoU loss between $HB^{\mathrm{pred}}$ and non-scaled $HB^{\mathrm{gt}}$ , we formed the regression loss as: + +![](images/20f8eef00637ab7600c03ee878ea6683fc07db4f9171afee28e7c45469de0d08.jpg) +Airplane + +![](images/45fc781940dddcb8806fd987a3b42f61e4fd13f1476d76fda1771d4abaa461d1.jpg) +Ship + +![](images/a2d1e58850e2cd6b5de90fa8fe55dff6b4f19935e977bc1b59efc803fba9d08a.jpg) +Tennis court + +![](images/ee66c9f2b21acbe6db6b232718f3f1b68a60af53fcaff428182869ab07575ae3.jpg) +Vehicle +Figure 4. Examples of symmetric objects in aerial images. In SPA loss, the $x,y$ coordinates and angle $\theta$ are used to define the symmetry axis, splitting the object into two parts for comparison. + +$$ +\mathcal {L} _ {\mathrm {r e g}} = \mathcal {L} _ {\mathrm {a s}} + \alpha \cdot \left(1 / N _ {p}\right) \sum_ {l = 1} ^ {N _ {p}} \mathcal {L} _ {\mathrm {I o U}} \left(H B _ {l} ^ {\text {p r e d}}, H B ^ {\mathrm {g t}, l}\right), \tag {11} +$$ + +where $\alpha$ is a hyperparameter which is set to 0.01 by default. + +# 3.3. Symmetric Prior Angle Loss + +In aerial images, objects such as airplanes, ships, tennis courts, and vehicles are often captured from top-down viewpoints, where most of these objects exhibit symmetries in their appearance, as shown in Fig. 4. + +In the previous pipelines [42, 48], both the regression loss associated with the bounding box's center point, width, and height, and the angle loss for accurate angle prediction were trained in a balanced manner. However, they tended to inaccurately predict the angles by maximizing the bounding box's IoUs at the same time. This issue stems from the fact that, since the angles could not be directly supervised due to the absence of angle annotations, the angles were indirectly supervised from augmented views with rotations and flips. This is problematic because, when the difference between two predicted angles for the same object in the original view and its rotated view are equal to the rotation angle applied for the original view, the angle loss is zero although the predicted angles are inaccurate. + +To mitigate such a predicted angle ambiguity, we propose a symmetric prior angle (SPA) loss. Based on the SPA loss, the model can be trained to predict precise angles by indirectly utilizing the object's symmetric characteristics. As shown in Fig. 4, the detected objects are symmetric against the symmetry axes (blue-dotted lines) passing the center points of their RBoxes. That is, the pixel contents in the two parts divided by the symmetry axis of the RBox are compared in similarity whose difference is used as supervision for our SPA loss. It is noted that our SPA loss utilizes only symmetric objects, incorporating the symmetry prior from GT class labels for proposals identified as symmetric, such as 'airplane,' 'ship,' 'vehicle,' and 'tennis court' + +To avoid applying the SPA loss when $RB^{pred}$ are inaccurate for the respective objects, we first check the fidelity scores of proposal, and sample the Top- $k$ proposals as supervision in the SPA loss as: + +$$ +\left\{R B _ {n} ^ {p r e d} \right\} _ {n = 1} ^ {N _ {\mathrm {s p a}}} = \operatorname {T o p - k} \left(\left\{R B _ {l} ^ {p r e d} \right\} _ {l = 1} ^ {N _ {p}} \mid \mathrm {s c} _ {\mathrm {c l s}} ^ {i} + \mathrm {s c} _ {\mathrm {l o c}} ^ {i}\right) \tag {12} +$$ + +where $\mathrm{sc}_{\mathrm{cls}}^{(i)}$ and $\mathrm{sc}_{\mathrm{loc}}^{(i)}$ are the classification and localization scores for the $l$ -th $RB^{pred}$ , and $N_{p}$ is the total number of proposals. From Eq. 12, the selected $N_{spa}$ proposals are considered in the SPA loss by which the predicted angles of $RB^{pred}(\theta_{rb}^{pred})$ are enforced to align with the orientations of objects in the sense of maximizing the similarity, Structural Similarity Index (SSIM [28]), between the pixel contents in the two parts of each $RB^{pred}$ . It should be noted that, even in cases where symmetric objects may not appear perfectly symmetric due to contextual factors like shadows or asymmetrical cargo arrangements, their symmetry is still maintained by the inherent structural symmetry between the two parts. Our SPA loss is defined as: + +$$ +\mathcal {L} _ {\mathrm {S P A}} = \left(1 / N _ {\mathrm {s p a}}\right) \sum_ {n = 1} ^ {N _ {\mathrm {s p a}}} \left(1 - \operatorname {S S I M} \left(I _ {p 1} ^ {(n)}, I _ {p 2} ^ {(n)}\right)\right) \tag {13} +$$ + +To remove the influence of object sizes in $L_{\mathrm{SPA}}$ computation, the proposals $(RB^{pred})$ are projected onto a fixed-size grid of $50 \times 50$ . Then, the pixel content $(I_{p1})$ in one part of the proposal's projection is compared with that $(I_{p2})$ of the other part that is flipped before the comparison. + +# 3.4. Loss Functions + +In the orientation learning branch (OLB), two angle-based losses [48], $\mathcal{L}_{\mathrm{rot}}$ and $\mathcal{L}_{\mathrm{flp}}$ , are adopted to leverage the consistency between the original, rotated, and flipped views of each object proposal. For the rotated and flipped views, $\mathcal{L}_{\mathrm{rot}}$ and $\mathcal{L}_{\mathrm{flp}}$ are computed by comparing with the predicted angle $\theta$ in the original view $(\mathrm{I}_{\mathrm{ori}})$ : + +$$ +\mathcal {L} _ {\mathrm {r o t}} = l _ {s} \left(\theta_ {\mathrm {r o t}} - \theta , R\right), \mathcal {L} _ {\mathrm {f l p}} = l _ {s} \left(\theta_ {\mathrm {f l p}} + \theta , 0\right), \tag {14} +$$ + +where $l_{s}$ denotes a smooth L1 loss-based snap loss [48], and $R$ denotes the angle applied to $\mathbf{I}_{ori}$ . The final angle loss is: + +$$ +\mathcal {L} _ {\text {a n g}} = \beta \left(\lambda_ {r} \mathcal {L} _ {\text {r o t}} + \lambda_ {f} \mathcal {L} _ {\text {f l p}}\right) + \gamma \mathcal {L} _ {\text {S P A}}, \tag {15} +$$ + +where $\lambda_r = 1.0, \lambda_f = 0.05, \beta = 0.6$ , and $\gamma = 0.05$ are empirically determined for all our experiments. In the shape learning branch (SLB), we use our IoU-based [45] regression loss $\mathcal{L}_{\mathrm{reg}}$ in Eq. 11. The overall loss is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \lambda_ {\text {a n g}} \mathcal {L} _ {\text {a n g}} + \lambda_ {\text {r e g}} \mathcal {L} _ {\text {r e g}} + \lambda_ {\text {c n}} \mathcal {L} _ {\text {c n}} + \lambda_ {\text {c l s}} \mathcal {L} _ {\text {c l s}} \tag {16} +$$ + +where $\mathcal{L}_{\mathrm{cn}}$ is the center-ness loss [24], and $\mathcal{L}_{\mathrm{cls}}$ is the classification loss based on the focal loss [20]. The weighting factors, $\lambda_{\mathrm{ang}}, \lambda_{\mathrm{reg}}, \lambda_{\mathrm{cn}}$ , and $\lambda_{\mathrm{cls}}$ are all set to 1. + +# 4. Experiments + +# 4.1. Datasets + +We trained and tested all the methods across four different datasets: DIOR [5, 13], DOTA-v1.0 [29], SIMD [9] and NWPU VHR-10 [4], which are summarized in Table 1. The details for the datasets and results for SIMD and NWPU are described in Suppl. + +
Datasets# of ImagesImage Widths# of Objects# of ClassesAnnotation Types
DIOR [13]22,463800190,28820T-HBox
DIOR-R [5]22,463800190,28820RBox
DOTA-v1.0 [29]2,806800 ~ 4K188,28215C-HBox, RBox
SIMD [9]5,000102445,09615T-HBox
NWPU VHR-10 [4]800~10003,77510T-HBox
+ +Table 1. Characteristics of datasets used for experiments + +# 4.2. Implementation Details + +Our proposed ABBSPO pipeline adopts the FCOS [24] detector as the baseline architecture, utilizing a ResNet-50 [10] backbone and an FPN [15] neck, based on the H2RBox-v2 [48] framework. To ensure fairness, all models are configured with the ResNet-50 [10] backbone and trained for 12 epochs on NVIDIA RTX3090 GPUs. + +# 4.3. Experimental Results + +# 4.3.1 Quantitative Comparison + +It should be noted that objects such as round-shaped pools have orientation ambiguities regardless of their annotations (RBoxes) [42]. In order to avoid confusion in orientation learning, annotations are modified as having horizontal orientations if the objects belong to the following categories: (i) DIOR-R: 'baseball field', 'chimney', 'golf field', 'stadium', 'storage tank', 'windmill'; and (ii) DOTA-v1.0: 'baseball diamond', 'stadium', 'roundabout'. Accordingly, their orientation learning is enforced to predict the horizontal orientations, similar to previous works [42, 48]. + +Results on DIOR-R. Table 2 shows the OOD results. In addition to $\mathrm{AP}_{50}$ metric, we use $3\text{-AP}_{50}$ that focuses on the detection performance of the three complex-shaped object categories: 'airplane' (APL), 'expressway service area' (ESA), and 'overpass' (OP). As shown, our ABBSPO outperforms all weakly supervised OOD methods. Especially, in terms of $3\text{-AP}_{50}$ , our ABBSPO is superior to the HBox-supervised SOTA methods, H2RBox and H2RBox-v2, with large margins of average $12.9\%$ -point and average $9.1\%$ -point improvements. In overall $\mathrm{AP}_{50}$ performance, our ABBSPO surpasses H2RBox by $5.13\%$ -point and the H2RBox-v2 by $3.03\%$ -point. It is noted that our ABBSPO not only surpasses our base detector (H2RBox-v2 [48]) but also performs comparably to other RBox-supervised OOD methods, such as FCOS [24] and Oriented R-CNN [32]. It is worth noting that, compared to the RBox-supervised OOD methods, our ABBSPO shows even superior performance with large margins from $6.5\%$ -point to $11.7\%$ -point, especially on the 'airplane' that has the most complex shape. Notably, the ABBS module is less effective for rectangular objects, such as 'tennis court' (TC) and 'vehicle' (VE), as scaling is often unnecessary. However, it proves highly beneficial for complex-shaped objects, such as the ESA. The SPA loss is applied only to symmetric categories and helps + +
Methods\( \underline{\mathbf{APL}} \)\( \mathbf{APO} \)\( \mathbf{BF} \)\( \mathbf{{BC}} \)\( \mathbf{{BR}} \)\( \mathbf{{CH}} \)\( \underline{\mathbf{ESA}} \)\( \mathbf{{ETS}} \)\( \mathbf{{DAM}} \)\( \mathbf{{GF}} \)\( \mathbf{{GTF}} \)\( \mathbf{{HA}} \)\( \mathbf{{OP}} \)\( \mathbf{{SH}} \)\( \mathbf{{STA}} \)\( \mathbf{{STO}} \)\( \mathbf{{TC}} \)\( \mathbf{{TS}} \)\( \mathbf{{WE}} \)\( \mathbf{{WM}} \)\( 3-AP_{50} \)\( AP_{50} \)
\( S_R \)RetinaNet [20]59.819.369.781.317.272.768.749.418.469.571.333.334.175.867.159.681.044.138.062.554.2054.64
FCOS [24]62.137.974.681.232.972.175.361.827.469.178.734.450.680.168.668.181.349.143.464.562.6760.66
Oriented R-CNN [32]63.036.771.981.641.172.677.865.524.872.982.140.956.581.273.462.481.553.365.665.7762.41
GWD [38] (RetinaNet)61.523.673.681.117.472.768.347.220.771.273.233.934.377.664.757.580.942.139.760.254.7055.07
KLD [39] (RetinaNet)57.822.671.581.216.972.768.952.120.673.571.033.733.277.168.959.980.943.939.160.953.3055.32
KFIoU [41] (RetinaNet)60.636.673.680.927.072.673.456.525.473.972.032.945.875.865.257.680.048.040.158.859.9357.84
\( \underline{\mathbf{S_I}} \)\( WSODet^† \)[23]20.729.063.267.30.265.50.40.10.349.028.90.31.51.253.416.440.00.16.10.17.5322.20
\( S_P \)\( PointOBB^† \)[17]58.215.370.578.60.172.269.61.83.70.377.316.740.479.239.632.429.616.833.627.756.0738.08
Point2RBox-SK [47]41.99.162.952.810.872.23.043.95.59.725.19.121.024.020.425.171.74.516.116.321.9727.26
\( S_H \)H2RBox [42]57.114.472.282.617.571.256.555.21467.777.93140.776.366.263.481.550.43857.651.4354.57
H2RBox-v2 [48]55.517.876.980.527.772.263.058.624.473.980.333.947.277.458.760.981.448.141.153.955.2356.67
ABBSPO (Ours)69.515.776.287.529.972.375.361.228.174.181.734.748.279.367.461.481.554.741.553.864.3359.70
+ +Table 2. Quantitative results of each category on the DIOR-R [5] test dataset for RBox-supervised $(S_R)$ , Image-supervised $(S_I)$ , Point-supervised $(S_P)$ and HBox-supervised $(S_H)$ methods. The $3-\mathrm{AP}_{50}$ represents the mean $\mathrm{AP}_{50}$ scores for three complex-shaped object categories: 'airplane' (APL), 'expressway service area' (ESA), and 'overpass' (OP). The notation $\dagger$ indicates its results in the paper [17]. + +
MethodsPLBDBRGTFSVLVSHTCBCSTSBFRAHASPHC3-AP50AP50
SRRetinaNet [20]87.575.139.959.666.366.378.290.555.062.747.163.659.455.143.061.8763.3
FCOS [24]88.874.046.859.170.181.487.790.767.768.360.266.164.958.744.063.8368.6
Oriented R-CNN [32]89.376.153.878.768.684.989.390.874.362.866.366.574.758.646.864.9072.1
Oriented RepPoints[14]89.780.150.574.475.082.088.790.464.070.045.760.673.660.442.864.3069.86
GWD [38] (RetinaNet)88.274.941.360.566.768.185.890.550.466.845.865.160.752.938.960.063.77
KLD [39] (RetinaNet)88.475.841.460.066.168.884.790.656.860.450.470.160.050.545.761.5364.65
KFIuU [41] (RetinaNet)84.474.340.755.257.956.976.471.246.164.854.365.058.348.742.958.6759.81
SPPointOBB [17]+FCOS32.467.30.853.62.39.718.80.39.912.80.554.011.034.111.425.9721.26
Point2RBox-SK [47]50.163.71.644.723.934.732.778.841.232.22.134.320.842.57.233.2734.03
SHH2RBox [42]89.573.137.355.170.776.485.490.366.567.359.664.960.657.936.561.3066.07
H2RBox-v2 [48]89.474.845.456.070.376.687.990.569.367.556.764.765.355.545.563.4767.69
ABBSPO (Ours)89.275.647.452.870.377.688.290.567.966.868.266.271.655.651.065.2769.26
+ +Table 3. Quantitative results of each category on the DOTA-v1.0 [29] validation dataset for $S_R$ , $S_I$ , $S_P$ and $S_H$ methods. The $\underline{3 - AP}_{50}$ represents the mean $\mathrm{AP}_{50}$ scores for three complex-shaped object categories: plane (PL), swimming pool (SP), and helicopter (HC). All the methods are re-trained using only train dataset for fair comparison. + +improve their performance, except for the categories with orientation ambiguities, such as 'storage tank' (STO). Since the predicted angles learned through the SPA loss are also utilized in the ABBS module for scale adjustment, both the SPA loss and the ABBS module jointly contribute to performance improvement in symmetric categories. This joint effect is particularly evident in complex-shaped symmetric categories, such as APL and ESA, where performance gains are more significant. Nevertheless, the performance gains for the two symmetric and rectangular categories, TC and VE, are marginal. This is mainly because the ABBS module has limited impact on rectangular shapes, and the small object sizes lead to an insufficient number of pixels for reliably determining the symmetry axis via the SPA loss. + +Results on DOTA-v1.0. Table 3 shows the detection performance results on the DOTA-v1.0 [29]. Due to the nonresponsiveness of the DOTA evaluation server, we report our experimental results on the validation dataset (458 images) instead of the test dataset (937 images). It should be noted that the validation dataset was not used for training all the methods for fair comparison. We use $3\mathrm{-AP}_{50}$ that measures the detection performance for the three complex-shaped object categories: 'plane', 'swimming pool' and 'helicopter'. Our ABBsPO achieves SOTA performance, outperforming H2RBox by $3.19\%$ -point and H2RBox-v2 by $1.57\%$ -point improvements. Moreover, our ABBsPO + +even surpasses the FCOS Baseline by $0.66\%$ -point lift. + +# 4.3.2 Qualitative Comparison + +Results on DIOR. As shown in the figures of the first row in Fig. 5, our ABBSPO is the only method that accurately captures both the orientation and scale of the airplane. Since DIOR annotations provide GT in T-HBox format, direct usage of T-HBoxes as GT for training to predict RBox leads to degradations in orientation and scale prediction accuracy for the existing HBox-supervised OOD methods as shown in the figures of columns 2 and 3 in Fig. 5. In contrast, our ABBSPO avoids such degradation by utilizing the ABBS module that optimally scales the GT HBox sizes for precise RBox prediction during training. It is also worthwhile to mention that the predicted orientations by our ABBSPO are more precisely obtained via our SPA loss. Furthermore, it should be noted that compared to the RBox-supervised baseline method (Rotated FCOS [24]), our approach demonstrates superior visual results, even under weakly supervised learning. + +Results on DOTA-v1.0. As shown in the figures of the second row in Fig. 5, ABBSPO very accurately predicts both the orientation and scale of the swimming pool, achieving similar accuracy for tennis court. Interestingly, only ABBSPO successfully detects the two tennis courts that are partially occluded by trees (red solid circle) while the other + +
ModuleDIOR-RDOTA-v1.0
ABBSSPA3-AP50AP50AP50
55.2356.6767.69
62.1358.3568.59
58.7758.9969.16
64.3359.7069.26
+ +Table 4. Ablation results on ABBS module and SPA loss $(\mathcal{L}_{\mathrm{SPA}})$ + +
SamplingDIOR-R
L SPAOthers3-AP50AP50
61.6758.93
64.3359.70
43.6350.51
45.150.91
+ +Table 5. Ablation results on proposal sampling in ${\mathcal{L}}_{\mathrm{{SPA}}}$ and other components. + +
Scale RangeDIOR-RDOTA-v1.0
MinMaxInterval3-AP50AP50AP50
0.91.10.0557.9758.1569.26
0.51.50.161.6759.6268.8
1.01.50.164.3359.7068.9
1.02.00.156.0755.4666.55
+ +Table 6. Ablation results on scale range in ABBS module. + +![](images/f838ad4df2e507e0e2ecfce0c5614d593565459003deab0ecdc911cd4cdab3c7.jpg) +Figure 5. Qualitative results on DIOR [5, 13] and DOTA-v1.0 [29]. Zoom-in for better visualization. Rotated FCOS was trained only with GT RBoxes, while H2RBox, H2RBox-v2 and our ABBsPO were trained with GT T-HBoxes (1st row) and GT C-HBoxes (2nd row). + +methods failed. These results visually support the effectiveness of our ABBS module and SPA loss in learning the scales and orientations of objects accurately. + +# 4.4. Ablation Studies + +Ablation study on SPA loss and ABBS module. As shown in Table 4, both components contribute to performance improvements. The ABBS module effectively scales the GT HBoxes, leading to an increase in $\mathrm{AP}_{50}$ performance on the DIOR dataset. Notably, it has a greater effect on complex-shaped object categories, resulting in a significant improvement in $3\text{-AP}_{50}$ . Similarly, the SPA loss enhances angle prediction accuracy, also bringing an improvement in $\mathrm{AP}_{50}$ . + +Ablation study on proposal sampling. As shown in Table 5, applying Top- $k$ proposal sampling exclusively to the SPA loss $(\mathcal{L}_{\mathrm{SPA}})$ yields the highest $\mathrm{AP}_{50}$ performance, as the symmetric proposals of high-quality benefits $\mathcal{L}_{\mathrm{SPA}}$ . But, additional proposal sampling to the others $(\mathcal{L}_{\mathrm{rot}},\mathcal{L}_{\mathrm{flp}},\mathcal{L}_{\mathrm{reg}},\mathcal{L}_{\mathrm{cn}},\mathcal{L}_{\mathrm{cls}})$ significantly lowers the performance. + +Ablation study on scale range in the ABBS module. As shown in Table 6, the optimal scale range is influenced by the type of GT HBoxes. For DIOR's T-HBoxes, a scale range of 1 to 1.5 works well because it ensures that the + +predicted RBoxes fully cover the objects boundary. On the other hand, for DOTA's C-HBoxes, which are already close to the optimal HBoxes, the optimal scale range is closer to 1. By adjusting the scale range based on the type of HBoxes, the ABBS module achieves high accuracy in predicting RBoxes for both datasets. + +# 5. Conclusion + +Our ABBSPO, a weakly supervised OOD framework, effectively learns RBox prediction regardless of the type of HBox annotations (T-HBox and C-HBox). With our proposed Adaptive Bounding Box Scaling (ABBS) and Symmetric Prior Angle (SPA) loss, we achieved enhanced orientation and scale accuracy for OOD, which is comparable to or even better than RBox-supervised methods. Extensive experimental results underscore the superiority of our approach, surpassing state-of-the-art HBox-supervised methods. Our method effectively bridges the gap between weakly supervised OOD and fully supervised OOD, making it a promising solution for applications requiring efficient and accurate object detection via training with relatively cheap annotations of HBoxes compared to RBoxes. + +# Acknowledgement + +This research was supported by Korea Institute of Marine Science & Technology Promotion (KIMST) funded by the Korea Coast Guard (RS-2023-00238652, Integrated Satellite-based Applications Development for Korea Coast Guard, $100\%$ ). + +# References + +[1] Liangyu Chen, Tong Yang, Xiangyu Zhang, Wei Zhang, and Jian Sun. Points as queries: Weakly semi-supervised object detection by points. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8823-8832, 2021. 3 +[2] Pengfei Chen, Xuehui Yu, Xumeng Han, Najmul Hassan, Kai Wang, Jiachen Li, Jian Zhao, Humphrey Shi, Zhenjun Han, and Qixiang Ye. 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While existing WB methods yield reasonable results, their effectiveness is limited. They either focus solely on global color adjustments applied before the camera-specific image signal processing pipeline or rely on end-to-end models that generate WB outputs without accounting for global color trends, leading to suboptimal correction. To address these limitations, we propose an Auxiliary Bimodal Cross-domain Transformer (ABC-Former) that enhances WB correction by leveraging complementary knowledge from global color information from CIELab and RGB histograms alongside sRGB inputs. By introducing an Interactive Channel Attention (ICA) module to facilitate cross-modality global knowledge transfer, ABC-Former achieves more precise WB correction. Experimental results on benchmark WB datasets show that ABC-Former performs favorably against state-of-the-art WB methods. The source code is available at https://github.com/ytpeng-aimlab/ABC-Former. + +# 1. Introduction + +White balance (WB) correction ensures consistent and accurate color production across varying lighting conditions. However, camera Image Signal Processing (ISP) can introduce color casts in sRGB images due to inaccurate or customized WB settings applied to raw-RGB inputs. These distortions can degrade the accuracy of tasks like image classification and segmentation, where precise color is crucial [10, 12, 23]. Consequently, WB correction has gained significant research interest. + +Significant effort has been made to improve WB within the camera's ISP pipeline. Raw-WB methods estimate the + +![](images/dc3a462b8e9f99c49514e17bdd64749d9d84856929305498c0a53ba146854fdf.jpg) + +![](images/d84a832deedf8ac4ac147fb047a3056f07187691fd7a0655c9afd11b305027a2.jpg) + +![](images/3ce855a07bd457cdced9502f45450bc79508178e0c0b9ea05bbe7a156d755c83.jpg) +Figure 1. (a) Traditional raw-WB methods predict the scene's illuminant, perform Illumination Correction (IC), and generate the sRGB output via camera-specific ISP. (b) DNN-based sRGB-WB methods apply end-to-end models directly to sRGB images for WB correction. (c) ABC-Former improves WB accuracy by converting the input into multiple modalities, enhancing illumination correction through auxiliary and primary models. + +scene's illuminant to correct color shifts in raw images before further processing. However, due to the non-linear transformations applied by the ISP during rendering, these corrections may not fully compensate for color shifts in the final sRGB output [1]. + +Several sRGB-WB methods address color shifts caused by imprecise WB in the camera's ISP, categorized into exemplar-based and DNN-based approaches. Exemplar-based methods like KNN [3] classify images from the Rendered WB dataset and apply the best-matching nonlinear + +mappings for correction. DNN-based methods such as DEEP-WB [2] use CNNs for single-illuminant color correction, while WBFlow [18] extracts pseudo-raw features via a reversible flow model for sRGB correction. SWBNet [19] employs a transformer in the DCT domain to refine color-sensitive features. While effective, these methods fail to fully integrate global color trends and scene information for more comprehensive WB correction. + +Our work utilizes alternative modalities, such as color histograms, to learn global color temperature for effective WB correction. Unlike images, which encode spatial and color information, histograms capture color distribution across channels without spatial details. While per-channel histograms do not fully preserve color relationships between pixels, we can explore both sRGB and CIELab color histograms to go beyond sRGB-input images, extracting global color information. Inspired by [26], we propose ABC-Former, an Auxiliary Bimodal Cross-domain Transformer architecture that integrates global color information from both sRGB and CIELab histograms. It consists of two auxiliary models for histogram-based learning and a target model for sRGB image WB correction, where the sRGB histogram supervises raw color intensity, and CIELab ensures perceptually uniform color distribution. To enhance WB correction in the target sRGB model, we introduce the Interactive Channel Attention (ICA) module, which transfers modality-complementary knowledge using re-parameterization, allowing the target model to adaptively reweight image features for improved accuracy. Our key contributions are listed as follows: + +- We propose ABC-Former, which leverages histogram-based global color features via auxiliary models to refine WB correction in the target sRGB model. +- We introduce the ICA module to facilitate effective cross-modality knowledge transfer, optimizing sRGB feature reweighting for better WB results. +- Extensive experiments on benchmark WB datasets demonstrate that ABC-Former outperforms state-of-the-art (SOTA) sRGB-WB methods. + +# 2. Related Works + +Raw-WB Approaches. The WB module in a camera's ISP corrects raw images for accurate color temperature, compensating for lighting variations. Traditional WB methods estimate the global light source color and apply uniform gain coefficients for illumination correction. However, they assume a consistent color temperature across the scene, making them ineffective under mixed lighting. Additionally, these methods irreversibly alter raw images, limiting precise sRGB adjustments in post-processing [4, 7-9, 15, 20, 21, 24]. + +sRGB-WB Approaches. To address the shortcomings of traditional WB methods, recent research has explored + +sRGB-WB approaches, which refine color correction beyond the ISP stage. These methods can be classified into exemplar-based methods [3, 5] and DNN-based methods [18, 19]. Exemplar-based methods apply trained nonlinear mappings for color correction. For example, Affi et al. [3] use histogram features to find images with similar color distributions and derive a correction matrix to adjust colors accordingly. Mixed-WB [5] generates multiple WB versions of an image, averaging their weighting maps to achieve optimal correction. However, these methods rely heavily on predefined training data, making them less adaptable to diverse lighting conditions. + +DNN-based methods, such as WBFlow [18], use neural flow for reversible color correction, mapping color-cast sRGB images to a pseudo-raw feature space for linear WB. WBFlow also incorporates a camera transformation module for few-shot adaptation, improving generalization ability. SWBNet [19] suppresses temperature-sensitive low-frequency information and employs a contrast loss to align scene features across varying temperatures, enhancing WB stability. It also uses adaptive weights to correct multiple color shifts under mixed lighting. Although these methods are effective, they remain constrained by the sRGB image modality. + +Multimodal Training Approaches. Unimodal training uses data from a single modality, limiting its ability to generalize across different modalities. In contrast, multimodal training enables models to learn from multiple modalities, which can be strongly correlated (paired data) or weakly correlated (irrelevant data). CLIP [22] exemplifies strongly correlated multimodal data, using contrastive learning to align image and text features, requiring paired data. In contrast, M2PT [26] integrates irrelevant data from different modalities by leveraging re-parameterization to transfer knowledge from pre-trained auxiliary models. While this enhances cross-modal learning, it increases data collection costs and pre-training demands. + +Inspired by M2PT, we adopt multimodal training to capture global color information from sRGB images to enhance WB correction. Unlike M2PT, which uses irrelevant data, we train sRGB images to learn corrected histogram-based color features from their color and CIELab histograms. Figure 1 compares conventional DNN-based raw-WB and sRGB-WB methods with the proposed ABC-Former. + +# 3. Proposed Method + +The proposed ABC-Former consists of three transformer models: two auxiliary transformers that learn to correct color and CIELab histograms, and a primary transformer that processes the input sRGB image for the final WB correction. Unlike M2PT [26], which tokenizes irrelevant multimodal data for unified processing, our approach leverages sRGB images with their strongly related color information. + +To efficiently transfer complementary color knowledge, we introduce the Interactive Channel Attention (ICA) module, which utilizes condensed histogram-based features to enhance color temperature correction, improving accuracy and visual quality. The overall architecture is shown in Figure 2. + +# 3.1. Auxiliary Model — PDFformer + +Most prior sRGB-WB works [2, 3, 5, 18] focus on local pixel information within the sRGB domain, often overlooking global color temperature and perceptual color relationships, which are crucial for effective WB correction. Therefore, integrating global color information from alternative modalities can enhance accuracy by providing a broader context for color adjustments. Given an input sRGB image $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ , where $H$ and $W$ denote the image's height and width, and the three channels represent the RGB color components, we first convert it to the CIELab color space, represented as $\mathbf{I}_{\mathrm{Lab}} \in \mathbb{R}^{H \times W \times 3}$ , where the three channels correspond to the $L^*$ , $a^*$ , and $b^*$ components. To efficiently capture global color temperature while maintaining low model complexity, we convert $\mathbf{I}$ into its probability density function (PDF) representation, $\mathbf{H}_{\mathrm{sRGB}} \in \mathbb{R}^{L \times 3}$ , where $L = 256$ represents the number of histogram bins per channel. Similarly, we transform $\mathbf{I}_{\mathrm{Lab}}$ into its PDF form, referred to as $\mathbf{H}_{\mathrm{Lab}} \in \mathbb{R}^{L \times 3}$ , with $L = 256$ , providing a histogram-based representation for each color space. + +The ABC-Former framework incorporates two auxiliary models to enhance the target model's performance. These models process global color PDF data, $\mathbf{H}^{\mathrm{sRGB}}$ and $\mathbf{H}^{\mathrm{Lab}}$ , which serve as distinct inputs. Each auxiliary model, called PDFformer, employs a 1D transformer architecture with a shared structure but separate training. Initially, the input histograms, $\mathbf{H}^{\mathrm{sRGB}}$ or $\mathbf{H}^{\mathrm{Lab}}$ , pass through a one-dimensional convolutional layer to produce histogram features $\mathbf{H}_0^{\mathbf{A}} \in \mathbb{R}^{L \times C}$ , where $\mathbf{A} \in [\mathbf{sRGB}, \mathbf{Lab}]$ , and $C$ is the feature dimension. These features are subsequently processed through a U-shape transformer structure with PDFformer blocks that facilitate upsampling and downsampling in the encoding and decoding paths. Each block consists of two sequences of Layer Normalization (LN), Channel Attention (CA) [14], and a feed-forward Multilayer Perceptron (MLP) [11], arranged in the following order: + +$$ +\hat {\mathbf {H}} _ {\mathbf {i}} ^ {\mathbf {A}} = \operatorname {C A} \left(\operatorname {L N} \left(\mathbf {H} _ {\mathbf {i} - 1} ^ {\mathbf {A}}\right)\right) + \mathbf {H} _ {\mathbf {i} - 1} ^ {\mathbf {A}}; \tag {1} +$$ + +$$ +\mathbf {H} _ {\mathbf {i}} ^ {\mathbf {A}} = \operatorname {G E L U} (\operatorname {M L P} (\operatorname {L N} (\hat {\mathbf {H}} _ {\mathbf {i}} ^ {\mathbf {A}}))) + \hat {\mathbf {H}} _ {\mathbf {i}} ^ {\mathbf {A}}, +$$ + +where $\mathrm{GELU}(\cdot)$ denotes the GELU activation function, and $\mathbf{i}$ is the block index, starting from 1. PDFformer has $K$ PDFformer blocks in the encoding path, followed by a bottleneck stage, which is also a PDFformer block. These blocks are interconnected via downsampling, implemented through a $4\times 1$ convolution with a stride of 2 and channel doubling. This process yields an output of $\mathbf{H}_{\mathbf{K} + 1}^{\mathbf{A}}\in$ + +$\mathbb{R}^{\frac{L}{2K}\times 2^K C}$ . Following the bottleneck, the decoding path contains $K$ PDFformer blocks, with upsampling and channel reduction applied between blocks. The first two blocks halve the number of channels, while the remaining blocks quarter them, as in [25]. Upsampling is achieved using a $2\times 1$ transposed convolution with a stride of 2. Additionally, each block in the decoding path takes the output from the previous block and concatenates it with the corresponding output from the encoding path of the same spatial size. The final output, $\mathbf{H}^{\mathbf{A}}\in \mathbb{R}^{L\times 2C}$ , passes through a convolutional layer with a residual connection to the input histograms and a softmax function to produce the corrected color or CIELab histograms $\mathbf{H}_{\mathbf{c}}^{\mathbf{A}}\in \mathbb{R}^{L\times 3}$ as: + +$$ +\mathbf {H} _ {\mathrm {c}} ^ {\mathbf {A}} = \operatorname {S O F T M A X} \left(\operatorname {C o n v} _ {3 \times 1} \left(\mathbf {H} _ {2 \mathrm {K} + 1} ^ {\mathbf {A}}\right) + \mathbf {H} _ {0} ^ {\mathbf {A}}\right). \tag {2} +$$ + +# 3.2. Target model — sRGBformer + +To achieve a color-calibrated correction, we employ sRGBformer, a vision transformer designed to address color deviations. It systematically processes input features $\mathbf{X}_0$ to generate the final WB-corrected image. Similar to PDFformer, sRGBformer employs a U-shaped transformer architecture with upsampling and downsampling. However, it uniquely integrates cross-modality knowledge from auxiliary models, using their corrected global color information as guidance. To enable this, we introduce our proposed Interactive + +Channel Attention (ICA) in each sRGBformer block, incorporating auxiliary model knowledge through dedicated pathways. Each sRGBformer block consists of two sets of LN, ICA, and an MLP, structured as follows: + +$$ +\hat {\mathbf {X}} _ {\mathbf {i}} = \operatorname {I C A} (\ln (\mathbf {X} _ {\mathbf {i} - \mathbf {1}})) + \mathbf {X} _ {\mathbf {i} - \mathbf {1}}; \tag {3} +$$ + +$$ +\mathbf {X} _ {\mathbf {i}} = \operatorname {G E L U} (\operatorname {M L P} (\ln (\hat {\mathbf {X}} _ {\mathbf {i}}))) + \hat {\mathbf {X}} _ {\mathbf {i}}, +$$ + +where $\mathbf{X_i}$ is the image features produced by the sRGBformer block at $i$ -th level. The encoder and decoder each consist of $K$ sRGBformer blocks, connected via a bottleneck stage with one sRGBformer block. In the encoder, downsampling is achieved using a $4\times 4$ convolution with a stride of 2 and channel doubling, while the decoder applies upsampling via a $2\times 2$ transposed convolution with a stride of 2 and channel halving. As in PDFformer, each decoder block receives the output from the previous block, concatenated with the corresponding output from the encoder of the same spatial size. The final decoder output $\mathbf{X_{2K + 1}}\in \mathbb{R}^{H\times W\times 2C}$ passes through a $3\times 3$ convolutional layer with a residual connection to the input, producing the final WB-corrected image, $\mathbf{X_c}\in \mathbb{R}^{H\times W\times 3}$ . + +Interactive Channel Attention. The goal of ICA is to facilitate knowledge transfer from auxiliary models to sRGBformer, enhancing WB correction. In sRGBformer, each encoder and decoder block is equipped with an ICA module to correspond to the respective blocks in the encoders and decoders of the auxiliary models. First, $\mathbf{X}_{\mathrm{i}}$ is condensed + +![](images/cbb3ff0b83c41d00a1bf7c82b0173d3179f0e6e159f7b222f16f183168a5fcbd.jpg) +Figure 2. The ABC-Former framework consists of two key components:: Auxiliary models (PDFformers) and a Target model (sRG-Bformer). The auxiliary models process sRGB and CIELab histograms to learn color features from different modalities, while the ICA module in the target model integrates this information to generate the final WB correction. + +into a vector with one value per channel by global average pooling (Avg.), followed by a convolution and sigmoid activation, generating a channel-wise weighting vector $\mathbf{W}_{\mathrm{i}}^{\mathrm{T}} \in \mathbb{R}^{1 \times 1 \times C}$ at the $i$ -th level of the sRGBformer block. Similarly, weighting vectors $\mathbf{W}_{\mathrm{i}}^{\mathrm{sRGB}}$ , $\mathbf{W}_{\mathrm{i}}^{\mathrm{Lab}} \in \mathbb{R}^{1 \times 1 \times C}$ are extracted by feeding $\mathbf{H}_{\mathrm{i}}^{\mathrm{sRGB}}$ and $\mathbf{H}_{\mathrm{i}}^{\mathrm{Lab}}$ into the CA module within their corresponding PDFformer's blocks, which include the average pooling $\mathrm{Avg}(\cdot)$ , convolution, the unsqueeze operation, and the excitation operation (sigmoid activation) at the $i$ -th level. Next, to integrate cross-modal knowledge, we apply cross-modal re-parameterization [26], introducing learnable parameters $\lambda_{\mathrm{i}}^{\mathrm{sRGB}}$ and $\lambda_{\mathrm{i}}^{\mathrm{Lab}}$ to adjust $\mathbf{W}_{\mathrm{i}}^{\mathrm{sRGB}}$ and $\mathbf{W}_{\mathrm{i}}^{\mathrm{Lab}}$ , respectively. These are then combined with $\mathbf{W}_{\mathrm{i}}^{\mathrm{T}}$ along the channel dimension to obtain $\mathbf{W}_{\mathrm{total}}$ as: + +$$ +\mathbf {W} _ {\mathbf {i}} ^ {\mathbf {T}} = \text {S i g m o i d} (\mathbf {C o n v} (\operatorname {A v g} (\mathbf {X} _ {\mathbf {i}}))) \tag {4} +$$ + +$$ +\mathbf {W} _ {\mathrm {i}} ^ {\text {t o t a l}} = \mathbf {W} _ {\mathrm {i}} ^ {\mathrm {T}} + \lambda_ {\mathrm {i}} ^ {\text {L a b}} \mathbf {W} _ {\mathrm {i}} ^ {\text {L a b}} + \lambda_ {\mathrm {i}} ^ {\text {s R G B}} \mathbf {W} _ {\mathrm {i}} ^ {\text {s R G B}}. +$$ + +At last, $\mathbf{X_i}$ is channel-wise re-weighted by $\mathbf{W_i^{total}}$ to gen- + +erate the refined sRGB features $\tilde{\mathbf{X}}_{\mathrm{i}}$ as: + +$$ +\tilde {\mathbf {X}} _ {\mathbf {i}} = \mathbb {F} _ {\text {s c a l e}} \left(\mathbf {W} _ {\mathbf {i}} ^ {\text {t o t a l}}, \mathbf {X} _ {\mathbf {i}}\right), \tag {5} +$$ + +where $\mathbb{F}_{scale}(\cdot, \cdot)$ represents the channel-wise multiplication function, applying scalar weights to the corresponding feature maps. Through ICA, we leverage calibrated global color information from modality-specific histogram-based features, enabling effective knowledge transfer for improved WB correction. + +# 3.3. Loss Function + +The proposed framework optimizes two auxiliary models and one target model. Specifically, two auxiliary PDF-formers process histogram inputs in a PDF format from either the sRGB or CIELab domains, while the target model, sRGBformer, is responsible for the final WB sRGB output. The cooperative interaction between the auxiliary and target models is crucial for achieving accurate WB in the output sRGB image. To train the auxiliary models, we use L2 loss + +to measure the difference between the PDFs of the predicted and ground-truth color channel histograms, formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {p d f}} ^ {s R G B} = \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {R}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {R}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {G}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {G}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {B}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {B}} \right\| _ {2}; \\ \mathcal {L} _ {\mathrm {p d f}} ^ {L a b} = \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {L}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {L}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {a}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {a}} \right\| _ {2} + \left\| \mathbf {H} _ {\mathbf {c}} ^ {\mathbf {b}} - \mathbf {H} _ {\mathbf {g t}} ^ {\mathbf {b}} \right\| _ {2}, \tag {6} \\ \end{array} +$$ + +where $\mathbf{H}_{\mathrm{c}}^{\mathrm{sRGB}} = [\mathbf{H}_{\mathrm{c}}^{\mathrm{R}};\mathbf{H}_{\mathrm{c}}^{\mathrm{G}};\mathbf{H}_{\mathrm{c}}^{\mathrm{B}}]$ and $\mathbf{H}_{\mathrm{c}}^{\mathrm{Lab}} = [\mathbf{H}_{\mathrm{c}}^{\mathrm{L}};\mathbf{H}_{\mathrm{c}}^{\mathrm{a}};\mathbf{H}_{\mathrm{c}}^{\mathrm{b}}]$ denote the corrected RGB and CIELab histograms, respectively, as estimated by PDFformers. $\mathbf{H}_{\mathrm{gt}}^{\mathrm{sRGB}}$ and $\mathbf{H}_{\mathrm{gt}}^{\mathrm{Lab}}$ represent the ground-truth histograms. We adopt L2 loss as it penalizes large deviations more heavily, encouraging the model to align histogram bins across the distribution evenly. + +For sRGBformer, we use the L1 loss for training, as follows: + +$$ +\mathcal {L} _ {\mathrm {r e c}} = \left\| \mathbf {X} _ {\mathbf {c}} - \mathbf {X} _ {\mathbf {g t}} \right\| _ {1}, \tag {7} +$$ + +where $\mathbf{X}_{\mathbf{c}}$ is the estimated WB image produced by sRGBformer, and $\mathbf{X}_{\mathbf{gt}}$ is the ground truth. The total loss is defined as $\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{pdf}}^{sRGB} + \mathcal{L}_{\mathrm{pdf}}^{Lab} + \mathcal{L}_{\mathrm{rec}}$ . + +# 4. Experimental Results + +Datasets. The commonly used public dataset, the Rendered WB dataset Set1 [3], is divided into three non-overlapping folds. For training, we randomly selected 12,000 rendered sRGB images with different WB settings from two of the folds. For testing, we use the third fold of Set1, also known as Set1-Test (21,046 images), as well as other datasets that have no overlap in scenes or cameras with the training data: Set2 of the Rendered WB dataset (2,881 images) [3] and the Rendered Cube+ dataset (10,242 images) [3, 6]. These datasets serve as benchmarks to evaluate the WB correction performance of our ABC-Former. + +Evaluation Metrics. We evaluated our results using three widely used metrics: Mean Squared Error (MSE), Mean Angular Error (MAE), and $\Delta E$ 2000 [13], which quantify the differences between the predicted WB images and the ground truth. For each metric, we reported the mean, first quantile (Q1), median (Q2), and upper quantile (Q3) of the error. Lower values in these metrics indicate better WB correction performance, consistent with those used in recent works [2, 3, 5, 18, 19]. + +Implementation Details. We implemented ABC-Former using PyTorch. During training, we optimize both the auxiliary and target models simultaneously over 350 epochs using the Adam optimizer [17] with $\beta_{1} = 0.5$ and $\beta_{2} = 0.999$ for each model. The learning rate is set to $2 \times 10^{-4}$ , and the embedding feature dimension to 16. For training, we randomly cropped four $128 \times 128$ patches from each training image as input. Additionally, we apply geometric transformations, including rotation and flipping, to augment the data. + +Quantitative Experimental Results. The quantitative results in Table 1 show that ABC-Former performs favorably against five SOTA methods [2, 3, 5, 18, 19] across three + +public benchmark datasets [3, 6]. The compared methods were evaluated using either their publicly available pretrained models or results directly cited from their respective publications. However, SWBNet [19] was retrained to be tested on the Set1-Test and Set2 datasets, as its code and original results for these datasets were not provided (marked with * in Table 1). SWBNet's scores on the Cube+ Dataset were taken from the original paper. On the Rendered WB Dataset Set1-Test and Set2, ABC-Former achieved the best performance on MSE, MAE, and $\Delta E$ 2000, indicating that it effectively removes color casts from images and achieves superior WB correction. On the Rendered Cube+ dataset, ABC-Former also delivered superior results, with the lowest mean scores in MSE, MAE, and $\Delta E$ 2000. Additionally, it maintains a competitive model size, only larger than Deep-WB [2] and Mixed-WB [5]. These results demonstrate ABC-Former's efficiency in achieving efficient WB correction across various datasets without significantly increasing model complexity, showcasing its robustness and generalization capabilities. + +Qualitative Experimental Results. We present the qualitative comparison results on the Rendered WB and Rendered Cube+ datasets in Figure 3 and Figure 4. Analyzing the color correction performance of different methods, we see that while KNN [3], Deep-WB [2], Mixed-WB [5], and WBFlow [18] generally reduce color casts, they often exhibit color inconsistencies across different regions of the image. For example, in Figure 3, these methods tend to correct the colors of objects while neglecting the sky's color accuracy, resulting in an undesirable yellow tint. Similarly, in Figure 4, strong color casts lead to suboptimal WB correction, often leaving the image with an overall blue or yellow tone. In contrast, our method, guided by corrected global color information from multiple modalities, achieves a more balanced and consistent color correction across the entire image, producing natural and harmonious results. + +In addition, Figure 5 demonstrates a comparative analysis of global color distribution accuracy in the average WB results across different methods. The Bhattacharyya coefficient, as introduced in [16], is employed to measure the similarity between the red, green, and blue histograms of the processed images and those of the ground-truth WB images across three benchmark datasets. This coefficient ranges from 0 to 1, with higher values indicating a closer match to the ground truth color distributions. The results show that ABC-Former achieves a higher similarity compared to other methods. Additionally, the visualization at the bottom of the figure illustrates an example of the color distributions in WB results obtained by the compared methods, highlighting that ABC-Former produces color distributions more consistent with the ground truth. + +Ablation Studies. In the ablation studies, we investigated the impact of various combinations of modalities used for + +Table 1. The quantitative results of ABC-Former and competing WB methods are evaluated on three public benchmark datasets, including Rendered WB Dataset (Set1-Test and Set2) [3], and Rendered Cube+ Dataset [3, 6]. The best results are highlighted in red, while the second-best results are highlighted in blue. + +
MethodMSE ↓MAE ↓ΔE 2000 ↓Size
MeanQ1Q2Q3MeanQ1Q2Q3MeanQ1Q2Q3MB
Rendered WB Dataset: Set1-Test (21,046 images) [3]
KNN [3]77.4913.7439.6294.013.06°1.74°2.54°3.76°3.582.073.094.5521.8
Deep-WB [2]82.5513.1942.77102.093.12°1.88°2.70°3.84°3.772.163.304.8616.7
Mixed-WB [5]142.2526.8167.17164.664.07°2.64°3.68°5.16°4.553.004.155.635.1
WBFlow [18]78.8912.9935.0979.352.67°1.73°2.39°3.24°3.131.922.793.9430.2
SWBNet* [19]111.6220.6160.68137.914.11°2.56°3.75°5.22°4.542.734.165.86258.8
ABC-Former20.474.6510.0221.051.99°1.25°1.73°2.33°2.181.381.862.5920.2
Rendered WB Dataset: Set2 (2,881 images) [3]
KNN [3]171.0937.0487.04190.884.48°2.26°3.64°5.95°5.603.434.907.0621.8
Deep-WB [2]124.0730.1376.32154.443.75°2.02°3.08°4.72°4.903.134.356.0816.7
Mixed-WB [5]188.7648.64112.32219.914.92°2.69°4.10°6.37°6.053.454.927.205.1
WBFlow [18]117.6031.2561.68143.903.51°1.93°2.92°4.47°4.643.164.075.5630.2
SWBNet* [19]219.0255.45113.98236.255.46°3.45°4.78°6.63°6.514.395.848.08258.8
ABC-Former104.3125.5558.61132.903.39°1.87°2.73°4.30°4.562.974.135.6320.2
Rendered Cube+ Dataset (10,242 images) [3, 6]
KNN [3]194.9827.4357.08118.214.12°1.96°3.17°5.04°5.683.224.616.7021.8
Deep-WB [2]80.4615.4333.8874.423.45°1.87°2.82°4.26°4.592.683.815.5316.7
Mixed-WB [5]161.8016.9619.3390.814.05°1.40°2.12°4.88°4.892.163.106.785.1
WBFlow [18]75.3914.2230.9072.913.34°1.87°2.82°4.11°4.282.683.775.2130.2
SWBNet [19]74.3520.4640.0486.953.15°1.33°2.09°4.12°4.282.403.565.09258.8
ABC-Former60.6012.1526.9257.202.99°1.63°2.45°3.69°3.952.353.404.8620.2
+ +![](images/c3378122664307760f9e6a413a22ad7619238a7db1f86bea05f23afd572a65da.jpg) + +![](images/551cab629c1264d4c5034413d796f07d772303580bd0321e0bc3ef9de370ef9e.jpg) + +![](images/69c9b7b603dfb72472638fb5c3629a1a454dae2c9ace30ec0928f92db10b3bb6.jpg) +Input + +![](images/90b21a6f37be26da2b82d186d668f88fc9a76970239aaf02882730645069fbc3.jpg) + +![](images/274b0d8ed5c490dbb989c157e6cd37ba4165830a18f653d82013dcf2c1e3f5eb.jpg) + +![](images/9debd5d7045bff73cf6f43ae9b287aa5aa349b99612a69c472fac61f555c7ed0.jpg) +KNN + +![](images/a8d6b41038be2e3c006563195444320ad8b2f8cb1b0c1b17352152cf76109389.jpg) + +![](images/52fe869da81c3a8d34549519c14dd5829523b1f8e1cd5d824fef1f26af155959.jpg) + +![](images/212fdce970499e8169dde75fe208fecc2c63f118d5034dc57c0bcd20b4bd2550.jpg) +Deep-WB + +![](images/4a8103d7ed0d9d2271b26bf02ccc13fea9c3c9e460305ae0abcfc9b43e8c6464.jpg) + +![](images/4a7f1af5212f11c2f2a2da4296eb909272aa9df93e68395c2042987e8021674e.jpg) + +![](images/a116ce8cadb8fe19d639c1c63f0e2fa9a8df48fba2e99a8804f20bd49da8b763.jpg) +Mixed-WB +Figure 3. Qualitative comparisons with other sRGB-WB methods on the Rendered WB dataset [3], with the $\Delta$ E 2000 indicated in the bottom-right corner of each image. + +![](images/816bbb8567944e4793334ba775b8e11f7738c51eb1f29c8c2cf843a1a8b1c998.jpg) + +![](images/1578e6473e3d4095fc6dc20e95f44b59944d7489d6bab7b7de44d58e920161b2.jpg) + +![](images/dba71879c777c4eaa2c389315803fc5fa1d3101f37d0a5fe8ca6be89f8c6d15f.jpg) +WBFlow + +![](images/6dcc78a119e3152c36728c6f826b20822c372edd29411248d6e2e8f6e6323eb6.jpg) + +![](images/61d8524cbfadf25a49d98c82d0001471003fc6001d52d82febe8be9c7fa8fe37.jpg) + +![](images/5e84cb823eda855f16fce087b5ca4795849e080d29892d97548f2378fee8f8fa.jpg) +Ours + +![](images/4c130dcc5f1dcc973e9fde452a1b89ff9d9e210238fe8db29599d8618bcac07b.jpg) + +![](images/f4794eb6ce4ff7737ac2b06d6440e95c88f0509c01d628b3e8bcffe08da8291f.jpg) + +![](images/069b3937070a01f3592c6d0ba272852ce9fc833a8312857090d40dd911351cdf.jpg) +GT + +![](images/687b9d42ba6f432d13f1b3edaaa2f1bf690bf6d0b0bb86325878ad1c95cb4593.jpg) +Figure 4. Qualitative comparisons with other sRGB-WB methods on the Rendered Cube+ dataset [3, 6], with the $\Delta$ E 2000 displayed in the bottom-right corner of each image. + +![](images/7b18e71146036143bf058e4ad6b666f46af9f089e0d2deea7bb6e19dfa269b42.jpg) +Figure 5. Evaluation of the Bhattacharyya coefficient [16] for color histograms across three benchmark datasets [3, 6], showing global color accuracy for red, green, and blue histograms in sRGB-WB methods. ABC-Former achieves more consistent color distributions by leveraging global color temperature features from both sRGB and CIELab histograms. + +WB correction on the Rendered Cube+ dataset. We report the mean values across three evaluation metrics, along with model sizes for each combination of auxiliary models. As shown in Table 2, using only the target model (sRGB-former) without additional guidance of global color information from other modalities results in suboptimal WB accuracy. Adding a single auxiliary model (e.g., $\mathrm{PDF}_{\mathrm{sRGB}} + \mathrm{sRGB}$ or $\mathrm{PDF}_{\mathrm{Lab}} + \mathrm{sRGB}$ ) improves WB performance over the target model alone. However, utilizing a single auxiliary model to jointly learn both sRGB and CIELab histograms $(\mathrm{PDF}_{\mathrm{sRGB:Lab}} + \mathrm{sRGB})$ proves less effective, as a single + +model struggles to disentangle the information from both modalities. Our full ABC-Former design leverages global color temperature features from multiple modalities through two auxiliary models to guide color adjustment, achieving the highest WB accuracy. To ensure a fair comparison across these combinations, we matched the model size to that of ABC-Former by doubling the bottleneck channels in sRGBformer (Baseline) and evenly increasing channels across layers when using a single auxiliary model. + +Table 3 compares different loss functions that train auxiliary models for learning sRGB and CIELab histograms. + +Table 2. Ablation studies of ABC-Former w/ and w/o guidance from different modalities on the Rendered Cube+ dataset [3, 6]. Here, sRGB denotes sRGBformer, while $\mathrm{PDF}_{\mathrm{sRGB}}$ , and $\mathrm{PDF}_{\mathrm{Lab}}$ represent auxiliary PDFformer models for sRGB and CIELab histograms, respectively. + +
ModalitiesMSE ↓MAE ↓ΔE 2000 ↓Size(MB)
sRGB76.563.35°4.3120.4
PDFLab + sRGB73.353.26°4.2020.4
PDFsRGB + sRGB68.653.12°4.0820.4
PDFsRGB:Lab + sRGB72.383.38°4.3820.4
PDFsRGB + PDFLab + sRGB60.602.99°3.9520.2
+ +Table 3. Ablation studies on the loss function used to train auxiliary models for learning sRGB and CIELab histograms. We compare the KL divergence, Wasserstein distance, and our chosen L2 loss on the Rendered Cube+ dataset [3, 6]. + +
Loss functionMSE ↓MAE ↓ΔE 2000 ↓Size(MB)
KL divergence72.673.29°4.1720.2
Wasserstein distance70.223.12°4.1520.2
L2 loss (Proposed)60.602.99°3.9520.2
+ +Table 4. WB manipulation on the Rendered Cube+ dataset [3, 6]. + +
MethodMSE ↓MAE ↓ΔE 2000 ↓
MeanQ1Q2Q3MeanQ1Q2Q3MeanQ1Q2Q3
Deep-WB [2]199.3832.3063.34142.765.40°2.67°4.04°6.36°5.983.444.787.29
ABC-Former82.370.0117.7665.362.78°1.06°2.85°3.22°2.890.072.364.12
+ +![](images/26fbe8e8784e5c94a3f3e9baf308d5e9b90f3978887521261dadca03bdd8f7ed.jpg) +Figure 6. Analysis on learned weights on Rendered Cube+ dataset [3, 6], $\lambda_{\mathbf{i}}^{\mathbf{sRGB}}$ and $\lambda_{\mathbf{i}}^{\mathbf{Lab}}$ , for cross-modality knowledge transfer. Here, $i \in \{e_0, e_1, e_2, b_0, d_0, d_1, d_2\}$ represents the level of the sRGBformer block, where $e, b,$ and $d$ denote the encoder, bottleneck, and decoder layers, respectively. + +As can be seen, the L2 loss shows better performance compared to KL divergence and Wasserstein distance, at + +tributed to its stability and effectiveness in aligning histograms. In contrast, KL divergence may encounter issues with zero-probability bins, and Wasserstein distance can be non-smooth and challenging to optimize in high-dimensional spaces. + +Analyzing Learned Weights for Cross-Modality Transfer. We present the learned weights, $\lambda_{\mathrm{i}}^{\mathrm{sRGB}}$ and $\lambda_{\mathrm{i}}^{\mathrm{Lab}}$ , at each level of ABC-Former to illustrate how modality-complementary knowledge guides WB correction. As shown in Figure 6, the influence of calibrated global color information from sRGB and CIELab histogram modalities intensifies toward the bottleneck block, peaking at the bottleneck. This indicates that high-level WB color histogram-based features from both modalities, capturing global, semantically rich color information, are crucial for reweighting sRGB image features for accurate WB correction. Notably, the sRGB histogram modality has a slightly greater impact than CIELab, though the difference is minimal. This suggests that both color modalities collaborate effectively, allowing ABC-Former to balance raw color intensity with perceptually uniform CIELab properties. + +WB Manipulation. Following the setup described in [2], we conduct experiments to alter the input image's colors to match the target white balance (WB) settings. These settings correspond to the following color temperatures: tungsten $(2850\mathrm{K})$ , fluorescent $(3800\mathrm{K})$ , daylight $(5500\mathrm{K})$ , cloudy $(6500\mathrm{K})$ , and shade $(7500\mathrm{K})$ . As shown in Table 4, ABC-Former significantly outperforms Deep-WB [2] in achieving accurate color transformations. + +# 5. Conclusion + +We presented ABC-Former, an Auxiliary Bimodal Cross-domain Transformer that enhances sRGB WB correction by leveraging complementary information from multiple modalities. ABC-Former uses Interactive Channel Attention to facilitate cross-modality knowledge transfer, integrating calibrated color features from both sRGB and CIELab histograms. This multimodal approach enables a more nuanced fusion of color information, allowing the model to handle diverse color temperatures and complex scenes with pronounced color shifts. Extensive experiments have demonstrated that ABC-Former consistently outperforms state-of-the-art methods in both quantitative and qualitative evaluations. For future work, extending into 2D histograms is a promising direction. + +# 6. Acknowledgments + +This paper was supported in part by the National Science and Technology Council, Taiwan, under grants NSTC 113-2221-E-004-001-MY3, 113-2622-E-004-001, 113-2221-E-004-006-MY2, 112-2634-F-002-005, 113-2634-F-002-008, and 113-2923-E-A49-003-MY2. + +# References + +[1] Mahmoud Afifi and Michael S Brown. What else can fool deep learning? addressing color constancy errors on deep neural network performance. In ICCV, 2019. 1 +[2] Mahmoud Afifi and Michael S Brown. Deep white-balance editing. 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In PSIVT, 2014. 2 +[10] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Arcface: Additive angular margin loss for deep face recognition. In CVPR, 2019. 1 +[11] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. ICLR, 2021. 3 +[12] Jun Fu, Jing Liu, Hajjie Tian, Yong Li, Yongjun Bao, Zhiwei Fang, and Hanqing Lu. Dual attention network for scene segmentation. In CVPR, 2019. 1 +[13] Sharma Gaurav. The ciede2000 color-difference formula: Implementation notes, supplementary test data, + +and mathematical observations. COLOR research and application, 2005. 5 +[14] Jie Hu, Li Shen, and Gang Sun. Squeeze-andexcitation networks. In CVPR, 2018. 3 +[15] Yuanming Hu, Baoyuan Wang, and Stephen Lin. FC4: Fully convolutional color constancy with confidence-weighted pooling. In CVPR, 2017. 2 +[16] Thomas Kailath. The divergence and bhattacharyya distance measures in signal selection. IEEE transactions on communication technology, 1967. 5, 7 +[17] Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. *ICLR*, 2015. 5 +[18] Chunxiao Li, Xuejing Kang, and Anlong Ming. WBFlow: Few-shot white balance for sRGB images via reversible neural flows. In IJCAI, 2023. 2, 3, 5, 6 +[19] Chunxiao Li, Xuejing Kang, Zhifeng Zhang, and Anlong Ming. SWBNet: a stable white balance network for sRGB images. In AAAI, 2023. 2, 5, 6 +[20] Yi-Chen Lo, Chia-Che Chang, Hsuan-Chao Chiu, Yu-Hao Huang, Chia-Ping Chen, Yu-Lin Chang, and Kevin Jou. CLCC: Contrastive learning for color constancy. In CVPR, 2021. 2 +[21] Taishi Ono, Yuhi Kondo, Legong Sun, Teppei Kurita, and Yusuke Moriuchi. Degree-of-linear-polarization-based color constancy. In CVPR, 2022. 2 +[22] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In ICML, 2021. 2 +[23] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster r-cnn: Towards real-time object detection with region proposal networks. NIPS, 2015. 1 +[24] Joost Van De Weijer, Theo Gevers, and Arjan Gijsenij. Edge-based color constancy. IEEE TIP, 2007. 2 +[25] Zhendong Wang, Xiaodong Cun, Jianmin Bao, Wengang Zhou, Jianzhuang Liu, and Houqiang Li. Uformer: A general u-shaped transformer for image restoration. In CVPR, 2022. 3 +[26] Yiyuan Zhang, Xiaohan Ding, Kaixiong Gong, Yixiao Ge, Ying Shan, and Xiangyu Yue. Multimodal pathway: Improve transformers with irrelevant data from other modalities. 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Lindell $^{1,2}$ Sergey Tulyakov $^{3}$ + +1University of Toronto 2Vector Institute 3Snap Inc. 4SFU + +*equal contribution + +https://snap-research.github.io/ac3d + +![](images/b817cae749f12438e773bb976adf99e6f8b2a973ab4df38ce66da003d63efb02.jpg) + +![](images/52516c7173e4846a6846b007e2a90e43104163aca0143472ddbef4ba84c1276e.jpg) +Figure 1. Camera-controlled video generation. Our method enables precise camera controllability in pre-trained video diffusion transformers, allowing joint conditioning of text and camera sequences. We synthesize the same scene with two different camera trajectories as input. The inset images visualize the cameras for the videos in the corresponding columns. The left camera sequence consists of a rotation to the right, while the right camera visualizes a zoom-out and up trajectory. + +![](images/511171fd4800824ac854c98baa2d66ee98e1865662ef20852b5d5958d8527144.jpg) + +# Abstract + +Numerous works have recently integrated 3D camera control into foundational text-to-video models, but the resulting camera control is often imprecise, and video generation quality suffers. In this work, we analyze camera motion from a first principles perspective, uncovering insights that enable precise 3D camera manipulation without compromising synthesis quality. First, we determine that motion induced by camera movements in videos is low-frequency in nature. This motivates us to adjust train and test pose conditioning schedules, accelerating training convergence while improving visual and motion quality. Then, by probing the representations of an unconditional video diffusion transformer, we observe that they implicitly perform camera pose estimation under the hood, and only a sub-partion of their layers contain the camera information. This suggested us to limit the injection of camera conditioning to a subset of the + +architecture to prevent interference with other video features, leading to a $4 \times$ reduction of training parameters, improved training speed, and $10\%$ higher visual quality. Finally, we complement the typical dataset for camera control learning with a curated dataset of 20K diverse, dynamic videos with stationary cameras. This helps the model distinguish between camera and scene motion and improves the dynamics of generated pose-conditioned videos. We compound these findings to design the Advanced 3D Camera Control (AC3D) architecture, the new state-of-the-art model for generative video modeling with camera control. + +# 1. Introduction + +Foundational video diffusion models (VDMs) trained on internet-scale data, acquire abundant knowledge about the physical world [10]. They not only learn appearance and + +plausible 2D dynamics, but they also have abundant understanding of 3D structure [7]. However, most of this knowledge is stored implicitly within the model, as these models do not expose fine-grained control mechanisms, such as camera motion control. We recently witnessed a surge of works that bring 3D camera control into foundational video models [39, 149, 166], but the control they provide is not very precise, and the synthesis quality is often compromised [6]. We analyze camera motion control in video diffusion models from first principles, and develop several findings that allow us to incorporate precise 3D camera conditioning without degrading synthesis quality. To perform our analysis we train a 11.5B-parameter VDiT (video latent diffusion transformer) [100] on a dataset of 100M text/video pairs. On this model, we perform three key studies. With what we learn, we adapt the camera control solution from VD3D [6] from a pixel-based to latent-based diffusion model, and significantly improve its performance. + +1) The spectral properties of camera motion. To study the statistical nature of motion control, we analyze motion spectral volumes (MSV) [75] of the videos generated by a large-scale video DiT model. MSVs show the amount of energy in different portions of the frequency spectra (i.e., high energy in the low frequencies indicate smooth motion) and we measure them across 200 generated videos of different types (camera motion, scene motion, scene plus camera motion) and at various stages of the denoising synthesis process. We observe that camera motion mostly affects the lower portion of the spectrum and kicks in very early ( $\approx 10\%$ ) in the denoising trajectory. Then, as diffusion models are inherently coarse-to-fine in nature [25], we restrict our camera conditioning to only being injected on the subset of the denoising steps corresponding to low-frequencies. This results in $\approx 15\%$ higher visual fidelity, $\approx 30\%$ better camera following, and mitigates scene motion degradation. + +2) Camera motion knowledge in VDiTs. Then, we consider our text-only VDiT, and determine whether such a model possesses knowledge about cameras, and where this knowledge is expressed within its architecture. With this objective, we feed the (unseen during training) RealEstate10k [199] videos to our VDiT, and perform linear probing [27] to determine if camera poses can be recovered from its internal representation. Our analysis revealed that a video DiT implicitly performs camera pose estimation under the hood, and the presence of camera knowledge in a disentangled form peaks in its middle layers. This implies that the camera signal emerges in its early blocks to allow the later ones rely on it to build subsequent visual representations. Therefore, we adjust our conditioning scheme to only affect the first $30\%$ of the architecture, leading to a $\approx 4\times$ reduction in training parameters, $15\%$ training and inference acceleration, and $10\%$ improved visual quality. + +3) Re-balancing the training distribution. Finally, to supervise camera control architectures, the typical solution is to rely on the camera pose annotations provided by RealEstate10k [199]. However, this dataset contains mostly static scenes, which results in significant motion degradation of the fine-tuned video model. To overcome this problem, we curate a subset of 20K diverse videos with dynamic scenes but static cameras. As the camera conditioning branch is still activated for these videos, this helps the model disambiguate the camera from scene movement. Our experiments show that this simple adjustment in the data is sufficient to recover the scene dynamism while still enabling an effective pose-conditioned video model. + +Contributions. We compound the knowledge gained from these three studies into the design of the Advanced 3D Camera Control (AC3D) method. We perform extensive ablation studies and compare against state-of-the-art models for camera control, including MotionCtrl [149], CameraCtrl [39], and VD3D [6]. We demonstrate $18\%$ higher video fidelity and $25\%$ more precise camera steering in terms of quantitative metrics than a closest competitor, and our generated videos are favored to others in $90\%$ of cases. + +# 2. Related work + +Our approach lies at the intersection of text-to-video, text-to-3D, and text-to-4D generation approaches. We refer to recent state-of-the-reports [101, 180] for a more thorough analysis of previous work. + +Text-to-video generation. Our approach builds on recent advancements in 2D video diffusion models. One prominent technique in this area enhances text-to-image models by adding temporal layers to support video generation [7, 8, 37, 119, 151]. While these methods use the U-Net architecture, more recent ones [10, 92, 93, 168] have been adapting transformer-based architectures for more scalable, realistic, and highly dynamic scene generation. We are interested in controlling the camera movements during the generation process of recent transformer-based video models based on precise camera extrinsics, i.e., cameras represented as rotation and translation sequences for each frame. + +4D generation. Early 4D generation works [2, 164] used 4D GANs to learn category-specific generators with an underlying dynamic 3D representation. More recent approaches [4, 5, 81, 120, 196] have tackled 4D generation by distilling motion priors from pre-trained video diffusion models into an explicit 4D representation, enabling category-agnostic 4D generation. Follow-up works investigate image or video conditioned 4D generation [33, 76, 81, 98, 109, 173, 182, 193, 196] instead of pure text inputs, improving flexibility in the generation process. While most of these works are object-centric, recent approaches [4, 159] shifted towards more complex scenes, including methods [23, 175] which + +![](images/7d90716174ed6253fcc66d5f7b61f599bd5530253f95e75ce8956865a8007427.jpg) +Figure 2. VDiT-CC model with ControlNet [71, 188] camera conditioning built on top of VDiT. Video synthesis is performed by large 4,096-dimensional DiT-XL blocks of the frozen VDiT backbone, while VDiT-CC only processes and injects the camera information through lightweight 128-dimensional DiT-XS blocks (FC stands for fully-connected layers); see Section 3.2 for details. + +model the background. However, all these methods are optimization-based, i.e., each scene is generated independently from scratch. Recently, L4GM [110] proposes a feed-forward 4D generator trained on object-centric synthetic 4D data. While these approaches are explicit and provide space-time control, they are limited in their photorealism compared to recent 2D video diffusion models. We investigate dynamic 3D scene generation from a different perspective by extending pre-trained video diffusion models with 3D camera control. + +Camera control for video models. Recently, there has been significant progress in adding camera control to video diffusion models. As the pioneering work, MotionCtrl [149] learns camera control by conditioning pre-trained video models [7, 17] with extrinsic matrices. Follow-up works [39, 65, 160] further improve the conditioning mechanisms by representing cameras as Plücker coordinates. Another line of work [49, 50, 82, 155] controls camera motion without training additional parameters. However, all of these approaches use U-Net-based architectures as their backbone. More recently, 4DiM [150] trains a space-time diffusion model from scratch for novel view synthesis from a single image input. Closely related to our work, VD3D [6] incorporates camera control into a pre-trained video diffusion transformer. While the motion and camera control improves over U-Net-based approaches, the synthesized motion in the scenes and the visual quality are still degraded compared to the base video model. In contrast to VD3D, we first thoroughly investigate the pre-trained base video model and its knowledge of camera motion. We derive an improved training and architecture design for high-quality and dynamic video generation based on our findings. + +Concurrent works. Concurrent approaches [68, 158, 177, 185, 194, 195] further improve camera control in U-Net-based architectures, while another work [22] tackles video diffusion transformer. However, the scene and visual quality + +is still limited in that approach. DimensionX [127] controls space and time in video diffusion transformers but the camera trajectories are pre-defined and not continuous. Chun-Hao et al. [51] explore pose estimation with a video DiT by pairing it with DUSt3R [145] and fine-tuning, while we perform linear probing without any training to assess its existing camera knowledge. CAT4D [152] proposes a multi-view video diffusion model fine-tuned from a multi-view model. + +# 3. Method + +We first describe our base video diffusion model (Sec. 3.1), and the baseline camera control method built on top of it (Sec. 3.2). Then, we proceed with the analysis of motion (Sec. 3.3), linear probing (Sec. 3.4) and dataset biases (Sec. 3.5), and additional insights on how to build an effective model for camera control (Sec. 3.6) + +# 3.1. Base model (VDiT) + +Following Sora [10], most modern foundational text-to-video generators use the diffusion framework [45, 122] to train a large-scale transformer [139] in the latent space of a variational autoencoder [64, 111]. We adopt the same design and, for a base video model, pre-train an 11.5B-parameter Video DiT model [100] with 32 blocks of hidden dimension 4,096 for text-to-video generation. We use the rectified flow diffusion parametrization [85] and learn in the latent space of CogVideoX [168] (using an autoencoder with a 16-channel output and compression factors of $4 \times 8 \times 8$ in the temporal and spatial dimensions). The T5 [108] encoder produces text embeddings, which are passed into VDiT via cross-attention. We train our base model on a large-scale dataset of images and videos with text annotations, with resolutions ranging from $17 \times 144 \times 256$ to $121 \times 576 \times 1024$ . This design is fairly standard and followed by many existing works with little deviation [32, 102, 168, 197]; we describe our specific architectural and training setup in detail in Appendix D. + +# 3.2. VDiT with Camera Control (VDiT-CC) + +To construct a baseline architecture for camera control, we implement ControlNet [18, 188] conditioning on top of the VDiT. Similar to previous work [6, 39, 149], we use the RealEstate10k [199] dataset, consisting of $65\mathrm{k}$ (text, video, camera trajectory) triplets $(\pmb{t}_n,\pmb{x}_n,\pmb{c}_n)_{n = 1}^N$ and train a new set of model parameters to input the camera information into the model. Camera trajectories $\pmb {c}\in \mathbb{R}^{f\times 25}$ are provided in the form of camera extrinsics $\pmb {C_f}\in \mathbb{R}^{4\times 4}$ and intrinsics $\pmb {K}_f\in \mathbb{R}^{3\times 3}$ for each $f$ -th frame $\pmb{x}_f$ . + +Camera conditioning. For base camera control, we adapt VD3D [6] since it was designed for transformer-based models and suits our setup the most, while other methods are built on top of UNet-based [112] backbones. We use Plücker camera representations [6, 16, 39, 59, 121], which are projected to the same dimensionality and resolution as the video tokens via a fully-convolutional encoder to produce camera tokens. These camera tokens are processed by a sequence of lightweight DiT-XS blocks with hidden dimension 128 and four attention heads each. To mix the camera information with the video tokens of VDiT, we use summation before each main DiT block. We also found it useful to perform cross-attention from video tokens to camera tokens as a form of a feedback connection [71]. We illustrate this model architecture, which we call VDiT-CC, in Figure 2; see implementation details in Appendix D. VDiT-CC describes the camera-controlled video model architecture used by AC3D, while AC3D describes our proposed work including analysis and additional adjustments based on the analysis. + +Training. Keeping the VDiT backbone frozen, we train the new parameters with a rectified flow objective [85] and standard (location of 0 and scale of 1) logit-normal noise distribution [28]. Similar to prior works [6, 150], we apply a $10\%$ camera dropout to support classifier-free guidance (CFG) [44] later. Notably, we train VDiT-CC only at the $256^2$ resolution: since camera motion is a low-frequency type of signal (which can be observed at lower resolutions) and the main VDiT backbone is frozen, we found that our design generalizes to higher resolutions out-of-the-box. During inference, we input text prompts and camera embeddings with classifier-free guidance at each time step. + +Model behavior. This baseline model, being built on top of our powerful VDiT, already achieves decent-quality camera control. However, it struggles with degraded visual quality and reduced scene motion, and sometimes, the camera control inputs are ignored. To improve the design, we analyze our VDiT backbone to understand how camera motion is modeled and represented. Then, we inspect VDiT-CC's failure cases and where they arise to address them. + +![](images/84e1ccc3b8c3684156cda0c6e94f1b00f3bf0f68361b47b1471f204f9c75627a.jpg) +Figure 3. Average magnitude of motion spectral volumes along spatial, temporal offset, and video batch dimensions for scenes with different motion types. We compute the flow of each video in a sliding window manner with temporal offsets and average the frequencies across all offsets. Videos with camera motion (purple) exhibit stronger overall motion than the videos with scene motion (orange), especially for the low-frequency range, suggesting that the motion induced by camera transitions is heavily biased towards low-frequency components. Frequency refers to the temporal frequency. + +# 3.3. How is camera motion modeled by diffusion? + +We start by analyzing how camera motion is modeled by a pre-trained video diffusion model (i.e., before camera control is incorporated). We hypothesize that the motion induced by changes in camera pose is a low-frequency type of signal and investigate the motion spectral volumes [75] of the generated videos at different steps of the denoising process. To perform this analysis, we generate 200 diverse videos with our VDiT model with 80 denoising steps and manually annotate them into four categories: videos with only scene motion, videos with only camera motion, videos with both scene and camera motion, and others; see Appendix E for details. During generation, we save the denoised predictions at each denoising step and estimate optical flow to compute the motion spectral volumes. + +Analysis. We visualize motion spectral volumes with $95\%$ confidence intervals in Figure 3. Videos with camera motion exhibit higher amplitudes than scene-motion-only videos for low-frequency components while having similar characteristics for high-frequency ones. This supports the conjecture that the camera motion is a low-frequency type of signal. We also depict an example of a generated video with both scene and camera motion with four denoising steps on Fig. 4a: one can observe that the camera movement has been fully produced by $t = 0.9$ (first $10\%$ of the rectified flow denoising process). In contrast, scene motion details like the hand movements of the subjects are not finalized even till $t = 0.5$ . + +Inspired by this finding, we pose the question: when exactly does a video diffusion model determine the camera pose? To answer this question, we plot aggregated spectral volumes for different timesteps in Figure 4b. We also show the ratio with respect to the last timestep $t = 0$ (i.e., + +![](images/8693ddc1f716218a31172eb0176c0cf1659c7715d807548d77bc27c89b978dc5.jpg) +(a) A generated video at different diffusion timesteps. The camera has already been decided by the model even at $t = 0.9$ (first $10\%$ of the denoising process) and does not change after that. + +![](images/9ea73aaf19caa9d407640a1ed89c9115a7296f0e1cb9290812cc347eaa8c3e6c.jpg) +(b) Motion spectral volumes of VDiT's generated videos for different diffusion timesteps (left) and their ratio w.r.t. the motion spectral volume at $t = 0$ (i.e., a fully denoised video). +Figure 4. How camera motion is modeled by diffusion? As visualized in Figure 4a and Figure 3, the motion induced by camera transitions is a low-frequency type of motion. We observe that a video DiT creates low-frequency motion very early in the denoising trajectory: Figure 4b (left) shows that even at $t = 0.96$ (first $\approx 4\%$ of the steps), the low-frequency motion components have already been created, while high frequency ones do not fully unveil even till $t = 0.5$ . We found that controlling the camera pose later in the denoising trajectory is not only unnecessary but detrimental to both scene motion and overall visual quality. + +![](images/23e1a2904a69fcdbc58bb5274bf44241e2989333975124d4518225d74c2d0e4e.jpg) + +when all motion has been generated). We then inspect when different types of motion appear during the denoising process. Figure 4b (right) shows that the low-frequency motion components fill up to $\approx 84\%$ at $t = 0.9$ (the first $10\%$ of the denoising process), while high-frequency components are not well-modeled until $t = 0.6$ . + +An immediate consequence of this observation is that trying to control the camera later in the denoising trajectory is simply unnecessary and will not influence the manipulation result. In this way, instead of using the standard logit-normal noise level distribution of SD3 [28] with a location of 0.0 and scale of 1.0 (which we use by default for VDiT), we switch to using truncated normal with a location of 0.8 and scale of 0.075 on the [0.6, 1] interval to cover the early steps of the denoising rectified flow trajectory. At inference time, we apply camera conditioning on the same [0.6, 1] interval. Surprisingly, we observe that not using truncation is detrimental to the scene motion and overall visual quality. Following this insight, we restrict both our train-time noise levels and test-time camera conditioning schedules to cover only the first $40\%$ of the reverse diffusion trajectory. As Sec. 4.3 shows, this improves FID and FVD by $14\%$ on average, and camera following by $30\%$ on MSR-VTT (the dataset used to measure generalization to diverse, out-of-fine-tuning-distribution scenes). Further, truncated noise sampling enhances the overall scene motion. + +# 3.4. What does VDiT know about camera pose? + +Foundational video models acquire rich knowledge about the physical world, and we hypothesize that they store information about the camera pose within their representations. To investigate this, we perform linear probing of our base VDiT model on the RealEstate10k [199] dataset (not seen + +during training) for camera extrinsics. + +Specifically, we take 1,000 random 49-frame videos from RealEstate10K, feed them into VDiT under 8 noise levels $(1/8, 2/8, \dots, 1)$ , and extract the activations for all 32 DiT blocks. Next, we split the random videos into 900 train and 100 test videos and train a linear ridge regression model to predict the rotation pitch/yaw/roll angles and translation vectors for the entire viewpoint trajectory $(49 \times 6$ target values in total). This results in $8 \times 32$ trained models, and we report the rotation and (normalized) translation errors [39] on a held-out test set of 100 videos in Figure 5. Surprisingly, VDiT can accurately predict the camera pose, achieving minimum test errors of $\approx 0.025$ for rotation and for $\approx 0.48$ translation prediction. The knowledge quality increases around layer #9 and peaks in the range of #13-21. We reason that since the camera information in block #13 is stored in such a disentangled manner, then the model is using it to build other representations; hence, conditioning the camera in this block is risky and unnecessary and would interfere with other visual features, as shown in our ablations. In this way, we propose to input the camera conditioning only in the first #8 blocks and leave the remaining 24 DiT blocks unconditioned. We find in Section 4.3 that this not only reduces the number of trainable parameters by $\approx 4$ times and improves training speed by $\approx 15\%$ , but also enhances the visual quality by $\approx 10\%$ . + +# 3.5. Mitigating training data limitations + +Estimating camera parameters from in-the-wild videos remains challenging, as leading methods like [114, 115, 145, 192] frequently fail when processing videos containing dynamic scene content. This limitation results in camera-annotated datasets being heavily biased + +![](images/81ea02059ff1477dd730701760e70616e713378dad921b2c3c191cac9198b885.jpg) +Figure 5. Video DiT is secretly a camera pose estimator. We perform linear probing of camera poses in each of VDiT blocks for various noise levels and observe that video DiT performs pose estimation under the hood. Its middle blocks carry the most accurate information about the camera locations and orientations, which indicates that the camera signal emerges in the early layers to help the middle and late blocks render other visual features aligned with the viewpoint. + +![](images/5b13402e9380f67cf4a5cc2290fae66fa5179e151f60267cd7fe2a1dbed59fa5.jpg) + +toward static scenes, which is particularly evident in RealEstate10K (RE10K) [199], the predominant dataset for training camera-controlled video models [6, 39, 149]. We hypothesize that models fine-tuned on such data interpret camera position information as a signal to suppress scene dynamics. This bias persists even when jointly training on unconstrained 2D video data [150], because the camera conditioning branch is only activated when camera parameters are available, which occurs exclusively for static scenes from RE10K, as static scenes remain the only reliable source for accurate camera annotation. + +To address this fundamental limitation, we propose an alternative approach: rather than attempting to annotate dynamic scenes, which proved unsuccessful in our extensive preliminary research, even with state-of-the-art methods [145], we curate a collection of 20K diverse videos featuring dynamic scenes captured by stationary cameras (see Figure 6). With stationary cameras, the camera position is inherently known, (we can assign fixed arbitrary extrinsic), allowing us to maintain active camera conditioning during training. This approach enables the camera conditioning branch to remain active during training while exposing the model to dynamic content, helping it distinguish between viewpoint conditioning and scene stillness. On top of this secondary dataset, following [150], we remove the scale ambiguity in RE10K by leveraging an off-the-shelf metric depth estimator; see Appendix H. Our experiments in Sec. 4.3 demonstrate that this straightforward yet effective data curation strategy successfully mitigates the distributional limitations of RE10K, restoring much of the lost scene dynamics, while maintaining precise camera control. + +# 3.6. Miscellaneous improvements + +In addition to our core analysis, we introduce several auxiliary techniques that enhance model performance. + +Separate text and camera guidance. Text and camera signals require different guidance weights due to their dis + +![](images/68916703f5541477f8f661f8e721d18c59c45cea7bc6d959220446f4f42366a8.jpg) +Figure 6. RealEstate10k [199] videos (upper 2 rows) contain diverse camera trajectories, but are strongly biased towards static scenes. To mitigate this bias and also increase the concepts diversity, we curate 20K videos with stationary cameras, but dynamic content (lower 2 rows). Such datasets are easy to construct, and surprisingly effective. Section 4.3 shows that integrating the dataset into our training improves visual quality on out-of-distribution prompts by $17\%$ . + +tinct nature, motivating us to separate their classifier-free guidance (CFG) [9, 44]. We formulate the equation as: + +$$ +\begin{array}{l} \hat {s} (\boldsymbol {x} \mid \boldsymbol {t}, \boldsymbol {c}) = (1 + w _ {y} + w _ {c}) s _ {\theta} (\boldsymbol {x} \mid \boldsymbol {t}, \boldsymbol {c}) \tag {1} \\ - w _ {y} s _ {\theta} (\boldsymbol {x} | \boldsymbol {c}) - w _ {c} s _ {\theta} (\boldsymbol {x} | \boldsymbol {t}), \\ \end{array} +$$ + +where $\hat{s}(.)$ denotes the final update direction used during synthesis, $s_{\theta}$ represents the model's predicted update direction, $\pmb{t}$ and $\pmb{c}$ are text and camera conditions, and $w_{y}$ and $w_{c}$ are their respective CFG weights. We zero-out the tensor for unconditional generation. + +ControlNet with feedback. Traditional ControlNet [188] conditioning, used in recent camera control methods [6, 39, 149], only processes conditioning signals without accessing the main branch. Our experiments show that using a bidirectional ControlNet produces better camera representations. + +
MethodHuman Preference
CAMQTAVQOverall
Ours vs. VD3D (FIT)89.5%79.0%87.5%97.5%95.0%
Ours vs. VD3D (DiT)65.0%87.5%83.5%95.0%92.5%
+ +Table 1. User study. We compare our approach to the original VD3D (FIT) and reimplemented VD3D (DiT) on top of our base model. We conduct a user study where participants indicate their preference based on camera alignment (CA), motion quality (MQ), text alignment (TA), visual quality (VQ), and overall preference (Overall). + +This modification behaves as a feedback mechanism [71] provided by the main synthesis branch to the camera processing branch. + +Dropping context in the camera branch. Applying cross-attention over the context information (text prompts, resolution, etc.) in the camera DiT-XS blocks worsens visual quality and camera steering due to harmful interference of the context embeddings with camera representations. + +# 4. Experiments + +Datasets. Our base VDiT model was trained on a large-scale dataset of text-annotated images and videos. VDiT-CC is fine-tuned from VDiT on RealEstate10K [199], contains $\approx 65\mathrm{M}$ video clips with per-frame camera parameters since it is the setup used by existing methods [6, 39, 149]. + +Metrics. To assess the performance, we rely on a wide range of automatic quantitative metrics. We use FID [43], FVD [136], and CLIP score [42] to evaluate visual quality, and rotation and normalized translation errors [39] of ParticleSfM [192]-reconstructed trajectories to assess camera steerability. We evaluate them both on RE10K and MSR-VTT [161], since the latter allows to assess zero-shot generalization on out-of-distribution data. Moreover, we conduct a user study with details in the appendix in Sec. J. + +# 4.1. Baselines + +We select three camera-control methods: MotionCtrl [149], CameraCtrl [39], and VD3D [6]. MotionCtrl and CameraCtrl use a UNet-based video diffusion backbone [37], while VD3D builds on top of FIT [21, 93] and as such, is easily extendable to our video DiT [100] setup. Hence, we re-implement VD3D on top of our VDiT model to obtain an additional "VD3D+DiT" baseline. Moreover, we provide comparisons for an open-source model, i.e., CogVideoX [169]. See Sec. C of the appendix for more details. + +# 4.2. Main results + +We present quantitative comparisons with the baselines in Tab. 2. One can observe that just switching from the 4B- + +parameter pixel-space FIT [21] backbone, employed by the original VD3D approach, to our larger 11.5B-parameter latent-space DiT yields clear improvements across most metrics. Next, the results demonstrate that AC3D establishes a new state-of-the-art in performance against all baselines. Evaluating the quality of camera motion from still images is difficult, so we instead visualize all qualitative results in the website provided within our supplementary material. Therein, we can observe that AC3D better follows pose conditioning and achieves higher visual fidelity. We conduct user studies against VD3D+FIT (the original model) and VD3D+DiT (our improved re-implementation on top of the bigger video transformer). The results are presented in Table 1: AC3D outperforms them across all qualitative aspects, achieving a $90\%+$ overall preference score. Finally, we encourage the reader to assess the visual quality by observing videos on our website. + +# 4.3. Ablations + +No camera conditioning. The first ablation we conduct is to drop all camera conditioning, which makes the model equivalent to the vanilla VDiT. This is needed to understand the degradation of visual quality and text alignment. The results (Tab. 2, row w/o camera cond) show that our model loses less only $\approx 7\%$ of the original visual fidelity on MSR-VTT (as measured by FVD), while (as expected) greatly improving on its in-domain RE10K data. In comparison, VD3D-DiT (the closest baseline) loses $\approx 20\%$ of its visual fidelity on MSR-VTT. + +Importance of biasing the noise towards higher levels. As Sec. 3.3 shows, we use the truncated normal distribution with location of 0.8 and scale of 0.075 with the [0.6, 1] bounds for training AC3D. We ablate the importance of biasing the noise sampling towards high noise and observe higher motion, visual quality, and camera controllability. + +Importance of truncating the noise schedule. We change the training and inference procedure by using no truncation during noise sampling. Instead, we condition the model with camera inputs over the whole noise range and observe decreased visual quality. + +No camera guidance. We assess the importance of classifier-free guidance [44] on the camera conditioning in Tab. 2 (w/o camera CFG). It attains the same visual quality on both indistribution (RE10K) and out-of-distribution (MSR-VTT) data, but degrades camera following, resulting in $\approx 5\%$ worse pose reconstruction errors. + +Training without our data with scene motion. To understand how well our curated data with scene motion but stationary cameras mitigates static scene bias, we train AC3D exclusively on RE10K, and report the results in Tab. 2 (w/o our dynamic data). The model maintains similar visual quality and text alignment on RE10K (in-domain data), but + +
MethodRealEstate10K [199]MSR-VTT [161]
TransErr ↓RotErr ↓FID ↓FVD ↓CLIP ↑TransErr ↓RotErr ↓FID ↓FVD ↓CLIP ↑
MotionCtrl (U-Net)0.4770.0942.9961.7026.460.5930.13716.85283.1224.11
CameraCtrl (U-Net)0.4650.0892.4855.6426.810.5870.13212.33201.3325.05
VD3D (FIT)0.4090.0431.4042.4328.070.5040.0507.80165.1826.89
VD3D (CogVideoX)0.4670.0631.6643.1428.080.5010.0687.45148.1127.65
AC3D (CogVideoX) (ours)0.3740.0391.2738.2028.620.4310.0395.52116.0428.38
MotionCtrl (VDiT)0.5040.1261.7443.8127.690.5890.1469.92150.2027.25
CameraCtrl (VDiT)0.5130.1381.6242.1027.730.5660.1438.15146.7727.51
VD3D (VDiT)0.4210.0561.2138.5728.340.4860.0476.88137.6227.90
AC3D (VDiT) (ours)0.3580.0351.1836.5528.760.4280.0385.34110.7128.58
w/o camera cond+0.233+0.153+4.02+53.83-1.63+0.266+0.157-0.48-8.53+0.35
w/o biasing noise+0.093+0.015+0.02+1.78-0.32+0.138+0.033+0.59+16.92-0.54
w/o noise truncation+0.020-0.003+0.06+1.69-0.20+0.016+0.005+0.76+6.63-0.18
w/o camera CFG+0.014+0.004+0.49+4.57-0.54+0.025+0.003+0.03+1.42-0.27
w/o our dynamic data-0.005-0.004-0.06+0.22-0.20+0.004-0.001+0.89+4.40-0.55
w/o metric scaled data+0.013+0.005+0.17+4.650.00+0.023+0.002-0.010.00-0.12
w/o dropping camera context+0.013+0.001+0.04+2.46-0.65+0.029+0.003+1.25+7.41-0.36
w/o limiting camera cond to 8 blocks-0.001+0.001+0.09+0.56-0.02+0.0030.000+0.32+9.23-0.33
w/ 2D training+0.129+0.068+2.60+33.85-1.17+0.128+0.093-0.26-3.83+0.21
+ +Table 2. Quantitative evaluation. We evaluate all the models using camera pose and visual quality metrics based on unseen camera trajectories. We compute translation and rotation errors based on the estimated camera poses from generations using ParticleSfM [192]. We evaluate both in-distribution performance with RealEstate10K [199] and out-of-distribution performance with MSR-VTT [161]. + +performance on out-of-distribution samples from MSR-VTT worsens ( $\approx 17\%$ worse FID and $\approx 4\%$ worse FVD). The quality of scene motion is better assessed by referring to our qualitative video comparisons in the supplementary. + +Importance of metric scaled cameras. We train AC3D using the original RE10K's camera parameters without our scaling procedure and present the results in Tab. 2 (w/o metric scaled data). This is a more ambiguous conditioning signal, and results in worse visual quality ( $\approx 10\%$ FVD on RE10K) and camera following performance ( $\approx 12\%$ worse trajectory reconstruction). + +Providing context into the camera branch. As discussed in Sec. 3.6, we chose not to input the context information (text embeddings, resolution conditioning, etc.) into the camera branch to avoid potential interference with the camera representations. As Tab. 2 (w/o dropping camera context) shows, providing this information indeed results in $\approx 4\%$ worse camera following and $\approx 15\%$ lower visual quality. + +Importance of limiting conditioning to the first 8 VDiT blocks. Following our insights in Sec. 3.4, we condition AC3D only in the first 8 blocks. Trying to condition in all the 32 DiT blocks (w/o limiting camera cond to 8 blocks) worsens the visual quality by $\approx 10\%$ , while keeping the quality control at the same level. This suggests that the middle and late VDiT layers indeed rely on processed camera information and conditioning them on external camera poses might lead to interference with other visual features. + +Joint training with 2D data. To mitigate visual quality and scene motion degradation, we attempted to perform joint fine-tuning on 2D video data (without camera annotations) + +which was used in base VDiT training by applying dropout on camera inputs for it. Prior work shows performance benefits with this strategy [150] and, as Tab. 2 (with $2D$ training) shows, it indeed helps to maintain slightly higher visual fidelity in our case ( $\approx 3\%$ better FVD on MSR-VTT). However, camera steering severely deteriorates, leading to up to $3\times$ worse results for translation/rotation errors. + +# 5. Conclusions + +Our findings demonstrate that principled analysis of camera motion in video diffusion models leads to significant improvements in control precision and efficiency. Through enhanced conditioning schedules, targeted layerspecific camera control, and better-calibrated training data, AC3D achieves state-of-the-art performance in 3D camera-controlled video synthesis while maintaining high visual quality and natural scene dynamics. This work establishes a foundation for more precise and efficient camera control in text-to-video generation. We discuss the limitations of our approach in Appendix B. In future work, we plan to focus on further improving data limitations and developing control mechanisms for camera trajectories far outside of the training distribution. + +# 6. Acknowledgements + +DBL acknowledges support from NSERC under the RGPIN program, the Canada Foundation for Innovation, and the Ontario Research Fund. + +# References + +[1] Jimmy Lei Ba. 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This work represents an innovative attempt to develop an adaptive cross attack framework via multi-modal response decoupling, generating multi-modal adversarial patches to evade RGB-T trackers. Specifically, a modal-aware adaptive attack strategy is introduced to weaken the modality with high common information contribution alternately and iteratively, achieving the modal decoupling attack. In order to perturb the judgment of the modal balance mechanism in the tracker, we design a modal disturbance loss to increase the distance of the response map of the single-modal adversarial samples in the tracker. Besides, we also propose a novel spatio-temporal joint attack loss to progressively deteriorate the tracker's perception of the target. Moreover, the design of the shared adversarial shape enables the generated multi-modal adversarial patches to be readily deployed in real-world scenarios, effectively reducing the interference of the patch posting process on the shape attack of the infrared adversarial layer. Extensive digital and physical domain experiments demonstrate the effectiveness of our multi-modal adversarial patch attack. Our code is available at https://github.com/Xinyu-Xiang/ACAttack. + +# 1. Introduction + +The adversarial attack on visual object tracking (VOT) [1, 26] aims to mislead the prediction results of the tracker through the generated adversarial disturbance, find the model vulnerabilities, and then promote the security of the tracking model in real-life. Single-modal tracking attack methods have been extensively studied, but with the wide application of multi-modal devices [19, 20, 24], multimodal trackers are widely used in safety-critical real-world + +![](images/c344516e1824eddade6022528581e550f426aeec60e7d6e47551d4607884a8b0.jpg) +Figure 1. Our attack strategy against RGB-T trackers. An adaptive attack strategy, sensitive to modality, is introduced to alternately and iteratively suppress the modality with a high contribution of shared information. Additionally, a modal disturbance loss is crafted to enlarge the response map distance for single-modal adversarial samples within the tracker. + +fields such as autonomous driving and urban security [16]. + +To address the urgent need to explore the security of trackers, adversarial attack techniques for trackers have emerged in rapid succession, including traditional gradient-based attack approaches and deep-network-based attacks. The former methods [10, 11] utilize hand-crafted parameters and apply many times of gradient ascent to maximize an adversarial loss function for misguiding deep networks. Although it can achieve certain attack effects for specific types of trackers, it is challenging to comprehensively explore and attack the potential vulnerabilities of the different trackers due to the limitations of inflexible pattern design. Nonetheless, the latter one [6] applies tremendous data to train an adversarial patches-generator including flexible architectures and optimization strategies to better automatically search for model weaknesses and realize tracker attacks. Therefore, in comparison with a traditional gradient-based attack approach, deep-network-based paradigm can more automatically and flexibly excavate the security issues within the tracker. + +Although prior efforts for adversarial attack methods are effective in interference trackers, several challenges still need to be addressed. Notably, existing adversarial attack methods [5, 15, 25] on tracking are designed for RGB modality, whereas the methodologies for attacking RGB-T multi-modal trackers are less explored so far. Considering the widespread deployment of multi-modal tracking technology [17, 27, 28] in several safety-critical areas, it is urgent to explore and implement adversarial attacks of multimodal tracking to understand the potential vulnerabilities of the trackers. However, as shown in Fig. 1, the unique modal coupling and structural design of RGB-T trackers make it a great challenge to successfully find model vulnerabilities. Firstly, due to the modal equilibrium mechanism and coupled multi-modal information, it is difficult to successfully jam the RGB-T tracking model itself. Specifically, the modal balancing strategy in the multi-modal tracker can effectively prevent the attack of adversarial perturbation in a single modal. Secondly, the coupling of multi-modal information can effectively weaken the attacks against the consensus region of the target. Thirdly, the deployment of patches in the physical world is also challenging because the stacked placement of multi-modal patches has a probability of compromising the expression of infrared adversarial shapes, reducing their synergy performance. + +Considering these challenges, we propose ACAttack, an adaptive cross attack framework via multi-modal response decoupling. It aims to generate multi-modal adversarial patches to evade RGB-T trackers in both digital and physical domains. Specifically, this framework can gradually and adaptively optimize, discover plenty of rough adversarial samples, and then map them to the high-dimensional adversarial space of different modalities according to the modal response contribution factor, forming multi-modal adversarial patches. Secondly, a modal-aware adaptive attack strategy is introduced to weaken tracker's deep semantic attention to the modality with high common information contribution according to the contribution degree of modal response alternately and iteratively, achieving the modal decoupling attack. When the contributions of two modalities are similar, we design a modal disturbance loss to search the modal imbalance vulnerabilities of the tracker, expand the distance of the response map of the single-modal adversarial samples in the tracker, and perturb the judgment of the balance modal in the tracker. We also design a spatio-temporal joint attack loss to build progressively enlarged pseudo-GT between consecutive frames, which progressively deteriorates the tracker's perception of the target. Thirdly, the design of the shared adversarial shape is deployed to eliminate the interference of visible patches on the expression of infrared adversarial shapes. After the shape is shared, it can not only reduce the consumption of the adversarial shape's inter-modal attack ability but also realize + +attacks other than texture in the visible modal. + +In summary, we make the following contributions: + +- We make an innovative attempt to propose an adaptive cross attack framework via multi-modal response decoupling. It can generate multi-modal adversarial patches to mislead RGB-T trackers effectively. +- We develop a novel modal attack flow, in which modal-aware adaptive attack strategy and modal attack constraints alternately disturb the modes with high contribution to achieve modal decoupling and destroy modal balance mechanism of tracker, respectively. +- We design the shape-shared stack strategy to linkage the visible and infrared adversarial shapes, reducing the attack consumption of multi-modal patches mutual deployment in physical scenarios. +- Experimental results show that multi-modal patches can efficiently fool RGB-T trackers in standard RGB-T tracking datasets and real scenes. + +# 2. Related Work + +# 2.1. Visual Object Tracking + +Given the tracked object in the first frame, object tracking aims to recognize and locate the object in subsequent frames. Many RGB tracking methods [2, 7, 14, 18, 21] have been proposed and achieved commendable tracking performance. However, RGB sensors struggle to capture objects effectively under challenging conditions such as occlusion and low light, limiting the performance of RGB trackers. To address this, the RGB-T tracking paradigm is introduced, which is not restricted to a single RGB modality but instead integrates the complementary information from both RGB and thermal modalities. This fusion enables more robust tracking capabilities. ViPT [29] introduces a vision prompt tracking framework that leverages the foundational model with strong representation capabilities, enabling interaction between the thermal and RGB modalities through a modality-complementing prompter. BAT [3] proposes a universal bidirectional adapter, which enables mutual prompt between the thermal and RGB modalities and further improves tracking performance. SDSTrack [9] designs a complementary masked patch distillation strategy based on self-distillation learning, which enhances the tracking robustness in extreme weather. + +# 2.2. Adversarial Attacks + +Currently, adversarial attacks in the tracking task primarily target RGB trackers. For instance, APYVOT [4] proposes an optimization objective function with a dual-attention mechanism to generate perturbations, disrupting tracking by interfering solely with the initial frame. MTD [8] introduces a maximum textural discrepancy loss function that misleads the visual trackers by decorrelating the template + +![](images/89724a5020b0aa2d41c2cccabb03770003a311051704048345ec27280933c31c.jpg) + +![](images/51abf7b5b1b9ea20cd809cc7842a0f6369b3ce07abf87277bc899e287d84adda.jpg) +Figure 2. The overall framework of our ACAttack. + +and search frame at hierarchical feature scales. These methods, however, fail to disrupt the significant feature enhancement resulting from the interactions between RGB and thermal modalities, which limits their effectiveness against RGB-T trackers. Therefore, it is essential to develop the attack strategy specifically designed for RGB-T tracking. + +# 3. Methodology + +# 3.1. Coarse-to-Fine Modality Attack Framework + +With the help of the progressive modality information integration strategy, the multi-modal trackers gradually strengthen the common scene representation and target response, thereby achieving a robust tracking performance superior to that of the single-modal trackers. Consequently, a coarse-to-fine architecture is designed to progressively degrade the modality integration capability of RGB-T models named ACAAttack, which can be divided into two stages. The overall architecture of our ACAAttack is illustrated in Fig. 2 and Algorithm 1. First, we employ projected gradient descent (PGD) in stage1 to identify a set of adversarial examples $\{p_i\}_{i=1}^k$ with sufficient aggressiveness, narrowing the search space for refined attacks and increasing the likelihood of discovering strong adversarial examples, formulated as: + +$$ +\left\{p _ {i} \right\} _ {i = 1} ^ {k} = P G D \left(p _ {i} ^ {\text {i n i t}}\right), \tag {1} +$$ + +where $p_i^{init}$ is randomly initialized with noise patches. The generated patches are subsequently loaded onto the visible image $I_{vi}$ to form a visible adversarial sample $I_{vi}^{adv}$ . This + +process can be formulated as follows: + +$$ +I _ {v i} ^ {a d v} = p _ {i} \odot M + I _ {v i} \odot (1 - M), \tag {2} +$$ + +where $M$ is the binary mask for applying adversarial patch. $\odot$ represents the element-wise Hadmard product. The adversarial visible image $I_{vi}^{adv}$ concat with clean infrared image $I_{ir}$ are sent to RGB-T tracker $T(\cdot)$ to predict final bounding box $Bbox_{pred}$ of target, which is expressed as: + +$$ +B b o x _ {p r e d} = T \left(I _ {v i} ^ {a d v}, I _ {i r}\right). \tag {3} +$$ + +We optimize this process by minimizing the conventional attack loss $L_{att}$ relative to the center point, which is defined as: + +$$ +L _ {a t t} = - \left\| \left(C p (B b o x _ {p r e d}) - C p (B b o x _ {g t})\right) \right\| _ {2} ^ {2}, \tag {4} +$$ + +where $C_p$ denotes the operator to obtain the center point of bounding box $Bbox$ . Specifically, when the attack loss $L_{att}$ reaches a predefined threshold, the iteration is halted, and a rough adversarial sample is generated. This process is repeated $k$ times to generate a set of $k$ rough adversarial samples. Considering the different imaging principles of infrared and visible modalities, the multi-modal patches will be specially designed according to their differences in principles. Specifically, the visible modal mainly employs the attack texture to interfere. For the infrared modal, it is difficult to detect the texture, so the adversarial shape is used to attack. Subsequently, the set of adversarial samples generated in the coarse attack stage (stage1) is fed into the + +subsequent fine attack process (stage2) for further refinement, resulting in the generation of multi-modal adversarial patches with strong attack performance. Finally, through continuous iterative optimization, the multi-mode patch will share the same attack shape, while the visible patch will also possess adversarial texture to confuse the tracker. The fine-grained attack phase targets the modality of the multi-modal tracker and consists of modal decoupling attacks and modal balance interference, which will be detailed in the subsequent sections. + +# 3.2. Modal Decoupling Attack + +The RGB-T tracker implicitly couples the contributions of the two modalities, thereby enhancing tracking accuracy. Given the significant role of modal contribution in the tracker, we propose a modal decoupling attack to adaptively diminish the influence of advantageous modalities. Specifically, we use the coarse adversarial samples from the stage1 as input for the stage2, feeding them simultaneously into the adversarial texture generation network $G_{tex}^{Adv}$ and the adversarial shape generation network $G_{shape}^{Adv}$ . For attacking the infrared modality, the rough adversarial sample set from the first stage is encoded into $r$ dimensions via continuous downsampling and an MLP, controlling the adversarial shape. The infrared patch $p_{ir}$ generation process can be expressed as follows: + +$$ +p _ {i r} = G _ {s h a p e} ^ {A d v} \left(\left\{p _ {i} \right\} _ {i = 1} ^ {k}\right). \tag {5} +$$ + +The adversarial texture generation network generates adversarial textures to attack the visible modality using residual connections and upsampling [23], which is defined as: + +$$ +p _ {v i} = \left(1 - p _ {i r}\right) \odot G _ {\text {s h a p e}} ^ {\text {A d v}} \left(\left\{p _ {i} \right\} _ {i = 1} ^ {k}\right), \tag {6} +$$ + +where the visible patch with adversarial textures is $p_{vi}$ . + +Subsequently, the modal contribution of the current network input is calculated as the reciprocal of the difference between the response map obtained from single-modal data and the response map from dual-modal input. A larger reciprocal distance indicates that the response maps from dual-modal and single-modal inputs are more similar, suggesting a greater contribution from the current single modality to the tracker. The modal response contribution can be expressed as follows: + +$$ +c _ {m} = \frac {1}{\operatorname {d i s} (R (m , m) , R (v i , i r))}, \tag {7} +$$ + +where $c_{m}$ represents the contribution value of $m \in \{vi, ir\}$ modal to the tracker. $dis$ stands for the distance function and is used to measure the Euclidean distance between response maps. $R(\cdot, \cdot)$ shows the response map acquired by the tracker under the current input. + +To normalize the modal contribution, a softmax operation is applied to the reciprocal distance, yielding the final + +Algorithm 1: The ACAcAttack Algorithm +Input: Random patches $p_i^{init}$ , parameters $k$ , $M_{stage1}$ , $M_{stage2}$ , $\xi$ , $\zeta$ +Output: Optimized multi-modal patches $p_{vi}, p_{ir}$ +1 Iteration: +2 Initialize a random patch $p_i^{init}$ ; +3 $i = i + 1$ ; +4 Iteration: +5 Generate $p_i$ through Eq. (1); +6 Use Eq. (2) to generate adversarial sample $I_{vi}^{adv}$ ; +7 Calculate $Bbox_{pred}$ using Eq. (3); +8 Optimize $PGD(\cdot)$ with Eq. (4); +9 Until: $L_{att} < \xi$ or iter $\geq M_{stage1}$ +10 Until: $i \geq k$ +11 Determine $\{p_i\}_{i=1}^k$ after optimization in stage1; +12 Iteration: +13 iter $= iter + 1$ ; +14 Obtain $p_{ir}, p_{vi}$ via Eqs. (5) and (6); +15 Apply multi-modal patches $p_{ir}, p_{vi}$ on $I_{ir}, I_{vi}$ ; +16 Calculate $c_{vi}, c_{ir}$ using Eq. (7); +17 Send to Tracker $T(\cdot)$ to predict bounding box; +18 if $|c_{vi} - c_{ir}| < \zeta$ ; +19 Optimize $G_{shape}^{Adv}$ with Eq. (9); +20 elif $c_{vi} - c_{ir} > \zeta$ ; +21 Optimize $G_{tex}^{Adv}$ with Eqs. (4) and (10); +22 elif $c_{ir} - c_{vi} > \zeta$ ; +23 Optimize $G_{shape}^{Adv}$ with Eqs. (4) and (10); +24 Until: iter $\geq M_{stage2}$ + +modal contribution score, formulated as: + +$$ +c _ {n o r m} = \operatorname {s o f t m a x} \left(c _ {v i}, c _ {i r}\right). \tag {8} +$$ + +Finally, an automatic discriminant attack is executed based on the modal contribution score. As illustrated, when the visible contribution is higher in the input data, only the visible modal is attacked, specifically by optimizing the generation of adversarial textures. When the infrared contribution is higher in the input data, only the adversarial shape is modified to attack the infrared modal, thereby reducing its contribution to the tracker. Given that the tracker employs a modal balance mechanism, the contributions of the two modalities may be similar in certain scenarios, as detailed in the subsequent section. + +# 3.3. Modal Balance Interference + +Previous work on tracking attacks has attempted to design explicit attack losses to detect model vulnerabilities, but this approach often fails to account for the inherent characteristics of the model, making it challenging to execute effective attacks. Inspired by the concept of implicit attacks [25] and the multi-modal aggregation properties in + +RGB-T tracker [22], we develop a loss function with modal-balanced interference to target multi-modal trackers. In cases where the contributions of infrared and visible modal are similar (i.e., modal balance), the response map of single-modal input closely resembles that of dual-modal input. To disrupt this balance, we extract the response maps of the two single-modal adversarial examples and increase the distance between them. The details are provided as follows: + +$$ +L _ {m i} = - \left\| R \left(v i _ {a d v}, v i _ {a d v}\right) - R \left(i r _ {a d v}, i r _ {a d v}\right) \right\| _ {2} ^ {2}. \tag {9} +$$ + +Notably, the infrared and visible patches in our method share the same adversarial shape to achieve simultaneous attacks on both modalities. Therefore, under conditions of modal balance, only the adversarial shape is optimized. Additionally, a spatio-temporal joint attack loss $L_{st}$ is employed in conjunction with the modal jamming loss $L_{mi}$ to disrupt the tracker's semantic perception. The specific design is presented in the following formula: + +$$ +L _ {s t} = \left\| \sum_ {i = 1} ^ {s} B b o x _ {p r e d} (w, h) - r _ {i} * B b o x _ {g t} (w, h) \right\| _ {2} ^ {2}, \tag {10} +$$ + +where $s$ denotes the consecutive $s = 5$ frames extracted from a video. $r_i$ represents the scaling factor over time to construct the pseudo-GT, which is set as [1.90, 1.95, 2.00, 2.05, 2.10]. + +# 3.4. Implementation Process in Real-world + +After completing the digital domain optimization, the multimodal adversarial patches require deployment in the real world. However, during real-world deployment, visible and infrared patches are stacked, leading to inevitable interactions between the two modalities, as illustrated in Fig. 3. Specifically, the coverage of visible patches impacts the adversarial shape expression of infrared patches, while the presence of infrared patches hinders the rendering of the adversarial texture in visible modality. To address these challenges, we propose a shape-shared stacking strategy, where both the visible and infrared patches adopt the same attack shape. This design not only effectively mitigates interactions between infrared and visible patches in the real world but also enhances the attack shapes of visible patches, thereby improving overall attack performance. + +# 4. Experiments + +# 4.1. Experimental Settings + +# 4.1.1. Datasets and Evaluation Metrics + +We conduct experiments on RGBT234 [12] and LasHeR [13] datasets and assess the effectiveness of our ACAttack by evaluating precision rate (PR) and success rate (SR), both of which are commonly used metrics in tracking tasks. Taking PR as an example, we + +![](images/d470705f12b1b300b95534ddb97c4a2699910e4e6ccda977f227ae26d4cb9532.jpg) + +![](images/33fd2f375730bee087e11a98a35e6edcbe43d2da12561454172fedc8fc9231ac.jpg) +VI on IR + +![](images/f47fed5e15b83cdc966600b10b48230bac13df87d5bf3c7dd049d110db4d9ce1.jpg) + +![](images/92e3c6e7196ddfdb7bb345e4c518f60529abae4065d0b6b0eada7eead6b613b9.jpg) +IR on VI + +![](images/40821a79e64f48b8da64814d87a2c2c1d6b209c40f83b609db0e4879db63ce81.jpg) + +![](images/fa0cf77ca4b32b732a765bd36dd7bdfd3dcfd54c3d62ad0c1d21287968a7e519.jpg) +Ours + +![](images/c883cfd57486865bd20823dd356d172a367ac79998c92b08debea92727b3fbb1.jpg) +Figure 3. Process of physical implementation. + +![](images/c4eee172f1a63caf416d7705ac5c5a4cb3db0beed313dcc8d3253a8746fc10d4.jpg) +(a) ViPT patch +Figure 4. Visualization of generated patches. + +![](images/1f1cba12750e6777c7d348e11705f7579722488aeb97c43eb0c5ba7f185d8c9c.jpg) +(b) BAT patch + +![](images/1a25403a0068d4992e805125a13cfebb745348e2e333de0c52b4c0685aebb6dc.jpg) +(c) SDSTrack patch + +calculate the Euclidean distance of the center between the predicted bounding box and ground truth box in both RGB and thermal modalities, using the smaller distance to represent the precision RGBT234 provides 234 pairs of RGB and thermal video, with a total frame of about $234\mathrm{K}$ and a maximum of 8K per sequence. LasHeR is comprised of 1224 visible and thermal video pairs, totaling over $730\mathrm{K}$ frame pairs. Since the tracking performance on the background is not of interest, LasHeR performs strict alignment of the object area, allowing the object to share the same ground truth of the bounding box in both visible and thermal modalities. Therefore, we use PR and SR as evaluation metrics. + +# 4.1.2. Victimized Trackers and Comparison Attackers + +We select several state-of-the-art trackers as targets for our attack, including ViPT [29], BAT [3], and SDSTrack [9]. To demonstrate the challenges in exploiting vulnerabilities in RGB-T trackers, we use a patch composed of random noise as a baseline for comparison, emphasizing the need for meticulous exploration. Furthermore, we compare the performance of our proposed ACAttack with the representative attack method MTD [8], which is specifically designed + +![](images/da6a446625886f71756aead6a4e9fa99c2780b36928a437cb31b58f954fcae24.jpg) +(a) ViPT on RGBT234 + +![](images/1a22cf3b0944a5bec6d422a63b67353ae6f7db902f57bf12db9a0a3abede9e4d.jpg) +(b) BAT on RGBT234 + +![](images/011457f325e1dc34bddb5ac62bfa101a76791122d58e04157c92d3d0388f4432.jpg) +(c) SDS on RGBT234 + +![](images/e522ecd422a23f3740a308ff9c1a063e2cb028f9532ad41a9413cd641d252e86.jpg) +Figure 5. Quantitative comparison of tracking performance on the RGBT234 dataset. The tracking performance of ViPT, BAT, and SDSTrack trackers is reported, including the original performance without attacks and the performance under attacks. Lower tracking metrics PR and SR represent better attack. Please zoom in for a better view. +Figure 6. Qualitative comparison of tracking performance on the RGBT234 dataset. + +for RGB trackers, highlighting the advantages of our approach in the multi-modal setting. + +# 4.1.3. Implementation Details + +The multi-spectral video in the physical domain is captured by a DJI Mavic 3T UAV equipped with thermal and RGB cameras, and the video frame rate is 30 fps. The hyperparameters in adaptive iteration $\xi$ and $\zeta$ is 9 and 0.02. Training epoch in stage1 is set as $M_{\text{stage1}} = 180$ . Experiments are conducted on the RTX 3090 GPU with PyTorch. + +# 4.2. Comparisons in the Digital Domain + +We first validate the attack effectiveness of our ACAttack in the digital domain. It is important to note that we only train on the RGBT234 dataset and generate multi-modal patches $\{p_{vi}, p_{ir}\}$ . As shown in Fig. 4, the RGB patch exhibits color and texture, while the thermal patch has an irregular shape, which aligns with the imaging characteristics of each modality. Subsequently, the patches $\{p_{vi}, p_{ir}\}$ generated on RGBT234 are directly applied to the LasHeR dataset to verify their generalization. + +# 4.2.1.Quantitative Evaluation + +Fig. 5 illustrates a quantitative comparison of the RGBT234 dataset. The results clearly show that, under our attack, the tracking performance of existing state-of-the-art trackers suffers a significant degradation compared to clean tracking conditions. In contrast, random noise only leads to a modest decline in PR and SR, emphasizing that exploiting tracker vulnerabilities goes beyond the simplicity of random noise—it requires a more sophisticated, optimized ap + +proach. Additionally, the performance drop observed with MTD is smaller than that of our ACAttack, suggesting that attack methods designed specifically for RGB trackers may not effectively mitigate the feature enhancement resulting from RGB-T coupling. On the other hand, our ACAttack achieves substantial attack success. For instance, against ViPT, ACAttack reduces PR from 0.835 to 0.621 and SR from 0.617 to 0.417. Similarly, for SDSTrack, it lowers PR from 0.848 to 0.616 and SR from 0.625 to 0.426. The substantial performance drops suggest that our ACAttack succeeds in keeping the predicted bounding box far away from actual object, which will be further confirmed in subsequent qualitative results. + +# 4.2.2. Qualitative Evaluation + +As shown in Fig. 6, we present the tracking results of BAT and SDSTrack. The clean trackers perform exceptionally well in maintaining precise tracking, while our attack leads to a significant decline in tracking performance. This degradation can be attributed to our progressive generation framework, which iteratively weakens the tracker's deep semantic attention on modalities with high commonality by decoupling multi-modal responses. + +# 4.3. Generalization Evaluation + +We conduct generalization experiments on the LasHeR dataset, with quantitative and qualitative results shown in Fig. 7 and Fig. 8, respectively. Compared to random noise and MTD, our ACAttack leads to a significant drop in tracking performance across all trackers, even without training on LasHeR. Additionally, we present the IoU plots for both + +![](images/28049c3409491173fd313b73b9d8f4d6052356dd6d98451600c8e1c68fb1c206.jpg) +(a) ViPT on LasHeR + +![](images/eac88dcb4a67c9b330ed788edd168ef45fb74938a144720157eb3a4c466bc779.jpg) +(b) BAT on LasHeR + +![](images/441f9cb12578aae2668934ce3ac88e833dca1fd762f2b926d0004f5b281ad12a.jpg) +(c) SDSTrack on LasHeR + +![](images/0ae041af7cf0486b92cdd41c3dd040b2df52ce10d7f53dd3fa1e52eca829af99.jpg) +Figure 7. Quantitative comparison of tracking performance on the LasHeR dataset. The tracking performance of ViPT, BAT, and SDSTrack trackers is reported, including the original performance without attacks and the performance under attacks. Lower tracking metrics PR and SR represent better attack. Please zoom in for a better view. + +![](images/323f39373e80e2cf23c802d775e4e96c7945d673ba0d02d40dec1231ad08dfb8.jpg) +Figure 8. Qualitative comparison of tracking performance on the LasHeR dataset. +Figure 9. Qualitative comparison of tracking performance on the LasHeR dataset. The blue and red lines represent the IoU variation over frames of the predicted boxes under the clean trackers and the victimized trackers, respectively. + +clean and attacked tracking results, as shown in Fig. 9. It is clear that our ACAttack can maintain a sustained attack over extended periods. Due to the existence of our adaptive attack strategy and the modal balance interference loss, the response value of the tracker for the real target is reduced, and then the tracker is easy to deviate from the original target and is attracted by similar targets. + +# 4.4. Application in the Physical Domain + +After having verified our adversarial patches in digital scenes, we also extend experiments to demonstrate their efficacy in the physical domain. We directly apply the patches trained in the digital domain to the real world and use aero + +gel and paper to make thermal and RGB patches for deployment on pedestrians, respectively. A dual-spectral camera in DJI Mavic 3T is used for video capture. Thirty sets of videos of different scenes are taken as test samples. The orientation results of the test are shown in Fig. 10. It can be seen that the tracking prediction bounding box is enlarged and cannot be accurately positioned due to the interference of the multi-modal adversarial patch. Specifically, the optimization of spatio-temporal joint loss makes the patch learn the effect of expanding the tracker's prediction box. Therefore, in the physical world, the tracker will not be able to accurately locate the target after being affected by the adversarial patch. + +# 4.5. Ablation Studies + +We conduct ablation studies to assess the effectiveness of our unique design and parameter configuration, including: (I) loss function, (II) parameter K, (III) iteration mode, and (IV) applied modal. The ablation studies are performed on the RGBT234 dataset against ViPT, with quantitative results presented in Table 1. + +# 4.5.1. Loss Function + +The loss $L_{st}$ interferes with the tracker from both temporal and spatial dimensions, while $L_{mi}$ is used to disrupt the tracker's semantic perception. To demonstrate their effectiveness, we remove each of them individually, with the results shown in Table 1. In the absence of $L_{st}$ or $L_{mi}$ , the attack performance weakens, demonstrating their role in diminishing the enhanced target localization accuracy achieved through multi-modal interaction. + +![](images/fa1865e09e72f7edb94a1940891936ea2867a523c0a89c624cf6ced42d48b9ec.jpg) +Figure 10. Practical application in the physical domain. + +
MetricViPTConfig. I: loss functionConfig. II: parameter KConfig. III: iteration modeConfig. IV: applied modalOurs
w/o Lstw/o LmiK = 0K = 9crosscombineOnly RGBOnly TIR
PR0.8350.7090.7350.6720.6510.6450.7030.6910.6690.621
SR0.6170.4860.5050.4500.4250.4280.4820.4820.4620.417
+ +Table 1. Quantitative comparison of ablation studies, which is performed on the RGBT234 dataset against the ViPT tracker. + +# 4.5.2. Parameter K + +In our progressive attack framework, we first employ projected gradient descent to identify K sets of coarse adversarial examples with effective attack performance. In order to verify its effectiveness, we set the number of coarse adversarial samples K growth from 0 to 9 and 18. As shown in the Table 1, as K increases from 0 to 9 and 18, the tracker's PR and SR consistently decrease. This indicates that such coarse-grained adversarial examples can effectively narrow the search space for refined attacks, thus facilitating a more effective attack. Specifically, this progressive method for finding adversarial examples prioritizes identifying multiple sets of coarse adversarial representations from a broad spectrum of noise. Subsequently, multi-modal patch generation refines the adversarial details to produce the final adversarial patch, leveraging numerous samples that contain adversarial information. Consequently, this approach results in an enhancement in performance. + +# 4.5.3. Iteration Mode + +One of the key contributions of this paper is the adaptive iterative strategy for attacking the RGB-T tracker. To demonstrate the effectiveness of the adaptive strategy, we conduct ablation experiments using the iterative strategy. The alternating iteration strategy and the joint optimization strategy are selected for the comparison test. The former alternately optimizes the adversarial texture network and the adversarial shape network, while the latter simultaneously propagates the gradient flow to both networks. As shown in Table 1, our adaptive iteration approach can more effectively identify model vulnerabilities and generate more aggressive adversarial patches. Specifically, according to the contribution degree, our strategy can weaken deep semantic attention and break the balance of modality in tracker. + +# 4.5.4. Applied Modal + +In order to verify the multi-modal patch joint and single-modal patch attack performance, we try to conduct patch apply modal ablation experiment. Multi-modal patches $\{p_{vi}, p_{ir}\}$ are generated to simultaneously disrupt both RGB and thermal modalities. As shown in the Table 1, we use only one of these patches in an ablation setup. The adversarial patch of a single modal produces a certain attack effect and makes the tracker confused. Evidently, our multi-modal patch achieves the best attack performance, underscoring the necessity of designing joint multi-modal attacks for RGB-T trackers. + +# 5. Conclusion + +In this work, we present a pioneering framework for adversarial attacks on RGB-T multi-modal trackers by introducing an adaptive cross-attack mechanism through multimodal response decoupling. Our approach leverages a modal-aware adaptive attack strategy and introduces novel modal disturbance loss and spatio-temporal joint attack loss to progressively impair the tracker's capability to perceive the target. The shared adversarial shape design also enhances our method's practicality, allowing seamless deployment of multi-modal patches in the real world. Experiments across digital and physical domains confirm the robustness and effectiveness of our approach in evading RGB-T trackers, highlighting the potential and significance of adaptive, multi-modal adversarial attacks in advancing the understanding of tracker vulnerabilities. + +# Acknowledgments + +This work was supported by National Natural Science Foundation of China (62276192). + +# References + +[1] Luca Bertinetto, Jack Valmadre, Joao F Henriques, Andrea Vedaldi, and Philip HS Torr. Fully-convolitional siamese networks for object tracking. 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Visual illustration of the generated high-quality multiview images and normal maps from a given single-view image by our Acc3D through fewer than four inference steps. $\mathbb{Q}$ Zoom in for details. + +![](images/cbbc1b20286d3428387a09bcdcc061972eb0d66e05592571bbac39ec744920ec.jpg) +Generated multi-view images and normal maps + +![](images/bc26b08ca9dcdc5a50a19be6e357b5f7bd581d0485d90358de7d92cb431dd626.jpg) + +![](images/1f9bb5eace801ba6083bbadce310aa41019c36504ce4dd7dd45be8f771d73761.jpg) + +![](images/d2184505ea64502b4193a65c12693e279525b16ff47dadab869620427e69d0f7.jpg) + +![](images/8c0b5a7334523c6b56f17060471fa4a2a6963efed667000a74cc33687806b0e4.jpg) +Textured mesh + +![](images/06b7f61b2cab01f4e4e647b081740f837db236883c395448cb9349d2ce28647f.jpg) + +# Abstract + +We present Acc3D to tackle the challenge of accelerating the diffusion process to generate 3D models from single images. To derive high-quality reconstructions through few-step inferences, we emphasize the critical issue of regularizing the learning of score function in states of random noise. To this end, we propose edge consistency, i.e., consistent predictions across the high signal-to-noise ratio region, to enhance a pre-trained diffusion model, enabling a distillation-based refinement of the endpoint score function. Building on those distilled diffusion models, we propose an adversarial augmentation strategy to further enrich the gen + +eration detail and boost overall generation quality. The two modules complement each other, mutually reinforcing to elevate generative performance. Extensive experiments demonstrate that our Acc3D not only achieves over a $20 \times$ increase in computational efficiency but also yields notable quality improvements, compared to the state-of-the-arts. + +# 1. Introduction + +Single image-based 3D reconstruction stands as a pivotal domain within the realms of 3D computer vision and computer graphics [5, 19, 31, 33], boasting extensive applications in virtual reality, 3D gaming, content creation, and precision robotics. Despite humans' innate ability to perceive three-dimensional structures from a single image, the swift and accurate generation of consistent content remains a formidable challenge. + +Diffusion models [9] have demonstrated their strong capability in image generation and video synthesis [15], + +paving the way for diffusion-based 3D content creation. Various studies [10, 32, 33] have been dedicated to distilling consistent 3D representations, such as neural radiance fields (NeRF) [30] or 3D Gaussian splatting [12], from 2D image diffusion models or vision language models using the Score Distillation Sampling (SDS) loss [32]. Although these methods yield visually pleasing results, the distillation process tends to be time-intensive for generating a single shape, requires intricate parameter tuning to obtain satisfactory quality, and often faces issues with unstable convergence and quality degradation. Another stream of research [7, 25] aims to directly generate 3D geometries, such as point clouds and meshes. However, the necessity for large-scale, open-source, native 3D samples inevitably hampers the development of these methods. + +Recent research, exemplified by Syncdreamer [19], Wonder3D [20], MVDream [38], and Era3D [14], has focused on generating multiview-consistent images directly to facilitate single-view 3D reconstruction of diverse objects. These approaches leverage the pre-trained diffusion pipeline for single image generation to model the joint probability distribution of multiview-consistent images. By improving the multiview consistency in image generation, these methods can reconstruct 3D shapes from the produced multiview images using neural reconstruction methods [46]. To improve the accuracy of 3D object reconstruction, the diffusion frameworks used in Wonder3D and Era3D directly generate normal maps and multiview images. These are then exploited in tandem with both normal maps and multiview images to reconstruct the 3D object. However, the lengthy sampling time required for the integration of the reversed differential equation burdens all these diffusion-based multiview image generation methods. This typically involves an iterative process that progressively denoises a Gaussian noise sample into an image, emphasizing the importance of sampling acceleration. + +In this paper, we tackle this challenge by introducing a consistency-based endpoint score-matching mechanism to achieve the few-step generation, which focuses on enhancing the accuracy of score function in low-SNR regions. Specifically, to regularize the score function for greater accuracy, we employ consistency training techniques to enforce stable score estimation in high-SNR regions, which can act as a score corrector, refining the coarse generation from the endpoint pure noise state. We subsequently introduce an adversarial training technique to further boost the alignment of the manifold of generated samples [8], where the pre-trained diffusion model is also introduced as a discriminator to fully leverage the pre-trained geometric knowledge. Our Acc3D is composed of two main components: edge consistency-guided distillation and disentangled adversarial regularization. These two components complement each other—distillation stabilizes adversarial + +training, reducing the risk of mode collapse, while adversarial learning enhances the perceptual richness of the model. Working in tandem, these components create a balanced and sophisticated model that delivers both stability and detail. + +Comprehensive experiments show that our accelerated generative model outperforms the baseline model and most other image-to-3D diffusion models. It offers high-quality 3D content across multiple views and provides faster inference. Remarkably, even with only a few iterative steps, our accelerated model can generate high-quality multiview images from a variety of 2D images with different styles. + +In summary, the main contributions of this work are as follows. + +- we have proposed an edge consistency-based paradigm to achieve distillation-based acceleration of single imaged-to-3D diffusion models, driving generation speeds up to $20 \times$ while simultaneously elevating performance; +- we have conducted a comprehensive analysis, incorporating both intuitive and theoretical manners to ensure the technical soundness of the proposed method; and +- we have carried out extensive experiments to demonstrate the performance of the proposed algorithm on both synthetic and real datasets. + +# 2. Related Work + +Image-to-3D Generative Models. Diffusion models [9] have achieved substantial success in 2D image generation, prompting various efforts to extend pre-trained 2D diffusion models to 3D generation. DreamFusion [32] marks a pioneering endeavor in distilling a 2D image generation model to craft 3D content from a single text prompt. Building upon this groundwork, Magic3d [42] generates 3D shapes from single images, refining the 3D representation for each instance. These methods [27, 33, 44, 48] commonly employ the SDS loss to guide the optimization of their 3D representations, such as NeRF, mesh or Gaussian Splatting. Notably, NVS-Solver [28] utilizes video diffusion models integrated with data manifold constraints to directly generate consistent multi-views for both static and dynamic scenes. + +In order to produce 3D content without the necessity of training each sample, numerous existing studies [3, 14, 17, 19, 20, 37, 38, 49] directly generate multiview images from a single-view image. These image-to-3D diffusion models, trained on a large-scale 3D object dataset [4], exhibit impressive generalization capabilities. Syncdreamer [19] synchronizes the intermediate states of multiview images at every step of the reverse process through a 3D-aware fusion. MVDream [38] introduces self-attention into multiview images in order to improve consistency. Wonder3D [20] generates both multiview normal maps and the corresponding images under a cross-domain self-attention mechanism. Following Wonder3D, Era3D [14] implements a camera prediction module to alleviate image shape distortions and + +![](images/4f5c41b75b048d9582a096028047aafd3ea9b54ebc745570bd39a62bd84735fe.jpg) +Figure 2. Overview of our Acc3D. The training pipeline unfolds in two core components: edge consistency-guided distillation and adversarial training. Each component bolsters the other's advantages—the distillation procedure stabilizes adversarial training, mitigating the risk of mode collapse, while adversarial learning can enhance perceptual richness. Collectively, these elements craft a balanced, refined model that excels in both stability and detail. + +increases the image resolution up to $512 \times 512$ . While these image-to-3D models typically demand a long inference time, our accelerated generative model stands in contrast. It can generate high-quality multiview images and normal maps with fewer iterative processes. + +Diffusion Model Acceleration. The iterative process of progressive denoising is a key characteristic of diffusion models, making the acceleration of the sampling process a significant area of interest [24]. Several studies [18, 26, 39, 40, 45] have focused on direct noise-to-data mapping with the objective of generating high-quality images in a single step. The study by Song et al. [40] introduces a consistency model that condenses the diffusion model process to a single step, training a one-step model to emulate the multi-step outcomes of the original model. Liu et al. [18], on the other hand, aims to keep the image generation trajectory as linear as possible between the final and current points. + +Generative Adversarial Networks. Several recent studies [13, 34, 35, 47, 51, 52] have adopted a generative adversarial training approach to maintain and boost the outcomes of accelerated diffusion models. Notably, [47] incorporates feedback from the discriminator by backpropagating it through the forward diffusion chain. The length of this chain is adaptively adjusted to strike a balance between noise and data levels. Kim et al. [13] combined GANs and denoising score matching loss to improve overall performance. Sauer et al. [34, 35] used the pre-trained diffusion model as the discriminator and updated the parameters in both raw and latent space. Yin et al. [52] designed the discriminator similar to [34], minimizing the difference between the generator and pre-trained model by comput + +ing the KL divergence of two score functions. Despite the abundance of methods aimed at achieving stable adversarial training, GANs are still prone to issues such as model collapse and unstable training, which makes scaling and adapting to different distributions challenging. + +# 3. Preliminary + +In this section, we introduce the basic knowledge of stochastic differential equation (SDE)-based formulation of diffusion models, its integrator, and consistency models. + +Diffusion Models. Denote by $\mathbf{X}_t$ the latent noised variable, $t\in [0,T]$ as the scalar indicating the time-stamp. Then, we can formulate the forward diffusion process as the following SDE, gradually shifting the clean image $\mathbf{X}_0$ towards a random noise $\mathbf{X}_T$ : + +$$ +d \mathbf {X} _ {t} = f (t) \mathbf {X} _ {t} d t + g (t) d \boldsymbol {\omega}, \tag {1} +$$ + +where $d\omega$ represents the standard Wiener process, with $f(t)$ signifying the drift coefficient function, and $g(t)$ denoting the diffusion coefficient function. By reversing the forward SDE given in Eq. (1), we can generate the corresponding clean latent from the easily sampled random noise. This process results in the subsequent ordinary differential equation (ODE) formulations: + +$$ +d \mathbf {X} _ {t} = [ f (t) \mathbf {X} _ {t} - \frac {1}{2} g ^ {2} (t) \nabla_ {\mathbf {X} _ {t}} \log p (\mathbf {X} _ {t}) ] d t, \tag {2} +$$ + +where $\nabla_{\mathbf{X}_t}\log p(\mathbf{X}_t)$ denote the data gradient, usually approximated by a learnable score function of $\mathbf{S}_{\theta}(\mathbf{X}_t)$ parameterized with $\theta$ . Consequently, the analytical solution of Eq. (2) to the arbitrary timestamp $t$ can be expressed as + +$$ +\mathbf {X} _ {t} = \mathbf {X} _ {T} + \int_ {T} ^ {t} \frac {d \mathbf {X} _ {t}}{d t} d t, X _ {T} \sim \mathcal {N} (\mathbf {0}, I), \tag {3} +$$ + +where $\mathcal{N}(\mathbf{0},I)$ denotes the standard Gaussian distribution. + +Integrators of Diffusion Models. To derive the generation samples from the differential equation-based diffusion models, we can calculate the integral of the reverse ODE trajectory in Eqs. (3) and (2) as $\mathbf{X}_0 = \mathbf{X}_T + \int_T^0\left[f(\mathbf{X},t) - \frac{1}{2} g^2 (t)\mathbf{S}_\theta (\mathbf{X}_t)\right]dt.$ Based on the semi-linear property of the diffusion models, DPM-Solver [22, 23] gives an exact solution as + +$$ +\mathbf {X} _ {t - \Delta t} = \frac {\alpha_ {t - \Delta t}}{\alpha_ {t}} \mathbf {X} _ {t} - \alpha_ {t - \Delta t} \int_ {\lambda_ {t}} ^ {\lambda_ {t - \Delta t}} e ^ {- \lambda} \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} (\mathbf {X} _ {\tau}, \tau) d \lambda , \tag {4} +$$ + +where $\lambda := \log \left(\frac{\alpha_t}{\sigma_t}\right)$ represents the log-SNR (Signal-to-Noise Ratio); $\epsilon_{\theta}(\cdot)$ indicates the noise estimation neural network. By computing this integral using the Taylor series, we can finally derive the reverse diffusion results. + +Consistency Models are introduced to train diffusion models that can consistently estimate high-quality samples from different noise levels [21, 39, 40]. Specifically, the consistency model can be parameterized as + +$$ +\mathcal {F} _ {\boldsymbol {\theta}} \left(\mathbf {X} _ {t}, t\right) = \mathbf {c} _ {k} (t) \mathbf {X} _ {t} + \mathbf {c} _ {o} (t) \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} \left(\mathbf {X} _ {t}, t\right), \tag {5} +$$ + +where $\mathbf{c}_k(\Delta t) = 1$ and $\mathbf{c}_o(\Delta t) = 0$ ( $\Delta t > 0$ and is sufficient small) to ensure the model meets the boundary condition of $\mathcal{F}_{\theta}(\mathbf{X}_0,0)\coloneqq \mathbf{X}_0$ ; and $\epsilon_{\theta}(\cdot)$ represents a learnable neural network. Note that the ODE-Solver formulation in Eq. (4) can also be treated as a special case of consistency model, only if we set $\Delta t = t$ , i.e., projecting each data point back to clean state $t = 0$ . And we utilize this formulation in the rest of our paper. Consistency models can be trained from scratch or in a distillation manner. However, both methods aim to minimize the inconsistencies of estimations between adjacent steps, i.e., + +$$ +\mathcal {L} _ {c} = d \left(\mathcal {F} _ {\boldsymbol {\theta}} \left(\mathbf {X} _ {t}, t\right), \mathcal {F} _ {\boldsymbol {\theta} ^ {-}} \left(\mathbf {X} _ {t - \Delta t}, t - \Delta t\right)\right), \tag {6} +$$ + +where $\mathbf{X}_{t - \Delta t}$ can be derived by solving inverse steps from $\mathbf{X}_t$ using a pre-trained diffusion model or be directly interpolated with the same noise sample as $\mathbf{X}_t$ ; $\theta^{-}$ indicates to apply the stop gradient operation on the running mean of $\theta$ ; and $d(\cdot)$ represents a discrepancy measurement, e.g., Frobenius Norm [2] or LPIPS [53]. + +# 4. Proposed Method + +Accurately estimating the score function is particularly challenging in states of pure random noise (i.e., the low-SNR edge). As a result, in existing diffusion-based single image-to-3D models, the few-step reverse process suffers from accumulated errors in the score function, leading to imprecise results at the final stage of denoising and significantly degrading generation performance. To address this issue, we propose Acc3D, which progressively improves the estimation of the score function at the endpoint (low-SNR side) during training, thus enhancing generative per + +![](images/c5d3db269b96c3a00205b32d586ded931187d297cd6039fa7981afd2705383aa.jpg) +Figure 3. Illustration of the progressive score matching by our edge consistency distillation, in a data manifold view, where $\mathcal{M}_t$ indicates the data manifold with the timestamp $t$ , e.g., $\mathcal{M}_T$ and $\mathcal{M}_0$ represent the manifolds of pure noise and clean samples, respectively; $\mathbf{X}_{0|T}$ represents the few-step estimation of the clean sample from Gaussian noise $\mathbf{X}_T$ ; $\widetilde{\mathbf{X}}_0$ represents a relatively accurate training target of $\mathbf{X}_{0|T}$ , refined by the edge consistency region; and $\mathcal{E}(\cdot)$ is the generation error, e.g., distance between its corresponding manifold surface. (a) shows the single-step reverse trajectory by the endpoint (pure noise) score function; (b) represents the noised latent interpolation using noise $\mathbf{X}_T$ and $\mathbf{X}_{0|T}$ ; and (c) indicates the score estimation in the region with consistency characteristic. The left subfigure illustrates that before being adapted by the proposed strategy. The right subfigure shows that after being trained by our method, the error of the score function at the initial pure noise state is gradually decreased as $\mathcal{E}(\mathbf{X}_{0|T}) > \mathcal{E}(\mathbf{X}_{0|T}')$ . It indicates that the result $\mathbf{X}_{0|T}$ can gradually approach the data manifold. + +formance in a few-step generation. To be specific, we propose an edge consistency model as a score corrector, enabling regularization and distillation for enhanced accuracy of score estimation at endpoints, as outlined in Sec. 4.1. Building on these insights, we introduce an adversarial regularization process in Sec. 4.2, aimed at further minimizing the discrepancy between generated and real samples. These two modules work in synergy, strengthening each other to improve generative performance. + +# 4.1. Edge Consistency-guided Distillation + +In this section, we propose edge consistency-guided distillation to reduce integral errors in the one-step inference outcomes of diffusion models. + +Technically, let $\mathbf{X}_{0|T}$ be the one-step coarse generation result from noisy latent at timestamp $T$ to 0 through the first-order approximation of ODE-Solver in Eq. (4), written as + +$$ +\mathbf {X} _ {0 \mid T} = \mathcal {F} _ {\boldsymbol {\theta} _ {G}} \left(\mathbf {X} _ {T}, T\right), \tag {7} +$$ + +where $\theta_{G}$ represents the parameters of the generator. Let $\mathbf{X}_0^*$ be the on-manifold sample corresponding to $\mathbf{X}_{0|T}$ , and $\mathcal{E}(\mathbf{X}_{0|T}) = \| \mathbf{X}_{0|T} - \mathbf{X}_0^*\| _F$ the error between $\mathbf{X}_{0|T}$ and $\mathbf{X}_0^*$ , as depicted on the left side of Fig. 3. Effectively and accurately minimizing the value of $\mathcal{E}$ thus becomes + +the paramount objective to improve the quality of $\mathbf{X}_{0|T}$ . However, obtaining $\mathbf{X}_0^*$ directly is challenging or even intractable: (1) taking the clean image $\mathbf{X}_0$ as $\mathbf{X}_0^*$ causes the model to predict blurry values, approximating a weighted average of $\mathbf{X}_0^*$ , since multiple $\mathbf{X}_0^*$ can be denoised by the diffusion model to produce the same noise; and (2) preparing the noise- $\mathbf{X}_0^*$ pairs by generating the entire training dataset from noise is a computationally intensive process. Thus, instead of directly deriving the sample $\mathbf{X}_0^*$ , we draw inspiration from the reward lifting process in reinforcement learning and propose to regularize $\mathbf{X}_{0|T}$ to approach a feasible sample $\widetilde{\mathbf{X}}_0$ with a reduced error, i.e., $\mathcal{E}(\widetilde{\mathbf{X}}_0) < \mathcal{E}(\mathbf{X}_{0|T})$ . With the progression of model iterations, the sample $\widetilde{\mathbf{X}}_0$ is expected to gradually improve to be closer to the data manifold surface $\mathcal{M}_0$ , while the coarse estimation $\mathbf{X}_{0|T}$ steadily approaches $\widetilde{\mathbf{X}}_0$ , leading to continuous refinement. Such a process is intuitively depicted in the right sub-figure of Fig. 3. + +Building on this progressive refinement intuition, the focus shifts to obtaining an accurate sample $\widetilde{\mathbf{X}}_0$ . Leveraging the consistency model's ability to generate high-quality outputs directly from the latent space with varying noise levels, we train our accelerated model with consistency constraints in Eq. (6) within the edge region (i.e., the region with high SNR), which we term "edge consistency." The accelerated model is trained to generate the refined estimation $\widetilde{\mathbf{X}}_0$ under the guidance of edge consistency constraints. As $\widetilde{\mathbf{X}}_0$ experiences the additional denoising step, it becomes more accurate and closer to $\mathbf{X}_0^*$ compared to the coarse estimation $\mathbf{X}_{0|T}$ . Specifically, the feasible refined estimation $\widetilde{\mathbf{X}}_0$ is computed as follows: + +$$ +\widetilde {\mathbf {X}} _ {0} = \mathcal {F} _ {\boldsymbol {\theta} _ {G} ^ {-}} \left(\mathbf {X} _ {t | 0, T}, t\right), \tag {8} +$$ + +where $\mathbf{X}_{t|0,T}$ denotes the forward diffusion process to evolve $\mathbf{X}_{0|T}$ to timestamp $t$ using the initial noise $\mathbf{X}_T$ . Here we utilize the same noise of $\mathbf{X}_T$ to keep the correspondence of data points between the noise and data manifolds. Through distilling the $\mathbf{X}_{0|T}$ , we can progressively correct the coarse estimation to approach the more accurate sample $\widetilde{\mathbf{X}}_0$ , i.e., + +$$ +\mathcal {L} _ {d} = d \left(\widetilde {\mathbf {X}} _ {0}, \mathbf {X} _ {0 | T}\right). \tag {9} +$$ + +Distilling the coarse estimation with consistency guidance enhances the accuracy of the score function in the one-step accelerated model, ultimately facilitating the generation of high-quality samples. + +Remark. We are not aimed at devising novel consistency training techniques. Instead, we utilize consistency constraints to train the high-SNR edge region as an effective refinement tool to guide the learning of the score function in the pure noise state (endpoint), which can give reasonable regularization and preserve generation diversity. Our edge consistency-guided score distillation method strategi- + +Algorithm 1 Training Pipeline of the Proposed Algorithm +Input: Pre-trained diffusion model parameterized with $\theta$ ; training dataset $S$ ; number of iterations $K$ ; learning rate $\eta_{G}$ and $\eta_{D}$ . +Output: Optimized generation model parameters $\theta_{G}^{*}$ +1: $\theta_{G} \gets \theta$ ▷ Initialize $G$ from pre-trained model +2: Initialize discriminator $\theta_{D}$ randomly. +3: for $k = 1$ to $K$ do +4: Sample data $\mathbf{X}_0$ from $S$ , draw gaussian noise $\epsilon \sim \mathcal{N}(0, \mathbf{I})$ , draw gaussian noise $\mathbf{X}_T \sim \mathcal{N}(0, \mathbf{I})$ +5: Sample timestep $t \sim \mathcal{U}(0, N)$ where $N < T$ and interval $\Delta t \sim \mathcal{U}(0, \delta]$ ▷ sample $t$ and $\Delta t$ for edge consistency +6: Interpolate noised latent: $\mathbf{X}_t = \alpha_t \mathbf{X}_0 + \sigma_t \epsilon$ and corresponding $\mathbf{X}_{t - \Delta t} = \alpha_{t - \Delta t} \mathbf{X}_0 + \sigma_{t - \Delta t} \epsilon$ +7: Compute edge consistency loss $\mathcal{L}_c$ Eq. (6) +8: Calculate coarse target using Eq. (7) +9: Calculate refined target $\widetilde{\mathbf{X}}_0$ using Eq. (8) +10: Compute score distillation loss $\mathcal{L}_d$ using Eq. (9) +11: Evaluate adversarial loss $\mathcal{L}_{GAN}$ using Eq. (10) +12: Update $G$ : $\theta_{G} \gets \theta_{G} - \eta_{G} \nabla_{\theta_{G}} (\mathcal{L}_{c} + \mathcal{L}_{d} + \mathcal{L}_{GAN})$ +13: Update $D$ : $\theta_{D} \gets \theta_{D} + \eta_{D} \nabla_{\theta_{D}} \mathcal{L}_{GAN}$ +14: return $\theta_{G}^{*}$ + +cally avoids consistency regularization in low-SNR challenging regions, potentially reducing the learning burden and thus enhancing generative performance. See the results in Table 3 for the advantage of our edge consistency over the traditional consistency model that applies consistency regularization to the entire region. We also refer readers to Sec. A of the Supplementary Material for a detailed theoretical analysis. + +# 4.2. Disentangled Adversarial Regularization + +To further calibrate the distribution of the generated data, in this section, we introduce the adversarial training technique to directly measure the error of generation by a learnable discriminator [36]. As shown in Fig. 2, to leverage the pre-trained geometric knowledge in the diffusion model, we utilize the pre-trained diffusion model as the discriminator. However, due to the huge distribution gap between the geometric (normal) and texture components, in this process, we separate the discriminative learning processes via introducing a dual-discriminator, as shown in Fig. 2. Moreover, the adversarial learning objective can be formulated as + +$$ +\mathcal {L} _ {G A N} = \mathcal {D} _ {\boldsymbol {\theta} _ {D}} \left(\mathcal {F} _ {\boldsymbol {\theta} _ {G}} \left(\mathbf {X} _ {T}, T\right)\right) - \mathcal {D} _ {\boldsymbol {\theta} _ {D}} \left(\mathbf {X} ^ {*}\right), \tag {10} +$$ + +where $\theta_{\mathcal{G}}$ and $\theta_{\mathcal{D}}$ are the network parameters of the generator and discriminator, respectively, $\mathcal{F}_{\theta_G}(\mathbf{X}_T,T) = \mathbf{X}_{0|T}$ and $\mathbf{X}^*$ indicates the real images and normal. + +Remark. Decoupling the learning of geometry and tex + +![](images/0896b15a4741d337f665ce0f76b0c47d532a91b672144a8969b726e2e3499fd0.jpg) +Figure 4. Visual comparisons of our Acc3D, Era3D [14], and Wonder3D [20] on the GSO [6] dataset. For each sample, we provide the generated view, normal map, and reconstructed 3D mesh, displayed from left to right, respectively. + +ture information is a simple yet effective strategy that enhances the adversarial training process. We also want to highlight that while leveraging adversarial training can significantly enhance generative capabilities, without robust guidance—such as our edge consistency-guided progressive distillation detailed in Sec. 4.1—adversarial learning is prone to instability and mode collapse, as demonstrated in the ablation studies outlined in Table 3 and Fig. 7. In essence, the decoupled adversarial regularization and edge consistency complement each other, mutually reinforcing to elevate generative performance. + +In all, Algorithm 1 summarizes the training pipeline of the proposed method. + +# 5. Experiments + +# 5.1. Experimental Settings + +Dataset. Our model was trained on the Objaverse [4] dataset. We have aligned our training dataset with that of Wonder3D [20], which includes approximately 35,000 objects. We prepared our rendered multiview images and normal maps with Blender protocols. The rendered results consist of six views, all adjusted to the same scale as Era3D, including the front, back, left, right, front-right, and front-left views. For the evaluation dataset, we adopt the Google Scanned Object dataset, following prior works [19, 20]. For the quantitative evaluation, we initially rendered the input image at a resolution of $512 \times 512$ , subsequently obtaining multiview results and 3D assets. + +Evaluation Metrics. We evaluated our Acc3D from multiple perspectives, including the quality of novel view synthesis and the consistency of 3D reconstruction. Following Liu et al. [19], we used common metrics for image quality assessment to evaluate the performance of generated multiview outputs, such as PSNR, LPIPS, and SSIM. Additionally, we utilize more unpaired and perceptual scores, e.g., MUSIQ, CLIPIQA and MANIQA, to validate the performance of our model. For single-view 3D reconstruction, + +Table 1. Quantitative comparison of different methods for single view reconstruction. The best and second-best results are highlighted in bold and underlined, respectively. + +
MetricsZe.123 [17]Sync. [19]Wo.3D [20]Era3D [14]One23 [16]Acc3D OursAcc3D Ours
NFE ↓505040405024
GSO Dataset [6]
MUSIQ ↑60.3964.4658.1963.6461.7967.8569.26
CLIPQA ↑0.480.520.450.530.430.620.65
MANIQA ↑0.560.630.550.420.540.590.64
DTC Dataset [29]
PSNR ↑17.8422.3123.0223.3616.0123.0624.01
SSIM ↑0.780.240.860.870.750.870.88
LPIPS ↓0.250.100.140.140.350.140.12
MUSIQ ↑58.1556.6755.2460.1359.3964.4665.52
CLIPQA ↑0.510.550.470.560.460.630.65
MANIQA ↑0.560.640.540.420.530.560.59
+ +we reported Chamfer Distances (CD) and Volume IoU between reconstructed shapes and ground-truth shapes. This demonstrated the rationality and multiview consistency of the image-to-3D diffusion model. + +Baselines. We compared our Acc3D with 11 state-of-the-art image-to-3D models, including Zero123 [17], RealFusion [27], Magic123 [33], One-2-3-45 [16], PointE [31], Shap-E [11], SyncDreamer [19], Wonder3D [20], Era3D [14], as well as two accelerated image-to-3D models, Stable-Fast-3D [1] and TripoSR [43]. RealFusion and Magic123 use SDS loss on Stable Diffusion for single-view reconstruction. Zero123, SyncDreamer, Wonder3D, and Era3D generate consistent multiview images, with Wonder3D and Era3D also producing normal maps. + +Implementation Details. We adapt the proposed model on the recent effective 3D generation method Era3D [14], which can concurrently generate normal maps and multiview images at a high resolution of $512 \times 512$ . We used AdamW as the optimizer with an initial learning rate set to $5e - 6$ , and the number of gradient accumulation steps of 8. The training process generally necessitates 24 hours on + +"A boy wearing a baseball cap." + +![](images/02c22c5f27fa13aa0e5b1424d8828fd74db2ef566c2f0bd54087869bbfe8ab9c.jpg) + +![](images/cd20b6641e68110760325e80ec06b3d82cc8486ce121286ee0ea56e2e59392b2.jpg) + +![](images/40cd0dbec5666b013f0632cac07ce6878ed625b7b3a86bfe92e53d4fa06c18a9.jpg) + +![](images/747ce0a5ab9e3d0f5c554058bf5ae0cca5cd8c4add6450c900838e7eebd813c8.jpg) + +![](images/f51e0f8c02d0b5c2d1d31cac6709884b37711c26d1f41028090e288f606aa536.jpg) + +"A crocodile in cowboy costume." + +![](images/582ee98ea92fa9d96c5488d9b470a564841286fff0ca32b4882890e170b67082.jpg) + +![](images/87992c217d0cd4220e7272cd75ed01bf595a9da82194f9b2cdc3367b32eb1082.jpg) + +![](images/d68b009fc1aefe09390ce1875433650064c37311038fc8244da7d375dcb09634.jpg) + +![](images/1b7090ec28bfa64fffb2200cc177785dce925912cd20e722a60d43d0fbca433f.jpg) + +"A mouse in chef hat." + +![](images/9e4f64f3016692848227998b7d5fa1fc0f886215957fd58b73a506e25621f341.jpg) + +![](images/9608342c26991af91bdd4d3cfc343329b5b2623603833e6af4eea1b652b03f0f.jpg) + +![](images/9c0ce0ee634f51eec1d802ccd4f8b18db82bc32bc5693cef362d45e6dda42935.jpg) + +"An elephant in circus performer outfit." + +![](images/807a79d553d905211c839d31137b94c326d9a44bf4a2657cb82b7e4b6c1544c0.jpg) + +![](images/bb2673fa311dae5778e015982d891a8d6199b973e9c127cb245c0d81bdb9ae3c.jpg) + +![](images/86ad0522e85beaea885c1d6d95c47b87a2c465562ca28a7a71ac083860fe4ceb.jpg) + +"A graceful robot with red hair." + +![](images/d349aa06f683b26a284c8726c9bec8e2a013bed2e3d2c14dbf108ad5fd80aff3.jpg) +Input images + +![](images/40a9f67659f8d3816584180dbdcd45f7bf630903d6f866b9d06354f38a795c14.jpg) + +![](images/e8ea377f55b59266a98639c5b6ae2eb17cf22ccb3c04879770ab1a924e2cf896.jpg) +Zero123 +(NFE=50) + +![](images/ba0198044fabae244f9f29fc8da10f7816f58e480003544faa028590a87b8be1.jpg) + +![](images/9fa7a87a2b64f6bb007bf2bb2eac3c817e2c93ae2ae7e73977229a07939a1abe.jpg) + +![](images/3142b2e02f12d533a89c366a69e4de811b46c568e686e166b2dc6042faf1eeb7.jpg) + +![](images/0c1fc7cf216cdd7b4a8cbbdaa224a490dfcbe7a06a53a47a7eb97d1657a31155.jpg) + +![](images/b0c18f32bb7cfb53e2faf205e7eaf0e787e15ceec92ecb5e0a0e51239a315076.jpg) +Magic123 + +![](images/2ca4c4c500be4d7f4e63e2cafb9a12cccb40f9685d50105b995c2bb95f07a162.jpg) + +![](images/8c0da267a0085f7b60064c582aa5ad98289b357b9310d0729b16860891d2dfbd.jpg) + +![](images/08c27a02ee523b060e7982dc8cafe9783ad5f3d4b31c729374aa86564c8966e0.jpg) + +![](images/be6f6b77ed21722ef0fcdf9edf9ead32ca8f891e97dea2eed72b7dc31dbf0967.jpg) + +![](images/73dac9e181640224df15df03717ff910424ec0ba70a25ad4c7300822ae16f726.jpg) + +![](images/96eeb761c1eec5f7b28a4cbad15b076434c47e462ff1561952b74f6a551aad18.jpg) + +![](images/e8a1b78d4442c3d0ef67e7f6e351f717344ddb6c502de0636ba36bfd006f183e.jpg) + +![](images/9df2593e3d395bee4e28766b2af336c8f2c66d3701c059b408c44d87553afcd0.jpg) + +![](images/7250e88bcc7bfe52cba98bd4f078035f81b7e86561340b88243cc7bea8dfb8e7.jpg) + +![](images/311cb41adbd03f583b8b0af49a68ed0ab87b95661256471575d2e74a8e847517.jpg) + +![](images/b08da0ddb4911dd35b2194d5cf0cf208585db4643ca1cbb2f13e983fc2376354.jpg) + +![](images/6947e31c5831fda425d5e3e7720c1d36e0d9c2afb830aeacdb0325af44d56c92.jpg) + +![](images/685d17bc8c803d6133550ae418e60e5845aa3f68569a3ef026cd478604c807b0.jpg) + +![](images/fc6fdda234b7ca73373c491435b9ab10ece8bf99e549577f6a5aa45aab2562c2.jpg) + +![](images/6aa204cbe5f3a85f103b73c85c1a82140f7109cd220a6fe2f4416b64802f5ec1.jpg) + +![](images/64c87f1e0fa10f5cf1eebdc4ddca1a2b393f523317054815cb14640289a597d7.jpg) + +![](images/0075b1492022cf28872bb90d6ef9f0001b3c6ec5a054e0eddfa1d098d2a91da3.jpg) + +![](images/3e391bc3472b727ac1b9536c6caf8b8424803d2ec7d512ee672e36c95898e6f1.jpg) + +![](images/6a6846a572f419f8601eb91f8175294dbc685b134b0d439bd769351683333246.jpg) + +![](images/198b54fa129edacc39823d49d8a2003b2e939d7bb999a4be5e56404cabe85a7b.jpg) + +![](images/e0d6782243955107649291a60f56d97adeed81243ccb3921149ded9abdcb297e.jpg) + +![](images/30d17de8ee953b293e75ca653f51bb0804c5b62563f5199ca1b5543e496b0512.jpg) + +![](images/264ae613e8829d890456a2e8c3210b62d0d2e0d9b3ea195ab0309bbb892a18f0.jpg) + +![](images/d4e643c755ea5b5b649ae8cd8d5c8d526a39f7db72078dbd36963cb4e7aa7dcc.jpg) +Ours (NFE=2) + +![](images/5e4bfd00a3cf7ff5902e15fef607307678eb20d6dbba546c799dd0f4e82bd6e5.jpg) +Textured mesh + +![](images/02d405fb7647ec2bb2e58d37d55a1707bbcf3d1e2eb0e09711b0d101e08def96.jpg) + +![](images/74d684db3f85618916c334c14061f2e804a1ace2c1447ee3aa5d6e9a0f5430ec.jpg) +Figure 5. The qualitative results generated by Acc3D on various styles of images generated by text-to-image model Flux [41]. Please refer to Fig. 6 for more comprehensive comparisons between our Acc3D and baseline model Era3D. Q Zoom in for details. +Figure 6. Visual results of our Acc3D and Era3D (baseline model). + +a cluster equipped with four 40GB NVIDIA GeForce RTX A6000 GPUs. For 3D reconstruction, we followed Era3D to generate 3D assets using NeuS [46]. + +# 5.2. Experimental Results + +Novel View Synthesis Results. We present the numerical results in Table 1 to quantitatively evaluate the quality of generated novel views. Our model is assessed on both the GSO [6] and DTC [29] datasets, with the DTC dataset being the most recent collection that offers a high degree of granularity and intricate 3D details. Acc3D achieves the + +Table 2. Quantitative results for 3D reconstruction on GSO. Symbol ${}^{ \dagger }$ indicates the method that directly generates 3D meshes. + +
MetricsCD↓IoU↑NFE↓
Realfusion [27]0.08190.2741-
One-2-3-45 [16]0.06290.408650
Point-E [31]0.04260.287564
Shap-E [11]0.04360.358464
Magic123 [33]0.05160.4528-
Zero123 [17]0.03390.503550
SyncDreamer [19]0.02610.542150
Wonder3D [20]0.01990.624440
Era3D [14]0.02170.597340
InstantMesh [50]0.04060.477875
Stable-Fast-3D†[1]0.04210.5141-
TripoSR†[43]0.03260.5326-
Acc3D (Ours)0.01910.66812
+ +highest average scores on most metrics, especially in natural image quality, highlighting our framework's superiority in novel view synthesis. We further visually compare different examples from the GSO dataset in Fig. 4. Our method achieves superior visualization results while reducing inference time. Besides those aforementioned datasets with reference multiviews, we also evaluate our method in the wild using T2I-generated images in Fig. 5. Our method consistently generates high-definition, detailed results compared to other methods, especially on the challenging samples of the crocodile $(2^{nd}$ row) and the face of the elephant $(4^{th}$ + +Table 3. Quantitative results of ablation studies on the GSO dataset. $\checkmark$ (resp. $\times$ ) indicates the presence (resp. absence) of the corresponding component. $\uparrow$ (resp. $\downarrow$ ) means the larger (resp. the smaller), the better. "Distill." stands for score distillation with Eq. (8). "Consis." represents the timestamp region of consistency loss, corresponding to $[0, N]$ in Alg. 1. $[0, T]$ indicates the consistency regularization is applied to all noise levels during training. "Adv." refers to adversarial learning. "Single" indicates the utilization of only one discriminator for both normal and texture components. The metrics were obtained under two-step inference. + +
Distill.Consis.Adv.PSNR↑CD↓MUSI.↑CLIPI.↑
(a)×[0, T]×18.110.06061.010.55
(b)×[0, T]20.790.02167.220.62
(c)[0, T]21.100.02565.390.60
(d)×20.470.02663.080.58
(e)×[0, 0.4T]20.320.02766.570.62
(f)[0, 0.2T]21.220.02767.240.58
(g)[0, 0.6T]22.130.02266.870.59
(h)[0, 0.8T]21.230.02465.060.61
(i)[0, 0.4T]×21.090.02951.050.45
(j)[0, 0.4T]single21.370.02266.410.57
Era3D[14]-Ours--20.170.02353.810.46
[0, 0.4T]22.470.01967.850.62
+ +row). We also compare our method with base model Era3D in Fig. 6. Our accelerated model achieves better results with NFE of 2, while Era3D struggles with few steps. + +3D Reconstruction Results. We conduct both quantitative and qualitative evaluations of the reconstructed geometry as presented in Table 2 and Fig. 4. In Table 2, our method attains excellent reconstruction results with the least number of function evaluations (NFE). Fig. 4 shows that Wonder3D is highly sensitive to the facing direction of input images; for instance, it fails to generate novel views for the sample of elephant in the left pose. Despite boasting a higher resolution of 512, Era3D still produces relatively coarse mesh outputs. + +# 5.3. Ablation Studies + +We perform comprehensive ablation studies (Table 3), training all models similarly except for the ablation term and evaluating on GSO dataset. + +Disentangled Adversarial Learning. Through comparing Table 3 (j) and "Ours", we find that separately learning different modalities can help stabilize adversarial learning and get better quantitative results. As depicted in Fig. 7 (3) and "Ours", the fusing of these two modalities adversely affect the discriminator/model's performance, shown obviously for the $1^{st}$ and $3^{rd}$ samples. + +Various Distillation Settings. We evaluate the effectiveness of our consistency-guided score distillation. Specifically, comparisons between Table 3 (e) and "Ours" validate + +![](images/14ae3d1d429b1225959958b8e68a6dc8e653906d3d2ac01bf452702ccf04bb87.jpg) +Figure 7. Visualizations of the ablation study conducted on GSO. All results are generated in two steps. The results (1), (2), and (3) correspond to the experimental configurations (b), (g), and (i) outlined in Table 3, respectively. + +the necessity of distillation. Without distillation loss, being solely trained with adversarial learning is hard to derive high-quality results. Table 3 (a)/(b) V.S. "Ours" also indicates the superiority of our edge consistency-guided distillation compared with full consistency model [39, 40]. We can also visually compared with Fig. 7 (1) and "Ours" that the setting of (b) generates strange samples, especially for the bag in the $1^{st}$ row. This suggests that GANs are prone to mode collapse without robust regularization. + +Parameter selections of consistency constraints. By comparing Table 3 (c), (d), (f), (g), (h) and "Ours", we can conclude that using a consistency model to guide score matching at the endpoint is more effective than directly utilizing the original diffusion model. Additionally, the choice of the region for the consistency constraint is crucial. Selecting an appropriate edge consistency region can significantly enhance the generation results + +# 6. Conclusion + +We introduced Acc3D, a novel and streamlined method designed to accelerate single image-to-3D diffusion models. 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Nonetheless, the iterative nature of diffusion models (DMs) results in high computation complexity, posing challenges for deployment. Although existing cache-based acceleration methods try to utilize the inherent temporal similarity to skip redundant computations of DiT, the lack of correction may induce potential quality degradation. In this paper, we propose increment-calibrated caching, a training-free method for DiT acceleration, where the calibration parameters are generated from the pre-trained model itself with low-rank approximation. To deal with the possible correction failure arising from outlier activations, we introduce channel-aware Singular Value Decomposition (SVD), which further strengthens the calibration effect. Experimental results show that our method always achieve better performance than existing naive caching methods with a similar computation resource budget. When compared with 35-step DDIM, our method eliminates more than $45\%$ computation and improves IS by 12 at the cost of less than 0.06 FID increase. + +# 1. Introduction + +Diffusion models (DMs) [14, 29, 37, 38] have emerged as one of the most popular generative models, exhibiting great generation quality and diversity especially in the area of contiguous modalities, including images [31], videos [36], and audios [6]. Throughout the reverse process of DMs, expected contents are gradually synthesized with a multistep refinement. Although initial DMs are based on U-Net architectures [32], recent works have demonstrated that transformer-based DMs, i.e., Diffusion Transformers (DiTs) can serve as a competitive alternative [30]. DiTs benefit from the exceptional scalability inherent in trans + +former architecture [40], which has been extensively validated in various tasks, including image recognition [9] and language modeling [18]. + +However, DiTs are still burdened with the iterative nature inherent in DMs. This means their high-fidelity synthesis results usually come at the cost of substantial latency, exacerbating deployment difficulties and necessitating efficiency improvement. The existing strategies to accelerate DiT models can be categorized into three primary approaches: timestep reduction, weight-oriented approximation [5], and cache-based acceleration [26, 35]. Research works within the first approach are devoted to reducing the required reverse steps, including adopting fast samplers [23, 24, 37, 44] or distilling the original trajectory into fewer timesteps [33, 39]. + +Methods that fall under the category of weight-oriented approximation are inspired by the general methodology to decrease the complexity of neural networks. These works typically concentrate on eliminating redundant weight elements through pruning [11], adopting low-bit quantization [5, 12], or employing low-rank approximation such as Singular Value Decomposition (SVD). However, enhancing generation efficiency by decreasing the model size of DiTs is a non-trivial task, especially when retraining is not feasible. Regarding the experimental results of SVD-based approximation, as shown in Fig. 2, even when approximately $33\%$ of the ranks are removed across all layers, the computational overhead does not diminish accordingly. Moreover, the generated images suffer from substantial quality degradation and lose the consistency with the original model. + +Cache-based acceleration techniques are proposed to leverage the multi-step property of diffusion process contrarily and exploit the inherent temporal similarities to bypass redundant computations [16, 26, 35]. In this case, the intermediate features of previous timesteps are cached and directly used to approximate the outputs of subsequent timesteps without any corrections. Current related works primarily focus on designing an optimal caching mechanism, while ignoring the calibration of the cached value. This oversight may lead to quality drop and constrain the + +![](images/4468a40731c0249baf1548e239bc11806c48000f50704500971da275770d6517.jpg) +Figure 1. Visualization of increment-calibrated caching on DiT-XL/2. + +![](images/6bdeac5f4856d280901b2aef67880cd123a9631dd00540edec20b91051616f0f.jpg) +Figure 2. Degraded generation results of directly performing SVD on DiT-XL/2 at the resolution of $256 \times 256$ . + +full potential of cache-based acceleration. + +In this paper, we present increment-calibrated caching, a novel training-free method to accelerate DiT that distinguishes itself from aforementioned three approaches. It can be seen as a complementary combination of weight-oriented approximation and cache-based acceleration, instead of roughly packing these two techniques together. Unlike methods that directly convert the original model into a reduced version with SVD, we treat the low-rank approximated weights as calibration parameters. During the reverse process, these calibration parameters are leveraged to refine the cached values derived from the original model through an increment term, instructing them towards the desired accurate results. This ensures that increment-calibrated caching achieves a superior balance between efficiency and performance compared to conventional naive caching mechanisms. + +Furthermore, we substitute the original SVD with channel-aware SVD, a refined variant that takes the channel sensitivity into consideration. In contrast to the original version, channel-aware SVD strengthens the calibration + +effect by placing greater emphasis on activation-sensitive channels. This is crucial because, as observed in various transformer-based models [43, 45], the outlier issues in DiT can adversely affect inference results. Main contributions of this paper are summarized as follows, + +- We introduce increment-calibrated caching, a training-free method tailored for the acceleration of DiT. To the best of our knowledge, it is the pioneering work that aims to calibrate the cache of DMs in a training-free manner. +- We propose channel-aware SVD, a refined SVD variant that improves increment-calibrated caching for DiT and mitigates outlier issues that could undermine the calibration effect. +- The proposed methods are validated on state-of-the-art DiT model DiT-XL/2 [30] for conditional image synthesis and for PixArt- $\alpha$ [4] text-to-image generation. Experimental results show that our proposed method largely outperform naive caching methods with a similar computation budget. Compared with 35-step DDIM, our method eliminates more than $45\%$ computation and improves IS by 12 at the cost of less than 0.06 FID increase. + +# 2. Related Works + +Diffusion Transformer. While early diffusion models (DMs) relied heavily on U-Net architectures, recent works has predominantly shifted towards transformer-based DMs, specifically Diffusion Transformers (DiTs). The introduction of DiT [30], initially applied to class-conditional image synthesis, demonstrated the scalability and effectiveness of transformer architectures within the diffusion framework. Subsequent works, such as PixArt- $\alpha$ [4] and its successors [2, 3], have further adapted and refined the original DiT by incorporating cross-attention mechanisms and merged adaptive layer normalization, thereby extending its capabilities to text-to-image tasks. Notably, the latest iteration of Stable Diffusion [10] has also turned to the multimodal DiT architecture. In the realm of video generation, the emergence of SORA [1] exemplifies the potential for establish + +ing a world simulator based on DiT, further highlighting the versatility and promise of DiT. + +Cache-based Acceleration. Although the iterative nature of DMs leads to significant complexity, it also brings with a unique opportunity for cache-based acceleration, leveraging the temporal similarity between consecutive denoising steps. This similarity allows for the caching and reuse of intermediate results, thereby bypassing redundant computations. Some early works are devoted to exploiting the redundancy of U-Net-based DMs. For instance, DeepCache [27] harnesses the temporal consistency of high-level features to streamline the computation in the main branch of U-Nets. Similarly, Block Caching [42] introduces a dynamic cache mechanism that relies on the accumulated input changes. + +More recent works have shifted focus towards applying these principles to DMs based on transformer architectures. FORA [35], for example, periodically stores and retrieves the outputs of all attention and MLP layers. Meanwhile, L2C [26] and HarmoniCa [16] aim to determine the optimal caching strategy via learning-based approaches. $\Delta$ -DiT [7] accelerates the rear DiT blocks during the early sampling stages and the front DiT blocks in the later stages. Lastly, TokenCache [22] and ToCa [47] adopt a token-wise caching approach instead of layer-wise caching by distinguishing the importance of different tokens. + +Low-rank Approximation. Low-rank approximation techniques, such as Singular Value Decomposition (SVD) and its variants, have found widespread application in the compression and acceleration of neural networks [17]. Recently, researchers have explored the use of SVD in the context of Large Language Models (LLMs). For instance, FWSVD [15] incorporates Fisher information to weigh the importance of parameters prior to applying SVD. ASVD [45] addresses the outlier issues by scaling the weight matrix based on activation distribution. Additionally, SVD-LLM [41] establishes a direct correlation between singular values and inference loss. However, there has been limited exploration of SVD's application to the acceleration of DMs. Our experimental results, presented in Fig. 2, demonstrate that a direct application of low-rank approximation to DiT significantly degrades the generation quality. + +# 3. Methodology + +# 3.1. Preliminary + +The basic framework of DMs consists of two parts, i.e., the forward process and reverse process. The former illustrates the procedure that gradually turns clean data $z_{0}$ into gaussian noise $z_{T} \sim \mathcal{N}(0, I)$ in $T$ timesteps. At each timestep $t \in [1, T]$ , random noise $\epsilon_{t}$ is added to the current data $z_{t-1}$ with the noise scheduler factor $\beta_{t}$ , + +$$ +z _ {t} = \sqrt {1 - \beta_ {t}} z _ {t - 1} + \sqrt {\beta_ {t}} \epsilon_ {t} \tag {1} +$$ + +Reverse process starts from $z_{T}$ sampling from standard normal distribution. To generate new samples obeying the real distribution, the reverse process iteratively estimates the accumulated noise and remove it from current data with a sampler $\Psi(\cdot)$ . Taking DDPM [14] as an example, it can be represented as, + +$$ +z _ {t - 1} = \Psi \left(\epsilon_ {\theta} \left(z _ {t}, t\right)\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(z _ {t} - \frac {1 - \alpha_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \epsilon_ {\theta} \left(z _ {t}, t\right)\right) + \sigma_ {t} \epsilon_ {t} +$$ + +where $\alpha_{t}$ , $\overline{\alpha}_{t}$ , and $\sigma_{t}$ are constants depending on timestep $t$ , and $\epsilon \sim \mathcal{N}(0, I)$ . $\epsilon_{\theta}(z_{t}, t)$ denotes a noise estimation network parameterized by $\theta$ , which usually adopts a U-Net [14, 29, 31, 37] or transformer [4, 10, 20, 25, 30, 46] architecture. + +# 3.2. Naive Caching for Diffusion Transformer + +DiT models are composed of stacked blocks, and each contains a Multi-Head Self-Attention (MHSA) layer and a Feed-Forward Network (FFN) layer. Then, it can be represented as $F_{l}(\cdot)_{l = 1}^{L}$ , where $L$ denotes the network depth, and $F_{l}$ can be either MHSA or FFN layer. Naive caching methods are proposed to reuse the results of both layer types and accelerate the reverse process, since the outputs from consecutive timesteps always exhibit inherent similarity. + +As shown in Fig. 3(a), key modules of naive caching mechanism are the cache $\mathcal{C}$ , gather $\mathcal{G}$ , and scatter $S$ . During generation process, the cache carries the intermediate outputs that may be reused in the future, which is jointly maintained by gather and scatter. Both gather and scatter can be represented as binary matrices, i.e., $\mathcal{G}, S \in \{0,1\}^{T \times L}$ where element $\mathcal{G}_{t,l}$ and $S_{t,l}$ denote whether stores or loads the results of layer $l$ at timestep $t$ , respectively. + +Given input $x_{s,l}$ at timestep $s$ , if corresponding bit $\mathcal{G}_{s,l}$ of gather matrix is activated, layer $l$ will be fully computed to update the cache: $\mathcal{C}_l(y) \gets F_l(x_{s,l})$ . Then, for a subsequent timestep $m$ , only when $S_{m,l}$ does not equal 1, layer $l$ is required to be re-computed. Otherwise, it will be approximated with the cached value to bypass the computations: $y_{m,l} \approx \mathcal{C}_l(y)$ . To minimize the total computation while ensuring the generation quality, the gather and scatter matrices should be carefully designed through handcrafting [35] or learning-based approaches [16, 26]. + +# 3.3. Increment-Calibrated Caching with SVD + +However, the naive caching strategy usually entails the risk of quality degradation. A potential remedy to this issue is to calibrate the cached value with an increment term, thereby guiding it towards the accurate result. We initiate the discussion from a simple linear layer with weight $W \in \mathbb{R}^{C_o \times C_i}$ , where $C_i$ and $C_o$ represent input and output channels, respectively. This method can be extended to MHSA or FFN by calibrating all the linear operations inside. Consistent with the notation established in the preced + +![](images/32c881c4798960fe538b90c8ede8ac4c1cec2c18f935940863729ae974242825.jpg) +(a) + +![](images/505f7f941428725764777301c0ef816f9d1e57499647fee10c6c0bf12c7df893.jpg) +(b) + +ing subsection, it is assumed that the input $x_{s,l}$ of previous step $s$ is also synchronously stored alongside output $y_{s,l}$ as $C_l(x)\gets x_{s,l}$ . Consequently, the accurate result $y_{m,l}$ at timestep $m$ can be reformulated as the sum of cached output and an increment term, + +$$ +y _ {m, l} = \mathcal {C} _ {l} (y) + W \left(x _ {m, l} - \mathcal {C} _ {l} (x)\right) \tag {3} +$$ + +Directly computing the increment term leads to unchanged $\mathcal{O}(NC_iC_o)$ complexity compared with full computation, where $N$ is the token number. To obtain a tradeoff between efficiency and performance, low-rank approximation is conducted on $W$ based on SVD. With SVD, the weight matrix $W$ can be factorized into three matrices: $U$ , $\Sigma$ , and $V^T$ , such that $W = U\Sigma V^T$ . The diagonal matrix $\Sigma$ consists of positive singular values sorted in the descending order. The truncation approximation keeps the largest $r$ singular values to minimize the reconstruction error with a rank- $r$ constraint. Then, $U$ , $\Sigma$ , $V^T$ are replaced with $U_r \in \mathbb{R}^{C_o \times r}$ , $\Sigma_r \in \mathbb{R}^{r \times r}$ , $V_r^T \in \mathbb{R}^{r \times C_i}$ , approximating $W$ as $W_r = U_r\Sigma_rV_r^T = W_r^a W_r^b$ . $W_r^a \in \mathbb{R}^{C_o \times r}$ and $W_r^b \in \mathbb{R}^{r \times C_i}$ are kept as the calibration parameters. Thus, the complexity is reduced to $\mathcal{O}(N(C_i + C_o)r)$ , and the cached output can be corrected as, + +$$ +y _ {m, l} \approx \mathcal {C} _ {l} (y) + W _ {r} ^ {a} W _ {r} ^ {b} \left(x _ {m, l} - \mathcal {C} _ {l} (x)\right) \tag {4} +$$ + +# 3.4. Improved Calibration with Channel-Aware SVD + +As demonstrated in prior works [15, 41, 45], the straightforward application of SVD-based low-rank approximation may induce unacceptable performance degradation of neural networks, particularly when only a limited number of ranks are retained. Original SVD methods solely focus on the static weights and fail to take the influence of input activations into consideration. Thus, this results in a mismatch between the reconstruction error and the actual model performance. For increment-calibrated caching of DiT, this is + +![](images/ee8e84ff12a0ead6b1f00ea50def298c613593477740aa304433c8336b8dfef8.jpg) +Figure 3. Overview of (a) naive caching and (b) proposed increment-calibrated caching. The former stores intermediate results of previous denoising steps and directly reuse in later timesteps which may induce unavoidable error. The proposed increment-calibrated caching corrects the cached value with calibration parameters approximated from model itself. +(a) + +![](images/5146c4c636478052017e8bcebb0dba7e5249e0a512fd46ff836ce455a1a653d2.jpg) +(b) + +![](images/da336bcf6c04987640c5f5cf83f11aeca3006d83a594e11f354658b55fa92027.jpg) +(c) + +![](images/5957b26f425724acf98af20d24a236defe52ce99b74076c59e561f474ea210c5.jpg) +(d) +Figure 4. Outlier issues of DiT models appearing in (a) input channel of FFN FC1, (b) output channel of FFN FC2, (c) input channel, and (d) output channel of MHSA output projection. + +sue may become even more severe. Fig. 4 illustrates the activation distribution across all the linear layers within a single block of DiT-XL/2 [30]. Notably, outliers are evident in both the input and output channel dimensions. This implies that even minor reconstruction errors can significantly weaken the effectiveness of calibration in certain channels. Therefore, during the correction process, it is imperative to give heightened attention to the weight elements of these sensitive channels. + +To this end, we adopt channel-aware SVD, which takes the sensitivity of both input and output channels into consideration when approximating a given weight matrix. Assum- + +ing the importance of different channels can be weighed by two diagonal matrices $S_{i} \in \mathbb{R}^{C_{i} \times C_{i}}$ and $S_{o} \in \mathbb{R}^{C_{o} \times C_{o}}$ , where each element corresponds to one input or output channel, respectively. Then, the weight matrix $W$ can be scaled to $W'$ to take the channel sensitivity into consideration, + +$$ +W = S _ {o} ^ {- 1} \left(S _ {o} W S _ {i}\right) S _ {i} ^ {- 1} = S _ {o} ^ {- 1} W ^ {\prime} S _ {i} ^ {- 1} \tag {5} +$$ + +To reduce its complexity, $W^{\prime}$ is factorized with SVD and approximated into $U_r^\prime \Sigma_r^\prime V_r^{\prime T}$ by only keeping the first $r$ singular values. Then, we re-scale the approximated $W^{\prime}$ with the inverse of matrix $S_{i}$ and $S_{o}$ to obtain the approximation of original matrix $W$ . It can be represented as the multiplication of matrix $\hat{W}_r^a\in \mathbb{R}^{C_o\times r}$ and $\hat{W}_r^b\in \mathbb{R}^{r\times C_o}$ , which will be used as calibration parameters, + +$$ +W \approx \left(S _ {o} ^ {- 1} U _ {r} ^ {\prime}\right) \Sigma_ {r} ^ {\prime} \left(V _ {r} ^ {\prime T} S _ {i} ^ {- 1}\right) = \hat {W} _ {r} ^ {a} \hat {W} _ {r} ^ {b} \tag {6} +$$ + +To obtain the matrix $S_{o}^{-1}$ and $S_{i}^{-1}$ , we propose two feasible methods: channel-activation-aware SVD (CA-SVD) and channel-delta-aware SVD (CD-SVD). The former is a extended version of ASVD [45], where the mean magnitude of activations across channels is calculated based on a small calibration dataset and used as the scale. CD-SVD utilizes the average inter-timestep difference to generate the scale matrices, as shown in Algorithm 1. + +Algorithm 1 Channel-delta-aware Singular Value Decomposition +Input: Calibration set $\mathcal{D}$ , DiT model $\epsilon_{\theta}(\cdot)$ , number of timesteps $T$ , sampler $\Psi(\cdot)$ , noise scheduler $\beta_{t}$ +Output: Scale matrix $S_{i}$ and $S_{o}$ of each linear layer $l$ of $\epsilon_{\theta}(\cdot)$ +1: for each linear layer $l$ of $\epsilon_{\theta}(\cdot)$ do +2: Initialize zero vector $S_{i}$ and $S_{o}$ +3: end for +4: for each $z_{0} \in \mathcal{D}$ do +5: $t \sim \mathcal{U}[2, T]$ +6: $z_{t} \sim \mathcal{N}(z_{t}, \alpha_{t} z_{0}, \sigma_{t}^{2})$ +7: $z_{t-1} \gets \Psi(\epsilon_{\theta}(z_{t}, t))$ and +8: for each linear layer $l$ of $\epsilon_{\theta}(\cdot)$ do +9: Cache both inputs and outputs +10: end for +11: $z_{t-2} \gets \Psi(\epsilon_{\theta}(z_{t-1}, t-1))$ and +12: for each linear layer $l$ of $\epsilon_{\theta}(\cdot)$ do +13: Compute input and output differences with cache, accumulate them to $S_{i}$ and $S_{o}$ +14: end for +15: end for +16: Turn $S_{i}$ and $S_{o}$ into diagonal matrices +17: return Outputs + +# 4. Experiment + +# 4.1. Experimental Setup + +Models, Datasets, and Metrics. To demonstrate the effectiveness of the proposed method, evaluation is conducted based on commonly used Diffusion Transformer model, DiT-XL/2 [30] for class-conditional image synthesis and PixArt- $\alpha$ [4] for text-to-image generation. The default samplers are DDIM [37] and DPM [23], respectively. 50,000 images from 1,000 classes in ImageNet [8] are sampled at the resolution of $256 \times 256$ , evaluating performance with Inception Score (IS) [34], Fréchet Inception Distance (FID) [28], sFID, Precision [19], and Recall. For text-to-image generation, we employ 30,000 captions randomly sampled from MSCOCO-2014 [21] to generate images. We use FID-30k and Clip Score [13] to assess the image quality and text-image alignment, respectively. The computation complexity is measured with the number of Multiply-and-Accumulate (MAC) operations, which is the basic unit of computation intensive matrix multiplications. + +Caching Pattern Setting. The naive caching pattern of FORA [35] is selected as the baseline, where the outputs of all MHSA and FFN layers are synchronously cached according to a fixed period $p$ . Thus, the gather matrix $\mathcal{G}$ is set as, $\mathcal{G}_{t,l} = \mathbb{1}_{p|t}, \forall t \in [1,T], l \in [1,L]$ . The scatter matrix $S$ can be seen as the complement of $\mathcal{G}$ : $S_{t,l} = 1 - \mathcal{G}_{t,l}$ . Besides, it should be noticed that, the proposed calibration method can not only be applied to this particular case, but is compatible with other naive caching mechanism of the format defined in subsection 3.2. + +Calibration Mechanism Setting. To simplify discussion, we employ a unified rank $r$ for all linear layers to generate the calibration parameters. To conduct CA-SVD or CD-SVD, 256 images are randomly selected from the training set as the calibration set. + +# 4.2. Comparison with Naive Caching + +Unified Caching Pattern. The proposed incremental-calibrated caching is compared to naive caching with the same caching pattern, i.e., FORA [35]. To ensure fairness, we constrain the computational overhead of all methods to be the same level and investigate their differences in performance with varying sampling settings. As shown in Tab. 1, for class-conditional synthesis, our incremental-calibrated caching achieves better results than naive caching in all performance metrics when both adopt the same FORA caching pattern, particularly under constrained computational resource budget. For instance, with a MAC limit of approximately 2.37T, the proposed increment-calibrated caching method achieves an IS score that is 22 points higher than naive caching, while also reducing FID and sFID by 1.22 and 3.37, respectively. Similar results can also be observed in text-to-image generation, as shown in Tab. 2. + +
MethodSampler#StepsIS↑FID↓sFID↓Prec.↑Recall↑#MACs↓(T)
DiT-XL/2 (cfg = 1.5)DDPM250278.22.274.600.830.5759.31
DiT-XL/2 (cfg = 1.5)DDIM40239.92.354.260.800.599.49
Naive Caching (p = 2)DDIM80243.42.294.460.810.599.51
Naive Caching (p = 3)DDIM120242.72.334.620.810.599.53
ICC (CA-SVD, r = 128, p = 2)DDIM66244.02.234.350.800.599.40
ICC (CD-SVD, r = 192, p = 2)DDIM62251.72.104.250.810.599.40
ICC (SVD, r = 256, p = 2)DDIM58257.82.144.290.820.589.35
DiT-XL/2 (cfg = 1.5)DDIM30235.02.644.380.800.597.12
Naive Caching (p = 2)DDIM60240.02.484.600.810.597.13
Naive Caching (p = 3)DDIM90243.82.524.910.810.577.15
ICC (CA-SVD, r = 128, p = 2)DDIM50241.72.314.330.800.607.11
ICC (CD-SVD, r = 192, p = 2)DDIM46253.02.284.260.820.576.98
ICC (SVD, r = 256, p = 2)DDIM44258.72.304.310.830.577.09
DiT-XL/2 (cfg = 1.5)DDIM20224.33.494.930.790.584.75
Naive Caching (p = 2)DDIM40235.42.954.930.800.574.75
Naive Caching (p = 3)DDIM60234.43.005.540.800.574.76
ICC (CA-SVD, r = 128, p = 2)DDIM32236.82.774.350.800.584.55
ICC (CD-SVD, r = 192, p = 2)DDIM30250.62.534.340.810.574.55
ICC (SVD, r = 256, p = 2)DDIM28257.12.664.470.820.564.51
DiT-XL/2 (cfg = 1.5)DDIM10160.412.3311.340.670.512.37
Naive Caching (p = 2)DDIM20193.336.738.770.740.532.38
Naive Caching (p = 3)DDIM30196.96.279.480.760.512.38
ICC (CA-SVD, r = 128, p = 2)DDIM16205.95.565.400.750.552.27
ICC (CD-SVD, r = 192, p = 2)DDIM14217.65.055.460.770.532.12
ICC (SVD, r = 256, p = 2)DDIM14219.55.105.590.780.522.26
+ +Table 1. Comparison of naive caching and increment-calibrated caching based on DiT-XL/2 evaluated on ImageNet. + +
MethodSampler#StepsFID-30k↓Clip Score↑#MACs↓(T)
PixArt-α (cfg = 4.5)DPM309.5430.668.33
PixArt-α (cfg = 4.5)DPM1539.5729.114.17
Naive Caching (p = 2)DPM3010.3930.544.17
ICC (SVD, r = 64, p = 2)DPM269.8030.603.94
ICC (CA-SVD, r = 64, p = 2)DPM269.2930.643.94
PixArt-α (cfg = 4.5)DPM1086.5427.212.78
Naive Caching (p = 2)DPM2025.4729.682.78
ICC (SVD, r = 64, p = 2)DPM1818.6930.042.73
ICC (CA-SVD, r = 64, p = 2)DPM1813.9430.292.73
+ +Table 2. Comparison of naive caching and increment-calibrated caching based on PixArt- $\alpha$ evaluated on MSCOCO-2014. + +Even without channel-aware SVD for improvement, the increment-calibrated caching outperforms naive caching in both FID and Clip Score. The application of CA-SVD further improves the results, offering $0.51 \sim 4.75$ FID reduction. + +Distinct Caching Pattern. In this work, we have not focused extensively on the design of caching patterns and + +have instead adopted the coarse-grained method employed by FORA [35]. L2C, on the other hand, is a caching-only acceleration technique that conducts fine-grained optimization, thereby further maximizing the potential of caching. However, as depicted in Tab. 3, our proposed caching method achieves comparable performance with L2C [26] and reduces the computation overhead by $23\%$ , thanks to + +
MethodSampler#StepsIS↑FID↓sFID↓Prec.↑Recall↑#MACs↓(T)
DiT-XL/2 (cfg = 1.5)DDIM40239.92.354.260.800.599.49
Naive Caching (L2C [26])DDIM50244.12.274.230.810.599.04
ICC (CD-SVD, r = 192, p = 2)DDIM46253.02.284.260.820.576.98
+ +the correction effect of increment-calibration. It is also worth noting that L2C employs a learning-based method to optimize its caching pattern, necessitating additional training. Conversely, our method's calibration parameters are derived in a training-free manner and can be obtained in just a few minutes on a single NVIDIA 4090D GPU, significantly reducing the complexity and efforts of deployment. + +# 4.3. Comparison with Fast Sampling + +For DMs, a common practice to reduce computation overhead is decreasing the sampling steps at the cost of quality loss. Fig. 5 and Fig. 6 illustrates the complexity-quality trade-off curves of increment-calibrated caching and fast samplers. For class-conditional synthesis, our proposed method outperforms DDIM in IS, FID, and sFID when a fixed computation budget is given, especially when the complexity is constrained. That means, with increment-calibrated caching, it is hopeful to accelerate the sampling greatly depending on the lower bound of specified metric. For example, when the maximum of FID is set to around 2.5, increment-calibrated caching with 30 steps outperform 35-step DDIM with 12 IS increase at the cost of less than 0.06 FID increase. Meanwhile, the computation is reduced by $45\%$ , which means the theoretical acceleration ratio of increment-calibrated caching of relative to DDIM reaches 1.8. For text-to-image generation, the proposed method can be used to reduce the computation overhead while maintain or even improve FID and Clip Score. For example, DPM sampler begins to converge when the number of steps reaches 30, where increment-calibrated caching can eliminate $45\%$ MAC operations and decreases FID by 0.67. + +# 4.4. Ablation Study + +Sensitivity of Input and Output Channels. This work applies scaling for both the input and output channels of weight matrices during the process of channel-aware SVD. To evaluate the sensitivity disparities between these two dimensions, we compare CD-SVD with two reduced variants: $\mathrm{CD - SVD}_i$ , which only scales the input channels, and $\mathrm{CD - SVD}_o$ , which only scales the output channels. As illustrated in Tab. 4, CD-SVD outperforms both $\mathrm{CD - SVD}_i$ and $\mathrm{CD - SVD}_o$ across all metrics. Notably, $\mathrm{CD - SVD}_i$ demonstrates a significantly better performance compared to $\mathrm{CD - SVD}_o$ . This suggests that, while outlier activations are present in + +Table 3. Comparison between increment-calibrated caching and L2C [26]. + +
Calibration MethodIS↑FID↓sFID↓
SVD (r = 128)207.15.115.69
CD-SVDi (r = 128)216.94.315.19
CD-SVDo (r = 128)209.14.975.51
CD-SVD (r = 128)217.34.275.13
+ +Table 4. The comparison of CD-SVD-based increment-calibrated caching with two reduced versions: CD-SVD $_i$ and CD-SVD $_o$ . Results are based on DiT-XL/2, evaluated on ImageNet wit 20-step DDIM. + +
Calibration Method#StepsIS↑FID↓sFID↓
SVD (r = 128)32227.03.134.71
CA-SVD (r = 128)32236.82.774.35
CD-SVD (r = 128)32234.12.864.51
SVD (r = 192)30244.52.584.34
CA-SVD (r = 192)30252.82.744.69
CD-SVD (r = 192)30250.62.534.34
SVD (r = 256)28257.12.664.47
CA-SVD (r = 256)28261.13.196.48
CD-SVD (r = 256)28261.42.694.57
+ +Table 5. Comparison of different calibration mechanisms with varying rank. Results are based on DiT-XL/2, evaluated on ImageNet with DDIM. + +both input and output channels, the weight elements associated with input channels are more sensitive to this issue. + +Comparison of Calibration Mechanisms. In this work, the calibration of increment-calibrated caching can be achieved through three methodologies: the original SVD, CA-SVD, and CD-SVD. Our findings indicate that no single method consistently outperforms the others across all scenarios. Table 5 presents the results for all three approaches with varying rank values. When only a limited number of ranks are retained as calibration parameters, CA-SVD and CD-SVD demonstrate superior performance compared to the original SVD. This advantage stems from their consideration of channel sensitivity, allowing them to filter the most significant ranks, which subsequently enhances the FID, sFID, and IS metrics. However, as the number of + +![](images/81e0bbb19c29167392ff381453a7cafc80d984e3ff22dc55799a15f83e2e7f25.jpg) +Figure 5. The trade-off between the number of MACs and (a) IS, (b) FID, and (c) sFID for class-conditional synthesis on ImageNet with DiT-XL/2. For increment-calibrated caching, the period $p$ is set to 2. + +![](images/14efed214a1d36364bdfc9bd91af8e6d49ae9bf03e95f0af8e5bd54c2c3e1bc2.jpg) + +![](images/19e2052acb4af4b74762f0c9b67793ec3ee0cd80f4388a8988a36240c4ee8986.jpg) + +![](images/6b07d6c3bd3e4d05f05727af5aaabd399de6ed515cc3460be0588c65c8aabeb8.jpg) +Figure 6. The trade-off of between the number of MACs and (a) FID-30k and (b) Clip Score for text-to-image generation on MSCOCO-2014 with PixArt- $\alpha$ . For increment-calibrated caching, the period $p$ is set to 2 and the rank $r$ is 64. + +![](images/add0020c271af10c443bb4bd344df95be6ec8a2c4fd91d3987e68db1e30e53da.jpg) + +![](images/d45e198dfebb1eac5cd602e428bd94780d5815fd81802c960ee6494085de0fb1.jpg) + +![](images/ffc454015b6bbda516d94c4cffc6137476cc1b6684b63cd71437fe03e2351e9b.jpg) + +![](images/dfa8539758dabb2af7a8e7418efe91b8156b0a24bfce4723f2b5824b1018546f.jpg) +Figure 7. The impact of increased rank $r$ on (a) IS, (b) FID for DiT-XL/2 on ImageNet with 30-step DDIM, and (c) Clip Score, (d) FID-30k for PixArt- $\alpha$ on MSCOCO-2014 with 20-step DPM. + +![](images/be75113067385d1daf91d3e9ee7a803e90d053ab1aa74c1d53c7417ce9f4978e.jpg) + +ranks used to generate calibration parameters increases, the application of either CA-SVD or CD-SVD may negatively impact both the FID and sFID, although they continue to improve the IS metric. + +Impact of Varying Rank. According to simple intuition, a natural assumption is that the image quality will be improved smoothly when the rank $r$ of calibration parameter is increased. However, our experiments indicate that this is not always the truth, as shown in Fig. 7. For results of text-to-image generation, although FID-30k decreases with the increasing $r$ at first, it begins to increase when $r$ reaches + +256. Although the adoption of channel-aware SVD improves the results, but its curve is still not monotonically decreasing. Another related phenomenon is that some calibration settings even outperform the non-caching sampling with the same number of step. It means not all the singular values have a positive influence on the effect of incremental calibration. Thus, the proposed method has the potential to obtain significant complexity reduction without sacrificing generation quality. + +# 5. Conclusion + +In this work, we propose increment-calibrated caching, a novel method to reduce the computation complexity of DiT in a training-free manner. Combining the ideology of low-rank approximation and caching-based acceleration, increment-calibrated caching corrects cached activations from previous timesteps and guides them towards required accurate results in the subsequent timesteps. This process is ensured with calibration parameters that are generated from the pre-trained model itself with SVD-based low-rank approximation. We further introduce channel-aware SVD, which takes the channel sensitivity into consideration and prevents harmful outlier issues. Experimental results show that our method largely outperforms naive caching method in performance. Besides, compared with 35-step DDIM, our method eliminates more than $45\%$ computations and improves IS by 12 at the cost of less than 0.06 FID increase. + +# Acknowledgements + +This work was supported in part by the National Key Research and Development Program of China under Grant 2023YFB4404603; and in part by the National Natural Science Foundation of China under Grant 92164301, Grant 62204003, Grant 62225401, and Grant 61927901. + +# References + +[1] Tim Brooks, Bill Peebles, Connor Holmes, Will DePue, Yufei Guo, Li Jing, David Schnurr, Joe Taylor, Troy Luhman, Eric Luhman, Clarence Ng, Ricky Wang, and Aditya Ramesh. Video generation models as world simulators, 2024. 2 +[2] Junsong Chen, Chongjian Ge, Enze Xie, Yue Wu, Lewei Yao, Xiaozhe Ren, Zhongdao Wang, Ping Luo, Huchuan Lu, and Zhenguo Li. 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Metaxas $^{1}$ Licheng Yu $^{2}$ + +$^{1}$ Rutgers University $^{2}$ Meta + +# Abstract + +Prevailing Multimodal Large Language Models (MLLMs) encode the input image(s) as vision tokens and feed them into the language backbone, similar to how Large Language Models (LLMs) process the text tokens. However, the number of vision tokens increases quadratically as the image resolutions, leading to huge computational costs. In this paper, we consider improving MLLM's efficiency from two scenarios, (I) Reducing computational cost without degrading the performance. (II) Improving the performance with given budgets. We start with our main finding that the ranking of each vision token sorted by attention scores is similar in each layer except the first layer. Based on it, we assume that the number of essential top vision tokens does not increase along layers. Accordingly, for Scenario I, we propose a greedy search algorithm (G-Search) to find the least number of vision tokens to keep at each layer from the shallow to the deep. Interestingly, G-Search is able to reach the optimal reduction strategy based on our assumption. For Scenario II, based on the reduction strategy from G-Search, we design a parametric sigmoid function (P-Sigmoid) to guide the reduction at each layer of the MLLM, whose parameters are optimized by Bayesian Optimization. Extensive experiments demonstrate that our approach can significantly accelerate those popular MLLMs, e.g. LLaVA, and InternVL2 models, by more than $2 \times$ without performance drops. Our approach also far outperforms other token reduction methods when budgets are limited, achieving a better trade-off between efficiency and effectiveness. + +# 1. Introduction + +Multimodal Large Language Models (MLLMs) usually leverage a pre-trained vision encoder to encode the input image(s) into vision tokens that are fed into pre-trained Large Language Models (LLMs). Recent studies [25, 45] + +demonstrate that increasing the number of vision tokens by using high resolution inputs significantly enhances the effectiveness of MLLMs. However, such large number of vision tokens leads to inefficiency of model inference, preventing MLLMs from real-world applications. + +To address such inefficiency, prompt-agnostic approaches are proposed to reduce the number of vision tokens before feeding them into LLMs. Various approaches have been proposed, including local attention pooling [20, 24, 32], re-samplers as compression layers [45, 52], or deformable convolutions [3], etc. One noticeable issue of prompt-agnostic approaches is the ignorance of the input text prompts from the user. Since different prompts may focus on different regions of the image, prompt-agnostic approaches are likely to preserve irrelevant vision tokens that can be potentially further removed. As a remedy, prompt-aware methods are proposed to leverage text prompts in the vision token reduction. For example, FastV [5], VTW [26], and PDrop [44] remove vision tokens at certain layers of the LLM within the MLLM. However, their token reductions are all designed with handcrafted rules that vary by MLLMs. They also focus more on reducing the computational cost without performance drops, while not addressing how to assign computations for better effectiveness with limited budgets. We believe the latter is in greater demand in practical edge-device applications. + +To address the aforementioned drawbacks, in this paper, we propose a prompt-aware approach via the automatic search of optimal vision token reduction strategies for given MLLMs. Moreover, we consider efficiency from two scenarios, i.e., (I) Reducing computational cost with minor performance drops, and (II) Improving the performance with given budgets. + +We first investigate correlations between vision tokens and instruction tokens (i.e., text tokens provided by users). Specifically, we sort the vision tokens of each layer based on their attention scores to instruction tokens and calculate the Kendall's Tau correlation coefficient [17] between the current layer and the next layer. Figures 1a and 1b illus + +![](images/033518780cd98511f71c1fe7bae4ca4d639622d5e76d406929a976fa34f232f3.jpg) +(a) + +![](images/d2bcf3c4185b48750d27295b0be08662107c5fd718d2435d2fb901aeaf79ec78.jpg) +(b) +Figure 1. (a): Kendall's Tau correlation coefficient between the current layer and the next layer of LLaVA-1.5-7B [28]. A value larger than 0.7 is high. (b): Kendall's Tau correlation coefficients for InternVL2-8B [7]. (c): Keeping rates along layers from G-Search (blue solid curve), and the fitted curve with P-Sigmoid (orange dash curve) for LLaVA-1.5-7B. + +![](images/84a62613585064635752425e5d59864e305364ecc323c47c11e8843681e448a1.jpg) +(c) + +trate the coefficients along layers for LLaVA-1.5-7B [28] and InternVL2-8B [7], respectively. As shown, the correlation coefficients are high since the second layer. We regard the relative importance of one vision token as its ranking. Our main finding can be stated as the relative importance of one vision token remains similar in each layer of MLLMs after the first layer. Based on the finding, we assume that the importance of vision tokens in deeper layers can be sorted by the attention scores of earlier layers. Concurrent works [22, 42] find that only top tokens with high attention scores are essential for LLMs' inference. Based on our main finding, we assume that the essential top vision tokens in deeper layers are also top tokens in earlier layers. Thus, the number of essential top tokens does not increase as the depth of the MLLM layer grows. + +Based on the above analysis, we propose a greedy search (G-Search) for Scenario I. Specifically, in each layer of a pretrained MLLM from the shallow to the deep, we rank vision tokens using the attention scores of the prior layer. Then, we find a keeping rate to retain the least number of top vision tokens with insignificant performance drops via Bayesian Optimization. Our main finding and assumptions enable G-Search to remove unnecessary vision tokens for current and later layers in the current layer. Sec. 3.2 shows our method can achieve the optimal vision token reduction strategy. We analyze keeping rates from G-Search, and find that they decrease along layers and can be fitted by a S-curve as shown in Fig. 1c. Accordingly, for Scenario II, we design a parametric sigmoid function (P-Sigmoid) to attain keeping rates along layers with given budgets, and search the optimal parameters that maximize the performance via Bayesian Optimization. + +We conducted thorough experiments on 12 popular benchmarks with various MLLMs of different sizes, i.e. LLaVA-1.5-7B [28], InternVL2 family [6, 7] with 1B, 2B, 4B, and 8B models. The extensive experiments demonstrate + +that for Scenario I, G-Search can significantly accelerate MLLMs by up to $2.3 \times$ with only a $0.2\%$ drop of average accuracy. It scales up well, resulting in larger reduction rates for larger models. Compared to existing prompt-aware methods, it runs $20\%$ or more faster and achieves better performance. Moreover, G-Search can further speed up prompt-agnostic methods [20, 46] by up to $1.5 \times$ . For Scenario II, on top of LLaVA-1.5-7B, P-Sigmoid outperforms FastV by $+3.38\%$ of average accuracy when $87.5\%$ of vision tokens are reduced. It goes to $+5.46\%$ with around $94\%$ of vision tokens reduced. On top of InternVL2-8B, P-Sigmoid achieves a larger gain of $+7.69\%$ when reducing $87.5\%$ of vision tokens. Moreover, our results indicate that different MLLMs need different reduction strategies. Thus, handcrafted reduction methods are likely to perform well with certain MLLMs and benchmarks but fail in other cases. + +Our contributions are summarized as. (1) We present a new insight that the relative importance of each vision token remains similar across layers of MLLMs, which paves the path for automatic reduction search. (2) We consider efficiency from two scenarios, and propose G-Search and P-Sigmoid that find the best reduction strategy by automatic search. G-Search significantly reduces the computational cost with minor performance drops. P-Sigmoid achieves great trade-offs between efficiency and effectiveness. (3) We conducted extensive experiments on various benchmarks and MLLMs, and show clear boosts from the proposed methods in terms of both efficiency and efficacy. + +# 2. Related work + +# 2.1. MLLMs + +Multimodal models are able to process multiple modalities and benefit various fields [54-56]. MLLMs are LLMs with the ability to understand multiple modalities beyond just natural language. Recent focus is the integration of visual perception with language [8, 15, 57]. LLaVA [27, 28] is one of the most powerful and popular MLLMs. It intro + +![](images/dccaf393fc348e0f5ca353bc6fe3c714cd160c757092307736386cc06e683918.jpg) +Figure 2. MLLM tokenization and inference with vision token reductions. The proposed G-Search and P-Sigmoid automatically search the optimal reduction strategy, i.e. the keeping rate of each layer. + +duces linear layers to project vision features into the text embedding space, and instruction-tune both the projector and the LLM on large-scale, machine-generated instruction-following data. To enhance the effectiveness, later studies explore high resolution inputs [25, 29], model design [1], and scaling up model size and data [6, 7]. Although with great performance, existing MLLMs require substantial computational resources, due to their large model sizes and the large number of vision tokens to handle. In this paper, instead of improving the performance, we focus on improving the efficiency of MLLMs and propose training-free solutions for two scenarios. + +# 2.2. Token reduction + +StreamingLLM [42] first shows that LLMs are likely to assign high attention scores to the first a few tokens, called attention sinks. With attention sinks and a fixed-length attention window in the key-value (KV) caches, LLMs are able to achieve the similar performance as the full KV caches are used. Later, SnapKV [22] automatically compresses KV caches by selecting clustered important KV positions for each attention head. Those methods reduce computational cost of the decoding phrase but still calculate the whole KV caches in the prefilling phrase. In contrast, our methods can reduce the cost of both prefilling and decoding phrases. + +Besides text token reduction in LLM, recent studies also explore vision token reduction in MLLMs. LLaVA-HR [32] and Mini-Gemini [24] fuse vision tokens of high resolution inputs into low resolution ones. LLaVA-UHD [45] and Beyond LLaVA-HD [52] learns local compression layers. + +LLaMA-PruMerge [37] removes vision tokens from a ViT model [11], which are not highly correlated to the class token. Honeybee [3], TokenPacker [20], and Deco [46] leverage convolutions, local attentions, and average pooling to down-sample the features of high resolution images. Those methods are prompt-agnostic, which reduce vision tokens before feeding them into the LLM. Thus, they ignore the user instructions that are important clues to remove irrelevant vision tokens. Prompt-aware approaches consider user instructions. LLaMA-VID [23] and VoCo-LLaMA [47] compress vision tokens into a few tokens based on vision-text cross attentions. However, their compression comes with a clear performance drop. FastV [5], VTW [26], and PDrop [44] reduce vision tokens at certain layers of LLM based on the attention scores between vision and instructions tokens. However, their reduction strategy is manually crafted based on a certain MLLM or a benchmark. In contrast, our method automatically finds the optimal reduction strategy, generalizes to various MLLMs and benchmarks, and achieves better efficiency-effectiveness trade-off. + +# 3. Searching optimal reduction strategy + +# 3.1. Correlation of vision & instruction tokens + +Preliminaries: Prevailing MLLM architecture comprises a vision encoder, a vision-to-text projector, and a pre-trained LLM. The vision encoder is usually a pre-trained vision transformer of CLIP [36] that encodes an image into vision tokens. The vision-to-text projector projects vision tokens of the vision encoder into the text space. Q-former [18] and + +Algorithm 1 G-Search with Bayesian Optimization +Input: Target Function $f(\cdot)$ MLLM $\theta$ Data Samples $\mathcal{D}$ Number of Bayesian Optimization Iterations $T$ +Output: Keeping Rate Sequence $\mathcal{R}$ $\triangleright$ Define a function for Bayesian Optimization function BAYESIANOPTIMIZATION(f, R, $\theta ,\mathcal{D},T$ Initialize a Gaussian Process model $\mathcal{GP}$ Define the acquisition function A(·) Expected Improvement (EI) is adopted as A(·) Uniformly sample $\mathcal{X}_0 = \{\hat{r}_{i < 10}|\hat{r}_i\in [0,min(\mathcal{R})]\}$ $\forall \hat{r}\in \mathcal{X}_0$ evaluate the target function $f(\hat{r} |\mathcal{R},\theta ,\mathcal{D})$ . for $n = 0$ to $T - 1$ do Fit $\mathcal{GP}$ to the observed data $(\mathcal{X}_n,f(\mathcal{X}_n|\mathcal{R},\theta ,\mathcal{D}))$ Get the next point $\hat{r}_{n + 1} = \arg \max_{r}\mathrm{A}(r;\mathcal{GP})$ Update $\mathcal{X}_{n + 1} = \mathcal{X}_n\cup \{\hat{r}_{n + 1}\}$ end for Find the point w/ the best observed value by Eq. 1 return $r^*$ +end function +Repeat searching for each layer + $\mathcal{R}\gets \emptyset$ +for layer depth $i\in [3,\dots,L]$ do $r_i =$ BAYESIANOPTIMIZATION(f, R, $\theta ,\mathcal{D},T$ $\mathcal{R}\gets \mathcal{R}\cup r_i$ +end for + +linear layers [28] are popular choices for the projector. The pre-trained LLM takes as input system prompt tokens, projected vision tokens, and instruction tokens, and generates responses. Usually, system tokens remain unchanged for a given LLM, and instruction tokens vary as the user inputs. We visualize the tokenization of MLLMs and how to feed tokens into the LLM in the left part of Fig. 2. + +Why cross-modality token correlation matters: Different user instructions usually refer to different regions of images or vision tokens, leaving others irrelevant. In this paper, we attempt to leverage instruction tokens as a clue to remove irrelevant vision tokens, thus accelerating MLLMs. Since attention scores are widely used to interpret the alignment between tokens [4, 22, 42], we leverage attention scores between vision tokens and instruction tokens to indicate their correlation. Vision tokens of high attention scores are highly correlated to the user instructions and thus are important tokens to keep. We run experiments on a holdout dataset of LLaVA [28] and have the following findings. + +Main finding: The ranking or relative importance of each vision token remains similar in each layer after the first layer. In each layer of the model, we rank the vision tokens + +based on their attention scores and calculate the Kendall's Tau correlation coefficient [17] between the ranking of the current layer and that of the next layer. Figures 1a and 1b visualize the correlation coefficients along layers for LLaVA-1.5-7B and InternVL2-8B, respectively. As shown, the correlation coefficients are high (usually $\geq 0.7$ ) except the one between the first two layers, which indicate the relative importance of each vision token remains similar across layers except the first layer. + +# 3.2. G-Search for Scenario I + +Assumption (1): The importance of vision tokens in deeper layers can be decided by attention scores of earlier layers. This is directly derived from our main finding in Sec. 3.1 that the ranking of vision tokens is similar across layers. + +Assumption (2): The number of essential top vision tokens does not increase along layers. This assumption is derived by the following. First, recent studies [22, 42] demonstrate that only top tokens with high attention scores are essential for LLMs' inference. According to our main finding, those essential top tokens in deeper layers should be top tokens in earlier layers. Second, if some tokens should be kept in deeper layers to preserve the performance, we cannot remove them from earlier layers. Otherwise, deeper layers cannot access those tokens. Thus, essential tokens in deeper layers are a subset of essential tokens in earlier layers. + +Greedy Search Algorithm (G-Search): Based on our assumptions, we propose the following greedy algorithm to find the least number of essential tokens at each layer, and prove that it can reach the optimal solution. + +For the $i$ -th layer $i = 3, \dots, L$ of a pretrained MLLM, we sort vision tokens based on their attention scores $(\mathbf{S}^{i-1})$ of the last layer, i.e. the $(i-1)$ -th layer. Note that we ignore the first layer because it is poorly correlated with other layers. Then, we search a keeping rate $r_i \in [0,1]$ that decides the number of top vision tokens $(n_i)$ to keep at the $i$ -th layer w.r.t. the total number of input vision tokens $(N)$ . That is, $r_i = n_i / N$ . We regard $r_i^*$ as the optimal keeping rate that maximizes the target function $f(\cdot)$ , + +$$ +r _ {i} ^ {*} = \underset {r _ {i} \leq r _ {i - 1}} {\operatorname {a r g m a x}} f \left(r _ {i}\right) \tag {1} +$$ + +$$ +f \left(r _ {i}\right) = E \left(r _ {i} \mid r _ {3}, r _ {4}, \dots , r _ {i - 1}, \theta , D\right) - \lambda \cdot r _ {i} \tag {2} +$$ + +where $E(\cdot)$ refers to the performance of the MLLM parameterized by $\theta$ on the dataset $D$ . The term $E(\cdot)$ refers to effectiveness, and the term with $r_i$ embodies efficiency. We set $\lambda = 0.01$ so that efficiency is improved when performance is maintained. Since $n_i$ and $N$ are bounded integers, we can always get the optimal $r_i^*$ via brute force. For a faster search, we employ Bayesian Optimization [35]. The pseudo implementation is provided in Algorithm 1. + +Inference with keeping rates: As shown in Fig. 2, the only different between the standard inference and inference with + +![](images/918b3473eb55504e3e8e11489ec4307e4707654a9dba8bba52828fa8bc0f0b0f.jpg) +Figure 3. Keeping rates of various MLLMs from G-Search. All curves are S-curve and can be fitted by P-Sigmoid. + +keeping rates is to add a plug-and-play Sort & Reduce module before each LLM layer. In Sort & Reduce of the $i$ -th layer, similar as G-Search, we first sort the vision tokens based on their attention scores of the $(i - 1)$ -th layer. Then, we keep the top $(r_i \cdot N)$ tokens and remove the rest. + +Proof of the optimality: Supposing the optimal sequence of keeping rates is $\mathcal{R}^* = [r_3^*, r_4^*, \dots, r_L^*]$ , the sequence from our search is $\mathcal{R} = [r_3, r_4, \dots, r_L]$ , and $\forall i < j, r_i = r_i^*$ . + +If $r_j^* > r_j$ , our method reduces more tokens (noted as $v^{+}$ ) than the optimal at the $j$ -th layer. That is, $v^{+}$ are not necessary in current layer and can also be removed in later layers. Otherwise, if later layers require $v^{+}$ , the current layer also needs $v^{+}$ based on our Assumption (2). Thus, we can replace $r_j^*$ with $r_j$ from our search. + +If $r_j^* < r_j$ , our method reduces less tokens than the optimal at the $j$ -th layer. Since our method always remains the performance, $r_j^*$ and $r_j$ results in the same performance. Based on our greedy strategy, we should find $r_j^*$ as $r_j$ . Thus, $r_j^* < r_j$ is impossible. + +In conclusion, we can always convert $\mathcal{R}^*$ to $\mathcal{R}$ , showing that $\mathcal{R}$ from our search is optimal. + +# 3.3. P-Sigmoid for Scenario II + +Scenario II requires improving the performance with a given budget. We start with analyzing the reduction strategies of G-Search and find that keeping rates along layers can be fitted into a sigmoid-like curve as shown in Fig. 1c. Keeping rates of different MLLMs are visualized in Fig. 3, which are all in sigmoid-like curves. We call the the sigmoid-like function to fit as the parametric sigmoid (P-Sigmoid) and define it as, + +$$ +\hat {r} (i) = \frac {2 b}{1 + e ^ {k (i - \alpha)}} \tag {3} +$$ + +where $\hat{r}(i)$ is the fitted keeping rate for the $i$ -th layer, and $b \in [0,1]$ refers to the rate of the numbers of vision tokens after and before the reduction. We take $b$ as the budget because computational cost is positively correlated to the number of tokens. $\alpha$ is the midpoint of the domain of $\hat{r}(\cdot)$ . For example, the function $\hat{r}(\cdot)$ for a MLLM has the domain + +of $[3,L]$ , and $\alpha = 17.5$ . Note that we do not reduce vision tokens of the first two layers. + +The integral of $\hat{r}(\cdot)$ within its domain of $[3, L]$ is always $(L - 2)*b$ regardless of $k$ , which enables vision token reduction at a given budget. We assume that, in Scenario II, the optimal keeping rates follow similar parametric sigmoid functions as $\hat{r}(\cdot)$ . Since $b$ and $\alpha$ are known for a specific MLLM, we search the optimal $k$ to maximize the performance on a small dataset. We leverage Bayesian Optimization to search a non-negative real number for $k$ . + +# 4. Experiments + +# 4.1. Experimental setup + +Benchmarks: We adopt 12 popular evaluation benchmarks and follow Cambrian-1 [39] to categorize them as, + +- General VQA: MME, MMBench [30], and GQA [14]. Those benchmarks include a wide range of visual question answering questions and indicate the general ability of MLLMs on visual understanding. +- Knowledge: MMMU [48], MathVista [31], and AI2D [16]. They mainly focus on knowledge test across disciplines, including Art, Business, Health & Medicine., Humanities, Math, and Tech & Engineering. +- OCR & Chart: TextVQA [38], ChartVQA [33], and DocVQA [34], which focus on the understanding of charts, diagrams, and documents. +- Vision-Centric: POPE [21], RealWorldQA [41], and HallusionBench [13]. They are used to evaluate MLLMs in terms of language hallucination and visual illusion. + +Metrics for effectiveness: We adopt default metrics of each benchmark. Specifically, the accuracy is the metric for most benchmarks. And we report the relaxed accuracy [33] for ChartQA, Average Normalized Levenshtein Similarity (ANLS) [2] for DocVQA, F1 scores for POPE, and the sum of perception and recognition scores for MME. When calculating the average accuracy, we normalize MME scores by dividing the full score, i.e. 2800. + +Metrics for efficiency: We evaluate the efficiency in terms of memory cost, FLOPs, and time cost. For the memory cost, we mainly consider the KV-Cache of vision tokens and report the rate of the numbers of kept vision tokens and vision tokens without reduction. To calculate FLOPs, we employ the tool calflops [43] and report Tera FLOPs (TFLOPs). For the time cost, we use optimum-benchmark from Huggingface to evaluate the pre-filling time at inference. This tool requires to preset the number of input text tokens and the number of output tokens. To mimic the evaluation on 12 benchmarks, we calculate the mean numbers of input and output text tokens on all samples. It ends up 75 input tokens and 5 output tokens after rounding. + +
MLLM ++ MethodAvg. acc. ↑Memory cost ↓TFLOPs ↓Time cost ↓
LLaVA-1.5-7B48.971.09.180.625
+ VTW44.320.55.190.385
+ PDrop48.700.4695.470.381
+ FastV (R=50%)48.700.5315.490.387
+ G-Search (Ours)48.770.3403.950.301
InternVL2-1B59.851.04.620.384
+ VTW41.130.53.730.331
+ PDrop53.700.5833.880.336
+ FastV (R=50%)54.850.5423.910.342
+ G-Search (Ours)59.190.5273.840.333
InternVL2-2B61.941.08.100.598
+ VTW37.840.55.500.439
+ PDrop58.980.5835.930.452
+ FastV (R=50%)59.910.5425.850.451
+ G-Search (Ours)61.220.5325.640.444
InternVL2-4B68.161.013.970.969
+ VTW49.010.58.720.649
+ PDrop66.940.4698.350.627
+ FastV (R=50%)66.190.5319.010.652
+ G-Search (Ours)67.650.4888.690.645
InternVL2-8B70.831.024.101.518
+ VTW52.510.513.710.927
+ PDrop69.190.46913.130.915
+ FastV (R=50%)69.420.53114.580.998
+ G-Search (Ours)70.100.42412.240.860
+ +MLLMs in experiments: In our experiments, we compare our methods and existing reduction methods on top of various MLLMs, including the popular LLaVA-1.5-7B, and InternVL2-1B/2B/4B/8B from the InternVL family [6, 7] that are one of SOTA open sourced MLLMs. + +Implementation details: LMMs-Eval [49] was adopted to evaluate MLLMs on the 12 aforementioned benchmarks. Note that for LLaVA-1.5-7B, a lower performance on TextVQA is expected because the official evaluation code adds extra reference OCR tokens for inference, which allows MLLMs to make choices between possible answers instead of understanding vision tokens. It is not necessary to search at each layer, as you can see flat regions in Fig. 1c. Thus, we conducted G-Search for every three layers. All searches were conducted on a small split of training data of LLaVA [28]. Since our methods are training-free, all experiments can be conducted using 8 NVIDIA A100 GPUs. + +# 4.2. Evaluation for Scenario I + +For Scenario I, we attempt to accelerate the MLLMs without significant performance drops. We first compare our G-Search with existing prompt-aware methods, i.e., + +Table 1. Comparison to prompt-aware reduction methods for Scenario I. "Avg. acc." refers to average accuracy on 12 benchmarks. + +
LLaVA-1.5-7B + MethodAvg. acc. ↑Memory cost ↓TFLOPs ↓Time cost ↓
TokenPacker47.601.03.270.268
+ G-Search (Ours)47.680.4112.120.182
Δ+0.08-0.589-1.15-0.086
DeCo46.971.03.260.268
+ G-Search (Ours)46.710.4322.160.198
Δ-0.26-0.568-1.1-0.070
+ +Table 2. G-Search improves prompt-agnostic reduction methods. + +VTW [26], PDrop [44], and FastV [5]. Then, we demonstrate that G-Search can further improve the efficiency on top of two recent prompt-agnostic methods that reduce vision tokens before feeding them into the LLM., i.e. TokenPacker [20], and DeCo [46]. + +Comparison to existing prompt-aware methods: We report the main results in Table 1 with the following findings. Please check the supplement for full results on all benchmarks. First, our G-Search reduces TFLOPs by $16.9\%$ , $30.4\%$ , $35.9\%$ , and $49.2\%$ on top of InternVL2-1B, 2B, 4B, and 8B, respectively, achieving larger reduction rates on larger models. This is probably because larger models are likely to have more computational redundancy. Second, compared to VTW [26], PDrop [44], and FastV [5], our G-Search either has much lower TFLOPs or achieves better average accuracy. For example, on top of LLaVA-1.5-7B, our method gets similar average accuracy as FastV with only $72\%$ TFLOPs. Third, on top of InternVL2 models, prior methods hardly maintain the performance as they do on LLaVA-1.5-7B. Since their reduction strategy is manually designed based on LLaVA-1.5-7B and specific benchmarks, their hand crafted reductions do not generalize to different MLLMs and benchmarks. In contrast, thanks to the automatic search, G-Search generalizes well to different MLLMs and benchmarks. + +Improving prompt-agnostic methods: We apply our G-Search on top of two recent prompt-agnostic methods, i.e. TokenPacker [20], and DeCo [46]. As shown in Table 2, our method consistently reduces TFLOPs by more than $33.9\%$ with less than $0.21\%$ drop on the average accuracy. TokenPacker and DeCo reduce vision tokens without considering user instructions. In contrast, our method is aware of user instructions and improves them probably by removing more irrelevant vision tokens. + +# 4.3. Evaluation for Scenario II + +P-Sigmoid with different budgets: FastV is configurable with a filtering ratio (R) that refers to the percentage of vision tokens to remove at the 2nd layer. We instantiate FastV with different R to set up different budgets. The values of R are set as $50\%$ , $75\%$ (i.e. $25\%$ vision tokens left), $87.5\%$ , $93.75\%$ . Then, we set $b$ of P-Sigmoid to match + +
MLLMMethodGeneral VQAKnowledgeOCR & ChartVision-Centric
TFLOPs ↓Avg acc. ↑RealWorldQAHallusionBench
LLaVA -1.5-7B+ FastV2.7443.141644.560.254.037.321.852.138.714.418.166.349.346.7
+ P-Sigmoid Δ2.6646.521700.463.758.337.122.054.544.115.723.378.053.647.1
-0.08+3.38+55.9+3.5+4.3-0.2+0.2+2.4+5.4+1.3+5.2+11.7+4.3+0.4
Intern VL2-1B+ FastV3.4343.161581.852.547.534.023.855.039.617.226.579.443.342.8
+ P-Sigmoid Δ3.3847.831691.756.650.833.326.655.549.633.936.283.244.842.9
-0.05+4.67+109.9+4.1+3.3-0.7+2.8+0.5+10.0+16.7+9.7+3.8+1.5+0.1
Intern VL2-2B+ FastV4.2647.661661.068.152.833.325.968.054.523.834.080.129.742.3
+ P-Sigmoid Δ4.1651.541710.768.155.033.228.666.761.343.046.582.230.142.8
-0.10+3.88+49.70.0+2.2-0.1+2.7-1.3+6.8+19.2+12.5+2.1+0.4+0.5
Intern VL2-4B+ FastV5.4854.831950.974.156.744.125.870.957.334.142.081.655.845.9
+ P-Sigmoid Δ5.3861.192039.176.359.445.830.074.366.160.857.384.057.849.7
-0.10+6.36+88.2+2.2+2.7+1.7+4.2+3.4+8.8+26.7+15.3+2.4+2.0+3.8
Intern VL2-8B+ FastV7.7155.172066.274.355.444.725.672.660.335.039.678.954.547.3
+ P-Sigmoid Δ7.4662.862176.679.359.745.833.076.370.561.859.984.159.546.7
-0.25+7.69+110.4+5.0+4.3+1.1+7.4+3.7+10.2+26.8+20.3+5.2+5.0-0.6
+ +Table 3. P-Sigmoid with different MLLMs. We set $R = 87.5\%$ for FastV and set the budget of P-Sigmoid close to that of FastV. + +![](images/2af3e8e2a8d38de5f2d94c94599a44a7195a621ffdb74a1bdc653051bf05becb.jpg) +Figure 4. Comparison of reduction methods with different budgets. The average accuracy of LLaVA-1.5-7B with reductions on 12 benchmarks are reported. Compared to others, Our P-Sigmoid achieves the accuracy with no reduction using less TFLOPs. + +the budgets of FastV. For P-Sigmoid, the number of vision tokens are different across layers, which requires slightly more TFLOPs than keeping the same number of vision tokens in every layer as FastV. See theoretical analysis in the supplement. Thus, to get close TFLOPs as FastV, we lower down the budgets for our method by $\sim 7\%$ . For PDrop, we use different $\lambda$ to set up different budgets. Our P-Sigmoid is compared with FastV and PDrop on top of LLaVA-1.5-7B in Fig. 4. As shown, P-Sigmoid outperforms both FastV and PDrop in a large margin when TFLOPs are low, which clearly demonstrates that our method achieves a better trade-off between effectiveness and efficiency. + +P-Sigmoid with different MLLMs: We set $R = 87.5\%$ for FastV, and compare it with the proposed P-Sigmoid on top of different MLLMs. As shown in Table 3, with similar TFLOPs, our method outperforms FastV by a large margin on top of all MLLMs, i.e., $+3.38\%$ for LLaVA-1.5-7B, and $+4.67\% / +3.88\% / +6.36\% / +7.69\%$ for InternVL2-1B/2B/4B/8B. Moreover, our method gets the most improvement on OCR & Chart and Vision-Centric benchmarks, and gets moderate gains on Knowledge benchmarks. For example, on top of InternVL2-8B, P-Sigmoid and FastV get the scores of 61.8 vs 35.0 on ChartQA, while they get 45.8 vs 44.7 on MMMU. Since ChartQA is more about visual recognition and understanding, our P-Sigmoid significantly outperforms FastV by providing a better way to preserve vision tokens. MMMU focuses on knowledge test where texts are usually sufficient to address the questions. Thus, how to reduce vision tokens matters less. + +# 4.4. Further Analysis + +Smaller $k$ of P-Sigmoid for lower budgets: As shown in Fig. 5, on top of LLaVA-1.5-7B, the value of $k$ of P-Sigmoid increases as TFLOPs increase. A larger $k$ means a sharper S-curve, and a smaller $k$ refers to a flatter curve. That is, we are assigning more percentages of the budget to early layers when the budget increases. A possible explanation is that there are a few essential tokens in deep layers. Without those tokens, the performance will signifi + +![](images/9d24ec716ab9dd819c7e37c0a16f132cf2c393aa7c18e79b9ba210fb46d1e1cd.jpg) +Figure 5. Values of $k$ of P-Sigmoid vs TFLOPs. + +![](images/faedb89cb4a2c7654f99cffaca07e823c33c07fa9472a9f899dcec73d48f66ec.jpg) + +Figure 6. Attention scores vs layers of LLaVA-1.5-7B. + +
MLLMReduction strategy ofAverage accuracy ↑
InternVL2-1BSelf59.19
InternVL2-1BInternVL2-2B57.58
InternVL2-2BSelf61.22
InternVL2-2BInternVL2-2B60.90
InternVL2-4BSelf67.65
InternVL2-4BLLaVA-1.5-7B65.91
InternVL2-8BSelf70.10
InternVL2-8BLLaVA-1.5-7B69.49
+ +cantly drop. As a result, when the budget is limited, we need to assign enough computations to deep layers for those essential tokens. When the budget increases, deep layers get enough computations for essential tokens, and the rest of the budget can be assigned to early layers. + +MLLMs need flexible reduction methods. For Scenario I, reduction strategies should be customized for different MLLMs with the following evidences. First, as shown in Fig. 3, the S-curves of MLLMs from G-Search are different. Since G-Search reaches the optimal solution based on our assumption (See Sec. 3.2), different MLLMs have their own optimal reduction strategies. Second, we apply the keeping rates of LLaVA-1.5-7B on InternVL2-4B and 8B models, and exchange the keeping rates of InternVL2-1B and 2B models. As shown in Table 4, all MLLMs suffer from performance drops when using reduction strategies (i.e. keeping rates) of others. As a result, handcrafted methods can hardly provide appropriate reduction strategies for various MLLMs, while our method is flexible and can adjust reduction strategies based on MLLMs. + +Why a steady decrease in keeping rates: Figure 3 shows that the keeping rates of G-Search decrease steadily. This is + +Table 4. Exchange reduction strategies of different MLLMs for Scenario I. The strategy (i.e. keeping rates) of one MLLM from the search of P-Sigmoid does not generalize to others. + +
ModelKeeping ratesAvg. acc. ↑
PretrainedG-Search48.965
Train w/ reductionfor Scenario I48.365
Fintune w/ reduction48.364
PretrainedP-Sigmoid46.52
Train w/ reductionfor Scenario II46.40
Fintune w/ reduction47.09
+ +Table 5. Training LLaVA-1.5-7B with reductions. Keeping rates are from G-Search and P-Sigmoid applied on a pretrained LLaVA-1.5-7B model. + +not only because keeping rates cannot increase based on our assumption. Moreover, as shown in Fig. 6, the median of the attention scores of vision tokens drops in deep layers of the LLM within LLaVA-1.5-7B. Check similar visualizations for various MLLMs in the supplement. As shown in recent studies [22, 42], tokens of low attention scores in LLMs are not important and can be removed during inference. We assume that the drop in attention scores of vision tokens leads to the drop in the number of important tokens with high attention scores. Thus, keeping rates decrease. + +Training with reductions: Although the proposed G-Search and P-Sigmoid are training-free, MLLMs can be trained with reductions using keeping rates from our method. We collect keeping rates of a pretrained LLaVA-1.5-7B model from G-Search and P-Sigmoid for Scenario I and Scenario II, respectively. Then, new LLaVA-1.5-7B models are trained or finetuned with reductions. The budget of P-Sigmoid is set as that of FastV with $R = 87.5\%$ . We use the same training data as LLaVA [28] for both training and finetuning. As shown in Table 5, there is no performance boost in training/finetuning with reductions for Scenario I. The finetuning slightly improves the performance for Scenario II. Considering the huge cost of MLLM training/finetuning, our method acts as a good plug-and-play reduction solution for MLLMs. + +# 5. Conclusion + +This paper improves the efficiency of MLLMs in two scenarios. (I) Reducing computational cost without degrading the performance. (II) Improving the performance with a given budget. We find that the relative importance of each vision token remains similar at different layers. 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Noisy gradients in hybrid neural fields. Normal images of *Blub the fish* [42] (inset), using gradients queried from its hybrid neural SDF using automatic differentiation (AD) and our approach. Naively using AD gradients as surface normals leads to grainy artifacts, which our method alleviates. + +![](images/5310445d7994dbb5a2d69b1556da722adc8daab12a8ff3713a0ff170fd5ca368.jpg) +AD gradients + +![](images/5a90d3b1c74922d7786c0e8a448b21e8b57f7d8d61532ca080c0b0b0c9d75e07.jpg) +Ours + +# Abstract + +Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that leverage small MLPs and explicit representations, these models train quickly and can fit large scenes. Yet in many applications like rendering and simulation, hybrid neural fields can cause noticeable and unreasonable artifacts. This is because they do not yield accurate spatial derivatives needed for these downstream applications. In this work, we propose two ways to circumvent these challenges. Our first approach is a post hoc operator that uses local polynomial fitting to obtain more accurate derivatives from pre-trained hybrid neural fields. Additionally, we also propose a self-supervised fine-tuning approach that refines the hybrid neural field to yield accurate derivatives directly while preserving the initial signal. We show applications of our method to rendering, collision simulation, and solving PDEs. We observe that using our approach yields more accurate derivatives, reducing artifacts and leading to more accurate simulations in downstream applications. + +# 1. Introduction + +Neural fields are neural networks that take spatial coordinates as input and approximate spatial functions such + +as images [41], signed distance fields [36], and radiance fields [31]. The advent of hybrid neural fields, which modulate the neural network using features from a feature grid, has enabled much faster training [11, 33, 38] and much better scaling to large-scale 3D structures with incredible detail, including entire cities [37, 43, 45, 49]. Hybrid neural fields are thus gaining popularity as a representation of choice in many applications. However, while these hybrid neural fields can be trained to represent large, complex spatial signals with high fidelity, we find that the derivatives (computed with automatic differentiation or autodiff) of the trained field do not match the derivatives of the ground-truth signal; e.g., compare the grainy normals obtained from a fully trained hybrid neural SDF to the much smoother normals from the mesh in Figure 1. Such artifacts in derivatives can cause significant artifacts in rendering [43] or simulation pipelines [12] which heavily rely on accurate derivatives. Thus, for hybrid neural fields to fulfill their promise of a practical representation for spatial signals, we need to eliminate these errors in the derivatives. + +Why are the derivatives of hybrid neural fields so noisy? We observe that to enable the capture of complex geometry with high fidelity, hybrid fields are designed to have high-frequency components (e.g., spatial grids of a high resolution). As such, they also have high-frequency noise. This noise will be of fairly low magnitude in a well-trained hybrid field. But even so, differentiation will significantly am + +plify this high-frequency noise (Section 3.1) resulting in the artifacts that we see. We posit that we need a new differentiation operator that is robust to high-frequency noise. + +In this paper, we propose a new approach to reduce noise in the derivatives of pre-trained hybrid neural fields. Our approach takes inspiration from classical signal processing where derivatives are typically done on a smoothed version of the signal to avoid amplifying high-frequency noise. Our key idea is to replace direct derivatives of the hybrid neural field with derivatives of a local low-degree polynomial approximation of the field. These low-degree polynomials can be fit in closed form and effectively remove high-frequency noise. Importantly, this approach is general and can apply to any hybrid neural field independent of architecture. + +While this approach yields accurate derivatives for off-the-shelf neural fields, it requires that downstream pipelines be changed to use our new derivative operator. To avoid altering downstream pipelines, we propose an extension of this approach where we use the accurate derivatives from the low-degree local polynomial fit to regularize the neural field during training/finetuning. Concretely, we add an auxiliary loss that penalizes the difference between the autodiff gradients of the neural field and the derivatives from the local polynomial approximation. This yields a new hybrid neural field where autodiff itself yields accurate derivatives. + +Our experimental results show that our new derivative operator yields more accurate derivatives than autodiff, reducing errors in gradients by $4 \times$ . It also outperforms other alternative derivative operators, such as finite difference stencils, reducing errors in curvature by $4 \times$ . We also show that using our operator to regularize neural field finetuning improves derivative accuracy, outperforming other regularization strategies that encourage smoothness like eikonal regularization [2, 22, 28], showing that existing approaches are not well-suited for hybrid fields. Lastly, we demonstrate that our approaches substantially reduce artifacts in downstream rendering and simulation applications. Thus our proposed methods open the door for using hybrid neural fields in a large set of downstream applications. + +Contributions. Our overall contributions can be summarized as follows: (1) We identify the issue of inaccurate derivatives in a given pre-trained hybrid neural field and point out its relationship to high-frequency noise. (2) We propose a local polynomial-fitting operator to improve the accuracy of neural field derivatives. (3) We also propose a fine-tuning approach to improve the quality of autodiff derivatives of hybrid neural fields. We provide an implementation of our operators at: https://justachetan.github.io/hnf-derivatives/ + +# 2. Related Work + +Neural Fields. Neural fields are neural networks approximating spatial fields given coordinates as input [51, 52]. + +They have been used to represent megapixel images [29], 3D shapes in implicit fields [14, 30, 36] and radiance fields [5, 31, 46]. Our work is applicable to hybrid neural fields in all these applications, although our primary evaluation is on SDFs. Typical neural field architectures are multilayer perceptrons [31, 41, 44], but these can be slow to train and may not scale to large scenes with fine-grained details. As such, more current approaches use hybrid representations that modulate an MLP with spatial features stored on a grid [11, 21, 33, 43, 53]. These hybrid techniques scale well [37, 45, 50], but we show that they yield noisy derivatives: the key issue we strive to address here. Accurate derivatives are particularly important when neural fields are used for applications such as rendering [43, 48, 55] and simulation [12, 13, 27, 41]. Recently, similar to our approach, Li et al. [28] used a finite differences-based regularizer for training hybrid neural fields for surface reconstruction. However, their motivation is to address the training dynamics of hybrid fields, instead of removing their high-frequency noise components. Additionally, past approaches for reconstructing surfaces from point clouds [3, 4, 7] also include regularization terms that could potentially lead to more accurate derivatives. However, they are specifically designed for non-hybrid neural fields like SIREN [41] with architecture-specific initialization and higher-order loss functions. In contrast, our approach targets hybrid neural fields like Instant NGP [33]. It is also non-trivial to apply these approaches to improve the spatial derivatives of pre-trained hybrid neural fields. + +Numerical Derivatives of Noisy Signals. Estimating derivatives of noisy signals is a classical problem in numerical differentiation. Previous works [24] propose different approaches to regularize the noise, such as total variation minimization, Tikhonov regularization, convolution smoothing, etc., depending on the type of noise model applied. However, these approaches are typically limited to computing derivatives on a uniform grid. In contrast, our operators can query the derivative at any arbitrary point in a continuous space; a desirable flexibility in downstream applications such as computing differential operators on 3D shapes. Furthermore, these methods are designed to compute derivatives on 1D [24] or 2D grids [10, 47], and scaling them to higher dimensions like 3D is a non-trivial extension. Our work is also closely related to past works in differentiable rasterization [16, 19] that estimate the derivatives of noisy signals using Monte Carlo estimation often by smoothing them first with a Gaussian kernel. If the signal is non-differentiable, they convolve the signal with a derivative-of-Gaussian filter or differentiate a locally-fitted differentiable surrogate signal [20]. + +Polynomial fitting for Shape Analysis. Polynomial-fitting approaches like Moving Least Squares (MLS) [15, 26, 34] have a rich history in 3D shape analysis. They + +have applications in tasks like surface reconstruction from point clouds [1], animating elastoplastic materials [32], and learning implicit functions from scattered data [35, 39]. In this paper, we apply polynomial fitting to a novel setting of hybrid neural fields to solve the important issue of obtaining accurate differential operators. Typically, in past works, given scattered data (point clouds with associated scalar values) as input, approaches like MLS compute fitting planes (or higher-order polynomials) to local subsets of surface points. In essence, the planes/polynomials serve as an interpolant for the given data (point clouds). In our setting, the hybrid neural field already exists as an interpolant. But, as we observe in Figure 1, the neural field interpolant does not yield accurate derivatives, and our approach attempts to alleviate this problem. + +# 3. Method + +We assume that we have a pre-trained neural field, $F_{\theta}$ . To concretize the problem, we focus on hybrid neural fields representing 3D shapes as signed distance fields (although our final approach is more general and applicable to other modalities too, see Appendix B.2). By hybrid fields [33] we refer to neural fields that have a spatial grid of feature vectors in addition to an MLP. The field value at any point is obtained by feeding to the MLP the point location as well as a feature vector obtained by interpolating into the grid. We begin by analyzing why hybrid neural fields yield noisy derivatives and then motivate our approach. + +# 3.1. Noisy Derivatives in Hybrid Neural Fields + +Why are the derivatives of hybrid neural fields incorrect? We observe that much of the capacity of hybrid neural fields lies in the high-resolution spatial grid of feature vectors. This spatial grid is essential for the neural field to capture fine-grained localized details. Consequently, this spatial grid also determines the high-frequency components of the fitted signal. Unfortunately, this abundance of capacity for high-frequency components means that there are likely many solutions with different high-frequency components that fit the training data well. This in turn can result in noise in the high-frequency components. We observe this noise in practice. Figure 2b compares the spectrum of the ground truth and learned signed distance function (SDF) for a circle in 2D. Note how the learned SDF has higher amplitudes in the high-frequency components. + +This high-frequency noise is the source of artifacts in the derivatives. This is because derivative computation accentuates high-frequency noise, scaling it up proportional to the frequency, as illustrated by a sinusoidal signal with frequency $\nu$ : $\frac{d\sin(2\pi\nu x)}{dx} = 2\pi \nu \cos (2\pi \nu x)$ . Thus, even when the high-frequency noise has a very low magnitude, the corresponding noise in the derivative has a much higher magnitude. Figure 2a shows this issue in practice: the same SDF + +of a 2D circle that we learned earlier provides an extremely noisy gradient when we use automatic differentiation. + +Derivatives and smoothing. This notion of high-frequency noise magnifying errors in derivative computation is well-known in signal processing, and the solution is to use smoothing to remove the high-frequency components. The degree of smoothing can be controlled and corresponds to the scale of the derivative. How this smoothing is done depends on how the signal is represented. For images represented as a 2D grid of pixel values, smoothing can be done by convolving with an averaging filter, and derivatives are typically only computed after smoothing. When 3D shapes are represented as meshes, the mesh automatically represents a smooth version of the signal: each face is effectively a local linear approximation of the surface. Derivatives can then be computed using the face normal. + +Unfortunately, no analogous notion of smoothed derivatives exists for arbitrary hybrid neural fields. To address this gap, we propose a new approach that computes derivatives on a local low-degree polynomial approximation of the neural field. We describe this approach in detail below (see Figure 3 for an overview). + +# 3.2. Local polynomial-fitting operators + +Given a hybrid neural field, $F_{\Theta} : \mathbb{R}^m \to \mathbb{R}^n$ , and a query point $\mathbf{q} \in \mathbb{R}^m$ , we want to compute accurate first-order derivatives of $F_{\Theta}$ at $\mathbf{q}$ . For simplicity, we choose $n = 1$ . + +First, we sample points $\mathbf{x}_i, i = 1,\dots,k$ from a local neighborhood $N(\mathbf{q})$ of the point $\mathbf{q}$ . We query the neural field to obtain corresponding field values $y_{i} = F_{\Theta}(\mathbf{x}_{i})\forall \mathbf{x}_{i}\in N(\mathbf{q})$ . We then use these values to fit a local linear approximation $y\approx \hat{F}_{\Theta}(\mathbf{x};\mathbf{q}) = \mathbf{g}^{T}\mathbf{x} + b$ using simple least squares: + +$$ +\hat {\mathbf {g}}, \hat {b} = \arg \min _ {\mathbf {g}, b} \sum_ {i = 1} ^ {k} \left(\mathbf {g} ^ {T} \mathbf {x} _ {i} + b - y _ {i}\right) ^ {2} \tag {1} +$$ + +Our estimate of the derivative is then $\hat{\nabla}_{\mathbf{x}}F_{\Theta}(\mathbf{q}) = \nabla_{\mathbf{x}}\hat{F}_{\Theta}(\mathbf{x},\mathbf{q}) = \hat{\mathbf{g}}$ . We can extend the same approach to the case of vector fields ( $n > 1$ ), where $\mathbf{g}$ is replaced by an $m\times n$ estimate of the Jacobian, $\mathbf{J}$ . Observe that this optimization problem is an unconstrained convex quadratic program that can be solved in closed form. + +Local neighborhood selection. Different sampling schemes can be considered in order to select a local neighborhood around the query point $\mathbf{q}$ . However, in our experiments, we found that sampling from a Gaussian distribution centered at $\mathbf{q}$ , $\mathcal{N}(\mathbf{q},\sigma)$ worked best for us. The standard deviation, $\sigma$ controls the amount of smoothing that we do at a particular point. The number of neighbors sampled, $k$ is another hyperparameter of our method and controls the variance of the operator that we compute. We discuss how we select these hyperparameters in detail in our experiments (Section 4). + +![](images/7093227cae6acfb7cc5199d8a038e35ba07fe528d34ba71d6971251adb49180f.jpg) +(a) + +![](images/61a4db0ef11fd9607630491a56729081a0fe4ef4a9461c0e46ab720a6bca900b.jpg) +(b) + +![](images/57c14e1f48e1e0d995122adecc8676b4bf18a3c30774400df51e7a387a3ad540.jpg) +Figure 2. (a) Inaccurate differential operators of hybrid neural fields. Hybrid neural SDF of a circle in 2D. As shown by the comparison with the ground truth, the $0^{\mathrm{th}}$ order signal accurately captures the SDF. But the $1^{\mathrm{st}}$ and $2^{\mathrm{nd}}$ -order signals, here shown as the gradient and the radius of curvature (inverse of the Laplacian) are quite noisy. (b) Fourier spectrum of a hybrid neural SDF. Computed over a 1D slice (dashed line in (a)) of the SDF of a 2D circle. Note the noisy high-frequency components that are captured by the hybrid neural field. +Figure 3. Problem setup. Given a pre-trained hybrid neural field with noisy autodiff derivatives, we propose two approaches for accurate derivatives. Our polynomial-fitting operator can be applied in a post hoc manner while our fine-tuning approach directly improves autodiff derivatives of the field. + +Hessian & Laplacian. To compute second-order differential operators like the Hessian or Laplacian, we fit a quadratic approximation in the neighborhood of $\mathbf{q}$ as opposed to a linear one. Specifically, for scalar fields, we minimize: $\sum_{i=1}^{k} (\mathbf{x}_i^T \mathbf{H} \mathbf{x}_i + \mathbf{p}^T \mathbf{x}_i + q - y_i)^2$ . Ideally, since the Hessian is symmetric and $\mathbf{H}$ is our estimate for the Hessian, we want $\mathbf{H}$ to be symmetric. We therefore parameterize $\mathbf{H}$ by its lower triangle. As before, this quadratic program can be solved in closed form. Once we obtain $\mathbf{H}$ , we can also obtain the Laplacian $(\Delta F_\Theta)$ as the trace of $\mathbf{H}$ . + +Given any pre-trained neural field with similar high-frequency noise, our operators can be applied to it in a post hoc manner to obtain accurate differential operators from the field. However, they do not alter the weights of the neural field, essentially acting as "test-time" operators. + +Comparison to alternatives. Our approach computes the derivative by sampling points locally and fitting a local + +polynomial approximation. However, one might consider other alternatives: + +1. Instead of autodiff, which yields the instantaneous derivative, we can compute derivatives using finite differences. However, this amounts to sub-sampling the signal without smoothing, which will cause aliasing and thus, inaccuracy in derivatives, as we demonstrate in our experiments (see Section 4). +2. A mesh also computes a local polynomial approximation, so we could convert the neural field to a mesh using Marching Cubes. However, computing a mesh is a global operation, as opposed to our polynomial fit which can be solved in closed form independently for every query point. As such, extracting a mesh is much more expensive, especially for applications like physical simulation where each simulation step may require gradient queries from an evolving signal (see Appendix C). + +# 3.3. Fine-tuning pre-trained hybrid neural fields + +The post hoc operator we describe above can be used to effectively query accurate differential operators from a given hybrid neural field. However, to use it, every downstream application must be altered to allow for our new operator. Unfortunately, for many applications, autodiff remains the prevalent way to obtain gradients from neural networks. Hence, we propose a method to update the hybrid neural field directly so that autodiff yields accurate gradients. + +Concretely, given a pre-trained neural field, we propose to fine-tune it to improve the accuracy of the differential operators obtained using autodiff. Let us denote the pretrained neural field and the fine-tuned neural field by $M$ and $F_{\Theta}$ respectively. $F_{\Theta}$ is initialized with the weights of $M$ . We fine-tune $F_{\Theta}$ using the following loss function: + +$$ +\begin{array}{r l} \mathcal {L} _ {f t} (\mathbf {x} _ {0}; \Theta) = & \underbrace {\left| F _ {\Theta} (\mathbf {x} _ {0}) - M (\mathbf {x} _ {0}) \right| ^ {2}} _ {\mathcal {L} _ {\text {c o n}}} \\ & + \underbrace {\left| \left| \nabla_ {\mathbf {x}} F _ {\Theta} (\mathbf {x} _ {0}) - \hat {\nabla} _ {\mathbf {x}} M (\mathbf {x} _ {0}) \right| \right| _ {2} ^ {2}} _ {\mathcal {L} _ {\text {g r a d}}} \end{array} \tag {2} +$$ + +Here, $\mathcal{L}_{\mathrm{con}}$ denotes the consistency loss which ensures that the output of $F_{\Theta}$ matches the pre-trained neural field, $M$ . $\mathcal{L}_{\mathrm{grad}}$ denotes the gradient loss that tries to align the autodiff gradient of $F_{\Theta}$ with accurate gradient estimates obtained by applying the operator $\hat{\nabla}_{\mathbf{x}}$ on $M$ . In our experiments, we use our polynomial-fitting gradient operator to obtain $\hat{\nabla}_{\mathbf{x}}M$ . + +Our approach resembles the Sobolev training approach proposed in Yuan et al. [54] with the distinction that they assume access to the ground-truth derivatives of the input signal, whereas we only assume access to noisy gradients of the pre-trained neural field. Note that this fine-tuning process is orthogonal to any kind of smoothed gradient operator. Our polynomial-fitting gradient for $\hat{\nabla}_{\mathbf{x}}$ is just one of the ways we can perform this fine-tuning. We can similarly use other approaches to compute accurate gradient estimates. In fact, in our experiments, we find that even less accurate estimates, like those obtained from finite differences, can suffice to regularize the fine-tuning effectively. + +We can also use the loss function described in Eq. (2) as an auxiliary regularizer when training a hybrid neural field from scratch. In this case, we train the model $(F_{\Theta})$ normally using MSE loss with the ground truth SDF initially for $s (> 0)$ steps. This warm-start phase allows $F_{\Theta}$ to learn a good initial fit for the zeroth-order signal. Then we train $F_{\Theta}$ with the loss in Eq. (2) for $n - s$ steps where $n$ is the total number of training steps. $M$ is the frozen weights of $F_{\Theta}$ at the end of $s$ steps. The choice of $s$ plays an important role in the accuracy of autodiff gradients of the resulting model (see Appendix F for a discussion). + +# 4. Experiments and Results + +We first evaluate the accuracy of our proposed operator and then evaluate our fine-tuning approach. For both sets of experiments, we use shapes from the FamousShape dataset [18]. We pre-train a hybrid neural field to learn the SDF of each shape. We experimented with three hybrid architectures: Instant NGP [33], Instant NGP without a hash grid (Dense Grid), and Tri-plane [9]. + +Metrics. We evaluate the estimates of surface normals (first-order operator) and mean curvatures (second-order operator) by comparing them to surface normals and discrete mean curvatures obtained from the provided meshes of the shapes (which we regard as ground truth, see sec:expdetails for details). For surface normals, we compute the mean L2 error, mean angular error in degrees (Ang), and the percentage of points having angle error below $1^{\circ}$ (AA@1) and $2^{\circ}$ (AA@2). For mean curvature, we + +use the rectified relative error (RRE) used by past works for evaluating curvature estimation [6, 23]. We report metrics averaged over all evaluated shapes (detailed results in Appendix B.1). For the detailed experimental setup, please refer to Appendix A. + +Choosing $\sigma$ and $k$ . As discussed in Section 3.2, our polynomial-fitting operators also require $\sigma$ and $k$ values as hyperparameters. The effect of these hyperparameter choices is shown qualitatively in Figure 4 and quantitatively in Figure 5 on the Armadillo and Bunny shapes. Generally, we find that (a) higher $k$ (more neighbors) are always better as this minimizes variance, and (b) no single value of $\sigma$ works for both shapes, but derivative accuracy varies smoothly with $\sigma$ . Intuitively, $\sigma$ trades off between fidelity and robustness to noise. As such, it is dependent on the nature of the downstream application. + +For the purpose of our experiments, we always choose $k = 256$ . We choose $\sigma$ to have the best consistency with differential operators obtained from the mesh. Specifically, + +- For post hoc operators, we do a telescopic search for the best value of $\sigma$ . +- For fine-tuning, we train an ensemble of models with different values of $\sigma$ and select the value that yields the best autodiff gradients after fine-tuning. + +# 4.1. Accuracy of operators. + +We first evaluate our polynomial-fitting operator by comparing it with automatic differentiation, finite differences (FD) baseline, a stochastic finite differences operator [16] (SFD) and a Monte Carlo estimate that aggregates information from samples in local neighborhoods [19] (GAD). Specifically, GAD does Gaussian averaging of autodiff derivatives with importance sampling, mathematically equivalent to convolution with a derivate-of-Gaussian filter [19]. Since SFD is a high-variance approach, we also compared against Monte Carlo averaging of SFD with 256 samples $(\mathrm{SFD}_{256})$ . Table 1 shows our results. We only compare FD and our approach for mean curvature, since our hybrid neural fields do not admit meaningful higher-order spatial gradients through autodiff (as they are piecewise linear) and Deliot et al. [16] do not discuss an SFD curvature operator. Our approach provides more accurate surface normals and mean curvature values from hybrid neural fields than the FD baseline. In particular, for Instant NGP [33] our approach yields $4\times$ reductions in the angular error for the surface normal, relative to the commonly used FD approach. Our approach performs comparable to GAD, showing that aggregating function values in local neighborhoods whether using polynomial fitting or Monte Carlo estimates can effectively address the high-frequency noise in hybrid neural fields. Our approach also yields higher accuracy when computing mean curvature relative to finite differences, leading to $4\times$ reduction in error for Instant NGP [33]. + +![](images/cf3abbf03b4475816506959b79ab338c3b1ed06dc2fa10259c07f216229bb075.jpg) +Figure 4. Effect of hyperparameters. The performance of our polynomial-fitting operator is influenced by the selected hyperparameter values. We demonstrate this on the Armadillo highlighting this from two different viewpoints, the torso and the head. For a fixed $\sigma$ , choosing a larger $k$ reduces the variance in our operator leading to smoother normals (see the first row for each viewpoint). For a fixed $k$ , choosing a large $\sigma$ can lead to over-smoothing, whereas choosing a smaller $\sigma$ can lead to no smoothing at all (second row of each viewpoint). Best viewed by zooming in. + +# 4.2. Improving pre-trained neural fields. + +We next evaluate whether the fine-tuning approach proposed in Section 3.3 improves the autodiff derivative estimates. Since our hybrid neural fields do not admit higher-order derivatives, we evaluate only the first-order derivatives. We evaluate two versions of our fine-tuning approach, one using finite difference-based gradient operators as supervision, and the other using our polynomial fit-based operator. We compare the autodiff gradients after fine-tuning to the un-finetuned network. We also compare with networks trained from scratch using the commonly used eikonal regularization [2, 22] for neural fields, proposed to learn smooth iso-surfaces without disturbing the fidelity of the original neural field, including its finite differences-based variant (FD-Eikonal) [28]. We only performed experiments on Instant NGP and Dense Grid as our Tri-plane implementation did not support higher-order derivatives. Our results (Table 2) demonstrate that fine-tuning improves derivative estimates significantly, with our polynomial fit-based operator providing better supervision. We also observe an improvement in gradient accuracy over + +
ModelMethodSurface NormalMean Curvature
L2 ↓Ang ↓AA@1 ↑AA@2 ↑RRE ↓
Instant NGP [33]AD0.2112.401.586.12-
FD0.074.2026.8655.223.67
GAD0.052.9938.3566.86-
SFD0.9557.670.010.07-
SFD2560.116.304.9017.15-
Ours0.052.8042.9267.900.89
Dense GridAD0.116.5511.4929.40-
FD0.073.9730.6655.062.62
GAD0.053.2440.5064.01-
SFD0.9457.620.010.07-
SFD2560.106.125.0917.64-
Ours0.063.3138.9562.650.89
Tri-plane [9]AD0.158.593.6113.13-
FD0.074.1923.4251.274.12
GAD0.052.9234.7564.23-
SFD0.9457.650.010.07-
SFD2560.106.234.8817.19-
Ours0.063.2335.6762.740.90
+ +Table 1. Operator evaluation. We compare our approach with the baselines on the FamousShape dataset [18]. We report the performance averaged over the dataset. + +
ModelFine-tuning/ Regularization* methodAutodiff Surface NormalMesh Reconstruction
L2 ↓Ang ↓AA@1 ↑AA@2 ↑CD ↓F-Score ↑
Instant NGP [33]-0.2112.401.586.129.24 × 10-493.07
Eikonal*0.116.5112.2431.489.23 × 10-492.90
FD-Eikonal*0.2012.460.486.049.20 × 10-493.09
FD0.085.1421.1646.639.35 × 10-490.24
Ours0.053.1933.6060.249.28 × 10-492.28
Dense Grid-0.116.5611.4229.379.26 × 10-489.83
Eikonal*0.169.8212.7027.429.24 × 10-487.79
FD-Eikonal*0.106.1713.7133.279.25 × 10-489.85
FD0.095.0918.8241.529.23 × 10-488.94
Ours0.084.4029.3251.409.25 × 10-487.66
+ +Table 2. Effect of fine-tuning. We compare autodiff operators before (first row) and after fine-tuning with different operators along with common regularization approaches $(\star)$ for neural fields. The accuracy of autodiff surface normals improves after fine-tuning. + +the regularization approaches (marked $\star$ ). Furthermore, the fine-tuning process preserves the zero-level set of the pretrained hybrid neural field, as highlighted by minor changes in Chamfer Distance (CD) and F-Score. + +# 5. Applications + +We now demonstrate the impact of our improved derivatives on downstream applications. For implementation details of the applications, see Appendix D. + +# 5.1. Rendering + +In rendering, accurate surface normals (which correspond to the gradient of the SDF) are needed to estimate how light will reflect off a surface [40]. We show the impact of our improved gradients on the rendering of a hybrid neural SDF representing a perfectly specular sphere, and another repre + +![](images/809a0ceb591a3d9085d8a68cd6ed72c4a136be6baf598452f9ae91af62094542.jpg) +(a) Armadillo + +![](images/9da19788171bab334404c4aab7af720cdb3a31efeaebfb5c717b5e8865708a69.jpg) +(b) Stanford Bunny +Figure 5. Hyperparameter Ablation. Variation in angle error for normal/gradient (top) and the mean curvature error (bottom) for different settings. $k$ and $\sigma$ refer to the number of neighbors sampled and the size of the neighborhood respectively. $\star$ denotes the best settings. + +senting a perfectly lambertian Armadillo [25]. + +For the sphere, we use the analytic SDF and surface normals for the ground truth, while we use a mesh as reference for the Armadillo. The sphere was lit with an environment map, and the armadillo with a light source from behind the camera. We use sphere tracing to compute the first ray intersection from the camera with the zero-level iso-surface. Subsequently, we queried the network to obtain gradients using automatic differentiation, finite differences, our post hoc polynomial-fitting operator, and autodiff gradients obtained from a network that was fine-tuned with our operator. + +Figure 6 presents our results. As predicted, for the supposedly smooth sphere, as well as the Armadillo, we observed severe surface artifacts using gradients from autodiff. The finite difference-based post hoc operator is able to tackle noise to an extent but still leads to artifacts. On the other hand, normals estimated by our approaches give a much more noise-free image that closely matches the reference. We also provide additional results in Appendix G. + +# 5.2. Simulating Collisions + +When simulating collisions between objects, normals help determine the impulse direction [8, 17]. When working with hybrid neural SDFs, we would need to query the normal at the local coordinates of the point of collision to the network. If the normals are inaccurate, this can lead to incorrect object trajectories after the collision. + +For our experimental setup, we consider two identical spheres undergoing head-on collision on a plane and simulate their trajectories post-collision. To obtain these trajectories, we use the normal estimates from the two hybrid neural SDFs at the point of contact. We model the collisions as perfectly elastic so that there is no loss of energy. Ideally, the spheres should rebound along the line joining the centers, but inaccurate normals will lead to incorrect trajectories. Figure 7 illustrates such a simulation and also shows how things fail when using autodiff to compute normals. Averaged over $10^{6}$ trials, the error obtained from our normals was $0.85^{\circ}$ , compared to $11.51^{\circ}$ for autodiff normals. + +# 5.3. PDE Simulation + +Recently, Chen et al. [12] proposed using Implicit Neural Spatial Representations (INSR) as the spatial representation of the PDE solution instead of explicit spatial discretization. We build upon their work and highlight that accurate gradient operators also enable the use of hybrid neural fields for PDE simulation. We simulate a 2D advection equation, $\frac{\partial u}{\partial t} = -a\nabla_{\mathbf{x}}u$ . For the initial condition, we use a Gaussian pulse centered at $(-0.6, -0.6)$ with a standard deviation of 0.1. We choose a constant velocity, $a = [0.25\ 0.25]^T$ . We run our simulations in a square of side length 2 centered at $(1,1)$ . We use the Dirichlet boundary condition, i.e., the field becomes 0 at the boundary, same as INSR [12]. For time integration, we use the forward Euler method, given by, $u^{t+1} = u^t - a\Delta t\nabla_{\mathbf{x}}u$ . While INSR uses a non-hybrid neural field (SIREN [41]) for representing the PDE solution, we use a hybrid neural field. In our setup, the gradient of the initial condition $(\nabla_{\mathbf{x}}u)$ can either be queried using autodiff or using our operator. For evaluation, we compare the error (w.r.t. the analytical solution) in the evolution using our polynomial-fitting gradient operator with autodiff (AD) gradients1. We also show the error from a finite difference-based grid solver to show where traditional methods stand. All the methods use a step size $(\Delta t)$ of 0.05, and we run our solvers for 100 time steps. Figure 8 shows our results. The grid solver accumulates errors over time due to numerical dissipation caused by its spatial discretization. Using hybrid neural fields with autodiff gradients leads to diverging solutions and the evolution collapses after 2 seconds. Using the same hybrid neural field with our operator leads to more accurate solutions at all time steps. + +# 6. Limitations and future work + +One limitation of our approach is the need to set the hyperparameter $\sigma$ based on the downstream application. However, note that analogous hyperparameters are common in + +![](images/1ae5077d17634b338721ea8b2c280763929fb41859ecfd42fcb6c16c5956c597.jpg) +Figure 6. Accurate Normals for Rendering. A perfectly specular sphere lighted by an environment map (top) and a diffuse Armadillo (inset) lit by a light source put in front of the object (bottom). In both cases, noisy normals from autodiff lead to artifacts in rendering as shown in the highlighted parts for the sphere and the chest of the Armadillo, that are mitigated by our approaches. + +![](images/692df0d96f44b763ba256d990344fbe436b43712a6c8c7920ffc7c8c2f44e1d4.jpg) +Figure 7. Illustration of how noisy normals affect collision. Two spheres undergoing perfectly elastic head-on collisions simulated using correct surface normals will re-trace their paths after a collision. However, inaccurate normal estimates from autodiff yield incorrect trajectories after bouncing (right). + +![](images/79ce9564ecd55c81694b7960c0b387f748c56a1895d5eb55914fb31b77833700.jpg) +Figure 8. Effect of inaccurate gradients in PDE simulation. Mean squared error (MSE) for 2D advection for a finite difference grid solver, autodiff gradients (AD), and our polynomial-fitting approach. Error for AD explodes after the first few seconds and eventually crashes (indicated by $\times$ ). + +other related problems where smoothing is required: e.g., derivative computation in image processing or fitting surfaces to point clouds with MLS [34]. One may argue that + +in these methods and in our approach, the ability to set $\sigma$ offers an additional degree of control. + +A second limitation is that our approach needs to sample the neighborhood of the query point, necessitating several forward passes per query (although we observed that our operator performs competitively with alternatives like finite differences, see Appendix B.3). This cost may be amortized by our fine-tuning approach. Alternatively, clever sharing of samples between neighboring query points is an interesting avenue for future work. + +Finally, our approach is primarily designed to remove high frequency noise. As such, it cannot help remove other, more lower frequency errors that are common in non-hybrid neural field architectures such as SIREN [41] (Appendix E). + +# 7. Conclusion + +In this paper, we have shown that automatic differentiation of trained hybrid neural fields yields extremely noisy derivatives and impacts several downstream applications. We tackle this problem with a new derivative operator that computes the derivative on a local polynomial approximation of the hybrid neural field. We further propose a self-supervised fine-tuning approach to improve the accuracy of autodiff gradients directly. We demonstrate significant improvements in derivative accuracy from these new techniques. We further demonstrate that our methods improve performance in rendering and physics simulation applications compared to directly using autodiff derivatives for hybrid neural fields. + +# Acknowledgements + +This work was partly funded by NSF IIS: 2144117, NSF IIS: 2107161 and NSF HCC: 2212084. We would like to thank Peter Michael for help with the initial implementation of the rendering experiments, Yihong Sun for help with some of the figures, and Gemmechu Hassena for providing meshes for some of the rendering results. + +# References + +[1] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C.T. Silva. 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In this work, we present an in-depth empirical analysis and demonstrate that, contrary to previous observations, scaling the decoder yields significant performance gains, always exceeding those achieved by encoder scaling alone. We also identify label noise as a key challenge in STR, particularly in real-world data, which can limit the effectiveness of STR models. To address this, we propose Cloze Self-Distillation (CSD), a method that mitigates label noise by distilling a student model from context-aware soft predictions and pseudolabels generated by a teacher model. Additionally, we enhance the decoder architecture by introducing differential cross-attention for STR. Our methodology achieves state-of-the-art performance on 10 out of 11 benchmarks using only real data, while significantly reducing the parameter size and computational costs. + +# 1. Introduction + +Scene Text Recognition (STR) aims to automatically transcribe text in natural scenes, enabling applications in autonomous driving [51], augmented reality [27], language translation [43], and assistive technologies. Unlike traditional Optical Character Recognition (OCR), which typically works with clean or scanned documents, STR faces unique challenges due to the diverse and uncontrolled nature of text in real-world environments. In particular, text in these settings can vary significantly in orientation, font style, shape, size, color, formatting, and aspect ratio. It often appears on complex backgrounds that may also include reflections, transparency, or occlusions. Furthermore, images might have poor quality, suffering from issues such as blurring, low resolution, and noise [23]. + +Recent research has led to notable performance improve + +![](images/9dbcf8125c3ee2e3c535f01df5633b45667d2a51a321da75b5d49ddd35ba6a1a.jpg) +Figure 1. Average word accuracy (\%) on 11 STR benchmarks for the models with ViT-T, ViT-S and ViT-B vision encoders and 4 different decoder sizes (see Sec. 4.1). Results are compared with the previous state-of-the-art model, CLIP4STR [54]. Results using Real training dataset (3.3M images) are depicted with solid lines and circle markers, while results using RBU training dataset (6.5M images) are shown with dashed lines and diamond markers. The x-axis represents the total number of model parameters (in millions) on a logarithmic scale. + +ments in STR by enhancing training methods [15], deploying novel architectures [1, 54], and exploring the effects of model scaling [31]. Despite these advancements, current STR models still face important challenges that limit their effectiveness. Our work is motivated by the following research question: + +What are the primary bottlenecks currently limiting STR, and what strategies can be employed to improve both accuracy and efficiency? + +Throughout our analysis, we identify three important limitations: (i) sub-optimal model scaling, (ii) noisy labels in training data, and (iii) architectural limitations within current model designs. + +Sub-optimal model scaling. Prior scaling analyses [31] have explored scaling laws for STR, demonstrating that + +increasing model size and data volume can lead to performance gains, following scaling trends similar to those observed in Natural Language Processing [16]. In particular, the CLIP4STR [54] methodology, which leverages CLIP [30] pre-training and integrates a cross-modal correction branch, achieves the best results at scale among all considered methods. However, [31] also found that increasing the decoder depth in PARSeq [3] results in decreased performance, leading to an emphasis on encoder scaling. + +In this work, we provide an in-depth analysis of the effects of independently scaling the encoder and decoder components under different data volumes. Contrary to previous findings, we demonstrate that decoder scaling is indeed essential for achieving optimal STR performance. + +As illustrated in Fig. 1, increasing the decoder size provides substantial benefits for any visual encoder and results in more favorable scaling laws. Notably, proper model scaling alone is sufficient to surpass (on average) previous state-of-the-art performance without the need for CLIP pre-training or additional cross-modal branches. Furthermore, this approach substantially reduces the number of parameters and FLOPs. + +Noisy labels in training data. Our analysis indicates that, under some conditions, scaling the vision encoder may lead to diminishing returns or a decrease in accuracy, especially when STR models are trained on limited real data. In this context, we observe that text annotations of STR datasets often suffer from inconsistencies, errors and noise, which can negatively impact STR performance (Fig. 2). To address this issue, we propose a novel Cloze Self-Distillation (CSD) technique. In CSD, a model serving as a teacher, is first trained and used to generate predictions on training data. These predictions are then refined using a cloze-filling approach: each character is re-predicted using all other characters as textual context, resulting in more accurate, informative and context-aware soft predictions. We then distill the teacher into an identical student model on the same training set by employing the teacher's hard predictions as ground truth and a knowledge distillation term [14] that minimizes the divergence between the student's limited-context predictions (obtained through permuted language modeling [49]) and the teacher's full-context cloze predictions. This technique enables the student to update its parameters with the richer, context-aware outputs of the teacher, while operating under the constraints of limited context. We provide empirical evidence demonstrating the effectiveness of CSD in mitigating label noise and inconsistencies, leading to substantial performance improvements. + +Architectural limitations. We extend our analysis on the decoder of our STR model by introducing additional architectural improvements. Inspired by Differential Transformer [50], we propose a novel Differential Permutation Language Decoder that employs Differential Cross + +![](images/29edb581ef7202fb4000a0dee25652e4960fe0b8e7ea92332c83efd8e0921e32.jpg) +(a) +L:ARTIPICAL P:ARTIFICIAL + +![](images/8e3061e97bea743606e0f491ab3c93ec0f98c2ff295e809a361477fb08ad19b4.jpg) +L: MEDALION +P: MEDALLION + +![](images/ab486a51182e3b136e40faca538d294448ec4ad417e2f1b9bf68b29e440bb8b4.jpg) +L:0 P:-interface + +![](images/f2b0f433752884fe17e1f93df7e04be0d1437fa0ee20d8b608810faa964951af.jpg) +(d) +L:EAT-OUT P:EAT-OUT! +Figure 2. Examples of label inconsistencies and errors in the training set. For each image, we show the ground truth label (L) and the teacher-generated pseudolabel (P). Subfigures (a-c) illustrate typical label errors, such as spelling mistakes or missing characters. Subfigures (d,e) highlight label inconsistencies, where punctuation or occluded parts are not annotated. Subfigure (f) demonstrates a labelling error caused by severe degradation in the image quality. + +![](images/11f5808810e064a48ad2e12bdf26d1ca1a4897135d9d221976f871d1c225e403.jpg) +L:NA P:NATIONAL + +![](images/9a0bae9b208476a98f4e3d52403ff6f910e76a039de1c0bd4779a4914251e304.jpg) +L: the P: she + +attention layers and SwiGLU activations [33], addressing the limitation of previous architecture in focusing on relevant context. + +Our contributions can be summarized as follows: + +- A detailed analysis of encoder-decoder scaling for STR (Sec. 4.1), demonstrating substantial performance improvements with decoder-focused scaling, contrary to findings in previous studies. +- Cloze Self-Distillation (CSD) technique that addresses label noise by leveraging context-rich cloze predictions (Sec. 4.2), improving the robustness and performance of models across different data regimes. +- An enhanced decoder architecture that incorporates Differential Cross-Attention and SwiGLU activations (Sec. 4.3), achieving further improvements in STR performance. + +Through extensive empirical evaluation (Sec. 5.6), we demonstrate that the our enhanced decoder architecture and CSD, together with proper model scaling, consistently outperform previous approaches. Specifically, our STR method achieves the state-of-the-art performance on 10 out of 11 benchmarks, with substantial reductions in parameter size and computational costs (FLOPs). + +# 2. Related work + +Scene Text Recognition. A branch of STR approaches relies on Connectionist Temporal Classification (CTC) [12]. These include approaches such as CRNN [35], DTRN [13] and Star-Net [22], that utilize Convolutional Neural Net + +works (CNNs) and Recurrent Neural Networks (RNNs), as well as Rosetta [5]. They utilize the character interactions using convolutions and recurrent structures. All these methods are trained with the CTC loss which enables to predict variable-length sequences without requiring explicit alignment. Another direction of approaches integrates attention mechanisms, as seen in RARE [36], R2AM [20], ASTER [38] and DAN [46], to capture the complex spatial dependencies of text characters. Similarly, VITSTR [1] uses an encoder-only Vision Transformer [9] to encode the image patches that are directly classified into characters. A limitation of these approaches is that language modelling is not incorporated, resulting in a weakness to strong perturbations and occlusions commonly encountered in STR. To address this issue, a subsequent amount of methods incorporates context-aware mechanisms by integrating external or internal architectures, such as NRTR [34], ABINet [10], TrOCR [21], and PARSeq [3]. In particular, PARSeq proposes to utilize an encoder-decoder transformer architecture and to train the model with an end-to-end scheme with permuted language modeling [49]. Similarly, DTrOCR [11] uses a decoder-only transformer (GPT-2 model [29]) to directly decode image patches. Exploiting a pre-training on a large-scale simulated dataset and a fine-tuning step on real data, this method demonstrates state-of-the-art performance in many STR benchmarks. + +Empirical analyses. Baek et al. [2] examine the impact of training datasets on performance and inconsistencies in evaluation in the field of STR. Recently, Rang et al. [31] investigate how model size, data volume, and computational resources affect the STR performance, revealing smooth power-law relationships between these factors and model accuracy. + +Knowledge distillation (KD) [14] is a technique to enhance the model efficiency by replicating the knowledge of a complex teacher model into a smaller student model. In the context of STR, [4] employs KD to unify STR and Handwriting Text Recognition models, while [48] explore a symmetrical distillation strategy to capture the visual and linguistic knowledge of CLIP. + +# 3. Setup + +Notation. We denote an input image as $\mathbf{x} \in \mathcal{X}$ , where $\mathcal{X}$ is the image space, and a sequence of characters as $\mathbf{y} = [y_1, y_2, \ldots, y_L] \in \mathcal{Y}$ , where $\mathcal{Y}$ is the sequence space, $L$ is the sequence length and $(\forall i) y_i$ belongs to a fixed vocabulary $\mathcal{C}$ (character set). We use $\mathbf{y}_{BlocksDimHeadsParamsGFLOPsEncoderViT-Tiny1219235.5 M2.2ViT-Small12384621.7 M8.6ViT-Base127681285.8 M33.9DECODERPLD-Tiny138462.5 M0.8PLD-Small1768129.6 M3.5PLD-Base27681219.1 M7.0PLD-Large37681228.8 M12.5PLD-Diff27681224.4 M7.1 + +Table 1. Details of ViT encoders and PLD decoders used in our scaling experiments. GFLOPs for the decoder refer to the average test sequence length $L = 5.5$ . + +ten contain a large number of label errors and inconsistencies, which can adversely impact the performance of STR models, as qualitatively presented in Fig. 2. We propose a novel technique, named Cloze Self-Distillation (CSD), to mitigate the impact of such errors and to improve the STR performance. In particular, CSD is motivated by two key observations: + +- After a complete training, the predictions of STR models are, in most cases, more accurate than the actual training labels (see Fig. 2). +- PLM allows to refine the predictions with the cloze-filling approach (end of Sec. 3) and to compute context-aware probabilities for each position $t$ in the sequence given all the other characters $\hat{\mathbf{y}}_{\neq \mathbf{t}}$ as context. + +Given a dataset $S_{\mathrm{noise}}$ with potential label noise, CSD involves three main steps: (i) a teacher STR model $p_{\theta_T}$ is fully trained on the noisy dataset $S_{\mathrm{noise}}$ ; (ii) $p_{\theta_T}$ is employed to compute pseudolabels and context aware-logits with the cloze-filling refinement for the dataset $S_{\mathrm{noise}}$ ; (iii) a new student model $p_{\theta_S}$ (with the same architecture and size of the initial model) is distilled from the teacher. Hence, teacher pseudolabels are used instead of the ground truth annotations to minimize the negative log likelihood (NLL) objective of Eq. 6 and an additional Knowledge Distillation (KD) loss term is introduced to minimize the divergence between the context-aware soft predictions of the teacher (obtained with cloze-filling) and the partial-context predictions of the student (obtained with PLM), as it is illustrated in Fig. 4. Formally, the KD term can be formulated by: + +$$ +\mathrm {K D} _ {\boldsymbol {\pi}, t} (\mathbf {x}, \mathbf {y}) = D _ {\mathrm {K L}} \left(p _ {\theta_ {T}} ^ {\tau} (\cdot | \mathbf {y} _ {\boldsymbol {\pi} \neq t} \mathbf {x}) \mid \mid p _ {\theta_ {S}} ^ {\tau} (\cdot | \mathbf {y} _ {\boldsymbol {\pi} < t}, \mathbf {x})\right) \tag {9} +$$ + +where the superscript $\tau$ is used to indicate that the logits of the models are scaled with temperature $\tau$ before computing the softmax outputs. We remark that the teacher soft-predictions are computed given the full context, $\mathbf{y}_{\pi \neq t}$ , while the student outputs are computed with the standard context of PLM, $\mathbf{y}_{\pi_{DatasetPLD-TPLD-SPLD-BPLD-LViT-TReal90.0891.0691.6391.67RBU90.1591.1391.8691.93ViT-SReal91.0491.6792.2192.36RBU91.2892.2492.6292.77ViT-BReal90.8191.4191.9792.52RBU91.5592.3892.7892.98 + +Table 2. Encoder-Decoder Scaling. Average word accuracy $(\%)$ on the 11 benchmarks $\left(\mathbf{AVG}_{11}\right)$ for different encoder-decoder configurations trained on Real or RBU dataset. + +
ViT-TViT-SViT-B
PXXX
KDXXXXXX
AVG1191.691.891.992.292.492.592.092.392.5
+ +Table 3. Effects of pseudolabels and KD. Average word accuracy $(\%)$ on 11 benchmarks $\left(\mathbf{AVG}_{11}\right)$ using the Real dataset with standard supervised training, pseudolabels $(\mathbf{P})$ and Knowledge Distillation (KD) with the cloze soft probabilities. Results are shown for different encoders paired with the base decoder (PLD-B). + +
RealRBU
10%25%50%100%200%
Sup.86.989.990.892.092.8
CSD89.191.191.792.593.2
+ +Table 4. Benefits of CSD. Average word accuracy $(\%)$ on the 11 benchmarks $\left(\mathbf{AVG}_{11}\right)$ of ViT-B and PLD-B scaling the data samples from $0.33\mathrm{M}$ $(10\%)$ to $6.5\mathrm{M}$ $(200\%)$ . Standard supervised training (Sup.) is compared to our approach (CSD). + +
DecoderParamsGFLOPsRealRBU
AVG11wAVG6AVG11wAVG6
PLD-B104.9 M40.992.597.393.297.5
PLD-D110.2 M41.092.797.493.397.6
+ +Table 5. Benefits of Differential Decoder (PLD-D). $\mathbf{AVG}_{11}$ and $\mathbf{wAVG}_6$ of ViT-B paired with the standard base decoder (PLD-B) and the differential decoder (PLD-D), trained on Real or RBU dataset. Parameters and GFLOPs refer to the full encoder-decoder architecture, considering the average test sequence length of 5.5. + +across both Real and RBU datasets, and for all decoder configurations. However, further scaling from ViT-S to ViT-B, shows a different effect: when data is abundant (on RBU), the larger encoder improves performance with all decoders, but on the Real dataset with smaller decoders, ViT-B decreases the performance compared to ViT-S. Part of this behavior can be explained due to the label noise sensitivity of ViT-B (when paired with a small decoder). In Subsection 5.4, we will show that the impact of label noise can be mitigated by our CSD technique. + +Permutation Language Decoder scaling. Our results demonstrate that scaling the decoder is more parameter + +(Fig. 1) and computational (Sec. 8) efficient than scaling the encoder only, leading to more favorable scaling laws than previous state-of-the-art approaches. Using the larger RBU dataset as a reference, increasing the encoder from ViT-T to ViT-B yields an average improvement (across decoders) of $1.16\% \mathrm{AVG}_{11}$ with an additional 80.3M parameters. In contrast, scaling the decoder from PLD-T to PLD-L results in an average improvement (across encoders) of $1.56\% \mathrm{AVG}_{11}$ with only 26.3M parameter increase. Furthermore, on RBU, ViT-B paired with PLD-L (114.6M total parameters) obtains an average accuracy $\mathrm{AVG}_{11}$ of $92.98\%$ surpassing the $92.80\%$ accuracy of CLIP4STR-H (1B parameters). Similar trends can be observed also on the Real dataset, where ViT-T, ViT-S and ViT-B configurations achieve notable performance gains when the decoder size is increases, and, the transition from PLD-T to PLD-L provides $+1.59\%$ , $+1.32\%$ and $+1.71\%$ , respectively. + +# 5.4. Cloze Self-Distillation results + +Table 3 presents the average word accuracy $(\mathbf{AVG}_{11})$ obtained with different training procedures: standard supervised training, training on teacher pseudolabels (P) and CSD (pseudolabels and Knowledge Distillation (KD)). In this experiment, we utilize ViT of varying sizes (Tiny, Small, Base) as encoders, paired with the base-size decoder (PLD-B). Notably, incorporating teacher pseudolabels during training significantly enhances the performance, since it reduces the label errors and inconsistencies in real datasets. Moreover, integrating the Knowledge Distillation component based on context-aware probabilities (computed with the cloze-filling approach) further strengthens the regularization effects, resulting in an additional performance gain. The superiority of CSD is evident also in Table 4, which reports the average accuracy of ViT-Base with PLD-B when scaling the data from $10\%$ to $100\%$ of the Real dataset, as well as on RBU (which represents approximately $200\%$ of the Real dataset). Compared to the baseline method of standard supervised training, CSD consistently provides notable improvements at all data scales. Our technique achieves $\sim 0.5\%$ accuracy gain both when the full Real dataset or RBU dataset are used (for comparison, doubling the training dataset, i.e., $\mathrm{Real}\rightarrow \mathrm{RBU}$ , yields a $+0.8\%$ performance increase). This demonstrates the effectiveness of CSD at any data scale. Additional considerations about the effectiveness of CSD are presented in the supp. material (Sec. 11). + +# 5.5. Differential decoder + +To enhance the performance of CSD without a significant increase in GFLOPs, we introduce the differential decoder PLD-Diff (Sec. 4.3). We evaluate its effectiveness in the base configuration with 2 layers, an inner dimension of 768 and 12 attention heads and with ViT-Base encoder (Tab. 1). Tab. 5 shows that PLD-Diff consistently improves the per + +
MethodDataParamsRegular textIrregular TextOccluded TextOtherAVG11
IC13IIIT5kSVTC80IC15SVTPHOSTWOSTArTCOCOUber
85710153000647288181120776452416241634k982589.5k
VITSTR-S [1]Real21.7 M97.697.798.195.896.188.487.191.464.5*77.9*81.174.178.285.8
CRNN [35]Real8.5 M94.194.594.690.789.182.078.580.6--66.862.251.0-
TRBA [2]Real49.6 M97.697.698.697.097.789.888.793.7--82.577.581.2-
ABINET [10]Real23.5 M98.097.898.697.897.790.288.593.972.2*85.0*81.276.471.587.5
PARSeq [3]Real22.5 M98.398.499.197.998.390.789.695.774.4*85.4*84.579.884.589.9
CLIP4STR-B [54]Real158 M98.4†98.399.298.399.391.490.697.277.587.585.881.186.891.1
CLIP4STR-L [54]Real446 M98.5†98.599.598.599.091.390.897.479.889.285.981.987.691.7
CSD-S (ours)Real40.8 M99.198.899.498.599.091.991.397.583.590.986.282.789.692.5
CSD-B (ours)Real104.9 M99.298.899.498.099.092.591.697.883.690.086.282.889.792.5
CSD-D (ours)Real110.2 M99.098.899.399.199.392.491.798.183.690.886.182.689.892.7
CLIP4STR-B [54]RBU158 M-98.699.598.399.091.491.198.079.388.885.881.392.192.0
CLIP4STR-L [54]RBU446 M-99.099.698.699.791.991.498.181.190.686.482.792.292.7
CLIP4STR-H [54]RBU1 B-98.999.599.199.091.791.098.082.690.986.483.091.792.8
CSD-S (ours)RBU40.8 M98.798.699.298.899.092.291.797.884.389.586.382.991.792.8
CSD-B (ours)RBU104.9 M98.898.799.598.899.392.692.298.384.291.286.483.493.193.2
CSD-D (ours)RBU110.2 M99.299.299.599.299.792.791.998.184.390.686.483.193.293.3
+ +Table 6. Comparison with state-of-the-art methods. The word accuracy (%) of our models trained with CSD is compared with state-of-the-art approaches both for the Real and RBU training datasets. Results marked with * are from [54], results marked with † are from [31]. The best results are highlighted in bold, while second-best results are underlined. + +formance using both Real and RBU datasets. As claimed in [50], in a traditional Cross-Attention mechanism, a small proportion of attention maps might focus on relevant context. Hence, this leads to poor predictions and decreases the performance. In contrast, Differential attention concentrates more on critical information, so that a performance increase can be observed. Furthermore, PLD-Diff adds 5.7M parameters (compared to PLD-Base), but only 0.1 GFLOPs by considering an average sequence length of 5.5. + +# 5.6. Comparison with State-of-the-Art + +We compare our CSD technique and differential decoder with previous approaches. Specifically, we focus on three different model configurations: + +- CSD-S (40.8M parameters): ViT-Small + PLD-Base +- CSD-B (104.9M parameters): ViT-Base + PLD-Base +- CSD-D (110.2M parameters): ViT-Base + PLD-Diff + +Table 6 shows that our models outperform previous state-of-the-art models in almost all benchmarks, whether they are trained on the Real or RBU dataset. Precisely, when they are trained solely on the Real dataset, our models outperform the previous state-of-the-art models on 10 out of 11 benchmarks, while requiring significantly less parameters and GFLOPs. Our best model, CSD-D, achieves an $\mathbf{AVG}_{11}$ accuracy of $92.73\%$ and a $\mathbf{wAVG}_6$ accuracy of $97.42\%$ , compared to CLIP4STR-L whose respective scores are $91.69\%$ and $97.04\%$ . Note that our models use only $24.7\%$ of the parameters and $23.9\%$ of the GFLOPs achieved by CLIP4STR-L. By expanding the training dataset to RBU, our models continue to outperform previous models, with CSD-D achieving an $\mathbf{AVG}_{11}$ accuracy of $93.30\%$ and a $\mathbf{wAVG}_6$ accuracy of $97.62\%$ , even outperforming the $97.42\%$ $\mathbf{wAVG}_6$ achieved by CLIP4STR-L when scaled to + +the larger RBU-Syn dataset whose size is 18M [31]. + +Even if our method also achieves similar performance compared to DTrOCR [11] in most benchmarks, we have not included their results in this section, since they employ a training set with billions of additional images and the code/weights have not been released. + +# 5.7. Additional analyses + +In the supplementary material, we report additional results and ablation studies. In Sec. 8, we provide a detailed analysis of GFLOPs by considering the impact of the decoder with varying sequence lengths. In Sec. 9, we analyze the effect of CSD hyperparameters (i.e., temperature $\tau$ and KD loss mixing parameter $\alpha$ ). In Sec. 10, 11 and 12 we present additional results and analyses to support the superiority of our model and methodology. + +# 6. Conclusion + +In this work, we present a comprehensive analysis of encoder-decoder scaling for STR by demonstrating the significant benefits of scaling the decoder. Additionally, we introduce a novel training strategy to address label noise in real-world STR datasets. We leverage context-aware predictions generated from a teacher model through a cloze-filling approach, to distill a student model with improved performance. Moreover, we propose architectural updates, including Differential Cross-Attention, to improve the effectiveness of the decoder to focus on relevant context during inference. Empirical evaluations show the superiority of our model, achieving SOTA across multiple benchmarks while using fewer parameters and reducing the computational overhead (FLOPs) compared to previous models. + +# References + +[1] Rowel Atienza. 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(a) Given a text-to-image (T2I) model, there are two common methods to adopt it to create undesired contents, i.e., generating new images based on text prompts or editing existing images. (b) Current concept erasure methods primarily focus on preventing the generation of erased concepts but fail to protect against image editing. In contrast, our ACE method can prevent the production of such content during both generation and editing processes. As shown, after erasing Pikachu, it successfully prevents the edits involving Pikachu. + +# Abstract + +Recent advance in text-to-image diffusion models have significantly facilitated the generation of high-quality images, but also raising concerns about the illegal creation of harmful content, such as copyrighted images. Existing concept erasure methods achieve superior results in preventing the production of erased concept from prompts, but typically perform poorly in preventing undesired editing. To address this issue, we propose an Anti-Editing Concept Erasure (ACE) method, which not only erases the target concept during generation but also filters out it during editing. Specifically, we propose to inject the erasure guidance into both conditional and the unconditional noise prediction, enabling the model to effectively prevent the creation of erasure concepts during both editing and generation. Furthermore, a stochastic correction guidance is introduced during training to address the erosion of unrelated concepts. We conducted erasure editing experiments with + +representative editing methods (i.e., LEDs++ and Ma-saCtrl) to erase IP characters, and the results indicate that our ACE effectively filters out target concepts in both types of edits. Additional experiments on erasing explicit concepts and artistic styles further demonstrate that our ACE performs favorably against state-of-the-art methods. Our code will be publicly available at https://github.com/120L020904/ACE. + +# 1. Introduction + +Recent text-to-image (T2I) diffusion models trained with large-scale datasets [49] have demonstrated an impressive ability to generate high-quality images [12, 42, 46]. Their extraordinary creative capabilities enable users to produce high-quality images, and facilitate a wide range of applications, such as image editing [4, 58] and artistic creation [13, 55, 67]. However, alongside these advancements, a significant concern has arisen regarding the potential mis + +use of these text-to-image models. For example, these models might be employed to generate unsafe content, such as copyrighted material or sexually explicit images. + +To prevent the creation of unsafe content, a straightforward solution is filtering training data and retraining the model. Nonetheless, such a process is both labor-intensive and resource-consuming. Post-hoc safety checker [45, 46] and negative guidance [48] are alternative plug-and-play ways to filter undesired contents, which heavily rely on pre-trained detectors or hand-crafted prompts. More recent, concept erasure methods [14, 17, 35, 36, 68] are proposed to directly unlearn undesired concepts through model finetuning. These methods mainly focus on precisely removing the target concept, while faithfully preserving the generation of non-target concepts. For instance, ESD [14] injects the negative erase guidance into target noise prediction to guide the image away from the target concept. SPM [36] employs a lightweight adapter to eliminate concepts and further adopts latent anchoring to preserve non-target concepts. + +Although these concept erasure methods can effectively prevent the generation of unsafe content giving corresponding text prompt, they can be circumvented by editing techniques. As illustrated in Fig. 1, after removing Pikachu from the model, users can still create an image of Pikachu wearing sunglasses by editing a Pikachu image using LEDIT++ [4]. This is because these methods are typically trained to remove target concept from conditional noise prediction (as shown in Fig. 2(b)), and rely on the input text (e.g., "Pikachu") to trigger the guard. Therefore, when editing the image with the text "Add sunglasses" as input, the guard fails. In practice, protection from editing should also be considered in concept erasure, which we refer to as editing filtration. + +To address the above issues, we propose an Anti-Editing Concept Erasure method, termed ACE, to prevent the production of unsafe content during both generation and editing. Based on the above analysis, we explore the capabilities of CFG [20], and propose incorporating erasure guidance into both conditional and unconditional noise for anti-editing concept erasure. During erasure training, ACE additionally aligns the unconditional noise prediction of the tuned model with the proposed unconditional erasure guidance. After that, during generation or editing, the CFG prediction in the tuned model can implicitly mitigate the presence of the erased concept, thereby preventing the production of unwanted content. A prior constraint loss further adopted address the overfitting of training. Additionally, to reduce the impact of the added target concept noise guidance on the generation of non-target concepts, we further incorporate a random correction guidance with unconditional erasure guidance by subtracting randomly sampled prior concept noise guidance. With that, our ACE can thoroughly erase the target concept while preserving the generation of + +non-target concepts. We conducted extensive evaluations across different erasure tasks, including intellectual property (IP), explicit content, and artistic style. Our method demonstrate significant advantages in both generation and editing filtration, showcasing its effectiveness. + +The contributions of this work can be summarized as: + +- We investigate the potential risks of unsafe content creation through image editing, and propose an Anti-Editing Concept Erasure (ACE) method to prevent the production of such content during both generation and editing. +- A unconditional erasure guidance is proposed for anti-editing concept erasure, along with concept preservation mechanism to ensure the generation of non-target concepts. +- Extensive experiments demonstrate that our ACE can successfully erase target concepts and exhibits superior filtration capabilities during both generation and editing. + +# 2. Related Work + +# 2.1. Concept Erasure in T2I Models + +The concept erasure [9, 11, 15, 16, 18, 21, 23-25, 28-30, 33, 39, 41, 43, 48, 51, 52, 59, 62-64, 71] in T2I models has been the subject of numerous studies. Fine-tuning models are an important method in concept erasure. ESD [14] suggests integrating negative guidance into target concept noise through training. SPM [36] proposes prior correction based on the cosine similarity of text and utilizes a comparable Lora approach to train the model. MACE [35] leverages a closed-form solution to amalgamate multiple erasure Lora weights. RECE [17] employs analytical methods to search inappropriate text embedding and integrates it into erasure closed-form solution. AdvUnlearn [68] incorporate adversarial training to improve the robustness of the erasure method. To the best of our knowledge, current fine-tuning methods lack consideration for editing filtration, thus rendering them ineffective in preventing customized editions to target concept images. + +# 2.2. Text-driven Image Editing + +Due to the broad generative capacities inherent in text-to-image DMs, the employment of DMs for image editing [3, 5, 7, 8, 26, 27, 32, 37, 38, 40, 47, 50, 54, 56, 57, 60, 65, 70] has progressively garnered traction. MasaCtrl [6] introduces source image data into the image editing process by substituting keys and values in the self-attention layer, thus modifying the actions of objects in the image. LEDITS++[4] uses inference guidance and attention masks from DM to confine editing regions while using DDPM inversion for enhanced restoration of source image. Image editing enables users to customize images to meet their specific requirements using only a single image, posing new challenges in terms of security for generative models. + +![](images/56a0845895c1ed71f7953c1f3585aa222381202b834edee24691efd4fe710399.jpg) +(a) Calculation of Classifier Free Guidance + +![](images/cbe3f74c88efc5ab447a9f20f7f97f47a512ac356d7b19a1584ef65b6c3b8dd6.jpg) + +![](images/340bd65aa6b021232b6fb1dd0489bd42985b7666fac10ce58f3a2d84d7b26f48.jpg) +(b) Concept Erasure on Conditional Noise Prediction +(c) Our ACE learns to erase concept on both Conditional and Unconditional Noise Predictions +Figure 2. Overview of our proposed ACE. (a) In CFG, both conditional noise and unconditional noise are adopted to generate high-quality images. (b) ESD [14] unlearns the target concept (e.g., Mickey) by aligning conditional noise prediction with conditional erasure guidance (CEG). (c) During the fine-tuning, our ACE injects erasure guidance into both conditional and unconditional noise prediction, preventing the production of unsafe content during both generation and editing. PG-UEG denotes the prior-guided unconditional erasure guidance calculated following Eqn 9. + +# 2.3. Attacks in T2I Models + +As research on concept erasure in T2I models advances, red team studies focusing on the robustness of detection erasure methods are also increasingly emerging. P4D [10] processes a method of inserting adversarial text into regular input text to facilitate the production of insecure images using the T2I model. Ring-A-Bell [53] extracts the discrepancy vector between the embeddings of insecure concept text and secure concept text and employs it to derive the attack text embedding. UnlearnDiff [69] employs Projected Gradient Descent (PGD) to tackle the optimization challenge inherent in adversarial attacks and maps the optimized text embeddings onto discrete tokens. + +# 3. Proposed Method + +Given a target concept (e.g., Fukushima), concept erasure task [14, 36] aims to unlearn it from pre-trained text-to-image (T2I) models, preventing the illegal use of these models to create copyrighted content. However, existing methods can be circumvented and fail to prevent users from producing new undesirable images through image editing, which raises new concerns. To address this, we propose an Anti-Editing Concept Erasure (ACE) method, as illustrated in Fig. 2, to prevent the production of undesirable content through both generation and editing. In this section, we will first introduce the prior knowledge of our method (Sec. 3.1), + +including employed T2I model and concept erasure method. To address the editing issue, we further propose to erase the target concept from both conditional and unconditional prediction for anti-editing erasure (Sec. 3.2). Finally, to preserve the generation of non-target concepts, a prior concept preservation mechanism is introduced (Sec. 3.3). + +# 3.1. Preliminaries + +Stable Diffusion. In this work, we adopt Stable Diffusion 1.4 [46] as text-to-image model, which is one of the representative T2I diffusion models. It first employs a variational autoencoder (VAE) to transform real images $x$ into an image latent $z$ . Then, a text-conditioned diffusion model $\epsilon_{\theta}$ is trained on the latent space to predict latent codes, and mean-squared loss is adopted, + +$$ +\mathcal {L} _ {\mathrm {L D M}} = \mathbb {E} _ {z _ {t}, t, c, \epsilon \sim \mathcal {N} (0, I)} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, c, t\right) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $\epsilon$ denotes the unscaled noise and $c$ is the text embedding encoded by text encoders. $z_{t}$ is the latent noised to time $t$ . During inference, a random Gaussian noise $z_{T}$ is iteratively denoised to $z_{0}$ , and decoded to final image. + +Classifier-Free Guidance. To improve the quality of generated images, classifier-free guidance [20] is adopted during diffusion inference. Based on Tweedie's formula and the principles of diffusion model, we have: + +$$ +\nabla_ {z _ {t}} \log p (c | z _ {t}) = - \frac {1}{\sigma_ {t}} \left(\epsilon_ {\theta} \left(z _ {t}, c, t\right) - \epsilon_ {\theta} \left(z _ {t}, t\right)\right). \tag {2} +$$ + +![](images/27190eb892c6b8bb4fe387846155a26a0b9452aa12300fb0627f3354f91f094c.jpg) +Figure 3. Qualitative comparisons of IP character removal. Our ACE effectively erases the target concept while generating other concepts successfully. + +Here, $\sigma_{t}$ is a constant. To increase the probability of text condition $c$ appearing in the final image, the final noise prediction is the composition of noise prediction from both conditional and unconditional texts, + +$$ +\tilde {\epsilon} = \epsilon_ {\theta} \left(z _ {t}, t\right) + \omega \left(\epsilon_ {\theta} \left(z _ {t}, c, t\right) - \epsilon_ {\theta} \left(z _ {t}, t\right)\right), \tag {3} +$$ + +where $\epsilon_{\theta}(z_t,t)$ denote the unconditional noise prediction, and $\omega$ is a hyperparameter controlling the guidance scale. + +Concept Erasure. Given a target concept indicated by text $c$ (e.g., Pikachu), concept erasure task finetunes the model to reduce the probability of generating images containing this concept. For example, ESD [14] removes the target concept from the conditional noise prediction, and a conditional erasure guidance (CEG) is defined as: + +$$ +\tilde {\epsilon} _ {c} = \epsilon_ {\theta^ {*}} \left(z _ {t}, t\right) - \eta_ {c} \left(\epsilon_ {\theta^ {*}} \left(z _ {t}, c, t\right) - \epsilon_ {\theta^ {*}} \left(z _ {t}, t\right)\right), \tag {4} +$$ + +where $\epsilon_{\theta^{\star}}(\cdot)$ represents the original T2I model, and $z_{t}$ is the encoded latent image contains target concept $c$ . $\eta_c$ is a control scale hyperparameter. During training, ESD aligns the noise prediction of the target concept in tuned model $\epsilon_{\theta}(z_t,c,t)$ with the above CEG, + +$$ +\mathcal {L} _ {\mathrm {E S D}} = \mathbb {E} _ {z _ {t}, t, c} \left[ \| \epsilon_ {\theta} (z _ {t}, c, t) - \tilde {\epsilon} _ {c} \| _ {2} ^ {2} \right]. \tag {5} +$$ + +After the training, the erasure guidance $-\nabla_{z_t}\log p(c|z_t)$ is introduced into conditional noise prediction of the target concept. Therefore, the prediction of tuned model will be guided away from the erased concept, preventing the generation of images containing the erased concept. + +# 3.2. Anti-Editing Concept Erasure + +Editing Filtration. Although existing erasure methods can successfully prevent the generation of an erased concept through text prompts, they can be easily circumvented by editing techniques. As shown in Fig. 1, when utilizing tuned ESD model to add sunglasses on an image of Pikachu using LEDs++ [4], it successfully produces an image of Pikachu with sunglasses, raising potential copyright concerns. This is because these methods are typically trained to erase the concept from the noise prediction of the target concept (as shown in Fig. 2 (b)), and rely on inputting concept text (e.g., "Pikachu" or "Mickey") to trigger the guard. However, during the editing process, the target concept may not necessarily be used in the text prompt. Therefore, these erasure methods fail to prevent the reconstruction of the erased concept. In practice, the erasure model should also have the ability to prevent the creation of undesired concepts through image editing, a feature we refer to as editing filtration. + +Unconditional Erasure Guidance. As we all know, current generation and editing methods heavily rely on classifier-free guidance [20] (CFG) to improve the quality of generated images, where unconditional noise prediction performs an important role. To address the issue of editing filtration, we further propose to erase the target concept from both conditional and unconditional noise prediction, thereby preventing edited images from containing target concepts. Specifically, similar to ESD, we define the unconditional erasure guidance (UEG) as, + +$$ +\tilde {\epsilon} _ {\mathrm {u}} = \epsilon_ {\theta^ {*}} \left(z _ {t}, t\right) + \eta_ {\mathrm {u}} \left(\epsilon_ {\theta^ {*}} \left(z _ {t}, c, t\right) - \epsilon_ {\theta^ {*}} \left(z _ {t}, t\right)\right). \tag {6} +$$ + +During training, we additionally align the unconditional noise prediction of the tuned model with the UEG, + +$$ +\mathcal {L} _ {\mathrm {U n c}} = \mathbb {E} _ {z _ {t}, t, c} \left[ \| \epsilon_ {\theta} (z _ {t}, t) - \tilde {\epsilon} _ {\mathrm {u}} \| _ {2} ^ {2} \right]. \tag {7} +$$ + +When fine-tuned unconditional noise (our UEG) is subtracted in the CFG process, the erased concept guidance will be subtracted, thereby reducing the probability of the erased concept appearing regardless of the input text prompt. Then, the CFG noise prediction during inference will move away from the target concept regardless of any text input, thereby effectively preventing the production image containing the target concept. As erasure models are usually trained on a small dataset, they are prone to be overfitting, where the erasure guidance is introduced into the noise prediction for other conditional text prompts. This weakens the erasure effects and leads to incomplete erasures. To address the issue of overfitting, we introduce a prior constraint loss during the training process. Specifically, we regularize the prediction of the prior concept in the new model to be consistent with that of the original model: + +$$ +\mathcal {L} _ {\text {C o n s}} = \mathbb {E} _ {z _ {t}, t, c _ {p} \in \mathcal {C} _ {p}} \left[ \| \epsilon_ {\theta} \left(z _ {t}, c _ {p}, t\right) - \epsilon_ {\theta^ {*}} \left(z _ {t}, c _ {p}, t\right) \| _ {2} ^ {2} \right], \tag {8} +$$ + +![](images/bb0ea50cff7f9b2c8b2419c85b5296709314c8902c1c00d0bf08c525e1efaf57.jpg) +Figure 4. Comparison of our ACE method with other methods in terms of editing filtering. After erasing Mickey Mouse, our method filtered out edits involving Mickey Mouse while not affecting edits related to other IP characters. In contrast, the competing methods either fail to prevent editing (e.g., ESD, SPM, RECE, and MACE) or cannot perform editing on non-target concepts (e.g., AdvUnlearn). + +![](images/5f7264cadb1e3e303dc91c35a8afcb0694688495744182e74bb856025ae21ba8.jpg) +Figure 5. Qualitative results of nudity removal. Figure (a) shows the results of explicit editing using SD-Inpainting, while Figure (b) displays images generated using text with explicit label. Static adversarial text is used for editing text, while dynamic adversarial attacks are employed for generation. It can be observed that our method effectively reduces exposure in both editing and generation tasks. Moreover, our method maintains its effectiveness when editing and generating using adversarial text, indicating its robustness. + +where $c_p$ represents prior concept, and $\mathcal{C}_p$ represents the set of prior concepts. Intuitively, the larger the set of priors, the better it helps mitigate overfitting. However, it is challenging to traverse all the prior concepts as the pre-trained models have a large general semantic space. Our goal is to preserve the concepts more likely to be affected, thus minimizing the influence to other concepts. We assume that these concepts are semantic-related concepts to the erased concept and use LLM [1] to obtain them. By adding this loss, it ensures that the erasure guidance introduced during training aligns with our conceptualization in the Eqn. 7. + +# 3.3. Prior Concept Preservation + +In practice, training with the method proposed in Sec. 3.2 affects the generation prior of relevant concepts (see Sec. 4.4). This is because incorporating UEG not only decreases the probability of producing erased concepts, but also decreases probability of adjacent concepts. Therefore, we reverse mechanism of UEG by subtracting the guidance of prior concepts from the unconditional noise, which prevents the probability reduction of these concepts and minimizes concept forgetting. The prior concepts are sampled from the semantic-related concepts obtained using LLM, + +(a) Generation Prevention +(b) Editing Filtration + +
MethodErase ConceptPrior ConceptOverallErase ConceptPrior ConceptOverall
ESDUncConsCorCLIPe↓LPIPSe↑CLIPp↑LPIPSp↓CLIPd↑LPIPSd↑CLIPe↓LPIPSe↑CLIPp↑LPIPSp↓CLIPd↑LPIPSd↑
(1)0.1710.4400.2460.2860.0750.1530.3010.0600.3050.0500.0040.011
(2)0.1660.5510.2830.2360.1170.3150.2850.1490.3050.0570.0190.092
(3)0.1590.5070.2540.3370.0950.1700.2740.1680.3000.0770.0260.091
(4)0.2110.3030.2930.1990.0820.1040.2730.1750.3010.0790.0280.096
(5)0.1750.3970.2950.1960.1200.2010.2740.1680.3030.0700.0290.097
+ +Table 1. Quantitative Evaluation of generation and editing after ablation. The best results are highlighted in bold. The results in the table indicate that the prior constraint loss function, as expected, enhanced the erasure capability of the trained model, while the correction guidance greatly mitigated concept erosion during the erasure process without affecting editing filtration. + +![](images/9db561db123c5c79efc21173cd92c2acc70444dc91671755919fd09b03fb7492.jpg) +Figure 6. Qualitative results of artistic style removal. Our method erases the target style effectively and has minimal impact on other artistic styles. + +which is mentioned in the previous section. We call this new guidance prior-guided unconditional erasure guidance (PG-UEG), which is defined as: + +$$ +\begin{array}{l} \tilde {\epsilon} _ {\mathrm {p u}} = \epsilon_ {\theta^ {*}} (z _ {t}, t) + \eta_ {\mathrm {u}} \left(\epsilon_ {\theta^ {*}} (z _ {t}, c, t) - \epsilon_ {\theta^ {*}} (z _ {t}, t)\right) \\ - \eta_ {p} \gamma_ {p} \left(\epsilon_ {\theta^ {*}} \left(z _ {t}, c _ {p}, t\right) - \epsilon_ {\theta^ {*}} \left(z _ {t}, t\right)\right), \tag {9} \\ \end{array} +$$ + +where $\gamma_{p}$ represents the guidance control term related to the prior retained concept. $c_{p}$ refers to the same prior concept in $\mathcal{L}_{\mathrm{Cons}}$ which are obtained through random sampling from the set $\mathcal{C}_p$ . We calculate $\gamma_{p}$ using the CLIP model to measure the relevance of different prior concepts to the target concept image and then compare it to the relevance of the target concept text to its image. Specifically, $\gamma_{p} = \frac{\mathrm{CLIP}(x,c_{p})}{\mathrm{CLIP}(x,c)}$ . The new loss for our ACE is: + +$$ +\mathcal {L} _ {\mathrm {P U n c}} = \mathbb {E} _ {z _ {t}, t, c, c _ {p} \in \mathcal {C} _ {p}} \left[ \| \epsilon_ {\theta} (z _ {t}, t) - \tilde {\epsilon} _ {\mathrm {p u}} \| _ {2} ^ {2} \right]. \tag {10} +$$ + +The final training loss for our ACE is summarized as: $\mathcal{L}_{\mathrm{ACE}} = \lambda_{\mathrm{PUnc}}\mathcal{L}_{\mathrm{PUnc}} + \lambda_{\mathrm{Cons}}\mathcal{L}_{\mathrm{Cons}} + \lambda_{\mathrm{ESD}}\mathcal{L}_{\mathrm{ESD}}$ + +In our implementation, we adopt LORA [22] for parameter-efficient tuning, and the training process follows [14]. More details are provided in Suppl. + +# 4. Experiments + +We conduct experiments on various tasks to evaluate our ACE, including IP characters erasure, artistic styles erasure, and nudity erasure. ESD [12], SPM [36], AdvUnlearn [68], MACE [35], and RECE [17] are adopted as competing methods. Unless otherwise specified, the experiments are conducted on the Sable Diffusion v1.4. + +# 4.1. IP Character Removal + +Experiment Setup. To access our ACE on IP character removal, we employ ten iconic IP characters as examples, including Hello Kitty, Snoopy, Mickey Mouse, Elsa, Donald Duck, Dora the Explorer, Winnie the Pooh, Sonic the Hedgehog, Elsa, and Fukushima. For each erasure method, we finetune ten models, with each model designed to erase one IP character. Following [14, 17], we adopted CLIP [44] score and LPIPS [66] score as metrics for evaluation. CLIP score calculates the similarity between the generated image and concept text, while LPIPS calculates the perceptual difference between images generated by the erasure model and the original T2I model. $\mathrm{CLIP}_e$ calculates the CLIP similarity between images generated with erased concept text and their corresponding text, where lower value indicates more thorough erasure. $\mathrm{CLIP}_p$ calculates the relevance under prior concepts, and higher value indicates better prior preservation. $\mathrm{LPIPS}_e$ calculates the LPIPS similarity between images generated with erased concept text by the trained model and the original model, and higher value indicates more thorough erasure. $\mathrm{LPIPS}_p$ calculates the similarity under prior concepts, in which lower values indicate better prior preservation. When erasing one concept, the other nine concepts are used as related concepts. Following RECE [17], we further calculate the overall scores between erased and related characters to measure the trade-off between the concept erasure and prior preservation, where + +(a) Generation Prevention +(b) Editing Filtration + +
MethodErase ConceptPrior ConceptOverallErase ConceptPrior ConceptOverall
\(CLIP_e\downarrow\)\(LPIPS_e\uparrow\)\(CLIP_p\uparrow\)\(LPIPS_p\downarrow\)\(CLIP_d\uparrow\)\(LPIPS_d\uparrow\)\(CLIP_e\downarrow\)\(LPIPS_e\uparrow\)\(CLIP_p\uparrow\)\(LPIPS_p\downarrow\)\(CLIP_d\uparrow\)\(LPIPS_d\uparrow\)
SD v1.4 [46]0.3010.0000.3010.0000.0000.0000.3080.0630.3080.0630.0000.000
ESD [14]0.2270.3310.2760.2550.0490.0760.3060.0420.3070.0410.0010.000
SPM [36]0.2390.2880.2960.1070.0560.1810.3020.0610.3030.0560.0010.005
AdvUnlearn [68]0.1660.4680.2090.4030.0430.0650.3100.0110.3110.0100.0010.001
MACE [35]0.2500.3170.2980.1340.0480.1840.3030.0560.3040.0540.0010.002
RECE [17]0.1760.4260.2570.2700.0810.1560.3000.0660.3030.0540.0030.012
Ours0.1750.3970.2950.1960.1200.2010.2740.1680.3030.0700.0290.097
+ +Table 2. Quantitative comparisons of IP character erasure. The best two results are highlighted with bold and underline. + +
ButtocksBreast (F)Genitalia (F)Breast (M)Genitalia (M)FeetArmpitsBellyTotal↓FID30k↓CLIP30k↑
SD v1.4 [46]612043738167024118385014.070.313
ESD [14]15295111037683621113.800.304
SPM [36]1429721241532818614.630.312
AdvUnlearn [68]46208131275215.350.293
MACE [35]724810935613518912.600.294
RECE [17]14207161039453518614.450.309
Ours323496573914.690.308
+ +Table 3. Exposure detection of generated images in the I2P dataset. The best two results are highlighted with bold and underline. + +
Erase ConceptRelate ConceptOverall
CLIPp↓LPIPSe↑CLIPp↑LPIPSp↓CLIPd↑LPIPSd↑
SD v1.4 [46]0.3100.0000.3100.0000.0000.000
ESD [14]0.2160.4440.2960.2410.0800.202
SPM [36]0.2660.2680.3080.0740.0420.195
AdvUnlearn [68]0.1860.4760.2290.4100.0430.066
MACE [35]0.2280.3660.2980.1960.0690.169
RECE [17]0.2530.3070.3090.0510.0570.255
Ours0.1600.4710.3030.1260.1430.345
+ +Table 4. Quantitative evaluation of artist style erasure. The best two results are highlighted with bold and underline. Our ACE performs better in terms of thorough erasure and also demonstrates comparable prior preservation. + +
Unlearn Diffusion↓P4D↓Ring a Bell↓Average↓
SD v1.4 [46]100%100%85.21%95.07%
ESD [14]73.05%74.47%38.73%62.08%
SPM [36]91.49%91.49%57.75%80.24%
AdvUnlearn [68]25.53%19.15%4.93%16.54%
MACE [35]64.53%66.67%14.79%48.66%
RECE [17]70.92%65.96%26.76%54.55%
Ours27.65%28.37%2.82%19.61%
+ +Table 5. Robustness evaluation of nudity erasure. The best two results are highlighted with bold and underline. We report the attack success rates (ASR) of different adversarial methods under various erasure models. Our method achieved the second-best results without using adversarial training. + +$\mathrm{CLIP}_d = \mathrm{CLIP}_p - \mathrm{CLIP}_e$ and $\mathrm{LPIPS}_d = \mathrm{LPIPS}_e - \mathrm{LPIPS}_p$ . Higher $\mathrm{CLIP}_d$ and $\mathrm{LPIPS}_d$ indicate better trade-off. + +For generation evaluation, we adopt 33 text templates for each character concept, and five images are generated for each text template using the erased model. To evaluate the effectiveness of editing filtration, we adopt the widely used LEDs++ [4] and MasaCtrl [6] as editing methods. For each concept, we utilize Stable Diffusion 3 [12] to generate 15 images based on 3 text templates as initial images, and + +then perform editing on them using erased models. Each image is manipulated using 11 editing texts, such as "sun-glasses". Finally, the CLIP score and LPIPS score are calculated based on edited images, concept text and original images. The final results are all reported by averaging 10 characters. More details can be found in Suppl. + +Experiment Results. Fig. 3 illustrates the comparison of generation results against competing methods. One can see that, our ACE can successfully erase the target concept (i.e., Donald Duck) while retaining the capability to generate related prior concepts (e.g., Mickey Mouse and Pikachu). In contrast, methods such as ESD, AdvUnlearn, and RECE generate examples with noticeable concept erosion. From Table 2, our ACE demonstrates a comparable CLIP score for both the erased and related concepts. This indicates that our ACE achieves a better trade-off between target concept erasure and prior concept preservation, as further validated by the overall metrics in Table 2 (a). SPM and MACE exhibit inferior performance in thoroughly erasing the target concept. While AdvUnlearn performs well at erasing the target concept, it shows poor performance in prior preservation. + +Fig. 4 further presents the comparison of editing results by LEDITS++. As shown in the figure, the competing method generates the erased concept with desired attributes after performing the editing on the given image, which is not wanted in practice. In contrast, our method can successfully hinder the editing of images containing erased concepts (e.g., Mickey), while keeping the editability of nontarget concepts (e.g., Hello Kitty and Elsa). Table 2 (b) reports the quantitative comparisons evaluated with LEDITS++. Our method shows a significant improvement in erasing concepts, demonstrating its ability to edit filtration. + +The comparison on MasaCtrl and more results can be found in Suppl. + +# 4.2. Explicit Content Removal + +Experimental Setup. To evaluate our ACE on explicit content removal, we employ "nudity" as the target concept to train the model. Following [36], we utilize the I2P dataset [48] to evaluate the performance of explicit content generation. Specifically, we select 856 text prompts with explicit labels, and each prompt generates one image. Then, Nudenet [2] is used to quantify the number of nude body parts in these generated images. Additionally, following [14, 36], we employ COCO-30k Caption dataset [31] to evaluate the conditional generation capability of erased models. Specifically, we generate one image for each caption in COCO-30k and FID [19] is calculated between generated and natural images. CLIP score is also calculated between the generated images and the captions to access the semantic alignment of generated images. For robustness evaluation, we adopt UnlearnDiff [69], P4D [10] and Ring-A-Bell [53] as adversarial tools to calculate attack success rate (ASR). Adversarial attacks were conducted on 142 sensitive texts provided by UnlearnDiff. More details can be found in Suppl. + +Experiment Results. From Table 5, we can see that our method has a lower success rate in adversarial attacks when trained only for "nudity", with only AdvUnlearn performing slightly better than us with using adversarial training. As shown in Fig. 5 and Table 3, our method can effectively erase nudity content and results in fewer exposure parts. In the generation evaluation, we dynamically attack the erased models using adversarial tools. As shown in Fig. 5, our method demonstrates excellent robustness. To further showcase our method's efficacy in editing filtration, we employ SD-Inpainting [46] as an editing tool to assess the exposure levels of images after different text-guided inpainting processes. In addition to conventional text editing (e.g., bikini) adversarial edited text in MMA-Diffusion [61] is also used for explicit editing. GroundingDINO [34] is used to detect clothing in the images. As shown in Fig. 5, our method successfully prevents inappropriate inpainting of exposed parts in masked areas, making it more practical for real-world applications. + +More results for robustness and editing filtration evaluation can be found in Suppl. + +# 4.3. Artistic Style Removal + +Experiment Setup. To validate the performance of our model in unlearning styles, we choose ten representative artistic styles, including Leonardo da Vinci, Pablo Picasso, Michelangelo, Van Gogh, Salvador Dali, Claude Monet, Andy Warhol, Jackson Pollock, Frida Kahlo, Georgia O'Keeffe. The evaluation process and metrics are simi + +lar to the IP character removal (Sec. 4.1). + +Experiment Results. Fig. 6 illustrates the results of erasing artistic styles. As shown in the figure, our method can erase the style of Van Gogh and Andy Warhol from the T2I model, while generating other styles faithfully. From Table 4, our method achieves better $\mathrm{CLIP}_e$ on erased concept. + +# 4.4. Ablation Study + +We further conduct the ablation study on the IP character erasure to evaluate the effectiveness of each component proposed in our ACE. Specifically, it contains the following variants: (1) Baseline: by only adopting the ESD loss to finetune the model. (2) Baseline + Unc: by employing unconditional erasure guidance alignment with ESD Loss to finetune the model. (3) Baseline + Unc + $\mathcal{L}_{\mathrm{Cons}}$ : by adopting ESD Loss, unconditional erasure guidance alignment, and $\mathcal{L}_{\mathrm{Cons}}$ to finetune the model. (4) Our method without ESD: Ours w/o $\mathcal{L}_{\mathrm{ESD}}$ is also effective in concept erasure and editing filtration, and performs better than ESD, indicating that our PG-UEG plays a crucial role in editing filtering. (5) Ours full method: by incorporating the ESD Loss, prior-guided unconditional erasure guidance alignment and $\mathcal{L}_{\mathrm{Cons}}$ together. From Table 1, we can see that: (i) Introducing unconditional erasure guidance improves the model's editing filtration performance, indicating its effectiveness in preventing unwanted edits. (ii) We use both unconditional erasure guidance and $\mathcal{L}_{\mathrm{Cons}}$ together leading to significant improvements in concept erasure and editing filtration performance, although it compromises the generation of related prior concepts. (iii) $\mathcal{L}_{\mathrm{PUnc}}$ enhances the prior preservation, and without affecting editing filtration. + +More ablation results are provided in Suppl. + +# 5. Conclusion + +In this paper, we investigate the potential risks of unsafe content creation through image editing, and propose an Anti-Editing Concept Erasure (ACE) method to prevent the production of such content during both generation and editing. In addition to the conditional erasure guidance used by existing methods, we further propose an unconditional noise erasure technique to enhance anti-editing concept erasure. This guidance steers the noise prediction away from the target concept, thereby effectively preventing the production of images containing the target concept. Moreover, a concept preservation mechanism is introduced to maintain the generation prior of non-target concepts. Experiments demonstrate that our ACE can successfully erase specific concepts and exhibits superior filtration capabilities during both generation and editing compared to existing methods. + +Acknowledgement. The work was supported by National Key R&D Program of China under Grant No. 2022YFA1004100. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023.5 +[2] P Bedapudi. Nudenet: Neural nets for nudity classification, detection and selective censoring, 2019. 8 +[3] Manuel Brack, Felix Friedrich, Dominik Hintersdorf, Lukas Struppek, Patrick Schramowski, and Kristian Kersting. Sega: Instructing text-to-image models using semantic guidance. Advances in Neural Information Processing Systems, 36: 25365-25389, 2023. 2 +[4] Manuel Brack, Felix Friedrich, Katharia Kornmeier, Linoy Tsaban, Patrick Schramowski, Kristian Kersting, and Apolinário Passos. Ledits++: Limitless image editing using text-to-image models. 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China + +$^{2}$ National University of Singapore, Singapore + +{guyubin,aprilmyy}@stu.xmu.edu.cn,jjyxmu@gmail.com,xssun@xmu.edu.cn + +# Abstract + +Image restoration (IR), a key area in computer vision, has entered a new era with deep learning. Recent research has shifted toward Selective State Space Models (Mamba) to overcome CNNs' limited receptive fields and Transformers' computational inefficiency. However, due to Mamba's inherent one-dimensional scanning limitations, recent approaches have introduced multi-directional scanning to bolster inter-sequence correlations. Despite these enhancements, these methods still struggle with managing local pixel correlations across various directions. Moreover, the recursive computation in Mamba's SSM leads to reduced efficiency. To resolve these issues, we exploit the mathematical congruences between linear attention and SSM within Mamba to propose a novel model, ACL, which leverages news designs to Activate the Capability of Linear attention for IR. ACL integrates linear attention blocks instead of SSM within Mamba, serving as the core component of encoders/decoders, and aims to preserve a global perspective while boosting computational efficiency. Furthermore, we have designed a simple yet robust local enhancement module with multi-scale dilated convolutions to extract both coarse and fine features to improve local detail recovery. Experimental results confirm that our ACL model excels in classical IR tasks such as de-raining and de-blurring, while maintaining relatively low parameter counts and FLOPs1. + +# 1. Introduction + +In the field of image processing, restoring degraded images to clarity is a crucial technology. High-quality image restoration (IR) methods play a key role in ensuring the smooth progression of downstream vision tasks. Vanilla IR methods rely primarily on manually designed feature extraction, but often perform poorly when faced with complicated degradation factors in reality. + +![](images/87e0ea1dca4d6347f547973ef4454a772c0dd4e8960c638c717732cde503c547.jpg) +Figure 1. Comparison of our method's core block design with those of recent mainstream approaches. + +Over the past decade, with the rapid development of deep learning, many fields have been propelled forward, such as image segmentation and generation [11, 12, 14, 17, 48], and of course, IR as well. The initial IR models were primarily based on CNN designs [6, 41], whose translational invariance and high inferential efficiency have made them widely applied, as depicted in the core structure in Fig. 1(a). However, these CNN-based models face challenges in processing global features and often require stacking additional network layers to compensate for this deficiency. With the rise of attention mechanisms [34], particularly the application of the Transformer, which boasts exceptional global feature modeling capabilities, an increasing number of researchers have shifted toward Transformer-based designs [23, 36, 44], achieving remarkable restoration results, as shown in the core structure in Fig. 1 (b). Although the Transformer broadens the global perspective, its softmax attention mechanism's quadratic computational complexity significantly reduces efficiency during inference. + +Recently, state-space models from the field of control science, especially the Mamba model [8], have been proposed by related IR methods [13, 30] demonstrating superior training and inference efficiency on sequential data. These models have even outperformed some Transformer- + +based IR methods in terms of performance. Mamba is initially designed for one-dimensional sequence data modeling, direct adaptation to two-dimensional image poses challenges. The improved SSM module in Mamba, a one-dimensional unidirectional scanning, recursive computing structure, faces major issues when applied to the image, including: 1) conversion of image data into a one-dimensional sequence increases the distance between adjacent pixels, leading to the loss of local relationships [30]; 2) unidirectional modeling neglects the spatial relationships of pixels in multiple directions. Recently, MambaIR [13] and VMambaIR [30] have adopted multi-directional scanning methods to mitigate these problems, as illustrated in the main structure in Fig. 1 (c), but these methods have yet to effectively and directly establish multi-directional connections in the spatial dimension of pixels. + +In response to the limitations of the Mamba model, we propose a method that aims to leverage the advantages of the Mamba structure while addressing its unidirectional modeling constraint. A direct approach to overcoming this limitation is to introduce a long-range dependency attention mechanism, such as Linear Attention (LA) or Softmax Attention (SA). Although SA generally outperforms LA in traditional vision tasks, its computational complexity is significantly higher than that of LA. Upon further analysis, we observe that LA and the State-Space Model (SSM) in Mamba share a highly similar mathematical formulation, which has also been deeply analyzed in the work [15]. Inspired by this insight, we replace the SSM module in Mamba with LA layers, thereby designing a novel foundational IR architecture, as illustrated in Fig. 1 (d), and propose a new IR model, ACL. + +Specifically, the proposed ACL consists of two main components: the Mamba-based module with LA at its core (denoted as LAMA), which serves as the central part of the encoder/decoder and establishes global feature dependencies with linear computational complexity. Additionally, optimizing local features is equally essential. A recent approach involves partitioning the global features in the spatial domain into small windows and optimizing attention within these windows to enhance local feature modeling. While this approach has shown some effectiveness, it incurs high computational costs. In contrast, we propose a simple yet efficient multi-scale dilated convolution module (MDC), which captures local features at varying granularities by employing different dilation factors, thus improving detail restoration. By combining the Mamba structure with LA, ACL activates the capability of LA, achieving advanced performance on two classic IR tasks—deblurring and deraining. Compared to Transformer-based models [32, 44], ACL not only significantly reduces computational cost and parameter count, but also achieves superior or comparable performance. + +Our contributions are summarized as follows: + +- We explore an alternative CNN and Transformer-based architecture for Image Restoration, providing global receptive fields while maintaining computational efficiency. Specifically, we propose ACL, which upgrades the SSM in Mamba with the LA structure, enabling the model to perform global multi-directional scanning. +- The proposed ACL consists of two modules: LAMA and MDC. LAMA captures global feature dependencies, and MDC captures local features at varying granularities. Both modules enhance detail restoration. +- The proposed ACL demonstrates advanced performance in de-raining and de-blurring tasks, proving its advantages in terms of parameter count and computational cost. + +# 2. Related Work + +# 2.1. Image Restorations + +Image restoration (IR) technology provides clear visual data essential for numerous advanced downstream visual tasks. In recent years, the advent of deep learning has eclipsed traditional methods that rely on manually designed features, shifting the paradigm toward deep-learning-based approaches [9, 13, 20, 22, 45]. Initially, models were predominantly designed using CNNs, achieving significant advancements through sophisticated network designs that incorporated encoder-decoder patterns [5], dense connections, and residual connections [10]. However, CNN-based techniques face challenges in establishing global feature dependencies. With the evolution of Transformers in both Natural Language Processing (NLP) and Computer Vision (CV), many researchers have pivoted towards Transformer-based IR methods [23, 38, 44], leveraging their robust global receptive capabilities and marking substantial progress. Despite these improvements, the computational burden of calculating SA remains a drawback. Recently, the Mamba model [8], known for its efficient training and inference capabilities, has introduced a new potential paradigm in the IR field. Methods such as VMambaIR [30] and MambaIR [13], which employ multidirectional scanning strategies, aim to address the issues of unidirectional modeling inherent in Mamba's SSM blocks. Nonetheless, these methods have yet to establish multidirectional pixel connections directly. Thus, exploring how to utilize Mamba's superior design to establish comprehensive multidirectional global pixel correlations remains a promising direction. + +# 2.2. Attention Mechanisms + +Originally applied in the NLP field, attention mechanisms [34], particularly the Transformer with its SA mechanism, have achieved remarkable success. Subsequently, these mechanisms have been successfully adapted to the + +visual domain. In recent years, numerous IR methods based on the Transformer structure have emerged [1, 3, 23, 24], primarily utilizing various design modules to leverage self-attention mechanisms and enhance model efficiency. SwinIR [23] introduces twin-shifted window attention to boost performance. IPT [1] enhances local detail restoration by dividing images into multiple small windows and processing each window's features independently. However, adopting SA to establish global or local feature dependencies inevitably leads to quadratic computational complexity. Linear attention, which operates with linear complexity, has yet to match the performance of SA in classical vision tasks, thus its application remains limited. In this paper, we introduce a new IR model, ACL, activating the potential of linear attention. + +# 2.3. State Space Model + +The Mamba model, a newly proposed state space model (SSM), effectively facilitates sequence modeling with linear complexity [8]. Owing to its efficient training and inference speeds, many researchers have adapted it for visual tasks [16, 25, 30, 39, 50]. For instance, Local-Mamba [16] employs a cross-scanning module to scan image spaces. VMambaIR [30] enhances multidirectional relationships between pixels by scanning images from six directions. These methods focus on overcoming the limitations of unidirectional modeling in SSMs by proposing various scanning techniques. However, the features captured in each direction remain unidirectionally connected and potentially lead to redundant computational costs. The Mamba model is efficient due to its structural design, yet its unidirectional scanning is not entirely suitable for images. Therefore, we combine linear attention with the Mamba structure to achieve a new balance between computational efficiency and restoration effectiveness. + +# 3. Methods + +# 3.1. Preliminary Analysis + +In recent years, very few IR models based on linear attention have been proposed, as they tend to perform slightly worse than SA in classical vision tasks. Leveraging the computational advantages of Linear Attention (LA) to further explore its potential in visual tasks is crucial. + +The improved SSM in Mamba shows significant potential in sequence processing. In fact, linear attention has a similar expression to SSM [15]. In linear attention, if the attention of the $i$ -th token is restricted to only be related to the previous $i$ tokens, it is expressed as follows: + +$$ +\mathbf {A} _ {i} = \frac {\mathbf {Q} _ {i} \left(\sum_ {j = 1} ^ {i} \mathbf {K} _ {j} ^ {\top} \mathbf {V} _ {j}\right)}{\mathbf {Q} _ {i} \left(\sum_ {j = 1} ^ {i} \mathbf {K} _ {j} ^ {\top}\right)} = \frac {\left(\mathbf {Q} _ {i} \mathbf {D} _ {i}\right)}{\left(\mathbf {Q} _ {i} \mathbf {U} _ {i}\right)}, \tag {1} +$$ + +where $\mathbf{D}_i = \sum_{j=1}^i \mathbf{K}_j^\top \mathbf{V}_j$ , $\mathbf{U}_i = \sum_{j=1}^i \mathbf{K}_j^\top$ . Therefore, the recursive expressions are: + +$$ +\mathbf {U} _ {i} = \mathbf {U} _ {i - 1} + \mathbf {K} _ {i} ^ {\top}, \tag {2} +$$ + +$$ +\mathbf {D} _ {i} = \mathbf {D} _ {i - 1} + \mathbf {K} _ {i} ^ {\top} \mathbf {V} _ {i}, \quad \mathbf {A} _ {i} = \frac {\left(\mathbf {Q} _ {i} \mathbf {D} _ {i}\right)}{\left(\mathbf {Q} _ {i} \mathbf {U} _ {i}\right)}. \tag {3} +$$ + +To enable applications in deep neural networks, it is necessary to discretize the initial SSM using zero-order hold [8]. This involves discretizing the continuous parameters $\mathbf{A}$ and $\mathbf{B}$ into $\bar{\mathbf{A}}$ and $\bar{\mathbf{B}}$ through the time scale parameter $\Delta$ . The specific expressions are as follows: + +$$ +\mathbf {h} _ {i} = \bar {\mathbf {A}} \mathbf {h} _ {i - 1} + \mathbf {B} \mathbf {x} _ {i}, \quad \mathbf {y} _ {i} = \mathbf {C h} _ {i} + \mathbf {D x} _ {i}, \tag {4} +$$ + +where $\bar{\mathbf{A}} = \exp (\Delta \mathbf{A})$ and $\bar{\mathbf{B}} = (\Delta \mathbf{A})^{-1}(\exp (\Delta \mathbf{A}) - I)\Delta \mathbf{B}\approx \Delta \mathbf{B}$ . For simplicity, we have omitted the feature dimension information of each part in the formulas. + +Further, Mamba enhances the discrete SSM by making $\bar{\mathbf{A}}$ , $\bar{\mathbf{B}}$ , and $\Delta$ dependent on the input $\mathbf{x}_i$ , breaking away from the assumption of input-independent models. Additionally, since $\bar{\mathbf{A}}_i$ in Mamba is a diagonal matrix, we have $\tilde{\mathbf{A}}_i = diag(\tilde{\mathbf{A}}_i)$ . The expression is thus transformed into: + +$$ +\mathbf {h} _ {i} = \tilde {\mathbf {A}} _ {i} \mathbf {h} _ {i - 1} + \mathbf {B} _ {i} (\Delta_ {i} \mathbf {x} _ {i}), \quad \mathbf {y} _ {i} = \mathbf {C} _ {i} \mathbf {h} _ {i} + \mathbf {D} \mathbf {x} _ {i}. \quad (5) +$$ + +The primary distinctions between Eq. 3 and Eq. 5 are as follows: 1) The improved State Space Model (SSM) incorporates an additional parameter for hidden state transitions, denoted as $\tilde{\mathbf{A}}_i$ . This parameter functions similarly to a forget gate, filtering previous states to enhance selective retention. 2) An additional term, $\mathbf{D}\mathbf{x}_i$ , is introduced, akin to an input skip connection. In the Mamba model, which aims to achieve input-dependent modeling, $\tilde{\mathbf{A}}_i$ must be recursively computed. Despite the utilization of hardware acceleration mechanisms, this process still adheres to unidirectional modeling. Linear attention represents an alternative form of SSM within Mamba and can transcend the limitations of unidirectional pixel modeling, presenting a potential capability. For a more in-depth analysis, one can refer to another outstanding analytical works [15]. + +# 3.2. Overall Structure of the Model + +As illustrated in Fig. 2 (a), the proposed IR model, ACL, is based on an encoder-decoder architecture. In this model, multiple downsampled degraded images are fed into the main pathway of the encoder through lateral convolution layers, and images restored at three different scales are output during the decoding phase. Both the encoder and decoder comprise three fundamental core blocks, the structure of which is depicted in Fig. 2. Each core unit consists of several successive LAMA modules. Furthermore, as shown in the framework diagram, following two core units with higher feature resolution in both encoding and decoding + +![](images/f7098aef4493c7621c002027cefe7603ad9677eede56e3b8f7c71f5544d7aadc.jpg) +(a) Overall Pipeline +(b) Encoder and Decoder + +![](images/73afeb19e508ef0c79efdc91ea6a607b59b6b98d0fc4a83f1a08de6ea5cfcd98.jpg) +Figure 2. (a) The overall framework of ACL, based on the encoder-decoder architecture. (b) The core structure of the encoder-decoder, which includes the improved LA-based Mamba (LAMA) module. (c) The structure of the LAMA module. (d) The MDC module. + +![](images/9ee6b870f30c4854b13c04ce5b0494c60e29179a3217150a08f1140cd8aff9ee.jpg) +(c) LA-based Mamba +(d) Multi-Dilated Convolutions Module + +![](images/ea2bdffdc71374fad9556828ff17a8829c90fc14006c21c4a18807ac64811baf.jpg) + +phases, a local enhancement module is appended to augment the model's capability for local detail restoration. The structure of this local enhancement module is presented in Fig. 2 (d). + +Specifically, the network process begins with a degraded image $\mathbf{I} \in \mathbb{R}^{3 \times 256 \times 256}$ . The model first transforms this image through a convolution layer into a feature map $\mathbf{I}' \in \mathbb{R}^{C \times H \times W}$ , expanding the number of feature channels from 3 to $C$ , where $C = 32$ . Subsequently, this feature map is further processed through three encoder units $E_{i}$ and a local enhancement module, each unit encoding the feature maps at different scales into a latent space state, denoted as $\mathbf{I}_e^i \in \mathbb{R}^{2^{(i-1)}C \times \frac{H}{2^{(i-1)}} \times \frac{W}{2^{(i-1)}}}$ , where $i = 1, 2, 3$ . Here, $C, H$ , and $W$ respectively represent the number of feature channels, the height, and the width of the feature maps. These processed feature maps are then passed to the decoder, where they are fused through direct or skip connections. In the decoder, the feature maps are gradually restored by decoding units $D_{i}$ , generating $\mathbf{I}_d^i \in \mathbb{R}^{2^{(i-1)}C \times \frac{H}{2^{(i-1)}} \times \frac{W}{2^{(i-1)}}}$ . Each feature map is processed by the subsequent $D_{i}$ and, following lateral convolution operations, yields multi-scale output results, with $D_{1}$ producing the final restored image. Subsequently, we will elaborate on the two key modules that constitute ACL and the model's optimization function. + +# 3.3. Linear Attention-based Mamba Module + +The original Mamba model is an auto-regressive model capable of efficiently capturing sequence dependencies, and it has been proven effective in modeling temporal causal sequence data. However, due to its unidirectional modeling approach, Mamba exhibits limitations when handling data with weak causality, such as images, necessitating further improvements to address these challenges. To overcome + +the limitations of unidirectional modeling, recent methods have proposed multi-directional cross-scanning techniques for image processing. Unlike these approaches, we embed linear attention into the Mamba structure, enabling it to establish global pixel dependencies when processing image data, and avoiding the need for recursive computation of the forget matrix $\mathbf{A}_i$ . The module structure is illustrated in Fig. 2 (c). + +The input to the model is a feature map $\mathbf{F} \in \mathbb{R}^{B \times C \times H \times W}$ . First, $\mathbf{F}$ undergoes a dimensional transformation, resulting in $\mathbf{F}' \in \mathbb{R}^{B \times HW \times C}$ . Subsequently, $\mathbf{F}'$ is passed into two branches: a main branch and a residual branch. The operations of the residual branch can be expressed as follows: + +$$ +\mathbf {F} _ {r e s} = \sigma (\operatorname {L i n e a r} \left(\mathbf {F} ^ {\prime}\right)), \tag {6} +$$ + +where $\sigma (\cdot)$ represents the SiLU activation function. + +The main branch comprises a linear mapping layer, a convolutional layer, and linear attention. The process can be expressed as follows: + +$$ +\mathbf {F} _ {1} = \operatorname {T o 4 D} \left(\operatorname {L i n e a r} \left(\mathbf {F} ^ {\prime}\right)\right), \tag {7} +$$ + +$$ +\mathbf {F} _ {2} = \sigma \left(\operatorname {C o n v} \left(\mathbf {F} _ {1}\right)\right), \tag {8} +$$ + +where $\mathrm{To4D}(\cdot)$ indicates reshaping the feature map into a four-dimensional tensor to adapt convolution operation. Next, linear attention is applied to $\mathbf{F}_2$ . The specific process is expressed as follows: + +$$ +\mathbf {F} _ {2} ^ {\prime} = \operatorname {T o 3 D} \left(\mathbf {F} _ {2}\right), \tag {9} +$$ + +$$ +\mathbf {Q} = \phi \left(\operatorname {L i n e a r} \left(\mathbf {F} _ {2} ^ {\prime}\right)\right), \quad \mathbf {K} = \phi \left(\operatorname {L i n e a r} \left(\mathbf {F} _ {2} ^ {\prime}\right)\right), \tag {10} +$$ + +$$ +\mathbf {K} \mathbf {V} = \mathbf {K} ^ {\top} \cdot \mathbf {F} _ {2} ^ {\prime}, \tag {11} +$$ + +$$ +\mathbf {F} _ {\text {a t t e n}} = \mathbf {Q} \cdot \mathbf {K V}, \tag {12} +$$ + +$$ +\mathbf {F} _ {\text {a t t e n}} = \mathbf {F} _ {\text {a t t e n}} + \operatorname {C o n v} _ {\text {p o s}} (\mathbf {F} _ {2}), \tag {13} +$$ + +where $\mathrm{To3D}(\cdot)$ reshapes the feature map into a three-dimensional tensor for linear attention layer, $\phi (\cdot)$ is the kernel function, and $\mathrm{Conv}_{pos}(\cdot)$ is learnable position embedding function. Subsequently, $\mathbf{F}_{atten}$ is multiplied by $\mathbf{F}_{res}$ , followed by a linear mapping layer, yielding $\mathbf{F}_{atten}$ , which is expressed as: + +$$ +\mathbf {F} _ {\text {e n h e n c e}} = \operatorname {L i n e a r} \left(\mathbf {F} _ {\text {a t t e n}} \times \mathbf {F} _ {\text {r e s}}\right). \tag {14} +$$ + +Finally, $\mathbf{F}_{\textit{enhence}}$ is processed through a simple feedforward neural network to produce the output of the LAMA. + +# 3.4. Multi-Dilated Convolutions Module + +The LAMA module primarily functions to establish global feature connections, necessitating the learning of local features to enhance the quality of detail restoration. While some previous methods employed feature window-based self-attention strategies and achieved certain advancements, they incurred substantial computational costs. Consequently, we adopted a more straightforward and effective approach, namely the multi-scale dilated convolution module, the structure of which is depicted in Fig. 2(d). This module is equipped with filtering operations using various dilation factors aimed at capturing local features of different granularities within the image to enhance the detail restoration effects. The module comprises two dilated convolutions along with skip connections. The input feature, denoted as $\mathbf{F}$ , is split into two pathways: one passes through a convolution layer with a kernel size of 5 and a dilation rate of 2, and the other through a convolution layer with a kernel size of 3 and a dilation rate of 2, resulting in two feature sets: + +$$ +\mathbf {F} _ {1} = \operatorname {C o n v} _ {5 \times 5, d = 2} (\mathbf {F}), \tag {15} +$$ + +$$ +\mathbf {F} _ {2} = \operatorname {C o n v} _ {3 \times 3, d = 2} (\mathbf {F}). \tag {16} +$$ + +These are then concatenated to form $\mathbf{F}'$ , which subsequently passes through a convolution layer with a kernel size of 1 to halve the channel count, aligning it with the dimensions of the input features. Furthermore, the input feature $\mathbf{F}$ is merged with $\mathbf{F}'$ via a skip connection, culminating in the output $\mathbf{F}_{out}$ . The expressions are as follows: + +$$ +\mathbf {F} _ {\text {o u t}} = \operatorname {C o n v} _ {1 \times 1} \left(\operatorname {C o n c a t} \left(\mathbf {F} _ {1}, \mathbf {F} _ {2}\right)\right) + \mathbf {F}. \tag {17} +$$ + +# 3.5. Optimization Objectives + +The ACL model, during its decoding phase, outputs restoration results at three distinct scales and computes the corresponding loss values. Following prior methodologies, we calculate the loss values concurrently in both the spatial and frequency domains. The traditional L1 loss function is employed to measure the discrepancy between the restored + +outputs and the pristine reference images. Consequently, the total loss is computed as follows: + +$$ +L _ {t o t a l} = \sum_ {i = 1} ^ {3} \frac {1}{N _ {i}} \left| \mathbf {P} _ {i} - \mathbf {I} _ {i} \right| + \lambda \cdot \sum_ {i = 1} ^ {3} \frac {1}{N _ {i}} | f f t (\mathbf {P} _ {i}) - f f t (\mathbf {I} _ {i}) | \tag {18} +$$ + +where $\mathbf{P}_i$ and $\mathbf{I}_i$ represent the restored result and the corresponding true image, respectively, and $N_i$ denotes the total number of pixels in the image. $fft(\cdot)$ signifies the fast Fourier transform function. The hyperparameter $\lambda$ , utilized to balance the contributions of spatial domain loss and frequency domain loss to the total loss, is set at 0.1, following previous methods. + +# 4. Experiments + +This section focuses on showcasing the effectiveness of our proposed ACL model in addressing various degraded image tasks, such as deraining and deblurring, evaluated across six test sets. We will outline the experimental procedures and datasets utilized, and confirm the impact of the proposed modules through a series of ablation studies. + +# 4.1. Implementation Setup + +For each type of degradation, datasets are trained and evaluated independently. Unless specifically mentioned, all tests are conducted with the same hyperparameters. The training set undergoes random cropping of $256 \times 256$ patches and random flipping as a data augmentation strategy. To compare computational complexity with other methods, FLOPs are tested at the mentioned crop size. A cosine annealing strategy is adopted to gradually adjust the learning rate each epoch, setting a minimum learning rate limit of 1e-6. The batch size is set to 8, and the Adam optimizer is adopted. Following the evaluation of previous methods, for deraining, the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are calculated on the YCbCr color mode. For other tasks, evaluation metrics are calculated on RGB color mode. All experiments are implemented in an environment equipped with the NVIDIA 24GB 3090 GPUs, based on the PyTorch. + +# 4.2. Single Image Deraining Results + +We utilized several different rain removal datasets, including Rain100L/H [40], Rain200L/H, and DID-Data [46], to evaluate the model's ability to restore images with streaklike degradation elements. Each dataset was independently trained for 800 epochs, with an initial learning rate set to 1e-3. We compared our approach with previous methods, including the advanced Restormer (Transformer) [44], NAFNet (CNN) [2], IRNeXt (CNN) [6], and MambaIR (Mamba) [13]. The comparative results are shown in Table 1 and Table 2. Upon comparison of PSNR, it can + +Table 1. Quantitative comparison results of the proposed model and seven other advanced models on the Rain100L and Rain100H. The larger the PSNR and SSIM values, the better the model effect. + +
MethodsRestormer [44]MAXIM [33]DRT [24]MPRNet [43]DAWN [19]IRNeXt [6]MambaIR [13]ACL(Ours)
DatasetPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Rain100L38.990.97838.060.97737.610.94837.840.95936.730.97138.240.97238.780.97739.180.983
Rain100H31.460.90430.810.90329.470.84630.410.87430.620.89631.640.90230.620.89332.220.920
Average35.230.94134.440.94033.540.89734.130.91733.680.93434.940.93734.700.93535.700.952
+ +Table 2. Quantitative comparison results of the proposed model with 13 other advanced models, including CNN and Transformer-based methods, on three datasets. + +
MethodsRain200LRain200HDID-DatasetAverage
PSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
RESCAN [21]33.820.95526.220.82232.600.92730.880.901
PreNet [29]37.120.97629.040.89033.370.91933.180.928
DRT [24]38.810.98328.670.88033.880.92833.790.930
CCN [28]38.260.98129.990.91432.130.92433.460.940
Restormer [44]40.580.98630.830.91433.190.92634.870.942
Uformer [38]40.200.98630.310.91134.360.93334.960.943
MPRNet [43]39.820.98629.940.90034.500.93734.750.941
SmartAssign [37]38.410.98127.710.85433.110.91533.080.917
SFNet [7]39.500.98229.750.90134.510.93834.590.940
NAFNet [2]39.480.98229.190.88834.690.93734.450.936
ELFformer [18]38.850.98028.930.88533.540.93633.770.934
ESDNet [31]39.850.98630.010.91334.520.93934.790.946
MSGNN [35]39.090.98729.630.91833.110.92733.940.944
ACL(Ours)40.740.98830.450.91634.810.93835.330.947
+ +![](images/37815c6aa058b9a6405ab77600645ab7d332da0c3b3d60c0e460aa9998dfc842.jpg) +Figure 3. Visual comparison of ACL and other recent SOTA models on rainy image removal. The first two scenes contain slight rain streak degradation, while the last two scenes contain severe rain streak degradation. + +Table 3. Quantitative results of our method compared to recent approaches in blurry image restoration. + +
MethodsGoPro
PSNR ↑SSIM ↑FLOPs(G) ↓Param(M) ↓
MIMO [4]32.680.95961716.1
DMPHN [47]31.200.940-21.7
DBGAN [49]31.100.94275911.6
MPRNet [43]32.660.95977720.1
Restormer [44]32.920.96114026.1
IRNeXt [6]33.160.96211413.21
Stripformer [32]33.080.96217020
SSAMAN [42]33.530.96516518.3
LoFormer [26]33.730.9664716.4
Ours33.250.964554.6
+ +![](images/7b1ad184733f9d1c1bdc3b844871a93fdd19a96b48c0b71c62d586b76608246b.jpg) +(a) Blur Region + +![](images/d8bb188f0206f44d352c3f2a8973a6ee5b55486f6590550ff554f846e0f9b565.jpg) +(b) Reference + +![](images/e08ef39dab8f576ee34504a74786659c508db7f5bbd9dbb360eed3ec41917282.jpg) +(c) DMPHN + +![](images/8ffbd4209bdf41e4b00615e6fc2da32be63acc10047ac432ed1a180a5b2b865e.jpg) +(e) IRNeXt +Figure 4. Visual results of ACL and four other advanced models on motion blurred image restoration. + +![](images/89f95e3017c67732be8fad5db1b74c8e4226d904de5a21aa699ac8ae56ee76db.jpg) +(f) Restormer + +![](images/65db8bcb34f6470354d3dfa31118106620092a3c69c4a6b9ad9508a49379462c.jpg) +(g) Ours + +be observed that our method outperforms the other compared methods, except for the powerful Transformer-based Restormer on the Rain200H. Additionally, Fig. 3 further illustrates the visual comparison results, where ACL demonstrates superior performance in restoring image details. + +# 4.3. Single Image Deblurring Results + +We conducted evaluations on motion blur image restoration using the GoPro dataset [27], which includes 2,103 training images and 1,111 testing images. The compared methods include the recently proposed 9 advanced methods. In Table 3, we present the comparative results of various metrics on this dataset. As shown, ACL achieves advanced performance while maintaining a low parameter count and low FLOPs. Additionally, Fig. 4 displays visual comparison results with other methods. We selected critical numerical information within the images, and it can be observed that ACL also exhibits good performance in restoring motion-blurred images. + +# 4.4. Ablation Studies + +To further understand the contributions of each module in the ACL model and other factors affecting model performance, we conducted a unified experiment on the + +Table 4. Comparison of ablation experiments between two modules on Rain100L. + +
SettingsPSNR ↑SSIM ↑
Baseline38.240.978
Baseline + LAMA38.890.981
Baseline + LAMA + MDC39.180.983
+ +Rain100L/H rain removal dataset. Specifically, we performed ablation studies on the two main modules of the model. Additionally, to verify that the linear attention capability can be restored using the Mamba structure, we conducted experiments by replacing LAMA with other structures to compare the results under different configurations. + +# 4.4.1. LAMA and MDC modules: + +To validate the roles of the two main modules in ACL, namely LAMA and MDC, as well as their respective importance, we conducted ablation experiments. We removed the MDC module and replaced the core encoder/decoder modules with the structure shown in Fig. 1(b), where the Transformer block in the baseline model is implemented based on Linear Attention. We then gradually replaced the encoder-decoder modules with LAMA and added the MDC module to the baseline model, resulting in two different configurations, which were trained and tested separately. The experimental results are shown in Table 4. By comparing the "Baseline" and "Baseline+LAMA" configurations, it is evident that the Mamba structure, implemented with linear attention, achieves better results, proving the potential of the Mamba structure to activate linear attention. Besides, adding the MDC further enhances the model's performance. + +# 4.4.2. Different Mechanisms for Core Modules: + +To validate the effectiveness of LAMA, we replaced the LA structure within LAMA with the original one-dimensional scanning SSM structure and the bidirectional scanning SSM structure for verification. Additionally, replacing LAMA with a standard LA structure resulted in a new configuration, referred to as the Baseline model. The results obtained from these various configurations are presented in Table 5. On one hand, the proposed method outperforms both the Baseline and the strategies employing unidirectional and multi-directional scanning for modeling. On the other hand, compared to the unidirectional Mamba model, the multi-directional scanning strategy demonstrates superior performance, indicating that unidirectional modeling is not optimal for image data. Furthermore, Fig. 5 provides visual examples corresponding to each configuration. It can be observed that while the SSM-based scanning methods are capable of removing rainy degradation elements, they result in significant loss of image details. In contrast, our method achieves superior visual outcomes. + +Table 5. Quantitative results of different mechanisms used in the core module on rainy streak removal. + +
SettingsRain100LRain100H
PSNRSSIMPSNRSSIM
Baseline38.240.97831.020.913
Mamba (w. 1D Scan)36.470.95929.720.887
Mamba (w. 2D Scan)38.070.97730.930.907
Ours39.180.98332.220.920
+ +![](images/c1962d22190b23d3ed72c9670333e8887485c1a4d67cadeceaf8cb51fb011c6d.jpg) +(a) Rainy Image + +![](images/fddcf20267e95036fb0977ecc48fb2158fc462def51c8fdfbe27a04bed83f37c.jpg) +(b) Ground Truth + +![](images/eab1499fe7a3b50ffb30b0b8d4b4e54ad984a41d25e252c2321f3a62c301ec7e.jpg) +(c) LA Block + +![](images/dd4adae9e59865b8b10aec2712fe7a09f10cb5b78fe0e4fefa7d18e0e8477e3a.jpg) +(d) 1D scan Mamba +Figure 5. Visual results of the encoder/decoder blocks adopting different mechanisms. + +![](images/37c0a6f77facfa54b45ca7c59e384fc385eb3a5dd5f8cfb631de832e997982b0.jpg) +(e) 2D scan Mamba + +![](images/16e07557232a2c55b7606977a7c8dd99488ea5d5dcdfdd2de206934c59680d5f.jpg) +(f) LA Mamba + +Table 6. Evaluation results of different $N_{i}$ configurations on the Rain100L dataset in ACL. $\star$ represents the combination we adopted. + +
(N1,N2,N3)PSNR↑SSIM↑
(3,3,3)38.950.978
(4,4,4)39.030.980
(6,3,3)★39.180.983
(6,6,6)39.190.983
+ +# 4.4.3. The Impact of the Number of Encoders/Decoders + +As mentioned in the above, a crucial hyper-parameter in the model is the number of feature processing blocks at each encoding/decoding stage, denoted as $N_{i}$ . To investigate the impact of $N_{i}$ , we conducted a series of experiments on the deraining dataset using different combinations, with the results presented in Table 6. Additionally, Fig. 6 illustrates the output images generated by the models with various configurations. The numerical results indicate that increasing $N_{i}$ contributes to performance improvement, but the effect is limited. Notably, a significant enhancement is observed when $N_{1}$ is increased, suggesting that learning high-resolution feature maps plays a critical role in improving the model's recovery performance. + +# 4.4.4. The Dilation Rate of Convolution in MDC Module + +We propose a local feature enhancement module, MDC, which includes two dilated convolution layers, as shown in + +![](images/1875a8b22794270df98e65352ba49d08c774fedf56a75a45dc43b159581210b1.jpg) +Input +Figure 6. Visual Results on Various $N_{i}$ + +![](images/839f75d4d7639e7277ccb9e8dafd60c2bfeeb00555847031c6ec9d169b31e7c7.jpg) +(4,4,4) + +![](images/5c3add7916c909abc38bbb4c408594f56e53af0c91358ce01a64077e95eb6f15.jpg) +(6,6,6) + +![](images/0dedf5c2df23be8be95ae911bbe953ce4845bb353d3404a5cbcdc3623e74c6e7.jpg) +(6,3,3) + +Table 7. The evaluation results of the MDC module's convolution operations with varying dilation rates on the Rain100L dataset. $\star$ represents the combination we adopted. + +
dilationPSNR↑SSIM↑
138.120.981
2★39.180.983
339.100.981
+ +Fig. 2 (d). We further investigate the impact of dilation rates on the module's performance. As shown in Table 7, the results indicate that compared to the non-dilated convolution setting $(d = 1)$ , the performance is inferior to the other two configurations. However, with increased dilation rates, performance improves to varying degrees, with the best overall performance observed at $d = 2$ . + +# 4.5. Conclusion and Limitations + +We introduced ACL, a novel image restoration model that addresses the limitations of traditional CNNs and Transformer-based approaches in handling global receptive fields and computational efficiency. By integrating linear attention into the Mamba structure, we developed the LAMA module, which enhances global feature dependencies with linear computational complexity. Additionally, the MDC module was designed to improve local detail restoration through multi-scale dilated convolutions. Our experiments confirmed that the ACL achieves promising performance in de-raining tasks, demonstrating its effectiveness in both quantitative metrics and visual quality. Furthermore, our work provides a new perspective on leveraging the Mamba structure in the IR domain. Nevertheless, our method also has some limitations. The ACL model does not have an advantage over CNN-based models when processing large-sized images. Moreover, in the image deblurring task, there is still a gap between ACL and SOTA Transformer models. In the future, the ACL model still has room for further optimization to adapt more IR tasks. + +# Acknowledgments + +This work was supported by the National Key R&D Program of China (No.2023YFB4502804), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No. U22B2051, No. 62302411), the Natural Science Foundation of Fujian Province of China (No.2021J06003), and China Postdoctoral Science Foundation (No. 2023M732948). + +# References + +[1] Hanting Chen, Yunhe Wang, Tianyu Guo, Chang Xu, Yiping Deng, Zhenhua Liu, Siwei Ma, Chunjing Xu, Chao Xu, and Wen Gao. Pre-trained image processing transformer. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 12299-12310, 2021. 3 +[2] Liangyu Chen, Xiaojie Chu, Xiangyu Zhang, and Jian Sun. Simple baselines for image restoration. In European conference on computer vision, pages 17-33. 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Comparison of SUPIR [91], DreamClear [3], and our proposed method. Our training dataset is constructed entirely from synthetic images. Trained with such data, our method achieves the most realistic restoration results with the lowest training cost. + +# Abstract + +Recently, pre-trained text-to-image (T2I) models have been extensively adopted for real-world image restoration because of their powerful generative prior. However, controlling these large models for image restoration usually requires a large number of high-quality images and immense computational resources for training, which is costly and not privacy-friendly. In this paper, we find that the well-trained large T2I model (i.e., Flux) is able to produce a variety of high-quality images aligned with real-world distributions, offering an unlimited supply of training samples to mitigate the above issue. Specifically, we proposed a training data construction pipeline for image restoration, namely FluxGen, which includes unconditional image generation, image selection, and degraded image simulation. A novel light-weighted adapter (FluxIR) with squeeze-and + +excitation layers is also carefully designed to control the large Diffusion Transformer (DiT)-based T2I model so that reasonable details can be restored. Experiments demonstrate that our proposed method enables the Flux model to adapt effectively to real-world image restoration tasks, achieving superior scores and visual quality on both synthetic and real-world degradation datasets - at only about $8.5\%$ of the training cost compared to current approaches. + +# 1. Introduction + +In real-world scenarios, images often suffer from diverse and unpredictable degradations during capture, storage and transmission, giving rise to a wide range of image restoration (IR) tasks, e.g., deblurring [12, 34, 54, 59, 67, 80, 98], denoising [7, 77, 96, 97], super-resolution [10, 17, 29, 37], and etc., for restoring the original high-quality images based on the type of degradation. These methods, however, struggle + +gle to maintain generalizability under complex real-world degradation due to the limited model capacity and constrained training data. To alleviate this problem, many researchers have developed methods [44, 73, 83, 91] based on pre-trained text-to-image (T2I) models [18, 50, 51, 60]. Trained on vast collections of real image-text pairs, these T2I models encapsulate extensive prior knowledge, enabling them to enrich low-quality images of any type with realistic details. However, an immense dataset and extensive training period are required to prevent alterations of image content and the generation of inaccurate details. + +Early generative-based IR methods [44, 47, 52, 53, 65, 66, 73, 83, 103] are typically built upon the Stable-Diffusion model, combining several publicly available datasets such as DIV2K [2], Flickr2K [42], LSDIR [39] and DIV8K [24] to create a diverse training set. As generative models have scaled up, the following work [91] increased the scale of training data by collecting more high-quality, high-resolution images. Nevertheless, acquiring large amounts of data remains challenging: manual data collection incurs high costs, while web scraping poses potential copyright and privacy risks. Furthermore, the resulting datasets remain limited in scope. The recent work [3] approaches these challenges by incorporating one million generated high-quality images. However, the utilization of the sophisticated multimodal large language model (i.e., Gemini-1.5-Pro [68]) and the necessity for finetuning the T2I model result in a less efficient data curation process. In this paper, we propose FluxGen, a streamlined and highly efficient data generation pipeline that operates without the involvement of LLMs. Specifically, we find Flux [36] can generate highly realistic and diverse images directly from random noise. We also incorporate no-reference image quality assessments (IQA) methods [31, 72, 88] for image filtering, along with advanced degradation techniques [75, 99] for constructing training image pairs. + +Typically, for generative-based IR methods [44, 73, 83], large-scale trainable adapters are needed to control T2I models external control signals. These adapters are usually replications of the U-Net [61] encoder from the T2I model or the full model, resulting in substantial training time and GPU resource demands. Moreover, with the continued growth in the parameter size of T2I models, recent efforts have concentrated on scaling up adapters to more effectively control these increasingly powerful models. For example, SUPIR [91] employs a 1.3B adapter for 3.5B SDXL [51], while DreamClear [3] introduces 2.2B adapter for 0.6B PixArt- $\alpha$ [9]. In this work, we carefully design a light-weighted ControlNet-like adapter FluxIR with only 0.4B trainable parameters to adapt the powerful 12B pretrained Flux [36] model to the IR task. The adapter consists of an MM-DIT [18] block and multiple squeeze-and-excitation (SE) layers, where the former extracts control + +signal features and the latter modulates the denoising process efficiently using these features. As illustrated in Fig. 1, our proposed method reduces training costs1 by approximately $93.5\%$ and $91.5\%$ compared to SUPIR [91] and DreamClear [3], respectively, while also achieving the best image restoration quality. The main contributions of this paper are summarized as follows: + +- We are the first to confirm that the Flux model exhibits the remarkable capacity to generate highly lifelike images for the curation of IR datasets. Our proposed FluxGen can automatically generate an unlimited number of training samples in a simple and effective manner. +- We design FluxIR, a light-weighted adapter equipped with a few squeeze-and-excitation layers, that can effectively manipulate the super-large T2I model like Flux to restore reasonable details for degraded images within 14 GPU-days. +- Extensive experiments demonstrate that our method achieves optimal performance in handling real-world degraded images and producing the most realistic and satisfactory results. + +# 2. Related Work + +Image Restoration. Image restoration aims to reconstruct clear, detailed images from degraded ones under various types of degradation. Early approaches often assumed specific degradation processes [14, 16, 26, 29, 37, 62, 101] or incorporated degradation prediction directly into the model [20, 49, 71, 74, 79, 95]. However, these methods struggle to generalize to real-world scenarios. Recent studies have advanced image restoration by building complex real-world degradation processes [75, 99]. These approaches simulate real-world degradation through varied random combinations of factors like noise, blur, JPEG compression, etc. These simulations have driven notable improvements in restoration performance, boosting image quality substantially [6, 40, 41, 75, 99]. Building on the successes of text-to-image diffusion models [18, 36, 51, 60], several studies [8, 11, 13, 19, 23, 30, 38, 70, 73, 82, 83, 86, 89, 91] have leveraged the generative prior from pre-trained T2I models to restore images with significantly enhanced quality and high-frequency details. In this work, we take a further step by leveraging the generative prior from the advanced pre-trained T2I diffusion model, Flux, and introduce a novel MM-DiT-based adapter to recover missing details and enhance the aesthetic quality of the input images. + +Large Text-to-Image Diffusion Model. Diffusion Model [15, 27, 63, 64] have achieved superior performance on image synthesis. Stable Diffusion (SD) [60] is one of the most famous models, which compresses images into + +the latent space using a high-fidelity high-compression ratio VAE [35]. Later, Diffusion transformer (DiT) [50] proposed replacing the traditional U-Net framework [61] with a transformer, aiming to improve scalability when trained on large datasets. As a result, SD3 [18], which adopts the multimodal diffusion transformer-based (MM-DiT) framework, has demonstrated outstanding performance in both text-to-image generation and visual quality. More recently, Flux [36] extended the MM-DiT [18] architecture and used a 16-channel VAE to scale the T2I diffusion model to 12B parameters. By integrating the T5 [56] text encoder, Flux achieved top performance in text-image alignment, visual quality, and aesthetic quality. In this paper, we leverage the generative prior of Flux to build a high-quality IR training dataset and restore the details of degraded images. + +Data Distillation. Scaling up datasets has proven essential for improving the performance of large-scale models across various fields, including natural language processing (NLP) [1, 69], text-to-image [18, 36, 51, 60], image restoration [91], and etc. However, collecting such large-scale real-world data is prohibitively expensive. As a result, researchers are increasingly turning to generated data, distilling datasets from generative models to make dataset expansion more efficient and cost-effective. For instance, BOOT [22] and DKDM [85] utilize synthetic data generated from pretrained models to optimize the diffusion models. GSDD [94] employs GAN inversion techniques [84] to learn a GAN distribution and generate images for the image super-resolution task. Recently, 800K training samples generated by DeepSeek-R1 [25] have been used to enhance the reasoning capabilities of small dense models like Qwen [87] and Llama[21]. Closest to our work, DreamClear [3] fine-tunes a text-to-image diffusion model to generate high-quality data with designed prompts. However, both [94] and [3] still require external data for either tuning or inversion, which is time-consuming and raises privacy concerns. To address this, we propose a novel data generation pipeline that distills a high-quality IR training dataset directly from pre-trained text-to-image models, without the need for external data and additional training. + +# 3. Method + +In Sec. 3.1, we introduce FluxGen, a pipeline for generating high-quality, realistic training images using Flux. Then, in Sec. 3.2, we present FluxIR, a ControlNet-like adapter that enables precise control over Flux for image restoration. Finally, Sec. 3.3 details efficient training strategies, including a novel timestep sampler and pixel-space loss functions. + +# 3.1. FluxGen + +Image generation. Both the quality and volume of training images are critical for neural network performance in image restoration tasks. Existing works [58, 91, 102] choose to + +![](images/9a58610b4a1ff82262658006f89a2f1555e316a767fbd97e90361c8d0863901d.jpg) +Figure 2. An overview of our FluxGen pipeline. First, an empty prompt and random Gaussian noise $z_{1}$ are input into Flux, generating an image latent $z_{0}$ over $T$ steps. A VAE decoder then maps $z_{0}$ to its corresponding image $x_{0}$ . High-quality images are curated by IQA-based selection, followed by image degradation to construct the final paired dataset. + +collect millions of images to build their training data. However, constructing such large datasets introduces four significant challenges: 1) The data collection process is labor-intensive, requiring extensive human effort for preprocessing; 2) The use of this data raises privacy and copyright concerns; 3) Commercially purchased datasets are prohibitively expensive, limiting access for many research institutions; 4) Handling large volumes of high-resolution images is difficult due to high bandwidth and storage requirements. + +Recently, Flux has effectively leveraged the scalable MM-DiT [18] alongside a 16-channel VAE to achieve leading performance in generating high-quality, high-resolution images. These images display realistic high-frequency texture details that far surpass those produced by other T2I models. In our proposed method, we utilize Flux for the first time to generate a large volume of high-quality training images at a low cost. Unlike [58, 91, 102], acquiring high-quality and realistic images from Flux is labor-free, copyright-compliant, cost-effective, and easy to implement. + +As shown in Fig. 2, we input an empty prompt into Flux and manipulate the initial random noise to generate millions of images using the capabilities of the pre-trained Flux model. Here we take advantage of the random text prompt-dropping design in diffusion-based text-to-image (T2I) models [18, 57, 60] which allows T2I models to produce a diverse range of realistic images from their generative prior without the designed prompt. Notably, we can also leverage large language models (LLMs) like GPT-4 [1] and LLaMA [69] to craft tailored text prompts for FluxGen. The corresponding generated images can be used to train image restoration models focused on specific objects (e.g., + +![](images/5017c6ee8f18bc9e0a017f59572d64ff6b3e4776405796ea8bd7970cccb62489.jpg) +Figure 3. Training and inference pipeline of the proposed FluxIR. FluxIR employs a single MM-DiT block with learnable T5 embedding $\theta_{p}$ and CLIP embedding $\theta_{y}$ to extract image feature $f_{z}$ and text feature $f_{p}$ from the low-quality control latent $z_{lq}$ . The squeeze-and-excitation (SE) layers $(\mathrm{SE}_z(\cdot)$ for image and $\mathrm{SE}_p(\cdot)$ for text) broadcast these features to all Flux MM-DiT blocks to enable precise and multi-modality control. + +animals, plants, and the moon) or particular domains (e.g., nighttime scenes and aerial photography). + +Image Selection. Although Flux is a powerful text-to-image model, the stability of the images it generates is not guaranteed. Low-quality images can significantly affect the training of image restoration models. To address this, we distill the dataset using various non-reference image quality assessment (IQA) models, including CLIP-IQA [72], MANIQA [88], and MUSIQ [31]. Specifically, we select images with CLIP-IQA, MANIQA, and MUSIQ scores within the top $95\%$ as our training set. This process ensures that low-quality and failed generated images are removed from the training dataset, thus significantly enhancing our image restoration performance. + +Pair-data Construction. The degradation of ground truth images has been widely studied in [75, 99], with common degradation types including blur, downsampling, noise, JPEG compression and etc. In this paper, we apply the synthetic degradation method [75] with the same settings as [83] to construct paired data for training. + +# 3.2. FluxIR Architecture + +A typical solution for the T2I-based image restoration is training a ControlNet [100] upon a T2I model, with a VAE encoder to project the input image into latent space. The ControlNet is initialized as a copy of the U-Net encoder, + +with zero convolution layers acting as bridges to integrate conditional controls. Then the extracted multi-level features are injected into corresponding layers of the U-Net decoder. Recently, DreamClear [3] introduced a DiT-based ControlNet model by duplicating all 28 DiT blocks from PixArt $\alpha$ [9]. With 2.2B trainable parameters in ControlNet, it requires 224 GPU days for training, which is surprisingly time-consuming. To solve this issue, we carefully design a training-friendly 0.4B adapter, integrated with Flux — a much larger MM-DiT-based text-to-image model with approximately 12B parameters. + +The detailed FluxIR architecture is illustrated in Fig. 3. To extract control signal from VAE embedding feature $z_{lq}$ , only one MM-DiT block is involved in our FluxIR adapter for lightweight purposes. The MM-DiT block, denoted as $\mathcal{D}(z,p,y,t;\Theta_d)$ , is initialized from the first MM-DiT block of the pre-trained Flux model, and its input can be reformulated as + +$$ +z _ {c} = z _ {t} + \mathcal {M} _ {i} \left(z _ {l q}; \Theta_ {i}\right), \tag {1} +$$ + +where $\mathcal{M}_i(\cdot;\Theta_i)$ is a multi-layer perceptron (MLP) with parameters $\Theta_i$ initialized to zero and $z_t = (1 - t)z_0 + tz_1$ represents the linear combination of the noise latent $z_1$ and the ground truth latent $z_0$ at timestep $t$ . To bridge the gap between the adapter and original T2I model, we employ a learnable T5 [56] embedding $\theta_p$ and a learnable CLIP [55] + +embedding $\theta_{y}$ and adjust the T5 embedding $p$ as $p_c = p + \theta_p$ and the CLIP embedding $y$ as $y_{c} = y + \theta_{y}$ . Finally, the MM-DiT block with parameters $\Theta_d$ outputs an image feature $f_{z}$ and a text feature $f_{p}$ as follows: + +$$ +f _ {z}, f _ {p} = \mathcal {D} \left(z _ {c}, p _ {c}, y _ {c}, t; \Theta_ {d}\right). \tag {2} +$$ + +Since Flux consists of 57 MM-DiT blocks, duplicating conditional features from a single MM-DiT adapter is insufficient to control the entire T2I model. We introduce a set of squeeze-and-excitation (SE) layers to broadcast control signals to all 57 MM-DiT blocks. Each SE layer selectively emphasizes informative features and suppresses less useful ones, enabling targeted control of its corresponding MM-DiT block. The SE layer comprises a squeeze MLP layer and an excitation MLP layer, formulated as follows: + +$$ +\operatorname {S E} (x) = \mathbf {W} _ {e} \left(\mathbf {W} _ {s} x + \mathbf {B} _ {s}\right) + \mathbf {B} _ {e}, \tag {3} +$$ + +where $\mathbf{W}_s\in \mathbb{R}^{r\times c}$ and $\mathbf{B}_s\in \mathbb{R}^r$ is the weight and bias of squeeze MLP layers with input channel of $c$ and rank of $r$ , while the weight $\mathbf{W}_e\in \mathbb{R}^{c\times r}$ and bias $\mathbf{B}_e\in \mathbb{R}^c$ of excitation layer are initialized to zero values. Unlike existing works [3, 44, 73, 91] that control only the image branch, we implement multi-modality controls on both the image and text information. The control signals of the $i$ -th SE layer, corresponding to the $i$ -th Flux MM-DiT block, can be computed as + +$$ +z _ {c} ^ {i} = \operatorname {S E} _ {z} ^ {i} (f _ {z}), p _ {c} ^ {i} = \operatorname {S E} _ {p} ^ {i} (f _ {p}). \tag {4} +$$ + +Compared with a full-rank MLP, our proposed SE layer is extremely lightweight with only approximately $2\%$ of the parameters. Our SE layer shares the same name as SE block in [28], but differs in both motivation and implementation. [28] squeezes spatial features to extract channel-level attention for recalibrating the original feature, while our SE layers reduce the channel dimension and distill the essential features for targeted control. + +# 3.3. Efficient Training Strategy + +Timestep Sampling. The timestep sampling strategy can improve the training process for diffusion model [90]. Stable Diffusion 3 [18] proposes a logit-normal sampling strategy to emphasize training velocity when $t$ is in the middle of $[0,1]$ . However, directly employing a logit-normal sampling strategy for IR model training is inappropriate. The starting point of the inference process is pure Gaussian noise at $t = 1$ , which is seldom sampled during training [43]. This leads to ineffective IR control at $t = 1$ , negatively affecting subsequent iterations. Therefore, we rewrite the timestep sampling function to ensure accurate control at + +the starting point. The sampling function is defined as follows: + +$$ +t = f (u) = \left\{ \begin{array}{l l} 0 & \text {i f} u < 0 \\ 1 & \text {i f} u > 1 \\ u & \text {o t h e r w i s e ,} \end{array} \right. \tag {5} +$$ + +$$ +u \sim \mathcal {U} (- \epsilon , 1 + \epsilon), \tag {6} +$$ + +where the hyper-parameter $\epsilon$ set to 0.05 in our experiments. Here we first sample the temporary timestep $u$ from a uniform distribution within the range of $(- \epsilon, 1 + \epsilon)$ . And then we clamp $u$ to the range [0, 1], resulting in a probability of $\frac{\epsilon}{1 + 2\epsilon}$ for sampling the values 0 and 1, respectively. + +Optimization Strategy. The typical rectified flow model [4, 45, 46] is trained to predict the velocity field $v_{p}$ , and the Mean Squared Error (MSE) loss is employed for supervising the error between predicted velocity field $v_{p}$ and ground truth velocity field $v_{gt}$ as + +$$ +v _ {g t} = z _ {1} - z _ {0}, \tag {7} +$$ + +$$ +\mathcal {L} _ {\mathrm {M S E}} = \left\| v _ {p} - v _ {g t} \right\| _ {2} ^ {2}. \tag {8} +$$ + +However, this loss function in latent space inevitably ignores the high-frequency information of image [93], which is crucial for image restoration tasks. Following [32, 33, 81, 89, 93], we incorporate a pixel-space loss function to supervise the error between the decoded latent $\hat{z}_t = z_0 + t \cdot v_p$ and the decoded ground truth latent $z_t = z_0 + t \cdot v_{gt}$ after applying the VAE decoder $\mathcal{V}_d$ into pixel space: + +$$ +\mathcal {L} _ {P} = \left\| \mathcal {V} _ {d} \left(z _ {0} + t \cdot v _ {p}\right) - \mathcal {V} _ {d} \left(z _ {0} + t \cdot v _ {g t}\right) \right\| _ {1}. \tag {9} +$$ + +The final loss function of FluxIR is defined as: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {M S E}} + \alpha \mathcal {L} _ {P}, \tag {10} +$$ + +where $\alpha$ is set to 1 in our experiment setting. + +# 4. Experiments + +# 4.1. Experimental Settings + +Test Datasets. Following [3, 44, 73, 83, 91], we evaluate our method on both synthetic and real-world datasets. For the synthetic one, we randomly crop 600 images from the validation dataset of DIV2K with size of $1024 \times 1024$ and degrade them using the same settings as training, named DIV2K-Val. For real-world datasets, we utilize the most commonly used RealSR [5] and DrealSR [78] datasets, center-cropping HQ images to $1024 \times 1024$ and LQ images to $256 \times 256$ . Additionally, we include RealLQ250 from [3, 83, 91], a dataset of 250 LQ images at $256 \times 256$ resolution without corresponding HQ images. + +Implementation Details. In the FluxGen pipeline, we generate images at a resolution of $1024 \times 768$ , using the + +Table 1. Quantitative comparison against state-of-the-art methods of image restoration on both synthetic and real-world datasets. The best and the second best performance for each metric are highlighted in red and blue, respectively. + +
DatasetsMetricsMethods
BSRGANReal-ESRGANSwinIRDASRStableSRDiffBIRResShiftSinSRSeeSRSUPIRDream-ClearOurs
DIV2K-ValCLIPQA ↑0.47410.46950.45130.39480.40850.56400.42400.49150.59090.52850.49610.5934
MUSIQ ↑63.622363.829263.685459.451555.999569.099660.490764.417170.816868.814367.150669.6956
MANIQA ↑0.47170.51970.52110.43160.49610.59780.49500.50590.59090.60430.59410.6331
PSNR ↑21.611821.507721.065321.508220.041621.392521.490620.788421.292320.169619.760519.3811
SSIM ↑0.57420.58210.57620.56740.53180.52970.55570.50150.56030.51450.49630.4574
LPIPS ↓0.33660.30450.31150.33200.34590.31720.30860.34430.27990.31840.28950.3888
RealSRCLIPQA ↑0.43780.41970.40200.31530.43180.53100.38740.44450.55130.45940.50940.5413
MUSIQ ↑63.425660.952658.602945.780058.833965.592454.440159.475869.011863.951064.177967.4536
MANIQA ↑0.50590.52770.47650.38750.54690.58880.46880.52320.61150.59030.59970.6334
PSNR ↑24.635424.177324.418425.095420.441323.974824.192524.241724.167622.388722.033020.7176
SSIM ↑0.74840.74820.75660.75690.63200.67660.68920.66370.69670.64500.64420.5269
LPIPS ↓0.21090.20820.20490.24950.23050.24840.24400.26010.21050.26740.25470.3672
DrealSRCLIPQA ↑0.42190.39220.38780.31650.42060.48890.40600.41880.52950.45440.40460.5136
MUSIQ ↑61.225558.381957.330846.486656.319562.086153.929358.307767.241564.750856.599966.6202
MANIQA ↑0.48230.49110.47100.38280.52240.55660.46110.48300.59280.57640.54230.6024
PSNR ↑24.048024.143623.887825.182121.935423.991222.915823.473724.169922.602322.803721.3549
SSIM ↑0.72680.73900.72900.76890.66160.63640.63300.61900.71470.64060.61860.5675
LPIPS ↓0.22570.22260.21750.24740.23570.31230.32630.35440.23960.30690.29050.4310
RealLQ250CLIPQA ↑0.47010.43590.44000.34860.40090.53770.41650.48100.55690.48080.48760.5639
MUSIQ ↑63.520662.516163.372453.023856.712167.532659.505663.864470.376865.780466.510270.7770
MANIQA ↑0.50070.52390.53350.44140.51440.58770.50050.51600.59270.58290.58530.6314
+ +![](images/e91c0c60f0002f47a7743da7fb1861552fd0ad6329355e0dcfd4af2968cc77f4.jpg) +GT + +![](images/dc66b40808cb9d6589515bb288d35fc9af3c97417d8d2fe8304753f3701193be.jpg) +LQ Input + +![](images/e85edac187f2f3f897045ef8e4a220e9b5cd205efd347c42beb0ec1b351d8039.jpg) +Real-ESRGAN + +![](images/25424b9e514e982a3957dc71681683097dcb51b304a2e967c4e818c6c9264cc8.jpg) +SeeSR + +![](images/82ab28f439ac480e2e8625fd99a8265a2908b9c6e85f9cb0988076403daa10d4.jpg) +SUPIR + +![](images/63a9a9a858bb91c181655257a97f22df09a58576b58fd9dc2d5700dc6644010d.jpg) +DreamClear +Figure 4. Qualitative comparison on the synthetic dataset DIV2K-Val. + +![](images/e3d1a39bfcfb393d041ecc16aaa55017c08740e9ea2e71bdc3f41c4a920a35c3.jpg) +FluxIR (Ours) + +guidance scale of 4 and timesteps of 20. In all experiments, we exclusively use 350,000 images generated by FluxGen, with no external data involved. We randomly center-crop the images to the sizes of $1024 \times 768$ , $768 \times 768$ , and $512 \times 768$ to accommodate different aspect ratios. We train our FluxIR model using the AdamW [48] optimizer with a learning rate of $1 \times 10^{-5}$ . The training process takes about 3.5 days on 4 NVIDIA H800 GPUs with a batch size of 64. For inference, we adopt 20 sampling steps to generate our IR results across all of our experiments. + +Metrics. Following [91], we use PSNR, SSIM, and LPIPS as full-reference metrics and MANIQA, CLIPIQA, + +and MUSIQ as non-reference metrics² for comprehensive evaluation. Our method, like other generative IR approaches [3, 44, 73, 83, 91], achieves strong results in non-reference metrics but performs less competitively on full-reference metrics. + +# 4.2. Comparison with Existing Methods + +We conduct both quantitative and qualitative comparisons of our FluxIR with state-of-the-art image restoration methods, including early approaches (BSRGAN [99], + +![](images/656b5dc19258d4b5a8d5821f4e69fb80e2ffc71505958222dd773e5db5fc8cef.jpg) +FluxIR (Ours) + +![](images/aa2c9bf2977db8a298f74b6a95cf4a9026d2fe06ccd81eb32542dd71d738c5c9.jpg) +LQ Input + +![](images/d13ea5a024c22f50419274291bf40790e73d4165feb03486a9359fbb591837b6.jpg) +Real-ESRGAN + +![](images/c847d7ffc4e97c8a5f70b36bd75f0c033838af8bf7efe9799ec6b93934bd3100.jpg) +SeeSR + +![](images/05207cff59727f1b8638ed0b4b29de2fefa88f03246ede9db5a1748aae3194e7.jpg) +FluxIR (Ours) + +![](images/1b6eec2b1018de341ef6f572f5673d936d9d1443bc5962da93b5910811fddb7c.jpg) +SUPIR + +![](images/ef22b8e9b0158e556ef0c2bd49af9891e830f5cf03fa4a4ab1d7d41dbd4f3013.jpg) +DreamClear + +![](images/f801bbddce68f6a6dd1143a7eb3984baac4a50d41856c9982e8da0a2fd6d90fe.jpg) +FluxIR (Ours) + +![](images/3f4ea7fe2d06661b701a87971e6823ae133b65b571df03edd30809e1dda23245.jpg) +LQ Input + +![](images/04ff94e6757cb76d10a44ca10ed053e98f935df1872cbecb2118622b79db2543.jpg) +Real-ESRGAN + +![](images/855766157b00c8898d88ad62f6b03921d804fb58bb2c1a6919909abd46d366be.jpg) +SeeSR + +![](images/8aa91850ce7004f055647765579e851f159b43369e1faacc9eb3bc89f7c71e55.jpg) +SUPIR + +![](images/6d3f0dea3a82cfdec205be9f055c010fb7c564be0d46c70927c36ce58c39822f.jpg) +DreamClear + +![](images/963c6715d54f0af3e0eea61ab498728cc0b04eb8ded797cbb1e13dea9abe8fa0.jpg) +FluxIR (Ours) +Figure 5. Qualitative comparison on the real-world dataset RealLQ250. + +RealESRGAN[75], SwinIR [40] and DASR[41]) and recent generative IR models (StableSR [73], DiffBIR [44], ResShift [92], SinSR [76], SeeSR [83], SUPIR [91], DreamClear [3]). + +Quantitative Comparisons. Tab. 1 shows the quantitative comparisons with the existing SOTAs on the four datasets. Our FluxIR model achieves the best score in MANIQA with a significant margin across all synthetic and real-world datasets. On the RealLQ250 dataset, our method significantly outperforms other methods across all non-reference metrics, while MANIQA even surpasses the second-best method by over $6.53\%$ . On the other three synthetic and real-world datasets, our approach achieves the best or second-best scores in all non-reference metrics (CILPIQA, MUSIQ, and MANIQA). It is worth mentioning that our proposed method trained within 14 GPU-days significantly reduces training costs by approximately $93.5\%$ and $91.5\%$ compared to SUPIR [91] and DreamClear [3], respectively. + +Qualitative Comparisons. We present a qualitative comparison on the synthetic dataset DIV2K-Val in Fig. 4. Our method demonstrates a notable advantage in generating high-frequency details, such as lip texture, hair, eyelashes, and pupils in portrait images. In contrast, SUPIR [91] and + +DreamClear [3] fail to accurately reproduce human skin textures, and SeeSR [83] produces overly smooth results, lacking the natural skin texture and fine details. For the real-world dataset RealLQ250, we provide a qualitative comparison in Fig. 5. In the first row, which shows restoration results for a low-quality image of a cat, our method effectively reconstructs realistic high-frequency details such as fur, whiskers, and eyes. SeeSR [83] restores some fur and whiskers but lacks overall realism, while other methods fail to produce a high-quality, realistic result. In the second row, focusing on text recovery, our method achieves the most accurate text reconstruction, whereas other methods introduce various text distortions. Specifically, SUPIR [91] produces blurry results, and SeeSR [83] mistakenly recovers incorrect text content. + +# 4.3. Ablation Study + +Effectiveness of SE layer. We evaluate the impact of different ranks of our SE layer by setting $r$ to 16, 32, 64, and 128, respectively. Another variant is replacing the SE layer with a single MLP, i.e., a full rank setting. As shown in Tab. 2, the SE layer with $r = 32$ achieves the best performance on CLIPIQA, MANIQA, and CLIPIQA. Compared to using full-rank MLPs, the SE layer with low-rank results in a comparable performance while saving over $72\%$ of + +Table 2. Ablation results of various SE layer ranks on the RealLQ250 dataset. The number of parameters in FluxIR without the SE layers is 387M. + +
RankCLIPIQA ↑MUSIQ ↑MANIQA ↑# Params
160.538969.720.6222387M + 11.6M
320.563970.780.6314387M + 22.8M
640.552970.370.6306387M + 45.2M
1280.560670.540.6292387M + 90.0M
Full0.572070.790.6324387M + 1076.2M
+ +![](images/14f1b9731f9f7231dc6cd79e5c0cfd8e6444ec11cdc1663b8f68e1e3adfc3e18.jpg) + +![](images/9e9312527ca8942fa584af20d13a1f8ea5b9931d8906699e609a5a81d55a1591.jpg) +LQ Input +Figure 6. The visual comparison results of our training strategies: timestep sampling function $f(u)$ and $\mathcal{L}_P$ loss. Please zoom in for a better view. + +![](images/1a6de7ca834b3f88d3f7af3d8a872e2828731d2e784e8fff4cf1ab243d9c9702.jpg) + +![](images/feec70cf80a59dc8d4055999310ca366b2cbdbde4d8acc30a1700f627d848dd7.jpg) +w/o $\mathcal{L}_P^+ \mathrm{w} / \mathrm{o} f(u)$ + +![](images/b064908a3ecf398ccafd1ed4e2105eae0ab903dc24773c29d0841a1ed8375700.jpg) + +![](images/bfaf1a549d16adcf74b094ceb2b1b1faf130f73fe6f2f2c80e20f1d4f4000f41.jpg) +w/o $\mathcal{L}_P$ + +![](images/defc1fcf84d46e5aa4a48c1497395ad6165210b4f6a8fb4a63c7447dcaa07207.jpg) +Figure 7. The visual comparisons of different FluxGen settings, where we study different T2I models, i.e. SDXL and Flux, and the usage of IQA selections. Please zoom in for a better view. + +![](images/d9cdba6bb3357300694135b91b2dd6836b921255080301de6a72cf011cb884c9.jpg) +Full Setting + +the parameters. This demonstrates the effectiveness of our designed light-weighted SE layers in controlling the Flux model. By utilizing our SE layers with a rank of 32, we can outperform other state-of-the-art (SOTA) methods using only 0.4B adapter parameters, which is only $30.8\%$ and $18.6\%$ the size of SUPIR and DreamClear, respectively. + +Effectiveness of Training Strategies. We conduct ablation studies to evaluate our proposed training strategies: timestep sampling function $f(u)$ and $\mathcal{L}_P$ loss. Firstly, we use the logit-normal sampling strategy [18] to train our model without $\mathcal{L}_P$ loss as a baseline. Then we include our proposed timestep sampling function $f(u)$ as the second setting. We compare these two experiments with our full training strategies in the Tab. 3, which clearly demonstrates the significant performance improvement of the new sampling function and $\mathcal{L}_P$ loss. Fig. 6 illustrates that the logit-normal sampling produces low-quality content, while our proposed sampling function $f(u)$ effectively addresses this issue by bridging the gap between training and inference. Additionally, applying the pixel-space loss $\mathcal{L}_P$ allows for the restoration of more high-frequency details. + +Table 3. Ablation comparison results of our training strategies on the RealLQ250 dataset. + +
StrategyCLIPIQA ↑MUSIQ ↑MANIQA ↑
w/o LP and w/o f(u)0.441662.180.5720
w/o LP0.508268.530.6128
Full Setting0.563970.780.6314
+ +![](images/f3c78f01e1038957ce8475a9589991650931a87d342ae32d9169fa538feb82b4.jpg) + +![](images/834e68659f2ddfd04dee1f05f10f398410ecb4098c4bab7823dfb673631ab178.jpg) +LQ Input + +![](images/5e6f4f33f7276d691ace286a7c37344d3d9265b8e2339e5182041d1f5da33c40.jpg) + +![](images/e2a8f3610cb20b7019898dccf2610c033ab62debff35886adcd18dd5132dea85.jpg) +SDXL w/ IQA + +![](images/48b1ef7a5733a9ebaddb319778bd02259eceb28da00ca25cd75a521095da3928.jpg) + +![](images/5da2690f0811ff5a24a3957b8aab5e4c89f997ccc0fcea2dedea7a0e0abed05c.jpg) +Flux w/o IQA + +![](images/e6f1bceac396be5cdbf569801022169625cb6c7174788366ba1d5a8866ef2078.jpg) + +![](images/8224f9e431e47b0e213eb05a542c1e5ee6c02ff46c31dc0c27abe18b7110826f.jpg) +Flux w/ IQA + +Effectiveness of FluxGen. We follow the same settings of our FluxGen pipeline but replace the T2I model from Flux with SDXL to generate 10,000 images. Additionally, we remove the IQA-based selection from the FluxGen pipeline. The results in Tab. 4 demonstrate that a high-quality image dataset from the Flux model, combined with IQA selection, leads to high-quality IR results. Fig. 7 shows that the visual results based on the SDXL dataset are abysmal, exhibiting a smearing and distortion effect. In contrast, images generated by Flux deliver the best visual aesthetic quality. Our IQA selection can eliminate poorly generated images to achieve more realistic results. The samples of generated images by FluxGen can be found in the supplemental materials. + +Table 4. Ablation results of different datasets generated by three FluxGen settings on the RealLQ250 dataset. + +
FluxGenCLIPIQA ↑MUSIQ ↑MANIQA ↑
SDXL w/ IQA0.578769.280.5630
Flux w/o IQA0.525468.660.6265
Flux w/ IQA0.548770.160.6267
+ +# 5. Conclusion + +In this paper, we squeezed out the powerful T2I model - Flux for image restoration, by acquiring training data from it and then building a lightweight adapter to control it. To tackle the challenge of acquiring a large-scale high-quality image dataset, we proposed FluxGen for streamlined and highly efficient data generation. We present FluxIR, a lightweight adapter designed to control the T2I model for real-world image restoration, where the SE layers broadcast the control signals to all Flux MM-DiT blocks and modulate both image and text embedding to enable precise and multi-modality control. 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While previous models are effective at capturing spatiotemporal features, they often lack a focused representation of key action details. To address this, we introduce FocusVideo, a framework designed for refining video action recognition through integrated global and local feature learning. Inspired by human visual cognition theory, our approach balances the focus on both broad contextual changes and action-specific details, minimizing the influence of irrelevant background noise. We first employ learnable action queries to selectively emphasize action-relevant regions without requiring region-specific labels. Next, these queries are learned by a local action streaming branch that enables progressive query propagation. Moreover, we introduce a parameter-free feature interaction mechanism for effective multi-scale interaction between global and local features with minimal additional overhead. Extensive experiments demonstrate that FocusVideo achieves state-of-the-art performance across multiple action recognition datasets, validating its effectiveness and robustness in handling action-relevant details. + +# 1. Introduction + +Video action recognition refers to the process of analyzing sequences of images in a video to identify and classify human actions or activities. When humans interpret actions in videos, attention is often drawn both to broad contextual changes and specific action details. This dual focus aligns with the Global vs. Local Processing theory [28] in the visual cognition field, which explains how our brains alternate between big-picture (global) and detail-oriented (local) processing, efficiently filtering out distractions to capture essential details. Inspired by this, models should learn + +![](images/d3d2ef72b2b23e0a6618cc394c8eb75b9c1da963c51b21c2878dc96a014ec8b5.jpg) +Figure 1. High-level illustration of the proposed method. We propose a method that combines both global view and local focuses for video action recognition. The global view captures the video's overall spatiotemporal structure, while the local focus targets action-relevant details. Integrating these two aspects allows for more accurate and refined action recognition. The highlighted areas in the visualization represent our method's attention scores, illustrating how it concentrates on key action regions. + +to capture global spatiotemporal features while focusing on action-specific details. + +In recent years, Transformers [6, 38] have emerged as mainstream backbone models in vision tasks, with notable adaptations in video processing [1, 2, 20, 40]. Central to Transformers is the attention mechanism, which assigns weights to sequence tokens via softmax. However, recent studies [24, 46] have shown that Transformers struggle to accurately retrieve key information due to "attention noise," which reduces the efficiency of key feature extraction and hinders performance. This phenomenon also manifests in video Transformers, where the model captures extraneous details such as background elements or unrelated objects. We visualize some examples of attention scores using a typ- + +ical video transformer [32] as shown in the global view of Fig. 1 and the first column of Fig. 5. In some cases, the model may even overlook the action's main subject altogether, resulting in misinterpretation or failure to recognize the video. While video-level global features remain essential, noise interference also highlights that action detail matters. Previous approaches [16, 37, 41, 42, 44, 45, 51] primarily leverage global features, leaving the representation of local, action-relevant details under-explored. Although some methods [31, 34, 48, 49] attempt to detect or represent objects, action-relevant areas are not always well-defined objects; they can be areas without clear boundaries, requiring focus on the specific area where the action actually occurs. Yet, how to effectively enhance action-relevant details remains challenging. + +This paper addresses the problem from two key perspectives: (i) How can we represent action-relevant areas? One possible solution could involve a separate region localization head or detection branch to identify action regions. However, this approach is resource-intensive and relies heavily on labeled region annotations which are not provided by current action recognition datasets. In fact, action details are already embedded in video features, so adaptively extracting these from global features may help bypass this issue. (ii) How can we efficiently integrate global and action-sensitive area features within a unified model? Local features need to be extracted from global features while maintaining harmony for video recognition. Achieving effective integration without excessive parameters, while balancing computational efficiency, presents a significant challenge. This requires careful design of the architecture, with a focus on controlling the number of learnable parameters to maintain model efficiency. + +Keeping these two points in mind, we propose FocusVideo, a framework designed to effectively Focus on both action-relevant details and global spatiotemporal features for Video action recognition. To address the first question, we introduce learnable action queries to automatically uncover action-relevant areas within the video, inspired by recent advancements in learnable query mechanisms [3, 4, 17, 27]. Concretely, each query is initialized randomly to capture diverse aspects of actions by attending to regions associated with the action. These queries then interact with global video features, allowing the model to dynamically emphasize action-relevant areas from video representations based on the network's learning. Additionally, we use existing video features to supervise the queries, effectively bypassing the challenge of lacking region-specific labels. For the second question, we propose a local action query streaming branch and an efficient feature interaction operation, supporting the learning of action queries and enabling layerwise interactions between local queries and global video features. We utilize shared query update + +parameters and an autoregressive-like propagation method to iteratively refine the queries, enabling them to progressively focus on action-relevant areas. Moreover, the feature interaction can be directly and seamlessly inserted into the self-attention module of the video branch to achieve action-related feature mining and global-local integration, improving both efficiency and reducing parameter count. Extensive experiments demonstrate that FocusVideo achieves state-of-the-art (SOTA) performance on multiple action recognition datasets, validating its effectiveness and robustness. + +Our main contributions can be summarized as follows: + +- We propose FocusVideo, a unified framework that facilitates the integration of global and local features together, using learnable action queries to focus on action-relevant areas and suppress noise. +- We design a local action query streaming branch that allows learnable queries to progressively self-strengthen to adapt action-relevant regions, capturing omni-level action subject information and enhancing sensitivity to action details. +- We boost feature interaction efficiency with a parameter-free attention reuse strategy, integrating local query features with video features effectively. + +# 2. Related Works + +In recent years, video action recognition methods have evolved from CNN-based approaches [8, 13, 21, 39, 52] to Transformer-based approaches [1, 20, 26], adapting to changes in mainstream neural networks. Early Video Transformers focused on modifying Transformer architectures for better temporal modeling [2, 7, 10, 19], such as designing temporal input blocks or temporal Attention mechanisms. With the rise of large pre-trained models [11, 17, 23, 35, 47], methods like ActionCLIP [40] and XCLIP [29] have incorporated CLIP into video action recognition by adding temporal modules. More recent work, such as ILA [37], introduced implicit learnable alignment for better temporal modeling. Despite strong performance, these models often require costly full model fine-tuning on video data, limiting broader adoption. + +To address this, Parameter-Efficient Fine-Tuning (PEFT) methods [14, 32, 33, 41, 42, 45] have emerged, aiming to adapt CLIP for video tasks by keeping most of the CLIP model frozen and only adding a few learnable parameters for efficient training. For example, EVL [22] uses a lightweight Transformer decoder on top of a fixed CLIP to achieve spatiotemporal fusion, and ST-Adapter [32], which inserts temporal adapters before attention or MLP blocks. $\mathbf{M}^2$ -CLIP [41] further introduces multimodal adapters and a multitask decoder for balanced supervised and generalization performance. Other methods refine image-to-video transfer from the perspective of label texts [12, 36], aiming to represent action content more clearly through language. + +![](images/7f8ab43c1834a9bf9fd77402e9734e294974e2db80458285b0ef5b12be700c33.jpg) +Figure 2. Overview of FocusVideo. The overall network architecture includes (i) a global video feature modeling branch with multiple video transformer layers to perform spatiotemporal modeling and extract video-level features, (ii) a feature interaction module for action query and video feature interaction, extracting relevant action details from the video, (iii) a local action query streaming branch with shared query propagation layers that progressively update action queries and perform spatiotemporal modeling for local action-related regions, and (iv) a classification head that integrates features from both branches (global and local) and performs the final classification. + +Considering the use of auxiliary branches, we discovered that both STAN [25] and UniformerV2 [18] have incorporated these mechanisms to enhance their models. Specifically, STAN utilizes CLIP's image encoder for advanced spatiotemporal modeling, while UniformerV2 strengthens its backbone with techniques for global spatiotemporal modeling. Despite this, most of these methods focus on holistic feature learning, leaving the representation of local action-relevant regions under-explored, making them susceptible to irrelevant noise. Drawing inspiration from the Global vs. Local Processing theory [28] in visual cognition, this paper proposes an approach that enhances the model focus on critical local action regions. + +# 3. Approach + +The overall framework structure of FocusVideo is illustrated in Fig. 2. Next, we will detail the specific design of FocusVideo in this section. + +# 3.1. Input Construction + +Formally, there are two types of inputs to FocusVideo. The first is the common video frames $\mathbf{V} \in \mathbb{R}^{T \times H \times W \times 3}$ , where $H \times W$ is the spatial size, and $T$ is the number of sampled frames, which are forwarded to the global video feature modeling branch. The other is a group of learnable queries $\mathbf{A} \in \mathbb{R}^{T \times K \times C}$ , representing $K$ action-related vectors with feature channel $C$ for $T$ frames, allowing efficient local feature extraction without repeated image input. + +# 3.2. Global Video Feature Modeling + +FocusVideo includes a video model $h_v$ for global spatiotemporal modeling of videos. Following the PEFT paradigm, we adopt a representative method [32] as the ba + +sis of our $h_v$ , which effectively incorporates spatiotemporal convolution adapters inside each CLIP Transformer layer. It comprises $L$ repeated blocks, each sequentially containing a spatiotemporal adapter (ST-AD), a multi-head self-attention (MHSA) layer, and a fully connected feed-forward network (FFN). Given the output video embedding of $(l - 1)$ -th block, $\mathbf{X}_{l - 1} = \{\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_T\} \in \mathbb{R}^{T\times N\times C}$ of $N$ tokens with $T$ sampled frames, the $l$ -th block performs the following: + +$$ +\operatorname {S T - A D} \left(\mathbf {X} _ {l - 1}\right) = \mathbf {X} _ {l - 1} + \operatorname {C o n v 3 D} \left(\mathbf {X} _ {l - 1} W _ {d n}\right) W _ {u p}, \tag {1} +$$ + +$$ +\tilde {\mathbf {X}} _ {l - 1} = \operatorname {S T - A D} \left(\mathbf {X} _ {l - 1}\right) + \operatorname {M H S A} (\ln (\operatorname {S T - A D} \left(\mathbf {X} _ {l - 1}\right))), \tag {2} +$$ + +$$ +\mathbf {X} _ {l} = \tilde {\mathbf {X}} _ {l - 1} + \operatorname {F F N} \left(\operatorname {L N} \left(\tilde {\mathbf {X}} _ {l - 1}\right)\right) \tag {3} +$$ + +where LN means layer normalization and Conv3D means 3D convolution. Here, ST-AD is learnable, while the other parameters remain frozen. After $L$ layers, the output $\mathbf{X}_L\in \mathbb{R}^{T\times N\times C}$ serves as the global video feature representation. + +# 3.3. Seamless Feature Interaction Operation + +Intuitively, to enable action queries to selectively capture local action-relevant features in a video, interaction with the video features is essential. Common interaction methods often require additional parameters, increasing the overall learning burden. To address this, we carefully devise a parameter-free feature interaction operation that can be seamlessly inserted into the video Transformer directly. + +As shown in Fig. 3(a), we start by concatenating the action queries $\mathbf{A}$ with the video features $\mathbf{X}$ from each corresponding layer to form the query $\mathbf{Q}$ input of the original MHSA of the video Transformer block. Meanwhile, the key and value inputs remain as the video features. Then we + +change the original self-attention mechanism in Sec. 3.2 to a cross-attention mechanism. The core attention operation can be formulated as: + +$$ +\hat {\mathbf {X}} = \operatorname {L N} (\operatorname {S T - A D} (\mathbf {X})), \hat {\mathbf {A}} = \operatorname {L N} (\mathbf {A}), \tag {4} +$$ + +$$ +\mathbf {Q} = \left[ \mathbf {Q} _ {X}, \mathbf {Q} _ {A} \right] = \left[ \hat {\mathbf {X}} \mathbf {W} _ {Q}, \hat {\mathbf {A}} \mathbf {W} _ {Q} \right], \tag {5} +$$ + +$$ +\mathbf {K} = \hat {\mathbf {X}} \mathbf {W} _ {K}, \mathbf {V} = \hat {\mathbf {X}} \mathbf {W} _ {V}, \tag {6} +$$ + +$$ +\operatorname {C A} \left(\left[ \hat {\mathbf {X}}, \hat {\mathbf {A}} \right], \hat {\mathbf {X}}\right) = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {T}}{\sqrt {d _ {k}}}\right) \mathbf {V} \tag {7} +$$ + +where $\mathbf{W}_Q, \mathbf{W}_K$ and $\mathbf{W}_V$ are the query, key, and value projection matrices, respectively. Softmax means softmax activation and $\sqrt{d_k}$ is a scaling factor. CA denotes cross-attention and $[\cdot]$ means concatenation along the token number dimension. + +This operation can directly reuse the original video modeling parameters in Eq. (1-3) without introducing any additional parameters. It inherently includes both (i) the self-attention enhancement for the video features and (ii) a cross-attention interaction between the action queries and video features, which aims to extract action-sensitive local features from the video features. We achieve this by splitting Eq. (7): + +$$ +\begin{array}{l} \operatorname {C A} \left(\left[ \hat {\mathbf {X}}, \hat {\mathbf {A}} \right], \hat {\mathbf {X}}\right) = \operatorname {S o f t m a x} \left(\frac {\left[ \mathbf {Q} _ {X} , \mathbf {Q} _ {A} \right] \mathbf {K} ^ {T}}{\sqrt {d _ {k}}}\right) \mathbf {V} (8) \\ = \left[ \begin{array}{l} \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} _ {X} \mathbf {K} ^ {T}}{\sqrt {d _ {k}}}\right), \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} _ {A} \mathbf {K} ^ {T}}{\sqrt {d _ {k}}}\right) \end{array} \right] \mathbf {V} (9) \\ = \left[ \begin{array}{l} \mathrm {S A} (\hat {\mathbf {X}}) \end{array} \right], \left. \begin{array}{l} \mathrm {C A} (\hat {\mathbf {A}}, \hat {\mathbf {X}}) \end{array} \right] \rbrack , (10) \\ \end{array} +$$ + +In Eq. (10), the first term corresponds to (i), while the second term corresponds to (ii). Note that, for simplicity, we describe the core single-head cross-attention computation in Eq. (4-10) and omit the description of the output linear layer and the layer subscript. The multi-head mechanism can be easily extended. Then, the output of video features is the same to Eq. (2-3) while the output of the action queries can be formulated as: + +$$ +\mathbf {A} ^ {F I} = \mathbf {A} + \operatorname {M H C A} (\hat {\mathbf {A}}, \hat {\mathbf {X}}) \tag {11} +$$ + +where MHCA means multi-head cross-attention. + +We seamlessly integrate the parameter-free feature interaction operation across all $L$ video transformer layers, enabling continuous interaction between the learned queries and video features layer by layer. This approach fully leverages omni-scale video features in all layers rather than solely relying on high-level representations from the final layer, enhancing the model's capacity to capture both low- and high-level temporal details throughout the video sequence. + +![](images/f6d1d215ce2ffa2b2b1ef3bac750e15d5a56de5526d4fe5bd51af798b4d2ee91.jpg) +Figure 3. Detail Structures. (a) Global video Transformer block integrated with feature interaction module: Performs video spatiotemporal modeling and feature interaction together. "T-AD" means temporal adapter in the global branch. (b) Query propagation layer: Progressively updates action queries across layers to refine action representations. The iterative process occurs iteratively across all $L$ video transformer layers, allowing for comprehensive interaction between the learned queries and the video features at each layer. (c) Local spatiotemporal modeling: Performs spatiotemporal modeling on local action queries. + +# 3.4. Local Action Query Streaming + +Relying solely on global video representations [1, 40, 42, 51] can dilute critical spatiotemporal details associated with specific actions. Queries are designed to extract and compress core information from the input data, serving the final task [3, 17, 27]. The core idea of "query" is based on the attention mechanism, which helps the models gradually focus on specific parts of the input data. This flexible and adaptive nature of queries allows the query-based models to self-optimize their focus and effectively represent the underlying structures within the data. + +Inspired by this, our method incorporates a local action query streaming branch that dynamically propagates action queries for self-enhancement across multiple feature scales within the video representation, enabling FocusVideo to accurately identify and focus on regions that are strongly correlated with the target actions, enhancing the model's attention to action-relevant areas. This branch consists of two main components: the Query Propagation (QP) layers and a local spatiotemporal modeling module, as shown in Fig. 3(b,c). The former propagates $\mathbf{A}$ by integrating the interacted information from $\mathbf{A}^{FI}$ sequentially across layers. The latter then performs spatiotemporal enhancement on all action-related queries across frames after the last QP layer. Query Propagation Layer. When given the action queries $\mathbf{A}_j$ and the interacted queries $\mathbf{A}_j^{FI}$ at the $j$ -th layer, the + +QP layer first performs cross attention between these inputs. Here, $\mathbf{A}_j$ serves as the attention query while $\mathbf{A}_j^{FI}$ provides the key-value pairs. Notably, this operation is done frame-by-frame without inter-frame interaction because $\mathbf{A}_j^{FI}$ has already interacted with the video features containing spatiotemporal information, selecting the action-relevant spatiotemporal features from the global video branch. Then, an FFN is attached to further adjust the features. The steps can be written as: + +$$ +\tilde {\mathbf {A}} _ {j} = \mathbf {A} _ {j} + \operatorname {M H C A} \left(\ln \left(\mathbf {A} _ {j}\right), \ln \left(\mathbf {A} _ {j} ^ {F I}\right)\right), \tag {12} +$$ + +$$ +\mathbf {A} _ {j} ^ {Q P} = \tilde {\mathbf {A}} _ {j} + \operatorname {F F N} (\operatorname {L N} (\tilde {\mathbf {A}} _ {j})) \tag {13} +$$ + +To further reduce parameter counts and simplify training, we share the QP Layer parameters across all $L$ layers, treating it as a single QP Layer applied iteratively in an autoregressive manner. Each iteration refines the representation, with the output from the previous pass serving as the input for the next, ensuring that only one set of parameters is needed throughout the entire process, thereby minimizing the number of learnable parameters and enhancing training efficiency. + +Local Spatiotemporal Modeling. After obtaining the fully propagated action-related queries $\mathbf{A}_L^{QP}$ , we apply a spatiotemporal self-attention mechanism to strengthen temporal and spatial dependencies between all the action queries across all frames. The features are first reshaped from $\mathbf{A}_L^{QP} \in \mathbb{R}^{T \times K \times C}$ to $\bar{\mathbf{A}} \in \mathbb{R}^{1 \times TK \times C}$ . We perform self-attention along the combined $TK$ dimension as follows: + +$$ +\tilde {\mathbf {A}} = \bar {\mathbf {A}} + \operatorname {M H S A} (\mathrm {L N} (\bar {\mathbf {A}})), \tag {14} +$$ + +$$ +\mathbf {A} ^ {S T} = \tilde {\mathbf {A}} + \operatorname {F F N} (\operatorname {L N} (\tilde {\mathbf {A}})) \tag {15} +$$ + +This block allows local action-related queries to capture spatiotemporal details across all frames effectively. + +# 3.5. Classification Head + +Once obtained the video feature representation $\mathbf{X}_L$ and the local action-related queries $\mathbf{A}^{ST}$ , we take the class token of $\mathbf{X}_L$ and perform mean pooling along the temporal dimension to obtain the final global video features. Similarly, for $\mathbf{A}^{ST}$ , we perform mean pooling over both the query dimension and temporal dimension to obtain the final local action-related features. Subsequently, we add these two features together as $\mathbf{F}$ and pass it through a Linear layer for classification. + +Training Objectives. To supervise the learning of FocusVideo, we utilize two loss functions. The first is the standard classification cross-entropy loss $\mathcal{L}_{cls}$ applied to the joint feature $\mathbf{F}$ to guide the network's overall learning. In addition, we use a frame-level video feature reconstruction contrastive loss $\mathcal{L}_{\mathrm{recon}}$ inspired by the distill loss [30, 34] to specifically guide the learning of action queries. This additional loss focuses on maximizing the alignment of action + +query features with the reconstructed video features. By doing so, it ensures that the query features are more consistent with the global video representation, while also guiding the queries to concentrate on areas relevant to the actions. + +$$ +c \left(\mathbf {A} ^ {R}, \mathbf {X} ^ {R}\right) = \sum_ {k = 1} ^ {K} \frac {e ^ {\langle \mathbf {A} _ {k} ^ {R} , \mathbf {X} ^ {R} \rangle / \tau}}{\sum_ {l = 1} ^ {K} e ^ {\langle \mathbf {A} _ {l} ^ {R} , \mathbf {X} ^ {R} \rangle / \tau}} \left\langle \mathbf {A} _ {k} ^ {R}, \mathbf {X} ^ {R} \right\rangle , \tag {16} +$$ + +$$ +\left\langle \mathbf {A} _ {k} ^ {R}, \mathbf {X} ^ {R} \right\rangle = \frac {\mathbf {A} _ {k} ^ {R} \cdot \mathbf {X} ^ {R}}{\| \mathbf {A} _ {k} ^ {R} \| \| \mathbf {X} ^ {R} \|}, \tag {17} +$$ + +$$ +\mathcal {L} _ {\text {r e c o n}} = - \sum_ {t = 1} ^ {T} \log \frac {e ^ {c \left(\mathbf {A} ^ {R} , \mathbf {X} ^ {R}\right) / \tau}}{e ^ {c \left(\mathbf {A} ^ {R} , \mathbf {X} ^ {R}\right) / \tau} + \sum_ {\mathbf {X} ^ {\prime} \sim \mathcal {N}} e ^ {c \left(\mathbf {A} ^ {R} , \mathbf {X} ^ {\prime}\right) / \tau}} \tag {18} +$$ + +where $\tau$ as the temperature parameter. Here, $\mathbf{A}^R$ is obtained by adding a linear layer to the spatiotemporal features $\mathbf{A}^{ST}$ to adjust region-specific features, while $\mathbf{X}^R$ represents the existing target video features for reconstruction. $\mathcal{N}$ refers to a negative sample pool consisting of other videos from the same batch that belong to different classes. $\mathcal{L}_{\mathrm{recon}}$ maximizes similarity between matching features of $\mathbf{A}^R$ and $\mathbf{X}^R$ while minimizing the similarity to unrelated ones. The final training objective is defined as $\mathcal{L} = \lambda_1\mathcal{L}_{cls} + \lambda_2\mathcal{L}_{\mathrm{recon}}$ , optimizing both classification accuracy and action query representation quality, where $\lambda_{1}$ and $\lambda_{2}$ are the weighting factors of the two losses, respectively. + +# 4. Experiments + +# 4.1. Experimental Setup + +We evaluate the performance of the proposed FocusVideo on two widely-used datasets: Kinetics-400 (K400) [15] and Something-Something-V2 (SSv2) [9]. We employ CLIP [35] with ViT-B/16 and ViT-L/14 as our backbones. Note that the backbones are frozen during the training process. Only spatiotemporal adapters [32] in the global branch and the whole local branch are leanable. The sparse frame sampling strategy is used with 8, 16 or 32 frames during both training and inference. The Transformer blocks of QP layer and local spatiotemporal modeling are equipped with 8 attention heads and FFNs where the hidden dimension equals the input feature size. Unless otherwise specified, our model operates with 8 action queries for every input frame. Additionally, both $\lambda_{1}$ and $\lambda_{2}$ are set to 1. The experiments are performed on four A100 for ViT-B models and eight A100 for ViT-L models. + +# 4.2. Main Results + +Results on Kinetics-400. Table 1 presents the comparisons with SOTA video models on K400 dataset. Our first observation is that the FocusVideo framework provides substantial enhancements over the baseline global video rep + +Table 1. Performance comparison on K400. The per-view GFLOPs is reported. Views mean crops $\times$ clips. + +
MethodTP (M)FramesViewsTop-1(%)Top-5(%)GFLOPs
MViTv2-B [20]52325 × 182.995.7225
EVL-B/16 [22]8681 × 382.9-444
ST-Adapter-B/16 [32]781 × 382.095.7148
ST-Adapter-B/16 [32]7321 × 382.796.2607
AIM-B/16 [45]1181 × 383.996.3202
ActionCLIP-B/16 [40]1423210 × 383.896.2563
X-CLIP-B/16 [29]13284 × 383.896.7145
Vita-CLIP B/16 [42]39164 × 382.996.3190
STAN-conv-B/16 [25]-81 × 383.196.0238
M²-CLIP-B/16 [41]1684 × 383.496.3214
M²-CLIP-B/16 [41]16324 × 384.196.8842
MoTE-B/16 [51]-84 × 383.096.3141
OST-B/16 [5]-161 × 183.2--
FocusVideo-B/161584 × 384.196.5204
FocusVideo-B/1615324 × 384.796.8816
ST-Adapter-L/14 [32]-81 × 386.797.5687
ST-Adapter-L/14 [32]-321 × 387.297.62749
AIM-L/14 [45]3881 × 386.897.2934
DUALPATH-L/14 [33]27321 × 387.797.8-
Text4Vis-L/14 [43]231324 × 387.197.41662
M²-CLIP-L/14 [41]54324 × 387.097.6-
MoTE-L/14 [51]-84 × 386.897.5649
MoTE-L/14 [51]-164 × 387.297.71299
FocusVideo-L/143384 × 387.297.7914
FocusVideo-L/1433324 × 388.097.93656
+ +presentation model, ST-Adapter [32]. In particular, FocusVideo achieves performance gains of $2.1\%$ on the 8-frame setting and $2.0\%$ on the 32-frame setting when ViT-B/16 serves as the backbone. These results demonstrate that our local action-focused branch significantly strengthens global spatiotemporal representation, directly validating the effectiveness of our approach in highlighting action-specific areas. Second, our FocusVideo with a ViT-B/16 backbone achieves $84.1\%$ accuracy with 8-frame input, outperforming other methods using the same backbone, including fully fine-tuned models like ActionCLIP [40] and XCLIP [29], while requiring fewer learnable parameters and frames. With a 32-frame input, our method further achieves top performance, surpassing recent methods like OST [5], MoTE [51] and M2-CLIP [41]. When using the larger ViT-L/14 backbone, our FocusVideo achieves further improvements, demonstrating its scalability and effectiveness with larger architectures. These results demonstrate FocusVideo's continued efficiency and strong performance on video tasks. + +Results on Something-something-v2. In Table 2, we present the performance comparisons on SSv2. Compared to the baseline global video representation model, ST-Adapter [32], FocusVideo still demonstrates a noticeable improvement, achieving a $1.3\%$ and $1.0\%$ performance boost when using the ViT-B/16 backbone. The extra learnable parameters added on top of ST-Adapter amount to + +Table 2. Performance comparison with the state-of-the-arts on SSv2. The per-view GFLOPs is reported. "F" means frames. + +
ModelFViewsTop-1(%)Top-5(%)GFLOPs
S-ViT-B/16 [50]162×369.392.1340
ST-Adapter-B/16 [32]81×367.191.2163
ST-Adapter-B/16 [32]321×369.592.6-
ILA-ViT-B/16 [37]84×365.089.2214
ILA-ViT-B/16 [37]164×366.890.3438
AIM-ViT-B/16 [45]81×366.490.5208
AIM-ViT-B/16 [45]321×369.192.2832
STAN-B/16 [25]161×369.592.7459
Vita-CLIP-B/16 [42]16-48.7--
DUALPATH-B/16 [33]321×370.392.9-
M²-CLIP-B/16 [41]321×369.391.81010
OST-B/16 [5]161×160.3--
FocusVideo-B/1681×368.491.0227
FocusVideo-B/16321×370.592.4908
ST-Adapter-L/14 [32]83×170.092.3-
ST-Adapter-L/14 [32]323×172.393.9-
EVL-ViT-L/14 [22]321×368.0-8086
DUALPATH-L/14 [33]321×371.493.41932
AIM-ViT-L/14 [45]81×367.691.6959
AIM-ViT-L/14 [45]321×370.692.73836
ILA-ViT-L/14 [37]164×370.291.83723
M²-CLIP-L/14 [41]321×372.193.2-
FocusVideo-L/1481×370.792.3985
FocusVideo-L/14321×372.994.03840
+ +only 8M, yet they significantly enhance the encoding of local action details, leading to a more refined and comprehensive video understanding representation. In addition, based on both ViT-B/16 and ViT-L/14, our method achieves competitive or superior performance compared to + +![](images/d3fc0d03be8163d011e55d755e2a318cae65fd89e911bc16a332e49cd2b44aa5.jpg) +Figure 4. Top 20 category-wise Improvements. We visualize the top 20 categories where our method brings the most improvement compared to the pure global video modeling baseline on K400 and SSv2 datasets. The results show significant enhancements in categories that require fine-grained action details. Particularly in complex categories like "Pretending to...", highlights the importance of representing action-specific details. + +most prior works. For example, compared to OST-B/16 [5], FocusVideo-B/16 outperforms it by $8.1\%$ with 8-frame input. With 32-frame input, FocusVideo leads M2-CLIP [41] by $1.2\%$ , while requiring fewer learnable parameters. These results demonstrate the effectiveness of our approach with the local action-focused queries, emphasizing its ability to enhance video action recognition. + +# 4.3. Ablation and Analysis + +We conduct ablation experiments on both K400 and SSv2 to validate the effectiveness of the proposed FocusVideo. Component-wise analysis of FocusVideo. In Table 3a, we perform a detailed ablation of each proposed component in FocusVideo, gradually adding them to assess their impact. Each component is integrated with its default ablation configuration. The QP layer in M2 applies cross-attention between video features and queries from the previous layer, bypassing self-propagation. Results show that M2 notably improves performance, underscoring the value of the local branch. M3 and M4 consistently improve performance, demonstrating the effectiveness and necessity of our proposed feature interaction operation and local spatiotemporal modeling. The final M4 model achieves the highest effectiveness, solidifying it as the complete FocusVideo. + +Varying Number of Action Queries. We ablate the number of action queries in Table 3b. We observe that using just 2 queries already yields good results. When increasing to 8 queries, the performance is the best, which is our final setting. However, further increasing the number of queries leads to saturation or even a slight decline in performance. We believe the reason for this is that too many queries may introduce unnecessary regions, which in turn affect the performance. + +Effect of Omni-scale Propagation. In Table 3c, we ablate + +the omni-scale propagation of the local branch. For the usage of video features, we experiment with using only the final top layer, every other layer (half), and all layers. Additionally, the QP layer is set to either shared or non-shared configurations. Results show that using shared parameters across all layers yields the best performance with minimal parameters, demonstrating the effectiveness of multi-scale feature utilization and our autoregressive-like setup. Interestingly, when QP layer parameters are not shared, performance declines, likely due to overfitting or inconsistent feature representations across layers. + +Design of Feature Interaction. We experiment with several different configurations of the feature interaction module. As shown in Table 3d, "None" indicates that this module is not used, and the video features from each layer directly replace $\mathbf{A}_j^{FI}$ in the QP layer for cross attention. The remaining three configurations represent different modules reused in the global video branch. It can be seen that reusing only the attention mechanism yields the best performance. Adding T-AD or FFN in addition to the attention mechanism imposes restrictions on local feature representation and has a negative impact on learning. + +Design of Global-local Combination. We simply try three different methods to fuse the features output from the pooling of the global and local branches, as shown in Table 3e. Besides basic addition, we test concatenation followed by a linear layer to match the feature dimension, and another setting using linear projections before addition. Direct addition, which requires no extra parameters, yielded the best performance, so we selected it as the final fusion method. + +Effect of Distinct Query Supervision. In Table 3f, we experiment with different supervision signals for the local branch. "None" represents using only the classification loss $\mathcal{L}_{cls}$ without additional losses. "Cls Cross entropy" adds + +Table 3. Ablation studies with 8-frame FocusVideo-B/16, reporting Top-1 accuracy on K400 and SSv2. Default settings are in gray . + +(a) Component-wise analysis of FocusVideo. + +
ModelsConfigurationK400SSv2
M1Global Video Branch82.466.8
M2M1 + QP Layer83.567.7
M3M2 + Seamless Feature Interaction83.968.0
M4M3 + Local Spatiotemporal Modeling84.168.4
+ +(d) Design of Feature Interaction. + +
TypeK400SSv2
None83.868.0
Attention84.168.4
Attention + T-AD82.767.2
Attention + FFN83.267.7
+ +(b) Varying Number of Action Queries. + +
NumbersK400SSv2
283.867.9
483.868.1
884.168.4
1684.068.2
+ +(e) Design of Global-local Combination. + +
TypeK400SSv2
Concatenation + Linear83.667.9
Add84.168.4
Linear + Add83.968.3
+ +(c) Effect of Omni-scale Propagation. + +
TypeLocal ParamsK400SSv2
Only top layer7.9M83.767.7
shared half layers7.9M83.968.0
shared all layers7.9M84.168.4
Non-shared all layers46.9M83.466.5
+ +(f) Effect of Distinct Query Supervision. + +
TypeK400SSv2
None82.767.0
Cls Cross entropy83.567.4
Reconstruction (online)83.467.2
Reconstruction (offline)84.168.4
+ +![](images/ab40b43d5714dbb04e6f351be320e884b7477f3ff2cdb13b461bfefcbad9382c.jpg) +Figure 5. Attention score visualizations. The first column represents the attention score of the entire frame from the class token of the global video representations. The subsequent three columns show the attention score distributions of three action queries across the entire frame, indicating how each query focuses on different parts of the video content. + +a linear projection to the pooled $\mathbf{A}^{ST}$ , followed by a classification cross-entropy loss supervised with the video labels. "Reconstruction" uses the $\mathcal{L}_{\mathrm{recon}}$ described in Sec. 3.5. "online" and "offline" respectively use synchronous video features and off-the-shelf trained video features for supervision. Results show that offline supervision with independently trained features performs best, helping compensate for the absence of ground truth action-region labels. + +# 4.4. Visualization + +To illustrate the effectiveness of our action queries, we visualize attention score distributions in Fig. 5. In the holistic video features shown in the first column, attention often disperses across the entire frame, capturing irrelevant areas + +like backgrounds or unrelated people in meanwhile. For instance, in the second row (robot dancing), attention covers the ground and bystanders rather than focusing on the action. In contrast, our action queries concentrate on crucial areas, such as the dancer's head, hands, and legs. It achieves finer-grained focus like hand-object contact in the third and fourth rows. Additionally, although we didn't explicitly enforce diversity among the queries, they effectively capture different regions, even when overlapping spatial areas. This indicates that each query can focus on distinct aspects of the action, enhancing the model's understanding of complex action patterns within overlapping yet specialized attention zones. + +Moreover, to better understand the impact of adding our designed local branch, we visualize the top 20 categories where our proposed FocusVideo model shows the most improvement compared to using only global video features in Fig. 4. We can observe that our method consistently excels in classes that demand attention to fine action details across both datasets like "dancing gangnam style", "answering question" and "pretending to turn something upside down". This enhancement suggests that the local branch better captures intricate action details, contributing to higher accuracy in detail-sensitive categories. + +# 5. Conclusion + +This paper demonstrates a unified framework for integrating global context with action-focused details, yielding state-of-the-art performance in video action recognition. Our success stems from: (i) the introduction of learnable action queries, which enable our model to effectively capture critical regions in videos while filtering out irrelevant noise; (ii) the propagating local query branch, which progressively self-enhances and efficiently integrates with the global branch by sharing parameters across layers, reducing computational costs; and (iii) a parameter-free feature interaction strategy, which ensures effective interaction between global and local features across omni-scale layers without excessive computational burden. + +# Acknowledgments + +This work was supported by the National Natural Science Foundation of China under Grant No. 62403429, No. 62476247, Zhejiang Provincial Natural Science Foundation of China under Grant No. LQN25F030008. + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. 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Existing methods often struggle with catastrophic forgetting, misclassifying old objects due to overreliance on shortcut local features. Our approach addresses this issue by learning a set of part concepts for part-aware features. Particularly, we only activate a small subset of part concepts for the feature representation of each part-aware feature. This facilitates better generalization across categories and mitigates catastrophic forgetting. We further improve the task-wise classification through a part relation-aware Transformer design. At last, we devise learnable affinities to fuse task-wise classification heads and avoid confusion among different tasks. We evaluate our method on three 3D CIL benchmarks, achieving state-of-the-art performance. Code is available at https://github.com/zenyatian/ILPC. + +# 1. Introduction + +A key aspect of human intelligence is the ability to continuously learn and adapt to new semantic concepts. This ability is crucial for 3D recognition in robotics and autonomous driving and mirrors Class-Incremental Learning (CIL) in machine learning [35, 36]. This work focuses on CIL in 3D recognition that trains the network one task by one task with each task containing 3D objects from different semantic categories. 3D CIL shares the same challenge of catastrophic forgetting in old class recognition as 2D CIL when adapting to a new task [3, 4, 8, 11, 39, 40, 47, 59-61]. Moreover, 3D CILs are still confronted with texture-less shapes and unstructured points in inputs, resulting in shortcut features [44] to mislead the shape classification. This problem further amplifies the catastrophic forgetting of 3D deep learning methods, e.g., [25, 26, 53]. + +2D CIL has been extensively studied and can be broadly + +categorized into two schemes: replay-based methods [3, 8, 20, 34, 40, 61] and dynamic network expanding-based methods [4, 32, 39, 47, 59, 60]. These methods can achieve wonderful performance in 2D tasks and are a good start for 3D CIL. Existing 3D CIL methods [10, 12, 21, 33, 49, 54] mainly extend 2D CIL methods based on 3D geometric structures, e.g., neighborhood-based feature aggregations. However, these methods still suffer from catastrophic forgetting. We owe partial reasons for catastrophic forgetting in 3D CIL to shortcut features [14, 16]. Particularly, 3D classifiers prioritize shortcut features for recognition, neglecting the importance of other shape parts and their overall composition. This can lead to misclassification of past tasks if new tasks share similar local features with old tasks. For instance, a 3D classifier that classifies a table in the old task perfectly may fail in classifying chairs in the new task when the classifier has learned a shortcut strategy relying on the legs. + +This work tackles the limitations of 3D CIL with two key designs. First, we leverage sparsely activated part concepts for local part feature representation. This is because common part concepts are usually shared among different classes, ensuring good generalization across different tasks. For example, legs, planes, and bases learned in an old task already provide discriminative enough information and make the adaption in novel tasks easier, e.g., chair recognition (see Fig. 1). Analysis of the generalization of part concepts is demonstrated in Fig. 3. Second, the catastrophic forgetting of a model is mainly caused by confusion among different task heads. Therefore, learning a dynamic mixture of task-wise classification heads can relieve catastrophic forgetting. + +To fulfill the above-mentioned observations, we address 3D Incremental Learning with Part Concepts Awareness, called ILPC. The overview is shown in Fig. 2. First, ILPC learns a set of shared part concepts as representative local geometric features among different classes. Then, we selectively activate related part concepts according to the similarity between a part concept and a geometric feature. Activated part concepts span the feature space of an input + +![](images/8342c9712a9035ced1603c743988e94dd5114d782db79c2b4e1c40ef7af84405.jpg) +Figure 1. Classes in different tasks can share a set of part concepts, which facilitate easy recognition with part compositions and their relations. + +and are used to produce part-aware features for incremental learning. We further encode mutual relationships between part-aware features within each task using a task-wise Transformer classifier. To avoid confusion among different classification heads, we dynamically update a learnable affinity to fuse task-wise classification heads. + +In conclusion, our contribution can be summarized as follows: + +- A 3D CIL framework based on sparsely activated part concepts. +- Learnable affinities for fusing multi-task classification head. +- Extensive experiments to demonstrate the superiority over other baseline methods on three 3D CIL benchmarks. + +# 2. Related Work + +# 2.1. 2D Class-Incremental Learning + +Class-incremental learning for image recognition has received lots of attentions. There are mainly two kinds of schemes: replay-based methods and dynamic network-based methods. Replay-based methods cache extra exemplars for early-stage task rehearsal during model updating, enabling the model to retain old knowledge while learning new concepts. Due to a limited memory buffer, representative extra exemplars can be selected from old tasks [2, 19, 29, 31, 34] and storage efficient strategies are also explored [3, 20, 22, 23, 40, 58]. Dynamic network-based methods [1, 4, 9, 17, 18, 24, 28, 32, 39, 45, 47, + +50, 59, 60] design additional model components to fit each task while freezing model parameters for previous tasks. Additional model components can be a dynamically expanded network [17, 18, 24, 45, 50, 60], duplicate subnetworks [1, 9, 32, 47], and a task-specific attention module [4]. These 2D methods provide inspiration for 3D CIL. + +# 2.2. 3D Class-Incremental Learning + +3D Class-Incremental Learning for point clouds is important for autonomous driving and indoor robotics and is rarely explored for now. Dong et al. [12] introduce 3D geometric information to learn distinctive 3D features in each class and correct biased weights caused by class imbalance to avoid forgetting. Liu et al. [21] propose a layer-wise task-shared knowledge factorization to reduce catastrophic forgetting. Chowdhury et al. [10] build a common set of basic descriptions to enhance the adaptability of the model to the open-world data. Zhao et al. [54] propose a static-dynamic co-teaching technique with one teacher only preserving previously learned knowledge and the other one consistently learning new knowledge. Tan et al. [33] decompose the learning tasks into the base task and new tasks, thus the model can adapt to new task with task-specific layers. Yang et al. [49] utilize geometric information of point clouds to capture point-wise feature relations. In this work, we introduce part concepts and part compositions as prompts to help mitigate catastrophic forgetting in CIL. + +# 2.3. Part-based 3D Recognition + +3D shape parts have a crucial role in 3D object recognition. Existing works can be classified into supervised part segmentation and unsupervised part discovery. Supervised methods [46, 57] require annotated part instances and can achieve better performance. On the other hand, unsupervised methods [10, 55, 56] explore the generalization of 3D shape parts. Weng et al. [43, 44] devise class-specific part prototypes for open-set recognition and shared part prototypes for novel class discovery, respectively. Inspired by these works, we present sparely activated part concepts as shared knowledge for novel tasks. + +# 3. Methodology + +This work aims at 3D class incremental learning, where the model is trained with different tasks and each task contains novel classes. The overall framework of the method is shown in Fig. 2. In light of the benefits of part compositions on 3D feature shortcuts, we build the method on a part concept-based method [43] (see Sec. 3.1). Then we present a selection mechanism and only use the most important part concepts to avoid confusions among novel classes and old classes (see Sec. 3.2). Afterward, we feed part features to a task-specific classification head by learning their mutual relations for task-aware shape classification (see Sec. 3.3). + +![](images/4d18cbe3d213ab4dbf32046a5219d44f0cc1bb358741f14ebb372776acb5a559.jpg) +Figure 2. The overall architecture. First, training dataset $\mathcal{D}_t$ for task $t$ and exemplar memory $\mathcal{E}_t$ for previous tasks are used to learn point-wise features from point cloud $x$ , which we further group into part-wise features $Z_l$ . By representing part features with a sparse set of part concepts from $P$ , we can construct part composite features $Z_p$ from $Z_l$ according to the concept activation map $S$ . Afterward, a task-specific classification head $f_t(\cdot)$ leverages part composite features $Z_p$ for mutual part relations for task-wise 3D recognition. At last, we fuse predictions from all task classification heads with learnable affinity as a unified classifier to mitigate the task bias. + +Then we fuse task-specific classification heads for different tasks as a unified classifier (see Sec. 3.4). + +# 3.1. Preliminaries + +Problem Statement. 3D CIL learns a classifier from a sequence of tasks with different sets of classes. For incremental task $t^{th}$ , the model takes a training dataset $\mathcal{D}_t = \{(x_t^i, y_t^i)\}_{i=1}^{N_d}$ , where $x_t^i \in \mathbb{R}^{L \times 3}$ denotes an input sample and $y_t^i \in Y_t$ denotes its semantic label. Let $Y_t$ be the semantic label set of task $t$ , then we have $Y_t \cap Y_i = \emptyset$ for any $i < t$ . Due to data privacy and storage constraints, it is impossible to access the whole dataset in previous tasks and only a small number of instances from previous tasks are selected as the exemplar set $\mathcal{E}_t \subseteq \cup_{i=1}^{t-1} \mathcal{D}_i$ . The model is then trained on $\mathcal{D}_t \cup \mathcal{E}_t$ and is evaluated on the test set of all seen classes. + +3D Part Concept Learning. Part concepts are important to the analysis of 3D shapes. In this work, we adopt DNIK [43] to learn 3D part concepts. Given a 3D point cloud, DNIK extracts point-wise features with PointNet [25], and then uses farthest point sampling (FPS) to sample $N_{p}$ points. Based on sampled points, we group $K$ neighboring points as a set of parts and accumulate these point features as part-level features $Z_{l} \in \mathbb{R}^{N_{p} \times D}$ . DNIK constructs a projection space with part codebook $P = \{P^{m}\}_{m=1}^{M}$ with each part concept $P^{m} \in \mathbb{R}^{D}$ representing prototypical features of a 3D part. We project + +part-level features $Z_{l}$ into the space spanned by $P^{m}$ as part composition features $Z_{p}$ : + +$$ +\boldsymbol {S} ^ {i} = \operatorname {S o f t m a x} (\varphi (\boldsymbol {Z} _ {l} ^ {i}, \boldsymbol {P} ^ {i})), +$$ + +$$ +\boldsymbol {Z} _ {p} ^ {i} = \boldsymbol {S} ^ {i} \cdot \boldsymbol {P} ^ {i} + \boldsymbol {Z} _ {l} ^ {i}, \tag {1} +$$ + +where $S \in \mathbb{R}^{N_q \times M}$ denotes the part activation map and distance function $\varphi(\cdot, \cdot)$ compares part-level features and part concepts and measures the distance in the hyperbolic space. We can sum $S$ along the first dimension and normalize accumulated part activations with $L2$ norm as a distribution $M$ along different part concepts. During optimization, DNIK applies the supervised contrastive loss (denoted as $\mathcal{L}_c$ ) to encourage part activations to be similar for same-category shapes and different from different-category shapes. + +# 3.2. Learning Sparse Part Concepts for 3D CIL + +Sparsely Activated Part Concepts. During incremental learning, different tasks may share some part concepts in common. By opting for part concepts that resonate most with the current task, the part codebook can leverage the homogeneity between part concepts in the new task and those learned in previous tasks and stored in the codebook. In Fig. 3, we demonstrate that part concepts learned on a set of old classes are already discriminative enough for both old classes and unseen new classes. Therefore learned part con- + +![](images/97ff0ed67c76e8c4e46d986df7966e3e6243f3588c3e52933b4e57da33b06494.jpg) +Figure 3. Similarity histograms of a class and the other ones. We select five classes from old tasks and five classes from new tasks and learn the part concepts from old tasks. First, we take the average of part distribution $M$ within each class as the class-wise part distribution. Then we calculate the cosine similarity between each sample of one class and its class-wise part distribution and plot the similarity distribution in green. We also plot that of samples of the other classes and their class-wise part distribution in red. + +cepts on old tasks can also ensure enough discriminativity on new tasks without any further training. + +However, part activations for different classes usually vary, and constructing part composite features with all part concepts may lead unnecessary confusion. To this end, we introduce a selection mechanism to avoid interference of irrelevant part concepts and an updatable part codebook to satisfy the command of continual learning as follows: + +$$ +\boldsymbol {Z} _ {p} ^ {i} = \operatorname {T o p K} \left(\boldsymbol {S} ^ {i}\right) \cdot \boldsymbol {P} ^ {i} + \boldsymbol {Z} _ {l} ^ {i}, \tag {2} +$$ + +where $\mathrm{TopK}(\cdot)$ is a one-hot embedding that sets all other elements in the output vector as zero except for the elements with the largest $k$ activations among different parts + +Regularization on Part Composite Features. Compared to the part loss in [43], we take a step further and devise a pseudo part label loss to encourage similar parts to be the same. We devise a loss based on the similarity of activated part maps. If the cosine similarity between the activated concept maps $S_{i}$ , $S_{j}$ of two parts is greater than a threshold (0.7 in our implementation), they are most likely to be the same part and we denote it with $\diamond(S_{i}, S_{j}) = 1$ , otherwise $\diamond(S_{i}, S_{j}) = 0$ . If two parts share the same geometry, their part composite features should be as similar as possible. On the other hand, parts with different geometry should have different composite features. Based on this observation, we construct a pseudo-part loss as follows: + +$$ +\mathcal {L} _ {p p} = \sum_ {i \in \mathcal {C} _ {p}, j \in \mathcal {C} _ {p}} - \diamond (S _ {i}, S _ {j}) \cdot \cos \left(Z _ {p _ {i}}, Z _ {p _ {j}}\right) + \tag {3} +$$ + +$$ +\left(1 - \diamond \left(S _ {i}, S _ {j}\right)\right) \cdot \cos \left(\overline {{Z _ {p _ {i}}}}, \overline {{Z _ {p _ {j}}}}\right), +$$ + +where $\cos (\cdot)$ calculates the cosine similarity, $\mathcal{C}_p$ collects all FPS parts from $Q$ , and $Z_{p_i}$ indexes the part composite features for part $i$ . $\overline{Z_{p_i}}$ takes the mean value of part composi + +tion features of all parts $i$ with a similar activated concept map (i.e., $\diamondsuit(5, S_{j}) = 1$ ) + +# 3.3. Part-Aware Task-Specific Classification Head + +After we obtain part composition features $Z_{p}$ , we build a task-specific classification head for 3D recognition. Each task-specific classification head has dependent parameters and only predicts the categories in each task. Prior works [48, 51, 52] have shown that self-attention can learn spatial relationships between local patches. So, after obtaining input part composition features $Z_{p}$ and position embeddings $Z_{c}$ , a classification head uses a shallow self-attention Transformer [13] with three layers to learn mutual relations between different shape parts as follows: + +$$ +\boldsymbol {F} _ {0} \leftarrow \operatorname {C A T} (\boldsymbol {c}, \boldsymbol {Z} _ {p}) + \boldsymbol {Z} _ {c}, +$$ + +$$ +\boldsymbol {F} _ {i} \leftarrow \operatorname {M S A} \left(\ln \left(\boldsymbol {F} _ {i - 1}\right)\right) + \boldsymbol {F} _ {i - 1}, i = 1, 2, \tag {4} +$$ + +$$ +\boldsymbol {F} _ {i} \leftarrow \operatorname {M L P} \left(\operatorname {L N} \left(\boldsymbol {F} _ {i}\right)\right) + \boldsymbol {F} _ {i}, i = 1, 2, +$$ + +where $c \in \mathbb{R}^{1 \times D}$ denotes a learnable class token, $Z_{c} \in \mathbf{R}^{(N_{p} + 1) \times D}$ is a linearly projected centroid position embedding of a part shape, and the centroid embedding is randomly initialized for the class token. We use $F_{*}$ to mark the intermediate features of each Transformer layer. CAT concatenates the class token $c$ and composition features $Z_{p}$ . We compute the LayerNorm (LN) of the concatenated features as keys, values, and queries of a multi-head self-attention module (MSA) with separate projection matrices for keys, values, and queries. We further apply a residual connection followed by a feed-forward network (MLP). The MSA and MLP modules are executed two times. At last, we apply a linear layer and a softmax function to output likelihood for each class of a task. The task-specific classification head $f_{t}(\cdot)$ for task $t$ is lightweight and can be adapted to easily + +![](images/f9f1c2c9bbb651ba20e52a2544d7a4041f451a4f71220423b1b819f5c437c2a8.jpg) +Figure 4. An illustration of task bias when fusing results of different tasks. Without task affinity, classes in different tasks may interfere with each other and be biased towards classes with more training examples. + +fit different new tasks with a small scale of parameters and memory consumption. + +# 3.4. Learnable Affinities for Multi-Task Fusion + +For the training of task $t$ , we freeze the part codebook-based backbone and classifier heads $\{f_i(\cdot)\}_{i=1}^{t-1}$ of the previous tasks and train a novel classifier head $f_t(\cdot)$ for the current task to recognize new classes in task $t$ . A vanilla approach to combine $\{f_i(\cdot)\}_{i=1}^{t-1}$ and $f_t(\cdot)$ can be written as: + +$$ +\mathbb {P} (\hat {y} | \boldsymbol {Z} _ {p}) = \left\{ \begin{array}{l l} \frac {f _ {i} \left(\boldsymbol {Z} _ {p}\right)}{\sum_ {j = 1} ^ {t - 1} f _ {j} \left(\boldsymbol {Z} _ {p}\right) + f _ {t} \left(\boldsymbol {Z} _ {p}\right)}, & \hat {y} \in \boldsymbol {Y} _ {i}, i < t, \\ \frac {f _ {t} \left(\boldsymbol {Z} _ {p}\right)}{\sum_ {j = 1} ^ {t - 1} f _ {j} \left(\boldsymbol {Z} _ {p}\right) + f _ {t} \left(\boldsymbol {Z} _ {p}\right)}, & \hat {y} \in \boldsymbol {Y} _ {t}. \end{array} \right. \tag {5} +$$ + +However, this fusion method is usually biased towards the classes of task $t$ as there are very few stored examples for learned classes of previous tasks. For example, in Fig. 4, a bench may be misclassified as a chair during the training of task 2 resulting in forgetting old classes in task 1. To account for the mutual influences of classes from different tasks, we introduce a learnable affinity term $\alpha_{k,i}$ to adjust the relative importance of predictions between task $i$ and task $k$ . For example, in Fig. 4, we learn an affinity $\alpha_{2,1}$ to balance the relative importance of predictions in task 1 and task 2. To ensure the correct prediction, $\alpha_{2,1}$ is adjusted to a value greater than 1, thus leading to the correct prediction of a bench shape. Therefore, the overall classifier head fusion can be formulated as follows: + +$$ +\mathbb {P} (\hat {y} | \boldsymbol {Z} _ {p}) = \left\{ \begin{array}{l l} \frac {\left(\prod_ {k = i + 1} ^ {t} \boldsymbol {\alpha} _ {k , i}\right) \cdot f _ {i} \left(\boldsymbol {Z} _ {p}\right)}{\sum_ {j = 1} ^ {t - 1} \left(\prod_ {k = j + 1} ^ {t} \boldsymbol {\alpha} _ {k , j}\right) \cdot f _ {j} \left(\boldsymbol {Z} _ {p}\right) + f _ {t} \left(\boldsymbol {Z} _ {p}\right)}, & \hat {y} \in \boldsymbol {Y} _ {i}, i < t, \\ \frac {f _ {t} \left(\boldsymbol {Z} _ {p}\right)}{\sum_ {j = 1} ^ {t - 1} \left(\prod_ {k = j + 1} ^ {t} \boldsymbol {\alpha} _ {k , j}\right) \cdot f _ {j} \left(\boldsymbol {Z} _ {p}\right) + f _ {t} \left(\boldsymbol {Z} _ {P}\right)}, & \hat {y} \in \boldsymbol {Y} _ {t}. \end{array} \right. \tag {6} +$$ + +The overall objective sums a standard cross-entropy loss $\mathcal{L}_{ce}$ for classification, contrastive loss $\mathcal{L}_c$ , pseudo part loss $\mathcal{L}_{pp}$ so that part concepts can be generalized and properly learned. The weight terms $\lambda_{*}$ to balance the above four losses are set to (1.0, 0.1, 0.3). + +# 4. Experiments + +In this section, we conduct comparisons with state-of-the-art methods on three different benchmarks and ablate core designs of the proposed method. + +# 4.1. Experimental Setup + +Evaluation Datasets. We evaluate the method on three datasets, including ShapeNetCore [7], Co3D [30], and nuScenes [5]. ShapeNetCore is composed of 51,127 3D CAD models from 55 common object categories. The total incremental tasks are set to 7 with the first task containing 25 classes and each incremental task containing 5 classes. Co3D consists of 18,619 objects in 50 classes. The total incremental tasks are set as 6 with the initial task having 25 classes and each incremental task having 5 classes. nuScenes contains $40\mathrm{k}$ annotated point cloud frames in 23 classes. We extract foreground instance point clouds from each point cloud frame with the instance labels. The total incremental states are set to 5 with the first task containing 11 classes and each incremental state having 3 classes. + +Evaluation Metrics. Following other baseline methods [29, 38, 39, 47, 59], we utilize top-1 mean accuracy [6, 42] of the prediction as the evaluation metric to conduct comparison experiments. We report the mean accuracy of all classes as last accuracy. In addition, we calculate the mean accuracy of seen classes at each task and take their average as avg accuracy. + +Baselines. We compare our method with typical CIL methods including replay-based methods (e.g., ER [11] and iCaRL [29]), dynamic network-based methods (e.g., DER [47], FOSTER [39] and MEMO [59]) and other latest methods (e.g., DS-AL [62] and DGR [15]). We adopt the same backbone for all methods for a fair comparison. The above methods release their codes. We implemented its 3D CIL version based on the released code and followed the same settings as the original paper. + +# 4.2. Comparisons + +In Tab. 1, we compare ILPC with competing methods on Co3D [30], ShapeNet [7], and nuScenes [5] dataset. For a fair comparison, all baseline methods employ PointNet [25] as the backbone to obtain local features of a point cloud and are trained with the same data augmentation mechanism. The dynamic network-based methods, e.g., DER, FOSTER, and MEMO, can achieve better results compared with replay-based methods. This is because these methods expand new modules to learn knowledge in new tasks and freeze old modules to retain learned knowledge, while replay-based methods only select a set of representative exemplars for 3D CIL leading to more serious catastrophic forgetting. We can observe that our method consistently outperforms other methods in last-task accuracy and average accuracy among all tasks on four bench + +![](images/1bc7b6ca7411756fb05df2fb5b83242a1ded52a4c031503e1707a068dd3d4615.jpg) +Figure 5. Task-wise performance on each incremental state for different methods. The numbers are the mean accuracy of classes in each task. + +![](images/a563e17c1f7f04fbfa142cb2f3237fc252f85bd25826b4c59394f563b995eb71.jpg) + +![](images/4f45300dbb3ad8655a9de0bc3796612770229d120a4ecfd30867b7467fa55fba.jpg) + +Table 1. Comparison results on Co3D, ShapeNet, and nuScenes dataset. + +
DatasetCo3DnuScenesShapeNet
LastAvgLastAvgLastAvg
ER [11]62.8269.7667.4075.9674.1078.68
iCaRL [29]61.0369.3655.2069.1274.9078.46
DER [47]69.7576.7277.2485.6780.3283.82
FOSTER [39]74.6080.1878.2882.6577.6583.40
MEMO [59]70.2777.1276.9285.2677.3182.21
DS-AL [62]78.8781.7476.5686.1180.9684.74
DGR [15]72.0676.2274.5880.6178.8883.67
Ours81.1886.3782.4487.2782.2786.08
Improvement+2.31+4.63+4.16+1.16+1.31+1.34
+ +mark datasets. For ShapeNet, our method outperforms the runner-up method by $1\% - 2\%$ on the last-task accuracy. The improvement on Co3D and nuScenes is much greater, which reaches $4\% - 6\%$ . The results demonstrate ILPC can achieve superior performance by leveraging part concept compositions and alleviating catastrophic forgetting for more robust 3D recognition ability. + +Fig. 5 demonstrates the task-wise performance of different models. Our proposed method retains the performance of previous tasks and performs well on the new task. However, the baseline models adapt to new tasks and forget the knowledge they have gained from previous tasks. By comparing the columns with the same task label, we can find that our method has less mean class accuracy decrease on most tasks compared with other methods. Especially, for classes in task 1, the mean class accuracy of our method drops $13.2\%$ , while the performances of baseline methods drop $26.95\%$ and $21.05\%$ , respectively. This evidence demonstrates that our method performs better in maintaining the learned knowledge and mitigating forgetting. + +# 4.3. Ablation Study + +We first analyze key components in our method and then evaluate the impact of different backbones. At last, we report results for different CIL settings and few-shot settings. All results are reported on the Co3D dataset. + +Model Components. Tab. 2 demonstrates the effectiveness of different components. The baseline employs PointNet as the backbone for point-wise feature learning and then uses max-pooling to obtain global features. The global features are fed to a linear layer followed by a softmax for task-specific 3D classification. At last, the baseline fuses predictions from all classification heads with Eq. 5. The component w/ PC augments the baseline by grouping FPS part features and learning a part concept codebook for generalizable part composite feature encoding (see the first two rows). Results show this component can significantly increase the overall performance for about $5.1\%$ , $3.9\%$ in the last accuracy and the avg accuracy, respectively. Even when we add this component (w/ PC) on the baseline with a Transformer classification head and affinity fusion (see row ⑤ and ⑥), the accuracy also boosts for about $3.1\%$ , $6.9\%$ indicating learned part concepts benefit 3D CIL recognition. + +The Transformer-based classification head (i.e., the Transformer in Eq. 4) also plays a critical role. For example, adding the component on the baseline and the baseline with an affinity fusion module improves the performance by huge margins (7.5%, 10.1% for row ① and row ③ and 18.8%, 13.6% for row ④ and row ⑤). This suggests learning mutual part relations with a Transformer is effective. + +The role of affinity-based fusion (i.e., Eq. 5 → Eq. 6) stands out when the transformer-based classification head is used. With the classification head of the baseline, adding affinity-based fusion to the baseline (see row ① and row ④) leads to very slight improvements (3.6%, 4.1%). However, combining the Transformer head and affinity-based fusion (see row ① and row ⑤) enhances the performance for + +Table 2. Ablation experiments on model components. PC adds the part codebook for part concept learning. The second column replaces a mean pooling with Eq. 4 as the classification head. + +
w/ PCEq. 4Eq. 5→6LcLppLastAvg
53.3560.72
58.4264.60
60.8570.80
56.9964.88
75.8178.48
78.9385.34
79.9785.73
80.3685.87
81.1886.37
+ +Table 3. Results on different TopK values. + +
LastAvg
0.278.8784.88
0.480.0485.77
0.681.1886.37
0.879.3285.45
1.078.1884.32
+ +(22.5%, 17.8%). Therefore, we can conclude that affinity-based fusion can properly adjust the relative importance of different tasks for better performance. Moreover, the part-relation-based classification head and affinity-based fusion can mutually reinforce each other for a significant result. + +Contrastive loss $\mathcal{L}_c$ encourages the model to learn more diverse part concepts and raises the performance (1.04% and 0.41%). Pseudo Part loss $\mathcal{L}_{pp}$ is also helpful for 3D incremental learning (1.43% and 0.53%). By combining all the above core components, the method achieves the best result. + +We report the results of different K in Tab. 3. We observe that if we use the full codebook, some useless part concepts will bring negative impacts on the results. On the contrary, if we select too few part concepts, the geometric information brought by the part features is not sufficient for precise classification. + +Different Backbones To show the influence of different backbones, we further conduct comparisons on three popular 3D backbones including PointNet++ [26], DGCNN [41], and PointNeXt [27]. We replace the backbone of the compared methods with the above network architectures and evaluate their performance on the 3D CIL task. The results are shown in Table 4. The final accuracy of different methods does not vary too much, which indicates designing a better network backbone cannot mitigate catastrophic forgetting. In contrast, our method can surpass all the baselines + +Table 4. Results on different backbones. + +
PointNet++DGCNNPointNeXt
LastAvgLastAvgLastAvg
iCaRL76.3381.5974.3681.6973.3381.09
DER80.0286.5079.5685.1180.4885.58
MEMO79.6884.4777.7183.8878.3583.84
Ours82.9786.6082.5887.0982.7986.34
+ +Table 5. Results on different incremental settings. For each incremental setting, we denote it with (#classes in the first task) (#classes in each subsequent task). + +
5-510-510-10
LastAvgLastAvgLastAvg
iCaRL55.7763.8155.1464.7657.9167.98
DER59.2468.6758.2667.4364.0367.25
MEMO56.7965.7358.8967.7260.9770.67
Ours63.3473.9966.7477.1075.7578.04
+ +on final accuracy and average accuracy. This superiority is primarily attributed to dedicated network designs that are more discriminative to mitigate catastrophic forgetting than other backbones. + +3D CIL Settings We introduce experiments with a setting of a different number of base classes and incremental classes as shown in Tab. 5. We observe that our method still outperforms other methods even though the number of classes in the first task and the number of classes in each task have changed. It validates the robustness of our method to help mitigate catastrophic forgetting across various experimental setups. By comparing the settings of 5-5 and 10-5, we can see that the final accuracy increases if more base classes are given. This is because the first task has more data to learn a better feature representation leading to good results in the final evaluation. The setting of 10-10 archives much higher final accuracy than that of 10-5. This is because fewer learning tasks will lead to less confusion between classes from different tasks and less forgetting of knowledge. + +# 4.4. More Analysis + +The Confusion Matrices. The confusion matrices of the final task are shown in Fig. 6 for different methods. The former 25 classes are base classes, and the rest 25 classes are incremental classes. In these figures, brighter colors indicate higher accuracy while darker colors denote lower accuracy. We can see that the diagonal line of Our method gets brighter colors, while ER and DER perform worse, especially for the first 25 classes. Both ER and DER are more likely to produce more wrong predictions above the diag- + +![](images/31884a9dde2e9300a58663ce62345502d1898469b7fe0d14e482fa1882676fca.jpg) +ER + +![](images/2142ca16901e5a2f90b60c6766bc88e5fcd252c78e5d719ff975b40b36120c14.jpg) +DER + +![](images/206ae891070fc1f6c8cb32a860f3b8dc73bde353170c851c1b9917aaef078c2d.jpg) +Ours + +![](images/d0efce400081766abab3889760e9a3291cbe82e8521ac3b5eca2ddc3ed034d20.jpg) + +![](images/4aef5c1d92bd537f0791971b9d421d70643af40251e2baf4470d8d4a4ff71759.jpg) +iCaRL + +![](images/0cd0c7b084abf8356add7b176ff5f248d6d5da08f11d5e4f29db56bc019a0680.jpg) +Figure 6. Visualization of the confusing matrix after the last incremental task. +DER + +![](images/751c000763e6bfa14b4d3a56d551896faa43cc7e9cc5ad0d5fa94171748798da.jpg) +MEMO + +![](images/294e1e4d84c9d12197d49afa9c50f4445e5a9de2f8c4461ccad2c842961584c7.jpg) +Ours + +![](images/4d03a863e9ed0dd8749d8ddae38a6edc7b15c954100a37a0e2940c6fffe75b35.jpg) +iCaRL +(b) Five classes in an old task & another five classes in a new task +Figure 7. Visualization of the embedding spaces of classes between two different tasks with 2D t-SNE for different methods. The first row shows the embedding of five old classes, and the second row shows the embedding of five new classes. + +![](images/5c91768a04e6d9cdd2b9bb708fc8b6524f88b0421530bf5c500f0f7a55c82894.jpg) +(a) Five classes in an old task +DER + +![](images/235014a05ab6973f5eb3a929278752f1dbf0b811a29416cb10b8f87df4dc3ade.jpg) +MEMO + +![](images/93c870e134bd7942ee187bc3eab60b4c88c35837f984391410f1d691b8d18f5d.jpg) +Ours + +onal line than ours, indicating these two methods bias the prediction towards classes from later tasks. The confusion matrices of ER also present more bright dots than DER and ours, suggesting the method is more probable to classify new classes from later tasks to old classes from early tasks. Feature Embedding. We visualize the embedding space in Fig. 7 with t-SNE [37], where learned features of five classes from two different tasks are shown in various colors, respectively. Compared to other baselines, ILPC can preserve the relatively compact embedding of old classes in previous tasks, while pushing away embedding regions of new classes to a greater extent. ILPC can discriminate classes from different tasks better therefore avoiding knowledge forgetting. + +# 5. Conclusion + +This work introduces a novel framework for 3D CIL that leverages part concepts and part-wise relations. These con + +cepts, widely shared across different tasks, improve the model's ability to recognize shapes consistently. Additionally, learning task-wise affinities for classification head fusion minimizes task bias. Extensive experiments demonstrate that our method outperforms all baselines on all three benchmarks. This work opens doors for further research on fine-grained concept learning in 3D data. + +While our method achieves strong performance, some limitations exist. 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Henaff2 1Google 2Google DeepMind 3Tübingen AI Center, University of Tübingen 4University of Cambridge + +# Abstract + +Knowledge distillation (KD) is the de facto standard for compressing large-scale multimodal models into smaller ones. Prior works have explored ever more complex KD strategies involving different objectives, teacher-ensembles, and weight inheritance. In this work, we explore an alternative, yet simple approach—active data curation as effective distillation for contrastive multimodal pretraining. Our simple online batch selection method, ACID, outperforms strong KD baselines across various model-, data- and compute-configurations. Further, we find such an active curation strategy to in fact be complementary to standard KD, and can be effectively combined to train highly performant inference-efficient models. Our simple and scalable pretraining framework, ACED, achieves state-of-the-art results across 27 zero-shot classification and image-text retrieval tasks with upto $11\%$ less inference FLOPs. We further demonstrate that ACED yields strong vision-encoders for training generative multimodal models, outperforming larger vision encoders on image-captioning and visual question-answering tasks. + +# 1. Introduction + +Deploying multimodal foundation models [14] like CLIP [119] on edge devices is challenging due to their high inference costs and memory footprints. This motivates the need for smaller, inference-efficient models that retain the performance of their larger counterparts. Knowledge distillation (KD) [65] is a classic model compression technique—a method for transferring knowledge from a large-scale “teacher” model into a smaller “student” model, via matching student and teacher logits, features or activations. KD has been extensively deployed for creating small, performant models like Gemma-2 [148], Phi-3 [4], Gemini-1.5 Flash [126], and SD3-Turbo [136]. + +![](images/577cff678e4e037602e7b4040a1e01d2695ef4515ae0a5a20246fbf55f3b149b.jpg) +Performance vs. Inference Compute Frontier +Figure 1. Performance-Inference Frontier. Our ACED models (Active Curation with Explicit Distillation, see Sec. 3), achieve a new pareto frontier for performance (measured by ImageNet top-1 zero-shot validation accuracy) vs. inference GFLOPs. + +Here, our primary goal is to downscale contrastive vision-language models, without compromising downstream performance. Prior works in this domain focus on complex KD strategies as the key solution—the current SoTA (TinyCLIP [173] and MobileCLIP [155]) use combinations of methods such as strong data-augmentation policies, multi-teacher ensembles, synthetic captions, weight-inheritance, weight-pruning, and bespoke model architectures. + +In this work, we seek a simplified approach. Specifically, we propose using active data curation as an effective strategy for distilling large vision-language models (VLMs) into smaller and more FLOP-efficient multimodal models. + +Our method, ACID (Active Curation as Implicit Distillation), automatically selects samples that reduce the performance gap between a small student model and a larger reference model. Under appropriate conditions, we find this is a surprisingly effective distillation approach. To the best of our knowledge, this is a novel finding since prior works in + +data curation assume that larger models can not be used to select data for smaller ones, due to the capacity gap [48, 107]. Through a novel theoretical interpretation and extensive experiments, instead, we demonstrate that ACID is not only effective but also improves over standard KD, exhibiting more favourable scaling with respect to training compute. We also conduct careful ablation studies that uncover factors influencing the quality of the trained student model, including, reference model capacity and training dataset. + +After comprehensively demonstrating the effectiveness of data curation as an alternative to KD, we further show how the two can be profitably combined to further improve performance. This suggests that the information distilled to the smaller model through each approach is complementary. + +Based on this finding, we propose our final pretraining recipe, $ACED$ (ACID with Explicit Distillation), and train very strong FLOP-efficient image-text contrastive models. Our method, absent bespoke components such as efficient architectures or data-augmentations, outperforms SoTA CLIP and SigLIP models with greater FLOP-efficiency at inference-time and shows a significant improvement over 27 downstream tasks against these prior SoTA FLOP-efficient models [155, 173]. We further demonstrate that our $ACED$ vision-encoders provide strong backbones for generative multimodal models, outperforming larger and FLOP-inefficient vision-encoders on image-captioning and visual-question-answering (VQA) tasks. + +# 2. Related Work + +Multimodal Data Curation. Recent works have emphasised the importance of data quality for multimodal pretraining [41, 48, 106, 109, 153]. Specifically, offline curation of noisy web-scale data can result in large pretraining efficiency gains [1, 2, 19, 20, 42, 69, 101, 103, 160, 169, 178]. However, these static methods that pre-filter data do not take into account the training dynamics of the current learner model. As a result, there have been many recent attempts to introduce online batch selection criteria that account for the current state of the learner (e.g., at each step select training samples that have the largest learner loss) [67, 70, 73, 100, 137, 143, 170, 177, 197]. The RHO-Loss [107] goes further to consider current learner state and a pretrained data selector (reference) model. This criterion has since been used in many efforts to improve the efficiency of foundation model pretraining [17, 31, 34, 35, 39, 66]. As these methods seek to improve pretraining efficiency, the pretrained reference models that are used as data selectors are typically smaller than the learner models they are used to train [34, 35, 42]. In fact, many works have shown that increasing reference model size can potentially hurt learner model performance [42, 48, 186]. Our work tells a different story, finding that large data selectors can effectively curate data for inference-time FLOP-efficient learner models. + +Knowledge Distillation. First introduced by Bucilua et al. [18] and further popularized by Ba and Caruana [7], Hinton [65], knowledge distillation (KD) is a classic technique for transferring knowledge from a larger model (teacher) to a smaller one (student) by optimizing the student to match outputs of the teacher. Such methods have been used for compressing large models in unimodal tasks like image-classification [12, 25, 113, 149, 158, 165] and language representation learning [5, 55, 76, 95, 134, 146, 179]. Further works have extended KD to use teacher-ensembles [21, 37, 105, 135, 141, 145, 185, 200], and different distillation training objectives [68, 92, 122, 147, 151, 175, 196]. + +Most relevant to our work, there are a number of recent efforts to distill CLIP models. SF-CLIP [133] explores masked distillation, while MobileCLIP [155] uses multi-teacher contrastive-KD, synthetic captions, and data-augmentations. TinyCLIP [173] proposes a weight inheritance method combined with an affinity-mimicking strategy. An empirical study (CLIP-KD [180]) also has explored different objective functions for effectively distilling CLIP models, across different scales. Finally, CLIP-CID [183] uses an image semantic balancing strategy coupled with cluster-instance discrimination for better teacher-to-student knowledge transfer during the KD process. We compare against all of these methods in our experimental results in Sec. 4. + +Accelerating Knowledge Distillation. Prior works have investigated accelerating vanilla KD using active learning in small-scale settings [83, 163, 176]. However, these approaches require a costly iterative process, involving synthetic generation, followed by active sample selection to produce pseudo-labels from a teacher model, thereby limiting their scalability. Other works have studied data-selection methods for improving KD, typically using uncertainty-based data, logit and feature selection [59, 90, 97, 123, 130, 161, 162, 172, 199], contextual retrieval and sample augmentation from a large data pool [50, 71, 94, 98, 118, 191], or influence-function based sample selection [83, 184]. Contrary to these works, others suggest that vanilla knowledge distillation is optimal in "infinite-data regimes" [12, 57]. Surprisingly, these studies operate primarily in the unimodal image/text classification regime, and none have been scaled to multimodal foundation model training. + +We showcase, for the first time, that simple data selection using online batch selection outperforms standard KD for pretraining multimodal models. We further study the optimal strategies for combining vanilla KD and active data curation in order to best leverage their complementary strengths. + +# 3. Methods + +# 3.1. Preliminaries + +Contrastive Vision-Language Pretraining. We follow standard multimodal pretraining frameworks like CLIP [119] + +and SigLIP [190]. We assume a large pretraining dataset $\mathcal{D}$ , containing image-text pairs. Our goal is to train a two-tower VLM with parameters $\theta$ whose image-encoder $f^{\mathrm{img}}$ and text-encoder $f^{\mathrm{xt}}$ are initialized from scratch. At each training step, we sample a mini-batch, $\mathcal{B} = \{x_1,\dots ,x_b\}$ , where $x_{i} = (I_{i},T_{i})$ denotes the $i^{\mathrm{th}}$ image-text pair in the minibatch and $b$ denotes the batch-size. We then encode and normalize the embeddings of each image-text pair in the mini-batch as $z_i^{\mathrm{img}} = \frac{f^{\mathrm{img}}(I_i|\theta)}{\|f^{\mathrm{img}}(I_i|\theta)\|_2}$ and $z_{i}^{\mathrm{xt}} = \frac{f^{\mathrm{xt}}(T_{i}|\theta)}{\|f^{\mathrm{xt}}(T_{i}|\theta)\|_{2}}$ . The pairwise similarities $l_{ij}(\theta) = \alpha z_i^{\mathrm{img}}\cdot z_j^{\mathrm{xt}} + \beta$ , where $\alpha, \beta$ are learnable inverse-temperature and offset hyperparameters, can be converted into pairwise probabilities with a row- or column-wise softmax as follows, + +$$ +p _ {i j} ^ {\mathrm {i m g} \rightarrow \mathrm {t x t}} = \exp (l _ {i j}) / \sum_ {k = 1} ^ {b} \exp (l _ {i k}) \tag {1} +$$ + +$$ +p _ {i j} ^ {\mathrm {t x t} \rightarrow \mathrm {i m g}} = \exp (l _ {i j}) / \sum_ {k = 1} ^ {b} \exp (l _ {k i}) \tag {2} +$$ + +or $p_{ij}^{\mathrm{sig}} = \sigma (l_{ij})$ with a sigmoid operation. The contrastive image-text losses align embeddings of paired images and texts $(z_i^{\mathrm{img}}, z_i^{\mathrm{txt}})$ , while pushing apart embeddings of mismatched images and texts $(z_i^{\mathrm{img}}, z_{j \neq i}^{\mathrm{txt}})$ . There are two widely used contrastive variants i.e., $\mathcal{L}_{\mathrm{softmax}}$ for CLIP [119] and $\mathcal{L}_{\mathrm{sigmoid}}$ for SigLIP [190], both of which can be framed as $\mathcal{L}(x_i; \mathcal{B}) = -\sum_{j=1}^{b} y_j(x_i) \log p_{ij} = \mathrm{CE}[y(x_i); p(x_i)]$ for a suitable choice of binary labels $y$ and probabilities $p$ , where CE is the standard cross-entropy loss (see Appendix B for details). By default, we use the sigmoid variant as it is more scalable, but also run ablations with the softmax variant. + +Contrastive Distillation. Given the student $\theta$ and a pretrained teacher model $\theta_{\mathrm{teacher}}$ , our aim is to distill the contrastive logit matrix from teacher to student. Formally, given a data-batch $\mathcal{B}$ , we extract teacher embeddings $(z_i^{\mathrm{img}}, z_i^{\mathrm{xt}})(\theta_{\mathrm{teacher}})$ and student embeddings $(z_i^{\mathrm{img}}, z_i^{\mathrm{xt}})(\theta)$ , yielding pairwise similarities $l_{ij}(\theta_{\mathrm{teacher}})$ and $l_{ij}(\theta)$ for the teacher and student respectively. Let $p$ and $q$ be the pairwise probabilities induced by teacher and student similarities (Eqs. (1) and (2)). Our knowledge distillation (KD) objective is simply the cross-entropy loss between these distributions: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {d i s t}} \left(x _ {i}; \mathcal {B}\right) = \mathrm {K D} \left[ p \left(x _ {i}\right), q \left(x _ {i}\right) \right] = \\ - \frac {1}{2} \sum_ {j = 1} ^ {b} \left(p _ {i, j} ^ {\mathrm {i m g} \rightarrow \mathrm {t x t}} \log q _ {i, j} ^ {\mathrm {i m g} \rightarrow \mathrm {t x t}} + p _ {i, j} ^ {\mathrm {t x t} \rightarrow \mathrm {i m g}} \log q _ {i, j} ^ {\mathrm {t x t} \rightarrow \mathrm {i m g}}\right) \tag {3} \\ \end{array} +$$ + +which has previously been explored in unimodal [45, 181] and multimodal contexts [183]. + +# 3.2. ACID: Active Curation as Implicit Distillation + +Setup. We refer to the small model we aim to train as the student model, with parameters $\theta$ . Given an image-text pretraining dataset $\mathcal{D}$ , the straightforward training approach is to sample uniformly random batches of data $\mathcal{B}$ (of size $b$ ), from $\mathcal{D}$ at each step $t$ , and minimize $\mathcal{L} \in \{\mathcal{L}_{\mathrm{softmax}}, \mathcal{L}_{\mathrm{sigmoid}}\}$ . We refer to this baseline strategy, minimizing $\hat{\mathcal{L}} = \frac{1}{b} \sum_{x_i \sim \mathcal{U}[\mathcal{D}]} \mathcal{L}(x_i; \mathcal{B})$ as the IID-baseline ( $\theta_{\mathrm{IID}}$ ) + +Active Data Curation employs a smarter way to select batches, using a pretrained reference model $\theta_{\mathrm{ref}}$ . At each step $t$ , we select a sub-batch $\mathcal{B}$ (size $b$ ) from a much larger super-batch $\mathcal{S}$ (size $B$ ) according to an active selection distribution $\mathcal{A}[\mathcal{S}]$ . We use two main criteria for scoring sub-batches $\mathcal{B}$ , following prior work in prioritized sampling [34, 107]. + +1. Easy-reference scoring uses the loss-values of the reference $\theta_{\mathrm{ref}}$ to preferentially sample batches that are easy for $\theta_{\mathrm{ref}}$ : $s^{\mathrm{easy\_ref}}(\mathcal{B}|\theta_{\mathrm{ref}}) = -\mathcal{L}(\mathcal{B}|\theta_{\mathrm{ref}})$ . +2. Learnability scoring uses the difference in loss-values of the current student $\theta$ and the reference $\theta_{\mathrm{ref}}$ to give high scores to learnable batches i.e., batches that are easy for the reference but difficult for the current student: $s^{\mathrm{learn}}(\mathcal{B}|\theta ,\theta_{\mathrm{ref}}) = \mathcal{L}(\mathcal{B}|\theta) - \mathcal{L}(\mathcal{B}|\theta_{\mathrm{ref}})$ . + +Prior model-based online batch curation methods used reference models that were of the same size or smaller than the model being trained. This was because of (1) training efficiency: since data-selection was originally used to reduce training set sizes, reference models were chosen to be small so as to reduce compute overhead, and (2) unlearnable prioritization: intuitively, samples that are easily learned (and thus prioritized) by a high-capacity reference might be unlearnable for the lower-capacity learner. Indeed Mindermann et al. [107] observed little effect when increasing reference model capacity, a key limitation of their original method. + +Active Data Curation as Implicit Distillation (ACID). We now show formally that active curation can be cast as "implicit distillation" and should benefit from larger reference models. The model now minimizes $\hat{\mathcal{L}} = \frac{1}{b}\sum_{x_i\sim \mathcal{A}[S]}\mathcal{L}(x_i;\mathcal{B})$ , which in expectation is $\mathcal{E} = \mathbb{E}[\hat{\mathcal{L}}] = \sum_{x\in \mathcal{D}}a(x)\mathcal{L}(x;\mathcal{B})$ given that super-batches $S$ are sampled uniformly. Recall that $\mathcal{L}(x;\mathcal{B}) = -\sum_{i = 1}^{b}y_{i}(x)\log q_{i}(x)$ where $y_{i}$ are the labels of the contrastive task and $q_{i}$ are the probabilities induced by the pairwise similarities of the student $\theta$ . Let $p_i$ be the probabilities induced by the reference model $\theta_{\mathrm{ref}}$ . In the case of easy-reference scoring and the softmax loss, $a(x) = \frac{1}{Z}\exp \sum_{i = 1}^{b}y_{i}(x)\log p_{i}(x) = \frac{1}{Z} p_{i^{*}}(x)$ where $i^{*}$ is the index of the one-hot label $y(x)$ . We derive the following equality (see Appendix C for details), + +$$ +\mathcal {E} _ {\text {e a s y - r e f}} = \frac {1}{Z} \sum_ {x \in \mathcal {D}} \mathrm {K D} [ p (x) \cdot y (x); q (x) ]. \tag {4} +$$ + +This demonstrates that by curating data according to the + +![](images/68b2d555f6eb1212005b5208a26ea97e7987e426831ec86d6748b996038b5a59.jpg) +Figure 2. Different Method Configurations. We depict all the different method configurations that we consider in our work. Each method can be independently recovered from the unified objective $\mathcal{L}_{\mathrm{full}}$ in Sec. 3.3. The iid-sample and acid-sample boxes denote the IID-sampling and our ACID online batch-selection sampling schemes respectively. For more details, refer to Sec. 3. + +reference model $\theta_{\mathrm{ref}}$ , we implicitly distill its knowledge via a novel data-driven objective, using a combination of model predictions and real labels as targets. Model predictions and real labels have independent sources of noise: false labels can occur due to human error, whereas models may underfit due to biases in training or architecture. As a result, retaining targets where the reference model and labels agree allows for mutual denoising of model predictions and data labels. + +Moreover, this suggests that in contrast to the standard active learning paradigm, in which reference models are similarly-sized or smaller than the student model [34, 107], ACID should instead benefit from pretrained reference models $\theta_{\mathrm{ref}}$ that are larger than the student model $\theta$ for scoring. While counter-intuitive from an active learning perspective, this configuration is natural given our new perspective of active data curation as an implicit form of distillation. + +Learnability-based Data Curation is Hard Distillation. When using learnability-based prioritization, the active selection distribution $\mathcal{A}$ factorizes as $a^{\mathrm{learn}} = \frac{1}{Z}\exp (s^{\mathrm{learn}}) = \frac{1}{Z}\exp [\mathcal{L}(\cdot |\theta) - \mathcal{L}(\cdot |\theta_{\mathrm{ref}})] = a^{\mathrm{easy - ref}}\cdot a^{\mathrm{hard - learn}}$ where $a^{\mathrm{hard - learn}} = \frac{1}{Z}\exp [\mathcal{L}(\cdot |\theta)]$ prioritizes examples with high loss according to the student. Since easy-reference prioritization yields implicit distillation (I-ACID, Eq. (4)), learnability prioritization yields + +$$ +\mathcal {E} _ {\text {l e a r n}} = \frac {1}{Z} \sum_ {x \in \mathcal {D}} a ^ {\text {h a r d - l e a r n}} (x) \mathrm {K D} [ p (x) \cdot y (x); q (x) ] \tag {5} +$$ + +i.e. implicit distillation on hard examples ("H-ACID") according to the student (see Appendix C for details). Prioritizing high-loss examples has been shown to reliably accelerate learning in settings where targets are high-quality [100], as is the case with the combined targets in our ACID. + +Joint Batch Sampling. Implementing our ACID method requires sampling examples $x$ from $\mathcal{A}[S]$ where $a(x|\mathcal{B}) = \exp(-\mathcal{L}(x|\mathcal{B}, \theta_{\mathrm{ref}}))$ for ACID or $a(x|\mathcal{B}) = \exp(\mathcal{L}(x|\mathcal{B}, \theta) - \mathcal{L}(x|\mathcal{B}, \theta_{\mathrm{ref}}))$ for Hard-ACID. As such, sampling from $\mathcal{A}[S]$ requires jointly selecting examples in a batch. Following Evans et al. [35] we utilise an iterative approach which incrementally populates the batch conditioned on already-sampled examples. Specifically, this algorithm uses $n$ iterations of a blocked Gibbs sampling approach. Given a subset of data-samples $\mathcal{B}_i$ at iteration $i$ , we compute the conditional batch-scores of all other candidate samples in the super-batch that have not yet been added to the minibatch $\mathcal{B}_i$ , $s^{\text{easy\_ref}}(\{\mathcal{B}_i, x\}) / s^{\text{learn}}(\{\mathcal{B}_i, x\}) \forall x \in S - \mathcal{B}_i$ , then sample a chunk $\{x_k\}$ of size $\frac{b}{n}$ according to these scores independently, and append to the constructed mini-batch, $\mathcal{B}_{i+1} = \mathcal{B}_i \cup \{x_k\}$ . The first chunk $\mathcal{B}_1$ is sampled using the independent scores $s^{\text{easy\_ref}}(\{x\}) / s^{\text{learn}}(\{x\})$ . The final sampled mini-batch is yielded after $n$ iterations, $\mathcal{B} = \mathcal{B}_n$ (see Evans et al. [35] for more details). Note that the ratio of the super-batch size and the mini-batch size determines how aggressively our data selection method filters out samples from the super-batch—we quantify this with the filtering ratio, $f = 1 - \frac{b}{B}$ . The larger the filtering ratio $f$ , the stronger is the data selection process at each training step. + +# 3.3. ACED: Active Curation & Explicit Distillation + +Towards explicit knowledge-transfer. ACID introduces an active curation strategy without using any auxiliary objective beyond the contrastive loss. This induces an implicit form of knowledge transfer from the larger reference model to the small student model. To augment this implicit transfer with an explicit distillation objective, we propose ACED, ACID with Explicit Disillation, which effectively combines ACID + +
MethodλBCEBKDEffective Batch-Size per Iteration
IID-Baseline=0IIDb
Softmax-KD>0IIDIIDb
I-ACID=0I-ACIDb
H-ACID=0H-ACIDb
ACED-IIDistill>0H-ACIDIID2b
ACED-ACIDistill>0H-ACIDH-ACIDb
+ +Table 1. Method Instantiations recovered from our unified objective (see Sec. 3.3), by specifying data-selection strategies across different batches and hyperparameter values. We further indicate the effective mini-batch size per-iteration used by each method, and colour-code different methods for easy referencing from Sec. 4. + +with a softmax contrastive distillation loss (see Eq. (3)). + +A unified objective. We now propose a general loss formulation that can flexibly model different instantiations of all our training methods (IID-Baseline, ACID, ACED, and Softmax-KD) under one unified objective. At each step $t$ , we first sample the super-batch $S$ based on the required final mini-batch size $b$ and filtering ratio $f$ (super-batch size is $B = \frac{b}{1 - f}$ ). We then sample two mini-batches from $S$ — the data mini-batch used for training the contrastive loss $(\mathcal{B}_{\mathrm{CE}})$ and the mini-batch used for distillation $(\mathcal{B}_{\mathrm{KD}})$ . The two minibatches can either be sampled using our ACID sampling scheme or random IID sampling. Our overall objective is written as, $\mathcal{L}_{\mathrm{full}} = \mathcal{L}_{\mathrm{softmax / sigmoid}}[\mathcal{B}_{\mathrm{CE}}] + \lambda \cdot \mathcal{L}_{\mathrm{dist}}[\mathcal{B}_{\mathrm{KD}}]$ . + +Tab. 1 and Fig. 2 depict how we can instantiate $\mathcal{L}_{\mathrm{full}}$ to recover different methods and baselines—we colour-code different methods to enable easy cross-referencing later from Sec. 4. Our IID-Baseline only uses the contrastive loss trained on an IID-sampled batch. Our implicit distillation methods $(\{I / H\} - ACID)$ also use only the contrastive loss but train on actively selected data-batches. For SoftmaxKD, we only sample an IID batch and use that same batch for both contrastive and distillation losses ( $\mathcal{B}_{\mathrm{CE}} = \mathcal{B}_{\mathrm{dist}}$ ). For our combined ACED method, we have two schemes—(1) ACIDstill which samples a single mini-batch from $S$ using $H$ -ACID, using that for both contrastive and distillation training ( $\mathcal{B}_{\mathrm{CE}} = \mathcal{B}_{\mathrm{KD}}$ ), and (2) IIDistill which samples $\mathcal{B}_{\mathrm{CE}}$ using $H$ -ACID and $\mathcal{B}_{\mathrm{KD}}$ using IID sampling. For both ACED methods, we only use the $H$ -ACID sampling scheme as empirically it is more performant than I-ACID (see Fig. 4). + +# 4. Experiments + +# 4.1. Implementation Details + +Model Architecture and Sizes. Unless otherwise specified, we use standard ViT-S [33] and BERT-small [32] models as our student image-text encoders. For some student ablations, we also use (ViT-Ti image, Ti text) and (ViT-B image, B text) configurations. For our references and teachers, we sweep over different sizes—(ViT-Ti, Ti), (ViT-S, S), (ViT-B, B), (ViT-L, L), (ViT-H, H), and (ViT-g, g) for (image, text) encoders respectively. We pretrain all our models ( $\theta_{\text{teacher}}$ , + +![](images/a062b2c2601583ae3e85831ed58e0ed5cac7174e567a0e19d88bad7059a5f515.jpg) +StableEval: Removing Unreliable Evals +Figure 3. StableEval: a reliable set of multimodal evaluations. (left) Variability across random pretraining seeds of individual evaluations. (right) Variability of average performance across incrementally larger sets of evaluations, starting from the most reliable. + +$\theta_{\mathrm{ref}}, \theta)$ from scratch. For more details, refer to Appendix F. + +Pretraining Datasets. We use the popular DataComp-1B [48] dataset for pretraining all our student models. For training our reference and teacher models, we sweep over four different datasets—WebLI-curated++ [35], WebLI-1B [24], LAION-400M [138], and DataComp-1B [48]. + +Evaluation Protocol: StableEval. We evaluate our models on a diverse set of benchmarks including zero-shot classification and image-text retrieval datasets following prior multimodal pretraining works [48, 84, 178]. However, many works select non-standardized sets of evaluations and fail to sufficiently justify the reliability of the evaluations they use. To rigorously define an evaluation suite, we collate a standard list of 34 candidate evaluations and conduct a systematic analysis of their reliability. By repeating the same canonical pretraining run multiple times (e.g., CLIP pretraining on DataComp with the exact same data ordering, see Appendix A for details), we evaluate the variability of each metric across random seeds. In Fig. 3 (left), we find an extreme range in variability across evaluations (stds from $0.15\%$ to $12.5\%$ ) which hinders comparisons among different methods. Inspired loosely by the continuous inverse-variance weighting (IVW) method for minimizing variance of aggregated random variables [58], we develop a method for choosing a discrete, stable subset of relevant evaluations. We compute the variability of a progressively growing set of evaluations, starting from least variable and incrementally adding more variable ones, in ascending order. For a subset of size $N$ , $\text{std}(E_1 \ldots E_N) = \sqrt{\frac{1}{N^2} \sum_i \text{var}(E_i)}$ . Because of the $1/N^2$ scaling, adding more datasets decreases the variability of the average (Fig. 3 (right)) to a critical point. However, adding highly variable evaluations outweighs this term, increasing the average variability. We limit the evaluation set to remain highly reliable (i.e. with lower variability + +![](images/7dc2575b785bc658a6bbf9c0e4beb0a0cc538fbb0bccd26397a29fe358824515.jpg) +Figure 4. Scaling behaviour of ACID. (left) We scale up the reference model used for training each student (Ti, S and B) with $H$ -ACID—there is an optimal scaling relationship (best reference for each student marked with $\star$ ) between student and reference sizes. (right) Our $H$ -ACID and $I$ -ACID comprehensively outperform Softmax-KD across all teacher scales. Importantly, our ACIDs outperform the IID baseline even for tiny reference models, whereas Softmax-KD struggles to improve over IID with smaller teachers. + +![](images/60649deef30a1332ec5c941b3c34df2514b168f5b7224042dd38b78b08e19b59.jpg) + +than the most reliable individual evaluation $(< 0.15)$ ) while still including as many evaluations possible to maximize coverage and diversity, yielding the 27 StableEval set. + +Training Configurations. Unless otherwise specified, we train for 3 billion total samples seen, with a batch-size of $b = 32$ , 678 with the sigmoid contrastive loss (Eq. (7)). The image-encoder takes images resized to $(256 \times 256)$ without additional augmentations. The text-encoder uses a sentencepiece tokenizer [80] trained on English-C4 [120], with a vocabulary size of 32,000. We truncate all text captions to the first 64 tokens. For most experiments, we use an rsqrt learning rate scheduler [189], with a peak learning-rate of 0.001, and linear-warmup and linear-coutdown applied for $10\%$ of total steps. By default, we use a filtering ratio of $f = 0.8$ when using ACID sampling, leading to a super-batch-size of $B = 163$ , 840. We sweep over $\lambda = \{0.5, 1.0, 2.0\}$ for finding the optimal loss-weight for the Softmax-KD loss (Eq. (3)). For more details, refer to Appendix E. + +# 4.2. ACID is an effective distillation method + +# 4.2.1. Scaling behaviour + +To study the efficacy of ACID as an effective distillation method, we first conduct a scaling study as the reference/teacher model size is increased. We use Hard-ACID as our sampling scheme, and start with three fixed student models, Ti, S and B. We train each student by sweeping over (Ti, S, B, L, H and g) reference model sizes. Each reference model is trained on the WebLI-curated++ dataset for 2B samples seen, to ensure that the only difference across the experimental sweep is the size of the reference. Fig. 4 (left) showcases the scaling behaviour of each of the trained students, as the reference model is scaled up. We observe that across all student and reference models, our ACID method always outperforms the IID-baseline (dotted lines). Moreover, we note that the best reference-student combination (high + +lighted with $\star$ ) changes as we scale up the student sizes—the B reference is best for the Ti student, L reference for S student, and g reference for B student. This suggests an optimal reference-student capacity ratio—we can continue scaling up the reference model for ACID sampling until we hit this capacity ratio, beyond which performance saturates. + +In Fig. 4 (right), we compare the scaling behaviour of our ACID variants (both I- and H-) with the Softmax-KD baseline, using an S student model. We note that across all reference/teacher scales, our ACID methods are more effective at distilling the knowledge into the smaller S student. Moreover, both versions of our method outperform the IID baseline, even when using a smaller Ti reference model. Contrarily, Softmax-KD only benefits when using much larger teacher models—this further demonstrates the scalability and flexibility of our ACID distillation. Since H-ACID demonstrates better scaling than I-ACID, we use that as our default in all further sections, and refer to it as our canonical ACID (dropping the H- for better readability). + +# 4.2.2. ACID outperforms standard distillation + +Having demonstrated the favourable scaling behaviour of ACID vs. Softmax-KD using a single teacher/reference model dataset, we next demonstrate that ACID outperforms explicit distillation across different teacher/reference pretraining datasets, objective functions, and student model sizes. + +Reference/Teacher Training Dataset. In Fig. 5 (left), we sweep over two different pretraining datasets for the references/teachers. We train an L-sized teacher/reference for 2B samples seen on WebLI-curated++ and WebLI. Using these models as teacher/reference, we train S students with ACID, that strongly outperform Softmax-KD for both datasets. + +Different Distillation Objectives. Prior works have explored several different objectives for multimodal distillation, beyond standard Softmax-KD. Here, we compare our ACID method to some of these, including a Sigmoid-KD loss [173] and a Feature-Matching KD loss [180] (see Appendix D for more details). Further, the SoTA multimodal distillation method, CLIP-KD [180], advocates combining these losses for best performance. We therefore also compare against two combination methods—Softmax+Sigmoid and Softmax+Feature-Matching. In Fig. 5 (center), we show that ACID, without any additional complexity, still comprehensively outperforms all of the other distillation objectives. Different Student Sizes. Finally, we also sweep across student sizes—Ti, S, and B. From Fig. 5 (right), we again observe that our ACID substantially improves over Softmax-KD. Interestingly, we note that our ACID method is more effective for smaller students (Ti, S) than the larger B student, whereas this is the opposite for the Softmax-KD baseline. + +# 4.3. ACED: ACID and KD are complementary + +Combining ACID and Softmax-Distillation—Why? Theoretically in Sec. 3.2, we show ACID is in fact a form of + +![](images/a2e10392d32b19752c2cd6904db371df4a1b4822e82e2fac2a6f3469ece204a1.jpg) +ACID vs KD across data configurations + +![](images/7b442eafed9cbb717fcdb2e7e7f8b13e744bdd373186dea298537ce9d8163d4d.jpg) +Figure 5. ACID significantly outperforms KD. (left) We vary the training dataset of the reference/teacher model, and use the same pretrained model as the reference for ACID and teacher for KD—across all configurations, we note strong gains for ACID. (center) Across different distillation objectives and a full hyperparameter sweep for optimal KD conditions, ACID is still the best performing method by large margins. (right) ACID further outperforms KD across three different student sizes. + +![](images/2ea1ff95157858cce28bebb04cd3a71bb505f3a60c9fd76d126d74218407225b.jpg) +ACID vs different KD method configurations +ACID vs KD across student configurations + +![](images/f78ccbbe7b05cfab0f28e926a35a35c6220d5bbded9cccc61d0d54bc897fa56b.jpg) +Figure 6. ACED for improved distillation. (left) Despite ACID outperforming KD across most benchmarks, it still suffers on 4 out of 27 evals (potentially due to filtering out data). This motivates that combining ACID and $KD$ would enable a stronger, more robust model. (right) Our combined ACED indeed outperforms both ACID and $KD$ , even when using an ensemble of teacher/reference models for ACID and $KD$ , showcasing its generality. + +![](images/c9a3987e3d29248b748ed0653e9ae495012a0f7626e3a9884d97c5145b357549.jpg) + +implicit distillation, yet the exact form of this objective is different from traditional distillation. As a result, here we ask if this form of distillation (although stronger than traditional KD) is in fact complementary to standard distillation. This line of inquiry is further supported by an empirical finding shown in Fig. 6 (left)—while ACID outperforms Softmax-KD by more than $5\%$ on tasks like COCO and Flickr retrieval, it underperforms Softmax-KD on more finegrained evaluations like Cars and DTD. This suggests that despite the implicit distillation performed by ACID, having an explicit distillation objective should further provide wider benefits. + +ACED—How to combine? We now discuss strategies for combining ACID and Softmax-KD. The simple strategy, ACIDistill, samples a training batch using ACID and applies both the contrastive and softmax-distillation loss on that batch. The alternative, IIDistill, samples two batches independently, one with ACID sampling and the other IID sampled, and applies the distillation loss on the IID batch while the contrastive loss is applied on the ACID batch. We study the scaling behaviour of both strategies by training ViT-S students with WebLI-L teachers and WebLI-curated++- + +references, for 3B, 6.5B and 13B samples seen. We observe ACIDistill showcases better performance across all compute budget scales (see Appendix H.1). Hence, going forward, we use ACIDistill as the default strategy for combining ACID and Softmax-KD, and refer to that as our main ACED method. How well does ACED perform? We now compare our optimal ACED method from before with the ACID and Softmax-KD methods applied independently. First, we find that our ACED indeed outperforms both the independent methods, demonstrating that we are effectively able to leverage both the reference and teacher models. As an additional ablation, we also conduct a comparison with an ensemble version of ACID and Softmax-KD, where we use both the WebLI-L and WebLI-curated++-L models as a two-teacher ensemble for Softmax-KD and a two-reference ensemble for ACID. We find that ACED even outperforms these ensemble methods, suggesting that the benefits of our ACED are not solely due to using multiple teacher and reference models, but rather due to optimally combining the two frameworks. + +# 4.4. Comparison to Prior Art + +We now pretrain ACED models at large compute budgets, across three FLOP-scales, and compare with SoTA inference-efficient two-tower VLMs, including MobileCLIP [155], TinyCLIP [173], CLIP-KD [180], CLIP-CID [183] and proprietary DatologyAI-CLIP [3] (see Appendix F). We train our ACED-F0, ACED-F1 and ACED-F2 models on DataComp-1B for 13B samples seen. From Tab. 2, we observe that our ACED models are the most FLOP-efficient and highly performant—ACED-F0 outperforms MobileCLIP-S0 by $0.4\%$ and TinyCLIP-63M/32 by $1.9\%$ , on average, while being $10.81\%$ and $41.5\%$ more FLOP-efficient respectively; our ACED-F1 outperforms MobileCLIP-S1 by $1.8\%$ , and TinyCLIP-39M/16 by $10.2\%$ , on average, while being $6.5\%$ and $24.6\%$ more efficient respectively; ACED-F2 outperforms MobileCLIP-S2 by $1.1\%$ on average, while being $4.8\%$ more FLOP-efficient. Notably, on the most widely-used evaluations like ImageNet, COCO and Flickr, our method surpasses the previous SoTA by large margins— + +
MethodSamples SeenInfer. GFlopsZero-shot ClassificationRetrievalAvg. Perf. (27 evals)
IN-valIN-shiftObject-CentricScene-CentricCOCOFlickr30k
DatologyAI-cls-S/322.0B2.8352.736.668.347.030.248.650.5
DatologyAI-ret-S/322.0B2.8345.635.961.944.941.564.049.3
TinyCLIP-RN30M15.2B**6.9359.143.070.252.743.371.256.6
TinyCLIP-45M/3215.8B**3.7062.748.374.856.645.472.160.4
TinyCLIP-63M/3215.8B**5.6564.550.476.458.347.775.562.1
MobileCLIP-S013B*3.7067.855.277.057.349.676.763.6
ACED-F013B3.3068.556.177.959.451.079.564.0
DatologyAI-cls-B/325.1B7.3963.247.175.452.238.560.858.5
DatologyAI-ret-B/325.1B7.3955.845.969.653.549.672.657.3
CLIP-KD-RN500.5B9.0954.941.661.850.043.571.452.2
OpenAI-RN5013B9.0959.844.665.250.938.768.653.6
OpenAI-CLIP-B/3213B7.3963.350.372.655.240.368.958.6
LAION-CLIP-B/3234B7.3966.652.478.459.547.775.563.7
DataComp-CLIP-B/3213B7.3969.256.180.059.345.470.164.6
MetaCLIP-CLIP-B/3213B7.3967.755.177.959.246.773.063.9
CLIP-CID-B/327.2B7.3962.750.5(-)(-)(-)(-)(-)
TinyCLIP-39M/1620B**9.4863.550.671.656.746.975.659.5
MobileCLIP-S113B*7.6472.663.380.461.653.080.067.9
ACED-F113B7.1474.967.381.864.055.684.769.7
OpenAI-RN10113B12.7562.349.768.453.740.368.656.5
MobileCLIP-S213B*10.8174.468.181.863.654.481.869.8
ACED-F213B10.2976.970.782.364.658.385.370.9
+ +Table 2. ACED outperforms all prior state-of-the-art methods. We showcase results for our method at three different model inference-GFlop scales. Across all three model scales, the performance of our ACED models improves on the prior SoTA across the 27 StableEval evaluation datasets, while using fewer inference FLOPs. For better interpretability, we also break down the evaluations into individual benchmarks (e.g., ImageNet, COCO) and groupings (e.g., ImageNet distribution shifts, other object categorization, and scene classification— for details, see Appendix A). *MobileCLIP samples seen include two captions for each image, effectively doubling the total unique pairs. **TinyCLIP models are not trained from scratch, but use a complex weight inheritance strategy from pretrained models. + +
MethodSamples SeenImage GFlopsCaptioningVQA
Flickr30kVQAv2GQA
SigLIP-B/1640B23.4553.464.554.9
SiLC-B/1620B23.4549.265.754.1
ACED (B/16)13B23.1955.566.655.4
+ +Table 3. LiT-Decoder Evaluations. Our ACED vision-encoders also improve performance of multimodal-decoders on captioning and VQA tasks, when compared to strong SigLIP and SiLC baselines. + +ACED-F0 outperforms MobileCLIP-S0 by $0.7\%$ on ImageNet, $1.5\%$ on COCO, and $2.8\%$ on Flickr; ACED-F1 outperforms MobileCLIP-S1 by $2.3\%$ on ImageNet, $2.6\%$ on COCO, and $4.7\%$ on Flickr, while ACED-F2 outperforms MobileCLIP-S2 by $2.5\%$ on ImageNet, $3.9\%$ on COCO, and $3.5\%$ on Flickr. In fact, our ACED-F1 model even outperforms MobileCLIP-S2 on ImageNet, while having $34\%$ lesser GFlops (see Fig. 1). This further validates the scalability of our ACED, especially given our models do not use any bespoke architectures or complex augmentations. + +# 4.5. ACED yields better encoders for other tasks + +We next evaluate the benefits of ACED specifically for training an auto-regressive text-decoder with a frozen image-encoder, in the LiT-Decoder setting [13]. We evaluate the trained models on Flickr30k [116] captioning (using CIDEr [156]) and visual-question-answering (using accu + +racy). Since prior works on these benchmarks use larger foundation models (e.g., SigLIP [190] and SiLC [108]), we also train a larger ACED (B/16) model for 13B samples seen Tab. 3 demonstrates that our ACED model outperforms both strong baselines across both tasks—particularly, our model outperforms competitors that have similar image-GFlops but are trained for a significantly higher number of samples seen (up to $\sim 3\mathrm{x}$ ). This further highlights the impact of ACED particularly for distilling knowledge in the image-encoders. + +# 5. Conclusion + +In this work we showed that active data curation implicitly implements a novel form of distillation, which combines knowledge from both a reference model and the data itself. With this insight, we developed ACID, a powerful method for distilling large multimodal encoders into much more efficient ones via online joint-example selection [35]. ACID strictly outperforms traditional forms of knowledge distillation in training contrastive VLMs. Given that ACID implicitly optimizes a different objective than traditional softmax-based KD, we further demonstrated these two objectives to be complementary, arriving at our final method, ACED, which combines the benefits of each. Using ACED we distilled models that set a new state-of-the-art for FLOP-efficient zero-shot classification and image-text retrieval. + +Acknowledgements. The authors would like to thank (in alphabetic order of first name) Alexander Kolesnikov, André Susano Pinto, Andrew Zisserman, Diego Martin Arroyo, Karsten Roth, Lucas Beyer, Marco Fornoni, Tianshi Cao, and Xiaohua Zhai for helpful comments, feedback and support throughout the project. + +# References + +[1] Amro Abbas, Kushal Tirumala, Dániel Simig, Surya Ganguli, and Ari S Morcos. Semdedup: Data-efficient learning at web-scale through semantic dedduplication. arXiv preprint arXiv:2303.09540, 2023. 2, 13 +[2] Amro Abbas, Evgenia Rusak, Kushal Tirumala, Wieland Brendel, Kamalika Chaudhuri, and Ari S Morcos. 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Multi-teacher knowledge distillation as an effective method for compressing ensembles of neural networks. arXiv preprint arXiv:2302.07215, 2023. 2, 13 \ No newline at end of file diff --git a/activedatacurationeffectivelydistillslargescalemultimodalmodels/images.zip b/activedatacurationeffectivelydistillslargescalemultimodalmodels/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ff784d935ec889b0641a8de45472c56dc82b30f7 --- /dev/null +++ b/activedatacurationeffectivelydistillslargescalemultimodalmodels/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f3d1040dca2d044fffd7a7831995a5a760c01b3ee3fbd4f3bfbfb992944c321d +size 484259 diff --git a/activedatacurationeffectivelydistillslargescalemultimodalmodels/layout.json b/activedatacurationeffectivelydistillslargescalemultimodalmodels/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c1156fd9b044397a17fb66886c4240a22d958952 --- /dev/null +++ b/activedatacurationeffectivelydistillslargescalemultimodalmodels/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:506764654c2a8431ce7a8187141de160dae3851af5f8fb7842a47be29891487a +size 684948 diff --git a/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_content_list.json b/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2b6480aaeeb33e28e5dc00c965c7038f4a5e98d9 --- /dev/null +++ b/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d3ab2689bdd2f0f39b113d99c2b645e891247d26aacbafb67e741531ddec20a +size 89297 diff --git a/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_model.json b/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b5efe9da6607ebe38a09f430d0f607af56b5085a --- /dev/null +++ b/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c2010864efd9af0805e9a321c9075ef7961c9901177c0e0535840cebfa057e35 +size 115680 diff --git a/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_origin.pdf b/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ecaf121f2ce2bfc5f85443785dd023b4e5ad2c61 --- /dev/null +++ b/activeeventbasedstereovision/facc70e9-e2cd-4cca-ac3d-9def9aed72a7_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:087c54a7b5d247cf9b0ca6578e8c6d4b083866dbdc0067c2a7f2c85205157ea2 +size 5268322 diff --git a/activeeventbasedstereovision/full.md b/activeeventbasedstereovision/full.md new file mode 100644 index 0000000000000000000000000000000000000000..564703d7150b45cf7c6bad3aacd34c9e83b93e89 --- /dev/null +++ b/activeeventbasedstereovision/full.md @@ -0,0 +1,360 @@ +# Active Event-based Stereo Vision + +Jianing Li Yunjian Zhang Haiqian Han Xiangyang Ji Tsinghua University + +lijianing@pku.edu.cn, sdtczyj@gmail.com, hanhq23@mails.tsinghua.edu.cn, xyji@tsinghua.edu.cn + +# Abstract + +Conventional frame-based imaging for active stereo systems has encountered major challenges in fast-motion scenarios. However, how to design a novel paradigm for high-speed depth sensing still remains an open issue. In this paper, we propose a novel problem setting, namely active event-based stereo vision, which provides the first insight of integrating binocular event cameras and an infrared projector for high-speed depth sensing. Technically, we first build a stereo camera prototype system and present a real-world dataset with over 21.5k spatiotemporal synchronized labels at $15\mathrm{Hz}$ , while also creating a realistic synthetic dataset with stereo event streams and 23.8k synchronized labels at $20\mathrm{Hz}$ . Then, we propose ActiveEventNet, a lightweight yet effective active event-based stereo matching neural network that learns to generate high-quality dense disparity maps from stereo event streams with low latency. Experiments demonstrate that our ActiveEventNet outperforms state-of-the-art methods meanwhile significantly reducing computational complexity. Our solution offers superior depth sensing compared to conventional stereo cameras in high-speed scenes, while also achieving the inference speed of up to 150 FPS with our prototype. We believe that this novel paradigm will provide new insights into future depth sensing systems. Our project can be available at https://github.com/jianing-li/active_event_based_stereo. + +# 1. Introduction + +Stereo vision [24, 36, 57], one of the longstanding and fundamental topics, supports a wide range of computer vision and robotic tasks. Passive stereo vision typically struggles in texture-less regions and low-light environments [33]. In contrast, active stereo vision [4, 19] addresses these challenges by projecting an infrared pattern, enabling more accurate depth maps compared to passive stereo systems. Nevertheless, conventional active stereo cameras are generally constrained by their depth frame rates (e.g., 30 FPS + +![](images/9b5a33cfe15808b16ee8d7fc341ea8817349a2a959777b2f6efa28ccf25b8cf8.jpg) +Figure 1. Our active event-based stereo camera system integrates binocular event cameras and an infrared 2D pattern laser for high-speed depth sensing. Our lightweight ActiveEventNet effectively converts stereo event streams into high-quality depth maps. + +for Kinect V2 and 90 FPS for RealSense D435), limiting their effectiveness in high-speed scenarios [18, 46]. For instance, a racing drone could suffer a severe collision in a short period between two adjacent depth frames. This may raise a key question: How can we develop a novel active stereo sensing paradigm for high-speed depth perception to overcome the limitations of conventional stereo cameras? + +Event cameras [21, 38, 42], also known as silicon retinas, operate differently from conventional frame-based cameras. Instead of capturing frames at a fixed rate, they detect changes in intensity at each pixel, generating asynchronous events with microsecond-level temporal resolution [7, 39]. This unique capability makes them ideal for various high-speed vision tasks [26, 40, 44, 55, 61, 69, 81, 83, 86] that require low-latency processing of visual information. Consequently, there is growing research interest in leveraging event cameras for high-speed depth sensing (i.e., monocular and binocular) in agile robots [17]. In particular, event-based stereo vision [53, 67, 85, 87] offers the advantage of providing more accurate and reliable depth information compared to monocular depth estimation [11, 27, 45, 89]. + +One problem is that current event-based stereo depth systems [1, 2, 14, 43, 68, 82] are passive stereo, resulting in inaccurate depth maps in texture-less regions and dark scenes. In other words, passive event-based stereo methods rely on feature matching, which may be challenging or even impossible in areas with little texture or low contrast. While some structured light systems with a single event camera [3, 20, 32, 41, 51, 52, 70, 71, 75] have attempted to achieve high-speed depth sensing, these active monocu + +lar depth methods may not always match the accuracy of stereo depth systems at long distances or in ambient light conditions. In fact, by combining active infrared structured light and passive visible light, stereo camera systems could be empowered to generate robust and accurate depth maps in diverse real-world settings, regardless of lighting conditions or surface textures. Yet, there is still no active stereo vision system that combines binocular event cameras and structured light. Meanwhile, most existing passive event-based stereo vision datasets [5, 8, 23, 30, 88] typically provide only sparse LiDAR depth maps, and there is a lack of event streams with structured light and dense depth labels. + +Another problem is that most existing event-based stereo matching algorithms [10, 13, 14, 43, 50, 53, 59, 67, 68] prioritize maximizing accuracy via more complex deep learning-based models, leading to slower inference on resource-constrained devices. This is contrary to the initial objectives of designing high-speed and energy-efficient event cameras. For example, constructing an efficient 3D or 4D cost volume is one critical step in end-to-end pipelines. This volume represents the similarity between pixels in a stereo pair, affecting the accuracy and computational speed of stereo matching models. Some event-based stereo matching algorithms [12, 15, 53, 68, 87] aim to build higher dimensional cost volumes to further enhance accuracy, there have been few endeavors to design a lightweight end-to-end model that specifically addresses computational cost and improves inference speed without sacrificing accuracy. + +To address the aforementioned problems, we propose a novel paradigm for high-speed depth sensing, namely active event-based stereo vision, which first integrates binocular event cameras and an infrared pattern projector for stereo matching with low-latency (see Fig. 1). In fact, the goal of this work is not to optimize passive event-based stereo matching algorithms for higher accuracy. In contrast, our goal is to overcome the following challenges: (i) Lack of prototype system and dataset - How do we establish an active stereo camera setup and build high-quality event-based datasets including both simulated and real-world scenes? (ii) Lightweight yet effective model - How do we design a lightweight stereo matching model that effectively reduces the computational expense without sacrificing accuracy? + +To this end, we first build an active event-based stereo camera prototype and present a real-world dataset with over 21.5k spatiotemporal synchronized true labels at $15\mathrm{Hz}$ while also creating a highly realistic synthetic dataset with 23.8k synchronized labels at $20\mathrm{Hz}$ . Then, we design a lightweight neural network (i.e., ActiveEventNet) for active event-based stereo matching, which mainly involves two strategies: incorporating lightweight blocks into event-based stereo matching frameworks and designing a novel cost volume for similarity measurement in stereo pairs. The results show that our ActiveEventNet achieves better per + +formance than state-of-the-art methods meanwhile significantly reducing computational complexity. Our prototype, integrating binocular event cameras and an infrared projector, offers superior depth sensing compared to conventional stereo cameras in high-speed scenarios, while also achieving the inference speed of up to 150 FPS. Our solution also highlights that active stereo surpasses passive stereo in low-texture regions and low-light scenarios. We believe that our prototype will provide novel insight into developing the next-generation neuromorphic stereo cameras. + +The main contributions of this work are summarized as: + +- We present a novel problem setting of active event-based stereo vision that combines infrared structured light and binocular event cameras for high-speed depth sensing. +- We propose a lightweight yet effective neural network for event-based stereo matching, namely ActiveEventNet, which significantly reduces the computational complexity meanwhile maintaining comparable accuracy. +- We establish a real-world dataset using our active event-based stereo camera prototype, along with a highly realistic synthetic dataset that contains temporally continuous labels. We believe these two standardized datasets open up opportunities for research in this novel problem. + +# 2. Related Work + +Event-based Stereo Vision. Event-based stereo matching methods can be broadly divided into two categories. Early model-based works [85, 87] usually find reliable local correspondences and global optimization algorithms to calculate the disparity. Although these model-based methods achieve sparse or semi-dense depth maps in real-time, they are hard to obtain global dense depth maps. Nowadays, deep learning-based methods [1, 14, 43, 53, 67, 68, 74, 82] have exhibited superior performance in predicting dense depth maps from stereo event streams. Moreover, some cross-modal learning-based methods [12, 13, 50] attempt to generate dense depth maps from stereo hybrid event-frame cameras. Nevertheless, these learning-based methods substantially improve accuracy meanwhile increasing computational complexity. In other words, they require a considerable amount of GPU memory, making them impractical for agile robots or mobile devices. Thus, this work aims to design a lightweight yet effective neural network for event-based stereo matching with low latency. + +Event-based Vision with Structured Light. Bio-inspired event cameras are increasingly being utilized in combination with infrared structured light for high-speed depth sensing. In general, structured light sources are commonly categorized into three types (i.e., point, line, and 2D pattern). For instance, Bramdli et al. [6] first integrates a laser line projector and an event camera for 3D reconstruction. Martel et al. [48] combine a laser light source with an event-based stereo setup. Muglikar et al. [51] design a structured light + +![](images/ffa484039970178763ccc8556c9c7fb8a021d3da36d1dc0a1a0d38d43f0b4476.jpg) +Figure 2. Sensing mechanism of active event-based stereo vision. Projecting a 2D pattern from an infrared projector enhances scene texture, enabling improved stereo matching performance. + +system with a laser point-projector and an event camera for depth estimation. Huang et al. [32] present a structured light system using an event camera and a laser pattern-projector for high-speed 3D scanning. Most systems [6, 32] using model-based methods achieve high-speed depth sensing but yield sparse depth maps. More recently, deep learning models [52, 71] have explored event-based structured light systems for dense depth estimation. While these monocular active event-based vision systems are generally simpler, stereo systems often provide more accurate depth maps due to triangulation. Hence, we design an active event-based stereo structured light system, which uses a lightweight learning-based model to generate dense depth maps. + +# 3. Problem Formulation + +Event cameras [21, 80], such as DVS [25, 35, 42, 54], respond to light changes with continuous asynchronous event streams. Each event $e_n$ is depicted by a tuple $\langle x, y, t, p \rangle$ , including spatial coordinates $\langle x, y \rangle$ , timestamp $t$ , and polarity $p$ . This sensing mechanism enables event-based stereo vision to achieve reliable disparity maps in high-speed dynamic scenes [56, 58, 72, 76, 79, 90]. Yet, passive event-based stereo vision meets challenges in scenarios with texture-less and low light. This work aims to overcome this gap by integrating binocular event cameras and an infrared pattern projector. We formulate this novel problem setting called active event-based stereo vision as follows. + +The goal of this work is to calculate the disparity map $d_{e}$ from the stereo stream pair $S_{l}$ and $S_{r}$ . Since the chip of event camera [65] is sensitive to a spectrum of 300-1000 nm (see Fig. 2), the generation of the event stream is mainly affected by natural light, laser light (850 nm), and noise, which can be mathematically formulated as: + +$$ +\boldsymbol {S} _ {l} = \mathcal {G} \left(\boldsymbol {W} _ {t} ^ {l} \cdot [ I (t) + P (t) ] + \mathcal {N}\right), \tag {1} +$$ + +$$ +\boldsymbol {S} _ {r} = \mathcal {G} \left(\boldsymbol {W} _ {t} ^ {r} \cdot [ I (t) + P (t) ] + \mathcal {N}\right), +$$ + +![](images/b3e085d045d028e5554a819559f003871990441116835c3fe37d0928b1ee0ac7.jpg) +Figure 3. Comparison with event streams using or without structured light. Our solution enables the event camera to generate dynamic events even in static scenarios or low-light conditions. + +where $\mathcal{G}$ denotes the event generation process of event cameras. $I(t)$ and $P(t)$ are the scene light intensity and the infrared laser intensity at time $t$ . $\pmb{W}_t^l$ and $\pmb{W}_t^r$ refers to the left and right warping operation via projecting a real 3D scene to each 2D camera plane. $\mathcal{N}$ is the event camera noise. Note that, the proposed system enables the event camera to generate dynamic events by adjusting the laser's frequency or intensity, even in static scenarios with constant light intensity $I(t)$ or in extremely low-light conditions. + +In general, event-based stereo matching estimates disparities between corresponding points in two streams as: + +$$ +\boldsymbol {d} _ {e} = \mathcal {M} _ {d} (\boldsymbol {S} _ {l}, \boldsymbol {S} _ {r}, \theta), \tag {2} +$$ + +where $\mathcal{M}_d$ is the proposed active event-based stereo matching model, and $\theta$ denotes the optimized parameters of $\mathcal{M}_d$ . + +Then, we can solve the following minimization problem: + +$$ +\hat {\theta} = \underset {\theta} {\arg \min } L _ {\mathcal {M}} \left(\boldsymbol {d} _ {e}, \boldsymbol {d} _ {g t}\right) + \lambda \Phi (\theta), \tag {3} +$$ + +where $L_{\mathcal{M}}(\pmb{d}_e, \pmb{d}_{gt})$ is the loss function between the predicted disparity $\pmb{d}_e$ and the ground truth $\pmb{d}_{gt}$ , and $\Phi(\theta)$ is the regularization term, and $\lambda$ is the trade-off parameter. + +# 4. Active Event Camera Stereo Dataset + +This section first describes how we built our Active-Event-Stereo dataset with our camera prototype and then provides statistics for a better understanding of this new dataset. + +Stereo Camera Prototype. To verify the effectiveness of our solution, we build a prototype stereo camera system by integrating binocular DAVIS346 cameras (i.e., resolution $346 \times 260$ ), an infrared pattern projector, and an Intel RealSense D455 camera (i.e., resolution $640 \times 480$ ). Unlike conventional passive vision, our prototype can detect dynamic events even in static scenarios or dark environments by adjusting the laser frequency or intensity of the signal generator (see Fig. 4 (a)). This capability is enabled by an + +![](images/aa171353b82e54f814c2ead35dcfd7f254d017b36c4c7a58833a913c4e663f05.jpg) +(a) Stereo camera prototype + +![](images/64c0661aa81be426e300029f84e60f560a5f7df8cb2d12af3a00dcd398cf934a.jpg) + +![](images/995f77fe0c18f768dfee07ade0c924b5d5a55b3d4973da22981de1d6feb41fea.jpg) +(b) Calibrated views +(c) Representative spatiotemporal synchronized examples +Figure 4. An event-based stereo camera prototype and the newly built dataset. (a) The experimental setup combines binocular event cameras and an infrared pattern projector. (b) Spatiotemporal calibration using a standard checkerboard. (c) Examples of the real-world dataset, the left in each image is from the left DAVIS346, and the right is the depth map from the RealSense D455. + +infrared projector operating at a wavelength of $850~\mathrm{nm}$ . Besides, we use the flagship RealSense D455 stereo camera at 15 FPS to capture depth ground truth in normal scenes and also as a fair comparison in high-speed motion scenarios. + +Spatiotemporal Calibration. In general, spatiotemporal calibration is a critical step for hybrid multi-camera systems. For temporal calibration, we synchronize the two stereo event cameras and the RealSense D455 camera by publishing each topic's timestamp in the robot operating system (ROS). For spatial calibration, our objectives are to establish a horizontal baseline correction for stereo matching between binocular event cameras and to align the RealSense camera's view with that of the left event camera. To achieve this, we place a standard checkerboard 1 meter in front of our prototype to ensure full visibility (see Fig. 4 (b)). We adopt a professional binocular stereo correction toolbox to correct the baseline alignment on RGB images from the two DAVIS346 cameras. Simultaneously, checkerboard keypoints are extracted from the RGB images of both the left DAVIS346 and the RealSense D455 cameras, and an affine transformation aligns the two coordinate sets [84]. Data Recordings and Statistics. Our Active-Event-Stereo dataset contains indoor and outdoor challenging scenarios (see Fig. 4 (c)) by considering velocity distribution, illumination change, scene diversity, varying distances, etc. We use the built stereo camera prototype to record 85 sequences including event stream pairs, RGB frames, infrared frames, and depth values. After spatiotemporal calibration, all labels are provided at a frequency of $15\mathrm{Hz}$ by the RealSense D455. As a result, the newly built dataset offers event streams in stereo pairs and $21.5\mathrm{k}$ synchronized true labels. Afterward, we split them into $14.6\mathrm{k}$ for training, $3.6\mathrm{k}$ for validation, and $3.3\mathrm{k}$ for testing. We compare our Active-Event-Stereo with the relevant camera prototype and representative datasets in Table 1. Notably, this is the first work + +
MethodTypeCameraResolutionProjectorLabels
Manasi [51]MonocularGen3640×480PointSparse
Muglikar [52]MonocularGen3640×480PointDense
Brandli [6]MonocularDVS128128×128LineNo
Wieland [49]MonocularGen3640×480LineNo
Takatani [64]MonocularDAVIS346346×260LineNo
Leroux [37]MonocularATIS304×240PatternNo
Ashish [47]MonocularDAVIS346346×260PatternNo
Huang [32]MonocularCeleX-V1280×800PatternNo
Fu [20]MonocularEVK41280×720PatternNo
Bajestani [3]MonocularGen3640×480PatternNo
Li [41]MonocularDAVIS346346×260PatternNo
Wang [71]MonocularDVXplorer640×480PatternDense
OursStereoDAVIS346346×260PatternDense
+ +Table 1. Comparison with event-based vision systems using active infrared light and depth labels. The laser shape emitted by the infrared projector can be classified into point, line, and 2D patterns. + +to build an active event-based stereo vision dataset. + +All in all, such a novel event-based stereo system with structured light and professional design enables our Active-Event-Stereo to be a competitive dataset with multiple characteristics: (i) High temporal resolution from event streams; (ii) Dynamic event generation with structured light even in static scenes or dark environments; (iii) Temporally long-term stereo event streams with depth labels at $15\mathrm{Hz}$ ; (iv) Real-world recordings with abundant diversities in moving speed, light change, scene category, and distance variation. + +# 5. Methodology + +# 5.1. Architecture Overview + +This work aims at designing a novel lightweight yet effective active event-based stereo matching neural network, termed ActiveEventNet, which generates high-speed dense disparity maps via integrating binocular event cameras and infrared structured light. As illustrated in Fig. 5, our framework mainly consists of four modules: event representation, feature extraction, dynamic interaction for cost volume and encoder-decoder. More precisely, the continuous event stream is first divided into event temporal bins, and each bin can be converted into a 2D image-like representation (i.e., event tensors [22]). Then, we introduce the lightweight MobileNet blocks [29, 62] to the corresponding 3D convolutions and show their necessity for event-based stereo matching models. The event embeddings in stereo pairs are fed into the feature extraction backbone and the channel reduction module to obtain compact yet powerful features. Moreover, we design a novel 3D cost volume via dynamically exchanging the channels and concatenating interaction stereo features, which refers to the costs of matching corresponding pixels between two event streams from slightly different viewpoints. Finally, the 3D cost volume is taken into an encoder-decoder module with a stack of + +![](images/972ca51f8e837b9356fdfc71d2637ce0ca0ecf754c96faf290ed89c922824e62.jpg) +Figure 5. Overview of active event-based stereo matching neural network (ActiveEventNet). Each event stream is first split into event temporal bins and encoded into event tensors [22]. Then, we incorporate MobileNet blocks for feature extraction and channel reduction. Meanwhile, we design a novel cost volume using dynamic interaction for similarity measurement in stereo pairs. Finally, an encoder-decoder component via a stack of lighter convolutional layers is utilized to predict dense disparity maps (along with a mask for enhanced visualization). + +lighter convolutional layers to predict dense disparity maps. + +# 5.2. Raising MobileNet for Event-based Stereo + +To achieve a trade-off between fidelity and inference speed, we first incorporate the lightweight yet effective MobileNet blocks [29, 62, 63] instead of standard convolution operations for active event-based stereo matching. As a pioneering work, MobileNet v1 utilizes depthwise convolutions followed by pointwise convolutions to achieve standard convolution while reducing computational complexity. In general, MoileNet v1 achieves significant computation compared to standard convolutions by effectively utilizing the depth separable convolutions. Furthermore, MobileNet v2 introduces linear bottlenecks and inverted residuals to improve accuracy while keeping comparable memory-efficient inference. We formulate the output $F_{\text{res}}$ of an inverted residual block as follows: + +$$ +\boldsymbol {F} _ {1} = \sum_ {c} ^ {t C} \boldsymbol {k} _ {p} (x, y, c) \cdot \boldsymbol {F} (x, y, c), +$$ + +$$ +\boldsymbol {F} _ {2} = \sum_ {x, y} \boldsymbol {k} _ {d} (x, y, t c) \cdot \boldsymbol {F} _ {1} (x - 1, y - 1, t c), \tag {4} +$$ + +$$ +\boldsymbol {F} _ {3} = \sum_ {c} \boldsymbol {k} _ {p} (x, y, c) \cdot \boldsymbol {F} _ {2} (x, y, c), +$$ + +$$ +\boldsymbol {F} _ {\text {r e s}} = \boldsymbol {F} + \boldsymbol {F} _ {3}, +$$ + +where $\pmb{k}_d(x,y,c)$ denotes the depthwise convolution kernel at position $(x,y,c)$ of the input feature map $\pmb{F}$ , and $\pmb{k}_p$ is the + +$1 \times 1$ pointwise convolution kernel. $F_{1}, F_{2}$ , and $F_{3}$ are intermediate feature maps in the inverted residual block. The channel dimension $c$ is expanded with an expansion factor $t$ in the pointwise and depthwise convolution operations. + +Overall, our ActiveEventNet mainly replaces standard 2D convolutions of lightweight MobileNet v2 blocks in the feature extraction module and the encoder-decoder module. + +# 5.3. Dynamic Interaction for Cost Volume + +Cost volume [36, 57, 66] is a crucial component in the stereo matching pipeline, which is the matching cost between pixels at different disparities. A 3D cost volume $C_d$ can be constructed via computing the dissimilarity between the left feature map $F_l$ and the right feature map $F_r$ as: + +$$ +\boldsymbol {C} _ {d} (x, y, d) = \mathcal {M} _ {c} (\boldsymbol {F} _ {l} (x, y, c), \boldsymbol {F} _ {r} (x - d, y, c)), \tag {5} +$$ + +where $d$ is the disparity between pixels in a stereo pair, and $\mathcal{M}_c$ is a similarity measurement function. For learning-based models, $\mathcal{M}_d$ usually adopts concatenation or correlation operations [50, 53, 73] between two feature maps. + +This work aims at designing a lightweight yet powerful 3D cost volume via dynamically exchanging the stereo channels and concatenating interacted features, which achieves satisfactory performance while maintaining comparable computational complexity to typical aggregation operations. As a result, we can mathematically describe the construction process of 3D cost volume as follows: + +$$ +\hat {\boldsymbol {F}} _ {l} = \sum_ {c} \boldsymbol {F} _ {l} (x, y, d - c) + \boldsymbol {W} _ {r} \cdot \boldsymbol {F} _ {r} (x, y, d - c), +$$ + +$$ +\hat {\boldsymbol {F}} _ {r} = \sum_ {c} \boldsymbol {F} _ {r} (x, y, d - c) + \boldsymbol {W} _ {l} \cdot \boldsymbol {F} _ {l} (x, y, d - c), \tag {6} +$$ + +$$ +\boldsymbol {C} _ {d} = \left[ \hat {\boldsymbol {F}} _ {l} (x, y, d), \hat {\boldsymbol {F}} _ {r} (x, y, d) \right], +$$ + +where $\hat{F}_l$ and $\hat{F}_r$ are the left and the right interacted feature maps after the dynamic interaction operation. $W_{l}$ and $W_{r}$ are weight matrices that determine how feature maps from the left and right views interact dynamically. + +In this study, the scaling factor of the batch normalization (BN) layer reflects the importance of the feature map in the $c$ -th channel. The feature map is dynamically interacted by the corresponding channel from the other view once the scaling factor is smaller than a preset threshold $\theta_{\gamma}$ . For example, the left camera's feature map is replaced by the corresponding feature map $F_{r,m,c}^{\prime}$ of the right camera as: + +$$ +F _ {r, m, c} ^ {\prime} = \gamma_ {r, m, c} \frac {F _ {r , m , c} - \mu_ {r , m , c}}{\sqrt {\sigma_ {r , m , c} ^ {2} + \varepsilon}} + \beta_ {r, m, c}, \gamma_ {r, m, c} < \theta_ {\gamma}, \tag {7} +$$ + +where $F_{rmc}$ is the $c$ -th channel before the $m$ -th BN layer in the right branch. $\varepsilon$ is a small constant, and $\mu_{r,m,c}$ and $\sigma_{r,m,c}$ denote the mean and the standard deviation. $\gamma_{r,m,c}$ and $\beta_{r,m,c}$ are the trainable scaling factor and the offset. + +
ScenarioSequenceRGB framesEvents
EPE↓RMSE↓D1-all↓>1px↓>2px↓>3px↓EPE↓RMSE↓D1-all↓>1px↓>2px↓>3px↓
Normal light05_indoorboxes1.8897.9880.0660.3590.1140.0661.9417.9720.0690.3970.1290.069
10_indoorboxes2.6368.9180.1960.5890.3380.1962.5948.9220.1710.6130.3210.171
26_indoorcheckerboard2.0487.91140.0860.4950.1980.0861.7327.8550.0630.3080.1020.063
70_outdoor_car1.0253.5150.0150.3190.1230.0151.1503.5550.0370.3990.1320.037
80_outdoor_deer2.4218.2170.160.5890.3180.162.3168.1220.1070.6240.2850.107
Low light15_indoor_officeDesk DARK3.31212.0180.1580.05750.2760.1583.28112.0670.1610.5230.2880.161
17_indoor_office Desk DARK3.45311.8050.2120.6310.3640.2122.89411.7560.1150.4140.1960.114
22_indoorPrinter DARK2.5147.7580.1870.6450.3530.1871.5977.5170.0620.2560.1030.061
27_indoorcheckerboard DARK2.1987.8250.2250.4770.2950.2251.7367.7590.0500.4090.1100.050
32_indoor_conferenceDesk DARK2.9457.1180.3370.7350.5140.3371.7066.6500.0740.4600.1640.074
58_indoor_washroom DARK2.3816.0180.2680.6260.3650.2691.0315.3380.0250.1880.0520.025
64_outdoor_car DARK1.0883.6730.0190.3980.0870.0190.8393.5910.0110.2170.0440.011
AllAverage2.2388.0950.1590.5450.2810.1591.9957.8210.0830.3990.1630.082
+ +Table 2. Performance evaluation of our real-world Active-Event-Stereo dataset. Note that, our solution, combining binocular event cameras with an infrared pattern projector, outperforms conventional frame-based stereo vision, particularly in challenging low-light conditions. + +
MethodEvent representationBackboneEPE ↓RMSE ↓D1-all ↓>1px ↓>2px ↓>3px ↓# Params. (M)Runtime (ms)
SGM [28]Reconstructed imagesNo learning3.62516.5670.5860.7510.6840.585-32.1
PSMNet [9]Event images2D CNN2.89411.7560.2040.6030.3520.2045.2215.6
DeepPruner-Fast [16]Event images2D CNN2.5148.7580.1130.5450.2530.1127.3939.4
AANet [77]Event images2D CNN2.3178.1230.1060.5250.2870.1063.6816.7
Unimatch [78]Event imagesTransformer1.9027.7590.0680.3610.1160.0664.7087.6
DDES [67]Event embeddings2D CNN2.6438.9200.1220.5910.3410.1222.3319.5
Our ActiveEventNetEvent imagesMobileNet1.9957.8210.0830.3990.1630.0822.236.5
Our ActiveEventNet*Voxel gridsMobileNet1.9877.8130.0790.3860.1580.0782.236.8
Our ActiveEventNet◇Reconstructed imagesMobileNet1.9727.7800.0760.3820.1560.0762.237.0
+ +Table 3. Comparison with state-of-the-art methods on our real-world Active-Event-Stereo dataset. + +# 6. Experiment + +# 6.1. Experimental Settings + +Realistic Synthetic Dataset. To obtain a large amount of labor-saving yet high-quality synthetic data, we build an active event-based stereo matching simulated dataset, namely RealSense-Event-Sim. An Intel RealSense D435 sensor is first utilized to record 119 infrared video sequences that consider velocity distribution, light condition, scene diversity, etc. Then, we use the V2E simulator [31] to convert infrared videos into dynamic events. As a result, the newly built dataset offers event streams in stereo pairs and $23.8\mathrm{k}$ synchronized true labels. Finally, we split them into 16k for training, 3.8k for validation, and 4k for testing. + +Implementation Details. We select event images [22] as the event representation to achieve an accuracy-speed tradeoff. We set the maximum disparity to 192 for stereo matching in all cases. We set the threshold $\theta_{\gamma}$ to $10^{-2}$ in dynamic interaction for cost volume. All networks are trained for 50 epochs using the Adam optimizer [34] on an NVIDIA 3090 GPU with a learning rate of $10^{-3}$ . For training losses, we utilize an $L_{1}$ loss to measure the absolute difference between the predicted maps and the labels. + +Evaluation Metrics. Mean average end-point-error (EPE), root mean square error (RMSE), the percentage of pixels with disparity error than 3 pixels and $0.05d_{gt}$ (D1-all), the + +percentage of pixels with disparity errors greater than 1 pixel, 2 pixels, and 3 pixels (i.e., $>1\mathrm{px}$ , $>2\mathrm{px}$ , and $>3\mathrm{px}$ ) are used to evaluate the accuracy in the stereo matching task. The model parameters (#Params) and the running time (ms) are adopted to evaluate the computation speed. + +# 6.2. Effective Test + +Evaluation on RGB Frames and Events. To compare our solution with conventional frame-based stereo, we report quantization results for each test set sequence using both RGB frames and events with structured light on our Active-Event-Stereo dataset (see Table 2). We can find that our solution with structured light is able to acquire high-quality dense disparity maps in both indoor and outdoor scenarios with light changes. Our solution achieves better performance than passive stereo vision with RGB frames in most indoor and outdoor scenes, especially in low-light scenarios. More precisely, our solution significantly reduces errors across five metrics compared to passive stereo vision, with EPE, RMSE, and D1-all decreased by 0.243, 0.274, and 0.076, respectively. To our surprise, our method using sparse events outperforms dense RGB images in most sequences, even under normal light scenes, with a few recordings showing comparable results. This may be the incorporation of structured light in stereo vision, which enhances scene textures and further boosts performance. + +![](images/74d5ac72dc879bdfd8220f76fa1ef7686ad6f439ede6fb2fcdcf9013f71e1e5b.jpg) +Figure 6. Representative examples of different stereo matching results on our real-world Active-Event-Stereo dataset. To enhance visualization and comparison, we implement a mask to the void areas of the ground truth to the predicted dense maps. + +
MethodEPE ↓RMSE ↓D1-all ↓Runtime (ms)
SGM [28]4.2988.3260.68143.2
PSMNet [9]2.7865.5830.21120.6
DeepPruner-Fast [16]1.4632.5130.08776.0
AANet [77]1.3972.4630.07728.5
Unimatch [78]1.1081.780.063172.6
DDES [67]1.6963.2410.12536.4
Our ActiveEventNet1.2232.3200.07021.9
+ +Comparison with State-of-the-Art Methods. To make a comparison with stereo matching methods as fair as possible, we first convert event streams to videos using the E2VID [60] and then use reconstructed gray images as the input of the classical SGM [28]. In addition, we compare our ActiveEventNet with four frame-based stereo matching networks (i.e., PSMNet [9], DeepPruner-Fast [16], AANet [77], and Unimatch [78]) and a popular event-based stereo matching framework (i.e., DDES [67]). For real-world dataset evaluation, we compare our ActiveEventNet with other methods in our Active-Event-Stereo dataset in Table 3. Note that, our ActiveEventNet achieves superior performance compared to five state-of-the-art methods while maintaining smaller parameters and faster inference times. Compared to the top-performing Transformer-based Unimatch [78], our approach delivers comparable performance with a $12\times$ improvement in inference speed. Furthermore, we compare three typical event representations (i.e., event images [22], voxel grids [89], and reconstructed images [60]) to verify the generality of our method for various event representations. It indicates that this improvement in event representation comes with an associated increase in computational speed. Furthermore, we present some representative examples of visualization comparison results on our Active-Event-Stereo dataset in Fig. 6. Ap + +Table 4. Comparison with state-of-the-art methods on our highly synthetic RealSense-Event-Sim dataset. + +
MethodBaseline(a)(b)Ours
MobileNet blocks
Dynamic interaction cost volume
EPE ↓2.1242.211.9681.993
RMSE ↓7.9357.9527.7507.821
D1-all ↓0.0920.0950.0750.083
Runtime (ms)33.86.235.76.5
+ +Table 5. The contribution of each component to our ActiveEvent-Net on our real-world Active-Event-Stereo dataset. + +parently, the conventional model-based SGM only generates sparse disparity maps, but our ActiveEventNet excels in obtaining high-quality disparity maps, even under varying light conditions in both indoor and outdoor scenes. For simulated dataset evaluation, we report quantization results in Table 4, showing that the conclusions from the simulation dataset are consistent with those from the real dataset. + +# 6.3. Ablation Test + +Contribution of Each Component. To explore the impact of each component on the final performance, our baseline uses standard convolutions and adopts a typical concatenation operation in the cost volume module. As shown in Table 5, three methods, namely (a), (b), and our ActiveEventNet, consistently indicate that leveraging MobileNet blocks boosts inference speed, while the introduction of the dynamic interaction cost volume enhances accuracy. Besides, our approach, using dynamic interaction for cost volume, obtains a 0.156 reduction in EPE while keeping a comparable computation speed. To our surprise, our method, employing MobileNet blocks to replace standard convolutions, achieves a nearly $6 \times$ increase in inference speed. + +Influence of MobileNet Blocks. To analyze MobileNet blocks in our ActiveEventNet, we deploy MobileNet v2 blocks instead of standard convolutions in the feature ex + +
Feature extractionEncoder-decoderEPE↓D1-all↓Runtime (ms)
Standard Conv.Standard Conv.1.9680.07535.7
Standard Conv.MobileNet v21.9720.07622.2
MobileNet v2Standard Conv.1.9830.07813.4
MobileNet v2MobileNet v21.9930.0836.5
+ +Table 6. The influence of MobileNet blocks in Our ActiveEvent-Net on our real-world Active-Event-Stereo dataset. + +
MethodEPE ↓RMSE ↓D1-all ↓Runtime (ms)
Concatenation2.5278.8230.1135.8
Correlation [53]2.3168.1240.1076.2
Dynamic Interaction1.9937.8210.0836.5
+ +Table 7. Comparison of our ActiveEventNet with various aggregation strategies of cost volume on our Active-Event-Stereo dataset. + +
SetupEPE ↓RMSE ↓D1-all ↓Runtime (ms)
Without structured light2.6148.8750.1976.3
Structure light1.9937.8210.0836.5
+ +Table 8. The impact of structured light on event-based stereo vision. Some static and slow-motion sequences are evaluated with and without structured light under the same scene. + +traction and the encoder-decoder modules. As shown in Table 6, Our approach, introducing MobileNet v2 blocks, consistently achieves faster computational speed. Comparing MobileNet v2 and standard convolution, the absolute decrease in EPE is only 0.025, while the inference time is reduced by nearly $6 \times$ . It indicates that our approach using MobileNet v2 instead of standard convolution achieves an accuracy-speed trade-off for practical applications. + +Influence of Cost Volume Construction. To evaluate the effectiveness of dynamic interaction for cost volume, we compare it with some typical aggregation operations in Table 7. Note that, our approach obtains the best performance against two aggregation operations (i.e., concatenation and correlation [53]). This is due to our dynamic interaction strategy, which effectively exchanges stereo channels and aggregates interacted features to enhance performance while keeping comparable computational speed. + +# 6.4. Scalability Test + +Analyzing the Role of Structured Light. To evaluate the impact of structured light on event-based stereo vision, we selected static and slow-motion sequences for quantitative assessment. As illustrated in Table 8, the stereo matching performance significantly improves by incorporating structured light. Besides, we present a representative instance in an extremely slow motion scenario (see Fig. 7). While the passive stereo generates almost no events, our camera prototype excels in producing dynamic events through the use of structured light. In other words, the solution, integrating the structured light for binocular event cameras, can overcome the limitation of most existing passive event-based stereo in static scenarios or dark environments. + +![](images/2103a9527f160b1c9cb408d49386928d0e92362aaa66d64bae9ccc73d20ae0c7.jpg) +Figure 7. Representative instance of our camera prototype in extreme slow motion scenes. Unlike passive vision, our solution with structured light produces dynamic events even in static scenes. + +![](images/9cf18f5cf840e5405ca37da4db41d15f269c0dd5faddf61c7fa2dec8872ef6a6.jpg) +Figure 8. Comparison with a conventional active stereo camera in high-speed motion scenarios. Note that, our camera prototype outperforms Realsense D455 for high-speed depth sensing. + +Test Camera Prototype in High-Speed Scenes. To verify our solution for high-speed depth sensing, we compare our camera prototype with a conventional RealSense D455. As shown in Fig. 8, our prototype empowers the acquisition of high-quality disparity maps in high-speed scenes, while RealSense D455 at 90 FPS is notably ineffective. In fact, conventional images from the RealSense D455 may suffer from motion blur, which impairs depth perception in high-speed scenes. In contrast, our solution leverages the event camera with high temporal resolution and structured light to improve scene texture, resulting in superior depth accuracy. Furthermore, our ActiveEventNet efficiently processes stereo event stream pairs, achieving an inference speed of up to 150 FPS on an NVIDIA 3090 GPU. + +# 7. Conclusion + +This paper presents a novel paradigm for high-speed depth sensing, called active event-based stereo vision, which first integrates binocular event cameras and active infrared structured light. Towards this end, we establish a real-world dataset using our active event-based stereo camera prototype, along with a highly realistic synthetic dataset. Then, we design a lightweight yet effective event-based stereo matching model, which significantly reduces the computational cost meanwhile keeping the comparable accuracy. We believe that our standardized datasets will open up an opportunity for the research of this challenging problem. + +Acknowledgments. This work was supported in part by the National Key R&D Program of China under Grant 2018AAA0102801, and the National Natural Science Foundation of China under Grant 61827804. + +# References + +[1] Soikat Hasan Ahmed, Hae Woong Jang, SM Nadim Uddin, and Yong Ju Jung. Deep event stereo leveraged by event-to-image translation. In AAAI, pages 882-890, 2021. 1, 2 +[2] Alexander Andreopoulos, Hirak J Kashyap, Tapan K Nayak, Arnon Amir, and Myron D Flickner. A low power, high throughput, fully event-based stereo system. In CVPR, pages 7532-7542, 2018. 1 +[3] Seyed Ehsan Marjani Bajestani and Giovanni Beltrame. Event-based rgb sensing with structured light. 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Unlike recent NeRF-based methods, which are computationally demanding and limit mapping performance, our approach leverages the efficient rendering capabilities of 3DGS to enable effective and efficient exploration in complex environments. The core of our system is a rendering-based information gain module that identifies the most informative viewpoints for next-best-view planning, enhancing both geometric and photometric reconstruction accuracy. ActiveGAMER also integrates a carefully balanced framework, combining coarse-to-fine exploration, post-refinement, and a global-local keyframe selection strategy to maximize reconstruction completeness and fidelity. Our system autonomously explores and reconstructs environments with state-of-the-art geometric and photometric accuracy and completeness, significantly surpassing existing approaches in both aspects. Extensive evaluations on benchmark datasets such as Replica and MP3D highlight ActiveGAMER's effectiveness in active mapping tasks. + +# 1. Introduction + +In computer vision, the ability to generate detailed 3D reconstructions from 2D images or videos has seen tremendous progress, enabling real-time, incremental 3D modeling as new visual data is assimilated. This process, often powered by Simultaneous Localization and Mapping (SLAM), plays a crucial role in robotic applications, where it supports tasks such as planning and navigation. When combined, these functions define Active SLAM, a framework that integrates localization, mapping, planning, and navigation to enable autonomous exploration. + +This paper focuses on a subproblem of Active SLAM + +![](images/e20bd958ef5aa50e7a4605b1a4aca7075d95a75180657d6fd4bd47c0e1634576.jpg) + +![](images/f44f921a90247344be417c192643218973ec0281a01edde278b74e9b0fc54100.jpg) +Figure 1. ActiveGAMER is built on a Gaussian Map backbone and autonomously performs coarse-to-fine exploration to optimize geometric accuracy and photometric fidelity. + +![](images/c12fccf2c86a28d2c4e7927b780b886a304c6a0522a4e20c346e3ebb42c3e58d.jpg) + +![](images/cb762873193a961442cd2262281d2859815971ea9efbf5f2084244f6b70bca5a.jpg) + +known as Active Reconstruction, where localization is assumed to be known, allowing the system to prioritize high-quality and complete scene reconstruction. We explore this task by introducing a novel approach based on 3D Gaussian Splatting (3DGS), which provides an efficient radiance field representation optimized for active exploration. + +Radiance fields, particularly implicit models like NeRFs, have shown promising results in applications such as 3D object reconstruction [45], novel view synthesis [40, 49, 71, 76], and surface reconstruction [2, 32]. However, NeRF's high computational demands hinder real-time applicability, especially in active vision tasks. To address this, recent efforts have explored hybrid neural representations, which incorporate both implicit and explicit components to enhance rendering efficiency [41, 62]. + +On the other hand, 3D Gaussian Splatting [26] is a recent and efficient radiance field representation that leverages Gaussian primitives in 3D space. Unlike NeRFs, which rely on dense, computationally intensive sampling, 3DGS uses a sparse set of Gaussian ellipsoids to approximate both geometry and color information. This representation allows for + +rapid rendering by projecting each Gaussian onto the image plane, where they are blended using alpha compositing. Due to its efficient design, 3DGS achieves real-time rendering speeds, making it particularly suitable for dynamic applications like SLAM and active vision, where computational resources and time are limited. Recent work [22, 72] has shown that 3DGS maintains high visual fidelity while reducing the computational overhead, enabling its use in scenarios that demand fast, high-quality 3D reconstructions. + +Despite these advances, integrating radiance fields into active vision remains challenging. While several studies have explored active reconstruction and path planning with NeRFs [1, 31, 44, 51, 75], these methods often focusing on geometric reconstruction tasks, especially surface reconstruction. Improving photometric reconstruction (rendering) is often ignored with the use of NeRF-based methods due to its slow rendering speeds. + +To address existing limitations and enhance photometric reconstruction, we introduce ActiveGAMER, an active mapping system that leverages the real-time rendering capabilities of 3D Gaussian Splatting. Our system enables unrestricted 6DoF movement, allowing flexible exploration and high-quality scene reconstruction even in complex environments. The key contributions of our work include: + +- An advanced active mapping system based on 3DGS, allowing real-time, unrestricted 6DoF exploration. +- A rendering-based information gain module that efficiently identifies the most informative viewpoints for next-best-view planning. +- A carefully designed system that balances exploration efficiency and reconstruction accuracy for both geometric and photometric reconstruction, through strategies like coarse-to-fine exploration, post-refinement, and global-local keyframe selection. +- Achieves state-of-the-art performance in active reconstruction, enhancing both geometric accuracy and rendering fidelity over existing approaches. + +# 2. Related Work + +Active Reconstruction Autonomous robotics relies on foundational capabilities such as localization, mapping, planning, and motion control [57]. These capabilities have spurred advancements in various areas, including visual odometry [53, 74], monocular depth estimation [3, 16, 73], multi-view stereo [6, 9, 21, 35, 56, 63, 70], structure-from-motion (SfM) [54], and path planning [20, 29, 30]. SLAM systems have also evolved significantly, facilitating simultaneous localization and mapping for autonomous navigation [5, 13, 15, 64, 66]. Active SLAM combines these approaches to enable autonomous localization, mapping, and planning, aiming to reduce uncertainty in the robot's environment representation [12]. Comprehensive reviews of active SLAM can be found in recent survey papers + +[5, 36, 48]. Our focus is on active reconstruction, a research area closely related to active SLAM but oriented towards achieving complete and accurate 3D representations. Active reconstruction is often formulated as an exploration problem, where the objective is to determine the most informative viewpoints for capturing detailed scene representations [4, 17, 37, 42, 58, 59, 65]. This approach has been widely applied in scene and object reconstruction from multiple viewpoints, with methods developed to handle occlusions, optimize viewpoint selection, and maximize information gain [11, 14, 23, 27, 39, 46, 47]. + +Radiance Fields Radiance Field representations have become a cornerstone in 3D scene modeling, enabling continuous and high-quality representations of complex environments. Neural Radiance Fields (NeRFs) [40] pioneered this field by modeling scenes as continuous radiance fields using multi-layer perceptrons (MLPs), achieving impressive results in applications such as novel view rendering [40, 49, 71, 76], object and surface reconstruction [2, 32, 40, 45], and generative modeling [43, 55], and Structure-from-Motion [10, 34, 67]. While NeRFs have set a high standard for rendering quality, they are computationally intensive, making real-time applications challenging. + +Recent advancements in 3D Gaussian Splatting [26] provide an alternative approach by representing scenes through a set of Gaussian primitives in 3D space, which can be rendered efficiently with lower computational overhead. 3D Gaussian Splatting has shown promise in achieving real-time rendering, making it suitable for dynamic applications like SLAM [25, 38]. Together, NeRFs and 3D Gaussian Splatting represent complementary approaches to scene representation, each with unique strengths and trade-offs in terms of rendering quality, computational efficiency, and suitability for active vision tasks. + +Active Radiance Fields Building on advancements in NeRF and 3D Gaussian Splatting, recent research has investigated the potential of these representations in active vision, particularly for autonomous scene exploration and mapping. Active radiance fields leverage the strengths of NeRF and 3DGS for tasks requiring continuous exploration and decision-making in 3D environments. + +NeRF-based approaches have been applied to path planning [1] and active reconstruction via next-best-view strategies [31, 44, 51], though they are often limited by NeRF's high computational demands, which restricts real-time applications [28]. To overcome these limitations, hybrid models such as ActiveRMAP [75] integrate implicit and explicit representations for improved efficiency. However, many NeRF-based methods still restrict camera motion to constrained spaces, reducing flexibility in complex 3D environments. NARUTO [18] addresses this by introducing an + +![](images/3c4aeff982657670fb0e0bd5bdcdd5c17355ea1471e4396814ef9c42b922f4e0.jpg) + +![](images/963f8a0b4566c884f4cfaaed03d6838de186cf2b630c84d23db151a5089b7a3a.jpg) + +![](images/4ead11f2783b542dcc804a019938a6e367905670d7065d7e0dccc63705da4b19.jpg) +Figure 2. ActiveGAMER Framework. At each keyframe step, HabitatSim [52] generates posed RGB-D images, which are stored in a keyframe database, with certain frames designated as Global Keyframes. These observations are used to update a Gaussian Map comprising a collection of 3D Gaussians. Map optimization is achieved by minimizing color and depth rendering losses, based on the rendered RGB-D images and silhouette masks. Using the up-to-date Gaussian Map, rendering-based planning evaluates the information gain across sampled candidate viewpoints and choose the one with highest information gain as the next-best-view. + +![](images/859b9cba96991ab09a218c4fa0757479b3daf90d7142ea7d6c4d2f2da7d556bf.jpg) + +![](images/e9869184ce80a2724a2f2a850594b04a7cb7cf31f4c0cd25fef5ba107d1731d3.jpg) + +active neural mapping system with 6DoF movement in unrestricted spaces, while [28] integrates Voronoi planning to scale exploration across larger environments. + +3DGS offers a faster alternative, making real-time mapping and exploration more feasible. Concurrent works like ActiveSplat [33] utilize a hybrid map with topological abstractions for efficient planning, and AG-SLAM [24] incorporates 3DGS with Fisher Information to balance exploration and localization in complex environments. In this work, we propose an Active Gaussian Mapping method that leverages the real-time rendering capability of 3DGS to enable effective planning and exploration. + +# 3. ActiveGAMER: Active Gaussian Mapping + +In this section, we present ActiveGAMER (Fig. 2), a pioneering 3D Gaussian Splatting framework for active reconstruction that incorporates rendering-based planning. Our approach begins with the Gaussian Splatting mapping module, an efficient representation for real-time, high-fidelity geometric and photometric reconstruction. We utilize SPLaTAM [25] as the mapping backbone, as detailed in Sec. 3.1, establishing a foundation for dense reconstruction using Gaussian Maps. Building upon this, Sec. 3.2 introduces our rendering-based planning module for goal-directed searching and path planning. To address the limitations of the map update process in SPLaTAM, we propose an enhanced update strategy in Sec. 3.3, incorporating a global-local keyframe selection strategy. This module leverages rendering-based information, ensuring seamless integration into existing incremental 3DGS to improve mapping robustness. We then present a post-refinement module that further improves the photometric reconstruction in Sec. 3.4. Finally, we conclude this section with an overview of the Active Gaussian Mapping process in Sec. 3.5. + +# 3.1. Gaussian Mapping + +Gaussian Splatting Recent advancements have established 3D Gaussian Splatting as both expressive and efficient. These representations effectively encode a scene's appearance and 3D geometry as a collection of 3D Gaussians, $\mathbf{G} = \{\mathbf{G}_i\}_{i=1}^N$ , enabling real-time rendering into high-fidelity color and depth images. A series of prior works, including [25, 38], have demonstrated the effectiveness of 3DGS in 3D reconstruction. Given a stream of RGB-D images, dense mapping is done by optimizing the 3D Gaussian representation through rendering supervision. + +Rather than using the comprehensive 3DGS representation originally proposed in [26], we adopt the simplified Gaussian Mapping suggested in SplaTAM [25]. This simplified approach utilizes only view-independent color and isotropic Gaussians, reducing the number of parameters needed for each Gaussian. The parameters for each Gaussian include color $\mathbf{c}$ , center position $\mu$ , radius $r$ , and opacity $o$ . A 3D point $\mathbf{x}$ is influenced by all Gaussians based on a standard Gaussian function weighted by its opacity: + +$$ +f (\mathbf {x}) = o \exp \left(- \frac {| \mathbf {x} - \boldsymbol {\mu} | ^ {2}}{2 r ^ {2}}\right). (1) +$$ + +Real-time Rendering A key strength of 3DGS is its real-time rendering capability, enabling high-fidelity color and depth image generation from arbitrary camera poses. Leveraging Gaussian Maps, 3DGS can efficiently render scenes by projecting 3D Gaussians into 2D pixel space. Following the approach proposed in [26], we achieve efficient rendering by transforming all 3D Gaussians to camera space, sorting them front-to-back, and projecting them onto the image plane. Each Gaussian is then splatted in 2D, where color and transparency are composited using alpha-blending. The + +color at a pixel, $\mathbf{p} = (u,v)$ , is defined as: + +$$ +C (\mathbf {p}) = \sum_ {i = 1} ^ {n} c _ {i} f _ {i} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} \left(1 - f _ {j} (\mathbf {p})\right), \tag {2} +$$ + +where $f_{i}(\mathbf{p})$ is derived from the Gaussian's position and size in 2D pixel space, computed as: + +$$ +\boldsymbol {\mu} ^ {2 \mathrm {D}} = K \frac {T _ {t} \boldsymbol {\mu}}{d}, \quad r ^ {2 \mathrm {D}} = \frac {f r}{d}, \quad \text {w h e r e} \quad d = \left(T _ {t} \boldsymbol {\mu}\right) _ {z}. \tag {3} +$$ + +Here, $K$ represents the camera intrinsic, including focal length $f$ and principal point, while $T_{t}$ encodes the camera's extrinsics, capturing its rotation and translation in world space at time $t$ . The variable $d$ represents the depth of the Gaussian in camera coordinates. + +Similarly, the depth map is rendered as: + +$$ +D (\mathbf {p}) = \sum_ {i = 1} ^ {n} d _ {i} f _ {i} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\mathbf {p})). \tag {4} +$$ + +We also generate a silhouette mask to indicate if a pixel contains information from the Gaussian map: + +$$ +S (\mathbf {p}) = \sum_ {i = 1} ^ {n} f _ {i} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\mathbf {p})). \tag {5} +$$ + +Optimization The differentiable nature of this rendering process enables end-to-end optimization, where gradients are calculated directly from the discrepancy between rendered images and RGB-D inputs. These gradients drive updates to each Gaussian's parameters through minimization of the following loss: + +$$ +L = \sum_ {\mathbf {p}} (S (\mathbf {p}) > 0. 9 9) (L _ {1} (D (\mathbf {p})) + 0. 5 L _ {1} (C (\mathbf {p}))). \tag {6} +$$ + +By thresholding the silhouette mask, we selectively optimize pixels in regions with high-quality visibility, enhancing the stability of the reconstruction. + +Gaussian Densification Gaussian Densification is designed to adaptively add new 3D Gaussians in response to incoming data. Using the known camera pose and depth measurements, we compute a densification mask to determine where additional Gaussians are needed, avoiding redundant creation in regions already well-represented by the current model. The densification mask is defined as: + +$$ +\begin{array}{l} M (\mathbf {p}) = (S (\mathbf {p}) < 0. 5) + \\ \left(D _ {\mathrm {G T}} (\mathbf {p}) < D (\mathbf {p})\right) \left(L _ {1} (D (\mathbf {p})) > \lambda \mathrm {M D E}\right). \tag {7} \\ \end{array} +$$ + +This mask identifies areas where: (1) the density of Gaussians is low ( $S < 0.5$ ), and (2) new Gaussians are required to refine the geometry, as indicated by a depth error exceeding a threshold of $\lambda = 50$ times the median depth error (MDE). + +# 3.2. Rendering-based Planning + +In Sec. 3.1, we introduce a Gaussian Mapping method using known camera parameters and incremental RGB-D observations. Typically, mapping is conducted in a passive manner, where the capture trajectory is controlled manually. However, passive capture does not ensure a complete, high-fidelity reconstruction of the scene. In this section, we propose an active mapping system that leverages the Gaussian Map, specifically exploiting its efficient rendering capabilities—advantages that are unattainable with neural radiance fields [18, 69]. We propose a rendering-based information gain to achieve active exploration. + +Our approach involves a two-stage active mapping strategy. First, a coarse-to-fine exploration stage reconstructs the scene as comprehensively as possible. Subsequently, a post-refinement stage further enhances the Gaussian Mapping representation for rendering purpose once the exploration phase is complete. + +In the exploration stage, our goal is to incrementally determine the next-best-view (NBV) to enhance the completeness of the Gaussian Map. Leveraging the real-time rendering capability of the Gaussian Map, we can extensively generate NBV candidates across the environment and evaluate the information gain for each candidate. We first present our exploration information gain formulation, followed by a mechanism for efficiently maintaining a candidate pool to enable rapid information gain evaluation. After that, we present a coarse-to-fine exploration strategy that further accelerates exploration efficiency. Finally, we introduce a local path planner introduced in [18]. + +Exploration Information Gain Given a candidate camera pose, we compute its exploration information gain, $\mathcal{I}$ , based on the rendered silhouette mask $S$ with respect to the up-to-date Gaussian Map. The number of missing pixels in the rendered silhouette mask, $N_{S_i}$ , quantifies the information gain for the candidate viewpoint. We further incorporate a motion cost represented by the $L_2$ distance between the current location $T_{t,x}$ and the candidate location $T_{i,x}$ , aiming to reduce overall travel distance during exploration. That is, we prefer a candidate closer to the current camera pose when two candidates yield the same information gain. The distance-weighted information gain is formulated as: + +$$ +\mathcal {I} = \left(1 - \sigma \left(l _ {i}\right)\right) \cdot \sigma \left(\log \left(N _ {S _ {i}}\right)\right), \tag {8} +$$ + +where $\sigma(\cdot)$ is the Softmax function, which normalizes both the distance weighting and $N_{S_i}$ in a relative form; $l_i = \| T_{i,x} - T_{t,x}\|_2$ represents the travel distance, and $N_{S_i} = \sum_{\mathbf{p}} \mathbb{I}(S_i(\mathbf{p}) = 0)$ counts the pixels in the silhouette mask that are zero. We select the candidate viewpoint with the highest $\mathcal{I}$ as the goal pose $T_g$ . + +Exploration Candidate Pool While Gaussian Maps provide real-time rendering capabilities, extensively sampling viewpoints within the scene and evaluating their information gain remains computationally expensive. To manage this, we maintain an Exploration Candidate Pool, allowing us to add new sampled candidate viewpoints, update their associated information gain, and remove them from the pool when necessary. + +Adding candidates from the current observation requires careful consideration, as redundant candidates with overlapping view frustums can occur. To ensure uniform spatial sampling, we incrementally update an occupancy grid for each incoming observation. We refer to the free space within this grid as the Exploration Map, which we use to sample exploration candidates. Rather than sampling the entire exploration map each time, we identify newly added free space voxels by comparing the latest Exploration Map to its previous state and sample candidates only from these new voxels. Candidate positions $T_{e,x}$ are generated from every $v_{1}$ meter, with evenly distributed $v_{2}$ viewing directions based on the Fibonacci lattice. Once candidate poses $T_{e}$ are added to the Exploration Pool, we evaluate all candidates using Eq. (8) and update their information gain, $\mathcal{I}_i$ . For candidates with associated $N_{S_i}$ values below 0.5% of the total pixel count, we consider the viewpoint to be well observed and remove the candidate from the pool to prevent its overpopulation. + +Coarse-to-fine Exploration Oversampling candidates enhances scene coverage and optimizes next-best-view selection but increases evaluation time. To improve exploration efficiency, we introduce a coarse-to-fine strategy, which initially covers the environment with minimal candidates and then refines the reconstruction with finer exploration. In the coarse stage, we sample new free voxels at specific heights, such as a single 2D plane, using larger spatial steps $(v_{1} = 1)$ and fewer viewing directions $(v_{2} = 5)$ . The fine stage increases sampling density, employing multiple height levels, smaller steps $(v_{1} = 0.5)$ , and more viewing directions $(v_{2} = 15)$ to refine the reconstruction. Initially, sampling is restricted to newly added free space; at the start of the fine stage, we sample the entire free space, quickly discarding redundant candidates as most regions have already been observed. This strategy effectively balances exploration speed and comprehensive scene coverage. + +Local Path Planning Once the goal pose is identified, our path planning module initiates to generate a viable path from the current pose, $T_{t}$ , to the goal pose, $T_{g}$ . For this, we use a sampling-based path planning approach similar to Rapid-exploration Random Tree (RRT) [30], with the Exploration Map as the basis. Executing standard RRT in a large-scale 3D environment can be highly time-intensive. + +Algorithm 1 ActiveGAMER +1: Initialization Camera Pose $T_{0}$ ; Gaussian Map $\mathbf{G}_0$ ; Exploration Map $\mathbf{M}_{e,0}$ ; Observations $\{O\}_{i=0}^{0}$ ; Exploration Pool $P_{e}$ ; PLAN_REQUIRED = True; $t = 0$ +2: # EXPLORATION +3: while $P_{e} \neq \emptyset \lor t = 0$ do +4: $t = t + 1$ +5: # Update Database in keyframe steps +6: Observation: acquire a new observation $O_{t}$ +7: Update Database: $\{O\}_{i=0}^{t} \leftarrow \{O\}_{i=0}^{t-1}$ +8: # Update Mapping Models +9: Map Update: $\mathbf{G}_{t} \leftarrow \mathbf{G}_{t-1}, \mathbf{M}_{e,t} \leftarrow \mathbf{M}_{e,t-1}$ +10: # Update Exploration Pool +11: $P_{e} \leftarrow$ PoolUpdate( $\mathbf{M}_{e,t}, \mathbf{M}_{e,t-1}$ ) +if PLAN_REQUIRED then +13: # Search a new goal from the maps +GoalSearch( $\mathbf{G}_{t}, P_{e}, T_{t}$ ) $\rightarrow T_{g}$ +15: # Plan a feasible path based on $\mathbf{M}_{e,t}$ towards $T_{g}$ +16: PathPlanning( $\mathbf{M}_{e,t}, T_{t}, T_{g}$ ) $\rightarrow \{T_{j}\}_{j=t}^{g}$ +17: # Set PLAN_REQUIRED to False +18: PLAN_REQUIRED $\leftarrow$ False +end if +20: # Update pose from planned path +Action $T_{t} \leftarrow \{T_{j}\}_{j=t}^{g}$ +22: # Replanning after reached goal +CheckPlanRequired: update PLAN_REQUIRED +end while + $t_{1} = t$ +26: # POST-REFINEMENT +for $t \leftarrow t_{1}$ to $t_{1} + T$ do +28: # Post-refinement based on $\{O\}_{i=0}^{t_{1}}$ +Map Update: $\mathbf{G}_{t} \leftarrow \mathbf{G}_{t-1}$ +end for + +To address this, we adopt the efficient RRT implementation proposed by [18], and we generate a collision-free path connecting the current and goal locations by sampling within the free space. Additionally, we implement a rotation planning module to ensure a smooth transition from the current orientation to the goal orientation. + +# 3.3. Global-Local Keyframe Selection + +Following SPLaTAM [25], we design our Gaussian Mapping backbone as detailed in Sec. 3.1. Instead of optimizing with every frame, SPLaTAM selects every fifth frame as a keyframe and updates the map using a subset of keyframes that overlaps with the current frame. This approach ensures that the map is optimized with keyframes that influence newly added Gaussians, providing sufficient multiview supervision without processing all prior keyframes. + +The $k$ selected local keyframes include the current frame, the last keyframe, and $k - 2$ keyframes with the highest + +overlap with the current frame. Overlap is determined by projecting the current frame's depth map into a point cloud and counting points within each keyframe's frustum. This local keyframe strategy yields accurate scene representation, especially in recently updated regions. However, it also causes potential overfitting in local areas. Gaussians that do not contribute directly to rendering may have their opacity minimized, particularly those within the view frustum but behind the primary surface. + +To mitigate this issue, we propose a global-local keyframe selection strategy that balances local supervision with global regularization. Global keyframes are selected based on the information they provide, determined by two criteria: (1) Completeness: A keyframe is included if it reveals over $10\%$ new pixels in the silhouette mask. (2) Quality: A keyframe is included if its rendering quality falls below a threshold. Type-1 global keyframes primarily support comprehensive scene reconstruction, while Type-2 keyframes focus on challenging regions. In conclusion, we select half of the keyframes from local overlapping frames and the other half from global supporting keyframes to maintain an effective balance of local detail and global structural accuracy. + +# 3.4. Post-Refinement + +The exploration stage focuses on achieving completeness in both geometric (3D) and photometric (rendering) reconstruction. However, rendering quality may be suboptimal due to limited optimization of the Gaussian Map. To address this, we introduce a post-refinement step, leveraging the global keyframes from Sec. 3.3 to enhance photometric reconstruction quality. + +We note, however, that post-refinement can degrade geometric reconstruction, as Gaussian Map optimizations for rendering involve operations that are unfavorable for preserving geometric detail. Specifically, optimizing the Gaussian Map for photometric quality may result in Gaussian pruning in low-texture areas and removal of redundant Gaussians, reducing geometric completeness. Despite these trade-offs, we observe overall improvements in rendering quality with post-refinement. + +# 3.5.ActiveGAMER System + +After capturing new RGB-D frames, a selection of keyframes is stored in keyframe a database to optimize mapping. Integrating the mapping module from Sec. 3.1 and Sec. 3.3 with the planning module in Sec. 3.2, we establish a comprehensive Active Gaussian Mapping system, namely ActiveGAMER, detailed in Algorithm 1 and illustrated in Fig. 2. This system maintains an up-to-date Gaussian Map in an incremental manner, leveraging the planning module for goal searching and path planning. + +
MethodsAcc. (cm) ↓Comp. (cm) ↓Comp. Ratio (%) ↑
FBE [68]/9.7871.18
UPEN [19]/10.6069.06
OccAnt [50]/9.4071.72
ANM [69]7.809.1173.15
NARUTO[18]6.313.0090.18
Ours1.662.3095.32
+ +Table 1. MP3D Results. Our method shows superior performance with better reconstruction quality and completeness. + +# 4. Experiments and Results + +# 4.1. Experimental Setup + +**Simulator and Dataset** Our experiments are conducted in the Habitat simulator [52] and evaluated on two photorealistic datasets: Replica [60] and Matterport3D (MP3D) [7]. We use 8 scenes from Replica [61] and 5 scenes from MP3D [69] for analysis. Each experiment runs for 2000 steps in Replica and 5000 steps in MP3D, with the extended steps in MP3D reflecting its larger scene sizes and need for thorough exploration. + +In these experiments, our system processes posed RGB-D images at a resolution of $680 \times 1200$ , with vertical and horizontal fields of view set at $60^{\circ}$ and $90^{\circ}$ , respectively. The voxel size for generating the Exploration Map is fixed at $5\mathrm{cm}$ across all experiments. + +Unlike prior active radiance field methods, which often constrain actions to teleporting between discrete locations [44, 51], moving within hemispheres [75], or navigating limited 2D planes [8, 69], our approach enables 6DoF movement in unrestricted 3D spaces. + +Geometric Metrics We evaluate geometric reconstruction using three metrics: Accuracy (cm), Completion (cm), and Completion ratio (\%) with a 5 cm threshold. To calculate these metrics, we evenly sample 3D points from the ground-truth meshes and compare them with a point cloud uniformly extracted from the Gaussian Maps. + +Rendering Metrics For measuring RGB rendering performance we use PSNR, SSIM and LPIPS. For depth rendering performance we use Depth L1 distance. + +# 4.2. Evaluation + +To the best of our knowledge, this work is among the first to address active mapping using 3D Gaussian Splatting. Concurrently, recent technical reports [24, 33] explore related concepts, highlighting the growing interest in this area. + +As discussed in Sec. 3.4, the Refined Model enhances rendering performance but reduces geometric completeness by removing redundant Gaussians. To accurately assess both aspects, we evaluate geometric performance using the Exploration Model and rendering performance using the Refinement Model. The choice of model depends on the + +![](images/396f8c2a58c41d2afae1a6e7c998aa5d9506559231e702693d9d7a4242315db6.jpg) +Figure 3. 3D Reconstruction Results on MP3D. Shown are two scenes (Left: pLe4; Right: HxpK) with results distinguished by border colors: [Ground Truth, NARUTO [18], Ours]. For NARUTO, black regions indicate neural mapping extrapolation, sometimes with inaccuracies. For our method, colored point clouds are extracted from the Gaussian Map for visualization; note that noisy points here do not reflect actual rendering quality. Unlike neural maps, the explicit Gaussian Map representation avoids inaccurate extrapolation artifacts. + +
MethodsMetricsAvg.Of0Of1Of2Of3Of4R0R1R2
SplaTAM [25]PSNR ↑29.0830.1533.6026.4023.9729.8731.1329.7427.79
SSIM ↑0.950.960.960.940.900.960.970.960.96
LPIPS ↓0.140.130.160.160.210.130.090.120.11
L1-D ↓1.381.340.891.753.281.260.640.841.02
NARUTO [18]PSNR ↑26.0128.8833.2724.2625.3222.7524.7026.1722.77
SSIM ↑0.890.930.960.890.910.880.870.900.82
LPIPS ↓0.410.400.270.380.380.440.490.430.52
L1-D ↓9.544.511.355.166.287.766.074.0841.14
OursPSNR ↑32.0233.7035.7829.9832.1733.5929.6430.2531.03
SSIM ↑0.970.970.970.970.980.980.960.960.97
LPIPS ↓0.110.100.130.100.080.080.140.120.10
L1-D ↓1.121.380.861.700.990.870.991.011.21
+ +Table 2. Novel View Rendering Performance on Replica [60]. + +specific application requirements, balancing the need for detailed geometry versus high-quality rendering. + +Geometric Evaluation Tab. 1 presents a quantitative comparison of our system against prior studies on MP3D. Our approach consistently outperforms previous methods across all evaluation metrics. The accuracy metric reflects the geometric precision of the Gaussian Map, which, given our initialization with observed depths, achieves high accuracy as expected. Additionally, both the Completion and Completion Ratio metrics, which measure the 3D space coverage through active exploration, show that our method attains exceptional completeness. This achievement stems from our rendering-based planning, which efficiently identifies the most informative viewpoints, combined with the agent's unrestricted movement capabilities. We also present qualitative comparisons in Fig. 3. + +Rendering Evaluation We evaluate rendering performance on the high-fidelity Replica Dataset, as shown in Tab. 2, using novel view trajectories for Novel View Rendering. Two baselines are used for comparison. + +The first baseline is the passive mapping method, SPLaTAM [25]. For a fair comparison, we disable its track + +ing thread and simulate handheld scanning with a manually defined capture trajectory. Since manual scanning doesn't cover the entire scene, we exclude uncovered regions from the evaluation, focusing only on captured areas. + +The second baseline is NARUTO [18], a state-of-the-art active mapping method that uses a neural radiance field. As NARUTO actively maps the environment, we evaluate all pixels in the novel views to assess its coverage fully. + +Our proposed method consistently outperforms both baselines by a significant margin, benefiting from actively building a Gaussian Map representation capable of high-fidelity rendering, as evidenced in the quantitative results and qualitative examples in Fig. 4. + +# 4.3. Ablation Studies + +The Replica dataset features photorealistic 3D indoor scenes, represented by dense meshes with higher completeness than MP3D scenes. Given this level of detail, we primarily conduct our ablation studies on Replica to obtain more representative and robust results. In the following experiments, we use Full as the reference system, with ablation studies performed with respect to this configuration. The results are shown in Tab. 3. + +Coarse-to-Fine Exploration We first investigate the effectiveness of the coarse-to-fine exploration strategy. While Coarse Exploration alone achieves substantial scene completeness, Fine Exploration—denoted as “w/o Refine”—further enhances both geometric and photometric reconstruction. Fig. 5 illustrates the progression of exploration completeness. As shown, our method quickly reaches high completeness in the Coarse Exploration stage and then refines missing details in the Fine Exploration stage. + +Post-Refinement As discussed in Sec. 3.4, the post-refinement step in our full method improves rendering qual + +![](images/6c008f6f6b452fd1ab7c4c5e2185ebebbb11a86e0eb7876c2cc1724904073c3d.jpg) +Figure 4. Rendering Results on Replica. Two scenes (office0, office4) are shown in the first and second rows, respectively. The results represent [Ground Truth, NARUTO, SplaTAM w/o tracking, Ours]. Our renders demonstrate higher fidelity across most regions. + +![](images/f4062fd74bda4d9a9107fda9be58e4744208c48bc80084c1d4c82ab0614bfdb2.jpg) +Figure 5. Reconstruction Progress in Replica-office. The distribution of rendering-based information $(N_{S_i})$ of candidate viewpoints is shown alongside reconstruction performance metrics. As information decreases, completeness and rendering performance improve, with Fine-Exploration yielding an additional boost. + +
Exp.Comp. (cm) ↓Comp. Ratio (%) ↑PSNR (dB) ↑L1-D (cm) ↓
Coarse Exploration1.7794.5329.771.80
w/o Global-KF2.1994.8730.731.23
w/o Refine.1.5696.5030.671.42
Full1.8095.4532.021.12
+ +Table 3. Ablation Studies on Replica. + +ity by further optimizing the Gaussian Map based on a rendering-oriented losses. However, this step may lead to Gaussian pruning, reducing the completeness of the map. When Post-Refinement is omitted ("w/o Refine"), the geometric reconstruction metrics improve due to the retention of redundant Gaussians, which are beneficial for geometry. Nonetheless, the post-refinement step significantly enhances rendering performance. + +Global-Local Keyframe Selection In the experiment "w/o Global-KF," we assess the impact of excluding Global Keyframes. Without the regularization from Global Keyframes, 3D reconstruction performance declines, underscoring the importance of supervising by local and global keyframes to optimize the Gaussian Map effectively. + +# 5. Discussion + +In this paper, we introduced ActiveGAMER, an active mapping system that leverages 3D Gaussian Splatting (3DGS) for efficient, high-fidelity real-time scene reconstruction and exploration. By harnessing the fast rendering capabilities of 3DGS, our approach overcomes limitations of traditional NeRF-based methods, enabling unrestricted 6DoF movement and enhancing both geometric completeness and photometric fidelity. + +Key features of ActiveGAMER include a rendering-based information gain module for optimal viewpoint selection and a balanced framework incorporating coarse-to-fine exploration, post-refinement, and global-local keyframe selection. Together, these components enable autonomous, high-quality exploration and reconstruction in complex environments, achieving state-of-the-art accuracy and fidelity. Extensive evaluations on challenging datasets like Replica and MP3D confirm that ActiveGAMER outperforms existing methods in both geometric accuracy, reconstruction completeness, and rendering quality, highlighting 3DGS as a valuable tool for real-time active vision applications + +While ActiveGAMER demonstrates strong performance, several directions for future work could enhance its applicability. First, real-world scenarios require a robust planning and localization module to address assumptions of known localization and perfect action execution. Second, to increase system versatility, future iterations should account for real-world motion constraints that affect the agent's movement. Additionally, the current rendering-based information gain approach may overlook certain regions, such as double-sided objects. For example, after reconstructing one side of an object, the system may not detect the need to explore the back side if it's not visible in the initial view, leading to incomplete reconstructions. Future work will aim to integrate additional semantic and surface cues to better understand scene complexity and enhance exploration guidance. + +# References + +[1] Michal Adamkiewicz, Timothy Chen, Adam Caccavale, Rachel Gardner, Preston Culbertson, Jeannette Bohg, and Mac Schwager. Vision-only robot navigation in a neural radiance world. IEEE Robotics and Automation Letters, 7(2):4606-4613, 2022. 2 +[2] Dejan Azinović, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural rgb-d surface reconstruction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6290-6301, 2022. 1, 2 +[3] Jiawang Bian, Zhichao Li, Naiyan Wang, Huangying Zhan, Chunhua Shen, Ming-Ming Cheng, and Ian Reid. 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Our event-based active hyperspectral imaging system achieves real-time capture up to 30 FPS as well as $59.53\%$ bandwidth reduction while maintaining accuracy comparable to frame-based methods. (a) System prototype. (b) Illustration of our working principle. (c) Reconstructed results in sRGB. (d) Spectral accuracy validation against ground truth. (e) Reconstructed hyperspectral images. + +# Abstract + +Hyperspectral imaging plays a critical role in numerous scientific and industrial fields. Conventional hyperspectral imaging systems often struggle with the trade-off between capture speed, spectral resolution, and bandwidth, particu + +larly in dynamic environments. In this work, we present a novel event-based active hyperspectral imaging system designed for real-time capture with low bandwidth in dynamic scenes. By combining an event camera with a dynamic illumination strategy, our system achieves unprecedented temporal resolution while maintaining high spectral fidelity, all at a fraction of the bandwidth requirements of traditional systems. Unlike basis-based methods that sacrifice spectral resolution for efficiency, our approach enables con + +tinuous spectral sampling through an innovative “sweeping rainbow” illumination pattern synchronized with a rotating mirror array. The key insight is leveraging the sparse, asynchronous nature of event cameras to encode spectral variations as temporal contrasts, effectively transforming the spectral reconstruction problem into a series of geometric constraints. Extensive evaluations of both synthetic and real data demonstrate that our system outperforms state-of-the-art methods in temporal resolution while maintaining competitive spectral reconstruction quality. + +# 1. Introduction + +Hyperspectral imaging, which captures detailed spectral information across a wide range of wavelengths, has become increasingly crucial in applications ranging from remote sensing [1, 14, 18] to medical diagnostics [5, 26, 50]. Traditional approaches typically suffer from a dilemma: they must balance spectral resolution, temporal resolution, and data bandwidth. While recent advances in computational imaging have made progress in addressing these challenges, existing solutions often require compromising among these competing factors. Specifically, current state-of-the-art methods broadly fall into three categories: i) scanning-based systems that achieve high spectral resolution at the cost of temporal resolution [4, 9, 10, 15, 21, 40], ii) snapshot systems that sacrifice spectral resolution for speed [31, 55, 59, 60], and iii) coded aperture approaches that require complex computational reconstruction [2, 22, 53]. Despite their respective merits, none of these approaches can simultaneously achieve high temporal resolution, high spectral resolution, and low bandwidth requirements—a capability increasingly demanded by emerging applications such as real-time material classification and dynamic scene understanding. + +Event cameras have recently revolutionized high-speed imaging by responding to local intensity changes rather than capturing full frames, offering microsecond temporal resolution and high dynamic range [24, 35, 43]. They can potentially benefit real-time capture of hyperspectral imaging [16]. However, leveraging their advantages for hyperspectral imaging presents several fundamental challenges. i) Spectral information must be reliably encoded into temporal events while maintaining spatial consistency—a task complicated by motion artifacts and temporal aliasing in traditional scanning methods. ii) The sparse nature of events can exacerbate the ill-posedness of spectral reconstruction. iii) Event cameras' inherent characteristics—logarithmic response, non-uniform pixel behavior, and refractory periods—introduce complex measurement inconsistencies. + +In this paper, we propose an active hyperspectral imaging system using an event camera. Our key insight is that by synchronizing precisely controlled active illumination with an event camera's superior temporal resolution, we + +can encode spectral information in the temporal domain, effectively decoupling spectral resolution from temporal resolution. Specifically, our system includes a novel optical design that creates a "sweeping rainbow" effect through a synchronized rotating mirror array and blazed grating combination. An illustration of our system's working principle using "sweeping rainbow" illumination to create temporal events encoding spectral information is shown in Fig. 1(b), where the scene contains objects with distinct single-peak spectral responses. This design integrates the cutting-edge features of event cameras, successfully transforming the complex problem of spectral reconstruction into a series of geometric constraints derived from event temporal information. Our mathematical framework shows that each event provides information about the underlying spectral distribution. Together with the usage of SVD and tailored constraints on the spectral solution, our method achieves robust reconstruction even with sparse temporal sampling and measurement inconsistencies in the event camera. + +Our approach offers three fundamental advantages: $i$ ) microsecond-scale temporal resolution inherited from event cameras, enabling the capture of rapid spectral phenomena; $ii$ ) dramatic reduction in data bandwidth through sparse, asynchronous event representation; and $iii$ ) basis-independent spectral resolution, limited only by optical design rather than computational constraints. These make our method excel in applications demanding simultaneous high temporal and spectral resolution. + +Our main technical contributions include: + +- a novel active illumination strategy that enables continuous spectral sampling through precise synchronization with event-based sensing; +- a mathematical framework that reformulates the spectral reconstruction problem as a geometric constraint optimization problem; and +- an efficient solver that leverages physical prior derived from events for spectral reconstruction. + +Through extensive experiments on both synthetic and real data, we demonstrate that our system achieves $59.53\%$ reduction in data bandwidth compared to traditional frame-based approaches. A comprehensive characterization of system performance and limitations is also conducted. Our approach enables the real-time capture (up to 30 FPS) of dynamic spectral phenomena with unconstrained spectral resolution, opening new possibilities in fields where real-time capture of spectral changes and minimal data bandwidth are essential. + +# 2. Related Work + +Hyperspectral imaging. Hyperspectral imaging systems have traditionally involved scanning the scene across either the spatial [4, 10, 40] or spectral [9, 15, 21] dimensions for passively capturing reflectance across different spectral + +bands. Techniques such as spectral filters [41, 55], filter wheels [8], and tunable filters [9, 12, 15, 51] have been widely used to separate incoming light into distinct spectral components. However, these methods typically rely on sequential scanning, which significantly limits their temporal resolution and dynamic sensing capability, often leading to motion artifacts and spectral misalignment. Some methods leverage coded aperture [20, 45], disperser [2, 31], or both [22, 25, 53, 58-60] to form a Coded Aperture Snapshot Spectral Imaging (CASSI) system, achieving computational hyperspectral imaging from a subset of measurements. While offering faster acquisition speeds, they face challenges in terms of hardware complexity, versatility, and spectral accuracy. Moreover, researchers have explored alternative active illumination schemes [17, 23, 37, 46, 52, 54, 56] to reach a balance. Park et al. [37] showed multiplexed illumination could boost independent measurements using multiple light sources and camera channels. Similarly, Chi et al. [7] proposed optimized wide-band filtered illumination to maximize signal and minimize ambient light influence. Recently, Shin et al. [46] developed a hyperspectral imaging system based on dispersed structured light, utilizing a diffraction grating to achieve hyperspectral 3D imaging with higher spectral resolution than filter-based methods. The current landscape of hyperspectral imaging systems highlights the need for approaches that effectively address the inherent trade-offs between spectral resolution, temporal efficiency, and adaptability. Our proposed system extends previous works by combining active dispersive illumination with event-based imaging in a novel manner. + +Event-based vision. Event cameras have reshaped imaging by enabling real-time data acquisition and robust performance in dynamic scenes. They can be used not only to directly reconstruct intensity videos [35, 36, 39, 42] or color videos [27, 30, 33, 44], but also to assist frame-based cameras in tasks like deblurring [48], high-frame-rate [49] and high-dynamic-range [29] imaging. Also, event cameras have improved deblurring in snapshot mosaic hyperspectral imaging [13]. In active lighting scenarios, event cameras capture rapid illumination shifts to enhance scene perception. Structured and intensity-varying lighting approaches trigger events for various applications. Structured lighting projects patterns onto objects, with event cameras capturing spatial disparities for 3D shape reconstruction [28]. High-speed digital light projection [19] facilitated 3D surface reconstruction through digital image correlation. ESL [34] synchronized projector and camera events, reducing noise in structured light applications. Besides structured light, researchers use light sources with intensity changes to trigger event signals. Morgenstern et al. [32] employed lookup tables for efficient real-time depth estimation under structure light. Takatani et al. [47] leveraged bispectral photometry under modulated light, enabling depth and concentration estimation in tur + +![](images/aa4518e833751da7434c9c3b42719e407a1ce79dd3649960bd2227d8e929de2d.jpg) +Figure 2. Illustration of our system. Our system combines a point light source, optical elements (convex lenses, vertical slit, and cylindrical lens), and a blazed grating to create a "sweeping rainbow" effect across the scene. The scattered light is collected through a beam-splitter and light panel arrangement before being captured by an event camera. This design enables rapid spectral scanning of the scene through the rotating mirror array's continuous motion, whose temporal brightness changes are rapidly captured by the event camera with microsecond-level resolution. + +bid media. EventPS [57] estimates the surface normal by analyzing the events triggered by a continuously rotating light source. Transient light triggers are employed [6, 16] to resolve intensity-distance ambiguity and capture radiance variations. Bajestani et al. [3] reconstructed color events with adaptive structured lighting, achieving an effective 1400 FPS with a monochrome event camera. Despite these advanced developments, active hyperspectral imaging with event cameras remains an unexplored area. + +# 3. Method + +# 3.1. Imaging Setup + +Optical architecture. Our system adopts spectral decomposition to analyze different wavelengths of light from a scene, combining spatial scanning (via the rotating mirror array) with spectral separation (via the blazed grating) to build a complete hyperspectral data cube. Our system consists of three key components: a point light source with a convex lens for collimation, a rotating mirror array, and a blazed grating, synchronized for spectral separation. This configuration creates a "sweeping rainbow" effect that systematically maps spectral information to temporal variations. Fig. 1(a) shows the real capture prototype, and Fig. 2 shows how the optical path creates the spectral separation and how + +the rotating mirror array facilitates the spatial scanning of the scene, with the rainbow pattern illustrating the spectral decomposition process. + +The optical path begins with a collimated beam passing through a vertical slit, which is then directed through a series of convex and cylindrical lenses. This vertically parallel light interacts with the blazed grating, creating a wavelength-dependent angular dispersion. The rotating mirror array, positioned at the system's core, continuously redirects the dispersed light at precisely controlled angles. This process results in a temporally varying spectral illumination pattern that dynamically sweeps across the scene. + +Temporal-spectral encoding. The key insight of our design is that the rotating mirror array creates a deterministic illumination pattern, which establishes the relationship between wavelength $\lambda$ and time $\tau$ . For a pixel $x,y$ in the scene, the incoming spectral radiance $L_{x,y}(\lambda,\tau)$ from our illumination device is a function as follows: + +$$ +L _ {x, y} (\lambda , \tau) = T (\lambda + \beta \omega (\tau + \hat {\tau} _ {x})), \tag {1} +$$ + +where $T$ is the spectral radiance of the narrow-band dispersed light, $\omega$ is the illumination pattern rotation speed (half of the mirror rotation speed), $\hat{\tau}_x$ is the initial time offset depending on the horizontal coordinate of the pixel, and $\beta$ is a coefficient describing the width of the rainbow in the unit of nanometer per rad. This relationship enables us to encode high-dimensional spectral information into a temporal sequence that can be efficiently captured by an event camera. + +# 3.2. Problem Formation + +Event formation model. Event cameras capture scene radiance changes on a logarithmic scale. Each pixel measures the radiance changes asynchronously. When the changes of logarithmic radiance at the pixel $x, y$ reaches a triggering threshold $C$ , an event $\{x, y, \sigma, \tau\}$ will be triggered, where $\tau$ is the timestamp, and $\sigma \in \{-1, +1\}$ is the polarity representing the decrease or increase of radiance. Assume there are totally $K$ events triggered at pixel $x, y$ during an illumination cycle. These events are represented as $\mathcal{E}_{x,y} = \{x, y, \sigma_k, \tau_k\}$ , where $k = \{1, 2, ..., K\}$ . The change of radiance value in pixel $x, y$ from $\tau_{k-1}$ to $\tau_k$ becomes: + +$$ +\log \left(I _ {x, y} \left(\tau_ {k}\right) + \epsilon\right) = \log \left(I _ {x, y} \left(\tau_ {k - 1} + \eta\right) + \epsilon\right) + \sigma_ {k} C, \tag {2} +$$ + +where $\epsilon$ is a small offset value to avoid taking the logarithm of zero, and $\eta$ is the refractory time of the pixel [11]. In our system, these intensity changes are induced by the sweeping spectral illumination. Combining the event generation model with our spectral illumination pattern, we can express the relationship between events and spectral content. + +Hyperspectral imaging model. Assuming that there is an object illuminated by an ideal white point light source, which exhibits a flat spectrum curve in the visible light range. For a pixel $x, y$ under spectrum $\lambda$ , the hyperspectral image pixel + +intensity $S_{x,y}(\lambda)$ has the following formula: + +$$ +S _ {x, y} (\lambda) = R _ {x, y} (\lambda) E (\lambda), \tag {3} +$$ + +where $R_{x,y}(\lambda)$ is the reflectance of pixel $x, y$ , and $E(\lambda)$ is the spectral radiance of the ideal white light source shared by all the image plane. Here we assume that the material is non-fluorescent to allow each spectrum be treated independently, omit inter-reflection and sub-surface scattering to have each pixel be treated independently. + +To capture spectrally relevant information using a monochromatic event camera, we design the illumination pattern $L_{x,y}(\lambda, \tau)$ that varies along both wavelength and time as shown in Eq. (1). For a pixel $x, y$ , the observed intensity $I_{x,y}(\tau)$ at time $\tau$ is determined by the interaction between the scene's spectral reflectance and our time-varying illumination $L_{x,y}(\lambda, \tau)$ as follows: + +$$ +\begin{array}{l} I _ {x, y} (\tau) = \int_ {\lambda} D (\lambda) R _ {x, y} (\lambda) L _ {x, y} (\lambda , \tau) d \lambda \\ = \int_ {\lambda} D (\lambda) S _ {x, y} (\lambda) \frac {L _ {x , y} (\lambda , \tau)}{E (\lambda)} d \lambda , \tag {4} \\ \end{array} +$$ + +where $D(\lambda)$ denotes the camera spectral response curve shared by all positions, and $S_{x,y}(\lambda)$ represents the hyperspectral image, which is our reconstruction target. + +Therefore, the event-based active hyperspectral imaging estimation task can be formalized as: by designing the changing light source function $L_{x,y}(\lambda, \tau)$ , given the events captured by an event camera, estimate the hyperspectral image $S_{x,y}(\lambda)$ as if it is illuminated by an ideal white point light source. + +# 3.3. Event-Based Spectral Reconstruction + +In order to estimate the continuous hyper-spectrum image function $S_{x,y}(\lambda)$ in a numerical way, the continuous equation should be discretized for practical implementation. Specifically, we separate the spectral response over the visible spectrum into a discrete set $\mathbb{S} = [\lambda_1,\lambda_2,\dots,\lambda_M]$ of $M$ centered wavelengths sampled from $400\mathrm{nm}$ to $760\mathrm{nm}$ with $\delta = \frac{360}{M}\mathrm{nm}$ interval. Then we can rewrite Eq. (4) into a discrete form: + +$$ +I _ {x, y} (\tau) = \sum_ {m} S _ {x, y, m} \int_ {\lambda_ {m}} ^ {\lambda_ {m} + \delta} D (\lambda) \frac {L _ {x , y} (\lambda , \tau)}{E (\lambda)} d \lambda . \tag {5} +$$ + +Denote the right part that can be pre-calibrated as: + +$$ +A _ {x, y, m} (\tau) = \int_ {\lambda_ {m}} ^ {\lambda_ {m} + \delta} D (\lambda) \frac {L _ {x , y} (\lambda , \tau)}{E (\lambda)} d \lambda , \tag {6} +$$ + +then we have + +$$ +I _ {x, y} (\tau) = \sum_ {m} A _ {x, y, m} (\tau) S _ {x, y, m} \tag {7} +$$ + +For the sake of simplicity, we convert the $M$ dimension of $S_{x,y,m}$ and $A_{x,y,m}(\tau)$ into vectors $\pmb{x} \in \mathbb{R}^M$ and $\pmb{a}_{\tau} \in \mathbb{R}^{M}$ . Also, we only focus on one pixel and omit the subscript $x,y$ in the following sections. The problem can be simplified + +using the dot product + +$$ +I (\tau) = \boldsymbol {a} _ {\tau} \cdot \boldsymbol {x}, \tag {8} +$$ + +at each pixel $x, y$ and moment $\tau$ . + +Null spectrum vector for spectral-temporal mapping. Recall that for each pixel $x, y$ , events are triggered when logarithmic intensity changes exceed threshold $C$ . To see what each pair of events reveals about the hyper-spectrum image, we combine Eq. (8) with Eq. (2) (omitting the non-ideal bias and refractory time) to get the following equation for each pair of events triggered at timestamps $\tau_{k}, \tau_{k - 1}$ : + +$$ +\boldsymbol {a} _ {\tau_ {k}} \cdot \boldsymbol {x} = e ^ {C \sigma_ {k}} \boldsymbol {a} _ {\tau_ {k - 1}} \cdot \boldsymbol {x}. \tag {9} +$$ + +We denote all the components besides $\pmb{x}$ as follows: + +$$ +\boldsymbol {n} _ {k} = \boldsymbol {a} _ {\tau_ {k}} - e ^ {C \sigma_ {k}} \boldsymbol {a} _ {\tau_ {k - 1}}. \tag {10} +$$ + +All the components in $\pmb{n}_k$ are either calibrated in advance, or extracted from the event stream. Then we can see that $\pmb{n}_k \in \mathbb{R}^M$ is perpendicular to $\pmb{x}$ because their dot product is 0, i.e., + +$$ +\boldsymbol {n} _ {k} \cdot \boldsymbol {x} = 0. \tag {11} +$$ + +Here, we name the vector $\pmb{n}_k$ as null spectrum vector. + +The event-triggered constraints provide a series of equations Eq. (9) that relate consecutive measurements. Each pair of events generates a null spectrum vector $\hat{n}_k$ according to equation Eq. (10), forming the basis of our reconstruction approach. + +Spectral reconstruction from augmented null spectrum vectors. Null spectrum vector provides information about the spectrum shape of the target image $S(\lambda)$ . However, the absolute value of the image is still ambiguous. To solve this problem, we add a direct light to the sensor and propose the following augmented null spectrum vector. + +The event signal captured previously lacks absolute intensity because the event only provides a relative intensity ratio between a pair of timestamps. To introduce the absolute intensity value into the event signal, we add a constant intensity value $c$ to the sensor. This addition is achieved by putting a beam splitter and another constant planner light in front of the event camera. The captured intensity $\hat{I}(\tau)$ with this constant light has the following formula: + +$$ +\hat {I} (\tau) = \boldsymbol {a} _ {\tau} \cdot \boldsymbol {x} + c = \left[ \begin{array}{l} \boldsymbol {x} \\ 1 \end{array} \right] \cdot \left[ \begin{array}{l} \boldsymbol {a} _ {\tau} \\ c \end{array} \right]. \tag {12} +$$ + +By concatenating another dimension with the added constant light intensity $c$ , we achieve the augmented null spectrum vector $\hat{n}_k$ as: + +$$ +\hat {\boldsymbol {x}} \cdot \hat {\boldsymbol {n}} _ {k} = 0, \tag {13} +$$ + +where + +$$ +\hat {\boldsymbol {x}} = \left[ \begin{array}{l} \boldsymbol {x} \\ 1 \end{array} \right], \quad \text {a n d} \quad \hat {\boldsymbol {n}} _ {k} = \left[ \begin{array}{l} \boldsymbol {a} _ {k} \\ c \end{array} \right] - e ^ {\sigma_ {k} C} \left[ \begin{array}{c} \boldsymbol {a} _ {k - 1} \\ c \end{array} \right]. \tag {14} +$$ + +The events $\mathcal{E}_{x,y}$ triggered at pixel $x, y$ over time within the static state of the scene can build up a system of constraints. + +Denote matrix $\hat{N} \in \mathbb{R}^{K \times (M + 1)}$ the matrix whose rows are $M + 1$ dimensional augmented null spectrum vectors $\hat{n}_k, k = 1, 2, \dots, K$ . We can calculate $\pmb{x}$ by solving the least square minimization problem + +$$ +\boldsymbol {x} ^ {*} = \operatorname {a r g m i n} _ {\boldsymbol {x}} \| \hat {\boldsymbol {N}} \hat {\boldsymbol {x}} \| _ {2}. \tag {15} +$$ + +The weight of hyper-spectrum image $\pmb{x}$ can be calculated by performing SVD, selecting the singular vector corresponding to the minimum singular value, and normalizing it according to the last dimension. However, there are three problems if deploying the SVD solution directly: + +- The SVD solution contains negative values, while all intensities should be positive. The SVD method tends to form a zero-crossing point around frequent events to reduce overall error. As a result, solutions containing zero-crossing points are mostly all wrong. +- The augmented null spectrum vectors $\hat{n}_k$ only provide relative intensity relations among event triggering timestamps. When there is a long gap between the event triggering time, there are no restrictions for the intensity value between the two endpoint timestamps. Drastically changing intensity between the gaps violates the event triggering model. +- For dark pixels or pixels with flat spectrum (white color). There are fewer events generated than the number of bases. The matrix from augmented null spectrum vectors $\hat{n}_k$ is degraded, and there are infinite solutions in this case. + +To solve the first SVD negative value problem, we introduce another set of inequality constraints $S(\lambda) \geq 0, \forall \lambda$ , which can be written as: + +$$ +\boldsymbol {x} _ {m} \geq 0, \quad m = 1, 2, \dots , M \tag {16} +$$ + +which convert the linear least square minimization problem Eq. (15) into a quadratic programming (QP) problem. + +To solve the second long-event-gap hallucinations problem, we introduce a regularization term to suppress drastic intensity drift in the gap of a pair of events. This regularization term adds an L2 penalty to the intensity values between two events and the linear interpolation between each pair of events as follows: + +$$ +R _ {\text {i n t}} = \sum_ {k} \sum_ {\tau \in \left(\tau_ {k - 1}, \tau_ {k}\right)} \left(\left(\boldsymbol {a} _ {\tau} - \boldsymbol {a} _ {\tau} ^ {\prime}\right) \cdot \boldsymbol {x}\right) ^ {2}, \tag {17} +$$ + +where + +$$ +\boldsymbol {a} _ {\tau} ^ {\prime} = \frac {\tau_ {k} - \tau}{\tau_ {k} - \tau_ {k - 1}} \boldsymbol {a} _ {\tau_ {k - 1}} + \frac {\tau - \tau_ {k - 1}}{\tau_ {k} - \tau_ {k - 1}} \boldsymbol {a} _ {\tau_ {k}}. \tag {18} +$$ + +To solve the third matrix degraded problem, we introduce another regularization term to suppress high-frequency changes in the spectrum as follows: + +$$ +R _ {\text {s p e c}} = \sum_ {k \in [ M _ {\text {s t a r t}}, M ]} \left(\boldsymbol {f} _ {k} \cdot \boldsymbol {x}\right) ^ {2}, \tag {19} +$$ + +where $\pmb{f}_k = \left[\cos \frac{1.5k\pi}{M},\cos \frac{2.5k\pi}{M},\dots,\cos \frac{k\pi(M + 0.5)}{M}\right]^\top$ and $M_{\mathrm{start}}$ represents the frequency to start adding penalty. + +To summarize, given a set of events at pixel $x$ , $y$ over time, + +![](images/dbc08e892da4544e8e25e64aa262c2318f6f2eb31dd55705405d38486c172e7c.jpg) + +![](images/650c82646d1914112e4b4e44affdce04fe92364dc4f97802c2164c342f833fd2.jpg) + +![](images/696f8b3f94052e6c9a7377a9e32e48d2dbf80eb752f2bba29c3ba0dc728a1861.jpg) +Figure 3. Influence of different constraints on spectral reconstruction quality. Four variants are compared: (a) without non-negative constraints, showing physically implausible negative spectral values (SAM: 30.23, PSNR: 26.62); (b) without low-frequency prior, resulting in high-frequency artifacts (SAM: 30.97, PSNR: 26.42); (c) with reduced anti-drift constraints, exhibiting temporal instability (SAM: 26.28, PSNR: 27.81); and (d) our full method incorporating all constraints, achieving the most accurate and stable reconstruction (SAM: 13.42, PSNR: 33.60). + +![](images/03fe226bfef99c1219a6c86e2495c6bfda7ce4962098e1efe47a92c2ffc3ba7c.jpg) + +the spectral reconstruction in Eq. (15) can be reformulated as a constrained optimization problem: + +$$ +\min _ {\boldsymbol {x}} \left(\| \hat {\boldsymbol {N}} \hat {\boldsymbol {x}} \| _ {2} ^ {2} + \alpha_ {\text {i n t}} R _ {\text {i n t}} (\boldsymbol {x}) + \alpha_ {\text {s p e c}} R _ {\text {s p e c}} (\boldsymbol {x})\right), \tag {20} +$$ + +subject to: $\pmb{x}_m \geq 0, \quad m = 1,2,\dots,M,$ + +where $R_{\mathrm{int}}(\pmb{x})$ is a sparsity regularizer addressing measurement noise, $R_{\mathrm{spec}}(\pmb{x})$ is a smoothness regularizer promoting spectral continuity, $\alpha_{\mathrm{int}}, \alpha_{\mathrm{spec}}$ are regularization parameters. + +Fig. 3 illustrates the critical role of different constraints in our reconstruction pipeline. The ablation study demonstrates that non-negative constraints prevent physically impossible negative spectral values, while low-frequency priors suppress high-frequency artifacts. Anti-drift constraints ensure temporal stability. + +# 3.4. Calibration + +Calibration is crucial for reliable hyperspectral reconstruction. Our system requires the calibration of several parameters: the time-varying spectral intensity of the sweeping rainbow illumination $L(\lambda, \tau)$ , the constant illumination $c$ , the event camera's spectral response curve $D(\lambda)$ , and the event triggering threshold $C$ . A detailed description of the calibration procedure of $c$ , $D(\lambda)$ , and $C$ can be found in the supplementary, while the calibration of $L(\lambda, \tau)$ is as follows. + +We decompose the calibration of $L(\lambda, \tau)$ into two subproblems using a laser point as a temporal-spatial reference. The laser beam, being reflected by the same mirror array, maintains a fixed relative position to the sweeping rainbow strip. First, the temporal relationship between the rainbow strip arrival and event triggering at each pixel is established. + +![](images/678977647331b797a3da35ea642a131155eb405eeeb0264e69efe72f68022938.jpg) +Figure 4. Temporal evolution of spectral illumination patterns of our system. Different narrow-band illuminations are projected to different locations of the scene, forming a sweeping rainbow strip pattern. Spectral characteristics of the broadband light source and reconstructed hyper-spectral imaging range are also elaborated. + +Assuming vertical alignment of the projected rainbow strip, pixels in the same column experience identical temporal patterns. We track the laser point position at the scene's bottom edge to determine these temporal relationships. Second, we characterize the spectral intensity distribution across time by operating the mirror array at a constant, low angular velocity while recording spectral measurements with a spectrometer. By modulating the laser between on and off during measurement and correlating with detected laser positions, we obtain a comprehensive mapping of spectral intensity variations across both time and wavelength. The real-world spectral radiance captured from our modulated illumination pattern is shown in Fig. 4, along with the input lamp spectral radiance and the position mapping to the rainbow strip. + +# 4. Experiments + +# 4.1. Implementation Details + +Our prototype system employs an IMX636 event camera as the primary sensor. Illumination is provided by a high-power xenon lamp, which delivers the broad spectral coverage and intensity stability necessary for reliable hyperspectral measurements. To establish a stable baseline illumination level, we utilize an iPhone 7's LCD display with DC dimming capability, eliminating potential temporal artifacts from screen flicker. The rotating mirror array operates at two distinct speeds: $180\mathrm{rpm}$ for static scene capture, and $600\mathrm{rpm}$ for dynamic scenes, enabling hyperspectral video capture at 10 frames per second. Our spectral reconstruction pipeline estimates 72 discrete channels spanning $400 - 760\mathrm{nm}$ at $5\mathrm{nm}$ intervals, providing detailed coverage of the visible spectrum. Details of the algorithm are in the supplementary. + +# 4.2. Experimental Protocol + +Ground truth acquisition. Ground truth spectral measurements are obtained using a calibrated EBA NH8 hyperspectral camera, capable of measuring spectra from 380-1000 nm. These measurements are conducted under the same xenon + +lamp used in our system, allowing direct calculation of surface reflectance spectra for validation. The measurements are spatially registered with our reconstructions. + +Data simulation. Our synthetic dataset generation pipeline simulates the complete optical and sensing characteristics of the system, including the non-ideal narrow-band illumination pattern, non-ideal event triggering, and frame camera imaging noises. More details can be found in the supplementary material. + +Compared methods. We evaluate the proposed system against the following baselines: i) Full-bandwidth frame-based method. ii) Bandwidth-matched frame-based method. iii) Parkkinen basis method [38]. iii) CASSI-based method [25, 58]. More details can be found in the supplementary material. + +# 4.3. Comparison Results + +High-frequency spectral feature recovery. We first evaluate our method's capability to recover high-frequency spectral features using a challenging rainbow pattern (Fig. 5). This test case is particularly demanding as it contains sharp spectral transitions and narrow-band features that are difficult to capture with traditional methods. As shown in Fig. 5(a-d), basis-based methods struggle to accurately represent these sharp spectral features, exhibiting significant smoothing artifacts. While the full-bandwidth frame-based method (1200 frames) captures these features accurately, it requires substantial data bandwidth, 100 times compared to ours. The bandwidth-matched frame-based method, operating under the same data constraints as our approach, shows degraded performance due to temporal undersampling. Our method (Fig. 5(b)) successfully recovers the sharp spectral transitions while maintaining high spatial fidelity. The spectral profiles in Fig. 5(i) demonstrate that our approach achieves acceptable accuracy using significantly low bandwidth. This superior performance stems from our event-based encoding scheme, which efficiently captures temporal changes in spectral information. + +We also compare our method with CASSI-based methods [25, 58] and evaluate the event efficiency comparing frame-based methods with our method. More details can be found in the supplementary material. + +# 4.4. Evaluation on Synthetic Data + +Evaluation on a ColorChecker. We conduct a systematic evaluation using a standard ColorChecker chart (Fig. 6), which provides a diverse set of well-characterized spectral signatures. The quantitative results show that our method achieves an RMS error of 0.204, SAM of 21.05, and PSNR of 28.46 on average across all 24 patches, with particularly strong performance in regions of smooth spectral variation. The reconstructed spectra (Fig. 6, bottom) demonstrate our method's ability to accurately recover both broad and nar + +![](images/93f489bcd1686d4307715177e88c6c0a54771c1b03a1a72537c2cb85ae42e0ba.jpg) +Figure 5. Comparative analysis of spectral reconstruction on a high-frequency rainbow pattern. Compared methods include (a) ground truth, (b) ours (SAM: 23.27, PSNR: 24.61, SSIM: 0.40), (c) basis-based method (SAM: 25.97, PSNR: 23.79, SSIM: 0.68), (d) bandwidth-matched frame-based method (SAM: NaN, PSNR: 18.73, SSIM: 0.14), with corresponding hyperspectral visualizations (e-h). Spectral profiles (i) validate our method's superior performance over the bandwidth-full and bandwidth-matched frame-based method. + +row spectral features. The error analysis reveals that our approach maintains consistent accuracy across different spectral patterns, with slightly higher uncertainty in regions of flat spectral curves. + +Evaluation on metameric samples. To evaluate our system's ability to distinguish subtle spectral differences, we analyze metameric samples of real and fake daisies (Fig. 7). Our method successfully captures the subtle spectral differences between the metameric pairs (Fig. 7(b)), demonstrating sensitivity to fine spectral features that are crucial for material classification applications. The full hyperspectral reconstruction (Fig. 7(c)) shows consistent performance across the entire spatial field. + +# 4.5. Evaluation on Real Data + +Evaluation on static scene. The real-world performance of our system is demonstrated through comprehensive static scene captures (Fig. 1). Our prototype achieves $59.53\%$ bandwidth reduction compared to traditional frame-based systems while maintaining comparable accuracy (Fig. 1(d)). The reconstructed hyperspectral images (Fig. 1(c,e)) show + +![](images/3a2fd67c519870605e187ba00946c2083c5ca8caafdbc0ab46fdb6881daf5065.jpg) + +![](images/36b837fe76afa7e8a14a37c0cb15549ff91603d09ab3dd0158334346b2dc9efc.jpg) +Figure 6. Evaluation on a ColorChecker. Our method achieves 21.05 SAM and 28.46 PSNR on average across all 24 patches. Top: Spectral accuracy evaluation in terms of RMS error and error bar from 14 measurements, where 2,500 pixels are used in evaluation for each patch. The blue column indicates the mean RMS error. Bottom: Reconstructed spectra of all 24 patches, where solid lines are ours, and the dashed lines are ground truth. + +![](images/ca16c43c1422f4166e839835247769c42a7e62fe4cf9e9f034c1f3502958e30c.jpg) + +![](images/4397671abd4a7d6faf0833d8719d88bed0e5d181afef1e7201bdc5c02f09a8ec.jpg) + +![](images/28c1da6476569591c9a4c9c2a49dc8cd4e063cfb23883728c3bc00635f79d71d.jpg) + +![](images/60a27b33e108f4686aa950df76d7638d66f7bfb28d8b43237421ca6241c624f6.jpg) +Figure 7. Evaluation on metameric samples of fake (left) and real (right) daisies. Our method achieves 10.8 SAM and 34.95 PSNR on average. (a) The reconstructed hyperspectral image in sRGB. (b) Spectra of metameric samples against ground truth measurements, highlighting the system's ability to capture subtle spectral differences. (c) Estimated hyperspectral images. + +![](images/bce7d4452552ba4b85e763e27af814b05ab57014538a5fdd631967dd5153fadb.jpg) + +![](images/8d2ea991cda44b0ec6ab05addc9216c95084b5b0319bf8201926597b75a0f947.jpg) + +excellent agreement with ground truth measurements at representative points. + +Evaluation on dynamic scene. A key advantage of our approach is its ability to capture dynamic spectral phenomena. Fig. 8 demonstrates this capability through the capture of an iridescent paper in motion. The system achieves a tem + +![](images/0dec9e5d0ebd70acfdda6de0bc90947578cda034e5d4b82708ec1f7166508ea8.jpg) + +![](images/0151a1d705d43ebf186529cb99183e7080cf3c5f594f3f53a42f4d6c29d676eb.jpg) + +![](images/f31943424387ff374977462693ae728053a0cad95199c4c0ceb2f2e1458ae52e.jpg) + +![](images/0ce95fc8c25e5282409a16113075b420c563430c6db16bd0941c622b3a5a8350.jpg) + +![](images/6032283b6897bab6b2c6e9dfb66513f191423674ca0efcab495283024f168050.jpg) + +![](images/14ddcb8596e82dfd49d95f7f5d23b408078a8700d7809cc9435efc1080e34590.jpg) + +![](images/08f52b62bdff0653628630a28b7cb49959f47beb94c7863c48ad252006a72bdd.jpg) + +![](images/3ae522b5848e79c83c3541e5ecdce39c800fc85b9a4bee1841561e28f9b96cd2.jpg) + +![](images/3f7fa2e04cd10027279cc953a144ebcd5e84a8b0edc6468a12debaf56798deca.jpg) + +![](images/f7c1fa6b41f57076e4ec3cc71d5ea13645c053634e0cbd0d9c74644ac551b0ea.jpg) + +![](images/68d7b012bf1b7e36a36b24c72abc79e3c4357c5030a7ff31d4ec107fe6d47905.jpg) + +![](images/3b426d92c426b1a84966878350c684c51f2801e098907b03c6c6e304d44e1e24.jpg) +490nm +510nm + +![](images/fbda3bf9cd798a2d9ee20e922f458a62bd8301e90125c2b77ad0131ee478e9eb.jpg) +Figure 8. Real-time hyperspectral imaging on a moving iridescent sticker paper. Top: Three consecutive estimated hyperspectral images rendered in sRGB captured within $0.3\mathrm{~s}$ . Bottom: Corresponding estimated hyperspectral images. + +![](images/2b3c3c192eaf7847d6782d8374faf41974d395ca0dc847506b1765d2396b09dc.jpg) +610nm + +![](images/f766b693fc8477ef035b385570f4bb0ad1e3c2f8c9c943a8310212e42803d79c.jpg) +630nm + +poral resolution of 10 FPS while maintaining high spectral fidelity, enabling the observation of rapid spectral changes that would be impossible to capture with traditional systems. + +# 5. Conclusion + +In this paper, we present the first event-based hyperspectral imaging system. By encoding spectral data through temporal contrast, our approach leverages the sparse, asynchronous nature of event cameras to achieve dramatic bandwidth reductions while maintaining high spectral and temporal resolution. The system demonstrates that breaking the resolution-bandwidth trade-off is possible through careful co-design of optical hardware and computational algorithms. Experimental results demonstrate that our approach enables real-time capture of dynamic spectral phenomena with unconstrained spectral resolution, achieving performance comparable to frame-based methods with only $40.47\%$ of the data. + +Limitations. Currently, the inter-reflection, scattering, and fluorescence of the material are not modeled. They will affect spectral estimation accuracy. The system requires precise optical calibration and the algorithm implementation still has room to speed up. Future work could address these limitations by improving optical systems or introducing deep learning techniques. + +# Acknowledgement + +This work is supported by National Natural Science Foundation of China (Grant No. 624B2006, 62088102, 62136001, 62302019), Beijing Natural Science Foundation (Grant No. L233024), JST-Mirai Program (Grant No. JPMJM123G1), and JSPS Kakenhi (Grant No. 20H05953). PKU-affiliated authors thank openbayes.com for providing computing resource. + +# References + +[1] Telmo Adão, Jonás Hruška, Luís Pádua, José Bessa, Emanuel Peres, Raul Morais, and Joaquim Joao Sousa. Hyperspectral imaging: A review on uav-based sensors, data processing and applications for agriculture and forestry. Remote Sensing, 9 (11):1110, 2017. 2 +[2] Seung-Hwan Baek, Incheol Kim, Diego Gutierrez, and Min H Kim. Compact single-shot hyperspectral imaging using a prism. ACM Transactions on Graphics, 36(6):1-12, 2017. 2, 3 +[3] Seyed Ehsan Marjani Bajestani and Giovanni Beltrame. 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However, most existing LLM-based models (e.g., VideoLLaMA, VideoChat) are constrained to processing short-duration videos. Recent attempts to understand long-term videos by extracting and compressing visual features into a fixed memory size. Nevertheless, those methods leverage only visual modality to merge video tokens and overlook the correlation between visual and textual queries, leading to difficulties in effectively handling complex question-answering tasks. To address the challenges of long videos and complex prompts, we propose AdaCM², which, for the first time, introduces an adaptive cross-modality memory reduction approach to video-text alignment in an auto-regressive manner on video streams. Our extensive experiments on various video understanding tasks, such as video captioning, video question answering, and video classification, demonstrate that AdaCM² achieves state-of-the-art performance across multiple datasets while significantly reducing memory usage. Notably, it achieves a 4.5% improvement across multiple tasks in the LVU dataset with a GPU memory consumption reduction of up to 65%. + +# 1. Introduction + +Video understanding is an important task in computer vision and artificial intelligence, which involves processing and reasoning over visual and textual information. While the recent success of large language models (LLMs) [5, 31, 34, 39] has significantly improved video-language models [27, 29], prior work has primarily focused on short video understanding tasks, typically with videos ranging + +![](images/2e39cd491203f16fb43919b9f8d2a4b579757ce24065b8e8b8942897439f5956.jpg) +Figure 1. (Left) Existing approaches compress visual features of videos via single-modality correlation; (Right) Our $\mathbf{AdaCM}^2$ reduces video memory adaptively based on cross-modality attention. + +![](images/5cd67d50f5d8f472235b5a9951a88eba94da73f62ccffe97628b372ed90c7df6.jpg) + +from 5 to 15 seconds. However, long-term video understanding [45], a sub-technique that develops models to process richer information, has played a crucial role in real-world applications such as movie analysis and video retrieval. Unfortunately, it poses significant challenges as video length increases, especially the large memory consumption challenge. The number of frames the model must process grows rapidly, leading to substantial memory consumption, thereby preventing prior approaches from processing such long videos. + +To solve the large memory consumption challenge, many approaches focus on compressing video tokens. For instance, MA-LMM [16] employs a memory bank to compress visual tokens based on the cosine similarities of adjacent two frames. Koala [37] passes multiple segments of video into tokenizer functions that aggregate visual tokens to handle long videos. Even though those methods reduce memory consumption, they still suffer from two significant limitations. 1) Ignoring text-driven information: As shown in Figure 1, existing works compress visual information without considering textual information, leading to the loss of vital visual tokens that are highly related to + +![](images/ac02b1417156b73ed22a28e4caa3d1a25ddf0a13c50276806347e30ae2df621f.jpg) +Figure 2. The case study of $\mathrm{AdaCM}^2$ zero-shot on Ego4D[15] dataset. As shown, $\mathrm{AdaCM}^2$ can 1) summarize an extremely long video lasting over 2 hours with limited memory consumption and identify the number on a person's back at the end accurately, 2) answer questions related to a mid-length video spanning more than 20 minutes. + +the text prompt, particularly in Visual Question Answering (VQA) [2, 12, 20, 50] tasks with complex text prompts. 2) The lack of similarity adaptability: Previous methods attempt to compress visual tokens within the fixed and predefined frame interval, failing to capture the dynamic nature of video information and leading to inefficient and inflexible memory reduction. As shown in Figure 3c, the similarities of adjacent frames vary across different layers. Moreover, temporally distant frames still exhibit high similarity in deep layers. Consequently, if not appropriately addressed, such limitations will severely hinder their performance in many practical applications. + +To address the above limitations, in this paper, we propose AdaCM $^2$ , on understanding extremely long-term video with adaptive cross-modality memory reduction. As illustrated in Figure 1, our key idea is to adaptively preserve a certain number of crucial visual tokens that are most relevant to text queries across different layers based on cross-modality attention. We introduce two intriguing observations: 1) Only a subset of visual key states exhibit high correlations with text query; 2) Correlation varies across different layers. Our observations open opportunities for effective memory reduction by fully exploiting the inherent cross-modal capabilities of the existing visual encoders to compress visual tokens. Specifically, we first extract visual representations from video frames using a frozen visual encoder, i.e., Q-Former [23]. Then, to solve the substantial memory consumption challenge and model long-term temporal connection, we propose AdaCM $^2$ attention to learn the "query" regressively in a frame-by-frame manner within + +the Q-Former. $\mathrm{AdaCM}^2$ attention mechanism enables different numbers of visual tokens preserved across different layers based on cross-modality correlation. Finally, the learned queries are sent to LLM to generate the answer. To the best of our knowledge, $\mathrm{AdaCM}^2$ is the first framework that leverages cross-modal attention integrated into the visual encoder to enable extremely long-term video understanding with efficient memory reduction. Moreover, our $\mathrm{AdaCM}^2$ can improve BLIP-based [11, 22, 23] models in a plug-and-play manner, enhancing their capability to process long-term video effectively. Our core contributions are summarized as follows: + +- We propose an efficient video memory reduction framework, AdaCM² for long-term video understanding based on cross-modality attention, which, for the first time, facilitates interaction between visual features and text prompts in video understanding. +- We present a cross-modality attention module that adaptively analyzes and evaluates visual tokens according to the correlation with input text prompts, enabling extremely long-term video tasks with a dynamic crucial video token-preserving strategy. +- We conduct experiments on multiple video understanding tasks. Our proposed AdaCM² achieves 4.5% accuracy improvement across multiple tasks in the LVU [45] dataset. Particularly, AdaCM² exhibits promising performance on the VQA and video captioning tasks. More importantly, AdaCM² reduces GPU memory consumption by 65%, highlighting superior performance and efficiency in practice. + +![](images/a1b4a54012fb771c3a2d2a0c2a18f89f820f4cfc7c053f69f2953b5374836b74.jpg) + +![](images/0decb422af4405239969602bb46fd5b2b33c42558e3825fa6d79c1594797c7fb.jpg) + +![](images/13b5bbaf60100fcc19c241d5bdf89eeb5aa953714a97c640af67ca58df2f51ec.jpg) +Figure 3. Visualization for cross-modality attention, generated using a randomly sampled video from the MSR-VTT [48] dataset. (a) Cross-attention score map of the 74th frame in the final layer and last head. (b) Cross-attention score distribution of the 80th frame in the final layer and last head. (c) The layer-wise cosine similarities of attention scores between the current frame and adjacent frames. + +# 2. Related Work + +Video-Language Models. With the recent advancements of large language models (LLMs) [5, 31, 34, 39], video-language models have been integrated by LLMs with image encoders for multi-modal understanding and reasoning [3, 7, 30]. BLIP-2 [23] introduces a lightweight querying transformer [23] to bridge the modality gap between the frozen pre-trained image encoder and LLMs. Instruct-BLIP [11] further extracts informative visual features tailored to the given instruction with instruction-aware Query Transformer. LLaVA [53] leverages language-model to generate multi-modal instruction-following data and improves model generalization ability. VisionLLM [7] provides a unified perspective for vision and language tasks by treating images as a foreign language. It aligns vision-centric tasks with language tasks, which can be flexibly defined and managed using language instructions. However, these models are prone to significant memory overhead when applied to long video understanding tasks. + +Long-Term Video Understanding. Long video understanding focuses on detecting long-range patterns in videos longer than 30 seconds or even several minutes. To reduce memory and computational requirements, [16, 35] reduce the redundancy of visual information based on the cosine similarities of adjacent visual tokens. Other works like Vis4mer [19] leverage a standard transformer encoder for short-range spatiotemporal feature extraction and a multiscale temporal Selective Structured State-Spaces (S4) [42] decoder for long-range temporal reasoning. Koala [37] splits a long video into multiple segments and then aggregates visual tokens to process long videos. Considering that the goal of long-term video understanding is to answer the text question corresponding to the video, our method considers the correlation between the visual features and the input text information based on adaptive cross-modality attention, significantly reducing memory consumption and enabling extremely long-term video understanding. + +KV Cache Eviction. KV cache eviction, a memory reduction method that retains important context key-value pairs, is widely adopted in LLMs inference. $\mathrm{H}_2\mathrm{O}$ [54] finds that keeping the recent tokens, together with "heavy-hitter" tokens measured by attention scores, is sufficient to maintain LLM's performance. Similarly, KeyFormer [1] retains only the key tokens in the KV cache by identifying these crucial tokens through a novel scoring function. In addition, based on the observation that KV cache states are highly similar between adjacent layers in the middle-to-deep sections of LLM, MiniCache [26] compresses the KV cache across layers using a novel depth-based approach, significantly reducing the memory footprint for LLM inference. Building on the success of the eviction-based method in managing long-context LLMs, we efficiently process long-term videos based on a similar philosophy. Moreover, our method focuses on reducing the redundancy of visual tokens in the long video understanding task, which is more challenging due to more information contained in videos and the interactions between visual and text modalities. + +# 3. Observations + +To investigate the main bottleneck that hinders long-term video understanding, we conduct a comprehensive study on the process between video frames and text prompts, which generally perform in the Q-Former. This process aligns visual and textual information and causes substantial memory consumption when video lengths increase. In this section, we will first analyze the cross-attention sparsity within a frame and then show the generalization of cross-attention sparsity across videos and layers. These observations demonstrate the redundancy in the dual-modality processing and inspire the foundation of our approach AdaCM $^2$ proposed in Section 4. + +# 3.1. Intra-Frame Cross-Attention Sparsity + +Existing approaches compress visual tokens solely based on the similarities among video frames. However, those ap- + +![](images/3b128d56dc7e66a4b9d833b76e27ac83c74e8ebb3e30de45234cb5ff316b54b1.jpg) +Figure 4. The framework of $\mathrm{AdaCM}^2$ . With video and text query as input, $\mathrm{AdaCM}^2$ first utilizes a visual encoder to extract visual features from video frames. Then, video Q-Former embeds the correlation between visual features and the text prompt into a learnable query in a regressive manner. Finally, LLM generates the answer based on the length-limited query embedding. To reduce memory consumption challenge during the process of Adaptive Memory Reduction, the Video Cache is partitioned into previous and recent parts. Based on cross-modality attention score, $\mathrm{AdaCM}^2$ then identifies important visual features and removes layer-wise unimportant visual tokens from cache. The snowflake denotes frozen pre-trained models, while the fire tag represents models that are fine-tuned. + +proaches may miss key visual tokens highly related to textual input, leading to accuracy loss for tasks with complex text questions. Motivated by [14, 46], which have shown that retaining only a subset of salient tokens responsible for the majority of attention scores can be sufficient to maintain the performance of LLMs, we observe the similar cross-attention sparsity in the visual-textual alignment process. + +Observation 1: Only a subset of visual tokens exhibits high correlations to the text query within a frame. In Figure 3a, we visualize the cross-attention scores for the 74-th frame in the final layer and the last attention head by performing inference on Q-Former with randomly sampling data from the MSR-VTT [48] dataset. The dark color indicates that the visual token exhibits a slight cross-modality correlation with the text token. We can observe that only a subset of visual tokens within a frame exhibits high correlations to text tokens. Moreover, the cross-attention scores exhibit a normal distribution as depicted in Figure 3b, with significant correlations primarily observed in the tail values. This observation motivates us to develop an algorithm that identifies necessary visual tokens according to cross-modality attention scores, thereby preserving crucial visual information most important to the textual prompts. + +# 3.2. Layer-Wise Cross-Attention Similarity + +We have demonstrated the cross-attention sparsity within a video frame. Due to the significantly increased frame length, a long-term video contains a substantial number of + +visual tokens. These tokens are grouped and undergo multilayer cross-attention operations with prompt tokens. To reduce the memory consumption of redundant visual tokens globally, we further analyze cross-attention sparsity across frames and layers. + +Observation 2: Correlation varies across different layers. Based on the BLIP2 [23] Model, we conduct zero-shot inference across multiple datasets and tasks. Figure 3c reveals that the cross-attention scores exhibit high similarity between adjacent frames, where cosine similarity exceeds $90\%$ among the recent five frames. More importantly, the similarity is more significant in deeper layers than in shallow layers. This observation highlights the consistent redundancy throughout the video and the diverse levels of redundancy across different layers. Correspondingly, we propose to adaptively reduce visual memory consumption across different layers according to layer-wise cross-modality attention, making memory compression dynamic and flexible. + +# 4. Methodology: AdaCM² + +We present AdaCM $^2$ , an adaptive cross-modality memory reduction framework for extremely long-term video understanding. AdaCM $^2$ consists of three stages, including 1) video feature extraction by a visual encoder; 2) adaptive memory reduction based on cross-modality attention with visual-textual embedding alignment; 3) text generation with a large language model, as illustrated in Figure 4. + +$\mathrm{AdaCM}^2$ adaptively reduces peak memory consumption by regressively generating learnable query tokens that preserve the temporal continuity of video and a layer-wise cross-modality memory reduction algorithm. + +# 4.1. Video Feature Extraction + +As shown in Figure 4, similar to common video understanding workflow [23], $\mathrm{AdaCM}^2$ extracts video features using a pre-trained visual encoder. Given a video with a sequence of $T$ frames, the encoder first encodes each frame and generates the corresponding video features $\mathbf{X} = [x_{1}, x_{2}, x_{3}, \dots, x_{T}]$ , where $\mathbf{x}_t \in \mathbb{R}^{P \times C}$ is the frame features at time $t$ , $P$ and $C$ denote the number of visual tokens about each frame and the channel dimension of each token, respectively. Then, to incorporate temporal information into the frame-level features, a positional embedding is applied as follows: + +$$ +\boldsymbol {f} _ {t} = \boldsymbol {x} _ {t} + \mathcal {E} (t), \boldsymbol {f} _ {t} \in \mathbb {R} ^ {P \times C}, \tag {1} +$$ + +where $\mathcal{E}(\cdot)$ represents the position embedding of a frame, and $f_{t}$ indicates the frame features with temporal information at time $t$ . + +# 4.2. Adaptive Memory Reduction with Cross-Modality Attention + +After extracting visual features from the video, a Q-Former is leveraged to align visual and textual features. By learning a query $\pmb{Q}_l \in \mathbb{R}^{N_l \times C}$ in the Q-Former model, the visual features are refined to align the text description based on multi-layers cross-modal attention mechanisms, where $N_l$ is the number of learnable query tokens and $C$ denotes the number of feature channels. + +Visual-Textual Feature Alignment in a Regressive Manner. Unlike existing methods that directly process all frames into the Q-Former and align visual and textual information by one shot, we propose to learn the query $Q_{l}$ regressively in a frame-by-frame manner, enabling the reduction of irrelevant visual tokens based on the cross-modality correlation in a limited memory size. + +AdaCM² utilizes video cache and current visual features to align text features. To be specific, let $K_{t} \in \mathbb{R}^{tP \times C}$ , $V_{t} \in \mathbb{R}^{tP \times C}$ to represent video cache at time $t$ , which are stored in memory by visual tokens before time $t$ and at time $t$ as: + +$$ +\boldsymbol {K} _ {t} = \left[ \boldsymbol {K} _ {\mathrm {t - 1}}, \boldsymbol {f} _ {t} \boldsymbol {W} _ {K} \right], \tag {2} +$$ + +$$ +\boldsymbol {V} _ {t} = \left[ \boldsymbol {V} _ {\mathrm {t} - 1}, \boldsymbol {f} _ {t} \boldsymbol {W} _ {V} \right], \tag {3} +$$ + +where $W_{K}$ and $W_{V}$ are weight matrices. Therefore, the cross-modality attention calculation in the Q-former can be defined as + +$$ +\boldsymbol {A} _ {t} = \boldsymbol {S} _ {t} \cdot \boldsymbol {V} _ {t} = \operatorname {s o f t m a x} \left(\frac {\boldsymbol {Q} _ {t} \cdot \boldsymbol {K} _ {t} ^ {T}}{\sqrt {C}}\right) \cdot \boldsymbol {V} _ {t}, \qquad (4) +$$ + +![](images/e243ae71c7a9bcc4a1aee8ea2b0cfdbd7b8bdd8f76d308675019a548f57c0fb0.jpg) +Figure 5. Illustration for our video memory reduction. The video cache is first partitioned into recent and previous parts. Important visual tokens with high cross-modality attention scores in the previous cache are then preserved. + +where $S_{t}\in \mathbb{R}^{N\times tP}$ is the attention score, $Q_{t}\in \mathbb{R}^{N\times C}$ is the concatenation of the learnable query $Q_{l}$ and the text embedding $X_{\mathrm{text}},N$ is the number of query and text tokens. + +Layer-Wise Video Memory Reduction. Storing all visual tokens in the video cache is impossible due to the increasingly large memory cost while processing video frames, especially for long video understanding tasks. As shown in Observation 3.1, there is substantial visual redundancy in videos where only a subset of visual tokens exhibit high correlations with text tokens. Based on this observation, in AdaCM $^2$ , we propose a cross-modality attention mechanism to reduce memory consumption according to the visual-textual redundancy. AdaCM $^2$ first identifies important visual features based on cross-modality attention score and then adaptively reduces video memory by removing layer-wise visual tokens not less correlated to textual information. + +1 Identifying Important Visual Features based on Cross-Modality Attention Score. For a video token $\pmb{f}_t(i)$ at spatial location $i \in \{1, \dots, tP\}$ , the cross-modality attention score $S_t^c(i)$ accumulates the attention scores between $\pmb{f}_t(i)$ and text tokens, which can be formulated as + +$$ +\boldsymbol {S} _ {t} ^ {c} (i) = \sum_ {j = 1} ^ {j = N} \boldsymbol {S} _ {t} (j, i). \tag {5} +$$ + +Cross-modality attention scores capture the correlation between visual and textual features. Therefore, we identify a video token as pivotal if it receives a high cross-modality attention score. + +2 Adaptively Reducing Video Cache Layer-Wise. As demonstrated in Observation 3.2, visual features exhibit different levels of similarity with textual features across different layers. Guided by cross-modal attention score, we further design an adaptive video memory reduction algorithm for the video cache, as shown in Figure 5. + +According to the order that visual token stored in the video cache, at time $t$ , we split the $K_{t}$ for the current layer + +into previous cache, $\hat{K}_t$ , and recent cache, $\hat{K}_t$ : + +$$ +\boldsymbol {K} _ {t} = \left[ \hat {\boldsymbol {K}} _ {t}, \tilde {\boldsymbol {K}} _ {t} \right], \tag {6} +$$ + +$$ +| \tilde {K} _ {t} | / | \tilde {K} _ {t} | = (1 - \alpha) / \alpha +$$ + +where $|\cdot|$ measures the number of tokens in cache, $\alpha$ is the split ratio. For the visual tokens in recent cache, $\tilde{\pmb{K}}_t$ , that reserves the latest information, we still keep it in the memory. On the other hand, for the previous cache, $\tilde{\pmb{K}}_t$ , we only retain visual tokens with top- $\beta$ cross-modality attention scores in memory and thus obtain the conserved cache $\overline{\pmb{K}}_t$ . The process is defined as follows: + +$$ +\overline {{\boldsymbol {K}}} _ {t} = \left\{\hat {\boldsymbol {K}} _ {t} (i) \mid i \in \operatorname {a r g t o p} \left(\hat {\boldsymbol {S}} _ {t} ^ {c}, \beta\right) \right\}, \tag {7} +$$ + +$$ +| \overline {{\boldsymbol {K}}} _ {t} | / | \hat {\boldsymbol {K}} _ {t} | = \beta , +$$ + +where $\operatorname{argtop}(\cdot, \beta)$ denotes the indices of visual tokens with top- $\beta$ cross-modality attention scores, $\hat{S}_t^c$ is the cross-modality attention scores of tokens in $\hat{K}_t$ , $\beta$ is the conserve ratio. Finally, the video cache $K_t$ can be compressed as $K_t = [\overline{K}_t, K_t]$ . Based on our Observation 3.2, i.e., redundancy across layers varies, our adaptive video memory reduction is performed layer-wise. Correspondingly, we set $\alpha$ 's and $\beta$ 's for different layers. It is worth noting that the adaptive reduction is also applied to another type of video cache, $V_t$ . + +Let $r = \alpha +(1 - \alpha)\beta \leq 1$ . Through deductive reasoning, the final size of video cache $\pmb{K}_T$ can be derived as: + +$$ +\left| \boldsymbol {K} _ {T} \right| = P \sum_ {t = 1} ^ {T} r ^ {t} = \frac {\operatorname {P r} (1 - r ^ {T})}{1 - r} \tag {8} +$$ + +With the continuous increase of video duration, $T \to \infty$ , $|\pmb{K}_T|$ is converged to a constant $Pr / (1 - r)$ , showing the maximum memory requirement of AdaCM² to processing unbounded video length. + +# 4.3. Text Generation + +With the regressive processing of video frames, the learnable query $\pmb{Q}_l \in \mathbb{R}^{N \times C}$ in Q-Former has modeled the long-term temporal connection from the input video. Then, the LLM will generate the answer based on the learned $\pmb{Q}_l$ , a length-limited vector aggregating the long-term input video information. Specifically, assume $\pmb{Y} = \{y_1, y_2, \dots, y_M\}$ is the answer comprising a sequence of $M$ words, we minimize the cross-entropy loss during training as follows: + +$$ +L (\boldsymbol {V}, \boldsymbol {P}, \boldsymbol {Y}) = - \sum_ {i = 1} ^ {M} y _ {i} \log p \left(y _ {i} \mid y _ {< i}, \boldsymbol {Q} _ {l}, \boldsymbol {X} _ {\text {t e x t}}\right) \tag {9} +$$ + +where $p(y_{i}|y_{ModelContentMetadataAvgRelationSpeakSceneDirectorGenreWriterYearObj_T4mer [45]54.833.252.947.752.736.337.845.1Performer [9]50.038.860.558.949.548.241.349.6Orthoformer [32]50.038.366.355.155.847.043.450.8VideoBERT [36]52.837.954.947.351.938.536.145.6LST [19]52.537.362.856.152.742.339.249.0VIS4mer [19]57.140.867.462.654.748.844.853.7S5 [43]67.142.173.567.365.451.348.059.2MA-LMM [16]58.244.880.374.661.070.451.963.0Ours63.140.286.275.468.077.062.567.5 + +Table 2. Comparison on the Breakfast and COIN datasets. Top-1 accuracy is reported. + +
ModelBreakfastCOIN
TSN [44]-73.4
VideoGraph [18]69.5-
Timeception [17]71.3-
GHRM [13]75.5-
D-Sprv. [25]89.990.0
ViS4mer [19]88.288.4
S5 [43]90.790.8
MA-LMM [16]93.093.2
Ours94.493.3
+ +# 5.3. Main Results + +Long-Term Video Understanding. We compare AdaCM² with state-of-the-art methods on the LVU [45] benchmark. As shown in Table 1, our model outperforms the existing long-term video understanding models, including Object transformer [45], S4 [43], VIS4mer [19], VideoBERT [36], LST [19], and MA-LMM [16] across both content understanding and metadata prediction tasks. The results indicate that AdaCM² achieves a significant improvement across most tasks, increasing Top-1 accuracy by $4\%$ compared to MA-LMM [16]. + +In Table 2, we evaluate our $\mathrm{AdaCM}^2$ on the Breakfast [21] and COIN [38] datasets. It is worth noting that these datasets present a greater memory consumption challenge due to the longer and more diverse videos they contain. It is seen that our $\mathrm{AdaCM}^2$ outperforms MA-LMM [16] by $1.4\%$ and $0.1\%$ in Top-1 accuracy, respectively. These results demonstrate that our approach achieves superior performance in long-term video understanding. + +Video Captioning. Table 3 summarizes the experimental results on video captioning datasets, including MSRVTT, MSVD, and YouCook2. AdaCM² achieves $51.4\%$ Meteor and $189.4\%$ CIDEr on the MSVD datasets. + +Table 3. Comparison on the MSRVTT, MSVD and YouCook2 datasets, with results for the METEOR(M) and CIDEr(C) metrics. + +
ModelMSRVTTMSVDYouCook2
MCMCMC
UniVL [28]28.249.929.352.8-127.0
SwinBERT [24]29.953.841.3120.615.6109.0
GIT [41]32.973.951.1180.217.3129.8
mPLUG-2 [47]34.980.348.4165.8--
VideoCoca [49]-73.2---128.0
VideoLLaMA [52]32.971.649.8175.316.5123.7
MA-LMM [16]33.474.651.0179.117.6131.2
Ours33.073.151.4189.417.6125.6
+ +The results show that $\mathrm{AdaCM^2}$ outperforms the prior state-of-the-art approach, MA-LMM [16], with gains of $0.4\%$ and $10.3\%$ , respectively. Although mPLUG-2 has slightly better performance on MSRVTT, it demands extensive data for pre-training, leading to a training overhead. + +Memory Analysis. In addition to performance evaluation, we also conduct experiments on memory usage with randomly selected videos from the LVU [45], MSRVTT [48], and MSVD [6] datasets. As shown in Figure 6, existing methods like InstructBLIP [11] and VideoLaMA [52] instantly exhibit rapid increases in memory consumption as the number of frames increases, leading to out-of-memory (OOM) errors. In contrast, $\mathrm{AdaCM}^2$ achieves a significant reduction in memory usage by nearly $65\%$ , and maintains almost constant memory consumption without sacrificing performance. Furthermore, most of the occupied memory is consumed by LLM, with only a small fraction allocated for adaptive cross-modality alignment, which can be further alleviated if we use a lightweight LLM. + +# 5.4. Ablation Studies + +Memory Reduction. Our method reduces video memory adaptively based on cross-modality attention scores, + +![](images/fb9480774cd36c6e9e45163470909db85a35e0765005a8730e10059c86c582ed.jpg) +Figure 6. Practical memory consumption analysis compared to existing methods. The GPU memory usage for InstructBLIP shows an exponential increase, leading to out-of-memory (OOM) errors after processing 100 frames. In contrast, VideoLLaMA exhibits a linear increase in memory usage. $\mathrm{AdaCM}^2$ maintains almost constant memory usage without sacrificing performance even as frames significantly increase. + +![](images/d5aaba6fe1c28348bfac0726517690804d4d120cb430240acd0409df98bd0358.jpg) +Figure 7. Performance Comparison between two memory reduction strategies, random eviction v.s AdaCM $^2$ . Top-1 accuracy is reported here. +Table 4. Ablation study of LLM decoding methods, with results reported for the METEOR(M) and CIDEr(C) metrics. + +achieving extremely long-term video understanding with low memory cost. To investigate the importance of our memory reduction, we compare our cache strategy with the random eviction on the LVU dataset, which randomly discards the same number of visual tokens, as shown in Figure 7. It is seen that our approach significantly outperforms the random one, indicating the effectiveness of our cross-attention-based memory reduction. + +Hyperparameters Analysis. Split ratio $\alpha$ and conserve ratio $\beta$ are hyper-parameters controlling the preservation of critical visual tokens. In order to determine the appropriate settings, we explore the influence of $\alpha$ and $\beta$ on memory reduction and performance on MSRVTT and MSVT datasets. Figure 8 shows that more retaining tokens result in higher memory usage. Moreover, with the increase of $\alpha (\beta)$ , the accuracy rises to a peak and then decreases. This decrease is due to the negative impact of retaining redundant information, which diverts the model's attention away from essential tokens. To achieve an optimal balance between performance and memory efficiency, we set $\alpha = 0.1$ and $\beta = 0.1$ + +![](images/760270ab8fa5690c288c0d10e82eea228c632cd61263ed1933fa943ea1ec8f39.jpg) +(a) MSRVTT-QA dataset, $\beta = 0.1$ + +![](images/9e77080acbd48e6df76c8cc3b01f484dfc1656a52a35d4a099b07c7716f48666.jpg) +(b) MSRVTT-QA dataset, $\alpha = 0.1$ + +![](images/9eed4f4f557a546770775e765fb56cf6fc9d60160977924b1521c4b3e8c5c4ea.jpg) +(c) MSVD-QA dataset, $\beta = 0.1$ + +![](images/8ebad2745ea679d44dec6b221462a0c45c434cfd456de60912c3341dd5867cd2.jpg) +(d) MSVD-QA dataset, $\alpha = 0.1$ +Figure 8. Influence of split ratio $\alpha$ and conserve ratio $\beta$ on performance and memory usage. + +
ModelMSRVTTMSVDYouCook2
MCMCMC
FlanT5-XL21.6↓58.9↓48.7↓166.9↓15.3↓107.6↓
Vicuna-7B33.073.151.4189.417.6125.6
+ +for all layers. + +LLM Decoding. LLM plays an essential role in producing instruction cues. To investigate the influence of LLMs on our $\mathrm{AdaCM}^2$ , we compare the results using multiple LLMs, including FlanT5-XL [10] and Vicuna-7B [8]. Table 4 indicates that Vicuna-7B achieves better performance in all tasks. Therefore, we choose the Vicuna-7B model as our LLM backbone. Since our $\mathrm{AdaCM}^2$ framework is designed to accommodate various modern LLMs, we plan to conduct further tests in future work. + +# 6. Conclusion + +In this paper, we present $\mathrm{AdaCM}^2$ , an adaptive cross-modality memory reduction framework for extremely long-term video understanding. The key idea of $\mathrm{AdaCM}^2$ is to adaptively preserve a certain number of crucial visual tokens most relevant to text queries across different layers based on cross-modality attention, addressing the substantial memory consumption and modeling long-term temporal connection. Moreover, our $\mathrm{AdaCM}^2$ enables BLIP-based [11, 22, 23] models in a plug-and-play manner, enhancing their capability to process long-term video effectively. Experiments on video question understanding and captioning tasks demonstrate the superiority of the proposed $\mathrm{AdaCM}^2$ over existing state-of-the-art approaches. + +# References + +[1] Muhammad Adnan, Akhil Arunkumar, Gaurav Jain, Prashant Nair, Ilya Soloveychik, and Purushotham Kamath. Keyformer: Kv cache reduction through key tokens selection for efficient generative inference. Proceedings of Machine Learning and Systems, 7, 2024. 3 +[2] Aishwarya Agrawal, Dhruv Batra, Marcus Rohrbach, Jiasen Lu, Michael Bernstein, and Devi Parikh. Visual question answering, 2015. 2 +[3] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. 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In this paper, we introduce AdaDARE-γ, an efficient approach that alleviates catastrophic forgetting by controllably injecting new task-specific knowledge through adaptive parameter selection from fine-tuned models without requiring retraining procedures. This approach consists two key innovations: (1) an adaptive parameter selection mechanism that identifies and retains the most task-relevant parameters from fine-tuned models, and (2) a controlled task-specific information injection strategy that precisely balances the preservation of pre-trained knowledge with the acquisition of new capabilities. Theoretical analysis proves the optimality of our parameter selection strategy and establishes bounds for the task-specific information injection factor. Extensive experiments on InstructBLIP and LLaVA-1.5 across image captioning and visual question answering tasks demonstrate that AdaDARE-γ establishes new state-of-the-art results in balancing model performance. Specifically, it maintains 98.2% of pre-training effectiveness on original tasks while achieving 98.7% of standard fine-tuning performance on target tasks. + +# 1. Introduction + +With the rapid development of artificial intelligence [7, 33, 41], multi-modal large language models (MLLMs) have gained significant attention due to their ability to capture rich representations from various data modalities [1, 5, 10, 28, 40, 45, 46]. Pioneering works such as GPT-4V [1], Qwen2-VL [45], InstructBLIP [10] and LLaVA + +1.5 [28] have played pivotal roles in shaping the landscape of general-purpose AI assistants, significantly enhancing their capabilities and versatility. + +The typical architecture of MLLMs consists of two key components: modality-specific sub-modules and a lightweight connector [46]. The modality-specific sub-modules, such as vision encoders and language models, are designed to process and extract information from different types of input data. The lightweight connector plays a crucial role in aligning these diverse representations, enabling the model to comprehend multi-modal inputs and thus generate coherent outputs [5, 27, 28]. This structure allows MLLMs to effectively combine information from text, images, and potentially other modalities, leading to more sophisticated and versatile AI systems. + +Despite their advanced capabilities, MLLMs often struggle with performance on unseen tasks [17, 31, 49] due to their unique architectural complexity and the inherent disparities in data characteristics across modalities. Consequently, continual fine-tuning [36] remains a crucial approach for rapidly adapting these models to specific downstream tasks and enhancing their performance. Nevertheless, this process frequently leads to catastrophic forgetting, a phenomenon where the model's performance on pretrained tasks deteriorates as it acquires new, task-specific knowledge, as shown in Fig. 1. This highlights a crucial challenge: how to efficiently strike a balance between enhancing MLLMs' performance on target tasks (plasticity) while preserving their effectiveness on original tasks (stability)? + +Current research on mitigating catastrophic forgetting predominantly focuses on traditional continual learning settings with smaller-scale or uni-modal models [2, 34, 42, 44], which exhibit inherent limitations in both representation capacity and cross-modal understanding. In context of MLLMs, Model-Tailor [61] made the first attempt to preserve pre-trained task capabilities during fine-tuning on im + +age captioning and visual question answering tasks. However, this approach, as illustrated in Tab. 1 and Tab. 2, achieves only sub-optimal performance in balancing pretrained and target task capabilities. Furthermore, it incurs substantial computational overhead due to the requirement of layer-wise Hessian inverse calculations. + +In response to these challenges, we introduce Adaptive Drop And REscale with a $\gamma$ factor (AdaDARE-γ): an efficient approach that alleviates catastrophic forgetting by controllably injecting new task-specific knowledge through adaptive parameter selection from fine-tuned models without requiring retraining procedures. Building upon the DARE framework, AdaDARE- $\gamma$ employs a probabilistic dropout mechanism for each delta parameter. This adaptive process selectively retains the most task-salient parameters. Furthermore, inspired by the Task-Arithmetic paradigm [20], which demonstrates the efficacy of simple arithmetic operations on delta parameters for model editing, we incorporate a $\gamma$ factor to characterize the intensity of task-specific information injection. This approach enables fine-grained control over the balance between preserving pre-trained knowledge and adapting to new tasks, effectively creating a dynamic equilibrium between generalization and specialization in MLLMs. + +In summary, our work makes several significant contributions: + +- We propose AdaDARE- $\gamma$ , an efficient framework that addresses catastrophic forgetting in MLLMs by combining principled adaptive parameter selection with controlled knowledge injection, enabling flexible trade-off between preserving pre-trained capabilities and acquiring task-specific adaptations. +- We provide theoretical analysis that establishes optimality guarantees for parameter selection and derives bounds for the task-specific information injection factor, offering theoretical insights into the trade-off between stability and plasticity. +- We demonstrate through comprehensive experiments that our method establishes new state-of-the-art performance in balancing the target task performance and pre-trained knowledge retention, with maintaining $\sim 98.2\%$ effectiveness on original tasks versus pre-training and achieving $\sim 98.7\%$ performance on the target task compared to standard fine-tuning, providing a more effective solution to the stability-plasticity dilemma in MLLMs. + +# 2. Related Work + +# 2.1. Multi-modal Large Language Models + +Multi-modal Large Language Models formally refers to the LLM-based model with the ability to receive, reason and generate with multi-modal information [46]. Ever since the release of GPT-4 [1], MLLMs have gained much at + +tention because of the amazing performance it shows. Recent advancements [4, 5, 24, 27, 45, 60] have emerged with stronger ability of understanding and reasoning, benefiting from the rapid development of LLMs [7, 9, 41]. Drawing inspiration of the success of instruction tuning in LLMs [33], researchers have extended this crucial technique to MLLMs [10, 28, 45]. This technique enables MLLMs to generate responses to instructions conditioned on both visual and textual inputs, thereby adapting to various tasks and meeting diverse user needs. For instance, LLaVA-1.5 [28] has built on LLaVA framework [27], improving performance by instruction tuning on a wide range of additional academic-task-oriented visual question answering datasets. Moreover, recently, there has been a growing focus on enhancing In-Context Learning (ICL) and Chain-of-Thought (CoT) performance in various multimodal scenarios [14, 23, 37, 55, 56]. Representative works include: MIMIC-IT [23], which combines in-context learning with instruction tuning by building an instruction dataset formatted with multi-modal context; Multimodal-CoT [55], which extended the chain-of-thought prompting to multi-modal scenarios, enhancing reasoning capabilities across different modalities. These advancements demonstrate the ongoing efforts to improve the versatility and reasoning capabilities of MLLMs, pushing the boundaries of multi-modal AI systems. + +# 2.2. Trade-off between Stability and Plasticity + +The trade-off between stability (the retention of previously learned knowledge) and plasticity (the ability to acquire new information) first emerged in continual learning, where models must learn new tasks sequentially without forgetting previously learned knowledge. This has been a longstanding challenge in machine learning [42]. With the rise of pre-trained language models, this challenge has evolved to focus on mitigating catastrophic forgetting during adaptation, specifically balancing pre-training stability with task-specific plasticity [11, 22]. (1) Continual Learning: Over the past few decades, numerous studies have focused on improving continual learning performance, primarily in the context of smaller models [2, 6, 21, 34]. Traditional approaches to continual learning typically fall into three categories: weight regularization [21]), structure expansion [34], and data replay [6]. However, these methods have become less suitable for large pre-trained models due to their computational costs, storage overheads and inability to leverage the unique properties of these pre-trained models, such as loss landscape flatness [53] and extensive world knowledge. Recent studies have explored the potential of leveraging pre-trained models for continual learning [12, 13, 43, 44, 50]. These approaches have significantly improved continual learning performance by utilizing the rich knowledge embedded and properties of flatness in pre + +![](images/fc5d6a75a58fe8efe4253cbf702f2d35031a9e0ed8b57701ebbf6c5e12c313f9.jpg) +Figure 1. Fine-tuning MLLMs on Target Task. Fine-tuning MLLMs on the target task often suffers from catastrophic forgetting, where acquiring new task-specific knowledge compromises performance on pre-trained tasks. + +trained models. While these methods have shown promise, they primarily focus on employing either full fine-tuning or PEFT techniques on uni-modal models. However, the application of these approaches to multi-modal scenarios, particularly in the context of MLLMs, remains limited, with only a few studies [8, 17, 31, 39, 49, 54, 57]. (2) Adaptation in Pre-trained Models: The challenge of mitigating catastrophic forgetting first gained prominence in language models, where studies revealed that fine-tuning on small datasets often degrades generalization[11, 22, 52]. In NLP filed, to address this challenge, Dong et al. [11] proposed an adversarial training method from an information-theoretical perspective and Lee et al. [22] proposed a mixout regularization technique to control parameter deviation during fine-tuning. In context of MLLMs, Model Tailor [61] addresses the same adaptation settings as our work and explores multimodal generation and reasoning tasks in MLLMs. However, it requires substantial computational overhead for layerwise Hessian inverse calculation and lacks flexibility in balancing stability and plasticity. + +# 3. Problem Formulation + +We consider a multi-modal large language model $\mathcal{M}$ with initial parameters $\Theta_{\mathrm{pre}}$ , obtained through pre-training on a diverse set of tasks $\mathcal{P} = \{\mathcal{D}_1, \dots, \mathcal{D}_n\}$ . When adapting $\mathcal{M}$ to a novel target task $\mathcal{T}$ through fine-tuning, we obtain a new set of parameters $\Theta_{\mathrm{sft}}$ . This adaptation process can be represented as: + +$$ +\Theta_ {\mathrm {s f t}} = \Theta_ {\mathrm {p r e}} + \Delta \Theta , \tag {1} +$$ + +where $\Delta \Theta$ denotes the change in parameters (referred to as delta parameters) between pre-trained and fine-tuned states. To mitigate the performance degradation on pretrained tasks while optimizing for the target task, we pro + +pose a fusion strategy $\mathcal{F}$ that processes $\Theta_{\mathrm{pre}}$ and $\Theta_{\mathrm{sft}}$ to derive $\Theta_{\mathrm{fusion}}$ : + +$$ +\Theta_ {\text {f u s i o n}} = \mathcal {F} \left(\Theta_ {\text {p r e}}, \Theta_ {\text {s f t}}\right). \tag {2} +$$ + +The objective is to find an optimal $\Theta_{\mathrm{fusion}}$ that satisfies: + +$$ +\left| \left| \mathcal {L} _ {\mathcal {P}} \left(\Theta_ {\text {f u s i o n}}\right) - \mathcal {L} _ {\mathcal {P}} \left(\Theta_ {\text {p r e}}\right) \right| \right| \leq \epsilon_ {\text {p r e}}, +$$ + +$$ +\left| \left| \mathcal {L} _ {\mathcal {T}} \left(\Theta_ {\text {f u s i o n}}\right) - \mathcal {L} _ {\mathcal {T}} \left(\Theta_ {\text {s f t}}\right) \right| \right| \leq \epsilon_ {\text {t a r g e t}}, \tag {3} +$$ + +where $\mathcal{L}_{\mathcal{P}}(\cdot)$ represents the aggregate loss on the pretraining tasks $\mathcal{P}$ , $\mathcal{L}_{\mathcal{T}}(\cdot)$ denotes the loss on the target task $\mathcal{T}$ . And $\epsilon_{\mathrm{pre}} > 0$ is the maximum allowable performance degradation on pre-training tasks. + +# 4. Method + +# 4.1. Overview of AdaDARE-γ + +In this section, we introduce AdaDARE- $\gamma$ , our novel approach to efficient adaptation in MLLMs. AdaDARE- $\gamma$ builds upon the foundation of DARE while introducing layer-wise optimization for adaptive parameter selection and a $\gamma$ factor for controlled task-specific information injection. The overall framework is illustrated in Fig. 2. The following subsections detail each component of our method, starting with our objective and a review of the DARE approach, followed by our enhancements and theoretical analysis. + +# 4.2. Layer-wise Objective + +Given a pre-trained model with parameters $\Theta_{\mathrm{pre}}$ and its finetuned version $\Theta_{\mathrm{sft}}$ , our goal is to find optimal fusion parameters $\Theta_{\mathrm{fusion}}$ that maintain performance on both pre-trained and target tasks. We formulate this as a layer-wise optima + +![](images/26062c6ba264366865704432bc8145622ecf1c19d9feee1883e492c677d478a1.jpg) +Figure 2. Illustration of Adaptive-DARE with $\gamma$ factor. Two-step parameter adaptation for task-specific learning: (1) Adaptive drop and rescale of task-specific delta parameters ( $\Delta \theta$ ), selectively removing parameters based on varying probabilities to eliminate redundant or task-irrelevant information. (2) Balancing pre-trained knowledge with adapted task-specific information using a scaling factor $\gamma$ to achieve optimal performance across general and target tasks. + +![](images/5b6c552479879e0a45057e500bfe410418f6fde19293e8d0a42ecc0f75e66aed.jpg) + +tion problem: + +$$ +\arg \min _ {\Theta_ {\text {f u s i o n}} ^ {\ell}} \mathcal {L} \left(f _ {\ell} \left(\mathcal {X} _ {\mathcal {T}} ^ {\ell}, \Theta_ {\text {s f t}} ^ {\ell}\right), f _ {\ell} \left(\mathcal {X} _ {\mathcal {T}} ^ {\ell}, \Theta_ {\text {f u s i o n}} ^ {\ell}\right)\right), \tag {4} +$$ + +$$ +\text {s . t .} \mathbb {E} \left[ \mathcal {L} \left(f _ {\ell} \left(\mathcal {X} _ {\mathcal {T}} ^ {\ell}, \Theta_ {\text {p r e}} ^ {\ell}\right), f _ {\ell} \left(\mathcal {X} _ {\mathcal {T}} ^ {\ell}, \Theta_ {\text {f u s i o n}} ^ {\ell}\right)\right) \right] \leq \epsilon . +$$ + +However, in practical scenarios, access to pre-training data is often restricted due to proprietary or privacy considerations. Therefore, we approximate the constraint by measuring the parameter distance between $\Theta_{\mathrm{fusion}}$ and $\Theta_{\mathrm{pre}}$ : + +$$ +\arg \min _ {\Theta_ {\text {f u s i o n}} ^ {\ell}} \left\| \Theta_ {\text {s f t}} ^ {\ell} \mathbf {X} _ {\mathcal {T}} ^ {\ell} - \Theta_ {\text {f u s i o n}} ^ {\ell} \mathbf {X} _ {\mathcal {T}} ^ {\ell} \right\| _ {2} ^ {2}, \tag {5} +$$ + +$$ +\mathrm {s . t .} \left. \left\| \Theta_ {\mathrm {f u s i o n}} ^ {\ell} - \Theta_ {\mathrm {p r e}} ^ {\ell} \right\| _ {1} < \eta . \right. +$$ + +# 4.3. Preliminary: Drop And REscale + +The Drop And REscale (DARE) method forms the basis of our approach. DARE introduced a groundbreaking insight: in Supervised Fine-Tuned (SFT) language models, a significant portion of delta parameters can be zeroed out while preserving model capabilities. This finding suggests that model adaptation often involves substantial parameter redundancy, which can be efficiently managed through randomly dropping and rescaling. + +The DARE process can be formally described by the following equations: + +$$ +M ^ {\mathcal {T}} \sim \operatorname {B e r n o u l l i} (p), +$$ + +$$ +\tilde {\Delta} \Theta^ {\mathcal {T}} = (1 - M ^ {\mathcal {T}}) \odot \Delta \Theta^ {\mathcal {T}}, \tag {6} +$$ + +$$ +\Delta \hat {\Theta} ^ {\mathcal {T}} = \tilde {\Delta \Theta} ^ {\mathcal {T}} / (1 - p), +$$ + +where $M^{\mathcal{T}}$ is a binary mask with each element sampled from a Bernoulli distribution with probability $p \in [0,1)$ , $\Delta \Theta^{\mathcal{T}}$ represents the delta parameters, $\odot$ denotes element-wise multiplication and / denotes element-wise division. + +Notably, the drop rate $p$ directly corresponds to the sparsity ratio, where a drop rate of $p$ yields a $(100p)\%$ sparsity + +of delta parameters. The rescaling factor $1 / (1 - p)$ ensures that the expected values of the remaining parameters compensate for the dropped ones. + +To understand the simple theoretical foundation of DARE, we can examine its effect on the expectation of embeddings. Consider the $i$ -th dimension: + +$$ +\begin{array}{l} \mathbb {E} [ \hat {h} _ {i} ] = \mathbb {E} \left[ \sum_ {j = 1} ^ {n} \left(w _ {i j} + \Delta \hat {w} _ {i j}\right) x _ {j} + \left(b _ {i} + \Delta \hat {b} _ {i}\right) \right] \\ = \sum_ {j = 1} ^ {n} x _ {j} \mathbb {E} \left[ w _ {i j} \right] + \mathbb {E} \left[ b _ {i} \right] + \sum_ {j = 1} ^ {n} x _ {j} \mathbb {E} \left[ \Delta \hat {w} _ {i j} \right] + \mathbb {E} \left[ \Delta \hat {b} _ {i} \right] \\ = \sum_ {j = 1} ^ {n} w _ {i j} x _ {j} + b _ {i} + \sum_ {j = 1} ^ {n} x _ {j} \left(\frac {(1 - p) \cdot \Delta w _ {i j}}{1 - p} + p \cdot 0\right) \\ + \left(\frac {(1 - p) \cdot \Delta b _ {i}}{1 - p} + p \cdot 0\right) \\ = h _ {i} ^ {\text {p r e}} + \Delta h _ {i}. \tag {7} \\ \end{array} +$$ + +This derivation shows that DARE approximates the fine-tuned embeddings while incorporating a scaled version of the changes introduced by fine-tuning. + +# 4.4. AdaDARE- $\gamma$ : Methodology + +Our method introduces a principled framework for efficient adaptation in MLLMs through two key innovations: adaptive parameter-wise probabilities and a $\gamma$ factor for controlled task-specific information injection. + +# 4.4.1. Adaptive Parameter Selection + +We propose an adaptive parameter selection mechanism that leverages the properties of parameter importance to determine optimal retention strategies. This approach extends beyond simple drop and rescale by introducing parameter-wise probabilistic selection. The process can be formalized + +as: + +$$ +M ^ {\mathcal {T}, \ell} \sim \operatorname {B e r n o u l l i} (P ^ {\ell}), +$$ + +$$ +\tilde {\Delta \Theta} ^ {\mathcal {T}, \ell} = (1 - M ^ {\mathcal {T}, \ell}) \odot \Delta \Theta^ {\mathcal {T}, \ell}, \tag {8} +$$ + +$$ +\hat {\Delta \Theta} ^ {\mathcal {T}, \ell} = \tilde {\Delta \Theta} ^ {\mathcal {T}, \ell} / (1 - P ^ {\ell}), +$$ + +where $P^{\ell}$ is a probability matrix with the same shape as $\Delta \Theta^{\mathcal{T},\ell}$ with each element in $P^{\ell}$ specifying the drop probability for the corresponding delta parameter in layer $\ell$ . $M^{\mathcal{T},\ell}$ is a binary mask, where each element is sampled from a Bernoulli distribution with the probability defined by $P^{\ell}$ . And / denotes element-wise division. By replacing $p$ with $p_j$ ( $j$ -th dimension of $P^{\ell}$ ) in Eq. (7), it's easy to show this process effectively drops parameters with their respective probabilities and rescales the remaining ones, maintaining the expected value of the embeddings for each dimension. + +# 4.4.2. Controlled Task-specific Information Injection + +We introduce a $\gamma$ factor to regulate the injection of task-specific information into pre-trained knowledge: + +$$ +\begin{array}{l} \Theta_ {\text {f u s i o n}} ^ {\mathcal {T}, \ell} = \mathcal {F} \left(\Theta_ {\text {p r e}} ^ {\mathcal {T}, \ell}, \Theta_ {\text {s t t}} ^ {\mathcal {T}, \ell}\right) \\ = \Theta_ {\text {p r e}} ^ {\mathcal {T}, \ell} + \gamma \cdot \hat {\Delta} \Theta^ {\mathcal {T}, \ell}. \\ \end{array} +$$ + +This equation combines the pre-trained parameters with a scaled version of the adaptive selected delta parameters. The $\gamma$ factor allows us to balance between retaining old knowledge (when $\gamma$ is closer to 0) and incorporating new information (when $\gamma$ is closer to 1). + +# 4.5. Theoretical Analysis + +# 4.5.1. Optimizing Drop Probabilities + +To determine the optimal drop probabilities, we formulate an optimization problem that minimizes the expected layerwise loss while maintaining a desired ratio of sparsity. This leads to our key theorem: + +Theorem 1 (Optimal Probabilities) Consider the optimization problem of minimizing the expected layer-wise loss: + +$$ +\arg \min _ {P ^ {\ell}} \mathbb {E} \left[ \left\| \Theta_ {s f t} ^ {\ell} \mathcal {X} _ {\mathcal {T}} ^ {\ell} - \Theta_ {f u s i o n} ^ {\ell} \mathcal {X} _ {\mathcal {T}} ^ {\ell} \right\| _ {2} ^ {2} \right], \tag {10} +$$ + +subject to the constraints: + +$$ +\frac {\sum_ {i = 1} ^ {n} p _ {i}}{n} > = p, \quad a n d \quad 0 \leq p _ {i} < 1 \quad \forall i. \tag {11} +$$ + +where $p$ represents the desired sparsity ratio. Then, the optimal probabilities $p_i^*$ that minimize the expected loss are given by: + +$$ +p _ {i} ^ {*} = \max (0, 1 - \frac {n (1 - p) \sqrt {H _ {i i} \delta_ {i} ^ {2}}}{\sum_ {j = 1} ^ {n} \sqrt {H _ {j j} \delta_ {j} ^ {2}}}) \quad \forall i. \tag {12} +$$ + +Here, $H_{ii}$ represents the $i$ -th diagonal element of the Hessian matrix, and $\delta_i$ is the $i$ -th element of $\Delta \Theta^{\mathcal{T},\ell}$ . + +The detailed proof of this theorem can be found in Appendix A. This theorem provides us with a way to adaptively determine which parameters are more important to retain based on their contribution to the loss and the model's sensitivity to their changes. + +# 4.5.2. Theoretical Bounds on $\gamma$ + +Theorem 2 (upper bound of $\gamma$ ) Given the constraint $\mathbb{E}\left[\left\| \Theta_{fusion}^{\ell} - \Theta_{pre}^{\ell}\right\|_{1}\right] < \eta$ , there exists an upper bound for $\gamma$ : + +$$ +\gamma \leq \frac {\eta}{\sum_ {i = 1} ^ {n} | \delta_ {i} |}, \tag {13} +$$ + +where $\delta_{i}$ represents the $i$ -th element of the delta parameters $\Delta \Theta^{\mathcal{T},\ell}$ . + +The detailed proof of this theorem can be found in Appendix A. This bound ensures that parameter changes remain within the constraint specified in Eq. (5), maintaining the optimization objective due to its monotonic relationship with $\gamma$ . The relationship between $\gamma$ and $\eta$ provides a theoretical guarantee for controlled information injection, enabling precise balance between knowledge retention and task adaptation. + +# 4.6. Pratical Implications of $\gamma$ Bounds + +As illustrated in Theorem 2, $\gamma \leq \frac{\eta}{\sum_{i=1}^{n} |\delta_i|}$ , where $\eta$ represents our desired pre-trained performance constraint and $\delta_i$ reflects parameter changes. This relationship has important practical implications. The $\eta$ parameter controls how much pre-trained task performance we aim to preserve. Similar to neural network training where absolute loss values don't directly map to dataset performance, we validate $\gamma$ 's effectiveness on validation sets, which represents generalization ability, rather than explicitly setting $\eta$ . This approach allows practical tuning while respecting theoretical bounds. + +# 5. Experiments + +# 5.1. Experiments Setup + +Architectures and Datasets. Our experiments focus on two representative multi-modal models: InstructBLIP [10] and LLaVA-1.5 [28], both based on Vicuna-7B [58]. These models differ in their fine-tuning approaches: InstructBLIP adjusts only the Q-Former, whereas LLaVA-1.5 fine-tunes the language model with an optional projector update [59]. For InstructBLIP, we evaluated image captioning datasets including COCO Caption [26] and NoCaps (with in-domain, near-domain and out-of-domain subsets) [3], as well as VQA tasks such as OKVQA [32], AOKVQA [35], and VQAv2 [15]. We fine-tuned InstructBLIP on Flickr30k [47] for image captioning and GQA [19] for VQA, both of which were unseen during InstructBLIP's pre-training phase. In the case of LLaVA-1.5, our evaluation encompassed a diverse range of datasets: VQAv2, + +GQA, Vizwiz [16], SQA [30], TextVQA [38], POPE [25], MM-Bench [29] and MM-Bench-CN [51]. For LLaVA-1.5, we conducted fine-tuning on Flickr30k for image captioning and OKVQA for VQA, both distinct from LLaVA-1.5's pre-trained datasets. + +Compared Baselines. We compare our method against three existing approaches. The first is Fine-Tuning, where for InstructBLIP, the process targets the Q-Former, a connector between the vision encoder and the LLM, involving approximately 188M parameters. For LLaVA-1.5, fine-tuning is applied to 11 layers, uniformly sampling from the 32-layer LLM at equal intervals, totaling 2.5 billion parameters (constrained by GPU memory limits). The second approach is Model-Tailor [61], which employs a two-step strategy: initially, it retains only about $10\%$ of delta parameters based on a specific selection strategy, discarding the rest; subsequently, it compensates the remaining delta parameters to mitigate performance loss on the target task, then fuses the selected and decorated parameters with pretrained parameters. The third method is DARE [48], which randomly selects and rescales delta parameters, then fuses them with pre-trained parameters to maintain the model's performance on the target task. Similar to our method, both Model-Tailor and DARE achieve parameter-efficient adaptation without requiring model re-training. + +Evaluation Metrics. We employ two complementary metrics to evaluate MLLM performance. The first is arithmetic mean across both pre-trained and target tasks, providing an overall performance measure: + +$$ +\operatorname {A v g} = \operatorname {M e a n} (\operatorname {s c o r e} (\mathcal {P}), \operatorname {s c o r e} (\mathcal {T})). \tag {14} +$$ + +The second is the H-score, defined as the harmonic mean between pre-trained and target task performances: + +$$ +\mathrm {H} - \text {s c o r e} = \frac {2 * \operatorname {M e a n} (\operatorname {s c o r e} (\mathcal {P})) * \operatorname {M e a n} (\operatorname {s c o r e} (\mathcal {T}))}{\operatorname {M e a n} (\operatorname {s c o r e} (\mathcal {P})) + \operatorname {M e a n} (\operatorname {s c o r e} (\mathcal {T}))}, \tag {15} +$$ + +where $\mathrm{score}(\mathcal{P})$ and $\mathrm{score}(\mathcal{T})$ represent performance scores on pre-trained and target tasks respectively. The H-score is particularly sensitive to performance imbalances, providing a rigorous measure of the trade-off between retaining pretrained knowledge and adapting to new tasks. + +Implementation Details. All experiments were conducted using 8 A100 GPUs, each with 40GB memory. For InstructBLIP fine-tuning on both Flickr30k and GQA, we performed a grid search over learning rates in the range [1e-6, 1e-5], identifying 1e-5 as optimal. The training utilized a batch size of 16 per GPU for 5 epochs. For LLaVA-1.5, we explored learning rates in the range [1e-6, 1e-4], with optimal values of 5e-6 for both Flickr30k and OKVQA. Similarly, we maintained a batch size of 16 per GPU and trained for 5 epochs in both cases. When combined with LoRA, we set the LoRA rank to 128 and learning rate to + +5e-6, maintaining the same batch size and training epochs as in the standard fine-tuning experiments. Specifically, we tune $\gamma$ within the range [0.4, 0.8], assessing specialization on the target validation dataset and generalization ability on the VQAv2 validation dataset. + +# 5.2. Experimental Results + +Now, we present the results of our empirical investigation, including the overall performance of our method and compared baselines, an ablation study of adaptive selection mechanism and the trade-off between stability and plasticity of tuning $\gamma$ and a complexity analysis. + +# 5.2.1. Overall Performance: + +Tab. 1 and Tab. 2 present the experimental results for fine-tuning InstructBLIP and LLaVA-1.5 across different datasets. For both models, we maintain a $90\%$ sparsity ratio across all parameter-efficient methods and set $\gamma = 0.5$ for AdaDARE- $\gamma$ . The results demonstrate that AdaDARE- $\gamma$ consistently achieves the best H-score across all experimental settings, achieving optimal trade-off between model stability and plasticity. Notably, while maintaining strong performance on pre-trained tasks, AdaDARE- $\gamma$ achieves comparable or even better performance on target tasks compared to full fine-tuning (99.7 vs. 101.3, 57.22 vs. 60.53 on InstructBLIP and 90.1 vs. 93.2, 57.21 vs. 55.72 on LLaVA-1.5). In contrast, although DARE achieves almost the same target performance as full fine-tuning, it shows significant performance degradation on pre-trained tasks. Model-Tailor, when only fine-tuning the Q-former in InstructBLIP, exhibits sub-optimal target task performance (e.g., 81.8 vs. 101.1 on Flickr30k and 54.36 vs. 60.53 on GQA). + +# 5.2.2. Combination with LoRA + +AdaDARE- $\gamma$ is compatible with existing parameter-efficient fine-tuning (PEFT) methods such as LoRA [18]. While LoRA dramatically reduces trainable parameters by freezing pre-trained weights and introducing low-rank decomposition matrices, our experiments fine-tuning LLaVA-1.5 with LoRA on Flickr30K and OKVQA demonstrate that it still encounters catastrophic forgetting. As shown in Fig. 3, incorporating AdaDARE- $\gamma$ into LoRA-based fine-tuning yields significant performance gains across multiple datasets, outperforming existing methods on most datasets as well as in Average and H-score metrics. This confirms AdaDARE- $\gamma$ 's effectiveness as a complementary technique to PEFT approaches. + +# 5.2.3. Ablation Study + +Adaptive Selection Enhances Target Task Performance and Drop Rate Robustness. We conduct ablation studies comparing our adaptive selection strategy with DARE's + +Table 1. InstructBLIP Fine-tuning on Flickr30k and GQA. All parameter-efficient methods maintain $90\%$ sparsity ratio with $\gamma = 0.5$ for AdaDARE- $\gamma$ . Results are reported on both pre-trained tasks (COCO, NoCaps, OKVQA, AOKVQA, VQAv2) and the target task (Flickr30k, GQA). #Params denotes the number of trainable parameters. The optimal and sub-optimal results are denoted by boldface and underlining. + +
Method#ParamsPre-trained tasksTarget taskMetrics
COCONoCaps-inNoCaps-nearNoCaps-outOKVQAAOKVQAVQAv2GQAFlickr30kAvgH-score
Zero-shot-143.0116.9124.0122.657.2660.7576.6549.1983.492.6488.29
Fine-tune188M123.2109.0120.0120.045.5455.3161.0343.91101.386.5892.28
DARE18.8M123.6110.1120.3119.945.5955.3460.9943.98101.186.7692.33
Model-Tailor18.8M139.7116.5125.0125.956.5060.7570.8449.1596.493.4194.69
AdaDARE-γ18.8M137.6116.2125.4126.655.7160.2970.4648.9599.793.4396.05
Method#ParamsPre-trained tasksTarget taskMetrics
COCONoCaps-inNoCaps-nearNoCaps-outOKVQAAOKVQAVQAv2Flickr30kGQAAvgH-score
Zero-shot-143.0116.9124.0122.657.2660.7576.6583.449.1992.6465.51
Fine-tune188M123.6101.4109.2110.734.9544.164.1772.560.5380.1369.85
DARE18.8M125.6102.1110.7112.235.8445.3264.3174.260.2881.1770.11
Model-Tailor18.8M141.5116.5122.7121.455.2359.7971.0481.854.3691.5969.47
AdaDARE-γ18.8M139.6114.1122.0120.351.5657.7570.1481.157.2290.4271.30
+ +Table 2. LLaVA-1.5 Fine-tuning on Flickr30k and OKVQA. All parameter-efficient methods maintain $90\%$ sparsity ratio with $\gamma = 0.5$ for AdaDARE- $\gamma$ . Results are reported on both pre-trained tasks (VQAv2, GQA, VizWiz, SQA, TextVQA, POPE, MM-Bench, MM-Bench-CN) and the target task (Flickr30k, OKVQA). #Params denotes the number of trainable parameters. The optimal and sub-optimal results are denoted by boldface and underlining. + +
Method#ParamsPre-trained tasksTarget taskMetrics
VQAv2GQAVizWizSQATextVQAPOPEMM-BenchMM-Bench-CNFlickr30kAvgH-score
Zero-shot-78.5261.9450.0670.2258.2186.164.658.112.259.9920.59
Fine-tune2.5B75.2760.0525.6366.2852.0787.756.752.9293.263.3172.68
DARE248M76.760.827.0566.8952.7886.257.353.8691.963.7272.74
Model-Tailor248M77.7461.4638.4169.0257.1787.065.1257.6491.967.2775.58
AdaDARE-γ248M77.8961.6147.8369.2857.5387.165.2157.9990.168.2875.89
Method#ParamsPre-trained tasksTarget taskMetrics
VQAv2GQAVizWizSQATextVQAPOPEMM-BenchMM-Bench-CNOKVQAAvgH-score
Zero-shot-78.5261.9450.0670.2258.2186.164.658.10.0258.640.04
Fine-tune2.5B70.2451.7942.3752.0653.1665.645.7957.9855.7254.9655.29
DARE248M71.3553.0842.8752.2553.926942.5257.6456.4555.4555.88
Model-Tailor248M75.0159.148.3369.1655.968564.1758.6754.8663.3659.25
AdaDARE-γ248M75.5259.5148.8169.4956.428564.7858.3357.2163.9060.74
+ +Note: We observed that fine-tuning only the last 12 layers of the LLM leads to substantially lower performance compared to PEFT methods, as reported in [59]. In response, we developed a more reasonable fine-tuning approach that, under limited GPU resources, achieves superior performance compared to both the baseline fine-tuning results and the Model-Tailor approach reported in Model-Tailor's paper. + +random selection approach. As shown in Fig. 3, adaptive selection not only improves target task performance but also significantly enhances model robustness under high drop rates. + +Performance Trade-off with $\gamma$ . Performance Tradeoff with $\gamma$ . We investigate the impact of different $\gamma$ values on model performance. As illustrated in Fig. 4, $\gamma$ regulates the injection of task-specific information, creating a balance of stability and plasticity. As established in Theorem 2, $\gamma \leq \frac{\eta}{\sum_{i=1}^{n} |\delta_i|}$ , where $\eta$ represents our desired pre-trained performance constraint and $\delta_i$ reflects parameter changes. This relationship manifests clearly in our experiments: (1) + +For full fine-tuning across datasets, we set $\gamma = 0.5$ as used in Tab. 1 and Tab. 2; (2) For parameter-efficient fine-tuning (PEFT) with LoRA shown in Tab. 3, we set $\gamma = 0.7$ . This difference arises because PEFT induces smaller parameter changes $(\delta_i)$ , allowing for larger $\gamma$ values while maintaining the theoretical bound. As shown in Fig. 4, the method remains highly stable for $\gamma \in [0.5, 0.8]$ . This stability across a range of $\gamma$ values demonstrates the robustness of our approach in practical settings. + +# 5.2.4. Computational Complexity Analysis + +The computational complexity of our method consists of two main components: (1) Initial Hessian Computation: + +Table 3. Combination with LoRA on LLaVA. Performance comparison of AdaDARE-γ ( $\gamma = 0.7$ , sparsity ratio $= 90\%$ ) combined with LoRA-based LLaVA-1.5 fine-tuning and Model-Tailor across multiple datasets. Results demonstrate significant improvements in maintaining both pre-trained and target task performance. + +
MethodPre-trained tasksTarget taskMetrics
VQAv2GQAVizWizSQATextVQAPOPEMM-BenchMM-Bench-CNFlickr30kAvgH-score
LoRA72.7657.458.2962.4440.4480.7051.6333.7689.5053.0362.33
Model-Tailor78.0461.2626.7968.0353.9686.5060.2253.7889.7064.2572.67
AdaDARE-γ78.3661.6532.4568.9255.8286.1062.9756.4489.2065.7773.73
MethodPre-trained tasksTarget taskMetrics
VQAv2GQAVizWizSQATextVQAPOPEMM-BenchMM-Bench-CNOKVQAAvgH-score
LoRA25.5153.2543.1162.1854.4770.0550.2556.7858.1152.6354.85
Model-Tailor74.1557.0948.0968.5255.4581.4963.1458.2459.2862.8261.21
AdaDARE-γ74.6658.1947.7668.6955.8784.2064.4358.6758.9763.4961.41
+ +![](images/bdd447d4db1e370e60c726814b45ef9ce5381f03c906ccfbcaf0cd6633df7ec6.jpg) +Figure 3. Performance comparison between AdaDARE- $\gamma$ ( $\gamma = 1$ ) and DARE on Flickr30k across various drop rates. Results demonstrate that AdaDARE- $\gamma$ consistently outperforms DARE, particularly showing enhanced robustness at higher drop rates. + +![](images/6b5b651eee9303a7f7c0cf48ff639cb9a6b3a7464e123bea4293695d7b15e385.jpg) + +![](images/855bf930d0ff7c004b59194baf43e3bb1df89123eb610484b2b51b93b67efd30.jpg) +Figure 4. Performance trade-off across different $\gamma$ values on InstructBLIP (Flickr30k, GQA) and LLaVA-1.5 (Flickr30k, OKVQA). The plots demonstrate that $\gamma$ effectively controls the stability-plasticity trade-off. + +Computing the initial Hessian matrix $(H = 2XX^{T} + \lambda I$ where $X$ represents input samples) has a time complexity of $\mathcal{O}(nd_{col}^2)$ , where $n$ denotes the number of input samples + +Table 4. Computational complexity comparison of different methods. $n$ denotes the number of input samples, ${d}_{col}$ and ${d}_{row}$ represent the column and row dimensionality of the weight matrix, respectively. + +
MethodComputational Complexity
DAREO(1)
AdaDARE-γO(nd2col + drowdcol)
Model-TailorO(nd2col + d3col + dcldrow)
+ +(set to 128 in our experiments) and $d_{col}$ represents the column dimensionality of the matrix. (2) Adaptive Drop and Rescale: This process primarily involves calculating optimal probabilities with a time complexity of $\mathcal{O}(d_{row}d_{col})$ , where $d_{row}$ denotes the row dimensionality of the matrix. + +# 6. Conclusion and Limitation + +In this paper, we present AdaDARE- $\gamma$ , demonstrating effective MLLM adaptation through principled parameter selection and controlled knowledge injection. Our method addresses the stability-plasticity dilemma by identifying crucial parameters and regulating their integration with pretrained knowledge, achieving state-of-the-art performance across multi-modal tasks with computational efficiency. While promising, our approach relies on manual tuning of $\gamma$ , and theoretical bounds may not directly align with optimal practical values. Future work could explore automatic optimization of $\gamma$ and better connections between theory and practice for optimal balance between adaptation and knowledge preservation. Our framework provides valuable insights for efficient multi-modal adaptation. + +# Acknowledgements + +This work was supported by the NSFC under grant No. 62401029 and No. 62206308. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023. 1, 2 +[2] Tameem Adel, Han Zhao, and Richard E. Turner. Continual learning with adaptive weights (claw), 2020. 1, 2 +[3] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. In 2019 IEEE/CVF International Conference on Computer Vision (ICCV). 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Sci. & Tech., Institute for AI, Tsinghua University, Beijing, China 2Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China 3State Key Laboratory of Multimedia Information Processing, Peking University, Beijing, China 4School of Software Microelectronics, Peking University, Beijing, China 5Institute of Intelligent Computing, Alibaba Group 6Shanghai Artificial Intelligence Laboratory, Shanghai, China 7Jiangsu Collaborative Innovation Center for Language Competence, Jiangsu, China 8ModelTC Open Source Organization, Beijing, China + +# Abstract + +Recently, model merging methods have demonstrated powerful strengths in combining abilities on various tasks from multiple Large Language Models (LLMs). While previous model merging methods mainly focus on merging homogeneous models with identical architecture, they meet challenges when dealing with Multimodal Large Language Models (MLLMs) with inherent heterogeneous property, including differences in model architecture and the asymmetry in the parameter space. In this work, we propose AdaMMS1, a novel model merging method tailored for heterogeneous MLLMs. Our method tackles the challenges in three steps: mapping, merging and searching. Specifically, we first design mapping function between models to apply model merging on MLLMs with different architecture. Then we apply linear interpolation on model weights to actively adapt the asymmetry in the heterogeneous MLLMs. Finally in the hyper-parameter searching step, we propose an unsupervised hyper-parameter selection method for model merging. As the first model merging method capable of merging heterogeneous MLLMs without labeled data, extensive experiments on various model combinations demonstrated that AdaMMS outperforms previous model merging methods on various vision-language benchmarks.2 + +# 1. Introduction + +Model merging [10] has gained increasing popularity in the field of large language models (LLMs) [10, 26, 29, 32]. This approach typically involves combining the parameters of two models with the same architecture, creating a new model without requiring additional training [10]. It has proven to be an efficient method for developing models that integrate the abilities of multiple existing models [26, 29, 32], avoiding the need for extensive data and computational resources, and has been widely adopted in building powerful LLMs [4, 6]. + +Despite its popularity with LLMs, model merging has yet to be widely adopted for multimodal large language models (MLLMs). Some recent studies have explored the application of model merging to MLLMs [1, 19] but either prioritize extending multimodal capabilities over enhancing the performance of existing models [1] or still require additional training after merging [19]. The primary obstacle in applying model merging to MLLMs lies in the heterogeneous nature of these models [8, 12, 14, 24, 28]. This heterogeneity arises from modifications to the transformer architectures [21] within their language models [8, 28], as well as differences in their choice of modality-specific encoders and tokenizers [8, 24]. Consequently, a significant challenge in merging MLLMs is that the process cannot be directly applied to models with different architectures, as their weights are not isomorphic. + +Recent efforts like FuseLLM [22] and FuseChat [23] have explored fusing the capabilities of heterogeneous LLMs by merging their generative distributions. Theoretically, these methods could also be applied to MLLMs. + +![](images/51d5daea1a3da83a9feb80c2d161b3501837e0f8d7cabb380f5ac47ecff794cf.jpg) +(a) AdaMMS overview. + +![](images/ccd94fa2d580d16e0d9840668d6bb61450dba79be9e6f95733bfa348a02f94cf.jpg) +(b) Gains from different merging methods. +Figure 1. (a) Illustration of three steps in AdaMMS: Step-1, mapping MLLMs with different model architecture; Step-2, merging MLLMs with linear interpolation; Step-3, searching for optimal merging hyper-parameter by approximate task performance through generation consistency without labeled data. (b) The gain performance of AdaMMS on a broad range of multimodal tasks in comparison with existing merging approaches. Gain refers to the improvement obtained by subtracting the average result from the result of the fused model on a certain task. The result here is the average of the gains from the two MLLM pairs merging. + +However, they rely on supervised continued training, which incurs significant computational costs and fails to address scenarios where labeled data is unavailable. For example, FuseLLM requires a training dataset with a total of 1.8 billion tokens and 33 hours of training time. This underscores the need for an unsupervised model merging technique to effectively integrate heterogeneous MLLMs. + +In this work, we address the challenges of merging heterogeneous MLLMs by introducing a novel model merging strategy named AdaMMS, as illustrated in Figure 1. First, to enable model merging across heterogeneous MLLMs with differing architectures, we design a parameter mapping framework. Specifically, we focus on the scenario where MLLMs have different language model architectures due to variations in transformer block duplications [8, 25, 28]. This mapping aligns corresponding components across models, enabling merging operations even with structural differences. Next, we apply adaptive linear interpolation on the mapped parameters during merging. By adjusting the interpolation coefficient, AdaMMS optimizes performance adaptively across different tasks. This coefficient adjustment is then optimized through an unsupervised procedure in the following step. Finally, we introduce an unsupervised hyperparameter selection method to determine the interpolation coefficient for each task. This approach leverages response consistency across candidate models as a performance estimate, based on our novel insight that model performance correlates with generation consistency. In addition to strong empirical support, we + +provide a theoretical analysis to explain this insight. + +Extensive experiments have demonstrated the effectiveness of our proposed AdaMMS in merging MLLMs. Our main experiments are conducted on two pairs of heterogeneous MLLMs, one of them is based on Qwen [27] architecture, another pair is based on LLaMA [20] architecture. Both experiments show that our model can effectively combine the capabilities of heterogeneous MLLMs by enabling model merging on models with different architecture. The experiments also demonstrated that the merging strategy of AdaMMS, accompanied with our unsupervised hyper-parameter selection method, outperforms previous model merging methods on various vision-language tasks. We also conducted experiments to show that the unsupervised hyper-parameter selection method can be performed with fewer unlabeled data without harming its performance, which shows the robustness of the method and further decrease the data requirements of AdaMMS. + +Our main contributions are as follows: + +- We introduce a novel model-merging strategy, AdaMMS, designed to address the challenges of merging heterogeneous MLLMs. By defining a parameter mapping between different models, AdaMMS facilitates model merging techniques even when architectural differences exist. +- We propose an unsupervised hyperparameter selection method inspired by the observation that model performance can be effectively estimated through generation consistency—measured by the variation in generated responses. Unlike previous approaches requiring labeled + +data, this method eliminates the dependency on annotations and can be applied to a small subset of 100 target sample without sacrificing effectiveness. + +- Comprehensive experiments conducted on various model pairs demonstrate the effectiveness of our approach. Specifically, evaluations on Qwen-based and LLaVABased heterogeneous MLLM pairs show that AdaMMS successfully combines capabilities from distinct MLLMs. Across various vision-language tasks, AdaMMS consistently outperforms baseline strategies, achieving superior overall performance. + +# 2. Related Work + +# 2.1. Model Merging + +Recent researches on model merging techniques have contributed to building more capable models by providing an efficient approach to combine abilities on various tasks from different models that requires less data and compute. Some studies focus on merging homogeneous models with identical architecture, while others focus on tackle the challenge on heterogeneous models which have different architectures. In merging homogeneous models, Task Arithmetic [10] proposes the concept of task vectors, which subtracts fine-tuned weights from pre-train weights to obtain task-related weight difference as the object of merging. Ties-Merging [26] and DARE [29] further improve the performance by mitigating parameter interference during the merging process through parameter pruning and conflict resolving. MetaGPT [32] scales the task vectors with task-agnostic coefficients in closed-form by separating data term and scaling coefficients in the optimization objective. Although these methods improves the performance of the merged models, they cannot be directly applied on models with architecture difference. In fusing heterogeneous models, DAMC [1] employs parameter decoupling and adaptive adjustment to enhance model merging strategies for fusing modalities on MLLMs with different modality encoders, but this work still focuses on merging identical language model architecture. To consolidate LLMs with different architectures, FuseLLM [22] and FuseChat [23] applies token alignment and model fusion strategies with knowledge distillation before continue training the model, but they need labeled data and computation resources for continue training. In fact, the majority of previous works on model merging requires labeled data for validation search or supervised training [1, 10, 22, 23, 26, 29]. In this work, we eliminate the need of labeled data by leveraging our unsupervised hyper-parameter selection method, and enable model merging strategies to be applied on heterogeneous MLLMs with architecture differences. + +# 2.2. Multimodal Large Language Models + +As large language models demonstrate huge success in obtaining great abilities in general, recent researches on MLLMs have successfully appending multimodal processing and generation ability on LLMs, especially on the vision modality [2, 12, 14, 24, 25, 28]. However, these models often adapts unique modifications on language model architecture, resulting in a set of heterogeneous MLLMs, which prevent model merging methods to be applied on them. Specifically, there are two levels of architecture differences among MLLMs. First, two MLLMs may be designed from different pre-trained language model. For example, Qwen2-VL [24] and LLaVA-OneVision-Qwen [12] are designed from Qwen2 [27], while LLaVA [14], mPLUG-Owl2 [28], CogVLM [25] and ShareGPT4V [2] are designed following the LLaMA [20] architecture. Second, two MLLMs developed from the same pre-trained language model can still be heterogeneous because they are designed with different modifications on the language model. For example, although CogVLM and mPLUG-Owl2 are both developed from LLaMA architecture, CogVLM adapts visual experts by duplicating query, key and value weights in attention head, while mPLUG-Owl2 is designed to duplicate key, value, and layer norm weights instead. The first level of differences is hard to merge, since model merging applies to parameters that are trained from the same pre-training weights [10]. In this work, we tackle the second level of architecture differences via our proposed AdaMMS method. + +# 3. Method + +To tackle the heterogeneous challenges in merging MLLMs, we propose a novel model merging method named AdaMMS. As shown in Figure 1(a), it involves three steps: mapping, merging and searching. In the mapping step, we define a mapping function that enables the merging of parameters from different architectures. Next, in the merging step, we apply linear interpolation to adaptively optimize the performance on specific downstream tasks. Finally, in the searching step, we design a unsupervised hyperparameter selection method for choosing linear interpolation coefficient during merging. This method is based on our novel discovery that the model performance in the parameter space can be approximated by the difference among model responses without the need of labeled data. + +# 3.1. Mapping + +To merge the parameters of two heterogeneous models $M_{1}$ and $M_{2}$ into $M_{1}$ 's architecture, we need to align their parameters by defining a mapping $f$ that maps each parameter $\theta_{1}$ in $M_{1}$ to its corresponding parameter $\theta_{2}$ in $M_{2}$ (or $\phi$ if there is no such corresponding parameter). As previously discussed in Section 2.2, we only tackle the hetero- + +genuine MLLMs that are designed from same pre-trained language model architecture, but adapts different modifications on model structure. + +The principle of designing the mapping $f$ is that for the shared weights between the models (e.g. the weights in the pre-trained model), we can map them directly, and for additional weights in $M_1$ , we map it to its original corresponding weight in $M_2$ if it is a duplicated multimodal parameter in $M_1$ 's specific design, otherwise we map $\phi$ with it and apply no operation later in merging. In this way, we leverage the additional weights as much as possible without mapping irrelevant parameters together. + +# 3.2. Merging + +We follow the paradigm in Task Arithmetic [10] to apply merging operation on task vectors and apply linear interpolation on them. Task vectors are defined as the finetuned parameters subtracted by pre-train weights: $\tau_{i} = \theta_{i} - \theta_{0}$ ( $i = 1,2$ ), where $\theta_{1}$ and $\theta_{2}$ is the models to be merged, and $\theta_{0}$ is their common initialization point (e.g. the shared pre-trained weights for two different finetuned model). Linear interpolation offers the availability to directly control the tendency between the two models alongside its simplicity. This allows us to actively adapt to different downstream tasks, as different downstream tasks often requires different combination or tendency on the two models for the best performance. Linear interpolation on task vectors can be simply formatted as: $\theta_{out} = \theta_0 + (1 - \alpha)\tau_1 + \alpha \tau_2$ , where $\alpha$ is the linear interpolation coefficient. This is equivalent to: $\theta_{out} = (1 - \alpha)\theta_{1} + \alpha \theta_{2}$ . Thus, leveraging our mapping functor $f$ in Section 3.1, we can apply our merging operation on heterogeneous MLLMs as follows: + +$$ +\theta_ {o u t} ^ {i} = \left\{ \begin{array}{l l} \theta_ {1} ^ {i}, & \text {i f} f \left(\theta_ {1} ^ {i}\right) = \phi \\ (1 - \alpha) \theta_ {1} ^ {i} + \alpha f \left(\theta_ {1} ^ {i}\right), & \text {o t h e r w i s e} \end{array} \right. \tag {1} +$$ + +Note that $f(\theta_1)$ is the parameter in $M_2$ that corresponds to $\theta_1$ , according to the mapping function $f$ . Now we can define the merging process of two model parameters $\Theta_1 = \{\theta_1^i\}$ and $\Theta_2 = \{\theta_2^j\}$ accordingly: + +$$ +\operatorname {M e r g e} \left(\Theta_ {1}, \Theta_ {2}; f; \alpha\right) = \left\{\theta_ {\text {o u t}} ^ {i} \right\} \tag {2} +$$ + +# 3.3. Searching + +Consider the base model, which is defined as the architecture that will be used after the merging process, containing $N$ scalar weight elements, then the merging process can be seen as the operation on a $N$ -dimensional vector space $\mathbb{R}^N$ , where the merging strategy $F$ transform two input points as initial parameters $\Theta_1$ and $\Theta_2$ to the merged parameters $\Theta_{out}$ . For simplicity, we consider the case when the merging strategy $F$ takes one hyper-parameter $\alpha$ (linear interpolation coefficient). + +$$ +\Theta_ {o u t} = F (\Theta_ {1}, \Theta_ {2}; \alpha), \quad \Theta_ {1}, \Theta_ {2}, \Theta_ {o u t} \in \mathbb {R} ^ {N} +$$ + +Given the inputs $t_i$ on a downstream task, this creates a landscape on $\mathbb{R}^N$ that each model parameter corresponds to the model performance $S_{t_i}$ on the inputs. + +$$ +S _ {t _ {i}} (\Theta_ {\text {o u t}}) = S _ {t _ {i}, F} (\Theta_ {1}, \Theta_ {2}, \alpha) +$$ + +Therefore, the goal of the hyper-parameter searching is to find the best $\alpha$ that maximize the merged model's performance on the tasks. For simplicity, we omit the F in the index. + +$$ +\alpha^ {*} = \underset {\alpha} {\operatorname {a r g m a x}} \left(S _ {t _ {i}} \left(\Theta_ {1}, \Theta_ {2}, \alpha\right)\right) +$$ + +Note that as the landscape varies greatly in different tasks, the best $\alpha$ may be different as well. + +Previous model merging methods mainly relies on a validation set to search for the best hyper-parameter $\alpha$ with supervised searching. Formally, they use the best $\alpha$ in validation set $\hat{t}_i$ to approximate the best $\alpha$ in test set $t_i$ . + +$$ +\hat {\alpha} = \operatorname * {a r g m a x} _ {\alpha} (S _ {\mathbf {t} _ {\mathrm {i}}} (\Theta_ {1}, \Theta_ {2}, \alpha)) \approx \operatorname * {a r g m a x} _ {\alpha} (S _ {\mathbf {t} _ {\mathrm {i}}} (\Theta_ {1}, \Theta_ {2}, \alpha)) +$$ + +However, this supervised way of searching has certain disadvantages: (1) labeled data with ground truth is hard to collect in some scenarios, and (2) the distribution shift between the validation set and the test set, even on the same task, will interfere the selection of the best hyper-parameter $\alpha^{*}$ . To get rid of these drawbacks, we propose an unsupervised hyper-parameter selection method through a performance estimation metric that requires no labeled data. + +Specifically, we discover that the difference of generated responses between two adjacent $\alpha$ candidates can be used to estimate the model performance, and the best $\alpha$ can be approximated by the one with the lowest adjacent difference. As shown in Figure 2, the trend of model performance is similar with its generation consistency which is measured by response differences, and the $\alpha$ with the highest generation consistency match the $\alpha$ with the highest performance. Formally, let $\alpha^{-}$ and $\alpha^{+}$ be adjacent candidates on both sides of $\alpha$ , respectively, and $D_{t_i}(\alpha; \alpha^{-}, \alpha^{+})$ denoting the difference of generated responses between, we take: + +$$ +\bar {\alpha} = \operatorname * {a r g m i n} _ {\alpha} (D _ {t _ {i}} (\alpha ; \alpha^ {-}, \alpha^ {+})) \approx \operatorname * {a r g m a x} _ {\alpha} (S _ {t _ {i}} (\Theta_ {1}, \Theta_ {2}, \alpha)) +$$ + +as the approximation of the best choice for $\alpha$ . This eliminates the need of labeled data with ground truth, and avoids the data distribution shift between validation set and test set. + +The discovery indicates that near the best performance point, the model response tends to be more stable. This can be explained via a convex hypothesis. Suppose the landscape on given task $t_i$ is convex in a subspace of the parameter space that covers the candidate results of merged models, that is, for any $\lambda \in [0,1]$ we have: + +$$ +S _ {t _ {i}} (\lambda \Theta_ {1} + (1 - \lambda) \Theta_ {2}) \geq S _ {t _ {i}} (\lambda \Theta_ {1}) + S _ {t _ {i}} ((1 - \lambda) \Theta_ {2}) +$$ + +This guarantee that the optimum is attained where the gra + +dient vanishes: + +$$ +\nabla_ {\Theta} S _ {t _ {i}} (\Theta^ {*}) = 0 +$$ + +where $\Theta^{*}\in \mathbb{R}^{N}$ is the optimal parameter value. In a convex function, the Hessian $H(\Theta^{*}) = \nabla_{\Theta}^{2}S_{t_{i}}(\Theta^{*})$ at the optimum $\Theta^{*}$ is positive semi-definite, which implies local stability in a neighborhood around $\Theta^{*}$ . The stability can be characterized by the second-order Taylor expansion: + +$$ +S _ {t _ {i}} (\Theta) \approx S _ {t _ {i}} (\Theta^ {*}) + \frac {1}{2} (\Theta - \Theta^ {*}) ^ {\top} H (\Theta^ {*}) (\Theta - \Theta^ {*}) +$$ + +Since $H(\Theta^{*}) \geq 0$ , small deviations from $\Theta^{*}$ will result in small increases in the performance, ensuring relative stability on the landscape. Although the convex hypothesis is ideal, we confirm the effectiveness of our unsupervised hyper-parameter selection method in various experiments. Proof in Appendix F further shows the relationship between generation consistency and model performance. + +We also find that while the landscape often changes between the validation and test sets and across different tasks, it remains consistent between the full test set and a small subset. This suggests that we can perform unsupervised hyper-parameter selection on a smaller subset of the data $\bar{t}_i$ without compromising its accuracy. + +$$ +\bar {\alpha} = \underset {\alpha} {\operatorname {a r g m i n}} (D _ {\mathbf {\bar {t} _ {i}}} (\alpha ; \alpha^ {-}, \alpha^ {+})) \approx \underset {\alpha} {\operatorname {a r g m a x}} (S _ {\mathbf {t _ {i}}} (\theta_ {1}, \theta_ {2}, \alpha)) +$$ + +In conclusion, the process of AdaMMS is described in Algorithm 1. + +# 4. Experiment + +# 4.1. Baselines + +Previous model merging methods cannot be directly applied to heterogeneous MLLMs with architecture difference, and our mapping method enables the fusion of heterogeneous models by transforming them into a homogeneous parameter space. Therefore, all the baseline experiments are conducted under the precondition of the mapping step of our proposed method. We consider the following model merging methods as our baselines: + +- Task Arithmetic [10] introduces the idea of task vectors and integrates them into the original pre-trained model for multi-task learning. +- Ties-Merging [26] further addresses interferences in Task Arithmetic by removing unnecessary parameters from Task Arithmetic [10]. This process eliminates redundant parameters and resolves symbol conflicts through Trim, Elect Sign, and Disjoint Merge steps. +- DARE [29] tackles the parameter conflict problem in model merging by applying a drop and rescale operation before merging model weights. There are two variants of DARE: Dare-Linear and Dare-Ties, which perform different merging strategies after the drop and rescale operation. Dare-Linear performs linear interpolation, and + +Algorithm 1 AdaMMS Procedure +Input: Original MLLMs $M_1, M_2$ , their parameters $\Theta_1, \Theta_2$ respectively, a subset of test inputs $\bar{t}$ , and the candidates of the hyper-parameter $\{\alpha_n\}$ +Output: Merged parameters $\Theta_{\mathrm{out}}$ on $M_1$ 's architecture +1: Define a mapping $f$ that maps each parameter $\theta_1$ in $M_1$ architecture with its corresponding parameter $\theta_2$ in $M_2$ architecture (if exists) $\triangleright$ Section 3.1 +2: Define a process Generate $(\Theta, \bar{t})$ that returns the generation responses $G$ of model with parameters $\Theta$ on inputs $\bar{t}$ +3: Define a function DiffCnt $(G_i, G_j)$ that counts the number of corresponding elements in $G_i$ and $G_j$ that do not exactly match +4: for $i = 1$ to $n$ do +5: for each hyper-parameter candidate $\alpha_i$ in $\{\alpha_n\}$ do +6: $\Theta_{cand}^i \gets \text{Merge}(\Theta_1, \Theta_2; f; \alpha_i) \triangleright \text{Equation}(2)$ +7: $G_i \gets \text{Generate}(\Theta_{cand}^i, \bar{t})$ +8: end for +9: end for +10: for $i = 2$ to $n - 1$ do $\triangleright$ Assuming $\{\alpha_n\}$ is monotonic +11: for each hyper-parameter candidate $\alpha_i$ in $\{\alpha_n\}$ do +12: $D_i \gets \text{DiffCnt}(G_i, G_{i-1}) + \text{DiffCnt}(G_i, G_{i+1})$ +13: end for +14: end for +15: $i^* \gets \text{argmin}_i(D_i)$ +16: $\Theta_{\mathrm{out}} \gets \Theta_{\mathrm{cand}}^{i*}$ +17: return $\Theta_{\mathrm{out}}$ + +Dare-ties performs Ties-Merging [26]. + +MetaGPT [32] separate the data term and scaling coefficients in the optimization objective, which leads to a task-agnostic closed-form solution for the scaling coefficient. + +# 4.2. Models + +We have conducted extensive experiments on the combinations of existing open-source 7B-scale MLLMs. Since most of the top-performing open-source MLLMs are currently based on two language model architectures, Qwen2 [27] and LLaMA [20], we selected representative and outstanding MLLMs derived from each model for our main experiments. Specifically, on Qwen2 architecture, we merge LLaVA-OneVision-Qwen-7B [12] into Qwen2-VL7B [24], and on LLaMA architecture, we merge LLaVAv1.5-7B [14] into CogVLM-Chat-7B [25]. + +We have also conducted experiments on combinations of LLaMA-based MLLMs, including combinations LLaVA-v1.5-7B, CogVLM-Chat-7B, ShareGPT4V-7B [2] and mPLUG-Owl2-LLaMA2-7B [28]. See Appendix A for more details. + +
ModelMMMUvalMMEsumSeedBenchallOCRBenchTextVQA valOKVQAGQAVizWiz valSUMTop2
Original Models
Qwen2-VL(base)50.1181.4475.8586.0084.1251.4361.8068.32559.072
LLaVA-OneVision43.4477.0475.4469.6078.4749.5759.8460.97514.370
Baselines
Task Arithmetic48.44(+1.67)82.33(+3.09)75.81(+0.17)77.90(+0.10)76.22(-5.08)50.60(+0.10)62.26(+1.44)62.76(-1.89)536.32(-0.40)1
Ties-Merging51.11(+4.34)82.65(+3.41)76.29(+0.64)84.40(+6.60)79.56(-1.74)52.56(+2.06)61.84(+1.02)66.34(+1.69)554.75(+18.03)4
DARE-Linear43.78(-3.00)66.06(-13.18)74.32(-1.33)72.40(-5.40)64.65(-16.65)43.41(-7.09)55.13(-5.69)50.18(-14.47)469.93(-66.79)0
DARE-Ties45.00(-1.78)54.43(-24.81)74.07(-1.58)75.20(-2.60)78.54(-2.76)49.61(-0.89)58.51(-2.31)58.05(-6.60)493.41(-43.31)0
MetaGPT50.67(+3.90)81.21(+1.97)76.35(+0.70)85.50(+7.70)83.63(+2.33)52.24(+1.74)61.99(+1.17)69.16(+4.51)560.75(+24.03)5
Our Method
AdaMMS51.11(+4.34)83.36(+4.12)76.20(+0.55)85.50(+7.70)83.41(+2.11)53.56(+3.06)62.02(+1.20)68.40(+3.75)563.56(+26.84)8
+ +Table 1. Results on merging LLaVA-OneVision-7B into Qwen2-VL-7B. All the scores have been scaled to 0-100. SUM refers to the sum of scores on all tasks after scaling. Top2 column represents the number of tasks obtained by this method from the top two among all methods. The number in the parenthesis indicates the performance improvement compared with the average score of original models. The results in the original models that are higher than all model merging methods are highlighted in italics. + +
ModelMMMUvalMMEsumSeedBenchallOCRBenchTextVQValOKVQAGQAVizWizvalSUMTop2
Original Models
CogVLM(base)34.8059.2361.2256.5077.5760.8259.4337.09446.662
LLaVA35.1066.6860.5231.3046.0453.4261.9454.29409.290
Baselines
Task Arithmetic36.20 (+1.25)65.99 (+3.03)65.85 (+4.98)51.20 (+7.30)68.21 (+6.40)61.92 (+4.80)58.82 (-1.87)35.70 (-9.99)443.89 (+15.91)4
Ties-Merging34.00 (-0.95)57.29 (-5.67)38.97 (-21.90)55.00 (+11.10)59.73 (-2.08)40.31 (-16.81)51.97 (-8.72)24.36 (-21.33)361.63 (-66.35)0
DARE-Linear36.80 (+1.85)64.08 (+1.12)65.07 (+4.20)47.90 (+4.00)65.35 (+3.54)60.96 (+3.84)58.01 (-2.68)36.12 (-9.57)434.29 (+6.31)2
DARE-Ties33.60 (-1.35)46.75 (-16.21)58.41 (-2.46)26.50 (-17.40)50.48 (-11.33)53.15 (-3.97)49.62 (-11.07)31.43 (-14.26)349.94 (-78.04)0
MetaGPT34.70 (-0.25)59.37 (-3.59)61.29 (+0.42)56.40 (+12.50)76.96 (+15.15)60.84 (+3.72)59.44 (-1.25)36.97 (-8.72)445.97 (+17.99)5
Our Method
AdaMMS34.90 (-0.05)69.09 (+6.13)64.12 (+3.25)55.70 (+11.80)76.90 (+15.09)61.11 (+3.99)60.12 (-0.57)37.27 (-8.42)459.21 (+31.23)7
+ +Table 2. Results on merging LLaVA-v1.5-7B into CogVLM-chat-7B. + +# 4.3. Benchmarks + +To evaluate the capabilities of the merged MLLMs, we have conducted experiments on various benchmarks that cover a wide range of vision-language abilities. According to the classification in [13], our benchmarks fall into three categories: (1) comprehensive-evaluation, (2) cognition and reasoning, (3) text-rich VQA. The comprehensive-evaluation tasks consist of MME [5], SeedBench [11] and VizWiz [7]. Cognition and reasoning type include MMMU [30], OK-VQA [16] and GQA [9]. Text-rich VQA type encompass OCRBench [15] and TextVQA [18]. + +To present the overall performance of the MLLMs in a standardized manner, we apply linearly normalization to the scores across all tasks, scaling them to a range from 0 to 100. Specially, the total score of MME is 2800, which we have divided by 28 for scaling purposes. + +# 4.4. Implementation + +To apply our unsupervised hyper-parameter selection method in the searching step, we need to specify the candidates of $\alpha$ (linear interpolation coefficient). We sample the candidates in a subinterval of [0, 1] with a fixed granularity. + +Subinterval We find that merging with $\alpha \geq 0.7$ often results in collapsing language ability of the merged model, therefore we empirically limit the subinterval of $\alpha$ candidi + +dates to [0, 0.6] for eliminating unnecessary search. + +Granularity We use granularity to determine the interval between two adjacent candidates of $\alpha$ . In our main experiments, we choose the granularity as 0.1 to obtain satisfying performance with acceptable computation cost. + +Evaluation Framework We evaluated the benchmarks with LMMs-Eval [31] and VLMEvalKit [3], two open-source evaluation frameworks for MLLMs. + +Subset Searching Instead of conducting search across the entire available input data, we strategically utilize a small subset of only 100 inputs during the search phase, reducing the data volume by at least an order of magnitude. Experimental results demonstrate that this maintains performance without compromising effectiveness. + +# 5. Results + +As described in Section 4.2, the main results on distinct vision-language benchmarks are conducted with two representative MLLM pairs. Specifically, Table 1 shows the results of merging LLaVA-OneVision-7B's parameters into Qwen2-VL-7B's parameters and architecture, and Table 2 shows the results of merging LLaVA-v1.5-7B's parameters into CogVLM-chat-7B's parameters and architecture. Results of other model pairs and larger models can be found in Appendix A. + +
Method\(MMMU_{val}\)\(MME_{sum}\)\(SeedBench_{all}\)OCRBench\(TextVQA_{val}\)ScienceQAOKVQAGQA\(VizWiz_{val}\)SUM
EM-Full51.1183.3676.3485.5083.4185.6953.5662.0268.40563.70
Emb-Full50.5683.3676.3485.5083.4185.6953.5661.4468.40562.57
EM-Sample10051.1183.3676.2085.5083.4186.5553.5662.0268.40562.12
Emb-Sample10051.1182.3676.3485.5083.4185.6953.5661.4468.40563.56
+ +Table 3. Results on AdaMMS when merging LLaVA-OneVision-7B into Qwen2-VL-7B using exact match (EM-) and sentence embedding (Emb-) to calculate the differences in searching phase, using full test set inputs (-Full) and a sampled subset of 100 inputs (-Sample100). + +
ModelMMMUvalMMEsumOCRBench
α-0.0050.1181.4486.00
α-0.1050.5681.4685.50
α-0.2051.1182.3685.20
α-0.3051.2283.3684.40
α-0.4050.6783.0380.70
α-0.5050.0081.3776.40
α-0.6047.0082.0671.20
Oracle51.22(0.30)83.36(0.30)85.50(0.10)
AdaMMS51.11(0.20)83.36(0.30)85.50(0.10)
+ +Table 4. Results with $\alpha$ granularity of 0.1 when merging LLaVA-OneVision-7B into Qwen2-VL-7B. The values in parentheses indicate the selected $\alpha$ . Oracle represents the best possible performance (upper bound) for each task, while AdaMMS shows the results achieved by our unsupervised selection method. + +
Original Models
LLaVA-OneVision69.6069.60
Qwen2-VL86.0086.00
Merging-BaseLLaVA-OneVisionQwen2-VL
Baselines
Task Arithmetic68.1077.90
Ties-Merging56.1084.40
DARE-Linear63.9072.40
DARE-Ties64.4075.20
MetaGPT38.4085.50
Linear Interpolation
α-0.1070.6085.50
α-0.2071.7085.20
α-0.3069.9084.40
α-0.4067.0080.70
α-0.5062.0076.40
α-0.6054.4071.30
Our Method
AdaMMS70.6085.50
+ +Table 5. Results on OCRBench when merging LLaVA-OneVision-7B and Qwen2-VL-7B. + +AdaMMS addresses the challenges of merging for heterogeneous MLLMs and outperforms strong baselines. As demonstrated in Table 1 and Table 2, our proposed AdaMMS model merging method achieves the highest cumulative performance scores across both MLLM + +pairs, indicating its effectiveness in merging heterogeneous MLLMs. Ranks among the top two performs in 8 out of 9 metrics in Table 1 and 7 metrics in Table 2, demonstrating its consistent ability to adaptively improve performance across most tasks. Moreover, our method stands out as the only approach where the merged model significantly outperforms both pre-merged models, achieving an average gain of +3.36 (total gain of +26.84) over Qwen2-VL and +3.90 over CogVLM across 8 tasks. Given that most baseline methods employ supervised search techniques that incorporate additional information, our unsupervised search approach demonstrates exceptional performance on vision-language benchmarks, as detailed illustrated in Appendix D. + +The proposed unsupervised hyper-parameter selection method is able to select a near-optimal $\alpha$ . We evaluate the performance across different coefficient values $\alpha$ , comparing the results obtained through our unsupervised hyper-parameter selection method against those achieved with the optimal $\alpha$ chosen by the actual best results, which serves as the theoretical upper bound. As shown in Table 4, our method consistently performs remarkably close to this upper bound, with a maximum deviation of only 0.5 points. These results demonstrate the capability of our method to accurately identify near-optimal $\alpha$ values, achieving performance levels approaching the theoretical best. + +Note that on the OCRBench and TextVQA benchmarks, all model merging methods, including AdaMMS, show a performance drop compared to the original base model. We hypothesize that this is due to the large performance gap between the two original models on these benchmarks. Even though, AdaMMS still outperforms most of the baselines, showing the robustness of our method on various scenarios. + +# 6. Analysis + +# 6.1. Different Factors for Calculating Generation Consistency + +We conducted analytical experiments on our generation consistency calculation methods, focusing on two key factors: the choice between using a 100-sample subset versus the complete dataset, and the selection of evaluation metrics. In the searching step of our method, we employed an exact match metric to calculate DiffCnt in Algorithm 1, + +![](images/f5e16dddad378d196a44b5c71a53f0e5da6de487759b95f1368501e877d0d86b.jpg) +Figure 2. Results on merging LLaVA-v1.5-7B into Qwen2-VL-7B. The $\alpha$ with the best performance are the same as the $\alpha$ with the fewest response differences. + +which serves as our generation consistency indicator for model performance prediction. Given that exact match is a binary, rigorous evaluation metric, we explored an alternative, more flexible approach to measure generation consistency. Specifically, we computed the cosine similarity between sentence embeddings generated by all-MiniLM-L6-v2 [17], which was used to calculate DiffCnt. The analysis results are presented in Table 3. Although embeddings theoretically offer more fine-grained semantic representations, our results demonstrate that the embedding-based metric performs comparably to the exact match metric. Furthermore, our experiments confirm that sampling 100 instances achieves results nearly equivalent to the complete dataset. + +# 6.2. Merging with Large Performance Gap + +As discussed in Section 5, all model merging methods experience performance drop after the merging on two benchmarks, OCRBench and TextVQA. It shows that merging a model with significant lower performance into the base model will decrease the performance on the task. Conversely, in Table 5, the merging from Qwen2-VL-7B to LLaVA-OneVision-7B shows that merging a model with significant higher performance into the base model will not necessarily improve the model performance. And in this case, AdaMMS is the only model merging method that resists the performance drop after merging. In general, we observed that original models with similar performance tends to benefit from model merging, while original models with large performance gap do not. + +# 6.3. Asymmetry in the Parameter Space of Heterogeneous Models + +In Section 4.4, we discussed that merging with large $\alpha$ often results in collapsing language ability. To validate our choice of the subinterval [0, 0.6] in determining candidates of $\alpha$ , we demonstrate this phenomenon in Figure 3, which shows + +![](images/05f9ce43b5c8aa4c5cbfbf8916bed40f5f17258a1cb42e471f0457ab33329f82.jpg) +Figure 3. Model responses with the change of $\alpha$ in linear interpolation. Similar colors indicate similar responses. + +that the model generates consistently near the parameters of the base model with small $\alpha$ , and collapses gradually with larger $\alpha$ . We attribute the phenomenon to the asymmetry in the parameter space, as the two original models have unequal status that comes from the choice of base architecture. + +# 6.4. Selection of Granularity for $\alpha$ + +To validate our choice of the granularity in Section 4.4, we conducted additional experiments with various granularities of $\alpha$ candidates on n MME and OCRBench when merging LLaVA-OneVision-7B into Qwen2-VL-7B. As shown in Appendix G, the result shows that the difference of selected $\alpha$ and model performance do not change significantly with different granularities. This shows that our choice of granularity as 0.1 would result in comparable performance, with less computation cost. + +# 7. Conclusion + +In this work, we propose a novel model merging method AdaMMS to address the challenges in merging heterogeneous MLLMs. We first connect the parameters of different MLLMs through a mapping function, enabling merging operations. We then apply linear interpolation to the mapped model weights to adaptively optimize performance across tasks. To optimize the interpolation coefficient without labeled data, we introduce an unsupervised hyperparameter searching method based on our discovery in the parameter space: model performance can be estimated through the generation consistency. We demonstrate that 100 data samples are enough to search for near-optimal coefficients effectively. Extensive experimental results show that AdaMMS outperforms existing model merging methods for MLLMs and successfully addresses the challenges in merging heterogeneous MLLMs. We hope that our work mitigates the limitations of heterogeneous model merging methods and provides valuable insights for future research on unsupervised performance estimation and optimization. + +# Acknowledgment + +This work is supported by the National Key R&D Program of China (2022ZD0160502) and the National Natural Science Foundation of China (No. 62276152). + +# References + +[1] Chi Chen, Yiyang Du, Zheng Fang, Ziyue Wang, Fuwen Luo, Peng Li, Ming Yan, Ji Zhang, Fei Huang, Maosong Sun, and Yang Liu. Model composition for multimodal large language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), 2024. 1, 3 +[2] Lin Chen, Jinsong Li, Xiaoyi Dong, Pan Zhang, Conghui He, Jiaqi Wang, Feng Zhao, and Dahua Lin. 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MetaGPT: Merging large language models using model exclusive task arithmetic. arXiv preprint arXiv:2406.11385, 2024. 1, 3, 5 \ No newline at end of file diff --git a/adammsmodelmergingforheterogeneousmultimodallargelanguagemodelswithunsupervisedcoefficientoptimization/images.zip b/adammsmodelmergingforheterogeneousmultimodallargelanguagemodelswithunsupervisedcoefficientoptimization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8b729665284d644b9ba9e87ac49d1ff42e661593 --- /dev/null +++ b/adammsmodelmergingforheterogeneousmultimodallargelanguagemodelswithunsupervisedcoefficientoptimization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bb7a4db5cf9d26473d7899914162edcf907b0056648b10dd576b426742456321 +size 471940 diff --git a/adammsmodelmergingforheterogeneousmultimodallargelanguagemodelswithunsupervisedcoefficientoptimization/layout.json b/adammsmodelmergingforheterogeneousmultimodallargelanguagemodelswithunsupervisedcoefficientoptimization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..3159fb4e27717e8b125c34834fcde2442857572a --- /dev/null +++ b/adammsmodelmergingforheterogeneousmultimodallargelanguagemodelswithunsupervisedcoefficientoptimization/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:062edc6db52afd268712206c34a0aa0393ddf20c071b5dce138b778f5ad96b6d +size 384434 diff --git a/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_content_list.json b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1832f285e10547ec114284ee658c94955eeb7428 --- /dev/null +++ b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2f484073807e2df945caa6c211dff35b6d19d83d85dc61062e8551ed19bf989a +size 82280 diff --git a/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_model.json b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_model.json new file mode 100644 index 0000000000000000000000000000000000000000..645ea56858b8d040dc9cdedbb39e922e5ba91cfc --- /dev/null +++ b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bf220483b48725e14ac97f90065a6d8fbfda2aacca4f2aeae21e4fe3035d815e +size 104308 diff --git a/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_origin.pdf b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..356644d8f3ec3d9f9163a75acddc12d7165f2d97 --- /dev/null +++ b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/73638180-8aa5-4d61-9e73-03b5c7fd1d88_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c5f537380531483a394a884b816e6def92f74e4faabf0f26a499eaa5e06086ba +size 1891979 diff --git a/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/full.md b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2c52e39fb92626042fda9e441c50428ee63caa31 --- /dev/null +++ b/adaptcmvcrobustadaptiontoincrementalviewsincontinualmultiviewclustering/full.md @@ -0,0 +1,339 @@ +# AdaptCMVC: Robust Adaption to Incremental Views in Continual Multi-view Clustering + +Jing Wang $^{1}$ , Songhe Feng $^{1*}$ , Kristoffer Knutsen Wickstrøm $^{2}$ , Michael C. Kampffmeyer $^{2}$ + +1 School of Computer Science & Technology, Beijing Jiaotong University + +$^{2}$ Department of Physics and Technology, UiT The Arctic University of Norway + +{jing_w,shfeng}@bjtu.edu.cn,{kristoffer.k.wickstrom,michael.c.kampffmeyer}@uit.no + +# Abstract + +Most Multi-view Clustering approaches assume that all views are available for clustering. However, this assumption is often unrealistic as views are incrementally accumulated over time, leading to a need for continual multi-view clustering (CMVC) methods. Current approaches to CMVC leverage late fusion-based approaches, where a new model is typically learned individually for each view to obtain the corresponding partition matrix, and then used to update a consensus matrix via a moving average. These approaches are prone to view-specific noise and struggle to adapt to large gaps between different views. To address these shortcomings, we reconsider CMVC from the perspective of domain adaptation and propose AdaptCMVC, which learns how to incrementally accumulate knowledge of new views as they become available and prevents catastrophic forgetting. Specifically, a self-training framework is introduced to extend the model to new views, particularly designed to be robust to view-specific noise. Further, to combat catastrophic forgetting, a structure alignment mechanism is proposed to enable the model to explore the global group structure across multiple views. Experiments on several multi-view benchmarks demonstrate the effectiveness of our proposed method on the CMVC task. The code is available at: AdaptCMVC. + +# 1. Introduction + +Nowadays, more and more data originating from multiple views, or multiple modalities offer plentiful information for multi-view applications, such as cross-modal image retrieval [56], visual question answering [8], and multimodal 3D object detection [26]. As a cornerstone of multiview learning, Multi-View Clustering (MVC) aims to discover underlying groups of data by leveraging the complementary information from multiple views. Existing multiview clustering algorithms can be classified into four pop + +![](images/6154ed149ca440547546c837833eac95b61616b32f0884daaad3052d066b9f8e.jpg) +Figure 1. Graphical comparison between the existing CMVC paradigm and our proposed AdaptCMVC. + +![](images/61d0935c5e70a92eebb0a50b3758dde9f1b20160df6710746816e8854b642458.jpg) + +ular paradigms, including multi-view subspace clustering (MVSC) [43, 45, 50, 57, 62], multi-view graph clustering (MVGC) [9, 38, 51, 52], multiple kernel clustering (MKC) [22, 53], and deep multi-view clustering (DMVC) [20, 22, 40, 41]. + +Although the current multi-view clustering algorithms [59, 61] have achieved excellent performance, they normally focus on clustering static multi-view data [24], which is unrealistic in many real-life settings. In many practical scenarios, different views of data arise in a continuous, incremental manner, where the number of views is unfixed and only the data of the current session can be accessed. For instance, in a medical diagnostic scenario, due to limitations in a patient's physical condition or medical equipment availability, different types of multimodal data (such as MRI, CT, and X-ray) are often collected at separate stages throughout the examination process. Similarly, in federated learning, data from edge devices are used exclusively for local model training, helping to prevent potential data breaches. In these cases, when a new view arrives, existing MVC methods need access to all historical views of the data in order to reuse them with the new view in order to retrain the model. This leads to high time and space complexity and can violate data privacy regulations. Thus, these methods struggle when deployed to continual multi-view clustering. + +In this paper, motivated by the aforementioned scenario, we focus on a more flexible and practical setting. The setting is Continual Multi-view Clustering (CMVC), which was first proposed in [60]. There are two differences between MVC and CMVC: 1) In CMVC, the multiple views are presented in a sequential nature, creating a continuously evolving feature space. Unlike traditional MVC, the model can thus not access all data views simultaneously. 2) At each incremental session, data from previous views is no longer accessible. In addition to discovering information in the new view, it is thus of critical importance to also preserve information about past views. This results in the following three challenges that need to be addressed to improve the continual clustering performance: View Discrepancy: Multi-view data describes samples from distinct feature spaces, creating a significant gap between previous views and incoming views. This discrepancy makes it difficult for the model to adapt effectively to new views. Noise in Views: Not all views contribute positively to clustering, as some may contain noisy features. Adjusting the adaption process to minimize the impact of noise is a critical challenge. Catastrophic Forgetting [47]: The adaption process of the model does not rely on previous views data. This can lead to catastrophic forgetting, causing the model to lose important clustering structure from earlier views. + +CMVC is a recent and emerging research area with some notable works [58, 60, 63]. However, some, such as [60, 63], require reusing either the most recent or all historical view data to update a consensus memory. This approach is impractical in data privacy-sensitive scenarios, where the model can only access data from the current view. For instance, [60] reconstructs a consensus similarity matrix using both the new and previous views, and applies sparse, connected graph regularization to mitigate noise. On the other hand, to prevent forgetting knowledge of previous views, existing CMVC methods attempt to learn a knowledge library and update it with data from each new view. For example, [58] aims to maintain a consensus partition matrix and update it with the incoming partition matrix of the new view. As shown in Figure 1 (a), these methods train a distinct model for each new view, exploring current-view knowledge and integrating it through an average updating mechanism. However, these late fusion multi-view clustering frameworks struggle to adapt effectively to the unique shifts between different views because they learn the knowledge of multiple views individually and only fuse them for clustering. + +To address the aforementioned issues effectively, we propose a view adaption-based solution, named AdaptCMVC, which enables the model to successfully adapt to incremental views in the continual clustering setting, as shown in Figure 1 (b). Concretely, in the initial session, we utilize the first view data to train the model, establishing a foundational feature extraction model. In the incremental sessions, we + +propose to effectively adapt the base model to the current view data under a self-training framework. Firstly, to discover view-specific information, we use a weighted-average teacher model to create target features for the base model to align with. This is inspired by the success of prominent works in self-supervised learning [4, 5], which has shown that such teacher-student learning can produce representations of high quality. Secondly, to mitigate the impact of noisy samples in the current session, we lessen their influence on model updates and adjust their weights based on the distance from the samples to the clustering prototype obtained from the last session. + +Furthermore, in order to prevent forgetting previous views, we propose a structure alignment mechanism to enforce consistency between the current and previous view group structure. By implementing an adaption strategy that allows for the simultaneous learning of new views while preserving previous knowledge, AdaptCMVC facilitates CMVC with incremental views. Extensive experimental results demonstrate the effectiveness of AdaptCMVC in continual clustering. Our contributions are: + +- We focus on the more realistic setting of CMVC and introduce a new perspective that redefines the problem by taking inspiration from domain adaptation. It allows the model to continuously adapt to new views while preserving knowledge from previous views. +- We propose a self-training framework where a weight-averaged teacher model is able to yield more accurate targets for the student model, enabling it to explore specific information from the new views. +- A structure alignment learning mechanism is proposed to mine the consistent group structure across multiple views, effectively avoiding catastrophic forgetting. + +# 2. Related Work + +In this section, we briefly review related work on MVC, CMVC, and domain adaptation. + +# 2.1. Multi-view Clustering + +By utilizing the complementary information from multiple views, multi-view clustering is able to outperform single-view approaches. MVC methods can broadly be categorized into subspace-based, graph-based, multiple kernel-based, and deep learning-based multi-view clustering approaches. Subspace-based methods [2, 11, 27, 37] encode the multiview data into a common subspace and apply different regularization terms to divide the data points into different clusters. For the graph-based multi-view clustering methods [10, 19, 29, 49], they discover the view-specific structure information to construct multiple graphs and fuse them to obtain a consensus one, which can then be cut into groups. Multiple kernel-based multi-view clustering methods [21, 25, 48] adopt different kernel functions to map the nonlinear data + +into a high dimensional space where the data can be separated. More recently, with the widespread adoption of deep learning, many recent works introduce deep learning into multi-view clustering [18, 40, 41, 46]. Deep learning-based MVC methods employ view-specific encoders to extract multiple representations and leverage single-view or multi-view self-supervised tasks to model a consensus representation, which is used as the input of the clustering module [41]. + +# 2.2. Continual Multi-view Clustering + +In real world applications, multiple views are hard to collect all at once. Unlike traditional MVC methods, which assume that all views are available in advance, CMVC aims to address the case where views are incrementally added over time. This distinctive characteristic enables CMVC to employ a sequential encoder training paradigm, thereby relaxing the constraint on data availability, and addressing data privacy regulations, while also potentially being beneficial for resource constrained settings (i.e. memory constraints). Accordingly, CMVC requires learning knowledge from new views as well as utilizing historical information, continually clustering when provided with a stream of view data. + +In recent years, there have been some initial efforts [36, 42, 44, 58, 60, 63], to address the CMVC setting. Specifically, [36] propose a generalized lifelong spectral clustering method to incorporate the new clustering task, which employs a dual memory to store the clustering centers and manifold representations for continual clustering. The most recent and current state-of-the-art approach to CMVC, aptly named CMVC [58] ${}^{1}$ , creates a category library to learn and preserve the historical categories and uses the new view to update the consensus partition matrix. These models make a preliminary attempt at CMVC, which still faces several challenges. First, these methods use the new view directly to update the consensus part which neglects the noise contained in the new view. Second, by continuously updating the consensus part, the historical knowledge will to some extent be forgotten. + +In this paper, we reconsider the CMVC setting from the perspective of domain adaptation and propose the AdaptCMVC model to address these shortcomings. + +# 2.3. Domain Adaptation + +Domain adaptation [31, 31] is an important branch of transfer learning [30], which aims at improving the target performance with the knowledge learned from the source domain. Continual domain adaptation [7] considers the adaption problem for a continually changing target environment. Our work is inspired by [47], which utilizes a self-training framework to help the model adapt to the continually changed environ- + +ment. They stochastically restore part of the parameters to the source model to prevent catastrophic forgetting. + +Unlike [47], our model proposes a noise robust objective function to directly address the potential noise contained in the new view in the CMVC setting. Furthermore, we explore the view-consistent group structure information to store the knowledge learned from the previous views. It should further be noted that training is conducted fully unsupervised in the CMVC setting, while training is conducted in a supervised manner on the source domain in domain adaptation. + +# 3. Method + +# 3.1. Problem Definition + +For CMVC, we define a sequence of $V$ clustering sessions $\{S^0,S^1,\ldots ,S^V\}$ , each session is composed of $n$ unlabeled samples $\mathbf{X}^v\in \mathbb{R}^{n\times d}$ , where $d$ denotes the feature dimension. According to the CMVC setting, the feature space is continually changing and only $\mathbf{X}^v$ is accessible in the $v$ -th session. Therefore, when the system encounters new view data, it should continuously perform clustering, integrating the knowledge from the new view and previous views to improve the clustering performance. Consequently, the final clustering performance should be expected to surpass any single view or keep the same performance in case new views have little additional information. + +# 3.2. Methodology + +To address the CMVC task, our proposed AdaptCMVC takes a base model pre-trained on the first view and adapts it to the continually incremental views. To successfully adapt to the large gap between different views, a noise robust self-training framework is introduced to accumulate view-specific knowledge of new view data and avoid the impact of view-specific noise. In addition, to help preserve knowledge from prior views, we define a structure alignment learning mechanism to discover the global structure across all views by aligning the current view with the last. An overview of the proposed method is presented in Figure 2. + +Base Model. Existing works on continual multi-view clustering require a view-specific model for each view to explore specific semantic details within views. However, in our proposed AdaptCMVC method, we redefine the problem from the perspective of domain adaptation. It focuses on leveraging a base model pre-trained on the first session data to effectively adapt to subsequent sessions. Therefore a robust base model should be trained in the first session. To achieve this, we adopt a Variational Autoencoders (VAE) [15] model to transform $\mathbf{x}_i^v$ to its representation $\mathbf{z}_i^v$ and use it to generate the original samples. + +![](images/183ec1967f9cfcf2393ea0d6b38dc39e8323df56e4ea22b91c7d2e15743fbff8.jpg) +Figure 2. An overview of the proposed AdaptCMVC. (a) The AdaptCMVC model reconsiders the CMVC setting from the domain adaptation perspective, resulting in a unified model capable of adapting to different sessions of view data. (b) Our noise robust consistency loss is particularly designed to enable the model robust to view-specific noise. (c) Our structure alignment learning module explores the global group structure information to prevent forgetting previous views. + +![](images/82aa898ab3d1efcc772b33bd063674900c34996900cfdb0a67e86691194ee4ab.jpg) + +Concretely, to enable the model to be robust to noise, we use a masking strategy, randomly blurring pixels of the original image, which enables the model to learn a noise-robust representation. The mask version $\mathbf{x}_i^{v'}$ is treated as the input of encoder $E_{\phi}(\cdot)$ with parameters $\phi$ and the approximate posterior of representation $\mathbf{z}_i^v$ can be inferred as follows: + +$$ +q _ {\phi} (\mathbf {z} _ {i} ^ {v} | \mathbf {x} _ {i} ^ {v \prime}) = \mathcal {N} (\mu^ {v}, \sigma^ {v ^ {2}}) \tag {1} +$$ + +where $\mu^v$ and $\sigma^v$ are parameterized with neural networks, whose input is $\mathbf{x}_i^{v'}$ . + +Since the approximate posterior $q_{\phi}(\mathbf{z}_i^v |\mathbf{x}_i^{v'})$ is intractable to optimize, we leverage the reparameterization trick [16] to facilitate optimization: + +$$ +q _ {\phi} \left(\mathbf {z} _ {i} ^ {v} \mid \mathbf {x} _ {i} ^ {v \prime}\right) = \mathcal {N} \left(\mu^ {v}, \sigma^ {v 2}\right) = \mu^ {v} + \sigma^ {v} \epsilon \tag {2} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ + +In the generative process, the representation $\mathbf{z}_i^v$ is utilized to generate samples. The decoder $D_{\theta}(\cdot)$ with trainable parameters $\theta$ can be expressed as: + +$$ +\hat {\mathbf {x}} _ {i} ^ {v} = p _ {\theta} \left(\mathbf {x} _ {i} ^ {v} \mid \mathbf {z} _ {i} ^ {v}\right) \tag {3} +$$ + +To enable the VAE to explore the knowledge of a particular view $v$ , the objective will maximize the likelihood function of the observed data. The base model can be trained by the evidence lower bound (ELBO) [1]: + +$$ +\begin{array}{l} \mathcal {L} _ {r} = \mathbb {E} _ {q _ {\phi} \left(\mathbf {z} _ {i} ^ {v} \mid \mathbf {x} _ {i} ^ {v ^ {\prime}}\right)} [ \log p _ {\theta} \left(\mathbf {x} _ {i} ^ {v} \mid \mathbf {z} _ {i} ^ {v}\right) ] \tag {4} \\ - K L \left(q _ {\phi} \left(\mathbf {z} _ {i} ^ {v} \mid \mathbf {x} _ {i} ^ {v ^ {\prime}}\right) \| p (\mathbf {z} _ {i} ^ {v})\right) \\ \end{array} +$$ + +where $KL(\cdot)$ denotes the Kullback-Leibler divergence. $p(\mathbf{z}_i^v)$ is the prior of the sample representation, which follows a standard Gaussian distribution, i.e., $p(\mathbf{z}_i^v)\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ + +Noise Robust Self-training Framework. In the CMVC setting, the view is incremental over time and the base model needs to successfully adapt to the new view data. While the base model typically works well on the first view, the quality of the extracted features drops significantly for continually changing view data because of the large gap between different views. To deal with the view discrepancy, a self-training framework is introduced, which follows a student-teacher model. Inspired by [33, 39], a weight-average teacher model is introduced to provide more robust features. + +Under a view incremental environment, the feature space of new sessions changes dramatically, thus we use augmented samples as the input of the teacher model to improve robustness. At time-step $t = 0$ , both the student and teacher models are initialized to be the same as the base model. At time step $t > 0$ , a consistency cost is introduced to supervise the update of the student model as below: + +$$ +\mathcal {L} _ {c} \left(\mathbf {z} _ {i} ^ {v}\right) = - \sum_ {d} p \left(\mathbf {z} _ {i d} ^ {v}\right) \log p \left(\mathbf {z} _ {i d} ^ {v ^ {\prime}}\right) \tag {5} +$$ + +where the $p(\mathbf{z}_{id}^{v})$ is the distribution of the features extracted by the student model, and $p(\mathbf{z}_{id}^{v'})$ is the distribution of the features extracted by the teacher model, which is obtained by a softmax function. + +To further facilitate a noise robust model, we need to consider that some views contain noise and thus might not be positive and might even be detrimental to the model adaptation. To ensure good CMVC performance, we thus need to mitigate the impact of the noise depending on the knowledge learned from the last views. According to the representation extracted from the last view, we obtain class prototypes $\mathbf{B}^{v - 1}\in \mathcal{R}^{k\times d}$ and a soft cluster assignments matrix $\mathbf{H}^{v - 1}\in \{0,1\}^{n\times k}$ by applying the K-means clustering [28], and then leverage these to adjust the weight of the consistency loss. The final noise-robust consistency loss that is applied to deal with noisy samples by reformulating Eq. 5 is: + +$$ +\mathcal {L} _ {c} \left(\mathbf {z} _ {i} ^ {v}\right) = - \frac {1}{\left(l \left(i , b _ {i} ^ {v - 1}\right)\right) ^ {2}} \sum_ {d} p \left(\mathbf {z} _ {i d} ^ {v}\right) \log p \left(\mathbf {z} _ {i d} ^ {v \prime}\right) \tag {6} +$$ + +where $l(i, b_i^{v-1}) = \|\mathbf{z}_i^v - \mathbf{h}_i^{v-1}\mathbf{B}^{v-1}\|^2$ is the distance between sample $i$ and its corresponding class prototype, and $\mathbf{h}_i^{v-1}$ is the $k$ -dimensional one-hot vector of cluster assignments. + +The intuition behind this approach is that we should use more reliable samples - those closer to the class prototypes - to help the model adapt, rather than relying on samples that are far from the prototypes. We demonstrate the effectiveness of this loss in Sec. 7.3 of the supplementary material. + +After updating the student model using Equation 6, the parameters $\psi_t' = \{\theta, \phi\}$ of the teacher model at step $t$ are defined by the exponential moving average (EMA) of successive $\psi_t$ : + +$$ +\psi_ {t} ^ {\prime} = \alpha \psi_ {t - 1} ^ {\prime} + (1 - \alpha) \psi_ {t} \tag {7} +$$ + +where $\alpha$ is a smoothing factor. + +By introducing the weight-averaged teacher model, our model is able to extract more accurate features of the new view. Meanwhile, the features learned by the teacher model contain information from past models, which is beneficial to prevent forgetting prior knowledge and to generalize the new view stably. Finally, the noise-robust consistency loss weakens the impact of noisy samples to reduce the error accumulation successfully. + +Structure Alignment Learning. Although the noise robust self-training framework can successfully adapt the base model to new view data, the continual adaption process over many views will cause forgetting, especially when the model suffers a strong view shift. + +To address the catastrophic forgetting problem, we propose a structure alignment module, which models the global structure across all views to enable the model to encode the + +view-consistent information for long time adaption. Specifically, to favorably enable the model to preserve the knowledge from previous views, we adopt an MSE loss to encourage that the samples keep a consistent structure with the previous session: + +$$ +\mathcal {L} _ {s} = \frac {1}{n ^ {2}} \sum_ {i = 1} ^ {n} \sum_ {j = 1} ^ {n} \left\| \mathbf {s} _ {i j} ^ {v - 1} - \mathbf {c} _ {i j} ^ {v} \right\| \tag {8} +$$ + +where $c_{ij}^{v} = \frac{<\mathbf{z}_{i}^{v},\mathbf{z}_{j}^{v}>}{\|\mathbf{z}_{i}^{v}\|\|\mathbf{z}_{j}^{v}\|}$ is the similarity between two features, which is measured by the cosine similarity and $\mathbf{s}_{ij}^{v - 1}$ denotes the specific element of the last view similarity matrix $\mathbf{S}^{v - 1}\in \mathcal{R}^{n\times n}$ . At the beginning of session $v$ , $\mathbf{S}^{v - 1}$ is initialized by the soft cluster assignments matrix $\mathbf{H}^{v - 1}$ obtained in the last view: + +$$ +\mathbf {s} _ {i j} ^ {v - 1} = \left\{ \begin{array}{l l} 0 & \mathbf {h} _ {i k} ^ {v - 1} \neq \mathbf {h} _ {j k} ^ {v - 1} \\ 1 & \mathbf {h} _ {i k} ^ {v - 1} = \mathbf {h} _ {j k} ^ {v - 1} \end{array} \right. \tag {9} +$$ + +In subsequent epochs, $\mathbf{S}^{v - 1}$ is updated by the current view similarity matrix to capture the joint structure: + +$$ +\mathbf {S} _ {t} ^ {v - 1} = \beta \mathbf {S} _ {t - 1} ^ {v - 1} + (1 - \beta) \mathbf {C} _ {t} ^ {v} \tag {10} +$$ + +where $\beta$ is a smoothing factor. + +The structure alignment learning module uses the similarity matrix obtained by the last session rather than accessing the last view data, maintaining a global structure across multiple views to prevent forgetting knowledge of prior views while avoiding access to data. The whole learning process of AdaptCMVC is summarized in Algorithm 1. + +# Algorithm 1 The proposed AdaptCMVC + +Initialization: A base model $g_{\psi_0}(\cdot)$ , student model $f_{\psi_0}(\cdot)$ and teacher model $f_{\psi_0}'(\cdot)$ initialized from $g_{\psi_0}(\cdot)$ . +Input: For each session $v$ , the similarity matrix $\mathbf{S}^{v-1}$ , the cluster assignments matrix $\mathbf{H}^{v-1}$ , the cluster prototype $\mathbf{B}^{v-1}$ from the last session and the current view data $\mathbf{X}^v$ . +1. for $\mathbf{t} = \mathbf{1}$ to $T$ +2. Augment $\mathbf{X}^v$ and get the average-weight representations from the teacher model $f_{\psi_v}'(\cdot)$ . +3. Updating the student $f_{\psi_v}^t (\cdot)$ by noise robust consistency loss in Equation 6, structure alignment loss in Equation 8, and reconstruction loss in Equation 4. +4. Updating teacher $f_{\psi_v}^{\prime}(\cdot)$ by moving average in Equation 7. +5. end for +Output: The updated student $f_{\psi_v}(\cdot)$ model, the teacher model $f_{\psi_v}'(\cdot)$ , the similarity matrix $\mathbf{S}^v$ , the cluster assignments matrix $\mathbf{H}^v$ , the cluster prototype $\mathbf{B}^v$ . + +
MethodE-MNISTE-FMNISTOffice-31COIL-100
ACCNMIACCNMIACCNMIACCNMI
Joint-VAE42.81±0.0335.45±0.0537.22±0.5826.94±0.3125.19±0.6029.30±0.3455.85±1.4977.53±0.61
β-VAE39.69±0.7224.97±0.1839.76±0.0238.37±0.0511.89±0.4413.53±0.0924.02±0.2340.96±0.26
MFLVC65.98±0.0659.08±0.0448.48±0.1546.62±0.1232.09±0.2129.39±0.0735.05±1.1473.19±1.16
CONAN50.22±0.0244.42±0.0148.70±0.1141.41±0.0113.51±0.2417.11±0.2254.04±1.3774.73±0.47
EAMC49.17±0.3246.28±0.3445.44±0.4242.76±1.0333.16±0.1930.08±0.1360.31±0.8473.13±0.91
GCFAgg67.10±0.8861.34±0.6243.09±0.0740.25±0.2131.17±0.2128.54±0.3145.71±1.3570.22±1.82
Multi-VAE60.74±0.2359.03±0.1853.16±0.1454.47±0.0631.27±0.2727.84±0.3948.87±0.0345.29±0.15
CMVC57.30±0.0047.54±0.0046.24±0.0045.08±0.0016.02±0.0018.7±0.0036.41±0.0061.98±0.00
CAC57.28±0.0048.18±0.0046.42±0.0045.49±0.0016.20±0.0018.98±0.0033.91±0.0059.37±0.00
AdaptCMVC67.10±0.06* (+9.8)54.14±0.03 (+5.96)54.13±0.02 (+7.71)46.98±0.02 (+1.49)22.81±0.03 (+6.61)33.39±0.13 (+14.41)57.12±0.01 (+20.71)79.29±0.02* (+17.31)
+ +Table 1. The clustering performance comparisons on E-MNIST, E-FMNIST, Office-31, and COIL-100 datasets. The best are highlighted in bold. The differences between our model and the best CMVC baseline model are shown in green. In addition, we provide results for traditional MVC approaches that use all views simultaneously. The * represents results where our proposed AdaptCMVC also outperforms the traditional MVC approaches despite not having access to all views simultaneously. Baseline results are taken from [13]. + +# 4. Experiment + +# 4.1. Setup + +Datasets. We adopt six common multi-view datasets [13, 41] to evaluate our proposed model and compare to the current state-of-the-art approaches. These datasets are: (a) E-MNIST [23], a widely used image dataset for multi-view clustering, which is based on the MNIST dataset [17] and consists of 70,000 handwritten digits from 0 to 9. Each digit is described by two views, the original MNIST version and an edge-detection version. (b) E-FMNIST is a fashion dataset with 10 classes corresponding to different clothing items. The first view consists of 70,000 images with $32 \times 32$ pixels, while the second view is an edge-detected version constructed following [13]. (c) COIL-100 [35] and (d) COIL-20 [35] contain RGB and grayscale images of 100 and 20 objects, respectively, captured from various angles. Three distinct views were generated following [13]. (e) Office-31 [34] is an office setting dataset that includes 2253 items from 31 categories, which is constructed into a three-view dataset by applying ColorJitter following [13]. (f) PatchedMNIST [41] is a subset of MNIST comprised of 3 classes and designed to evaluate the performance for cases with a large number of views. In [41], they divide the original images into $127 \times 7$ non-overlapping patches, where the 6 center patches containing the most information were used in our experiments. + +Baselines. Our proposed method AdaptCMVC is compared with nine state-of-the-art methods, including three categories of baseline methods: (i) single view clustering methods: Joint-VAE [3] and $\beta$ -VAE [6]; (ii) Deep multi-view clustering methods: Multi-level Feature Learning for contrastive multi-View Clustering (MFLVC) [55], End-to-end Adversarial attention network for Multi-modal Clustering (EAMC) [64], CONtrAstive fusion Networks for multi-view + +clustering (CONAN) [12], Global and Cross-view Feature Aregation for multi-view clustering (GCFAgg) [57], and learning disentangled view-common and view-peculiar visual representations for multi-view clustering (Multi-VAE) [54]; (iii) Continual multi-view clustering methods: Continual Multi-View Clustering (CMVC) [42] and Continual Action Clustering with incremental views (CAC) [58]. We report the average values and variance over 10 training runs. For the shallow MVC methods, we treat the features extracted by our backbone as the input data to ensure fair comparisons. Furthermore, for the single-view clustering methods, we report the results for the best performing view as the evaluation result. For deep methods that were not designed to deal with image datasets, we replace the backbone with ours. + +Implementation Details. Our proposed method is implemented in PyTorch [32]. We train the model for 50 epochs in each session using the Adam [14] optimizer with a batch size of 256 and the learning rate of $1 \times 10^{-4}$ . We report the results from the epoch resulting in the lowest value of the unsupervised training loss $\mathcal{L}_c + \mathcal{L}_s + \mathcal{L}_r$ . The encoder and decoder are built using convolutional networks as described by [13]. The decoder has a symmetric structure. For the random augmentations, we follow [47] and employ random horizontal flipping, color jitter, Gaussian blur, and the addition of Gaussian noise. Additional implementation details are provided in the supplementary material. + +Evaluation Metrics. We employ two widely used metrics to evaluate our model, namely Accuracy (ACC) and the Normalized Mutual Information (NMI). For completeness, we provide the definitions in the supplementary material. + +# 4.2. Comparison Results and Analysis + +In this section, we compare our proposed AdaptCMVC with nine baselines on six datasets. The baselines include single- + +
MethodCOIL-20PatchedMNIST
ACCNMIACCNMI
Joint-VAE61.98±2.6074.14±0.8275.51±0.0552.58±0.11
β-VAE35.80±0.7144.67±0.8661.06±0.0741.86±0.10
MFLVC36.98±20.767.16±1.9977.28±0.0544.84±0.04
CONAN55.94±0.8863.98±0.4676.89±0.0647.34±0.08
EAMC58.19±1.9375.13±1.21
GCFAgg55.79±1.6675.08±1.3883.20±0.0254.40±0.02
Multi-VAE65.77±1.0478.22±1.0359.38±0.0627.37±0.05
CMVC68.15±0.0075.62±0.0071.03±0.0040.70±0.00
CAC68.50±0.0075.43±0.0069.89±0.0039.60±0.00
AdaptCMVC64.32±0.1567.72±0.2384.33±0.03*55.87±0.02*
(-4.18)(-7.90)(+13.30)(+15.17)
+ +view clustering methods, multi-view clustering methods, and continual multi-view clustering methods. + +Table 1 and 2 show the results of our proposed AdaptCMVC and nine baselines across all datasets. Based on these results, the following observations can be made: + +(i) Under the continual multi-view clustering setting, compared with other state-of-the-art CMVC baselines (CMVC and CAC), AdaptCMVC achieves superior performance in most cases, particularly in the PatchedMNIST dataset which has the largest number of views. The results indicate that the adaption strategy introduced by our model leads to a significant improvement compared to previous CMVC methods, illustrating that AdaptCMVC can successfully deal with the incremental view setting and maintain the clustering performance. +(ii) Compared with other traditional MVC baselines, despite only having access to the views in sequential order, our AdaptCMVC demonstrates superior performance over the majority of baselines. For the few that it does not outperform, the difference in performance remains marginal. The results demonstrate that our method can accumulate knowledge from new incremental views and explore the view-consistency information even if the previous views are inaccessible. This highlights the effectiveness of AdaptCMVC. + +Table 3 displays the performance and ranking of all methods averaged over all datasets for both accuracy and NMI. To compute the rank, we order the performance (ACC or NMI) of all methods on each dataset from best to worst and use the position as the rank, such that the best performing model has rank 1 and the least performing one rank 10. This summary shows that single view clustering methods result in poor performance. Furthermore, the performance of other CMVC methods, i.e. CAC and CMVC, are lower than traditional multi-view clustering methods, sometimes giving a comparable performance with them. AdaptCMVC, instead, achieves the best performance compared with all baselines. + +Table 2. The clustering performance comparisons on COIL-20 and PatchedMNIST datasets. Same formatting as in Table 1. ${}^{\prime \prime }{}_{4}^{* * }$ means that training resulted in NaN loss. + +
MethodsAvg ACCAvg RankAvg NMIAvg Rank
Joint-VAE49.76649.325.83
β-VAE35.379.334.069
MFLVC48.71552.634.33
CONAN49.895.348.176.67
EAMC49.255.544.565.5
GCFAgg54.344.354.974.33
Multi-VAE53.203.848.704.33
CMVC49.194.848.275.67
CAC48.704.747.845.83
AdaptCMVC58.302.356.233.5
+ +Table 3. The comparison of Accuracy and NMI averaged over all datasets. Additionally, we provide the average rank both based on ACC and NMI. Results show that our proposed method results in better performance across all metrics. + +![](images/4f93bff31624fa3727bd3d6e6dc35df91cec0287e380a154a7bdac1a610f0c30.jpg) +Figure 3. ACC of AdaptCMVC, CAC, CMVC, and GCFAgg as the number of views increases on PatchedMNIST. SC represents single-view clustering. Unlike the continual multi-view clustering methods, GCFAgg assumes access to all the views simultaneously. + +# 4.3. Result of Adaption Process and Analysis + +In Figure 3, we show the clustering performance of AdaptCMVC and the other two CMVC methods as the number of views increases on the PatchedMNIST dataset. We observe that the performance of our AdaptCMVC steadily improves as the number of views increases. Compared to the other two CMVC approaches, i.e., CAC and CMVC, the performance of AdaptCMVC improves more quickly and CAC and CMVC performance stagnates as the number of views increases. This demonstrates that AdaptCMVC is able to effectively leverage additional views by continually accumulating knowledge in the presence of incremental views, while also being less effected by the catastrophic forgetting problem that hampers other CMVC methods as the number of views increases. Ultimately, AdaptCMVC can reach or even exceed the performance of the top traditional MVCs baseline, GCFAgg. + +Interestingly, we observe that while AdaptCMVC leverages additional views most efficiently from current CMVC approaches, single high-informative views do not necessarily lead to immediate improvements as indicated by the introduction of view 4 when compared to the single-view clustering performance SC. + +![](images/a59b7ece775eb49b13c1c98a0ddda33c694cbb94e2ab190cefc8f271af996d23.jpg) +Figure 4. Ablation study on the different components. + +![](images/ba8f58c67df2f23b3e695650a49f0d288cc5d5bca35a957339cdfea71666c4e5.jpg) + +![](images/8901afe1164733f69317ecf7202786cad05eb057711c5ca7ca79c38fd7cb7e4a.jpg) + +![](images/aa3c706ed4867de65e70446bfa8f6b00e67bd6ec2639a0c73227b0f3219fdcb9.jpg) + +
E-MNISTCACCMVCAdaptCMVC
View1 to View257.3057.2866.98
View2 to View157.4457.2967.08
SCView1View2
ACC62.1054.09
+ +# 4.4. Impact of View Order + +In the CMVC setting, the model is exposed to different views in a sequence. Thus, in this section, we observe the impact of the view appearance order on the E-MNIST. For the E-MNIST dataset, there are two data views and we present the results for both orders in Table 4. We can observe that our AdaptCMVC always outperforms other CMVC methods with different kinds of view orders and that results are robust. More experiments about the impact of view order are given in the supplementary materials. + +# 4.5. Catastrophic Forgetting Analysis + +In CMVC, the model can only access the data from the current view during each incremental session. In this analysis, we evaluate whether the final model can retain the knowledge from previous views. This is done by evaluating the final model, which has been continuously trained on all views, to cluster the data from individual views. + +From the results in Table 5, we see that the final model achieves good performance on most of the views. Further, when compared to a "Base Model" that is only trained on the corresponding available view, we observe that performance of the final model is either on-par or better than considering the single view, demonstrating the ability of AdaptCMVC to preserve the knowledge of prior views. + +# 4.6. Ablation Study + +We further perform an ablation study to evaluate the effectiveness of the proposed components of AdaptCMVC. Specifically, we train AdaptCMVC with and without the proposed noise robust consistency loss and structure alignment mechanism, on the E-MNIST, Office-31, COIL-100, and COIL-20 datasets. When we remove the noise robust + +Table 4. The view order impact of E-MNIST dataset on CAC, CMVC, and AdaptCMVC.SC presents the accuracy of individually using single view clustering. + +
PatchedMNISTView1View2View3
Base Model0.63480.83710.6141
Final Model-0.7568-0.7962-0.5889
(+12.2)(-4.09)(-2.52)
PatchedMNISTView4View5View6
Base Model0.65010.58260.6228
Final Model-0.6429-0.7843-0.8433
(-0.72)(20.14)(22.05)
+ +Table 5. Catastrophic forgetting analysis on the PatchedMNIST dataset. The result of the final model represents the evaluation of the final model on the previous view data. The base model is trained by only the corresponding view data. The differences between the two models are highlighted in green. + +consistency loss, we utilize the reconstruction loss $\mathcal{L}_r$ directly and use the structure alignment loss $\mathcal{L}_s$ to train the student model. Results in Figure 4 demonstrate that the full AdaptCMVC model always outperforms the ablated models, which clearly demonstrates that both the noise robust consistency loss and structure alignment mechanism have positive effects on continual clustering. In particular, we observe that the effect of the losses differs across datasets, meaning that for some datasets noise robustness is more important than structure alignment and vice versa. + +# 5. Conclusion + +Our work focuses on the recent and emerging research area of CMVC, which aims at continually clustering data with incremental views. We propose an AdaptCMVC model to reconsider the CMVC setting from the domain adaptation perspective, which is for the first time introduced to CMVC. A self-training framework is proposed to adapt the base model to new views, which is trained via a noise robust consistency loss to utilize the view-specific information safely. Additionally, we introduce a structure alignment mechanism to preserve group structure across all views, mitigating knowledge forgetting from previous views. Extensive experiments demonstrate the superiority and robustness of our method over state-of-the-art CMVC methods. + +# Acknowledgments + +This work was supported by the Fundamental Research Funds for the Central Universities (2024YJS194), the Beijing Natural Science Foundation under Grant 4242046, and the Research Council of Norway (Grant 309439 and 315029). + +# References + +[1] David M. Blei, Alp Kucukelbir, and Jon D. McAuliffe. Variational inference: A review for statisticians. CoRR, 2016. 4 +[2] Xiaochun Cao, Changqing Zhang, Huazhu Fu, Si Liu, and Hua Zhang. Diversity-induced multi-view subspace clustering. In CVPR, pages 586-594, 2015. 2 +[3] Emilien Dupont. Learning disentangled joint continuous and discrete representations. In NeurIPS, pages 708-718, 2018. 6 +[4] Jean-Bastien Grill, Florian Strub, Florent Altché, Corentin Tallec, Pierre H. 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While existing methods involve a trade-off between inference time and accuracy, ACMap consolidates task-specific adapters into a single adapter, thus achieving constant inference time across tasks without sacrificing accuracy. The framework employs adapter merging to build a shared subspace that aligns task representations and mitigates forgetting, while centroid prototype mapping maintains high accuracy by consistently adapting representations within the shared subspace. To further improve scalability, an early stopping strategy limits adapter merging as tasks increase. Extensive experiments on five benchmark datasets demonstrate that ACMap matches state-of-the-art accuracy while maintaining inference time comparable to the fastest existing methods. The code is available at https://github.com/tf63/ACMap. + +# 1. Introduction + +In real-world applications, data often arrives sequentially, which requires continual learning [44] to adapt to evolving data distributions. Class incremental learning (CIL) [36] is a branch of continual learning designed for scenarios where tasks with new classes appear sequentially. A primary challenge in CIL is catastrophic forgetting [10]—the difficulty of learning new tasks while preserving knowledge from previous ones. Traditional CIL methods mitigate catastrophic forgetting by retaining representative data (exemplars) from previous tasks [3, 29, 38] or by dynamically adjusting network structures [48, 54, 57]. However, privacy concerns [39] often limit the use of exemplars. This limitation highlights the need for exemplar-free methods in practical applications. + +In contrast to traditional approaches, recent CIL meth- + +![](images/01f0f4b14b538a87e2545baddfe13bf8826b26a9ae533aaa9955cb0b659683f0.jpg) +Figure 1. Comparison of the final top-1 accuracy and inference time for task 40 of ImageNet-R in class-incremental learning. The comparison includes L2P [50], DualPrompt [49], CODA-Prompt [41], SimpleCIL [61], APER [61], EASE [59], and our method. All methods use the same backbone (ViT-B/16). Our method performs well in terms of both inference time and accuracy by consolidating task-specific adapters into a single adapter. + +ods [58] using pre-trained models have attracted attention. These methods leverage the strong generalization of pretrained models to mitigate catastrophic forgetting. Typically, these methods incorporate parameter-efficient modules for task-specific training on each CIL task, such as prompts [21] or adapters [33]. Although effective for domain adaptation, task-specific classifiers often hinder scalability at inference. Figure 1 compares the final top-1 accuracy and inference time on task 40 of ImageNet-R for these methods. The results demonstrate a trade-off between accuracy and inference time. This trade-off highlights the challenge of achieving both high accuracy and scalability. + +To address the dual challenges of catastrophic forgetting and scalability in CIL, we propose Adapter Merging with Centroid Prototype Mapping (ACMap), a framework that consolidates task-specific adapters into a single adapter. ACMap enables scalability by maintaining con + +stant inference time, without sacrificing accuracy. Furthermore, ACMap's exemplar-free design addresses privacy concerns commonly associated with traditional exemplar-based methods. + +ACMap consists of two components: adapter merging and centroid prototype mapping. Adapter merging incrementally combines task-specific adapters into a shared subspace by averaging their weights. This shared subspace mitigates catastrophic forgetting by aligning tasks within the parameter space. While simple weight averaging alone may not ensure optimal performance, ACMap enhances alignment by initializing each adapter from a common starting weight. This initialization promotes consistent training paths across tasks, helping form a low-loss basin in the parameter space. Centroid prototype mapping further supports ACMap's effectiveness by preserving previously learned representations through consistent adaptation across the shared subspace. To further improve scalability, early stopping limits adapter merging, thereby reducing training costs. Evaluations on five benchmark datasets demonstrate that ACMap simultaneously achieves state-of-the-art accuracy and efficient inference. Specifically, on task 40 of ImageNet-R, ACMap improves final accuracy by more than $16\%$ compared to the fastest existing method with similar inference speed, while achieving a 39-fold speedup over the state-of-the-art method with comparable accuracy (see Figure 1). + +In summary, our contributions are as follows: + +1. We propose ACMap, a continual learning framework that consolidates task-specific adapters into a single shared subspace without storing previous data samples, effectively mitigating catastrophic forgetting. +2. To preserve previously learned representations, we incorporate centroid prototype mapping, ensuring consistency across tasks through adaptive subspace alignment. +3. Extensive experiments on five benchmark datasets demonstrate that ACMap achieves performance comparable to the state-of-the-art in both speed and accuracy, validating its effectiveness and scalability for real-world applications. + +# 2. Related Work + +This section discusses traditional class-incremental learning methods and recent approaches with pre-trained models. + +Class-Incremental Learning (CIL): Class-incremental learning (CIL) [60] is a learning paradigm in which a model incrementally learns new class information without forgetting previously learned classes. A major challenge in CIL is catastrophic forgetting [10, 22], where learning new classes overwrites previously acquired knowledge. This often results in significant performance degradation on earlier tasks. Prior work addresses catastrophic + +forgetting via three main approaches [60]. The first approach [3, 4, 28, 29, 32, 38, 45] selects and retains representative data (exemplars) from previously learned classes. The second approach [2, 9, 34, 48, 54, 57] dynamically modifies the model architecture to accommodate new class information. The third approach [6, 8, 18, 26, 36, 40] leverages knowledge distillation [16] to transfer knowledge from previously learned classes. However, even with these methods, catastrophic forgetting still leads to significant performance degradation. Additionally, many of these approaches rely on the use of exemplars, which can pose challenges related to privacy or storage constraints [60]. Therefore, unresolved issues remain for real-world applications. + +CIL with Pre-Trained Models: Recently, there has been growing interest in utilizing large pre-trained models for CIL [12, 58]. In these studies, parameter-efficient modules [13] are commonly employed to learn new tasks while preserving the strong generalization capabilities of the pretrained model. Two primary approaches have emerged: (i) using learnable parameters (prompts) [21] concatenated to input vectors in pre-trained models, and (ii) incorporating adapter modules (e.g., LoRA [17]) into pre-trained models. + +(i) Prompt-based Approaches: The first approach focuses on learning prompts for each task using visual prompt tuning (VPT) [21]. VPT introduces learnable prompts into the input of a frozen pre-trained model, tuning only the prompts. L2P [50] is one such method that employs VPT, retrieving instance-specific prompts from a learned prompt pool through key-query matching. DualPrompt [49] utilizes both task-agnostic and task-specific prompts, while CODA-Prompt [41] retrieves prompts from a prompt pool using an attention-based weighted combination. These exemplar-free methods outperform those without pre-trained models. +(ii) Adapter-based Approaches: The second approach uses parameter-efficient adapter modules, such as LoRA. SimpleCIL [61] is a foundational method that constructs a cosine classifier [11] from the average of class-specific feature vectors (prototype) [42] extracted from a pretrained model using validation data. Despite its simplicity, SimpleCIL performs comparably to VPT-based methods. APER [61] builds on SimpleCIL by using a pre-trained model with an adapter trained on the first task. EASE [59] achieves state-of-the-art performance by using task-specific adapters to extract prototypes for each task and constructing a cosine classifier from the concatenated prototypes. In an exemplar-free setting, where prototypes from previous classes cannot be extracted, EASE compensates using cosine similarity-based mapping. While APER has limited domain adaptation capabilities due to training an adapter only for the first task, EASE shows high adaptability by training adapters for all tasks. However, EASE incurs higher inference costs as the number of tasks grows, since feature vectors are extracted using each adapter individu + +ally. To address this scalability issue, our method merges multiple adapters into a single one. + +CIL with model merging: Several recent methods have explored model merging in CIL. iTAML [35] and TKIL [52] adopt merging strategies, but follow exemplar-based CIL, unlike ACMap's exemplar-free design. The assumptions and challenges in exemplar-based and exemplar-free settings differ considerably. In particular, exemplar-free methods like ACMap must overcome the absence of memory replay. RAPF [19] and ACMap both rely on adapter merging but take different approaches. While RAPF employs a computationally intensive SVD-based merging method, ACMap uses simple averaging, making it more lightweight. Moreover, RAPF leverages CLIP's text embeddings to enhance feature alignment, whereas ACMap is a vision-only method, better suited for scenarios without multi-modal supervision. Although both rely on merging, effective feature alignment remains crucial to strong performance. + +# 3. Preliminaries + +This section introduces the problem formulation of CIL and provides the background on CIL approaches with pretrained models. + +# 3.1. Problem Setting + +Class-Incremental Learning: Class-incremental learning is a learning paradigm where a model is required to sequentially learn a series of $T$ task datasets, $\mathcal{D}_1,\ldots ,\mathcal{D}_T$ , while retaining knowledge of previously learned tasks. Each dataset $\mathcal{D}_t = \{(x_t,y_t)\}$ consists of input data $\pmb {x}_t\in \mathcal{X}$ and corresponding class labels $y_{t}\in \mathcal{V}_{t}$ . For any two distinct tasks $t$ and $t^\prime$ , the class sets are disjoint, i.e., $\mathcal{V}_t\cap \mathcal{V}_{t'} = \emptyset$ . The objective in the $t$ -th task is to learn a model $f_{\theta}:\mathcal{X}\to \mathcal{Y}_t$ , parameterized by $\pmb{\theta}$ , that accurately maps inputs to their class labels. During testing on $t$ -th task, the model is evaluated on the cumulative test dataset $\mathcal{T}_1\cup \dots \cup \mathcal{T}_t$ , where $\mathcal{T}_i$ is the test dataset for the $i$ -th task. + +Exemplar and Exemplar-Free CIL: Many traditional CIL approaches retain a subset of representative data from previous tasks, known as an exemplar set. This set for the $t$ -th task is denoted $\mathcal{E}_t = \{(x^{\mathrm{e}},y^{\mathrm{e}})\}$ . In exemplar-based CIL, the training dataset for $f_{\theta}$ includes $\mathcal{D}_t$ and exemplars from previous tasks, combined as $\mathcal{D}_t \cup \mathcal{E}_1 \cup \dots \cup \mathcal{E}_t$ . However, privacy concerns and other constraints often limit the use of exemplars. In exemplar-free settings, $f_{\theta}$ is trained exclusively on the current task dataset $\mathcal{D}_t$ . We evaluate our approach under exemplar-free conditions for broader applicability in privacy-sensitive scenarios. + +# 3.2. Pre-Trained Models for CIL + +Following previous studies [59, 61], we utilize a pre-trained Vision Transformer (ViT) [7, 46] to initialize $f$ . The model is decomposed into a linear classifier $\mathbf{W} \in \mathbb{R}^{d \times |\mathcal{V}_t|}$ and a feature embedding function $\phi : \mathbb{R}^D \to \mathbb{R}^d$ , where $D$ is the dimension of the input vector and $d$ is the embedding dimension. The function $\phi$ denotes the final [CLS] token embedding in ViT, which represents the global image representation. For an input $\mathbf{x} \in \mathbb{R}^D$ , the model output is given by $f(\mathbf{x}) = \mathbf{W}^T\phi (\mathbf{x})$ . + +Adapter-based CIL: Trainable parameter-efficient adapter modules are often employed when applying a pre-trained model to a task. The adapter has a bottleneck structure, consisting of a down-projection layer $\mathbf{W}_{\mathrm{down}} \in \mathbb{R}^{d \times r}$ and an up-projection layer $\mathbf{W}_{\mathrm{up}} \in \mathbb{R}^{r \times d}$ , where $r$ is the bottleneck dimension and satisfies $r \ll d$ . To introduce non-linearity, a ReLU layer is positioned between the projection layers. The adapter is added to the MLP layer via a residual connection. Given the input of the MLP layer as $\mathbf{x}_{\mathrm{in}} \in \mathbb{R}^{d \times d}$ , the modified output $\mathbf{x}_{\mathrm{out}} \in \mathbb{R}^{d \times d}$ with the adapter becomes: + +$$ +\boldsymbol {x} _ {\text {o u t}} = \operatorname {M L P} \left(\boldsymbol {x} _ {\text {i n}}\right) + \operatorname {R e L U} \left(\boldsymbol {x} _ {\text {i n}} \boldsymbol {W} _ {\text {d o w n}}\right) \boldsymbol {W} _ {\text {u p}}. \tag {1} +$$ + +The adapter is inserted across each $N_{\mathrm{blocks}}$ transformer block. We refer to these $N_{\mathrm{blocks}}$ adapters collectively as "the adapter", denoted as $\mathcal{A}$ . In adapter-based CIL, a task-specific subspace is formed by training an adapter $\mathcal{A}_t$ for each task $t$ . + +Prototypical Classification in CIL: After training the adapter on the $t$ -th task, a prototypical classifier is constructed using the $t$ -th validation dataset $\mathcal{V}_t$ . Specifically, we calculate the prototype $\pmb{p}_{t,c} \in \mathbb{R}^d$ , which is the mean of the feature vectors for each class $c \in \mathcal{V}_t$ , as follows: + +$$ +\boldsymbol {p} _ {t, c} = \sum_ {\left(\boldsymbol {x} _ {t}, y _ {t}\right) \in \mathcal {V} _ {t}} \phi \left(\boldsymbol {x} _ {t}\right) \mathbb {I} \left(y _ {t} = c\right), \tag {2} +$$ + +where $\mathbb{I}(\cdot)$ is the indicator function. Then, the prototypes are concatenated to define the prototype matrix $P_{t}\in$ $\mathbb{R}^{C_t\times d}$ , where $C_t = |\mathcal{V}_t|$ and + +$$ +\boldsymbol {P} _ {t} = \left[ \begin{array}{l l l} \boldsymbol {p} _ {t, 1} & \dots & \boldsymbol {p} _ {t, C _ {t}} \end{array} \right]. \tag {3} +$$ + +This calculation is performed within $\mathcal{A}_1$ 's subspace [61] or across all subspaces [59]. During inference, the prototype matrices are used as the classifier weights $W = [P_1 \cdots P_t] \in \mathbb{R}^{C \times d}$ , where $C$ is the total number of classes $\sum_{i=1}^{t} C_i$ learned so far. The model output $f$ is redefined with a cosine classifier [11] as follows: + +$$ +f (\boldsymbol {x}) = \frac {\boldsymbol {W} ^ {\top} \phi (\boldsymbol {x})}{\| \boldsymbol {W} \| _ {2} \| \phi (\boldsymbol {x}) \| _ {2}}, \tag {4} +$$ + +![](images/96dec44d1d67bad023ba4d3b3d67dda02643f092c1d65f511619ab6817e901e0.jpg) +Figure 2. An Illustration of ACMap. ACMap sequentially trains an adapter for each task, starting from shared initial weights and incrementally merging them into a single adapter. In the subspace formed by the merged adapter, the prototypes for the current task are computed, while previous prototypes are updated via centroid prototype mapping. + +![](images/56e648e0dda0fec3415791a464cab54bb9a5567d0c45b35dc2998d8ce4209dd6.jpg) + +where $\| \cdot \|_2$ denotes the $\ell_2$ -norm. The predicted class of $\pmb{x}$ is determined as the class with the highest cosine similarity among the elements of $f(\pmb{x})$ . Note that prototypes for previous classes are not included in $\mathcal{V}_t$ and thus cannot be computed. In other words, in $\mathcal{A}_t$ 's subspace, it is impossible to calculate $P_1, \ldots, P_{t-1}$ . These prototypes must be complemented with appropriate alignments. + +# 4. ACMap: Adapter Merging with Centroid Prototype Mapping + +In this paper, we propose Adapter Merging with Centroid Prototype Mapping (ACMap) for scalable CIL. Existing methods that rely on task-specific training for CIL often struggle with scalability during inference. ACMap addresses this challenge by training task-specific adapters and consolidating them into a single unified adapter via adapter merging. This approach allows ACMap to maintain scalability, requiring only the merged adapter during inference, while ensuring efficiency as tasks increase. + +# 4.1. Adapter Merging in CIL + +As illustrated in Figure 2a, ACMap follows a sequential process where a task-specific adapter is trained for each task, and the merged adapter $\bar{\mathcal{A}}$ is incrementally updated via adapter merging. + +Adapter Merging: Adapter merging is a model merging technique that combines multiple adapters, inspired by previous work on model merging [20, 30, 51, 53]. A common approach for model merging is average merging [51], which averages the weights of multiple models with a shared initial weight. In ACMap, each task-specific adapter starts + +![](images/95661183c14164a774e7a917c3ff0f514385f6ab316908d69d0b458d943e2790.jpg) +Figure 3. Visualization of the test error using linearly interpolated adapter weights $\pmb{\theta} = u\pmb{\theta}_{t-1} + v\pmb{\theta}_t + (1-u-v)\pmb{\theta}_{t+1}$ , $(0 \leq u, v \leq 1)$ across three consecutive adapter weights $\pmb{\theta}_{t-1}, \pmb{\theta}_t, \pmb{\theta}_{t+1}$ . Test errors for the adapters $\pmb{\theta}_2, \pmb{\theta}_3, \pmb{\theta}_4$ are shown on the left, and for the adapters $\pmb{\theta}_5, \pmb{\theta}_6, \pmb{\theta}_7$ on the right. The star symbol indicates the average merging $(u = 1/3, v = 1/3)$ . Additional results are provided in Appendix G. + +![](images/2889c973905126e28c0093ff28dc7526533bd6662535a3e7b39c6ddf4ea5acdc.jpg) + +with shared initial weights $\theta_{\mathrm{init}}$ and undergoes task-specific training to update the weights $\theta_t$ for each task. The merged adapter is initialized as $\bar{\mathcal{A}}_1 = \mathcal{A}_1$ , and weights $\bar{\theta}_t$ are iteratively updated via average merging: + +$$ +\bar {\boldsymbol {\theta}} _ {t} = \left(1 - \frac {1}{t}\right) \bar {\boldsymbol {\theta}} _ {t - 1} + \frac {1}{t} \boldsymbol {\theta} _ {t}, \quad t = 2, \dots , T. \tag {5} +$$ + +Through this process, the adapter $\bar{\mathcal{A}}_t$ constructs a task-shared subspace that integrates the knowledge from all previous tasks. Weight averaging generally enhances both accuracy and robustness to distribution shifts compared to using a single model [24]. + +Towards Effective Weight Averaging: However, simply + +averaging the weights of different models does not guarantee optimal performance, particularly without proper alignment [1, 24, 25, 43]. For effective averaging, models should ideally originate from a common pre-trained model or be fine-tuned in similar regions of parameter space. This alignment helps reduce variance, enhances regularization, and ensures that interpolated weights remain within a low-loss basin, thereby supporting stable and improved performance [24]. + +**Landscape Analysis for Adapter Merging:** We analyze the loss landscape of three successive adapters, as shown in Figure 3, through the linear interpolation $\pmb{\theta} = u\pmb{\theta}_{t-1} + v\pmb{\theta}_t + (1 - u - v)\pmb{\theta}_{t+1}$ , $(0 \leq u, v \leq 1)$ , where $\pmb{\theta}_{t-1}, \pmb{\theta}_t,$ and $\pmb{\theta}_{t+1}$ represent the adapters trained on tasks $t-1, t$ , and $t+1$ , respectively. The test dataset is a combination of all three tasks: $\mathcal{T}_{t-1} \cup \mathcal{T}_t \cup \mathcal{T}_{t+1}$ . This analysis shows the existence of a low-loss basin (red region), indicating that the interpolated weights exhibit consistent performance across the tasks. This basin likely forms because each adapter is initialized with the same starting parameters. This initialization leads to similar training paths in the parameter space and helps form a shared low-loss region. + +Initial Weight Replacement: To further encourage the formation of a low-loss basin, we propose initial weight replacement. After training on the first task, a shared initial weight $\theta_{\mathrm{init}}$ , which is typically initialized randomly, is replaced with $\theta_{1}$ , the parameters learned from the first task. Hence, adapters for subsequent tasks $i (> 1)$ are trained with $\theta_{1}$ as its initial parameter. By sharing the weight of the first adapter, subsequent tasks are more likely to follow similar training paths, helping convergence within a shared low-loss region. + +# 4.2. Prototype Mapping + +In ACMap, a key challenge is an inability to compute previous prototypes within the subspace of the current adapter $\bar{A}_t$ , due to restricted access to data from previous tasks. Specifically, for task $t$ , previous prototypes $P_i(\bar{A}_t)$ , $i = 1,\dots,t-1$ cannot be computed within the current subspace, where $P_i(\bar{A}_t)$ denotes the prototypes for task $i$ computed using the current adapter $\bar{A}_t$ . This limitation is because, in CIL, data from previous tasks is unavailable, as shown in Figure 2b (top). + +While the unavailable prototypes can be substituted with $P_{i}(\bar{A}_{i}), i = 1, \dots, t - 1$ from previous subspaces, such substitutions may lead to an alignment problem. Figure 4a shows the cosine similarity $\mathrm{Sim}(P_1(\bar{A}_1), P_1(\bar{A}_t))$ when substituting $P_{1}(\bar{A}_{1})$ for $P_{1}(\bar{A}_{t})$ where $\mathrm{Sim}(\cdot, \cdot)$ denotes cosine similarity. This result shows that earlier task prototypes, such as from $t = 1$ , shift significantly when applied to later subspaces, indicating poor alignment. Therefore, aligning prototypes within the current adapter is crucial for + +Algorithm 1 Centroid prototype mapping on the $t$ -th task. + +Input: Merged adapters $\bar{\mathcal{A}}_1,\dots ,\bar{\mathcal{A}}_t$ , previous prototypes $P_{1}(\bar{A}_{1}),\ldots ,P_{t - 1}(\bar{A}_{t - 1}).$ + +Output: Prototypes aligned within the current subspace. + +1: $P_{t}(\bar{A}_{t})\gets$ Calculate $t$ -th task prototype with $\bar{A}_t$ +2: $\triangleright$ Centroid prototype mapping +3: for $i = 1, \dots, t - 1$ do +4: $P_{t}(\bar{A}_{i})\gets$ Calculate $t$ -th task prototype with $\bar{A}_i$ +5: $\Delta \pmb{p} \gets \frac{1}{|\mathcal{Y}_t|} \sum_{c=1}^{|\mathcal{Y}_t|} (\pmb{p}_{t,c}(\bar{\mathcal{A}}_t) - \pmb{p}_{t,c}(\bar{\mathcal{A}}_i))$ +6: $\Delta P\gets [\Delta p\dots \Delta p]\in \mathbb{R}^{d\times |\mathcal{V}_t|}$ +7: $\dot{\pmb{P}}_i(\bar{\mathcal{A}}_t)\gets \pmb {P}_i(\bar{\mathcal{A}}_i) + \Delta \pmb{P}$ +8: end for +9: return $\hat{P}_1(\bar{\mathcal{A}}_t),\dots,\hat{P}_{t-1}(\bar{\mathcal{A}}_t)$ + +accurate and consistent prototype mapping. In contrast, Figure 4b shows using $P_{5}(\bar{A}_{5})$ as a substitute for $P_{5}(\bar{A}_{t})$ maintains high cosine similarities. This suggests that the alignment problem is not as severe. We will discuss this at the end of this section. + +Centroid Prototype Mapping: The above alignment problem can be formulated as finding a mapping $f \colon P_i(\bar{A}_t) = f(P_i(\bar{A}_i)), i = 1, \dots, t - 1$ . However, since the mapping $f$ is generally unknown, we approximate it with an affine mapping: + +$$ +\boldsymbol {P} _ {i} \left(\bar {\mathcal {A}} _ {t}\right) \approx \boldsymbol {P} _ {i} \left(\bar {\mathcal {A}} _ {i}\right) + \Delta \boldsymbol {P}. \tag {6} +$$ + +We estimate $\Delta P$ as the difference between the centroids of the available prototypes $P_{t}(\bar{A}_{t})$ and $P_{t}(\bar{A}_{i})$ , i.e., + +$$ +\Delta \boldsymbol {P} = \mathbb {E} \left[ \boldsymbol {P} _ {t} \left(\bar {\boldsymbol {A}} _ {t}\right) - \boldsymbol {P} _ {t} \left(\bar {\boldsymbol {A}} _ {i}\right) \right], \tag {7} +$$ + +where the expectation is taken over the prototypes. This approach assumes that the alignment for task $t$ , which is computable, also applies to previous tasks $i (< t)$ . The validity of this assumption is demonstrated experimentally. We refer to this mapping as centroid prototype mapping; the algorithm is detailed in Algorithm 1. + +Early Stopping for Adapter Merging: As shown in Figure 4b, the alignment problem is not severe for tasks relatively close to the current one. Building on this observation, we introduce early stopping for adapter merging, which halts the merging process once the number of tasks exceeds a specified threshold. While efficient during inference, average merging increases training costs because adapters must be trained for each task. In Equation (5), as $t$ grows, the difference between $\theta_{t-1}$ and $\theta_t$ becomes negligible, with the coefficient $1/t$ approaching zero. This supports the effectiveness of early stopping, as further merging becomes redundant. + +![](images/db53c8dbbef157f7deb1927f974a994d2eba5b40508aaf97f8273b736334e4b7.jpg) +Figure 4. The curve showing the differences in cosine similarity that arise when earlier task prototypes are substituted for prototypes in subsequent subspaces. + +![](images/f4222203ccb639f22a5b06340fdf1c211d9899d61c704066a19baf00381f3307.jpg) + +# 5. Experiments + +We follow the protocol in [59] to evaluate performance and inference time, and conduct an ablation study to validate our method. + +# 5.1. Experimental Setup + +Datasets: We evaluate our method on five benchmark datasets: CIFAR-100 [23] (CIFAR), CUB [47], ImageNet-R [15] (IN-R), ImageNet-A [14] (IN-A), and VTAB [56]. Dataset details are provided in Appendix A. CIFAR-100 contains 100 classes, CUB, ImageNet-R, and ImageNet-A each contain 200 classes, and VTAB consists of 50 classes. For all datasets except VTAB, the class order is randomized for each seed. For VTAB, the class order is fixed. We divide these datasets into $T$ tasks, using the notation "B- $m$ Inc- $n$ ", where $m$ is the initial number of classes, and $n$ is the number of classes added incrementally per task. + +Evaluation Metrics: Following the standard protocol in CIL [36], we use two evaluation metrics: the average accuracy $\bar{A}$ across all tasks and the accuracy $A_{T}$ of the final task (final accuracy). + +Baselines: We compare our method with several baselines and state-of-the-art methods. The baseline is fine-tuning the pre-trained model for each task, referred to as Finetune. We also test finetuning only the adapter, referred to as Finetune Adapter. For comparison, we select CIL approaches using a pre-trained model: L2P [50], DualPrompt [49], CODA-Prompt [41], SimpleCIL [61], APER [61], and EASE [59]. Among these, SimpleCIL, APER, and EASE are prototype-based methods. SimpleCIL, a prototype-based CIL method without adapters, serves as the baseline. APER trains an adapter only on the first task and extracts features from the pre-trained model with and without the adapter. EASE, by contrast, trains separate adapters for each task and individually extracts feature vectors from each adapter. + +Training Details: We follow the training settings used in [62]. For the pre-trained model, we use the ViT-B/16 + +model, pre-trained on ImageNet-21K [37]. Adapter training is optimized using SGD with a cosine annealing learning rate scheduler. The learning rate, batch size, and number of training epochs are set for each dataset, following the values specified in [62] (see Appendix B). + +# 5.2. Main Results + +Table 1 presents the average accuracy $\bar{A}$ and final accuracy $A_{T}$ for the five benchmark datasets. The results for the comparison methods are taken from [59], while the values for ACMap (ours) represent averages from five runs. Figure 5 shows the top-1 accuracy curve during CIL. The comparison methods include SimpleCIL, APER, and EASE, all of which are prototype-based methods. The values in the figure also represent averages from five runs for all methods. Additional results are provided in Appendix E.1 and Appendix E.3. + +ACMap performs comparably to or slightly better than EASE across all datasets, except VTAB B0 Inc10, and significantly outperforms APER on all datasets except CUB B0 Inc10. ACMap achieves notable improvements on domain-shifted datasets, such as IN-R, IN-A, and VTAB, compared to APER, which reuses the first adapter for all tasks. This suggests that ACMap's approach to training and merging adapters enhances domain adaptation. However, on CUB B0 Inc10, adapter learning and merging did not improve performance, as even SimpleCIL, which lacks adapters, performs comparably to both APER and EASE. + +In the VTAB B0 Inc10 experiment, EASE outperforms ACMap. This difference is likely due to the VTAB setup, which includes five datasets from distinct domains, each corresponding to a separate dataset. This setup enables EASE to use five separate adapters, one per dataset, while ACMap uses a single adapter to learn across all five datasets. Additionally, a closer analysis of VTAB reveals that the fourth task has a larger dataset than the others, potentially leading to overfitting on the fourth task (see Appendix E.2). Consequently, as shown in Figure 5 (far right), + +Table 1. Average accuracy $\bar{A}$ and final accuracy $A_{T}$ . CIFAR refers to CIFAR-100, and IN-R/A refers to ImageNet-R and ImageNet-A. Results for the comparison methods are taken from those reported in [59]. All evaluations are conducted in an exemplar-free setting. In our methods, IR denotes initial weight replacement. + +
MethodCIFAR B0 Inc5 ACUB B0 Inc10 ACUB B0 Inc10 AIN-R B0 Inc5 AIN-A B0 Inc20 AVTAB B0 Inc10 AVTAB B0 Inc10 A
Finetune38.9020.1726.0813.9621.6110.7924.28
Finetune Adapter [5]60.5149.3266.8452.9947.5940.2845.41
L2P [50]85.9479.9367.0556.2566.5359.2249.39
DualPrompt [49]87.8781.1577.4766.5463.3155.2253.71
CODA-Prompt [41]89.1181.9684.0073.3764.4255.0853.54
SimpleCIL [61]87.5781.2692.2086.7362.5854.5559.77
APER + Adapter [61]90.6585.1592.2186.7372.3564.3360.47
EASE [59]91.5185.8092.2386.8178.3170.5865.34
Ours w/o IR (L=10)91.5387.3591.7487.0276.4769.8863.95
Ours w/o IR (L=∞)91.5487.3591.7486.9676.5670.0864.00
Ours (L=10)92.0187.7391.5986.6177.1070.2565.14
Ours (L=∞)92.0487.8191.5686.6677.3170.4965.19
+ +![](images/f1b5f7990eefc3a2207cfa6630c75887b6709cc72fe9dabba48e59d2d0fdd9f0.jpg) +Figure 5. Top-1 accuracy curve during CIL, comparing prototype-based methods: SimpleCIL (denoted as Simple), APER, and EASE. Additional results are provided in Appendix E.1. + +![](images/1598e8f55509335febc9142a958f71476108a9908afdd91d0c799104ca404b3d.jpg) + +![](images/32e1183bda883b5072484087aa33b20711c99600d775f267ce88cd877f060d53.jpg) + +![](images/1f1d2224451496a5706d25391776b97e4726780aa343a6e49e8c8b1e9259433b.jpg) + +![](images/b7d0bd2df4703657a9a14f94eac0a435a325f8243db9325f37d9d13b8a5764d9.jpg) + +Table 2. Comparison of inference time for task 40 of IN-R B0 Inc5 among SimpleCIL, APER, EASE, and ACMap (ours). Time Ratio indicates how many times longer each comparative method's inference time is compared to ACMap. ACMap achieves accuracy comparable to EASE while maintaining efficient inference. + +
MethodTime (s)Time Ratio
SimpleCIL [61]22.6×0.96
APER [61]44.1×1.88
EASE [59]916.5×39.0
ACMap (ours)23.5-
+ +model accuracy declines starting from the fourth task, resulting in lower performance for ACMap than EASE. + +# 5.3. Inference Time + +Table 2 shows the inference time for task 40 of ImageNet-R B0 Inc5. The compared methods include SimpleCIL, + +APER, and EASE, with computational complexities of $\mathcal{O}(1)$ , $\mathcal{O}(1)$ , and $\mathcal{O}(T)$ , respectively, where $T$ denotes the number of tasks. ACMap achieves $\mathcal{O}(1)$ complexity by using a single adapter across tasks. + +The results show that ACMap significantly outperforms EASE in terms of inference time, achieving a 39-fold speedup for 40 tasks. This speedup is particularly advantageous for real-world applications requiring many tasks and efficient inference. Compared to SimpleCIL, ACMap achieves similar inference time while improving final top-1 accuracy by over $16\%$ (Table 1). Similarly, ACMap demonstrates comparable inference time to APER but surpasses it by over $6\%$ in final top-1 accuracy. These results confirm ACMap's success in balancing high accuracy and inference efficiency. Additional experiments on inference time are in Appendix C. + +# 5.4. Ablation Study + +We conducted experiments on CIFAR-100 B0 Inc5 and ImageNet-R B0 Inc5 to conduct ablation studies. + +Table 3. Ablation study for initial weight replacement (IR) and centroid prototype mapping (CM) with the symbol $\checkmark$ indicating the method used. Both components contribute to the improvement of performance. + +
IRCMCIFAR B0 Inc5IN-R B0 Inc5
AATAAT
90.4686.3275.9969.55
91.5387.3576.4769.88
91.0786.8576.5669.80
92.0187.7377.1070.25
+ +![](images/2f6b925d417a7ddb70ae2b61b91528419c42a7d60139ca8b54c3815b31bfaf2d.jpg) +Figure 6. Cosine similarity curves of $\mathrm{Sim}(\hat{P}_1(\bar{\mathcal{A}}_1), P_1(\bar{\mathcal{A}}_t))$ , with solid lines showing the similarity between mapped and true prototypes, and semi-transparent lines between unmapped and true prototypes. The prototypes aligned through centroid prototype mapping move closer to the true prototype in subsequent tasks. Additional results are provided in Appendix F. + +Centroid Prototype Mapping and Initial Weight Replacement: We conduct ablation studies on two key components: centroid prototype mapping (CM) and initial weight replacement (IR). The results of this study are presented in Table 3. These experiments fixed the early stopping parameter $L$ at 10. The results indicate that both CM and IR contribute to performance improvement, emphasizing their role in enhancing the model's overall effectiveness. + +We further evaluate the effectiveness of centroid prototype mapping by examining how well the mapped prototypes $\hat{P}_1(\bar{A}_t)$ align with the true prototypes $P_1(\bar{A}_t)$ using cosine similarity. The true prototypes are computed using the validation datasets from previous tasks, which are unavailable in the CIL setting. The cosine similarity curve, $\mathrm{Sim}(\hat{P}_1(\bar{A}_t), P_1(\bar{A}_t))$ , as adapter merging progresses, is shown in Figure 6, where $\mathrm{Sim}(\cdot, \cdot)$ denotes cosine similarity. The solid line represents the cosine similarity between the mapped and true prototypes, while the semi-transparent line shows the similarity between the unmapped prototypes $P_1(\bar{A}_1)$ and the true prototypes. The colors of the curves correspond to the classes from the first task. The results indicate that centroid prototype mapping effectively aligns the mapped prototypes with the true prototypes, as seen from + +Table 4. Evaluation of the impact of the early stopping threshold $L$ . By applying early stopping at around $L = 10$ , unnecessary computations can be reduced without sacrificing model accuracy. + +
ThresholdCIFAR B0 Inc5IN-R B0 Inc5
AATAAT
L=091.0786.8576.5669.80
L=591.8887.6176.8169.87
L=1092.0087.7677.0970.25
L=2092.0487.8077.2770.37
L=∞92.0487.8077.3170.49
+ +the high cosine similarity values. + +Early Stopping Threshold: We also evaluate the impact of the early stopping threshold, $L$ , with results shown in Table 4. Since CIFAR-100 B0 Inc5 has 20 tasks, results for $L = 20$ match those for $L = \infty$ . The experiments show that increasing $L$ generally improves performance; however, the gains diminish as $L$ increases. Furthermore, setting $L = 10$ achieves performance comparable to $L = \infty$ . This indicates that early stopping avoids extra computation without sacrificing accuracy. See Appendix D for details on how the early stopping threshold $L$ is set. + +# 6. Conclusion + +ACMap effectively addresses the challenges of CIL by retaining knowledge across tasks while scaling efficiently with an increasing number of tasks. By merging task-specific adapters into a unified adapter, ACMap ensures efficient and consistent inference over time. The centroid prototype mapping mechanism refines task representations within a shared subspace, preserving accuracy as tasks accumulate. Experimental results on five benchmark datasets demonstrate that ACMap not only matches the accuracy of state-of-the-art methods but also maintains constant inference time. This combination of competitive performance and scalability makes ACMap a promising approach for scenarios requiring efficient, scalable inference. + +While ACMap demonstrates strong performance, further refinements are needed when dealing with tasks with significantly different datasets, such as those found in VTAB. A promising future direction is the concept of adapter bank. 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IJCV, 2024. 1, 2, 3, 6, 7 +[62] Da-Wei Zhou, Hai-Long Sun, Han-Jia Ye, and De-Chuan Zhan. https://github.com/sun-hailong/CVPR24-Ease, 2024. 6, 2 \ No newline at end of file diff --git a/adaptermergingwithcentroidprototypemappingforscalableclassincrementallearning/images.zip b/adaptermergingwithcentroidprototypemappingforscalableclassincrementallearning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..408f4d3db4ddce85f214a2fb59bab92c153f1f47 --- /dev/null +++ b/adaptermergingwithcentroidprototypemappingforscalableclassincrementallearning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2f8935cfd444d1eb6d47b4325fe3168a9aabee249766410636ecd3cef4ae7fec +size 501051 diff --git a/adaptermergingwithcentroidprototypemappingforscalableclassincrementallearning/layout.json b/adaptermergingwithcentroidprototypemappingforscalableclassincrementallearning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..50424c68186cf2bb919b349a2789b9ad5af1c1cb --- /dev/null +++ b/adaptermergingwithcentroidprototypemappingforscalableclassincrementallearning/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d5448f54bdb9e4b636bb3c1ef46bce3ab7df1f75a9e3c07406d72038ba2743dd +size 473736 diff --git a/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_content_list.json b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..55bb14050ff91350d96549cb002ef6d570182183 --- /dev/null +++ b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:342f8f31b33f3a28ce60656691501ee946f5ed562a99961983b9a74389f26e80 +size 78351 diff --git a/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_model.json b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..66724a46192a2ba9c35d16472f730b83c5be5f01 --- /dev/null +++ b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cceee7ec97cf82bdd6e472a517d692e95f728a8363eb15c0c1d27021cfc1a938 +size 96025 diff --git a/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_origin.pdf b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..48a2547af70eb9f062e9ff04b9ae9619b806f624 --- /dev/null +++ b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/2f8fff98-4047-461c-a364-929dae730a0f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:919fe71cb46bc1a2c08165ba8a0b5e6f2d959c3c5208cc431431d17a1e4ca1aa +size 1881554 diff --git a/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/full.md b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3fe51c80bc92d36a86d1a11bc6bb7c6711341ea8 --- /dev/null +++ b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/full.md @@ -0,0 +1,287 @@ +# Adapting Dense Matching for Homography Estimation with Grid-based Acceleration + +Kaining Zhang $^{1}$ Yuxin Deng $^{1}$ Jiayi Ma $^{1*}$ Paolo Favaro $^{2}$ $^{1}$ Wuhan University, China $^{2}$ University of Bern, Switzerland +{zkn707196, acuo.dyx, jyma2010}@gmail.com paolo.favaro@unibe.ch + +# Abstract + +Current deep homography estimation methods are typically constrained to processing low-resolution image pairs due to network architecture and computational limitations. For high-resolution images, downsampling is often required, which can greatly degrade estimation accuracy. In contrast, image matching methods, which match pixels and compute homography from correspondences, provide greater resolution flexibility. So in this work, we revisit the traditional image matching paradigm for homography estimation and propose GFNet, a Grid Flow regression Network that adapts the high-accuracy dense matching framework for homography estimation while enhancing efficiency through a grid-based strategy—estimating flow only over a coarse grid by leveraging homography's global smoothness. We demonstrate the effectiveness of GFNet on a wide range of experiments on multiple datasets, including the common scene MSCOCO, multimodal datasets VISIR and GoogleMap, and the dynamic scene VIRAT. Notably, on $448 \times 448$ GoogleMap, GFNet achieves an improvement of $+13.5\%$ in auc@3 while reducing MACs by $\sim 47\%$ compared to the SOTA dense matching method. Additionally, it shows a $1.8 \times$ improvement in auc@3 over the SOTA deep homography method. Code is available at https://github.com/KN-Zhang/GFNet. + +# 1. Introduction + +Homography estimation is the task of determining the transformation that aligns two planes. This is a basic low-level computer vision task widely used in various downstream applications, including image/video stitching [47], image fusion [38], GPS-denied UAV localization [36, 39], stereo vision [19], and planar object tracking [24]. + +Deep homography estimation methods, which typically parameterize homography using corner offsets or the homography matrix, have demonstrated high accuracy on low- + +resolution images. However, their scalability to higher resolutions is constrained by limitations in (1) network architecture and (2) computational capacity. Specifically, 4-point-based methods [5, 6, 11, 20, 30, 49] extract matching information from image pairs and aggregate it to regress corner offsets, followed by homography estimation using DLT [17]. The aggregation process is typically implemented through a fixed number of large-kernel pooling operations. Consequently, the network's downsampling factor is predefined and constrained by the kernel sizes, inherently limiting the input image resolution—typically to $128 \times 128$ . Matrix-based methods [7, 43-45] explicitly use the IC-LK iterator [1] with deep features to refine the homography matrix. This approach requires multiple iterations to achieve feature-metric alignment across all pixels, resulting in significant computational and memory overhead. As a result, current methods are forced to work with inputs at low resolution. Unfortunately, doing so has also a direct negative impact on the accuracy of the estimated homography. + +Image matching methods, which first find correspondences and then estimate homography with robust estimators [16, 17], offer greater flexibility for high-resolution inputs. However, they are often criticized for their limited effectiveness in low-texture scenarios [23], which are common in homography applications. Recently, this issue has been well-addressed by the powerful dense matching methods [13, 14, 35], which find correspondences for every pixel. Yet, this strong performance comes with nonnegligible computational costs. For example, training the SOTA dense matcher RoMa [14] on a 24GB GPU only supports a batch size of 1 for $560 \times 560$ images. This heavy resource demand arises from attempting to resolve every possible match between images, which is redundant for homography estimation, as it only has 8 degrees of freedom. + +In this paper, we aim to solve the resolution issue of deep homography methods by introducing the dense matching framework, while tackling the computational challenges of dense matching by considering the globally smooth nature of homography transformations. This leads to Grid Flow regression Network (GFNet). As shown in Figure 1, GFNet + +![](images/3b4e2daf74133b5a052b5cd77e45c3f092a888a3d39ae5e1a69faed46abf952c.jpg) +Figure 1. Homography estimation results of GFNet and existing deep homography estimation methods (red spot) and image matching methods (blue spot) on MSCOCO (natural) and GoogleMap (multimodal). We test on an RTX3090 with batchsize = 1. + +![](images/d9d1c3807e495f62612f7160e524affa2519f0769286f181ce8257be97ee9c83.jpg) + +achieves superior accuracy over deep homography estimation methods and outperforms the SOTA dense matching method RoMa with higher efficiency on both MSCOCO and GoogleMap. Key contributions include: + +- We incorporate pre-trained self-supervised learning features of DINOv2 [27] with a lightweight feature pyramid network to construct robust multi-scale features. This fusion solves the low-resolution limitation of DINOv2, allowing our model to benefit from its strong cross-domain feature matching capabilities across multiple scales. +- We sparsify pixel-level dense matching to a coarse grid prediction, greatly reducing computational costs while keeping the high accuracy of dense matching. Compared to previous deep homography estimation methods, our grid-flow representation provides greater resolution flexibility and enhanced accuracy. +- We introduce a novel synthetic data generation method for self-supervised learning to improve generalization and an iterative flow regression approach to prevent suboptimal multi-scale flow optimization in challenging scenes. + +# 2. Related Works + +Deep homography estimation methods are generally categorized into 4-point-based and matrix-based approaches based on how they parameterize homography. 4-point-based methods employ neural networks to regress corner offsets and estimate homography with DLT. The first such approach, DHN [11], uses a VGG-style network to process a stacked image pair and output corner offsets. Subsequent methods improve accuracy by cascading multiple networks for progressively prediction [15, 20, 30]. More recently, end-to-end learning with a single network has become the preferred approach due to better accuracy, facilitated by techniques such as iterative estimation in IHN [5], the recurrence strategy in RHWF [6], and the multi-scale iterative framework in MCNet [49]. However, these 4-point-based methods are constrained to low-resolution in + +puts (typically $128 \times 128$ ) due to the network's inherent inflexibility. Matrix-based methods employ neural networks to extract features and leverage non-linear optimization to refine the homography matrix, achieving feature-metric alignment. These methods enhance estimation accuracy either by ensuring a good initialization[43] or by improving the convergence basin for optimization[7, 44, 45]. These matrix-based methods are also limited to small-resolution images due to their high computational overhead. There are also alternative parameterizations, such as the homography flow proposed in BaseHomo [23, 40]. It does not impose a resolution limitation but is restricted to small-baseline scenes, which significantly limits its applicability. + +Image matching methods can be categorized into sparse, semi-dense, and dense methods. Sparse methods rely on keypoint detection and description, followed by matching the descriptors [10, 12, 22, 28, 29]. While efficient, they often struggle with accuracy in textureless regions, which are common in homography estimation tasks [43]. Semi-dense methods degrade less in such areas by bypassing keypoint detection. Instead, they perform global matching at a coarse level, where initial coarse matches that pass the mutual nearest neighbor test are then refined at a finer level. Regarding the dense methods, they can handle textureless situations well by predicting matches for every pixel. Although they achieve impressive accuracy, they require substantial computational resources in terms of both time and memory, which limits their applicability in resource-constrained scenarios [13, 14, 34, 35]. + +Common challenges in homography estimation are twofold and arise from practical application requirements, according to recent literature [5, 20, 25, 30, 41, 43, 45]. The first one is photometric inconsistency caused by changes in illumination or modality, such as images taken at different times, with different sensors, or in different types [18, 48]. The second challenge is whether methods can handle violations of the homography assumption due to dynamic occlusions, which frequently occur in real-world scenarios. + +# 3. Method + +We aim to predict an accurate homography transformation $\mathbf{H}$ that spatially aligns a source image $I_{S}$ with a target image $I_{T}$ . Rather than directly regressing the global homography, we follow the dense matching paradigm but estimate the flow over a regular grid and utilize the resulting correspondences to compute the homography. This process begins by extracting multi-scale features from both images, which are then used to predict grid flow across multiple scales. + +# 3.1. Multi-scale Feature Extraction + +We use DINOv2 to enhance the feature representation capability [42]. Specifically, DINOv2 divides the input image into $14 \times 14$ patches and generates a feature vector for each patch. As these patch descriptors are typically high-dimensional, we apply a linear projection layer to reduce their dimensionality, setting it to 64 in our implementation. To further enrich the features with cross-view information, which is crucial for matching, we add a normalized 2D positional encoding [4, 8] and pass the features through stacked cross-attention layers. The resulting feature is denoted as $\mathcal{F}^1 \in \mathbb{R}^{64 \times \lfloor \frac{H}{14} \rfloor \times \lfloor \frac{W}{14} \rfloor}$ , where $H$ and $W$ are the height and width of the original image, $|\cdot|$ is the round down operation. + +Since DINOv2 produces relatively low resolution features, relying solely on these features for homography estimation would lead to limited matching accuracy [3]. To address this issue, we introduce a Feature Pyramid Network (FPN) to construct multi-scale features, ranging from the original image size down to a $1/8$ scale. We keep the network lightweight by configuring the channel numbers of each layer to $[8, 16, 32, 64]$ . Furthermore, to improve the representation capability of the lightweight FPN, we bilinearly upsample $\mathcal{F}^1$ to the $1/8$ scale and merge it with the $1/8$ scale features produced by the encoding stage of the FPN. The final output features used for homography estimation consist of five scales, denoted as $\{\mathcal{F}^l\}_{l=1,2,3,4,5}$ , corresponding to spatial sizes of $1/14$ , $1/8$ , $1/4$ , $1/2$ , and $1$ relative to the original image, as illustrated in Figure 2. + +# 3.2. Background: Dense Matching + +We derive our grid flow regression based on the framework of the SOTA dense matcher RoMa [14]. Here is a brief introduction to it. RoMa aims to find pixel-wise correspondences between two images $I_S, I_T \in \mathbb{R}^{H \times W \times 3}$ by estimating a dense displacement field, or flow, $\mathbf{w} \in \mathbb{R}^{H \times W \times 2}$ . Given the pixel coordinates in $I_S$ as $\mathbf{x} \in \mathbb{R}^{H \times W \times 2}$ , the relationship $\mathbf{y} = \mathbf{x} + \mathbf{w}$ denotes the corresponding pixel positions in $I_T$ that align with those in $I_S$ , representing the same physical locations in the scene. $\mathbf{w}$ is predicted in a multi-scale manner, from the coarsest $(l = 1)$ to the finest: + +$$ +\mathbf {w} ^ {l} = \operatorname {u p} \left(\mathbf {w} ^ {l - 1}\right) + \Delta \tilde {\mathbf {w}} ^ {l}, \Delta \tilde {\mathbf {w}} ^ {l} = \operatorname {d e c o d e r} _ {\theta} ^ {l} \left(\mathcal {F} _ {S} ^ {l}, \mathcal {F} _ {T} ^ {l}, \operatorname {u p} \left(\mathbf {w} ^ {l - 1}\right)\right), \tag {1} +$$ + +where $\theta$ represents learnable parameters, $\mathbf{w}^0$ is an all-zero field, and $\mathrm{up}(\cdot)$ is the bilinear upsampling operation. There is a feature correlation layer included in each $\mathrm{decoder}_\theta^l (\cdot)$ , which is computed as: + +$$ +c \left(\mathcal {F} _ {S} ^ {l}, \mathcal {F} _ {T} ^ {l}; r ^ {l}\right) = \mathcal {F} _ {S} ^ {l} \left[ \mathbf {x} ^ {l} \right] \odot \mathcal {F} _ {T} ^ {l} \left[ \mathbf {x} ^ {l} + \operatorname {u p} \left(\mathbf {w} ^ {l - 1}\right) + \delta \right], \tag {2} +$$ + +where $\mathbf{x}^l\in \mathbb{R}^{H^l\times W^l\times 2}$ is the pixel coordinates in $\mathcal{F}_S^l$ $[\cdot ]$ is bilinear interpolation, $\odot$ is the dot product, and $\delta \in [-2r^l -$ $1,2r^{l} + 1]\times [-2r^{l} - 1,2r^{l} + 1]$ defines a local window with radius $r^l$ . This operation leads to a 4D tensor of shape $\mathbb{R}^{H^l\times W^l\times (2r^l +1)\times (2r^l +1)}$ , which captures visual similarity within a local neighborhood. While this correlation step is crucial for producing accurate results, it also introduces the main computational bottleneck in RoMa. + +# 3.3. Grid Flow Regression + +Grid-based strategy for efficiency. To alleviate the computational burden of Eq. 2, previous works typically reduce the radius $r$ as the scale increases [30, 34, 49]. However, this saving is limited for high-resolution images, where the first two dimensions of $c(\mathcal{F}_S^l,\mathcal{F}_T^l;r^l)$ dominate the computational load. So to further minimize computational costs, we leverage the global smooth pattern of homography transformations and focus on learning a sparser representation of $\mathbf{w}$ to replace the original dense, pixel-wise one. + +To achieve this, we sparsify $\mathbf{w}$ through a grid-based strategy. We redefine $\mathbf{x} \in G \times G \times 2$ to represent the coordinates of a regular grid on $I_S$ with $G \times G$ being the grid size. Our goal is to estimate a grid-based displacement field $\mathbf{w} \in G \times G \times 2$ and a confidence map $\mathbf{m} \in G \times G \times 1$ that reflects the reliability of each flow estimate. Our grid subsampling strategy is as follows: we use features predicted by the FPN to refine and proportionally scale the grid flow, with the patch matching results from DINOv2 serving as initialization. Under this strategy, the grid sizes from $l = 1$ to $l = 5$ are $\frac{H}{14} \times \frac{W}{14}$ , $\frac{H}{14} \times \frac{W}{14}$ , $\frac{H}{7} \times \frac{W}{7}$ , $\frac{2H}{7} \times \frac{2W}{7}$ , $\frac{4H}{7} \times \frac{4W}{7}$ , respectively. + +Using DINOv2 for initialization is crucial, as it excels at semantic matching, providing a strong starting point for refinement, as shown in our experiments. This implies that the core idea of our method is to refine and scale the patch matching results provided by the foundation model. Therefore, other visual foundation models with strong semantic information could also be considered for this purpose. + +Direct regression vs. Iterative regression. The decoder $(\mathcal{F}_S^l, \mathcal{F}_T^l, \mathrm{up}(\mathbf{w}^{l-1}))$ , which estimates the flow only once at each scale (as shown in Eq. 1), is referred to as direct regression. This is the default regression paradigm in dense matching. However, as the convergence basin shrinks with increasing scale, obtaining an optimal estimation with this approach requires that the estimate from the previous level falls within the convergence basin of the next level. If this condition is not met, the result will be suboptimal, as + +![](images/b81b356d864e94f1dc965d76314be57be015711e7c6d8495f92b3a9fa9b47f4f.jpg) +Figure 2. Left: the overview of GFNet. Using multi-scale features, GFNet regresses the grid flow and confidence map progressively from the coarsest scale to the finest. Right: flow optimization across multiple scales. + +![](images/d6b15f754ce3cfc573ec38f9ef25a82656f9e484dca7f1ef433ec7d3bd8bd3a5.jpg) + +illustrated in the right plot of Figure 2. The precondition for obtaining a reliable estimate at each scale is that $\mathcal{F}_S^l$ and $\mathcal{F}_T^l$ must be well-aligned with $\mathrm{up}(\mathbf{w}^{l - 1})$ . This alignment is relatively easy to achieve for images within the similar modality. But in cases where images have significant representational gaps, it becomes challenging for the decoder to make an accurate estimate in a single pass. To address this issue, we propose an iterative regression strategy to improve the reliability of each grid flow. Our formulation for estimating the grid flow and its confidence map is given by: + +$$ +\mathbf {w} ^ {l, n} = \mathbf {w} ^ {l, n - 1} + \Delta \tilde {\mathbf {w}} ^ {l, n}, +$$ + +$$ +\mathbf {m} ^ {l, n} = \mathbf {m} ^ {l, n - 1} + \Delta \tilde {\mathbf {m}} ^ {l, n}, +$$ + +$$ +\Delta \tilde {\mathbf {w}} ^ {l, n}, \Delta \tilde {\mathbf {m}} ^ {l, n} = \operatorname {d e c o d e r} _ {\theta} ^ {l} \left(\mathcal {F} _ {S} ^ {l}, \mathcal {F} _ {T} ^ {l}, \mathbf {w} ^ {l, n - 1}\right), \tag {3} +$$ + +where $n \in [1, N]$ represents the iteration number, with $N$ total iterations per scale. When $N = 1$ , Eq. 3 reduces to direct regression. All predictions are made at the image scale, and the flow and confidence map are updated between scales as $\mathbf{w}^{l + 1,0}, \mathbf{m}^{l + 1,0} = \mathrm{up}(\mathbf{w}^{l,N}), \mathrm{up}(\mathbf{m}^{l,N})$ . + +Multiscale+iteration is a common way to learn iterative updates, mimicking first-order optimizers. The key difference between prior methods and GFNet lies in the variable being optimized. For example, RAFT [33] optimizes optical flow, IHN [5] and MCNet [49] optimize corner offsets, while GFNet optimizes grid flow. GFNet is more efficient than pixel-based flow for homography and more flexible than corner offsets across resolutions. Besides, the design of flow decoders may vary across different methods. + +Adaptive resolution recurrence. During training, images are consistently resized to a fixed resolution before being fed into the network to maintain a uniform grid shape. To handle varying resolutions, we adopt a simple recurrent strategy similar to [34] during inference: + +$$ +\begin{array}{l} \mathbf {w} _ {1}, \mathbf {m} _ {1} = \mathrm {G F N e t} (I _ {S}, I _ {T}; \mathbf {w} _ {0}), \\ \mathbf {w} _ {0}, \mathbf {m} _ {0} = \operatorname {G F N e t} \left(I _ {S} ^ {\prime}, I _ {T} ^ {\prime}; \mathbf {0}\right), \\ I _ {S} ^ {\prime}, I _ {T} ^ {\prime} = \operatorname {r e s i z e} \left(I _ {S}, I _ {T}\right), \tag {4} \\ \end{array} +$$ + +where $I_S$ and $I_T$ are the original images, $I_S'$ and $I_T'$ are resized to match the training resolution, and GFNet $(\cdot; \mathbf{w})$ denotes GFNet is initialized with $\mathbf{w}$ . The linear combination of $\mathbf{m}_0$ and $\mathbf{m}_1$ is regraded as the final confidence map. For images with resolutions lower than the training resolution, we use the training resolution recurrently, while for higher-resolution images, we apply the recurrence at a higher resolution. Computing $\mathbf{w}_0, \mathbf{m}_0$ spans all scales, whereas the computation of $\mathbf{w}_1, \mathbf{m}_1$ begins at the 1/8 scale, skipping the global initialization at 1/14 scale. + +Besides, a symmetric approach is used during inference. This involves swapping the input sequence of $I_{S}$ and $I_{T}$ to compute the flow for the regular grid on $I_{T}$ . The resulting flows, $\mathbf{w}_{S\rightarrow T}$ and $\mathbf{w}_{T\rightarrow S}$ , along with their corresponding confidence maps $\mathbf{m}_{S\rightarrow T}$ and $\mathbf{m}_{T\rightarrow S}$ , are then combined to form the final matches. From these, $K$ matches are selected by thresholding the confidence maps and sampling according to a uniform distribution rule [14]. Then RANSAC [16] is used to compute homography. + +# 3.4. Loss Function + +For flow estimation, we use $L_{2}$ loss between the ground truth grid flow $\mathbf{w}_{gt}$ and the predicted flow $\mathbf{w}$ at every scale $l \in [1,L]$ and iteration $n \in [1,N]$ : + +$$ +L _ {f l o w} = \sum_ {l = 1} ^ {L} \frac {\mathbf {m} _ {g t} ^ {l}}{G ^ {l} \times G ^ {l}} \sum_ {n = 1} ^ {N} \lambda^ {(N - n)} \rho \left(\left\| \mathbf {w} ^ {l, n} - \mathbf {w} _ {g t} ^ {l} \right\| _ {2}\right), \tag {5} +$$ + +where $G^{l}$ represents the grid size at scale $l$ , and $\lambda \in (0,1)$ assigns higher weights to later iterations, similar to the "learning to optimize" approach [33]. $\rho$ is a robust cost function that mitigates the impact of outliers [2], as employed in RoMa [14]. $\mathbf{m}_{gt} \in \{0,1\}$ is a binary mask that indicates which pixels in $I_{S}$ have correspondences in $I_{T}$ . + +For the confidence map, we learn it using a Binary Cross-Entropy (BCE) loss: + +$$ +L _ {c o n f} = \sum_ {l = 1} ^ {L} \frac {1}{G ^ {l} \times G ^ {l}} \sum_ {n = 1} ^ {N} \lambda^ {(N - n)} \mathbf {B C E} \left(\mathbf {m} ^ {l, n}, \mathbf {m} _ {g t} ^ {l}\right). \tag {6} +$$ + +$L = L_{flow} + \alpha L_{conf}$ is the total loss, where $\alpha$ is a hyperparameter balancing the two terms. All predicted $\mathbf{w}^{l,n}$ are in image space, while $\mathbf{m}^{l,n}$ are in log space. + +![](images/38c9c258c1b67239c190ca326cf2666e59a2e6e2cca83beda84d76c6f10fdc61.jpg) +Figure 3. Left: data generation. Middle: training samples. Right: test samples. In the mask, white for 1, while black for 0. + +# 3.5. Data Generation for Self-supervised Learning + +Composite homography. Following prior works [5-7, 11, 15, 20, 30, 43-45], as shown in Figure 3, we generate synthetic homography datasets for both training and testing. Specifically, we first define a deformation area by selecting four squares at the image's corners, with a deformation ratio $d \in (0, 0.5)$ . Here, $d$ is the ratio between the deformation area height and the image height. From each of these squares, four random points are selected and transformed to the center of the respective squares, yielding a homography matrix. This process is performed independently on each image in the pair, producing two homography matrices, $\mathbf{H}_1$ and $\mathbf{H}_2$ . The images $I_S$ and $I_T$ are then generated by cropping the deformed images, with the centers of the deformation areas serving as the corners of the squares. The homography between $I_S$ and $I_T$ is then computed as $\mathbf{H}_{S \to T} = \mathbf{H}_2\mathbf{H}_1^{-1}$ . Different from prior homography estimation approaches which use only a single homography (i.e., setting $\mathbf{H}_2 = \mathbf{I}_{3 \times 3}$ ), we introduce two homographies and use their composite to generate training data. This modification is crucial for ensuring that our method remains invariant to the input sequence. + +Augment with dynamic occlusions. To enable GFNet to handle real-world scenarios with dynamic occlusions, we follow [35], which augments training data with dynamic objects. Specifically, we treat the images generated in Figure 3 as background. Objects are first added to $I_{S}$ , then transformed with new planar transformations and added to $I_{T}$ as the foreground, simulating moving occlusions in real-world scenarios. In this case, the ground truth confidence map $\mathbf{m}_{gt}$ is also updated, where the area occupied by the object in $I_{S}$ and its reprojection from $I_{T}$ to $I_{S}$ are set to 0. Moving objects are from MSCOCO [21] and augmented training examples are shown in Figure 3. + +# 4. Experiment + +# 4.1. Datasets + +Basic training. Following [34], we use the CityScapes [9] and ADE-20K [46] datasets, both containing images larger than $750 \times 750$ , to generate 33,398 training samples offline, as described in the pipeline in Sec. 3.5. The model + +trained on this split serves as the basic model, which is subsequently fine-tuned for application on multimodal datasets. + +Fine-tuning. Following [5, 6, 43-45], we select GoogleMap and VIS-IR as the multimodal scenarios for evaluation. For GoogleMap, we create 5,000 satellite-map pairs from the Google Static Map API, each with a resolution of $1280 \times 1280$ , sourced from various countries. For VIS-IR, we select 5,000 visible-infrared pairs with a resolution of $640 \times 512$ , captured by UAVs, from the training split provided by [32]. The final training samples for GoogleMap and VIS-IR fine-tuning are generated on-the-fly from the selected aligned image pairs. + +Inference. We test on MSCOCO, VIS-IR, GoogleMap and VIRAT datasets, examples are shown in Figure 3. For VIS-IR, we generate test samples from its test split, and for GoogleMap, test samples are generated from regions not overlapping with the training data. VIS-IR and GoogleMap are used to assess the model's ability to handle photometric inconsistencies caused by modality changes, while MSCOCO [21] serves as a standard unimodal dataset, commonly used in previous works for evaluation. For each of these three datasets, we generate 1,000 test samples. Note that our MSCOCO and GoogleMap test sets have a different resolution setting $(448\times 448)$ from those $(128\times 128)$ used in prior works [5, 6, 49]. Besides, scale information in the GoogleMap test set is also different. + +VIRAT is a dataset featuring dynamic scenes captured in a surveillance context [26], which we use to evaluate performance on dynamic scenes with occlusions. To create the dataset, we utilize the provided object annotations to identify dynamic objects in the videos. Image pairs are generated by cropping patches centered on the dynamic objects and aligning them with the same patches from different timestamps where the dynamic objects are absent. After removing similar samples, 144 test samples are finally collected from various video scenarios. + +# 4.2. Experimental Settings + +Implementation details. We use a batch size of 16 on each GPU, with a learning rate of $2 \cdot 10^{-4}$ for training the basic model, and $1 \cdot 10^{-4}$ for fine-tuning. We use the AdamW optimizer with a weight-decay factor of $10^{-2}$ , and + +Table 1. Comparative results with ${448} \times {448}$ resolution. Bold: best,underline: second. Group A: homography estimation. Group B: image matching. Relative improvement or decrease is shown for GFNet. + +
GroupMethodMSCOCOVIRAT
auc@3auc@5auc@10auc@20auc@3auc@5auc@10auc@20
ARHWF93.0295.8197.998.7746.5753.761.5370.64
MCNet91.2394.7397.3698.6842.4150.7659.9269.83
PRISE88.6492.8396.2397.1441.4449.3659.1269.09
GFNet (ours)97.69 (+5.0%)98.61 (+2.9%)99.3 (+1.4%)99.65 (+0.8%)46.92 (+0.7%)54.47(+1.4%)61.73(+0.3%)70.78(+0.1%)
BSIFT+LightGlue89.4393.4896.6498.2738.2547.1557.6768.14
LoFTR94.1996.5198.2599.1242.2950.6159.5469.26
Efficient LoFTR95.6597.3998.6999.3443.3451.1760.1369.83
RoMa96.0197.6198.899.447.554.3961.9170.88
GFNet (ours)97.69 (+1.7%)98.61 (+1.0%)99.3 (+0.5%)99.65 (+0.2%)46.92 (-1.2%)54.47(+0.1%)61.73(-0.2%)70.78(-0.1%)
GroupMethodVIS-IRGoogleMap
auc@3auc@5auc@10auc@20auc@3auc@5auc@10auc@20
ARHWF18.1632.0554.4872.8418.3237.4761.0976.43
MCNet16.130.5951.5171.8216.3135.2859.5175.63
PRISE13.2824.248.666.611.4131.6854.7870.54
GFNet (ours)21.28(+17.1%)35.72(+11.4%)58.44(+7.2%)76.23(+4.6%)51.44(+180.7%)66.34(+77.0%)80.62(+31.9%)89.66(+17.3%)
BSIFT+LightGlue2.568.9123.3339.99----
LoFTR10.1722.5145.9365.844.9913.8732.2751.24
Efficient LoFTR13.2826.3249.4369.15.3714.4933.652.73
RoMa25.7439.7962.4980.1445.2962.1878.6388.23
GFNet (ours)21.28(-17.3%)35.72(-10.2%)58.44(-6.4%)76.23(-4.8%)51.44(+13.5%)66.34(+6.6%)80.62(+2.5%)89.66(+1.6%)
Group AGroup BGFNet (ours) w/o iterationGFNet (ours) w/ iteration
RHWFMCNetPRISESIFT+LightGlueLoFTREfficient LoFTRRoMa
Learnable parameters1.29M0.85M19.24M11.88M11.56M16.02M111.28M3.86M
MACs23.43G4.56G55.25G38.51G249.72G179.81G2503.19G1657.62G
Runtime79.70ms28.11ms204.67ms390.11ms42.68ms31.29ms212.97ms118.90ms
+ +use CosineAnnealing to schedule the learning rate. Both the basic training and fine-tuning stages use 2,000,000 training samples drawn from their respective datasets. Each epoch processes 25,000 samples, resulting in a total of 80 epochs. We train at a resolution of $448 \times 448$ , with the higher resolution in the recurrence set to $560 \times 560$ . We test MSCOCO and VIRAT with the basic model, while VIS-IR and GoogleMap with the fine-tuned models. Trained on 2 24GB RTX 3090 GPUs; Xeon Silver 4210R CPU. + +For data generation, we set $d = 0.3$ following prior work, and use composite homography during training only. The model adopts DINOv2-large with 4 cross-attention layers, and each decoder uses 8 stacked depthwise conv blocks as in [13, 14]. The local radius from coarse to fine is [7,6,4,2,0]. We set $N = 2$ iterations (only for multimodal cases) to balance performance and efficiency. For loss, we use $\lambda = 0.85$ , $\alpha = 0.01$ . For estimation, $K = 5,000$ matches are selected, and RANSAC is applied using the default cv2.findHomography setting. + +Metrics. We evaluate accuracy using the Average Corner Error (ACE, truncated at 70 pixels) and the AUC of ACE at thresholds of 3, 5, 10, and 20 pixels [5, 6, 29]. Efficiency is measured by runtime and Multiply-Accumulate Operations (MACs). + +# 4.3. Comparative Results + +Baselines. Comparative methods are divided into two groups: homography estimation methods (Group A) and image matching methods (Group B). In Group A, + +we compare with RHWF [6], PRISE [44], and MCNet [49]. RHWF and MCNet are 4-point-based methods, whereas PRISE is a matrix-based method, initialized with MHN [15]. In Group B, we compare with the sparse matcher SIFT+LightGlue [22], the semi-dense matchers LoFTR [31] and Efficient LoFTR [37], and the dense matcher RoMa [14]. For a fair comparison, all methods in Group A are trained under the same settings as ours. For methods in Group B (excluding SIFT+LightGlue), we fine-tune their official outdoor models using our training data. During evaluation, we use RANSAC with consistent settings to compute the homography, limiting correspondences to 2,048 for sparse and semi-dense matchers. + +Evaluation on MSCOCO. As shown in Table 1, GFNet outperforms all comparative methods on MSCOCO. Compared to methods in Group A, GFNet's ability to train at higher resolutions, beyond the $128 \times 128$ limitation of Group A methods, leads to improved accuracy. Compared to methods in Group B, GFNet benefits from the accuracy of the dense matching framework, while the grid-based strategy is highly effective for homography estimation. + +Evaluation on multimodal datasets. GFNet demonstrates significant improvements over SOTA homography estimation methods, with a $17.1\%$ auc@3 increase on VIS-IR and a $1.8 \times$ auc@3 improvement on GoogleMap. Beyond the advantage of high-resolution training, this improvement is largely due to the integration of DINOv2, which excels in cross-domain feature matching, boosting performance in multimodal scenarios. + +![](images/1cf0fb9c777711694a1ba6d6a80f5a4132056f3640a75f7fdf6ff5aec1644269.jpg) +Figure 4. Visualization results on GoogleMap and VIS-IR. Top: homography estimation results. The green polygon is the ground-truth location of $I_S$ on $I_T$ , while the red one is the predicted location. The right plot shows ACE at different resolutions on GoogleMap. Bottom: image matching results. We randomly visualize 50 predicted matches. Matches with reprojection error lower than 3 pixels are drawn in green, otherwise red. Only keypoints will be displayed when no matches are predicted. + +![](images/0e5537465a9c061fce5882daa65fd6faf1ef31758014c64b74c583d40ebdb84e.jpg) +Figure 5. Visualization of inlier information in VIRAT. Darker indicates lower values, and $1 - |I_{T\rightarrow S} - I_S|$ is GT. While other methods recognize occlusion implicitly, GFNet handles it explicitly. + +GFNet outperforms both sparse and semi-dense matchers on the two multimodal datasets. As shown in Figure 4, SIFT+LightGlue struggles with large modality gaps, while LoFTR-based methods yield low accuracy. Compared to RoMa, GFNet achieves a $13.5\%$ gain in AUC@3 on GoogleMap but performs worse on VIS-IR, likely due to low-light image degradation where RoMa's high-dimensional features offer better robustness. + +Evaluation on datasets with dynamic occlusions. Generally, image matching methods are trained on the 3D datasets to handle two- or multi-view matching, which gives them an inherent ability to address dynamic occlusion. Thus here we mainly discuss how homography estimation methods, which only involve planar information, learn to manage dynamic occlusion. As shown in Figure 5, RHWF and MCNet aggregate matching information to estimate homography, with occluded areas being implicitly filtered during this process. PRISE aligns the feature maps of two images to + +find the homography, also learning occlusion implicitly. In contrast, GFNet explicitly predicts a mask to identify occlusion, providing more precise occlusion information, which results in better performance on VIRAT compared to methods that implicitly predict occlusion (see Table 1). + +Computational analysis. From the bottom table in Table 1, we observe that although GFNet is under the framework of dense matching, it reduces the MACs by $33.7\%$ without iteration and by $31.7\%$ with iteration compared to the SOTA dense matcher RoMa. We attribute it to our smaller network architecture and the grid-based strategy. + +Robustness to resolution. In addition to the $448 \times 448$ GoogleMap test set presented in Table 1, we create two more test sets, each containing 1000 image pairs, with resolutions of $224 \times 224$ and $672 \times 672$ . The results are presented in Figure 4. Since homography estimation methods in Group A only accept $128 \times 128$ inputs, errors are calculated at this scale and rescaled to the original resolu + +Table 2. Grid size ablation. MSCOCO: w/o iteration. GoogleMap: w/ iteration. + +
DatasetModelDINOv2 grid size (l=1)FPN grid size (from l=2 to l=5)Training costs on 1 GPURuntime (ms) ↓MACE (pixel) ↓
MSCOCOHalf1/141/28, 2/28, 4/28, 8/28bs=12, 10.9GB, 16h5m115.30.068
Full1/8, 1/4, 1/2, 1bs=12, 22.3GB, 22h23m134.20.083
Ours1/14, 2/14, 4/14, 8/14bs=12, 14.0GB, 17h18m118.90.063
GoogleMapHalf1/141/28, 2/28, 4/28, 8/28bs=7, 8.3GB, 24h2m117.93.31
Full1/8, 1/4, 1/2, 1bs=7, 23.6GB, 33h42m146.34.02
Ours1/14, 2/14, 4/14, 8/14bs=7, 12.0GB, 25h20m124.62.57
+ +Table 3. Ablation on the iterative strategy. + +
NMSCOCOGoogleMap
MACE (pixel) ↓Runtime (ms) ↓MACE (pixel) ↓Runtime (ms) ↓
10.063118.93.01109.6
20.135134.22.57124.6
40.207163.32.62153.6
+ +Table 4. Ablation on the network architecture and evaluation protocol. In w/o DINOv2, we use a trainable pre-trained ResNet50. + +
w/o DINOv2w/o Cross-Att.w/o symmetricw/o recurrenceBaseline
MSCOCOMACEpixel)↓0.0560.0710.0690.0480.063
Runtime(ms)↓91.8117.2119.370.8118.9
GoogleMapMACEpixel)↓8.352.972.953.192.57
Runtime(ms)↓99.6121.5119.070.5124.6
+ +tion, leading to a near-linear increase in error as resolution grows. Moreover, the resizing process leads to loss of image details, which can further amplify the error beyond the expected near-linear growth. In contrast, GFNet does not impose input resolution constraints, making it more robust to resolution changes. + +# 4.4. Ablation Studies + +Ablation experiments are conducted on MSCOCO (natural images) and GoogleMap (multimodal images). We mainly ablate our grid-based strategy, network architecture, iterative strategy, evaluation strategy, and data generation. + +Grid size. We fix the initial grid size based on DINOv2 and ablate the following 4 scales (Table 2). Grid-based flow reduces costs without sacrificing accuracy, validating that pixel-based flow is redundant for homography. However, too small a grid may slightly decrease accuracy. Our subsampling strategy—initial patch matching with DINOv2 followed by refinement and scaling—offers an intuitive balance between accuracy and efficiency. + +Iteration. Results in Table 3 demonstrate that iteration is helpful for multimodal data but not for natural images. We attribute this to the challenge of precisely aligning the same physical positions in multimodal image pairs due to photometric inconsistencies, making only approximate alignment possible. The iterative strategy helps learn the process of optimization by mimicking this approximate alignment. However, for natural images where exact alignment is achievable, the iterative approach, which is designed for approximate alignment, can reduce accuracy. Setting $N = 2$ strikes a balance between accuracy and efficiency. + +![](images/f16000269abc9bfb1d1f654faacf03808489e8fc33c95aea80b4e6d565b84afa.jpg) +Figure 6. Impact of data generation during training. + +Data generation. As illustrated in Figure 6, if we only apply the deformation to $I_{S}$ during training (w/o dynamic occlusions), the network tends to overfit to the input sequence $(I_S, I_T)$ and fails to work on the reversed sequence $(I_T, I_S)$ . However, by incorporating the composition homography during training, the network learns to generalize to both input sequences. + +Network architecture. As shown in Table 4, replacing DINOv2 initialization with the $1/16$ feature map from ResNet50 leads to a significant performance drop on GoogleMap. This highlights the effectiveness of DINOv2, which excels in semantic matching, as a reliable choice for grid flow initialization in multimodal scenarios. Regarding cross attention layers, it provides a stable accuracy improvement on MSCOCO and GoogleMap. + +Evaluation protocol. As shown in Table 4, symmetry and adaptive recurrence have a limited impact on MSCOCO, as the matches predicted in the initial stage are already sufficiently accurate. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 25932-25941, 2024. 1, 2, 3, 4, 5, 6 \ No newline at end of file diff --git a/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/images.zip b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..0ed384aabbd1bb923f3eab997202a8d1a00bc13a --- /dev/null +++ b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5aa9a7ff05a5421e2aad13398cd80d2a8a1dfbf36467396aaab8cf3b2924806b +size 685389 diff --git a/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/layout.json b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f5e02cb1e154e4e6d8f4e2541196f5021c5376b0 --- /dev/null +++ b/adaptingdensematchingforhomographyestimationwithgridbasedacceleration/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:25300e7b7da09adb1066f10704dcf783999969504c18aa3bf931e37d15e53a78 +size 423315 diff --git a/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_content_list.json b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c8a57361ef61d77252945735bfc6e8b9f8f586e6 --- /dev/null +++ b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ce2483bc750819198c50767510e7cc26aae87bb361ec2381524d20053043fc1f +size 94349 diff --git a/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_model.json b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f0a5bba91dc915345467b09b95d8abc9bbd46f13 --- /dev/null +++ b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:50a176f8ad8b14fbea8f016d55e6b63fe9b5d1d9a55376e09896f3336f1a6097 +size 116506 diff --git a/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_origin.pdf b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0e1234e29d2378e40759d9b289eaea74c188c5bc --- /dev/null +++ b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/e29ca394-45e6-4bf5-b8ea-58a74dbe24fa_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f3df26c69ae14512d82cfe26bdfd573df8a709cbed6e7cc88db4d3f9518f15d2 +size 2848816 diff --git a/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/full.md b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d3198434b6440a0be203ae46ec5d57696a8c8540 --- /dev/null +++ b/addattributiondrivendataaugmentationframeworkforboostingimagesuperresolution/full.md @@ -0,0 +1,470 @@ +# ADD: Attribution-Driven Data Augmentation Framework for Boosting Image Super-Resolution + +Ze-Yu Mi Yu-Bin Yang* + +State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China + +mizeyu@smail.nju.edu.cn yangyubin@nju.edu.cn + +# Abstract + +Data augmentation (DA) stands out as a powerful technique to enhance the generalization capabilities of deep neural networks across diverse tasks. However, in low-level vision tasks, DA remains rudimentary (i.e., vanilla DA), facing a critical bottleneck due to information loss. In this paper, we introduce a novel Calibrated Attribution Maps (CAM) to generate saliency masks, followed by two saliency-based DA methods—Attribution-Driven Data augmentation (ADD) and $\text{ADD+}$ —designed to address this issue. CAM leverages integrated gradients and incorporates two key innovations: a global feature detector and calibrated integrated gradients. Based on CAM and the proposed methods, we have two new insights for low-level vision tasks: (1) increasing pixel diversity, as seen in vanilla DA, can improve performance, and (2) focusing on salient features while minimizing the impact of irrelevant pixels, as seen in saliency-based DA, more effectively enhances model performance. Additionally, we find and highlight the key guiding principle for designing saliency-based DA: a wider spectrum of degradation patterns. Extensive experiments demonstrate the compatibility and consistency of our method, as well as the significant performance improvement across various SR tasks and networks. Our code is available at https://github.com/mizeyu/ADD. + +# 1. Introduction + +Data augmentation (DA) is a fundamental technique for improving the generalization ability of deep neural networks (DNNs). In high-level vision tasks such as image recognition and semantic segmentation, early vanilla approaches like Mixup [35] and CutMix [34] laid the groundwork. Recently, saliency-based DA methods [13, 14, 18, 28, 29] have gained considerable attention, demonstrating superior performance over vanilla counterparts in high-level vision tasks. + +However, applying saliency-based DA techniques directly to low-level vision tasks remains challenging due to a mismatch in task objectives, inconsistent feature requirements, differences in data characteristics, and inappropriate method designs (see Appendix for further details). These challenges have led to the continued use of vanilla DA techniques, such as rotation, flipping [27], Mixup [8], and Cutblur [33], in low-level vision tasks. + +In low-level vision tasks [2, 3, 5-7, 10, 12, 15, 16, 19, 25, 31, 36, 40], the use of vanilla DA methods [8, 20, 27, 32, 33] is hindered by the issue of information loss, which can severely degrade the quality of the reconstructed images. As shown in Fig. 1, vanilla DA techniques often generate images with flat regions and simplistic edges (e.g., a3), which provide minimal support for model learning in tasks like super-resolution (SR), leading to significant loss of crucial information. In contrast, saliency-based DA methods [13, 14, 18, 28, 29] target information-rich regions (e.g., b3), which facilitate better reconstruction performance. The phase spectrum analysis in Fig. 1 (c, d, e) further illustrates that augmented images incorporating saliency information (b3) retain more critical details, alleviating the problem of information loss. This observation motivates the need for new DA techniques that focus on more meaningful regions in low-level tasks. + +Existing saliency methods, however, are often prone to background noise and struggle to accurately capture important features. To address these limitations, we propose a new attribution method, the Calibrated Attribution Maps (CAM), which is capable of identifying important features without being influenced by background noise. CAM builds upon LAM [9] and integrated gradients (IG) [11, 26], introducing two key innovations: a global feature detector and calibrated integrated gradients. Using CAM, we introduce Attribution-Driven Data augmentation (ADD) techniques, and its enhanced version $\mathrm{ADD+}$ , which represent the first attempt to explore saliency in DA from an attribution analysis perspective. + +Through CAM, we derive two key insights for low-level vision tasks: (1) incorporating a broader range of pixels, + +![](images/9cfe4b07aef406f7a6bdb632db291bd7f959082c28a745dd69279a0b10dacd6a.jpg) +a1. Input Image + +![](images/82b42d05c83757c35ee88269e2fc72ef657f1e54b232c8de1aa63008149e0b42.jpg) +a2. Vanilla DA + +![](images/e29336ef1308576ee9111fb70e67a41bc17c845d203b3e55e3335b07c9993406.jpg) +a3. Aug. Image of (a2) + +![](images/a844a318a7ef23c68787b56b64d2d4a4fed7fc5099662a225f6d378a1bff8d22.jpg) +c. Phase Spec. of (a3) + +![](images/c14b315881d6e50a7e1126fb8a88a351dfffc2332a3e779f812b22a3bd62d9fa.jpg) + +![](images/1050ae2b62ee86c0b84c62947421b066973762ce3380424b0b891935a6c81063.jpg) +b1. Saliency Image + +![](images/82d1761302c81b97ff9877bbe53989a67e5674e89bcc3f489a7b05a4fbdefd07.jpg) +b2. Saliency-based DA + +![](images/e372be01e9a42d5c42d638fea638a6ea2afed3aeddd766be787a72305c27a556.jpg) +b3. Aug. Image of (b2) +Figure 1. Motivation: Provide more meaningful information for vanilla DA to address the critical bottleneck of information loss. (a1) Input image. (a2) Vanilla DA randomly selects an area. (a3) Augmented image of vanilla DA. (b1) Saliency map of the input image. (b2) Select the maximum saliency region. (b3) Augmented image of saliency-based DA. (c) Phase spectrum of augmented image (a3). (d) Phase spectrum of augmented image (b3). (e) Residual map calculated between (c) and (d). + +![](images/2f586e6390cb193d68c725a516e757c3d711c1c47a297699c96cc4ee831642f5.jpg) +d. Phase Spec. of (b3) + +![](images/3e3804e93aaedbdab3982e38b538a2ea383249b7db05abb0b826828c2dd3d783.jpg) +e. Residual Map of d & c + +as in vanilla DA, can improve model performance, and (2) focusing on more influential pixels—using saliency information—while minimizing the inclusion of irrelevant pixels, as in saliency-based DA, results in more effective enhancement. This insight explains why ADD, which utilizes saliency to prioritize important pixels, alleviates information loss and outperforms traditional vanilla DA methods, which indiscriminately incorporate additional pixels. + +Furthermore, to design effective saliency-based DA methods in low-level vision tasks, we propose the key guiding principle: a wider spectrum of degradation patterns. Specifically, DA methods should: (1) prefer maintaining continuous boundaries to avoid boundary effects, and (2) prioritize diverse augmentation strategies over single augmented images to provide richer learning signals. + +# Contributions: + +- We introduce CAM, a robust attribution method that accurately identifies important features while mitigating background noise, improving saliency map generation in low-level vision tasks. +- We propose ADD, a novel attribution-driven DA method, which overcomes the limitations of vanilla DA and significantly reduces information loss in low-level tasks. +- We provide new insights and guiding principles for saliency-based DA in low-level vision, offering a framework for improving model performance. +- Our extensive experiments validate the effectiveness of our methods, demonstrating significant performance gains across a range of super-resolution tasks. + +# 2. Related Works + +# 2.1. Image Super-Resolution + +Image super-resolution (SR) is a key technology in computer vision [21, 39]. Since SRCNN [5], numerous CNN-based methods have emerged, incorporating residual [12, + +36] and dense blocks [25, 31, 40], as well as attention mechanisms [2, 19]. More recently, transformer-based SR models [6, 7, 16] have achieved state-of-the-art performance. + +# 2.2. Data Augmentation in Vision Tasks + +Traditional data augmentation (DA) methods in high-level vision include geometric and intensity transformations [4, 41], as well as mixed-based techniques [34, 35]. Recently, saliency-based DA has gained popularity, focusing on preserving critical regions [13, 14, 18, 28, 29]. In low-level vision, DA remains largely limited to conventional approaches [27]. Some works explore Mixup [8] and Cutblur [33], with CutMIB extending them to light-field SR [32]. + +# 3. Methods + +In this section, we first discuss the key challenges and motivations for incorporating saliency-based data augmentation (DA) in low-level vision tasks in Sec. 3.1. Then, in Sec. 3.2, we briefly review prior attribution methods, which serve as the foundation for our proposed approach. Next, we introduce the concept of Calibrated Attribution Maps (CAM) in Sec. 3.3, followed by the presentation of saliency-based DA techniques, ADD and $\mathrm{ADD + }$ , in Sec. 3.4. + +# 3.1. Integrating Saliency into Low-Level DA + +Why introduce saliency into low-level vanilla DA? As discussed in Sec. 1, leveraging saliency provides valuable insights into the most important image features, addressing the problem of information loss. This motivates the integration of saliency information into data augmentation strategies for low-level vision tasks, where preserving critical image details is essential for enhancing performance. + +How to introduce saliency into low-level vanilla DA? Traditional saliency methods, such as LAM and integrated gradient (IG), are limited by the challenge of distinguishing + +relevant features from irrelevant background noise. To overcome this limitation, we build upon LAM and IG and introduce a novel approach, CAM, which incorporates two new components: a global feature detector and a calibrated integrated gradient. These innovations, detailed in Sec. 3.3, effectively address the noise issue and improve the accuracy of saliency estimation in low-level tasks. + +# 3.2. Overview of Vanilla Attribution Methods + +Before presenting our method, we first provide a brief overview of existing attribution methods that form the foundation for our approach [1, 11, 22-24]. Let $\mathcal{I} \in \mathbb{R}^d$ be the input image, and let $\mathcal{C}: \mathbb{R}^d \mapsto \mathbb{R}$ represent a classification network. Gradient-based methods, such as Integrated Gradients (IG), quantify the impact of changes in the input dimensions by computing the gradient of the output with respect to the input image: + +$$ +\mathrm {I G} _ {\mathcal {C}} \mathcal {I} = (\mathcal {I} - \mathcal {I} ^ {\prime}) \int_ {0} ^ {1} \frac {\partial \mathcal {C} (\mathcal {I} ^ {\prime} + \alpha (\mathcal {I} - \mathcal {I} ^ {\prime}))}{\partial \mathcal {I}} d \alpha , (1) +$$ + +where $\mathcal{I}'$ is a baseline image (often a blank image in high-level tasks) and $\alpha$ is a continuous parameter that interpolates between the baseline and the target input. + +In the context of image SR, Local Attribution Maps (LAM) convert the original baseline image $\mathcal{I}'$ to a blurred version $\mathcal{I}' = \omega(\sigma) \otimes \mathcal{I}$ , where $\omega(\sigma)$ is a Gaussian blur kernel with width $\sigma$ , and $\otimes$ represents convolution. Besides, LAM adapts IG for SR tasks by using a gradient detection method $D$ that focuses on local feature detection in SR networks. However, LAM suffers from the limitation of irrelevant gradient accumulations, which can easily lead to a focus on irrelevant areas. To address this issue, we introduce CAM to eliminate irrelevant area interference. + +# 3.3. Calibrated Attribution Maps (CAM) + +In this section, we introduce the concept of Calibrated Attribution Maps (CAM) as shown in Fig. 2 (a), which is inspired by the IG [26] and LAM [9]. The goal of CAM is to provide a more accurate and reliable estimation of feature importance, particularly in the context of image SR tasks. + +Global Feature Detector (GD). Given an input image pair $\mathcal{I}^{LR}$ (low resolution) and $\mathcal{I}^{HR}$ (high resolution), we aim to learn a mapping function $\mathcal{F}$ that produces the super-resolved image $\mathcal{I}^{SR}$ . Traditional attribution methods such as LAM detect local pixel-wise gradients, which can easily lead to saturation effects, as shown in Fig. 2 (d). To alleviate this problem, we introduce a Global Feature Detector (GD), which aims to capture global features in the image by applying convolutional filters such as the Sobel filter. This approach smoothes the detected gradients and enhances the robustness of saliency maps. To achieve a more robust global feature representation, the GD operation is defined + +as: + +$$ +\boldsymbol {G} \boldsymbol {D} (\mathcal {I} ^ {S R}) = \| \boldsymbol {S o b e l} _ {x y} (\mathcal {I} ^ {S R}) \| _ {2}, \tag {2} +$$ + +where $Sobel_{xy}$ denotes the Sobel filter applied in both the $x$ and $y$ directions to capture edge features in the image. This approach smooths the gradients and reduces the saturation problem, as demonstrated in Fig. 2 (d) & (g). + +To analyze the attributes of the SR network, given the current input image $\mathcal{I}$ , a baseline image $\mathcal{I}'$ satisfies that $\mathcal{F}(\mathcal{I}')$ absent certain features existed in $\mathcal{F}(\mathcal{I})$ is also needed. Accordingly, feature scalar $GD(\mathcal{F}(\mathcal{I}))$ will show significant numerical advantage over $GD(\mathcal{F}(\mathcal{I}'))$ . We calculate the path-integrated gradient along the gradually changing path from $\mathcal{I}'$ to $\mathcal{I}$ and obtain the attribution map for $GD(\mathcal{F}(\mathcal{I}))$ . Then, the $i$ th dimension of the calibrated attribution maps is defined as follows: + +$$ +\phi_ {i} ^ {C A M} (\mathcal {F}, \boldsymbol {G D}) = \left(\mathcal {I} _ {i} - \mathcal {I} _ {i} ^ {\prime}\right) \int_ {a = 0} ^ {1} \frac {\partial \boldsymbol {G D} \left(\boldsymbol {F} \left(\mathcal {I} ^ {\prime} + \alpha \left(\mathcal {I} - \mathcal {I} ^ {\prime}\right)\right)\right)}{\partial \mathcal {I} _ {i}} d \alpha . \tag {3} +$$ + +Calibrated Path Integrated Gradient (CPIG). We now introduce the Calibrated Path Integrated Gradient (CPIG), which can efficiently and effectively analyze global attribution. In SR tasks, the high-frequency components (e.g., edges and textures) contribute much more than the low-frequency components (e.g., color and brightness) to the network performance. In this work, we obtain baseline inputs by eliminating high-frequency components, setting them as the blurred version of LR images denoted as $\mathcal{I}' = \omega(\sigma) \otimes \mathcal{I}$ . Here, $\omega(\sigma)$ represents the Gaussian blur kernel parameterized by the kernel width $\sigma$ and $\otimes$ is the convolution operation. Following previous works, we construct a smooth transformation from $\mathcal{I}'$ to $\mathcal{I}$ , which is expressed as $\gamma(a) = \omega(\sigma - \alpha\sigma) \otimes \mathcal{I}$ . Accordingly, we have $\gamma(0) = \mathcal{I}'$ and $\gamma(1) = \mathcal{I}$ . The gradients at points are sampled in $k$ steps along the path and the gradient of the $i$ -th step is: + +$$ +\phi_ {i} ^ {C A M} (\mathcal {F}, \boldsymbol {G D}, \gamma) = \tag {4} +$$ + +$$ +\left(\gamma \left(\frac {i}{k}\right) - \gamma \left(\frac {i + 1}{k}\right)\right) \times \frac {\partial G D \left(\mathcal {F} \left(\gamma \left(\frac {i}{k}\right)\right)\right)}{\partial \gamma \left(\frac {i}{k}\right)} d \alpha . +$$ + +To improve the stability and accuracy of the path-integrated gradients, we introduce a calibration step that limits the deviation at each step and ensures that the gradients focus on the most relevant features of the image. This is achieved by limiting the range of each step to fluctuate around a central value, $a_{\mathrm{min}} = \max (a - d,0.0)$ and $a_{\mathrm{max}} = \min (a + d,1.0)$ . + +Attribution analysis progressively adjusts the value of each pixel to make the interpolated image $\mathcal{I}'$ gradually approach the target image $\mathcal{I}$ , and the overall loss function can be defined as: $\mathcal{L}_{OA} = \| \mathcal{I}' - \mathcal{I}\|_1$ . Correspondingly, the target loss function for approximating the target image with the interpolation image in step $i$ is: $\mathcal{L}_{TG} = \| \mathcal{I}' - \mathcal{I}\|_1 \times (1 - \frac{i}{k})$ . Then, the difference between the actual current interpolated image and the target image can be represented by the current loss: $\mathcal{L}_{CU} = \| \gamma (\frac{i}{k}) - \mathcal{I}\|_1$ . + +![](images/936fbdbf84c83a2257bd1936f5f8fbe9399dc7195c449c4c14210c65bec2dda8.jpg) +Figure 2. The illustration of CAM, the ADD framework, and the CAM-LAM comparison. (a) Illustration of CAM. (b) Process of ADD and $\mathrm{ADD + }$ . (c) Comparison of global attribution analysis between CAM and LAM, with red boxes highlighting regions where gradients are presented after global attribution analysis. + +To further prevent instability caused by large gradient changes and to maintain the smoothness of the path, we select only those pixels with gradient magnitudes below a predefined threshold $T_{f}$ for updating: + +$$ +T _ {f} = \operatorname {s o r t e d} \left(\left| \phi_ {i} ^ {C A M} \right|\right) _ {\left[ p _ {f} \cdot \text {n u m . p i x e l s} \right]} ^ {\min }, +$$ + +$$ +M _ {f} = \left\{ \begin{array}{l l} 1, & \text {i f} | \phi_ {i} ^ {C A M} | \leq T _ {f}, \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {5} +$$ + +where $M_{f}$ is a binary mask representing the pixels that need to be calibrated. Based on the difference between the current loss $\mathcal{L}_{CU}$ and the target loss $\mathcal{L}_{TG}$ , combined with the mask threshold loss function $\mathcal{L}_{MF}$ between the pixels to be corrected and the target image, we generate calibration factor $\delta$ to control the step size of each update: + +$$ +\mathcal {L} _ {M F} = \left\| M _ {f} \odot (\gamma (a) - \gamma \left(a _ {\max }\right)) \right\| _ {1}, +$$ + +$$ +\delta = \frac {\mathcal {L} _ {C U} - \mathcal {L} _ {T G}}{\mathcal {L} _ {M F}}. \tag {6} +$$ + +With the calibration factor $\delta$ , the calibrated interpolation image $\gamma_{c}(a)$ can be formulated as: $\gamma_{c}(a) = \gamma (a + \delta \times (a_{\mathrm{max}} - a))$ . Accordingly, the calibrated gradient $\psi_i^{CAM}$ in step $i$ can be updated by the calibrated interpolation image $\gamma_{c}(a)$ and represented as: $\psi_i^{CAM} = \phi_i^{CAM} + (\gamma_c(a) - \gamma (a))\times$ $\phi_i^{CAM}$ . Finally, we obtain the approximate integrated gra + +dient by summing up the calibrated gradients of $k$ steps: + +$$ +\mathcal {I} _ {s} ^ {L R} = \sum_ {i = 0} ^ {k} \psi_ {i} ^ {C A M}. \tag {7} +$$ + +As shown in the Fig. 2 (f) and (i), our calibrated attribution maps focus on the most important edge texture information compared to LAM, and are not affected by the noise of flat areas and background. + +# 3.4. Attribution-Driven Data Augmentation (ADD) + +In this section, as depicted in Fig. 2 (b), we introduce the specific process of the proposed ADD and the enhanced version $\mathrm{ADD + }$ . Let $\mathcal{I}^{LR}\in R^{H\times W\times C}$ be the input LR image, and the corresponding saliency map $\mathcal{I}_s^{LR}$ can be obtained with Eq. (7). To accurately obtain the region of maximum saliency, we follow the principle (1) of continuous boundaries in Sec. 3.5 and select the maximum saliency pixels with a proportion of $p$ and obtain the corresponding irregularly shaped patch: + +$$ +T _ {p} = \operatorname {s o r t e d} \left(\mathcal {I} _ {s} ^ {L R}\right) _ {\lceil p \cdot \text {n u m . p i x e l s} \rceil} ^ {m a x}, +$$ + +$$ +M (i, j) = \left\{ \begin{array}{l l} 1, & \text {i f} \mathcal {I} _ {s} ^ {L R} (i, j) \geq T _ {p}, \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {8} +$$ + +where the $T_{p}$ represents the maximum saliency value of the top $p$ proportion in the $\mathcal{I}_s^{LR}$ and the $M\in \{0,1\}^{H\times W}$ is a + +binary mask indicating the area to be cut. Following the second principle (2) of diverse augmented images in Sec. 3.5, we use the mask $M$ to cut the patch to the corresponding position on another image and combine it with different DA strategies. Given the LR-HR image pair $\{\mathcal{I}_i^{LR},\mathcal{I}_i^{HR}\}$ and the corresponding binary mask $M$ , the augmentation process is explained below. + +ADD. We first adopt a mixed strategy to generate augmented input images to enable the model to learn richer and more complex degradation patterns. We cut the patch and mix it with the patch from another LR-HR image pair $\{\mathcal{I}_j^{LR},\mathcal{I}_j^{HR}\}$ and generate new training samples: + +$$ +P _ {m i x} ^ {L R} = \lambda \times M \odot \mathcal {I} _ {i} ^ {L R} + (1 - \lambda) \times M \odot \mathcal {I} _ {j} ^ {L R}, \tag {9} +$$ + +$$ +P _ {m i x} ^ {H R} = \lambda \times M \odot \mathcal {I} _ {i} ^ {H R} + (1 - \lambda) \times M \odot \mathcal {I} _ {j} ^ {H R}, +$$ + +$$ +\mathcal {I} _ {i} ^ {L R} = P _ {m i x} ^ {L R} + (1 - M) \odot \mathcal {I} _ {j} ^ {L R}, \tag {10} +$$ + +$$ +\mathcal {I} _ {i} ^ {H R} = P _ {m i x} ^ {H R} + (1 - M) \odot \mathcal {I} _ {j} ^ {H R}. +$$ + +Then we adopt an intensity strategy to make the model learn how and where to augment the input images. We cut the patch $P_{i}^{LR}$ by $M \odot \mathcal{I}_{i}^{LR}$ and upsample it by scale $s$ with bicubic kernel, get $P_{i}^{LR(s \times \uparrow)}$ . The HR patch can be generated similarly and we can get augmented samples as: + +$$ +\hat {\mathcal {I}} _ {i} ^ {L R \rightarrow H R} = P _ {i} ^ {L R (s \times \uparrow)} + (\mathbf {1} - M) \odot \mathcal {I} _ {i} ^ {H R}, \tag {11} +$$ + +$$ +\hat {\mathcal {I}} _ {i} ^ {H R \rightarrow L R} = P _ {i} ^ {H R (s \times \downarrow)} + (\mathbf {1} - M) \odot \mathcal {I} _ {i} ^ {L R}. +$$ + +$\mathbf{ADD}+$ . To validate the efficacy of saliency in mixed enhancement and surpass the performance limits, we proposed the method with an enhanced version. We additionally generate a pair of new training samples with another LR-HR image pair $\{\mathcal{I}_j^{LR},\mathcal{I}_j^{HR}\}$ : + +$$ +\mathcal {I} _ {i} ^ {L R} = M \odot \mathcal {I} _ {i} ^ {L R} + (1 - M) \odot \mathcal {I} _ {j} ^ {L R}, \tag {12} +$$ + +$$ +\mathcal {I} _ {i} ^ {H R} = M \odot \mathcal {I} _ {i} ^ {H R} + (1 - M) \odot \mathcal {I} _ {j} ^ {H R}, +$$ + +where $\odot$ denotes the element-wise Hadamard product operation. Following previous work [33], in each training iteration, using $\mathrm{ADD + }$ , each above augmentation method and traditional augmentation method (e.g., color, channel) have a probability $p$ of being applied by the model to enhance the input image. + +# 3.5. Discussions + +Incorporate saliency into vanilla DA. Incorporating saliency into existing vanilla DA methods revolves around two key aspects: patch cutting and pasting. Consequently, two fundamental questions arise: (1) What manner should be used for segmenting the source image? (2) Where should the cut patches be pasted? To address these questions, we + +conduct a comprehensive analysis and reveal the key principle: a wider spectrum of degradation patterns. Specifically, it includes: (1) continuous boundaries rather than abrupt boundaries, and (2) diverse augmented images over single augmented images. The results and analysis of saliency in DA methods are presented in Tab. 1 and further elaborated in the experiments (see Sec. 4.4). + +Table 1. Quantitative PSNR comparison of various saliency incorporation methods in super-resolution. $Patch_{n \times n}$ denotes image division into $n \times n$ patches. $X\mathcal{Q}Y$ indicates cutting a patch from area $X$ and pasting it onto region $Y$ in another image, where 'Sa' stands for 'Saliency', 'Non' for 'Non-saliency', 'Ce' for 'Center', and 'Cor' for 'Corresponding'. + +
MethodScaleTypes of Saliency UtilizationDIV2KRealSR
PSNRΔPSNRΔ
EDSR×4baseline29.21-28.86-
Patch1×1×4Granularity29.28+0.0729.10+0.24
Patch2×2×4Granularity29.26+0.0529.07+0.21
Patch3×3×4Granularity29.24+0.0329.02+0.16
Patch4×4×4Granularity29.22+0.0128.91+0.05
Patch5×5×4Granularity29.14-0.0728.75-0.11
Patch6×6×4Granularity29.07-0.1428.61-0.25
Patch7×7×4Granularity28.92-0.2928.45-0.41
Sa2Cor×4Diversity29.27+0.0629.11+0.25
Ce2Ce×4Diversity29.26+0.0529.08+0.22
Sa2Sa×4Diversity29.21+0.0028..89+0.03
Sa2Non×4Diversity29.24+0.0329.97+0.11
Non2Sa×4Diversity29.19-0.0228.79-0.07
Non2Non×4Diversity29.16-0.0528.76-0.10
ADD+×4Granularity&Diversity29.32+0.1129.14+0.28
+ +# 4. Experiments + +# 4.1. Preliminaries + +Network structures. We adopt several advanced and typical SR networks to verify the effectiveness and compatibility of our ADD and the proposed three new DA strategies. We consider CNN-based methods: RCAN [38], and EDSR [17], in which well-designed CNN-based structures are proven effective on SR tasks. The transformer-based method, SwinIR [16], is also adopted in our experiments. + +Datasets and implementation details. We use the DIV2K and RealSR datasets for training. We select ten images (index 0801-0810) from the DIV2K validation set for validation during training. For evaluation, we use six benchmark datasets, including Set5, Set14, BSD100, Urban100, Manga109, and test sets of RealSR. We keep the hyperparameters (e.g., learning rate, batch size) the same as reported in the original paper. All experiments are conducted using PyTorch on NVIDIA V100 GPUs. + +# 4.2. Comparison of Interpretation Capability + +We conduct visualization experiments to evaluate the effectiveness of the proposed CAM. As shown in the left part of + +![](images/1b5dec18cf36a63ed299da488981529b64291193ef0d01134a64b2dbfb2504b8.jpg) + +![](images/a51527f8612d1b895ed066df1139b55f63b5f74cb19216ff7b6aee3ec6157fd2.jpg) +Fig. 3, the blue arrow highlights important regions, while the red arrow points to areas considered background noise. CAM accurately identifies relevant information, demonstrating robustness to background noise, unlike LAM. + +![](images/c47120e0d2e103ac181511fcee2064834384487ffb6a7e10ac27b4425edd8fe8.jpg) + +![](images/67d264ba064a6235f2bca34effcdd7bf772d3f4e4fc03a82d96c35276ee2a132.jpg) +Figure 3. Saliency maps (Left) and Insertion/Deletion curves (Right) on DIV2K etc. super-resolution sets. The blue arrow indicates that the proposed CAM accurately reflects important and intuitive content without being affected by background noise, while the red arrow indicates that LAM is affected by background noise and produces undesired attribution results. + +![](images/28fac85b2f8652710df47a3617e71950b617503ff67d4973df4dd1d554faed0b.jpg) + +![](images/54c4214e32f28a30ef9793e9dc51e7ef60acf8f602069eb4ef4fb0c5940ebcf5.jpg) + +Table 2. Quantitative PSNR (dB) comparison of our ADD and existing DA methods in SR on DIV2K and RealSR datasets. $\Delta$ denotes the performance gap. + +
MethodScaleTraining SetDIV2KTraining SetRealSR
PSNRΔPSNRΔ
RCAN×4DIV2K29.22-RealSR29.20-
+ CutMix×4DIV2K29.24+0.02RealSR29.25+0.05
+ CutMixup×4DIV2K29.28+0.06RealSR29.30+0.10
+ CutBlur×4DIV2K29.25+0.03RealSR29.29+0.09
+ ADD×4DIV2K29.32+0.10RealSR29.34+0.14
+ ADD+×4DIV2K29.36+0.14RealSR29.46+0.26
EDSR×4DIV2K29.21-RealSR28.86-
+ CutMix×4DIV2K29.22+0.01RealSR28.90+0.04
+ CutMixup×4DIV2K29.26+0.05RealSR28.97+0.11
+ CutBlur×4DIV2K29.25+0.04RealSR28.94+0.08
+ ADD×4DIV2K29.30+0.09RealSR29.01+0.15
+ ADD+×4DIV2K29.32+0.11RealSR29.14+0.28
SwinIR×4DIV2K29.40-RealSR29.26-
+ CutMix×4DIV2K29.40+0.00RealSR29.29+0.03
+ CutMixup×4DIV2K29.43+0.03RealSR29.34+0.08
+ CutBlur×4DIV2K29.43+0.03RealSR29.32+0.06
+ ADD×4DIV2K29.46+0.06RealSR29.37+0.11
+ ADD+×4DIV2K29.48+0.08RealSR29.43+0.17
+ +Following established protocols [30, 37], we perform Insertion and Deletion tests, as shown in the right part of Fig. 3. In the Insertion test, a progressively increasing fraction $(3.6\%)$ of pixels from the high-resolution (HR) image is inserted into the super-resolved image, guided by the pixel + +importance values in the attribution map, until the reconstructed image closely matches the HR image. In the Deletion test, $3.6\%$ of the pixels in the HR image, starting from those with the highest attribution map values, are progressively replaced with black pixels until the entire image is replaced. The Insertion and Deletion curves provide further evidence that CAM more effectively captures the network's critical information compared to LAM. + +# 4.3. Results on Various Models and Datasets + +We conduct quantitative comparisons between the proposed ADD method and existing vanilla DA approaches across classical benchmark datasets, namely DIV2K and RealSR, as detailed in Tab. 2. The results demonstrate that both ADD and $\mathrm{ADD + }$ consistently outperform vanilla DA methods on both synthetic (DIV2K) and real-world (RealSR) datasets, with performance improvements reaching up to $0.28\mathrm{dB}$ . Further comparisons between $\mathrm{ADD + }$ and baseline models on the Set5, Set14, Manga109, Urban100, and BSD100 datasets, presented in Tab. 3, show that networks trained with $\mathrm{ADD + }$ consistently achieve superior reconstruction performance. Qualitative results, depicted in Fig. 4, reveal that networks trained with $\mathrm{ADD + }$ exhibit enhanced visual quality compared to their baseline counterparts, capturing finer details. Notably, in the area of stripes on the building in Fig. 4 (img_012), $\mathrm{ADD + }$ yields more accurate and sharper details than the baselines. + +Table 3. Quantitative comparison with baseline methods in SR and the $\Delta$ denotes the performance gap. + +
MethodScaleTraining DatasetSet5Set14Manga109Urban100BSD100
PSNRΔPSNRΔPSNRΔPSNRΔPSNRΔ
RCAN×2DIV2K38.23-34.11-39.41-33.29-32.37-
+ ADD+×2DIV2K38.34+0.1134.21+0.1039.55+0.1433.55+0.2632.44+0.07
EDSR×2DIV2K38.11-33.92-39.10-32.93-32.32-
+ ADD+×2DIV2K38.20+0.0934.04+0.1239.27+0.1733.16+0.2332.43+0.11
SwinIR×2DIV2K38.31-34.41-39.89-33.75-32.46-
+ ADD+×2DIV2K38.43+0.1234.49+0.0839.99+0.1033.90+0.1532.51+0.05
RCAN×4DIV2K32.58-28.84-31.22-26.75-27.74-
+ ADD+×4DIV2K32.64+0.0628.91+0.0731.43+0.2126.92+0.1727.79+0.05
EDSR×4DIV2K32.43-28.76-31.04-26.63-27.66-
+ ADD+×4DIV2K32.51+0.0828.88+0.1231.24+0.2026.81+0.1827.77+0.11
SwinIR×4DIV2K32.63-28.92-31.54-27.01-27.82-
+ ADD+×4DIV2K32.71+0.0828.99+0.0731.60+0.0627.13+0.1227.85+0.03
+ +![](images/de78c63daab6cb5676c36cbb3e05b5e5c2037249f5c661a5cbb062873cccab89.jpg) +Urban100(x4): img_092 + +![](images/b8dcd9a020f089120ca5f77ceaae038355b671ae4387b9cd7b79ca8ceee8d468.jpg) +HR + +![](images/9d5f9288b54d82ea721ecdd5835fe9f08cd97b76c4f47c920c500863b8604f9e.jpg) +Bicubic + +![](images/70699b286b4656ac3076cd033ade92ea423b6036377f2e715fd309df9ff01b4e.jpg) +RCAN + +![](images/2c2975adaeceddc2bf474e7d336aad9d229acb77f823039b3c3d5da2e330ce41.jpg) +RCAN + +![](images/5b87a9b328dc134e1a97d913d09221fd3c49b15fa763bcb31943e62b5f28a0e6.jpg) +EDSR + +![](images/815bef0c5bcafc4cb0b87ea2b5d8e17621a0aedc88e0a64512aaf559ff7934d9.jpg) ++proposed +proposed +proposed +EDSR + ++proposed +proposed + +![](images/4365e0c60e58b836d1a0ffb62d2f0b31d8c3ec3126a0db25585bfecefdd40e29.jpg) +Urban100(x4): img_095 + +![](images/394ddbae49b2e969b327cc1919e2d371c9d503baed8b70d18e6d29aebcfe7bb9.jpg) +HR + +![](images/e2bbb8bdbb4f64783534f7f4a84aaffe542879dd79976f53122a8385abb22ef9.jpg) ++proposed +proposed +proposed + +![](images/a8a67a75522fbbcec87fdcc179cce34065f9b8a189ce8ea9710fb1a04d28724c.jpg) +RCAN + +![](images/de517a8cbaf25badbbc76af14d3c877274f3e175e7ec8b20ca0d9f6d7378f62e.jpg) +RCAN + +![](images/d5d7b376389ee0689ecd44b2122f8f74a29030a27ac346c306122d30124a4cea.jpg) +EDSR + +![](images/a0e4d907bfceff3845f90f61f65285ebcc6f4789bd267ad6c12c8994de11b624.jpg) +EDSR + +![](images/44d3686a627368ef66274250ead23a913256805c7a960591562cd3671e6edfba.jpg) +SwinIR + +![](images/fe44a5b7289d1c45e50d5c15f294601c872f22e9ba49caab6f4ca2aea0c4da17.jpg) +SwinIR + +![](images/c0ddf29918d715819df72d701c97fd9aae29410a10ebf71b8ee85ff35c85fa99.jpg) +Manga109(x4): +PrayerHaNemurenai + +![](images/50306f619c9bbc1c238522afdea410cdbcca9b717218ff6c77d8f5356176a48e.jpg) +HR + +![](images/bbbf594ba4c0d3868b8677c002ea7001a4fbe9a388b7a78301ae7bd8399f66b8.jpg) +Bicubic + +![](images/0b97099247bdfe10d322b539a93f3b8ebdd7b2bd9e34a2fbb1c3c15de90be3df.jpg) +RCAN + +![](images/19b018a5f89507203598c74da818b2968adadacd67ebbde97711ac034ab4f7a4.jpg) +RCAN ++proposed +proposed +proposed + +![](images/e4cfb74893081c95da7bbac00f08dc76b2134bfb11b6636c19f79aa879b916fe.jpg) +EDSR + +![](images/2132558eb107d99f4a7353ff35e8e07d5a0f4d3cc5130f5c1b40d15dfa01f61d.jpg) +EDSR + ++proposed +proposed + +![](images/ce79336787e0335553da22f47ce92f9fb791087c0ad0bdd74bc563b0979eb5b6.jpg) +SwinIR + +![](images/099a0f5063333cdc69c08a32d3cafd8c1cfafda055e1b421f0a953f4a69f417e.jpg) +SwinIR + +![](images/858c5dd4401389fcb34065de8b066c768585fcc3366efbde50841a38607b9f40.jpg) +Urban100(x4): img_012 +Figure 4. Visual comparison on $\times 4$ SR with the baseline model and proposed method. The patches for comparison are marked with red boxes in the original images. Please zoom in for better visualization. + +![](images/e6c5d12eba070fa80ec1d9d6b0e4c721cf6c911a765e0a801e481624f851c59c.jpg) +HR + +![](images/1898ea22869ed4be957d153bf955ff103862bfc3889ae37df2dc95891492872e.jpg) +Bicubic + +![](images/0367aa6b50e523d989e88e1ed39f06e2023eb75f1c59cbca6d423bc6f53cec1e.jpg) +RCAN + +![](images/f43556d28230571eb0f771e115255dcb32f60ed8fcf70e9a16237990dbe96041.jpg) +RCAN ++proposed +proposed +proposed + +![](images/ed9aa450dc2c069dea4e5c803f499d4a9c4e8f86487d60fd357eaa076a1b987f.jpg) +SwinLR + +![](images/3cc5764d44d96cb7d3b5442a77bafae88c5c0fe287cb0117ec5382cb8e06aebe.jpg) +SwinIR + +# 4.4. Guiding Principles for Saliency-based DA methods + +As discussed in Sec. 3.5, the key questions for incorporating saliency are: (1) the manners for segmenting the source image, and (2) the position for pasting the patches. We define the following settings for a comprehensive analysis. For question (1), we examined the impact of different granularities on DA strategies. We categorized granularity into coarse $(1\times 1,2\times 2)$ , medium $(3\times 3,4\times 4)$ , and fine $(5\times 5,6\times 6,7\times 7)$ patches. We observed a decline in network performance with increasing granularity refinement as shown in Tab. 1, indicating that a lack of continuity at the boundary can cause serious boundary effects and subsequently impair performance. For question (2), we investigate six schemes for extracting and merging patches from the source image to + +the target image: (i) Saliency to Corresponding, extracting the most salient region from the source image and merging it with the corresponding region of the target image; (ii) Center to Center, extracting the central region from the source image and merging it with the central region of the target image; (iii) Saliency to Saliency, extracting the most salient region from the source image and merging it with the most salient region of the target image; (iv) Saliency to Non-Saliency, extracting the most salient region from the source image and merging it with the non-salient region of the target image; (v) Non-Saliency to Saliency, extracting the non-salient region from the source image and merging it with the most salient region of the target image; (vi) Non-Saliency to Non-Saliency, extracting the non-salient region from the source image and merging it with the non-salient + +![](images/b772bacf0636b335b1cdd69e8c91870951003a0ff6eda6ca857eff909bca9193.jpg) +Figure 5. Attribution results for the baseline model, vanilla DA (CutMixup), and saliency-based DA (ADDCutMixup). The attribution results showcase the importance of each pixel in the input LR image for reconstructing the marked path. The diffusion index (DI) reflects the range of involved pixels, with a higher DI indicating a broader range of utilized pixels. Two key observations from the attribution and DI results emerge: (1) Vanilla DA methods enhance network performance by involving more pixels. (2) Saliency-based DA methods guide the model to focus more on meaningful details, reducing attention to irrelevant pixels. Please zoom in for better visualization. + +region of the target image. As depicted in Tab. 1, scheme (i) Sa2Cor (with source 'Sa')—which incorporates a broader range of target positions such as 'Sa', 'Non', and others— aligns with a diversity principle and outperforms others. This highlights the importance of the saliency region in the source image and diverse augmented patterns. Based on these findings, we propose the key principle for low-level DA: a wider spectrum of degradation patterns. + +# 4.5. What Vanilla And Saliency-Based DA learn + +We conduct attribution analysis on baseline models, models trained with vanilla DA strategies, and models trained with our proposed saliency-based DA strategies. As depicted in Fig. 5, the model trained with DA methods exhibits a higher diffusion index (DI), indicating a broader range of involved pixels. Our ADD, highlighted by black arrows, focuses on more accurate details. Notably, we observe two key findings: (1) Both vanilla and saliency-based DA methods enhance the model's ability to involve more pixels, leading to improved performance. (2) Saliency-based DA directs the model to concentrate on influential pixels rather than indiscriminately incorporating more pixels. + +Table 4. Gradients comparison with and without global feature detector (GD) on the DIV2K validation dataset. + +
MethodBackbonestep = 1step = 10step = 20step = 30step = 50
LAMEDSR33.9k108.7k119.9k120.0k120.0k
w/ GDEDSR228.6k419.2k643.8k784.9k869.1k
LAMRCAN29.8k660.0k962.6k969.5k987.3k
w/ GDRCAN174.9k494.1k749.2k815.7k1291.3k
+ +# 4.6. Ablation Studies + +The effectiveness of the CAM was demonstrated in Sec. 4.2. To further evaluate the impact of the proposed global feature detector (GD), we conduct additional experiments using EDSR and RCAN as backbone models, as outlined in Sec. 4.1. In these ablation studies, we substitute the global feature detector with the absolute cumulative value of the entire image. The results, shown in Tab. 4, highlight that the + +inclusion of GD leads to smoother gradient changes, making uniformly sampled points more effective. + +# 4.7. Extensions: Other Low-level Vision Tasks + +We explore the applicability of our method to various low-level vision tasks, specifically examining its effectiveness in JPEG artifact removal. Utilizing CNN-based EDSR and Transformer-based SwinIR as baselines, we train the models from scratch. Following the prior works [33], we create a synthetic dataset with a compression quality parameter $q$ set to 10 (lower $q$ indicating stronger artifacts) for color images. Results in Tab. 5 reveal substantial improvements in PSNR and SSIM metrics, particularly at low compression levels ( $q$ ), highlighting the versatility of our method in benefiting various low-level vision tasks. + +Table 5. Quantitative comparison of JPEG compression artifact reduction on the LIVE1 dataset. The best results are highlighted, where $q$ denotes the compression level, with a smaller value indicating a higher compression level. + +
Methodq = 10q = 20q = 30
PSNRSSIMPSNRSSIMPSNRSSIM
EDSR30.140.839131.830.884032.450.8992
+ ADD30.150.839432.310.894933.440.9173
SwinIR29.860.828732.250.890933.690.9174
+ ADD29.860.828532.560.895734.480.9287
+ +# 5. Conclusion + +In this work, we introduce CAM and ADD, specifically designed for SR. Through a dedicated analysis, we reveal two new insights (i.e., involving more pixels and focusing on influential pixels rather than incorporating irrelevant pixels) for low-level tasks. Besides, We propose the key principle of the wider spectrum of degradation patterns for designing DA in low-level tasks. Experimental results underscore the effectiveness and adaptability of our method, significantly improving the performance of various SR tasks. Our work opens new avenues for exploring a more effective way to utilize image information in DA and low-level tasks. + +# Acknowledgments + +This work was supported by the Natural Science Foundation of China (Grant No. 62176119), and the Jiangsu Graduate Research Innovation Program (Grant No. KYCX24_0258). + +# References + +[1] Naveed Akhtar and Mohammad A. A. K. Jalwana. Towards credible visual model interpretation with path attribution. 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Krishnamurthy $^{1}$ , Basak Guler $^{1}$ , Ananthram Swami $^{4}$ , Samet Oymak $^{3}$ , Amit Roy-Chowdhury $^{1}$ $^{1}$ University of California, Riverside $^{2}$ Brookhaven National Laboratory + $^{3}$ University of Michigan, Ann Arbor $^{4}$ DEVCOM Army Research Laboratory +{cxian008@, fnilo001@, sahme047@, krish@cs, basakg@, amertc@ece}.ucr.edu +ananthram.swami.civ@armi.mil, oymak@umich.edu + +# Abstract + +Incorporating transformer models into edge devices poses a significant challenge due to the computational demands of adapting these large models across diverse applications. Parameter-efficient tuning (PET) methods (e.g. LoRA, Adapter, Visual Prompt Tuning, etc.) allow for targeted adaptation by modifying only small parts of the transformer model. However, adapting to dynamic unlabeled target distributions at the test time remains complex. To address this, we introduce AdMiT: Adaptive Multi-Source Tuning in Dynamic Environments. AdMiT innovates by pre-training a set of PET modules, each optimized for different source distributions or tasks, and dynamically selecting and integrating a sparse subset of relevant modules when encountering a new, few-shot, unlabeled target distribution. This integration leverages Kernel Mean Embedding (KME)-based matching to align the target distribution with relevant source knowledge efficiently, without requiring additional routing networks or hyperparameter tuning. AdMiT achieves adaptation with a single inference step, making it particularly suitable for resource-constrained edge deployments. Furthermore, AdMiT preserves privacy by performing an adaptation locally on each edge device, without the need for data exchange. Our theoretical analysis establishes guarantees for AdMiT's generalization, while extensive benchmarks demonstrate that AdMiT consistently outperforms other PET methods across a range of tasks, achieving robust and efficient adaptation. + +# 1. Introduction + +Pretrained transformers [1-5] have achieved remarkable success across diverse tasks, but their large parameter counts—often reaching billions [2, 5]—present challenges for deployment, especially on edge devices with limited computational resources. To address these limitations, parameter + +efficient tuning (PET) methods, such as prefix/prompt tuning [6-9], adapters [10], and LoRA [11], have been introduced. These methods allow the pretrained model to remain fixed while only adjusting a small set of additional parameters tailored to specific target distributions, significantly reducing memory and computation needs while often achieving performance comparable to that of full fine-tuning. + +Most existing PET methods are either single-source—focusing on a single PET module trained for one distribution—or, when incorporating multiple PET modules, require additional computational resources such as routing networks [12] or extensive hyperparameter tuning [13, 14]. These approaches lack the ability to directly integrate knowledge from multiple PET modules, each trained on different source distributions. In dynamically evolving environments, adaptation methods benefit from leveraging multiple sources of pre-trained knowledge. Instead of relying on a single PET module trained on a single source, integrating multiple PET modules enables more robust adaptation to shifting distributions by drawing from a diverse set of source-specific knowledge[15]. This multi-source approach is particularly advantageous when access to the original source data used for training each module is restricted due to privacy, storage, or other constraints. In such scenarios, training a unified PET module across combined sources is infeasible, making it both practical and effective to adaptively employ and integrate an array of pre-trained PET modules during test time, resulting in performance improvements often unattainable with single-source PET adaptation. + +In this work, we introduce AdMiT (Adaptive Multi-Source Tuning in Dynamic Environments), a novel framework designed to efficiently adapt pre-trained PET modules across multiple dynamic distributions. AdMiT pre-trains a structured set of PET modules, each specifically tuned to a different source distribution, providing a versatile foundation for multi-source adaptation. During test time, when faced with new, small-batch target data from a new distri + +![](images/9ee965955f9e1ef4fb6a5b7f85312de38159231945bbaffdb1299fed740fe30f.jpg) +Source Data + +![](images/3928bc16d6cc73d86dadd53b55995ba48c8de8df5d6cfc9eb9589bf056a988d1.jpg) +Target Data + +![](images/40ac0a1d3ee05cc75158304ccdd2e03faff7119de3df265453b84015b1bad0cb.jpg) +Figure 1. The diagram illustrates the AdMiT workflow, which includes pretraining source modules, matching modules during deployment, and updating the integrated module. In the pretraining stage, given a loss function $\mathcal{L}$ and source distributions $\{\mathcal{D}_{S}\}_{j=1}^{N}$ , we freeze the base model $f$ and fine-tune each module $\theta_{j}$ for its respective distribution. We also map the source data to an embedding space $\mathcal{H}$ as empirical Kernel Mean Embeddings (KMEs) $\{\widehat{\mu(S_j)}\}_{j=1}^N$ . During the KME module matching stage (Sec. 3.1), AdMiT maps the target data $T$ to an empirical KME $\widehat{\mu(T)}$ and approximates it as a weighted combination of source KMEs, determining the weight coefficients $\hat{w}_j$ . In the module integration and adaptation stage (Sec. 3.2), AdMiT integrates the source modules with the highest weights to create an adaptive module $\theta(t)$ for the current target batch. This module $\theta(t)$ can then be directly applied to the target distribution or further adapted using sharpness-aware pseudo-label minimization for enhanced alignment with the target data. + +![](images/f3e33bdfb0ce563dd6dc0e2629551cc00200436955a9d98f7b01d1300fb8f247.jpg) + +bution, AdMiT (1) selects a relevant subset of PET modules based on their alignment with the target distribution, and (2) integrates these selected modules into a newly composed module optimized for the current target batch. This integrated module can then be directly applied to the target distribution, achieving efficient adaptation with lower computational overhead compared to existing PET methods [12, 14, 16]. Additionally, this integrated module enables further fine-tuning if desired, allowing AdMiT to dynamically enhance its alignment with the target distribution. This dual capability—of zero-shot applicability and optional on-the-fly adaptation—enables AdMiT to adapt robustly to evolving target distributions with low computational cost. Our experiments demonstrate AdMiT's effectiveness in both zero-shot and test-time adaptation settings, highlighting its adaptability and strong performance across dynamic distributions. + +AdMiT offers two key advantages. First, by dynamically matching and adapting multiple pre-trained PET modules to the target distribution using small batches of target data, AdMiT achieves superior performance over traditional single-source PET adaptation methods. The ability to integrate multiple PET modules enables AdMiT to more effectively capture complex target distributions by leveraging a diverse set of source-specific knowledge through Kernel Mean Embedding (KME)-based matching (Sec. 3.1). Second, AdMiT bypasses the need for additional hyperparameter tuning or routing network training during deployment by using KME to align the target with relevant source distributions. This approach eliminates the computational burden of full model inference, allowing for fast multi-source PET adaptation. + +As a result, AdMiT is particularly well-suited for resource-constrained edge deployments, where both efficiency and flexibility are essential. Moreover, this KME-based distribution matching ensures data privacy, as no raw data exchange is required during adaptation. + +Main Contributions. We present a new multi-source PET approach, AdMiT, that enables edge devices to selectively integrate a minimal subset of PET modules from a pre-trained collection, adapting in real-time to new, unlabeled data in an unsupervised, few-shot setting. Our contributions include the following: + +- Adaptive Multi-source Module Selection and Integration. AdMiT efficiently selects and integrates a subset of pre-trained PET modules from a structured collection, based on the distributional characteristics of incoming target data. This adaptive integration avoids the computational burden associated with training routing networks or hyperparameter tuning for each new target distribution. By selectively combining relevant modules, AdMiT achieves performance comparable to that obtained by using all modules simultaneously but with significantly reduced storage and computational requirements, making it practical for edge deployment. +- Efficient, Privacy-preserving Adaptation. Unlike existing PET methods that utilize additional routing networks or data-alignment steps for multi-source adaptation [12], AdMiT achieves adaptation by transforming empirical data distributions in a kernel embedding space [17, 18]. This approach avoids the need to exchange raw data, preserving data privacy and reducing computational costs. Moreover, + +AdMiT performs efficient module selection and combination without additional inference steps, enabling real-time adaptation on edge devices. + +- Theoretical Guarantees. We provide theoretical guarantees on AdMiT's generalization performance, showing how it can effectively balance the sample sizes of source modules and the target batch size to ensure reliable multi-source adaptation. This guarantee highlights that well-trained source modules can provide robust adaptation even with limited target data. +- Comprehensive Empirical Evaluation and Insights. Extensive evaluations on challenging datasets, including Digit-Five, CIFAR-100C, and ImageNet-C, demonstrate that AdMiT consistently surpasses existing PET methods across various adaptation distributions. AdMiT shows a notable improvement in accuracy when adapting to new distributions (Table 1) and effectively preserves knowledge from source distributions (Table 2), showcasing strong performance in adaptation and retention. Additionally, AdMiT effectively identifies and integrates the most relevant modules (Figure 3) consistently achieving optimal results with minimal computational overhead. Additional results on the segmentation task, using Cityscapes [19] and ACDC [20] datasets, are provided in the Appendix, demonstrating AdMiT's effectiveness in handling dynamic distributions across different tasks. + +# 2. Related Works + +Parameter Efficient Tuning (PET). Large-scale pre-trained models have greatly enhanced performance in natural language processing [1] and computer vision [21] by transferring learned knowledge to downstream tasks. PET methods, such as prompt tuning [21] and adapters [10], allow efficient adaptation by fine-tuning a small subset of parameters. Techniques like CoOp [22] and CoCoOp [23] leverage prompt optimization for out-of-distribution generalization, while CLIP-Adapter [24] and Tip-Adapter [25] fine-tune CLIP using adapters or key-value cache models, improving adaptability to target distributions. However, most PET methods are not designed to handle continuously shifting small-batch target distributions effectively; they adapt independently to each distribution, creating distribution-specific PET modules and often forgetting previously learned information. In contrast, our method enables consistent adaptation to dynamic target distributions while preserving knowledge of the pretrained source distributions, addressing a gap in existing PET approaches. Our approach is compatible with various PET modules, including LoRA [11], VPT [21], and adapters [10]. Test Time Adaptation (TTA). Unsupervised Domain Adaptation (UDA) requires extensive target distribution data for offline adaptation, whereas TTA operates continuously on incoming test batches [26-28]. Initial TTA approaches [29] used test-batch statistics rather than training data, with meth + +ods like TENT [30] updating batch-normalization parameters to reduce entropy on target data. DUA [31] further refines alignment with target distributions by persistently updating batch-norm statistics across test batches. While these single-source TTA methods are effective, they often struggle with forgetting source knowledge over time, particularly in dynamic settings. Approaches like CoTTA and BeCoTTA [32, 33] use stochastic source restoration to mitigate drift, and EATA [34] employs regularization to preserve critical parameters, thus reducing forgetting. However, these methods often adapt to each batch separately, requiring substantial computational resources to balance adaptation and forgetting. In contrast, our multi-source approach dynamically matches relevant source modules to the target distribution, integrating them efficiently and minimizing forgetting with minimal computational overhead. + +Ensemble Learning and Multi-source Adaptation. Ensemble learning, a well-known technique, enhances model robustness by combining outputs from various models [35]. Techniques like SESoM [12] and mixture models [14] aim to handle dynamic target distributions by combining multiple pre-trained models or PET modules. However, due to privacy constraints or storage limitations, direct access to source data from pre-trained models or PET modules is often unavailable. This limitation requires ensemble methods to rely on additional hyperparameter tuning [14, 16] or routing networks [12] to match the target and source distributions, leading to substantial computational overhead and frequent forward inference. For CNN-based applications, such adjustments are manageable [15, 36], but in the context of large pre-trained transformers, this tuning becomes prohibitively costly. Our approach bypasses these constraints by performing source-target matching through Kernel Mean Embeddings (KMEs), enabling efficient and privacy-preserving adaptation without requiring raw data or extensive computation, making it well-suited for large-scale pre-trained models in dynamic environments. + +# 3. Proposed Method: AdMiT + +Our method, AdMiT, leverages a pretrained transformer model $f$ along with a collection of parameter-efficient tuning (PET) modules, each pretrained on distinct source tasks or domains. These PET modules, represented by parameters $\{\theta_j\}_{j=1}^N$ , have significantly fewer parameters than the base model $f$ and can be flexibly integrated into $f$ as needed, thus forming a structured repository of source knowledge. We denote the transformer $f$ combined with a module $\theta$ as $f_\theta$ . The core idea of AdMiT is to optimize adaptation to a target task or domain by selectively blending these pretrained modules based on their distributional representations in an embedding space and combining their weights to maximize relevance. The adaptation to target distribution is shown in figure 1. + +Algorithm 1 AdMiT: Adaptive Multi-Source Tuning in Dynamic Environments. + +1: Input: Pretrained transformer model $f$ , Pretrained source modules $\{\theta_j\}_{j=1}^N$ , empirical KME of source modules $\{\widehat{\mu(S_j)}\}_{j=1}^N$ , number of modules to be selected $M$ ( $M < N$ ), streaming sequential unlabeled test data $T^{(1)} = \{x_i^{(1)}\}_{i=1}^{|T|} \to T^{(2)} = \{x_i^{(2)}\}_{i=1}^{|T|} \to \dots$ $T^{(t)} = \{x_i^{(t)}\}_{i=1}^{|T|} \to \dots$ + +2: Output: $M$ scaled weights, finetuned new module $\theta (t)$ size of synthetic dataset $Z$ + +3: Use Alg. A (in the Appendix) to generate synthetic data and estimate $\{\widehat{\mu(S_j)}\}_{j=1}^N$ + +4: while $t \geq 1$ do + +5: for Each $x_{i}$ in the $t$ -th batch do + +6: Calculate the empirical KME of the target batch (Eqn. 3) + +7: end for + +8: Obtain mixture weights $\{\hat{w}(t)^j\}_{j=1}^N$ by solving Eqn. 4 + +9: Find and select the top $M$ in $\{\hat{w}(t)^j\}_{j=1}^N$ + +10: Rescale selected weights to sum up to 1, thus obtain $\{\overline{w} (t)^j\}_{j = 1}^M$ +11: Create a new module $\theta(t)$ by a weighted averaging of the selected pretrained modules + +$$ +\theta (t) = \sum_ {j = 1} ^ {M} \bar {w} (t) ^ {j} \theta_ {j} +$$ + +12: Finetune $f_{\theta(t)}$ with Eqn. 8 +13: end while + +- Pretraining stage: Pretraining and KME calculation. Given a loss function $\mathcal{L}$ and a set of source tasks or domains $\{\mathcal{D}_{S_j}\}_{j=1}^N$ , we freeze the base transformer model $f$ and only update the PET modules, rather than fully fine-tuning $f$ on each domain. For each source $\mathcal{D}_{S_j}$ , we optimize the parameters $\theta_j$ as $\theta_j = \mathrm{argmin}_{\theta} \mathcal{L}(f_{\theta}; \mathcal{D}_{S_j})$ . To capture the source distributions, we map the source data to an embedding space $\mathcal{H}$ and represent the empirical distributions using Kernel Mean Embeddings (KMEs) $\{\widehat{\mu(S_j)}\}_{j=1}^N$ . +- Deployment stage: KME Module matching. (Sec. 3.1) In this stage, AdMiT maps the target data $T$ to an empirical Kernel Mean Embedding (KME) $\widehat{\mu(T)}$ and approximates it as a linear combination of source KMEs $\{\widehat{\mu(S_j)}\}_{j=1}^N$ , expressed as $\widehat{\mu(T)} = \sum_{j=1}^{N} w_j \widehat{\mu(S_j)}$ . This approach to multi-source distribution estimation, commonly applied in previous works [15, 16, 36], enables us to interpret the mixture weights $\{w_j\}$ as relevance scores for each source module. These weights guide the selection and integration of source modules, ensuring that the target is adapted efficiently and effectively. We also provide a theoretical bound on the estimation error for this approximation. + +- Deployment stage: Module integration and adaptation. (Sec. 3.2) Using the computed mixture weights $\hat{w}_j$ , AdMiT selects the source modules with the highest weights and integrates them to create a combined module $\theta$ . This integrated module $\theta$ is subsequently fine-tuned on the target domain $\mathcal{D}_{\mathcal{T}}$ to refine its alignment with the target distribution. For further enhancement, we apply sharpness-aware pseudo-label minimization [37, 38] to adjust the ensemble module and improve its robustness on the target domain. + +Throughout the deployment stage, only a small number of unlabeled target samples are required to identify and integrate the source modules most relevant to the current target distribution. A detailed pseudocode for AdMiT can be found in Algorithm 1. In the following sections, we provide an in-depth explanation of the principles guiding the design of AdMiT. + +# 3.1. Module Matching using KME + +In the pretraining stage, given the heterogeneous feature spaces across different models, we assume a unified feature space facilitated by a public feature extractor $G(\cdot)$ , which maps the original data $x'$ from both source and target distributions into a shared representation space $x = G(x')$ . This setup is practical, as publicly available pre-trained models can serve as feature extractors. In our experiments, we use a DenseNet201 model [39] pre-trained on ImageNet for this purpose. Since source data are inaccessible during the deployment stage, we require a metric to assess the similarity between source and target distributions without exchanging data or performing forward model inference. + +Kernel Mean Embedding (KME) [40-43] provides a powerful tool for measuring distribution similarity. KME maps probability distributions into vectors in a high-dimensional Reproducing Kernel Hilbert Space (RKHS) $\mathcal{H}$ using a positive semi-definite bounded kernel $0\leq k(\cdot ,\cdot)\leq K$ simplifying the similarity evaluation of two distributions to inner product calculations in RKHS. Given a distribution $\mathcal{P}$ of an $\mathcal{X}$ -valued random variable, its KME is defined as: + +$$ +\mu_ {k} (\mathcal {P}) := \int_ {x \in \mathcal {X}} k (x, \cdot) d P (x). \tag {1} +$$ + +The norm of the KME in $\mathcal{H}$ can be expressed by the inner product: + +$$ +\left. \left| \left| \mu_ {k} (\mathcal {P}) \right| \right| _ {\mathcal {H}} ^ {2} := \left\langle \mu_ {k} (\mathcal {P}), \mu_ {k} (\mathcal {P}) \right\rangle = \mathbf {E} _ {x, y \sim \mathcal {P}} k (x, y). \right. \tag {2} +$$ + +Since true distributions $\mathcal{P}$ are typically unknown, we estimate the KME and its norm using a finite batch $X = \{x_{n}\}_{n = 1}^{|X|}\sim \mathcal{P}$ : + +$$ +\widehat {\mu (X)} := \frac {1}{| X |} \sum_ {n = 1} ^ {| X |} k \left(x _ {n}, \cdot\right), \tag {3} +$$ + +$$ +\| \widehat {\mu (X)} \| _ {\mathcal {H}} ^ {2} := \frac {1}{| X | ^ {2}} \sum_ {x _ {i}, x _ {j} \in X} k (x _ {i}, x _ {j}). +$$ + +These empirical KMEs are computed on source datasets $\{S_j\}_{j=1}^N \sim \mathcal{D}_{S_j}$ during the pretraining stage, and on the target batch $T \sim \mathcal{D}_{\mathcal{T}}$ in the deployment stage. + +In the deployment stage, we assume the target distribution can be approximated as a linear combination of source distributions, such that $\mathcal{D}_{\mathcal{T}} \approx \sum_{j=1}^{N} w_j \mathcal{D}_{\mathcal{S}_j}$ for some mixture weights $\{w_j\}_{j=1}^N$ . Using the linearity of expectation, we can express the KME of the target as $\mu_{\mathcal{D}_{\mathcal{T}}} \approx \sum_{j=1}^{N} w_j \mu_{\mathcal{D}_{\mathcal{S}_j}}$ . Each source KME $\{\widehat{\mu(S_j)}\}_{j=1}^N$ serves as a basis in the Hilbert space $\mathcal{H}$ , allowing us to decompose the target empirical KME $\widehat{\mu(T)}$ using these bases. By solving the following optimization, we obtain the mixture weights $\{\hat{w}_j\}_{j=1}^N$ to match source and target distributions: + +$$ +\min _ {\left\{w _ {j} \right\} _ {j = 1} ^ {N}} \left\| \widehat {\mu (T)} - \sum_ {j = 1} ^ {N} w _ {j} \widehat {\mu (S _ {j})} \right\| _ {\mathcal {H}}. \tag {4} +$$ + +This KME-based approach serves as a reliable metric for distribution similarity (See Section H), enabling efficient and privacy-preserving matching between source and target distributions. + +Theorem 3.1. For a bounded kernel $0 \leq k(\cdot, \cdot) \leq K$ , with probability at least $1 - \delta$ , the (biased) empirical MMD (obtained by drawing $m$ samples from $p = \mathcal{D}_{\mathcal{T}}$ and $n$ samples from $q = \sum_{j=1}^{N} w_j \mathcal{D}_{\mathcal{S}_j}$ , with $\sum_{j=1}^{N} w_j = 1$ ) is bounded by: (Proof in the Appendix Corollary H.3.) + +$$ +\frac {1}{2} \left\| \widehat {\mu (T)} - \sum_ {j = 1} ^ {N} w _ {j} \widehat {\mu (S _ {j})} \right\| _ {\mathcal {H}} < \sqrt {\frac {K}{m}} + \sqrt {\frac {K}{n}} + \sqrt {\frac {K (m + n) \log \frac {1}{\delta}}{2 m n}}. +$$ + +The mixture weight solution $\hat{w}_j$ from optimization 4 also implies the similarity of the distribution of source domain $\mathcal{D}_{\mathcal{S}j}$ and the target domain $\mathcal{D}_{\mathcal{T}}$ , leading to the module selection strategy in Alg. 1. + +Practical Considerations. In real-world applications, not all source modules are closely aligned with the target distribution, and calculating Kernel Mean Embeddings (KMEs) of source data in Eqn. 4 can be computationally intensive, as it involves summing up to $|S_{j}|$ kernel functions for each source. To enhance efficiency and reduce computational overhead, we employ the following strategies: (1) instead of using all source modules during adaptation, we select only the modules with the highest weights $\hat{w}_{j}$ (as shown in Alg. 1), thus focusing on the most relevant sources, and (2) to approximate each source KME $\widehat{\mu(S_j)}$ , we generate a smaller synthetic dataset $\{z_m\}_{m=1}^Z$ (where $Z \ll |S_j|$ ). This synthetic dataset enables efficient computation by reducing the number of kernel functions involved, and it preserves + +privacy by eliminating the need for raw data exchange during KME decomposition [44]. Details of the synthetic data generation algorithm for source KMEs are provided in the Appendix, Alg. A. + +Using synthetic datasets to approximate KMEs offers two major advantages. First, direct access to original source data is often restricted due to privacy or storage constraints, making it necessary to rely on the accessible information from source modules. Generating synthetic data allows us to create accurate KME approximations for each source module in a privacy-preserving way. Second, synthetic datasets provide a computationally efficient alternative to direct KME calculations using source data. By involving fewer data points, synthetic KMEs significantly reduce the computational load for matching the target distribution with source KMEs, making adaptation feasible even in resource-limited settings. We have theoretically demonstrated that (see Appendix Alg. A) the synthetic KMEs closely approximate the one calculated from the raw data. This fidelity ensures that the adaptation performance remains reliable and robust, as shown in our experiments, and enables efficient yet effective alignment of target and source distributions. + +# 3.2. Module Integration and Adaptation + +Drawing inspiration from the benefits of a good initialization in test-time adaptation and transfer learning [12, 16, 36, 45], we integrate PET modules trained on distributions related to the target distribution, as these modules are presumed to contain valuable knowledge relevant to these distributions. This integration is achieved through a weighted mixture of the selected modules, aiming to achieve a transfer gain: + +$$ +\theta (t) = \sum_ {i = 1} ^ {M} \bar {w} _ {i} \theta_ {i}, +$$ + +where $\bar{w}_i$ is obtained from Alg. 1, and $\theta(t)$ represents the integrated module. Directly applying the integrated module on the target distribution results in a zero-shot adaptation, whose performance can be bounded by the following theorem. + +Theorem 3.2 (Zero-shot adaptation loss bound). Assume that the source training error is at most $\epsilon$ ; the loss $L(f_{\hat{\theta}_j}(x),f(x))\in \mathcal{H}_k$ ; and the empirical MMD between $\sum_{j = 1}^{N}w_{j}\mathcal{D}_{S_{j}}$ and $\mathcal{D}_{\mathcal{T}}$ is from Theorem 3.1. Then, the finite-sample loss is: + +$$ +\begin{array}{l} \mathcal {L} \left(\mathcal {D} _ {\mathcal {T}}, g, f _ {\sum \boldsymbol {w} _ {j} \hat {\theta} _ {j}}\right) = \sum_ {x _ {i} \sim \mathcal {D} _ {\mathcal {T}}} \left[ L \left(f _ {\sum \boldsymbol {w} _ {j} \hat {\theta} _ {j}} \left(x _ {i}\right), g (x _ {i})\right) \right] \\ \leq \epsilon + O (\sqrt {\frac {1}{m}} + \sqrt {\frac {1}{n}}) \\ \end{array} +$$ + +Proof can be found in the Appendix, Theorem H.5. + +To further boost performance, we fine-tune $\theta(t)$ for the target distribution $\mathcal{D}_{\mathcal{T}}^{(t)}$ at time $t$ : + +$$ +\theta (t) ^ {*} = \underset {\theta (t)} {\arg \min} \mathcal {L} (f _ {\theta (t)}; \mathcal {D} _ {\mathcal {T}} ^ {(t)}). +$$ + +Starting from the integrated PET module $\theta(t)$ offers an efficient initialization, as the fine-tuning does not incur additional forward inference costs even as the number of candidate modules $N$ or selected modules $M$ increases. + +Practical Considerations. Although test-time adaptation (TTA) can stabilize the adapted models, it risks model collapse during the tuning process, where the model may incorrectly classify all inputs as belonging to a single category over time [38]. To mitigate this, we incorporate sharpness-aware techniques [37, 38] to make the model less sensitive to large gradients that may arise from test samples [34]. + +Once we obtain the new module $\theta(t)$ for the target batch $T^{(t)} = \{x_i^{(t)}\}_{i=1}^{|T|}$ at time step $t$ , we compute the entropy of the pseudo-labels predicted by the model with this module. The entropy of the predictions for the $t$ -th target batch from the model $f_{\theta(t)}$ is: + +$$ +\mathcal {L} ^ {(t)} = - \mathbf {E} _ {\mathcal {D} _ {T} ^ {(t)}} \sum_ {c = 1} ^ {K} \hat {y} _ {c} ^ {(t)} \log \left(\hat {y} _ {c} ^ {(t)}\right), \tag {5} +$$ + +To properly fine-tune the new module $\theta(t)$ with this pseudo-label entropy minimization, we aim to make the model insensitive to large gradients by encouraging convergence to a flat region of the entropy loss surface. This approach, which seeks a flat minimum, provides good generalization and robustness against large gradients [37, 38]: + +$$ +\min _ {\lambda} \mathcal {L} ^ {S A (t)} \left(\left\{x _ {i} ^ {(t)} \right\} _ {i = 1} ^ {B}; \lambda\right), \tag {6} +$$ + +$$ +\text {w h e r e} \mathcal {L} ^ {S A (t)} \triangleq \max _ {\| \epsilon \| _ {2} \leq \rho} \mathcal {L} ^ {(t)} \left(\left\{x _ {i} ^ {(t)} \right\} _ {i = 1} ^ {B}; \lambda + \epsilon\right) \tag {7} +$$ + +"SA" denotes sharpness-aware. The gradient for this optimization can be approximated (see Appendix A for details): + +$$ +\nabla_ {\lambda} \mathcal {L} ^ {S A (t)} \approx \nabla_ {\lambda} \mathcal {L} ^ {(t)} (\{x _ {i} ^ {(t)} \} _ {i = 1} ^ {B}; \lambda) | _ {\lambda + \epsilon^ {*} (\lambda)}. \qquad (8) +$$ + +Applying Eqn. 8 instead of standard SGD to update the parameters of $\theta(t)$ based on Eqn. 5 results in a more robust solution for pseudo-label entropy minimization. The effect of sharpness-aware adaptation is discussed further in the ablation study. + +# 4. Evaluations + +In our experiments, we evaluate AdMiT's effectiveness by adapting PET modules pre-trained on source distributions to target data drawn from stationary or dynamically evolving + +Table 1. Static Adaptation on ImageNet-C. Following a similar experiment setup in Fig. 2, we adapt to a target corruption domain by taking the rest $15 - 1 = 14$ domains as source domains, given varying target batch size. Due to space limitations, we report only the averaged accuracy across all target domains. + +
SourceMethodBS=256BS=128BS=64BS=16BS=1
SingleTENT-Best [30]52.252.352.052.451.7
TENT-Worst [30]34.734.535.334.731.6
BECoTTA-Best [33]60.461.562.061.155.4
BECoTTA-Worst [33]35.336.437.937.330.4
SAR-Best [38]58.162.361.460.354.1
SAR-Worst [38]37.538.638.238.131.1
GT-Tuning67.768.869.765.460.3
Multiπ-tuning-PL [16]61.462.462.761.557.1
SESoM-PL [12]62.362.662.562.056.3
CONTRAST [15]63.563.163.161.757.9
Model soup [46]52.353.452.251.749.5
AdMiT63.863.762.462.358.7
AdMiT-ZeroShot60.259.658.455.953.3
AdMiT-Plain63.562.262.161.056.6
+ +distributions (See experiment setting details in Appendix Sec. F). The target distributions involve the same task as the source but differ due to distribution shifts relative to the source distributions on which the PET modules were trained. + +We consider two adaptation scenarios: (1) a static adaptation setting where the target data are drawn from a stationary distribution, and (2) a dynamic adaptation setting where the target data are drawn sequentially from an evolving distribution. The former scenario demonstrates AdMiT's effectiveness in adapting to a stationary target distribution using pre-trained source modules, while the latter highlights AdMiT's robustness in adapting to evolving target distributions over time. + +Datasets. For the static adaptation scenario, we evaluate AdMiT on the Digits-Five dataset [47], which includes five digit datasets—MNIST (MT), MNIST-M (MM), USPS (UP), SVHN (SV), and Synthetic Digits (SY)—each covering 10 classes (0-9). In these experiments, four distributions are used as sources, with the remaining one reserved for testing. We also use the ImageNet-C dataset [48], which applies 15 types of severe corruptions (details in Appendix Sec. G) to ImageNet images [49], following the setup in [38]. + +For the dynamic adaptation scenario, we utilize the CIFAR-100C benchmark [48], which extends the CIFAR-100 dataset [50] by introducing 15 types of noise at varying levels of severity (1 to 5). This setup results in up to 75 distinct distributions, allowing us to assess AdMiT's capacity for continuous adaptation as the target distribution evolves. + +Finally, although our primary evaluation focuses on image classification tasks, our method is not limited to this setting. It can be extended to other tasks, such as semantic segmentation, with results for segmentation tasks provided in the Appendix E. + +# 4.1. Baseline Methods + +Our evaluation includes comparisons with state-of-the-art (SOTA) single-source test-time adaptation (TTA) methods, + +![](images/6a81700c338bc92f129d0e9aea536be2a31560407bad677f9333acfa1369a9e5.jpg) +Figure 2. Static adaptation on Digits-Five. (Left): Sample images from the source and target domains used in the adaptation task, which include MNIST (MT), MNIST-M (MM), SVHN (SV), Synthetic (SY), and USPS (UP). (Center): Heatmap depicting the mixture weights assigned to various source modules during adaptation to the target domain. Larger mixture weights $(w_{j})$ indicate a higher similarity between the target and source domains. The weights in each column sum to 1, as the four remaining domains are used to adapt to the target domain. (Right): We train the source modules using 4 digits datasets to perform adaptation on the remaining dataset. All the results are the average of 5 runs. Best performance is bolded, and second-best performance is underlined. The table clearly demonstrates that the average accuracy of AdMiT outperforms other baselines and is closest to the performance achieved by tuning with ground-truth labels. We also report the module integration (without tuning) results as AdMiT-ZeroShot, and the module adapation using plain SGD tuning results as AdMiT-Plain. + +
SourceMethodGNSNINDBFGBMBZBSnowFrostFogBrightContrastElasticPixelJPEGAvg
SingleTENT-Best [30]74.265.351.050.747.345.842.036.935.224.324.614.211.911.98.236.2
SAR-Best [38]71.271.769.264.456.054.259.859.356.252.749.446.848.242.044.956.4
BECoTTA-Best [33]69.771.465.868.754.353.455.752.455.747.252.446.349.642.441.955.1
Multiπ-tuning-PL [16]79.876.381.175.766.262.568.161.661.958.763.452.950.753.156.064.5
SESoM-PL [12]75.076.074.869.065.660.460.354.555.854.555.349.750.851.453.960.5
Model soup [46]52.155.349.648.048.749.143.273.076.574.174.356.351.247.858.357.2
CONTRAST [15]78.275.374.476.172.270.871.772.173.971.474.671.569.571.365.472.5
AdMiT79.174.474.475.269.271.873.773.178.975.274.973.270.572.865.073.3
+ +Table 2. Dynamic adaptation forgetting evaluation on CIFAR-100C. We take $N = 4$ source modules pretrained on Snow, Frost, Fog, and Bright for all the involved methods in the table. The table illustrates the average test accuracy (with all corruption domains of severity level 5) on the 4 source domains during a sequential adaptation across different target domains for various methods. AdMiT selects $M = 3$ modules to adapt to new domains. All the results are the average of 5 runs. We employ these models for adaptation on 15 sequential target domains. Best performance is bolded, and second-best performance is underlined. + +such as TENT [30], BECoTTA [33], and SAR [38]. These methods serve as benchmarks for adapting individual source models to target distributions, providing insight into how well a single-source approach performs in adapting to unseen distributions. As our problem setting involves adapting pre-trained models to new, dynamic distributions during deployment, it is closely related to the objectives of TTA. Therefore, these widely recognized single-source TTA methods are natural baselines for evaluating AdMiT's ability to adapt effectively. Following a setup similar to that in [36], we apply each source model independently to specific test distribution data, reporting Best and Worst results, corresponding to the highest and lowest performance achieved across individual source models. + +We also compare against leading multi-source ensemble methods in both static adaptation and dynamic adaptation settings, as these approaches simultaneously leverage multiple sources and provide a baseline for assessing the benefits of multi-source adaptation. SESoM [12] trains an attention-based routing network for adaptive weighting + +across source outputs, while $\pi$ -tuning [16] fine-tunes hyperparameters based on a weighted mix of source modules, and CONTRAST [15] computes optimal weights for combining multiple source model outputs through gradient descent. These multi-source methods allow us to evaluate the effectiveness of combining knowledge from multiple distributions and highlight the computational trade-offs involved. For fair comparison, we implement pseudo-label (PL) entropy minimization for tuning mixture weights in SESoM and $\pi$ -tuning, denoting these as SESoM-PL and $\pi$ -tuning-PL, and apply a greedy model soup approach to minimize PL entropy by averaging module mixtures, following [46]. All baseline methods, including those originally based on CNN architectures, have been reproduced on a transformer architecture for consistency in our comparisons. Additional implementation details are provided in the Appendix. + +Lastly, we provide an upper-bound baseline, GT-Tuning, which tunes a new PET module using ground-truth labels, offering insight into the best achievable performance with full label access on the target distribution. Together, these base- + +![](images/124acfb4fdec8f9cbd6a6acca6d99617168a0ce5def6b2b8d8eba6b02b89f3d9.jpg) +Figure 3. Module Selection on CIFAR-100C. Performance of AdMiT on various domains of CIFAR-100C with different numbers of selected source modules. We pretrain a set of 75 modules (each for a corruption domain and severity level) and select top- $k$ modules based on empirical KME weights. $M = k$ indicates the number of selected source modules. Results show that with limited target data (batch size=128), selecting just a few modules ( $k > 1$ ) maintains performance comparable to that from using all modules ( $k = 75$ ). Mean performance across domains (shown as markers) improves with more modules but with diminishing returns, demonstrating our method's efficiency even with significantly fewer modules. + +lines capture both single-source and multi-source strategies, illustrating AdMiT's effectiveness in adapting to dynamic target distributions efficiently and without label access. + +Module adaptation. We evaluate AdMiT on the Digits-Five [47] dataset for digit classification, with $N = 4$ source modules and all $M = N$ modules used for inference on each target distribution. As shown in Figure 2, GT-Tuning achieves the best performance (serving as an upper bound with labeled data), while AdMiT achieves the second best results (underlined) in most target distributions. The accompanying heatmap illustrates the average weights assigned to each source module, with higher weights corresponding to greater similarity between target and source distributions. We also include results from AdMiT-Plain, which uses plain SGD instead of sharpness-aware tuning for adaptation. In some cases (star-marked cells), plain SGD leads to decreased performance, underscoring that sharpness-aware adaptation provides more stable tuning results. + +Module integration. We also assess the performance of the integrated module without any tuning to gauge the efficiency of AdMiT in a zero-shot adaptation setting, as shown in Figure 2. AdMiT-ZeroShot denotes the accuracy achieved by directly applying the integrated module on target distributions without further adaptation, achieving higher average accuracy than most single-source TTA methods and demonstrating AdMiT's efficiency and effectiveness in leveraging multi-source knowledge. We further evaluate AdMiT on 15 target distributions of the ImageNet-C dataset, varying the target batch sizes to assess stability. Due to space constraints, we report the average accuracy across target distributions in Table 1. The results show that AdMiT + +is less sensitive to batch size variations compared to other TTA methods, providing stable performance across different batch sizes. + +Module selection. In previous experiments, all source modules were used regardless of their relevance to the target. To investigate selective module integration, we conduct experiments on the CIFAR-100C dataset with a set of $N = 75$ pre-trained modules. For each target batch, AdMiT selects the top $M = k$ modules based on mixture weights. Results in Fig. 3 indicate that AdMiT effectively identifies and uses only the most relevant modules, achieving strong adaptation performance with fewer modules. + +Forgetting of source knowledge. To evaluate the resistance of AdMiT to catastrophic forgetting in dynamic test distributions, we use the CIFAR-100C dataset with four source modules pretrained on Snow, Frost, Fog, and Bright distributions. AdMiT selects $M = 3$ modules for adaptation to each new target distribution, maintaining higher accuracy on the original source distributions after adaptation. Table 2 shows that AdMiT outperforms other methods, including multi-source approaches like $\pi$ -tuning and SESoM, as well as anti-forgetting methods like BECoTTA and SAR. Methods like Model Soup and TENT, which adapt solely to the current target, show a faster rate of forgetting. + +Computational efficiency. To demonstrate AdMiT's computational advantages, we compare the overhead of our module matching approach against the additional costs incurred by hyperparameter tuning and routing network training. The results show that AdMiT achieves efficient source-target matching with lower computational cost and without any need for forward inference or retraining during deployment. Additionally, we evaluate the compatibility of AdMiT with various PET methods to confirm its minimal overhead and adaptability across different configurations. See the Appendix for the results. + +# 5. Conclusion + +We present AdMiT, a novel framework for transformers that dynamically integrates multiple source parameter-efficient tuning (PET) modules to address diverse and evolving target distributions. Unlike traditional PET methods that focus on single-source adaptation or require extra computation for multi-source integration, AdMiT selects and integrates relevant modules without the need for hyperparameter tuning, routing networks, or raw data sharing. This makes it well-suited for settings with privacy or resource constraints. AdMiT performs well in both zero-shot and dynamic adaptation scenarios, using a multi-source approach to handle distribution shifts while keeping source knowledge. 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Tolstikhin, "Towards a learning theory of cause-effect inference," in International Conference on Machine Learning, pp. 1452-1461, PMLR, 2015. 9 \ No newline at end of file diff --git a/admitadaptivemultisourcetuningindynamicenvironments/images.zip b/admitadaptivemultisourcetuningindynamicenvironments/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..61237df4260bdc0a88c76096e31208e9500ce416 --- /dev/null +++ b/admitadaptivemultisourcetuningindynamicenvironments/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0454968806a99b35d2bd20b3efa2b5b177eee4829e1bd4ec32a878b41b2665d5 +size 369000 diff --git a/admitadaptivemultisourcetuningindynamicenvironments/layout.json b/admitadaptivemultisourcetuningindynamicenvironments/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..1d81126017bc63d636e3c9b028ac0d2dc09cd848 --- /dev/null +++ b/admitadaptivemultisourcetuningindynamicenvironments/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:141eaa31906f7b02c6ce7f3d1789ee6c342ed0749625172d32e60dbf8e90678f +size 435119 diff --git a/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_content_list.json b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e9f7e0d5a288515e6716f9c0bce279f09128175f --- /dev/null +++ b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ef0f98e7ca0c691d8a6be3a8de02658498f811c495c004d479d9d19326571156 +size 80167 diff --git a/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_model.json b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_model.json new file mode 100644 index 0000000000000000000000000000000000000000..32092b3f620c8d18a80f622b85770a8f8f7e3757 --- /dev/null +++ b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0ad13b2eff5fc57bbaaefbc60e6c802a656e3b0ae6b2776a1bf9271e5dcacac7 +size 100429 diff --git a/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_origin.pdf b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8d2d5431dab7e331458bb1ad019be6109f81e1dd --- /dev/null +++ b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/a3a5f623-9c8e-40c7-93d2-175e52310d81_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:952d68df6a80fa2d08de5dd0311f74693b5e0e8c4aded71dda12dad135eac89a +size 653879 diff --git a/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/full.md b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c8fd0e3da03d5e4f4fb03c6ecdb4d196133f75f9 --- /dev/null +++ b/aduadaptivedetectionofunknowncategoriesinblackboxdomainadaptation/full.md @@ -0,0 +1,307 @@ +# ADU: Adaptive Detection of Unknown Categories in Black-Box Domain Adaptation + +Yushan Lai, Guowen Li, Haoyuan Liang, Juepeng Zheng*, and Zhiyu Ye School of Artificial Intelligence, Sun Yat-Sen University + +{laiysh6,ligw8,lianghy68,yezhy26}@mail2.sysu.edu.cn,zhengjp8@mail.sysu.edu.cn + +# Abstract + +Black-box Domain Adaptation (BDA) utilizes a black-box predictor of the source domain to label target domain data, addressing privacy concerns in Unsupervised Domain Adaptation (UDA). However, BDA assumes identical label sets across domains, which is unrealistic. To overcome this limitation, we propose a study on BDA with unknown classes in the target domain. It uses a black-box predictor to label target data and identify "unknown" categories, without requiring access to source domain data or predictor parameters, thus addressing both data privacy and category shift issues in traditional UDA. Existing methods face two main challenges: (i) Noisy pseudo-labels in knowledge distillation (KD) accumulate prediction errors, and (ii) relying on a preset threshold fails to adapt to varying category shifts. To address these, we propose ADU, a framework that allows the target domain to autonomously learn pseudo-labels guided by quality and use an adaptive threshold to identify "unknown" categories. Specifically, ADU consists of Selective Amplification Knowledge Distillation (SAKD) and Entropy-Driven Label Differentiation (EDLD). SAKD improves KD by focusing on high-quality pseudo-labels, mitigating the impact of noisy labels. EDLD categorizes pseudo-labels by quality and applies tailored training strategies to distinguish "unknown" categories, improving detection accuracy and adaptability. Extensive experiments show that ADU achieves state-of-the-art results, outperforming the best existing method by $3.1\%$ on VisDA in the OPBDA scenario. + +# 1. Introduction + +Unsupervised domain adaptation (UDA) [12] aims to transfer knowledge from a well-labeled source domain to an unlabeled target domain, which can ease the burden of manual labeling. Recently, UDA has been applied in a range of computer vision tasks, including image classification + +[13, 33, 48], objection detection [7, 20, 56] and semantic segmentation [6, 35, 47]. However, UDA methods may raise concerns about data privacy and portability issues due to their requirement for access to raw source data and source model parameters. Therefore, source-free domain adaptation (SFDA) [19, 27, 58] is proposed to protect the source data privacy. In the SFDA scenario, only the source model is provided to the target domain without access to source data. However, it still faces the issue of source information privacy, which can be compromised through techniques such as white-box attacks [45, 46]. To mitigate these concerns, Black-box Domain Adaptation (BDA) [28, 61] has been proposed recently, as shown in Figure 1(a), which aims to learn a model solely using the unlabeled data from the target domain, based on the predictions from a black-box predictor trained on the source data. This setting can effectively mitigate data privacy issues related to data and model parameter leakage. + +However, traditional BDA [28, 57, 60] always assumes that the source and target domains share identical category sets, which frequently fails to apply in practice. In real-world scenarios, the target domain is typically unlabeled, making it difficult to satisfy this assumption due to potential category shifts. Currently, there are two UDA settings that involve unknown classes in the target domain: Open-Set Domain Adaptation (OSDA) [36, 42] and Open-Partial Domain Adaptation (OPDA) [25, 41, 59]. OSDA deals with scenarios where the target domain contains private classes that are unknown to the source domain, while OPDA handles cases where both the source and target domains each have their own private classes. Black-box Domain Adaptation has been applied to OPDA recently [9]. As shown in Figure 1(b), this setting is designed to learn a robust model for the target domain that not only recognizes classes shared by two domains but also identifies "unknown" categories absent in the source domain despite having no information about difference of two label sets. + +Currently, only one study has addressed the above problem. [9] applies knowledge distillation to train the target model to mimic source predictor outputs and uses a man + +![](images/c7e73379d0d7153b199e6d7b6e853ccf121aa10dbaaf0d288d16850c7ba1e900.jpg) +(a) Black-box Domain Adaptation + +![](images/679d31d87a5b79f77bb55edf66b522db859480439b2b9c951e3e153089bc6abb.jpg) +(b) Open-patial Black-box Domain Adaptation +Figure 1. Black-box domain adaptation and Open-partial black-box domain adaptation settings with respect to label sets of source and target domains (red labels indicate common labels of two domains). Compared to BDA, ADU is able to deal with BDA with unknown classes in the target by adaptively detecting unknown categories. + +ually preset threshold to identify "unknown" categories. Though inspiring, it still has the following limitations. (i) Due to domain and category shifts between the source and target domains, predictions from the source model are inevitably noisy. Directly utilizing these noisy pseudo-labels will accumulate model prediction errors, making the adaptation process unreliable. (ii) Employing a preset threshold fails to accommodate the variability and complexity of category shifts in different target domains, which is inadequate for accurately detecting "unknown" classes across diverse domains, often resulting in misclassification and reduced adaptability. + +To address the issues mentioned above, we propose a simple yet effective framework called ADU, specifically designed for Open-Set BDA (OSBDA) and Open-Partial BDA (OPBDA). ADU incorporates two core modules: Selective Amplification Knowledge Distillation (SAKD) and Entropy-Driven Label Differentiation (EDLD). For the first challenge, SAKD enhances traditional knowledge distillation techniques, specifically tailoring KD to BDA with unknown classes in the target domain by amplifying learning from high-quality pseudo-labels produced by source API. This refinement ensures that the target model emphasizes learning from high-quality pseudo-labels, effectively mitigating the impact of noisy data. For the second challenge, EDLD enhances the framework's ability to handle diverse domain conditions. Initially, EDLD categorizes pseudo-labels based on their quality and then applies tailored training strategies to widen the distance between "unknown" classes and the others, while minimizing the impact of noisy pseudo-labels. This adaptive differentiation of labels heightens the effectiveness of employing the av + +erage entropy of the target model's predictions as a threshold. Consequently, this refined approach significantly improves the detection accuracy of "unknown" categories and adapts more adeptly to category shifts across various target domains. Additionally, we iteratively refine the pseudolabels generated by the source API, which can significantly enhance their quality. + +Our main contributions in this paper could be summarized as follows: + +1. We propose Selective Amplification Knowledge Distillation (SAKD), a refined knowledge distillation technique specifically designed for the OPBDA and OSBDA scenarios, which can effectively mitigate the impact of noisy pseudo-labels. +2. We introduce Entropy-Driven Label Differentiation (EDLD), which categorizes pseudo-labels by quality and applies customized training strategies to enhance the distinction between "unknown" and others, thereby improving detection accuracy and domain adaptability through adaptive entropy-based thresholding. +3. Extensive experiments on four public benchmarks demonstrate the superior performance of our proposed method compared with existing SOTA works, surpassing the best existing method by $3.1\%$ on VisDA in the OPBDA scenario. + +# 2. Related work + +Black-box domain adaptation. Unsupervised Domain Adaptation (UDA) [12] aims to adapt a model trained on a labeled source domain to an unlabeled target domain. Many early methods relied on techniques such as instance weighting [52, 55], feature transformation [18, 26, 43], and feature + +space [30, 51]. Despite their effectiveness, these methods require access to source domain data, raising privacy and portability concerns [22]. To address privacy issues associated with UDA, Source-Free Domain Adaptation (SFDA) methods [19, 27, 58] have been proposed. These methods adapt models using only the source model and unlabeled target data, eliminating the need for source data during adaptation. Techniques such as entropy minimization [2] and pseudo-labeling [62] have been explored. However, SFDA methods still face potential privacy risks due to the use of generative models and other techniques that might inadvertently reveal source data characteristics. Therefore, Black-box Domain Adaptation (BDA) [28, 61] has emerged as a solution to further mitigate privacy concerns by only accessing the source model's outputs without any internal details. This approach ensures better privacy preservation compared to traditional UDA and SFDA methods. Recent methods such as DINE [28] and BETA [57] have made significant strides in this area. Nevertheless, they struggle with inconsistent label sets between domains. + +Open-set and open-partial domain adaptation. Closed-set domain adaptation assumes identical label sets between source and target domains, focusing on minimizing distribution shifts using techniques like discrepancy minimization [31, 32] and adversarial training [8, 15]. However, these methods often struggle when label sets are not perfectly aligned. To address this issue, Partial Domain Adaptation (PDA) assumes that only the source domain contains private classes, with methods such as SAN [4] employing class-wise domain discriminators, and ETN [5] using progressive weighting schemes. Meanwhile, Open-Set Domain Adaptation (OSDA) handles scenarios where the target domain has private classes unknown to the source. Besides, Open-Partial Domain Adaptation (OPDA) addresses both domains having their own private classes. UAN [59] quantifies sample-level uncertainty using entropy and domain similarity, and Fu et al. [11] combines entropy, confidence, and consistency for better uncertainty measurement. To address the challenges faced by black-box domain adaptation, [9] combines OPDA with BDA to address both category shift and privacy concerns. It applies knowledge distillation to train the target model to emulate source predictor outputs, using a preset threshold to identify "unknown" categories. Though inspiring, it still faces significant limitations regarding pseudo-label quality and the detection of "unknown" categories. To address these issues, we propose the ADU framework, applying it to Open-Set BDA (OSBDA) and Open-Partial BDA (OPBDA) to mitigate the impact of noisy pseudo-labels and enhance adaptability to category shifts across varied target domains. This approach provides a robust solution to the limitations of existing methods. + +Learning with noisy labels. Deep learning models often + +overfit on noisy labels, leading to poor generalization [60]. To address this, various approaches have been proposed, including noise-robust losses [23, 44], noise-transition matrix estimation [14], clean sample selection [53], and loss reweighting [34]. However, these methods often require noise-free validation sets or make assumptions about the noise distribution, which are impractical in BDA settings. These methods [29, 34] differ by not assuming any specific noise distribution and leveraging noisy scores from source training classes. Recently, NEL [1] introduced a novel approach by integrating a Negative Learning loss with a pseudo-label refinement framework that leverages ensembling techniques. Negative Learning [23] is an indirect learning method that employs complementary labels to address noise issues effectively. In our work, we use Negative Learning to refine high-quality pseudo-labels without ensembling, reducing computational cost and making our approach more flexible and robust for OSBDA and OPBDA. + +# 3. Methodology + +In this paper, we are provided with a target domain $\mathcal{D}_t = \left\{x_t^i\right\}_{i=1}^{N_t}$ with $N_t$ unlabeled samples where $x_t^i \in \mathcal{X}_t$ , and a black-box predictor $f_s$ trained by a source domain $\mathcal{D}_s = \left\{\left(x_s^i, y_s^i\right)\right\}_{i=1}^{N_s}$ with $N_s$ labeled samples where $x_s^i \in \mathcal{X}_s$ . We use $L_s$ and $L_t$ to denote the label spaces of the source domain and target domain respectively. In general, model $f$ consists of a feature extractor $G$ and a fully connected layer-based classifier $C$ . We have no access to the source domain data $\mathcal{D}_s$ and the parameters of the source model $f_s$ . Only a black-box predictor trained on the source domain, i.e., an API, is available. The objective is to leverage the predictions of the API of the source domain to learn a mapping model $f_t$ which can label the target samples with either one of the $L_s$ labels or the "unknown" label. The overall workflow is shown in Fig. 2. + +# 3.1. Selective amplification knowledge distillation + +Knowledge distillation (KD) [17] has been widely applied to address the black-box domain adaptation problem [9, 28, 57], as it enables the transfer of knowledge from one model (teacher) to another (student) by guiding the target model (student) to emulate the predictions of the source model (teacher). This approach is particularly suitable for BDA scenarios, where only the predictions of the source model are accessible. To better leverage the information available from the source domain's API, we use a knowledge distillation loss with both the source model's probabilities and hard pseudo-labels. This can be formulated as: + +$$ +\mathcal {L} _ {K D} = \mathbb {E} _ {x _ {t} \sim \mathcal {X} _ {t}} \left[ C E \left(\tilde {\boldsymbol {y}} _ {t}, p _ {t}\right) + C E \left(p _ {s}, p _ {t}\right) \right], \tag {1} +$$ + +where $CE(\cdot ,\cdot)$ denotes the cross entropy function, and + +![](images/e78f2281412e7b1985b1f6c1d82c971484177a84c607abf68d737a3067bb3a8d.jpg) +Figure 2. An overview of the proposed ADU framework. We utilize the black-box source predictor solely as an API service, obtaining only the source predictions from it. "PL" in the figure means pseudo-labels. + +$\tilde{\pmb{y}}_t$ is a one-hot pseudo-label derived from $f_{s}(x_{t})$ . In addition, we use $p_s$ and $p_t$ to replace $f_{s}(x_{t})$ and $f_{t}(x_{t})$ for simplicity. However, due to domain and category shifts, the predictions from the source model are inevitably noisy. Consequently, Eq. (1) processes information from these predictions equally, which can adversely affect the performance of the target model. In order to solve the issue, we propose Selective Amplification Knowledge Distillation (SAKD), a method that enhances knowledge distillation by leveraging the confidence of pseudo-labels produced by the source model. + +Firstly, we simplify Eq. (1) to derive the following formulation: + +$$ +\begin{array}{l} \mathcal {L} _ {K D} = - \mathbb {E} _ {x _ {t} \sim \chi_ {t}} (\log p _ {t} ^ {\hat {c}} + \sum_ {c = 1} ^ {| L _ {s} |} p _ {s} ^ {c} \log p _ {t} ^ {c}) \\ = - \mathbb {E} _ {x _ {t} \sim \chi_ {t}} [ (1 + p _ {s} ^ {\hat {c}}) \log p _ {t} ^ {\hat {c}} + \sum_ {\substack {c = 1 \\ c \neq \hat {c}}} ^ {| L _ {s} |} p _ {s} ^ {c} \log p _ {t} ^ {c} ], \end{array} \tag{2} +$$ + +where $\hat{c}$ represents the label predicted by the source model, defined as $\hat{c} = \arg \max_c p_s^c$ . Subsequently, we formulate the SAKD loss by incorporating a modulating parameter $\theta \geq 1$ into the term $(1 + p_s^{\hat{c}})$ , which only pertains to $\hat{c}$ : + +$$ +\mathcal {L} _ {S A K D} = - \mathbb {E} _ {x _ {t} \sim \chi_ {t}} \left[ \left(1 + p _ {s} ^ {\hat {c}}\right) ^ {\theta} \log p _ {t} ^ {\hat {c}} + \sum_ {\substack {c = 1 \\ c \neq \hat {c}}} ^ {| L _ {s} |} p _ {s} ^ {c} \log p _ {t} ^ {c} \right], \tag{3} +$$ + +Discussion of SAKD loss: For simplicity, we consider the case with a single sample, where the SAKD loss simplifies to: + +$$ +\mathcal {L} _ {\mathrm {S A K D}} = - \left[ \left(1 + p _ {s} ^ {\hat {c}}\right) ^ {\theta} \log p _ {t} ^ {\hat {c}} + \sum_ {c = 1, c \neq \hat {c}} ^ {| L _ {s} |} p _ {s} ^ {c} \log p _ {t} ^ {c} \right] \tag {4} +$$ + +Next, we apply the generalized binomial theorem to expand $\left(1 + p_s^{\hat{c}}\right)^\theta$ as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {S A K D}} = - \left[ \sum_ {k = 0} ^ {\infty} \binom {\theta} {k} \left(p _ {s} ^ {\hat {c}}\right) ^ {k} \log p _ {t} ^ {\hat {c}} + \sum_ {c = 1, c \neq \hat {c}} ^ {| L _ {s} |} p _ {s} ^ {c} \log p _ {t} ^ {c} \right] \\ = \mathcal {L} _ {\mathrm {K D}} - \left[ \sum_ {k = 1} ^ {\infty} \binom {\theta} {k} \left(p _ {s} ^ {\hat {c}}\right) ^ {k} - p _ {s} ^ {\hat {c}} \right] \log p _ {t} ^ {\hat {c}} \\ \approx \mathcal {L} _ {\mathrm {K D}} - \left[ (\theta - 1) p _ {s} ^ {\hat {c}} + \frac {\theta (\theta - 1)}{2} \left(p _ {s} ^ {\hat {c}}\right) ^ {2} \right] \log p _ {t} ^ {\hat {c}} \tag {5} \\ \end{array} +$$ + +In Eq. (5), the first term $\mathcal{L}_{\mathrm{KD}}$ represents the original KD loss in Eq. (2), while the second term introduces an additional term, which is positive and solely depends on the target class $\hat{c}$ . We demonstrate that this additional term enables the SAKD loss to capture more information from pseudolabels with high confidence, meaning those with higher values of $p_s^{\hat{c}}$ , thereby reducing the impact of noisy pseudolabels. A comprehensive proof of this claim is provided in the supplemental material. + +# 3.2. Entropy-driven label differentiation + +As stated above, the outputs from the source model are highly likely to be inaccurate and noisy due to the domain shift [3] and category shift. Even if we propose a promising solution in Eq. (3), we still face a tough challenge to detect the "unknown" categories, which means we should widen the difference between "unknown" and others. [59] shows entropy is an effective tool to detect "unknown" in domain adaptation. Entropy quantifies the prediction uncertainty, and smaller entropy represents a more certain prediction. In order to effectively address the influence brought by the category shift, we implement an automatic threshold determined by average entropy. The prediction process can be formulated as follows: + +$$ +y _ {t} = \left\{ \begin{array}{l l} \arg \max _ {c} p _ {t} ^ {c} & H \left(p _ {t}\right) < w \\ \text {u n k n o w n} & H \left(p _ {t}\right) \geq w, \end{array} \right. \tag {6} +$$ + +where $H(p_{t})$ and $w$ are computed as: + +$$ +H \left(p _ {t}\right) = - \sum_ {c = 1} ^ {\left| L _ {s} \right|} p _ {t} ^ {c} \log p _ {t} ^ {c}, \tag {7} +$$ + +$$ +w = \mathbb {E} _ {x _ {t} \sim \mathcal {X} _ {t}} H (p _ {t}). \tag {8} +$$ + +Taking the average as a threshold eliminates the requirement of per-dataset hyper-parameter tuning and makes our selection process highly adaptive. As we employ entropy as a threshold to detect "unknown" categories, we still face a challenge to widen the gap between "unknown" and others. In order to address the issue, we propose Entropy-Driven Label Differentiation (EDLD) to make the "unknown" distinguishable and enhance the quality of pseudo-labels with high certainty. We use entropy to calculate the uncertainty level of pseudo-labels. Higher entropy always shows more uncertain predictions. We define the EDLD loss by dividing pseudo-labels into high-quality (HQ) and low-quality (LQ) by their entropy, the loss is defined as follows: + +$$ +\mathcal {L} _ {E D L D} = \mathbb {E} _ {x _ {t} \sim \mathcal {X} _ {t}} \left[ \left\{ \begin{array}{l l} \mathcal {L} _ {H Q} (p _ {t}) & \text {i f} H (p _ {t}) < w \\ \mathcal {L} _ {L Q} (p _ {t}) & \text {i f} H (p _ {t}) \geq w \end{array} \right. \right], \tag {9} +$$ + +$$ +\mathcal {L} _ {H Q} = H \left(p _ {t}\right) + \mathcal {L} _ {N L} \left(p _ {t}, \bar {y} _ {t}\right), \quad \mathcal {L} _ {L Q} = - H \left(p _ {t}\right), \tag {10} +$$ + +In the EDLD module, we not only use the entropy loss to widen the entropy gap between high-quality and low-quality pseudo-labels but also use a negative learning loss [21] to refine the high-quality pseudo-labels, the negative loss is the following: + +$$ +\mathcal {L} _ {N L} \left(p _ {t}, \bar {y} _ {t}\right) = - \sum_ {c = 1} ^ {| L _ {s} |} \bar {\mathbf {y}} _ {t} ^ {c} \log \left(1 - p _ {t} ^ {c}\right), \tag {11} +$$ + +where is $\bar{y}_t$ a complementary label $\bar{y}_t \in \{1, \dots, |L_s|\} \setminus \{y_t\}$ chosen randomly from the set of labels, and $\bar{y}_t$ is one-hot label derived from $\bar{y}_t$ . Eq. (11) enables the probability value of the complementary label to be optimized as zero, resulting in an increase in the probability values of other classes, which can effectively refine the high-quality pseudo-labels. + +# 3.3. Adaptive refinement of pseudo labels + +To further mitigate the impact of noise in the pseudo-labels generated by the source model, we employ an exponential moving average (EMA) of the target predictions. This allows for a gradual and controlled update of the pseudolabels supplied by the source model at each iteration. The update process is defined as follows: + +$$ +p _ {s} \leftarrow \gamma p _ {s} + (1 - \gamma) f _ {t} \left(x _ {t}\right), \quad \forall x _ {t} \in \mathcal {X} _ {t}, \tag {12} +$$ + +where $\gamma$ is a smoothing factor that determines the extent to which the pseudo-labels should adapt to the most recent predictions from the target model. A higher value of $\gamma$ places more weight on the existing pseudo-labels, while a lower value allows quicker adaptation to new information. + +This strategy refines the pseudo-labels iteratively, balancing consistency with adaptability. By adjusting the pseudo-labels in a controlled manner, the model can better handle noise and gradually align the source model's outputs with the distribution of the target data. The EMA strategy ensures that updates are not overly reactive to fluctuations, thus enhancing the robustness of the model and improving performance in scenarios with diverse target domains. + +# 3.4. The overall objective + +Integrating these objectives introduced in Eqs. (3, 9) together, we obtain the final loss function as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {S A K D} + \lambda \mathcal {L} _ {E D L D}, \tag {13} +$$ + +where $\lambda$ is a hyper-parameter empirically set to 1.0, controlling the importance of $L_{SAKD}$ and $L_{EDLD}$ during distillation. + +# 4. Experiments + +# 4.1. Setup + +Datasets. To assess the effectiveness of our approach, we conduct experiments using the Office31 [40], OfficeHome [50], VisDA [38], DomainNet [39] datasets. Office31 is a popular benchmark for UDA, consisting of three domains (Amazon, Webcam, Dslr) in 31 categories. OfficeHome is a more challenging benchmark for its distant domain shifts, which consists of four domains (Art, Clipart, Product, Real World) in 65 categories. VisDA is a large-scale benchmark containing 2 different 12-class domains, with a source domain with 152k synthetic images and a target domain with + +Table 1. H-score (\%) comparison in OPBDA scenario on the OfficeHome dataset. + +
MethodAr→ClAr→PrAr→ReCl→ArCl→PrCl→RePr→ArPr→ClPr→ReRe→ArRe→ClRe→PrAvg.
No Adapt.55.867.372.864.262.370.565.752.171.766.156.769.264.5
DINE [28]45.346.154.651.045.352.449.944.552.152.446.745.748.8
BETA [57]45.947.454.849.345.150.149.345.553.551.545.848.848.9
SEAL [54]40.646.847.844.542.745.247.340.047.145.546.746.645.1
UB²DA [9]60.969.676.374.469.276.574.560.376.274.162.071.170.4
ADU61.272.777.970.372.577.375.962.084.773.264.174.972.2
+ +Table 2. H-score (%) comparison in OPBDA scenario on the Office31, VisDA, and DomainNet datasets, respectively. + +
MethodOffice31VisDADomainNet
A→DA→WD→AD→WW→AW→DAvg.S→RP→RP→SR→PR→SS→PS→RAvg.
No Adapt.79.971.980.191.578.789.882.037.752.835.043.632.535.751.841.9
DINE [28]50.351.456.663.054.060.155.943.548.439.543.438.137.645.642.1
BETA [57]52.454.051.661.253.457.655.045.549.240.343.138.238.048.442.9
SEAL [54]73.870.351.155.647.057.059.145.652.739.943.638.439.249.743.9
UB2DA [9]80.978.292.692.689.487.986.945.257.147.254.844.041.451.549.3
ADU87.585.287.094.483.890.588.148.759.847.852.546.642.756.451.0
+ +55k real images from Microsoft COCO. DomainNet is the largest DA dataset with about 0.6 million images. Like [11, 24], we conduct experiments on three subsets of it, i.e., Painting, Real, and Sketch. Following existing works [11, 24, 59], we separate the label set into three parts: common $(|L_s \cap L_t|)$ , source-private $(|L_s - L_t|)$ and target-private $(|L_t - L_s|)$ . The classes are separated according to their alphabetical order. We evaluate ADU in OPBDA using the four datasets, and in OSBDA using the first three datasets. + +Evaluation protocols. Considering the trade-off between the accuracy of known and unknown classes is important in evaluating OSDA and OPDA methods. We evaluate methods using H-score [11]. H-score is the harmonic mean of the accuracy on common classes $(\mathrm{Acc}_c)$ and accuracy on the "unknow" classes $(\mathrm{Acc}_u)$ and is defined as: + +$$ +h = 2 \cdot \frac {A c c _ {c} \cdot A c c _ {u}}{A c c _ {c} + A c c _ {u}} \tag {14} +$$ + +So, this metric is designed to provide a more comprehensive evaluation by ensuring that improvements in one area do not come at the expense of the other. It can measure both accuracies well. + +Implementation details. All experiments are implemented in Pytorch [37]. For fair comparisons to previous methods, we use the same backbone of ResNet50 [16] pre-trained on ImageNet [10] as the feature extractor in all experiments. For the source model, we fine-tune the model on source examples optimizing with cross-entropy loss function and then treat it like a black-box by only requiring the input-output interfaces of this model in our experiments. We + +use SGD optimizer with a learning rate of 0.01, a momentum of 0.9 with a weight decay of 5e-4 and a batch size of 128. Concerning the parameters in ADU, We set $\theta = 1.1$ , $\gamma = 0.6$ and $\lambda = 1.0$ for all datasets and tasks. Additionally, following [23], we set the ratio of $L_{NL}(p_t,\bar{y}_t)$ to $H(p_{t})$ as 0.01:1 in Eq. (10). + +Baselines. We compare the proposed ADU with (i) BDA: DINE [28], BETA [57], SEAL [54] (ii) OPBDA: $\mathbf{UB}^2\mathbf{DA}$ [9]. These methods represent the state-of-the-art in their respective settings. Notably, owing to black-box DA lacking the capability to identify "unknown" categories, we apply the average entropy as the threshold to them, similar to our setting. The term "No Adapt." refers to the baseline scenario where the source model is used directly for target label prediction, without any form of adaptation. + +# 4.2. Results + +Results for OPBDA. We first perform experiments under the most challenging scenario, namely OPBDA, in which both the source and target domains contain private categories. The results for the OfficeHome dataset are presented in Table 1, while those for the Office31, VisDA, and DomainNet datasets are shown in Table 2. As illustrated in these tables, our proposed ADU method achieves a new state-of-the-art, surpassing all existing methods across the four datasets. Notably, ADU consistently improves the H-score compared to the "No Adapt." baseline in each experimental setting, with a significant increase of $11.0\%$ on the VisDA dataset. This improvement demonstrates that our method effectively mitigates the influence of noise from + +Table 3. H-score (\%) comparison in OSBDA scenario on the OfficeHome dataset. + +
MethodAr→ClAr→PrAr→ReCl→ArCl→PrCl→RePr→ArPr→ClPr→ReRe→ArRe→ClRe→PrAvg.
No Adapt.59.668.175.767.166.770.463.854.955.771.458.670.565.2
DINE [28]47.045.852.249.747.150.048.243.850.452.646.046.848.3
BETA [57]46.648.354.947.748.450.549.142.951.850.245.248.948.7
SEAL [54]43.346.547.143.745.945.445.340.845.643.541.346.544.6
UB2DA [9]65.570.475.567.869.374.471.256.775.070.763.369.869.1
ADU66.070.577.472.270.175.069.063.676.173.464.175.271.1
+ +Table 4. H-score $(\%)$ comparison in OSBDA scenario on the Office31 and VisDA datasets, respectively. + +
MethodOffice31VisDA
A→DA→WD→AD→WW→AW→DAvg.S→R
No Adapt.81.480.885.388.178.088.083.644.6
DINE [28]60.554.656.869.056.361.559.843.1
BETA [57]48.353.054.360.654.457.354.748.3
SEAL [54]50.443.753.444.854.050.849.540.6
UB2DA [9]85.787.491.089.285.184.187.148.1
ADU86.984.989.791.386.389.288.150.8
+ +source model predictions on the target model and accurately identifies unknown categories within the target data. An examination of Tables 1 and 2 reveals that methods such as DINE [28], BETA [57], and SEAL [54] perform poorly compared to our approach and $\mathrm{UB}^2\mathrm{DA}$ [9], with performance even falling below the "No Adapt." baseline on the Office31 and OfficeHome datasets. This underperformance is likely due to the lack of design tailored specifically for the OPBDA scenario in these methods, which hinders their ability to effectively differentiate unknown categories from other classes. These results underscore the importance of our ADU approach, which is specifically designed for OPBDA. When compared to $\mathrm{UB}^2\mathrm{DA}$ [9], ADU achieves higher H-scores on the Office31, OfficeHome, VisDA, and DomainNet datasets, with improvements of $1.2\%$ , $1.8\%$ , $3.5\%$ , and $1.7\%$ , respectively. These gains further highlight the effectiveness of our proposed approach. + +Results for OSBDA. We subsequently conduct experiments under OSBDA scenarios, where only the target domain includes categories absent from the source domain. The results for the OfficeHome dataset are provided in Table 3, while those for the Office31 and VisDA datasets are presented in Table 4. As shown in these tables, our proposed ADU method achieves performance that surpasses the current state-of-the-art. Specifically, ADU consistently outperforms the "No Adapt." baseline in terms of H-score across all experimental settings. Notably, for the $\mathrm{Pr} \rightarrow \mathrm{Re}$ scenario, it achieves an improvement of $20.4\%$ . This substantial enhancement demonstrates that our method effectively reduces the influence of noise from source model pre + +Table 5. Ablation Study. H-score $(\%)$ of different variants in OPBDA scenarios. $\mathcal{L}_{HQ}^{1}$ , $\mathcal{L}_{HQ}^{2}$ , $\mathcal{L}_{LQ}$ refer to the objectives corresponding to the negative loss in $\mathcal{L}_{HQ}$ , entropy loss in $\mathcal{L}_{HQ}$ , and loss associated with low-quality labels, respectively. + +
L1HQL2HQL2QOffice31OfficeHomeAvg.
A → WD → WAr → ClCl → RePr → ArRe → Cl
---82.992.661.272.971.562.073.7
--84.393.561.173.072.062.774.6
--83.592.761.774.372.162.574.5
--84.193.861.474.172.662.674.8
-84.394.162.773.771.761.374.6
-83.194.263.374.772.362.675.0
-85.194.062.674.672.162.875.2
85.294.461.277.375.964.176.3
+ +dictions on the target model, allowing for accurate identification of unknown categories within the target data. Compared to $\mathrm{UB^{2}DA}$ [9], ADU achieves higher H-scores on the Office31, OfficeHome and Visda datasets, with improvements of $1.0\%$ , $2.0\%$ , and $2.7\%$ , respectively. These results further validate the effectiveness of our proposed approach. + +# 4.3. Analysis + +Ablation study. To comprehensively assess the individual contribution of the components comprising our method, we conduct extensive ablation studies on two tasks from the Office31 dataset and four tasks from the OfficeHome dataset in OPBDA scenarios. The results are summarized in Table 5. Here, $\mathcal{L}_{HQ}^{1}$ , $\mathcal{L}_{HQ}^{2}$ , $\mathcal{L}_{LQ}$ refer to the objectives corresponding to the negative loss in $\mathcal{L}_{HQ}$ , entropy loss in $\mathcal{L}_{HQ}$ , and loss associated with low-quality labels, respectively. More detailed results can be found in supplementary material. It is important to emphasize that in all ablation experiments, we consistently employ the SAKD loss, which is a critical component of the ADU framework. Without it, the model would be unable to transfer knowledge from the source domain to the target model effectively. From the ablation study results, we can draw the following conclusions: (i) The introduction of any component alongside the SAKD loss leads to performance improvements, underscoring the vital role of the EDLD module. (ii) The full EDLD loss, which includes the negative loss term, yields better performance compared to its version without the negative loss, + +![](images/4484827b5b8c63032e103d251105fe0b4bb9899dce6ca76aba4e8a7b83e52bb8.jpg) +Figure 3. Parameters sensitivity analysis for six tasks. (a-b) plot the H-score with different values of $\lambda$ , $\theta$ ; (c) plot the H-score, $\mathrm{Acc}_c$ , $\mathrm{Acc}_u$ with different values of $\gamma$ . The default values of these hyperparameters are set to $\lambda = 1.0$ , $\theta = 1.1$ , and $\gamma = 0.6$ . + +![](images/08c225f96d48980126e7f969dfe663e036f9dfaf482f30dae474a9f76f098d72.jpg) + +![](images/0adff36860afc575c9c033912b7b501e3e31ed6569084e9ee11cda382153ac60.jpg) + +![](images/1355f2a705c8410e1d496dcc7c31f228a86a6862ec4e2355b6692ffc730caac4.jpg) +(a) No Adapt. +Figure 4. t-SNE feature visualization of target representations in $\mathrm{D}\rightarrow \mathrm{A}$ OPBDA task. Blue dots represent target "known" examples $(L_{s}\cap L_{t})$ while red dots are unknown" examples $(L_{s} - L_{t})$ + +![](images/bdf150df8dc7c29414b5907ff567505aba668e7afc1ab553079aa505144a5981.jpg) +(b) ADU + +demonstrating the effectiveness of incorporating this term. (iii) The integration of all components results in the highest H-scores, providing clear evidence of the synergy and efficacy of the combined modules. + +Feature visualization. Fig. 4 displays the visualization of the target feature with t-SNE [49], providing a clear representation of the feature distribution. As expected, ADU achieves excellent alignment between the source and target domain features. Taking a closer look at the visualization, it is evident that ADU excels in distinguishing the "unknown" categories from the other classes. This improvement aligns well with the intended function of the EDLD module, which is designed to enhance the separation of "unknown" categories from known categories. This result further highlights the effectiveness of ADU in handling the challenges posed by unknown classes in black-box domain adaptation tasks. + +Parameters sensitivity analysis. To better assess the impact of different hyperparameters, we conduct a detailed sensitivity analysis. We investigate the sensitivity of the parameters $\lambda$ , $\theta$ , and $\gamma$ by performing experiments on two tasks from the Office31 dataset and four tasks from the OfficeHome dataset in OPBDA scenarios, as shown in Fig. 3. + +The parameter $\lambda$ is varied over the range [0.0, 0.2, 0.5, 1.0, 2.0, 5.0], $\theta$ spans [1.00, 1.05, 1.10, 1.15, 1.20, 1.25], and $\gamma$ is explored within the range [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]. It is evident that the results are stable around the selected values of $\lambda = 1.0$ , $\theta = 1.1$ , and $\gamma = 0.6$ . Additionally, as shown in Fig. 3(b), we examine the effect of varying $\theta$ in Eq. (3). The results around the chosen parameter $\theta = 1.1$ remain stable, and we also observe that increasing $\theta$ slightly from 1.0 leads to an improvement in the H-score, thereby highlighting the effectiveness of Eq. (3). Finally, we analyze the impact of $\gamma$ . As shown in Fig. 3(c), there is an inverse relationship between $\mathrm{Acc}_c$ and $\mathrm{Acc}_u$ . However, when $\gamma = 0.6$ , the two metrics reach a relatively balanced state, and at this point, the H-score achieves an optimal result. + +# 5. Conclusion + +In this paper, we introduce the ADU model, a framework specifically designed to tackle Black-box Domain Adaptation with unknown classes in the target domain. ADU integrates two key innovations: Selective Amplification Knowledge Distillation (SAKD) and Entropy-Driven Label Differentiation (EDLD). SAKD enhances model accuracy by selectively amplifying high-confidence pseudolabels, thereby effectively mitigating the influence of noisy pseudo-labels. Meanwhile, EDLD improves the recognition of unknown categories through an entropy-driven threshold, expanding the difference between unknown categories and others and bolstering the robustness of the method across a range of diverse target domains. Experiments across four benchmark datasets demonstrate that ADU outperforms existing state-of-the-art approaches, highlighting its exceptional adaptability and efficacy, setting a new benchmark for future research in the field. + +Acknowledgement. This work was supported by the National Natural Science Foundation of China (Grant T2125006 and 42401415) and Jiangsu Innovation Capacity Building Program (Project BM2022028). + +# References + +[1] Waqar Ahmed, Pietro Morerio, and Vittorio Murino. Cleaning noisy labels by negative ensemble learning for source-free unsupervised domain adaptation. In Proceedings of the IEEE/CVF winter conference on applications of computer vision, pages 1616-1625, 2022. 3 +[2] Mathilde Bateson, Hoel Kervadec, Jose Dolz, Herve Lombaert, and Ismail Ben Ayed. Source-free domain adaptation for image segmentation. Medical Image Analysis, 82: 102617, 2022. 3 +[3] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. 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Our AFL draws inspiration from analytic learning—a gradient-free technique that trains neural networks with analytical solutions in one epoch. In the local client training stage, the AFL facilitates a one-epoch training, eliminating the necessity for multi-epoch updates. In the aggregation stage, we derive an absolute aggregation (AA) law. This AA law allows a single-round aggregation, reducing heavy communication overhead and achieving fast convergence by removing the need for multiple aggregation rounds. More importantly, the AFL exhibits a property that invariance to data partitioning, meaning that regardless of how the full dataset is distributed among clients, the aggregated result remains identical. This could spawn various potentials, such as data heterogeneity invariance and client-number invariance. We conduct experiments across various FL settings including extremely non-IID ones, and scenarios with a large number of clients (e.g., $\geq 1000$ ). In all these settings, our AFL constantly performs competitively while existing FL techniques encounter various obstacles. Our codes are available at https://github.com/ZHUANGHP/Analytic-federated-learning. + +# 1. Introduction + +Federated learning (FL) [24] aims to collectively train a machine learning model over data silos by aggregating their individual trained weights, while preserving the privacy of their source data. This training paradigm has received high popularity, particularly in sensitive domains where data privacy is crucial, such as in banks [27, 41] and hospitals [11, 13]. + +Conventional FL techniques rely on weight aggregation + +among clients over multiple rounds of training. The objective is to achieve convergence and approximate its joint-training counterpart, where all clients' data are accessible in a single location. To accomplish this, many contributions have been made. One widely recognized method is FedAvg [24]. Relying on a large number of aggregation rounds, the FedAvg employs a simple yet effective weight averaging technique across local clients. Building upon this, various methods have been proposed (e.g., the FedProx [17] and the FedNova [35]), each with its own specific focus within the field of FL. + +However, training a model from scratch via FL can be computationally intensive and demanding in terms of communication bandwidth, especially with large models and numerous participating clients. Several efforts have explored utilizing pre-trained models to mitigate these challenges [23, 45]. Typically, this involves freezing the backbone and only updating and sharing lightweight parameters, such as prototypes [29, 30] or prompts [7, 40], to reduce the substantial training costs. + +Although leveraging pre-trained models can circumvent the high costs associated with training backbones from scratch, existing FL techniques with pre-trained models are primarily based on a gradient-based iterative approach, necessitating iterative optimization on each client and multi-round aggregation across clients. The gradient-based optimization used in the existing FL faces various challenges and imposes several constraints. The faced challenges include, but are not limited to: 1) Data heterogeneity, where the data distribution in each client is not independently identical (non-IID), even with mutually exclusive data categories across different clients (i.e., pathological distribution), 2) Large client number, where the aggregation involving a significant number of clients (i.e., $\geq 1000$ ) can lead to substantial performance degradation in FL systems as the client count increases [16], 3) Slow convergence: where FL methods may struggle to converge within limited communication rounds, especially + +in severe non-IID scenarios, and 4) High communication cost, where multi-round aggregation in existing FL methods escalates the communication costs associated with parameter sharing between clients and servers. + +In this paper, we propose a new FL training framework named analytic federated learning (AFL), which provides a single-round aggregation for federated learning with pretrained models. The AFL draws inspiration from analytic learning [8, 32, 48]—a gradient-free technique with a closed-form solution obtained from reshaping the network training into linearized formulation. The AL paradigm receives several benefits over gradient-based techniques. First, it is gradient-free, thereby avoiding gradient-related issues, such as vanishing and exploding gradients. Second, the analytical solution frees AL from convergence issues during training. Also, the AL requires only one visit to the dataset while gradient-based mechanism usually needs hundreds of epochs or beyond. These properties are attractive in FL to accomplish fast convergence and low communication cost. Here, we are able to incorporate this mechanism into the FL domain to overcome limitations inherent in gradient-based techniques. Our contributions are summarized as follows: + +- We propose the AFL, a gradient-free FL framework with analytical (closed-form) solutions. These analytical solutions apply both in the local client training stage and the aggregation stage. +- In the local stage, we adopt a pre-trained network to harness input embeddings, and formulate the training in each client into a localized linear regression problem. This leads to a least squares (LS) based one-epoch client training, eliminating the need for multi-epoch training and enabling fast convergence in local clients. +- In the aggregation stage, we derive an absolute aggregation (AA) law in analytical form, optimally establishing a single-round aggregation. That is, the aggregation happens only once, avoiding multiple FL rounds that bring high communication costs. Additionally, in scenarios where the AA law becomes suboptimal due to a large number of clients, we introduce a regularization intermediary (RI) process to restore its optimality. +- Owing to analytical solutions, the AFL exhibits a property that invariance to data partitioning. This means that regardless of how the full dataset is distributed (e.g., nonIID) among local clients, the result remains identical. This property spawns several appealing characteristics: i) Data heterogeneity invariance where the result is invariant to arbitrary heterogeneous data partition scenarios. ii) Client-number invariance, which produces identical results regardless of the number of clients involved. +- We conduct extensive experiments spanning diverse scenarios, including a wide variety of non-IID partitions and large client number (up to 1000) settings. Our AFL consistently showcases competitive performance throughout all + +these settings when compared with other methods. + +# 2. Related Works + +In this section, we review existing related FL literature. Additionally, we explore various AL techniques and their variants to reveal their underlying mechanisms. + +# 2.1. Federated Learning Methods + +Following the FedAvg [24], to address non-IID issues in FL, various methods have been proposed. One common approach involves assessing the significance of parameters during aggregation to ensure that local updates do not diverge substantially from the global model. For instance, the FedProx [17] restricts the size of local updates, while the FedNova [35] employs a normalized averaging method to eliminate target inconsistency while maintaining fast error convergence. These methods are frequently used as baselines, and we compare our results against them in our experiments. Another set of methods focuses on determining adaptive aggregation weights obtained from multiple clients. The Fed-LAW [19] learns these weights to achieve a global model with state-of-the-art performance, though it requires a proxy dataset to learn the weights, making the results sensitive to the selection of the proxy dataset. To address this sensitivity, the FedCDA [34] proposes a proxy-free method that reduces each client's deviation from the local models of other participants and selects a local model from its multiple recent models acquired over several rounds. + +Some methods address the parameter order mismatch issue across clients, which can occur during global aggregation. The Fed2 [43] designs a model structure adaptation method to ensure explicit feature allocation across different network structures. Similarly, the method in [18] seeks a position-aware neuron to fuse position-related values (i.e., position encodings) into neuron outputs. Distillation methods [2, 9, 33, 38] represent another branch, where the average of logits from client models is used for the local model aggregation, thereby enhancing generalization. [21] pioneers to apply knowledge distillation on the server side, transferring knowledge from multiple local models to the global model using an unlabeled proxy dataset. To overcome the limitation of using a proxy dataset, recent studies such as [47] and [44] suggest substituting the proxy dataset with generated data. + +Existing FL techniques have several significant drawbacks, including challenges with data heterogeneity, large client numbers, convergence issues and high communication costs. Our AFL framework addresses these issues by utilizing a gradient-free, closed-form analytic learning approach, avoiding gradient-related problems (e.g., multi-epoch training, convergence issues and multi-round aggregation). + +# 2.2. Analytic Learning + +The AL has been developed as a strategy to address issues associated with gradient-based update, such as gradient vanishing/exploding, divergence during iteration, and long training time due to multi-epoch training. The AL is also referred to as pseudoinverse learning [8] owing to its utilization of matrix inversion. The AL starts from shallow learning, which is investigated prior to the advent of deep networks in the realm of research. For instance, the radial basis network [26] trains parameters using an LS estimation after performing a kernel transformation in the first layer. The multilayer AL [31, 37] comes up with a one-epoch training style, using LS techniques to resolve linear segments transformed by nonlinear network. One instance of this method is the dense pseudoinverse autoencoder [36], which uses LS solutions to combine shallow and deep features to train a stacked autoencoder layer-by-layer. + +Nonetheless, earlier AL techniques train their weights by processing the entire dataset simultaneously, therefore facing memory challenge. This memory concern is alleviated by the block-wise recursive Moore-Penrose inverse [48], which equivalently replaces the joint learning with a recursive approach. This recursive equivalent property echoes well with the continual learning community. Naturally, analytic continual learning techniques [50, 51, 53] adopt this equivalent characteristic, thrive in handling the catastrophic forgetting problem, and are invariant to the sequential data partition in continual learning. Our AFL draws inspiration from these adaptations, aiming to introduce similar equivalent patterns (e.g., invariant to heterogeneous data) to the FL community. + +# 3. Analytic Federated Learning + +In this section, we provide a detailed exposition of AFL derivations, organized into a local training stage and a centralized aggregation stage. In the local stage, a pre-trained backbone serves as a feature extractor, facilitating an AL network learning that allows the training to be completed in one epoch. In the aggregation stage, we introduce the AA law, establishing a single-round aggregation. We elaborate on AFL's invariance to data partitioning here, bringing benefits such as data heterogeneity invariance, client-number invariance and fast convergence in a single round. An Overview of the proposed AFL paradigm is depicted in Figure 1. + +Prior to further developments, here let $\mathcal{D} = \{\mathcal{D}_k\}_{k=1}^K$ be the complete training data, where $\mathcal{D}_k \sim \{\mathcal{X}_{k,i}, y_{k,i}\}_{i=1}^{N_k}$ suggests an $N_k$ -sample sub-dataset accessible to the $k$ -th client with $\mathcal{X}_{k,i}$ and $y_{k,i}$ representing the $i$ -th input-label pair. In this paper, all these $K$ clients share the same backbone network $f_{\mathrm{backbone}}$ parameterized by $\Theta$ to map their inputs (e.g., $\mathcal{X}$ ) to embedding vectors. + +# 3.1. Local Stage: Localized Analytic Learning + +In this stage, each local client's network is trained using the AL technique. This involves transforming the neural network's classification head into a linear regression problem, thereby enabling the derivation of a closed-form LS solution. + +At the initial step, client $k$ extracts its embedding vector $\mathbf{x}_{k,i}$ by passing the $i$ -th data $\mathcal{X}_{k,i}$ from $\mathcal{D}_k$ through the frozen backbone network $f_{\mathrm{backbone}}$ , i.e., + +$$ +\boldsymbol {x} _ {k, j} = f _ {\text {b a c k b o n e}} \left(\mathcal {X} _ {k, j}, \Theta\right) \tag {1} +$$ + +where $\pmb{x}_{k,j} \in \mathbb{R}^{1 \times y_{\mathrm{e}}}$ , with $y_{\mathrm{e}}$ indicating the embedding length. + +For the $k$ -th client (with $N_{k}$ samples in $\mathcal{D}_k$ ), we can stack the extracted embeddings and their corresponding one-hoted labels via mapping $\mathcal{D}_k \sim \{\mathcal{X}_{k,i}, y_{k,i}\}_{i=1}^{N_k}$ to $\bar{\mathcal{D}}_k \sim \{\pmb{X}_k, \pmb{Y}_k\}$ , i.e., + +$$ +\boldsymbol {X} _ {k} = \left[ \begin{array}{c} \boldsymbol {x} _ {k, 1} \\ \boldsymbol {x} _ {k, 2} \\ \vdots \\ \boldsymbol {x} _ {k, N _ {k}} \end{array} \right] = \left[ \begin{array}{c} f _ {\text {b a c k b o n e}} \left(\mathcal {X} _ {k, 1}, \Theta\right) \\ f _ {\text {b a c k b o n e}} \left(\mathcal {X} _ {k, 2}, \Theta\right) \\ \vdots \\ f _ {\text {b a c k b o n e}} \left(\mathcal {X} _ {k, N _ {k}}, \Theta\right) \end{array} \right] \boldsymbol {Y} _ {k} = \left[ \begin{array}{c} \text {o n e h o t} \left(y _ {k, 1}\right) \\ \text {o n e h o t} \left(y _ {k, 2}\right) \\ \vdots \\ \text {o n e h o t} \left(y _ {k, N _ {k}}\right) \end{array} \right], \tag {2} +$$ + +where the embedding matrix $\mathbf{X}_k \in \mathbb{R}^{N_k \times y_e}$ , and the label matrix $\mathbf{Y}_k \in \mathbb{R}^{N_k \times C}$ has $C$ classes. The onehot(*) operator converts the index label $y_{k,j}$ into a $C$ -dimension one-hot row vector. + +Subsequently, we approach the local client training with AL technique [8]. Specially, the target of the $k$ -th client is to linearly map the extracted embeddings onto the one-hoted labels by minimizing the mean square error (MSE) loss function as follows. + +$$ +\mathcal {L} \left(\boldsymbol {W} _ {k}\right) = \left\| \boldsymbol {Y} _ {k} - \boldsymbol {X} _ {k} \boldsymbol {W} _ {k} \right\| _ {\mathrm {F}} ^ {2}, \tag {3} +$$ + +where $\| *\|_{\mathrm{F}}$ indicates the Frobenius norm. This leads to an optimal weight estimation $\hat{\mathbf{W}}_k$ , i.e., + +$$ +\hat {\boldsymbol {W}} _ {k} = \underset {\boldsymbol {W} _ {k}} {\operatorname {a r g m i n}} \mathcal {L} (\boldsymbol {W} _ {k}) = \boldsymbol {X} _ {k} ^ {\dagger} \boldsymbol {Y} _ {k}, \tag {4} +$$ + +where $\dagger$ denotes the Moore-Penrose (MP) inverse (also referred as generalized inverse or pseudoinverse) [8, 48]. + +The solution presented in (4) optimally addresses the MSE loss function described in (3), effectively establishing an LS-based AL solution for localized network learning. + +Why One-epoch Analytic Learning Works. AL methods are generally effective for training shallow networks but face challenges when applied to deeper ones. This can be attributed to the fact that AL techniques are often designed as classifiers rather than end-to-end learning approaches. Despite this limitation, recent research has demonstrated that with a well-trained backbone, the AL performs adequately in various complex scenarios [52]. The practice of using a "pre-trained backbone + downstream tasks" has become increasingly common. This has allowed the one-epoch AL + +![](images/582017bc5eb43d7259bbb83073d5d142d26e7139c39702bfc297a583a1d56d04.jpg) +Figure 1. An overview of the AFL. During the local stage, each client calculates $C_k^{\mathrm{r}}$ and $\hat{W}_k^{\mathrm{r}}$ based on the same pre-trained backbone and its own dataset. The server obtained the $C_{\mathrm{agg},K}^{\mathrm{r}}$ and $\hat{W}_{\mathrm{agg},K}^{\mathrm{r}}$ then get $\hat{W}$ in the aggregation stage. + +to thrive in various areas such as continual learning [50] and reinforcement learning [22]. Hence, it could also be well incorporated in the individual client training. + +Adopting AL is the key to enforcing the upcoming single-round aggregation (by deriving the AA law). The affine characteristic of linear regression in each client opens up new possibilities for exploration in FL. We provide a comprehensive explanation of such an exploration in later sections. + +# 3.2. Aggregation Stage: Absolute Aggregation Law + +In the aggregation stage, we introduce the Absolute Aggregation (AA) law, a key contribution in AFL. The AA law facilitates a single-round aggregation, i.e., the aggregation happens only once. Additionally, in scenarios where the AA law becomes suboptimal due to a large number of clients, we introduce a regularization intermediary (RI) process to restore its optimality. + +The MP inverse partition [4] inspires our derivation, which is reformulated into Lemma 1. + +Lemma 1. Let $\mathbf{X} = \begin{bmatrix} \mathbf{X}_u \\ \mathbf{X}_v \end{bmatrix}$ with $\mathbf{X}_u$ and $\mathbf{X}_v$ having full column ranks, and $\mathbf{X}$ follows a partition + +$$ +\boldsymbol {X} ^ {\dagger} = \left[ \begin{array}{l l} \bar {U} & \bar {V} \end{array} \right], \tag {5} +$$ + +where + +$$ +\left\{ \begin{array}{l} \bar {U} = X _ {u} ^ {\dagger} - R _ {u} C _ {v} X _ {u} ^ {\dagger} - R _ {u} C _ {v} (C _ {u} + C _ {v}) ^ {- 1} C _ {v} X _ {u} ^ {\dagger} \\ \bar {V} = X _ {v} ^ {\dagger} - R _ {v} C _ {u} X _ {v} ^ {\dagger} - R _ {v} C _ {u} (C _ {u} + C _ {v}) ^ {- 1} C _ {u} X _ {v} ^ {\dagger} \end{array} \right., +$$ + +$$ +\left\{ \begin{array}{l} \boldsymbol {C} _ {u} = \boldsymbol {X} _ {u} ^ {\top} \boldsymbol {X} _ {u} \\ \boldsymbol {C} _ {v} = \boldsymbol {X} _ {v} ^ {\top} \boldsymbol {X} _ {v} \end{array} , \quad \left\{ \begin{array}{l} \boldsymbol {R} _ {u} = \boldsymbol {C} _ {u} ^ {- 1} \\ \boldsymbol {R} _ {v} = \boldsymbol {C} _ {v} ^ {- 1} \end{array} . \right. \right. \tag {6} +$$ + +Proof. See Supplementary Materials A. + +Lemma 1 points out that, a matrix's MP inverse (e.g., $X^{\dagger}$ ) can be computed using the inverse matrices of its block + +components (e.g., $\pmb{X}_u^\dagger$ and $\pmb{X}_v^\dagger$ ). This introduces possibilities for aggregating a weight $\pmb{W} = \pmb{X}^\dagger \pmb{Y}$ equally from manipulating constituent counterparts $\pmb{W}_u = \pmb{X}_u^\dagger \pmb{Y}_u$ and $\pmb{W}_v = \pmb{X}_v^\dagger \pmb{Y}_v$ . That is, $\pmb{W} = f_{\mathrm{agg}}(\pmb{W}_u, \pmb{W}_v)$ , i.e., a single-aggregation strategy. + +Bearing the above intuition in mind, we are able to derive such a single-aggregation strategy in action. This is delivered in Theorem 1. + +Theorem 1. Absolute Aggregation Law: Let $\hat{W} = X^{\dagger}Y$ , where $X = \begin{bmatrix} X_u \\ X_v \end{bmatrix}$ and $Y = \begin{bmatrix} Y_u \\ Y_v \end{bmatrix}$ with $X_u$ and $X_v$ having full column ranks. Let $\hat{W}_u = X_u^\dagger Y_u$ , $\hat{W}_v = X_v^\dagger Y_v$ , and we have + +$$ +\boldsymbol {W} = \boldsymbol {\mathcal {W}} _ {u} \boldsymbol {W} _ {u} + \boldsymbol {\mathcal {W}} _ {u} \boldsymbol {W} _ {v}, \tag {7} +$$ + +where + +$$ +\left\{ \begin{array}{l} \mathcal {W} _ {u} = I - R _ {u} C _ {v} - R _ {u} C _ {v} \left(C _ {u} + C _ {v}\right) ^ {- 1} C _ {v} \\ \mathcal {W} _ {v} = I - R _ {v} C _ {u} - R _ {v} C _ {u} \left(C _ {u} + C _ {v}\right) ^ {- 1} C _ {u} \end{array} \right. +$$ + +$$ +\left\{ \begin{array}{l} \boldsymbol {C} _ {u} = \boldsymbol {X} _ {u} ^ {\top} \boldsymbol {X} _ {u} \\ \boldsymbol {C} _ {v} = \boldsymbol {X} _ {v} ^ {\top} \boldsymbol {X} _ {v} \end{array} \quad \left\{ \begin{array}{l} \boldsymbol {R} _ {u} = \boldsymbol {C} _ {u} ^ {- 1} \\ \boldsymbol {R} _ {v} = \boldsymbol {C} _ {v} ^ {- 1} \end{array} \right. \right. \tag {8} +$$ + +Proof. See Supplementary Materials B. + +The AA law, as stated in Theorem 1, provides a powerful insight. It establishes an intuition that we can aggregate two independently trained weights, such as $W_{u}$ and $W_{v}$ , into their jointly trained counterpart $W$ . This is achieved in an optimal way without any approximation or parameter tuning. + +Invariance to data partitioning. To a certain extent, the achievement in Theorem 1 attains the ultimate goal of FL, i.e., the equivalence between weights trained in FL fashion and that trained on a centralized joint dataset. Traditionally, the FL aims to approximate or converge to the performance of the joint-trained model through multiple rounds of aggregation in a central server. However, the AA law provides a + +more direct path to this goal. It allows for an equivalence (not approximation or convergence) to manifest in a linear regression standpoint. + +Supported by the AA law, the AFL achieves a level of performance that is on par with the joint-trained model, without the need for multiple rounds of aggregation. This direct equivalence could establish significant advancement in FL, as it simplifies the process and reduces the heavy computational overhead associated with multiple aggregation rounds. + +Although the AA law in Theorem 1 admits the absolute aggregation between two clients (i.e., $\hat{W}_u$ and $\hat{W}_v$ ), this pattern can be trivially broadcast to multi-client scenario. To elaborate, without loss of generality, we denote $\hat{W}_{\mathrm{agg},k - 1}$ as the accumulated aggregation (AcAg) weight that has aggregated $k - 1$ clients. By rewriting (1), the next aggregation with $\hat{W}_k$ ( $i = k,\dots ,K$ ) reads + +$$ +\hat {W} _ {\text {a g g}, k} = \mathcal {W} _ {\text {a g g}} \hat {W} _ {\text {a g g}, k - 1} + \mathcal {W} _ {k} \hat {W} _ {k}. \tag {9} +$$ + +According to (1), let $C_u \to C_{\mathrm{agg},k-1}$ , $C_v \to C_k$ , and we have $C_{\mathrm{agg},k} = C_{\mathrm{agg},k-1} + C_k$ . Hence, + +$$ +\left\{ \begin{array}{l} \mathcal {W} _ {\text {a g g}} = I - C _ {\text {a g g}, k - 1} ^ {- 1} C _ {k} \left(I + C _ {\text {a g g}, k} ^ {- 1} C _ {k}\right), \\ \mathcal {W} _ {k} = I - C _ {k} ^ {- 1} C _ {\text {a g g}, k - 1} \left(I + C _ {\text {a g g}, k} ^ {- 1} C _ {\text {a g g}, k - 1}\right), \end{array} \right. \tag {10} +$$ + +where + +$$ +\left\{ \begin{array}{l} C _ {\text {a g g}, k} = C _ {\text {a g g}, k - 1} + C _ {k} = \sum_ {i} ^ {k} C _ {i}, \\ C _ {i} = X _ {i} ^ {\top} X _ {i}. \end{array} \right. \tag {11} +$$ + +As such, the joint-trained weight $\hat{W} = \hat{W}_{\mathrm{agg},k}$ is produced by aggregating among individual clients in a pair-wise manner. It is interesting to find that the optimal aggregation is in fact a linear combination between two matrices (e.g., $\hat{W}_{\mathrm{agg},k - 1}$ and $\hat{W}_k$ ) weighted by $\mathcal{W}_{\mathrm{agg}}$ and $\mathcal{W}_k$ respectively. + +Note that the aggregation does NOT necessarily follow a sequential index from 1 to $K$ . We can randomly sample an available client to aggregate with the AcAg weight. This is revealed by the fact that elements in the weighting matrices are somewhat interchangeable (e.g., see (10)). + +# 3.3. RI Process: AA Law in Rank-deficient Scenario + +As indicated in Theorem 1, the equivalence in AA law relies on an assumption of a full-column rank in each client, e.g., $X_{k}$ having full-column rank. This may not hold in the large client number scenario where each client has limited data (e.g., $N_{k} < y_{\mathrm{e}}$ ), rendering the full-column rank assumption invalid. To address this, we implement the AA law with an RI process. Specially, we include a regularization term as an intermediary during the local stage, and remove it after the aggregation stage. + +To this end, we include an regularization term controlled by $\gamma$ in the objective function, i.e., + +$$ +\mathcal {L} \left(\boldsymbol {W} _ {k} ^ {\mathrm {r}}\right) = \left\| \boldsymbol {Y} _ {k} - \boldsymbol {X} _ {k} \boldsymbol {W} _ {k} ^ {\mathrm {r}} \right\| _ {\mathrm {F}} ^ {2} + \gamma \left\| \boldsymbol {W} _ {k} ^ {\mathrm {r}} \right\| _ {\mathrm {F}} ^ {2}, \tag {12} +$$ + +which rewrites the MP inverse based solution in (4) into + +$$ +\hat {\boldsymbol {W}} _ {k} ^ {\mathrm {r}} = \underset {\boldsymbol {W} _ {k} ^ {\mathrm {r}}} {\operatorname {a r g m i n}} \mathcal {L} \left(\boldsymbol {W} _ {k} ^ {\mathrm {r}}\right) = \left(\boldsymbol {X} _ {k} ^ {\top} \boldsymbol {X} _ {k} + \gamma \boldsymbol {I}\right) ^ {- 1} \boldsymbol {X} _ {k} ^ {\top} \boldsymbol {Y} _ {k}. \tag {13} +$$ + +Such a solution does not suffer from rank-deficiency issues, as $\pmb{X}_k^\top \pmb{X}_k + \gamma \pmb{I}$ is positive-definite thereby a full-rank matrix. + +During aggregation, we substitute $\hat{\mathbf{W}}_k$ in (4) with $\hat{\mathbf{W}}_k^{\mathrm{r}}$ using (13). This substitution would clearly result in deviations (i.e., $\hat{\mathbf{W}}_{\mathrm{agg},k}^{\mathrm{r}}\neq \hat{\mathbf{W}}_{\mathrm{agg},k}$ ), which is depicted in Theorem 2. + +Theorem 2. RI-AA Law: The relation between $\hat{W}_{agg,k}^{r}$ and $\hat{W}_{agg,k}$ follows + +$$ +\hat {W} _ {\text {a g g}, k} ^ {\mathrm {r}} = \left(C _ {\text {a g g}, k} ^ {\mathrm {r}}\right) ^ {- 1} C _ {\text {a g g}, k} \hat {W} _ {\text {a g g}, k}, \tag {14} +$$ + +where + +$$ +C _ {\text {a g g}, k} ^ {\mathrm {r}} = C _ {\text {a g g}, k} + k \gamma I = \sum_ {i} ^ {k} C _ {i} ^ {\mathrm {r}}, \quad C _ {i} ^ {\mathrm {r}} = X _ {i} ^ {\top} X _ {i} + \gamma I. \tag {15} +$$ + +Proof. See Supplementary Materials C. + +Theorem 2 establishes the relation between $\hat{W}_{\mathrm{agg},k}^{\mathrm{r}}$ and $\hat{W}_{\mathrm{agg},k}$ , which is a one-to-one mapping, such that $\hat{W}_{\mathrm{agg},k}$ can be restored by manipulating $\hat{W}_{\mathrm{agg},k}^{\mathrm{r}}$ , i.e., + +$$ +\begin{array}{l} \hat {W} _ {\text {a g g}, k} = \left(C _ {\text {a g g}, k}\right) ^ {- 1} C _ {\text {a g g}, k} ^ {\mathrm {r}} \hat {W} _ {\text {a g g}, k} ^ {\mathrm {r}} \\ = \left(\boldsymbol {C} _ {\text {a g g}, k} ^ {\mathrm {r}} - k \gamma \boldsymbol {I}\right) ^ {- 1} \boldsymbol {C} _ {\text {a g g}, k} ^ {\mathrm {r}} \hat {\boldsymbol {W}} _ {\text {a g g}, k} ^ {\mathrm {r}}. \tag {16} \\ \end{array} +$$ + +That is, we are able to attain $\hat{W}_{\mathrm{agg},k}$ by removing the impact of the regularization term $\gamma$ to counter the ill-conditioned constraint in the large client number scenario. The implementation of AFL is summarized in Algorithm 1. + +Benefits of Adopting AL in AFL. Inheriting from the AL technique, the AFL admits several merits over its gradient-based counterparts as follows. i) Fast training and convergence: the analytical solutions allow AFL to finish the training and aggregation in one shot, exhibiting fast training and convergence. Also, the analytical solutions free the AFL from any convergence issue as no iterative-search based action is executed. ii) Low communication cost: the single-round aggregation only requires a single communication between the clients and the server, which significantly reduces the communication cost. iii) Data heterogeneity invariance: the invariance to data partitioning does not pose any constraint on data partition strategy. That is, the equivalence is hold across all possible data heterogeneous scenarios (e.g., see Section 4.2). iv) Client-number invariance: for a complete dataset $\mathcal{D}$ partitioned among $K$ clients (i.e., $\{\mathcal{D}_k\}_{k=1}^K$ ), according to Theorem 1 and (9), when the weights from all $K$ clients are aggregated, the resulting weight is identical to that trained on the full dataset $\mathcal{D}$ . To validate AA law with RI-process, we conduct an experiment on a dummy dataset and show the invariance (see Supplementary Materials D). + +Algorithm 1 Analytic Federated Learning +Input: $\mathcal{D}_k, k = 0, \dots, K$ , $\gamma$ , and pre-trained backbone $\Theta$ . +Server Executes: +1. for each client $k$ in parallel do +2. $\hat{W}_k^{\mathrm{r}}, C_k^{\mathrm{r}} \gets \text{Local Stage}(k, \mathcal{D}_k, \gamma)$ . +3. end for +4. $\hat{W} \gets \text{Aggregation Stage}(\{\hat{W}_k^{\mathrm{r}}, C_k^{\mathrm{r}}, \gamma\}_{k=1}^K)$ . +Local Stage: client $k$ with $\mathcal{D}_k$ and $\gamma$ . +1. Get embedding and label matrices using (2). +2. Obtain weight matrix $\hat{W}_k^{\mathrm{r}}$ by (13). +3. Get $C_k^{\mathrm{r}} = X_k^\top X_k + \gamma I$ . +4. Return $\hat{W}_k^{\mathrm{r}}, C_k^{\mathrm{r}}$ . +Aggregation Stage: with $\{\hat{W}_k^{\mathrm{r}}, C_k^{\mathrm{r}}, \gamma\}_{k=1}^K$ . +1. Initialize $\hat{W}_{\text{agg},0}^{\mathrm{r}} = 0$ , $C_{\text{agg},0}^{\mathrm{r}} = 0$ . +2. for $k$ in range(K): + i) Aggregate $\hat{W}_{\text{agg},k}^{\mathrm{r}}$ with $\hat{W}_k^{\mathrm{r}}$ using (9). + ii) Update $C_{\text{agg},k}^{\mathrm{r}} = C_{\text{agg},k-1}^{\mathrm{r}} + C_k^{\mathrm{r}}$ . +3. end for. +4. Restore $\hat{W} = \hat{W}_{\text{agg},K}$ with $\hat{W}_{\text{agg},K}^{\mathrm{r}}$ in (16). + +An AL Branch of Federated Learning. The AFL incorporates the AL technique and can be considered as an AL branch within the FL context. The AL and its recursive formulation have demonstrated remarkable adaptability in continual learning utilizing a well-trained backbone [52, 54]. In this case, this intuition has been extended to the FL field through non-trivial derivations. + +# 4. Experiments + +In this section, we provide extensive experiments to validate the proposed AFL, including comparison with FL state-of-the-arts and analysis under various settings. The training time and ablation study of regularization are also investigated. + +# 4.1. Comparison with FL Techniques + +We conduct comparison with FL state-of-the-arts, including FedAvg [24], FedProx [17], MOON [15], FedGen [46], FedDyn [1], FedNTD [14] and FedDisco [42] under various non-IID settings. + +Dataset and Model. We validate the baselines and our proposed AFL in 3 popular benchmark datasets in FL: CIFAR-10 [12], CIFAR-100 [12] and Tiny-ImageNet [25]. For all datasets, we use a ResNet-18 [10] pretrained on ImageNet-1k [5] as backbone. We freeze the backbones in all FL methods. + +Data Partition. For simulating Non-IID scenarios in FL, we specify two Non-IID data partition methods including Latent Dirichlet Allocation [20] (LDA, denoted as NIID-1) and Sharding [20] (denoted as NIID-2). In the LDA setting, data assigned to each client is forced to satisfy the Dirichlet distribution, and degree of the data heterogeneity is controlled + +by parameter $\alpha$ . Smaller $\alpha$ leads to a more heterogeneous data distribution. In the Sharding strategy, the data is sorted by labels and divided into same-sized shards, and $s$ controls the heterogeneity, i.e. the number of shards per client. When $s$ takes a smaller value, the data is more heterogeneous. We choose $\alpha = 0.1, 0.01$ and $s = 10, 4$ for CIFAR-100 and Tiny-ImageNet. For CIFAR-10, $\alpha$ is set to 0.1 and 0.01, and $s$ is set to 4 and 2. Most existing methods are validated on data partition of $\alpha = 0.3$ to 1.0 and $s = 10$ [14, 19]. Here we provide more challenging settings to validate the robustness under extremely heterogeneous cases. + +Implementation Details. In all the experiments, we use 100 clients for each method and use the same partitioned dataset within experiments of the same data setting. We implement the AFL with a $\gamma = 1$ RI process (any $\gamma$ would suffice, see the ablation study). Each experiment setting is run 3 times and the mean and standard deviation of the best top-1 classification accuracy during training are reported. The implementation details of gradient-based compared methods can be found in Supplementary Materials E. + +Experimental Results. We report the results of the compared methods under the setting of NIID-1 and NIID-2 in Table 1. As shown in the table, except for slightly weaker results than those of FedDyn in the NIID-2 setting, the AFL obtains very competitive performance compared with other methods across various settings. The degree of data heterogeneity does not at all affect the AFL. For instance, the accuracy remains $80.75\%$ on CIFAR-10 for various NIID-1 and NIID-2 settings. Although slight differences could occur among various settings, it barely impacts the classification accuracy (an AL property indicated in [48]). The same pattern repeats on CIFAR-100 and Tiny/ImageNet. Uniquely, the AFL obtains identical results for all 3 repeated runs, i.e., the standard deviations are zeros! This is because the AFL does not introduce any stochastic element, so the repeated computation in each run is naturally equivalent to one another, hence the zero standard deviation. + +Notably, when introducing a pre-trained backbone, the compared methods yield similar results and even FedAvg can become a competitive baseline. The reason could be that, when incorporating a pret-trained backbone, the FL process can be more stable with a better start point and methods stabilizing the FL process could be less effective. This phenomena has also been witnessed in other FL studies [3, 7]. However, other FL methods still experience performance reductions under severe non-IID scenarios. For example, FedDyn performs relatively well (e.g., $57.55\%$ ) under NIID-1 $(\alpha = 0.1)$ on CIFAR-100 but undergoes a performance degradation (to $36.12\%$ ) when $\alpha = 0.01$ . This pattern is rather consistent in other compared methods, such as FedAvg $(56.62\% \rightarrow 32.99\%)$ , FedProx $(56.45\% \rightarrow 33.37\%)$ , and MOON $(56.58\% \rightarrow 33.34\%)$ , and is also true across all datasets. The performance distributions regarding NIID-2 for + +Table 1. The top-1 accuracy (%) of compared methods under two non-IID settings. Settings controlled by $\alpha$ and $s$ are NIID-1 and NIID-2 respectively. The data is reported as average and standard deviation after 3 runs. Results in bold are the best within the compared methods in the same setting. + +
DatasetSettingFedAvgFedProxMOONFedGenFedDynFedNTDFedDiscoAFL
CIFAR-10α = 0.164.02±0.1864.07±0.0863.84±0.0364.14±0.2464.77±0.1164.64±0.0263.83±0.0880.75±0.00
α = 0.0560.52±0.3960.39±0.0960.28±0.1760.65±0.1960.35±0.5461.16±0.3359.90±0.0580.75±0.00
s = 468.47±0.1368.46±0.0868.47±0.1568.24±0.2873.50±0.1170.24±0.1165.04±0.1180.75±0.00
s = 257.81±0.0357.61±0.1257.72±0.1557.02±0.1864.07±0.0958.77±0.1858.78±0.0280.75±0.00
CIFAR-100α = 0.156.62±0.1256.45±0.2256.58±0.0256.48±0.1757.55±0.0856.60±0.1455.79±0.0458.56±0.00
α = 0.0132.99±0.2033.37±0.0933.34±0.1133.09±0.0936.12±0.0832.59±0.2125.72±0.0858.56±0.00
s = 1055.76±0.1355.80±0.1655.70±0.2560.93±0.1761.09±0.0954.69±0.1554.65±0.0958.56±0.00
s = 548.33±0.1548.29±0.1448.34±0.1948.12±0.0659.34±0.1147.00±0.1945.86±0.1858.56±0.00
Tiny-ImageNetα = 0.146.04±0.2746.47±0.2346.21±0.1446.27±0.1447.72±0.2246.17±0.1647.48±0.0654.67±0.00
α = 0.0132.63±0.1932.26±0.1432.38±0.2032.33±0.1435.19±0.0631.86±0.4427.15±0.1054.67±0.00
s = 1039.06±0.2638.97±0.2338.79±0.1438.82±0.1641.36±0.0637.55±0.0938.86±0.1254.67±0.00
s = 529.66±0.1929.17±0.1629.24±0.3029.37±0.2535.18±0.1829.01±0.1427.72±0.1854.67±0.00
+ +these compared methods resemble those in NIID-1, where smaller $s$ values invite performance degradation among existing FL counterparts. For instance, the FedDyn exhibits $73.50\% \rightarrow 64.07\%$ for $s = 4 \rightarrow 2$ on CIFAR-10 while the AFL obtains competitive and identical results (e.g., $80.75\%$ ). + +# 4.2. Analysis on Data Partition + +Here we provide broaden non-IID partitions to demonstrate AFL's invariance to data partitioning. This includes varying the client number and the non-IID degree. We also provide the IID partition results. + +Client-number Invariance. We compare our AFL and the FedAvg under NIID-1 setting on CIFAR-100 and TinyImageNet with $\alpha = 0.1$ , and vary the number of clients from 100 to 500 and 1000. The results are shown in Figure 2. We observe that the AFL keeps an identical performance when scaling the number of clients, while the FedAvg experiences a performance decline along the increasing number (e.g., $56.57\% \rightarrow 41.01\%$ for $K = 100 \rightarrow 1000$ on CIFAR-100). This provides a strong evidence to support the invariance to data partitioning in our AFL. It also showcases the capability of pushing the AFL to large-scale client training scenario without any performance compromise. + +Data Heterogeneity Invariance. Here, we fix the client number to 100 and partition the CIFAR-100 under the setting of NIID-1 with $\alpha = 0.005, 0.01, 0.1, 1$ , including the IID setting as well. We report the results of AFL and FedAvg in Table 2. The FedAvg suffers from more accuracy losses (e.g., $57.72\% \to 24.74\%$ for $\alpha = 0.1 \to 0.005$ ) as the data heterogeneity grows higher. Under the IID partition, the FedAvg receives its best performance (i.e., $57.89\%$ ), which is still less competitive than our AFL (i.e., $58.56\%$ ). On the other hand, AFL obtains identical results (i.e., $58.56\%$ ) across various settings, including non-IID and IID ones. This is another strong proof of the AA law indicating the weight-invariant property of AFL. Our AFL is invariant to any degree of data heterogeneity, leading to unchanged performance in all possible data heterogeneous partition scenarios, even in extreme data heterogeneous cases (e.g., $\alpha = 0.005$ ). + +Table 2. The top-1 classification accuracy $(\%)$ of AFL and FedAvg under different data heterogeneity. + +
Acc. (%)α = 0.005α = 0.01α = 0.1α = 1IID
FedAvg24.7433.0956.5757.7257.89
AFL58.5658.5658.5658.5658.56
+ +![](images/ff5af59812f9babf3ac3fc8c43a0eba868f57c76cb75c5f8153422642c402f1a.jpg) +(a) CIFAR-100 +Figure 2. Accuracy over various number of clients. + +![](images/6468592f6c73bab37b6e26c227cf4add993262f230521630c46372ad8edfce85.jpg) +(b) Tiny-ImageNet + +# 4.3. Training Efficiency + +Fast Training with Single-round Aggregation. We plot the training evolution curves of accuracy on CIFAR-100 and Tiny-ImageNet in Figure 3 and report the execution time for each method in the legend bars. Compared FL methods take 60s to 100s on CIFAR-100 (100s to 160s on Tiny-ImageNet) to complete an aggregation round, leading to a total training time of 30,000s to 50,000 (50,000s to 80,000s). AFL, however, spends 236.61s on CIFAR-100 and 349.50s on Tiny-ImageNet, achieving approximately $150 \times -200 \times$ speedups over its FL counterparts due to only one aggregation. + +![](images/ad6d44bb618aeb472a976ec50a48b4bb738d8cfa9a1ce154bb9775abe9f16f1a.jpg) +Figure 3. Accuracy curves with communication rounds. Average training time is reported in the legends. + +![](images/eae531ba3b2bccc94bba3e40f17de8a8e43fd8a49d8594597a61cc95c530dfa8.jpg) + +# 4.4. Ablation Study of RI Process + +Here, we conduct an ablation study regarding the RI process by reporting accuracies of AFL with $\alpha = 0.1$ and $K = 100,500,1000$ under different values of $\gamma$ . The results without and with the RI process are provided in Table 3. When $\gamma = 0$ (i.e., no regularization involved), the AFL stops working with $K = 500$ and 1000 due to the ill-conditioned matrix scenario (e.g., $N_{k} < y_{\mathrm{e}}$ ). Such an ill-conditioned case is avoided by introducing $\gamma$ . However, the lack of RI process (see left columns in Table 3) could lead to accuracy loss. For instance, for $\gamma = 100$ , the AFL could suffer a loss of $9\%$ (i.e., $58.56\% \rightarrow 49.62\%$ ). This is the result of regularization accumulation (see (15)). With the RI process, the AFL obtains an identical result across various $\gamma$ values. More importantly, this demonstrates that adopting the RI avoids the need to find proper $\gamma$ values. That is, the regularization is a removable intermediary, not a hyperparameter that requires tuning. + +Table 3. Ablation study of RI under various $\gamma$ and $K$ . The left/right results are performance w/o and w/ the RI process in (16). + +
Acc.(%)γ = 0γ = 0.1γ = 1γ = 10γ = 100
K=10058.56N/A58.5458.5658.5158.5658.1558.5655.7758.56
K=5001.11N/A58.5258.5658.3058.5656.7258.5651.7758.56
K=10000.75N/A58.5158.5658.1558.5655.7758.5649.6258.56
+ +# 4.5. Validation with Different Backbones + +To explore the effect of different backbones used in the AFL, we extend the experiments with VGG11 [28] and ViT-B-16 [6]. All these backbone are pre-trained in ImageNet-1k and we conduct the experiments under the same setting in Section 4.2. Due to the invariance to data partitioning, we only report one result in single dataset. As shown in the Table 4, with different pre-trained backbones, the AFL can all obtain competitive results. + +# 5. Limitations and Future Work + +Utilizing Pre-trained Backbone. The AFL approach is both facilitated and constrained by the requirement of having a well-trained feature extractor. However, this limitation has + +Table 4. The results of top-1 accuracy in % of the AFL with different backbones including ResNet-18, VGG11 and ViT-B-16. + +
Acc.(%)CIFAR-10CIFAR-100Tiny-ImageNet
ResNet-1880.7558.5654.67
VGG1182.7260.4354.73
ViT-B-1693.9275.4582.02
+ +been significantly mitigated by the emergence of reusing pretrained models for new tasks. This "pre-trained backbone + downstream task" paradigm has become a standard practice in numerous deep learning domains, offering improved generalization and reduced computational costs. FL can further enhance this paradigm and we validate that collaboration can still be beneficial with pre-trained backbones in Supplementary Materials F. The proposal of the AFL aligns with these recent research trends, making it a sensible FL advancement. + +Partially Participating and Stragglers. The AFL formulates a single-round aggregation for FL systems, promoting rapid convergence and reducing communication overhead. However, challenges arise when clients engage partially or when stragglers impede progress. Since clients can only contribute to the aggregation after finishing local computations, the AFL needs to wait for all the clients. This potentially hampers the AFL's overall efficiency and inspires us to further refine the AFL to address these issues. + +Linear Assumptions of AFL. The AFL is established upon linear classifiers and may be less effective with nonlinear data distribution. To address this, AFL can incorporate non-linear projections including non-linear activations or kernel functions. Also, for multi-layer model, AFL can formulate local least-square problem at each layer by label projection [49]. These techniques have been utilized in various AL-based work [39] and the AA law holds theoretically. We will conduct a further exploration in future. + +# 6. Conclusion + +In this paper, we introduce a gradient-free FL framework named analytic federated learning (AFL). The AFL unveils analytical solutions both in the local client training stage and the aggregation stage. This leads to one-epoch local training, single-round aggregation, and fast convergence. In particular, the single-round aggregation property is theoretically supported and proved by the well-formulated AA law. Additionally, by introducing the RI process, we re-establish the AFL's optimality which could be compromised in the scenario of rank-deficient with normally a large number of clients. The AFL demonstrates its invariance to data partitioning, a property that allows several appealing FL characteristics such as data heterogeneity invariance and client-number invariance. These characteristics are empirically validated through experiments across various settings, where the AFL achieves a consistent and competitive performance. + +# Acknowledgment + +This research was supported by the National Natural Science Foundation of China (62306117, 62406114), the Guangzhou Basic and Applied Basic Research Foundation (2024A04J3681, 2023A04J1687), GJYC program of Guangzhou (2024D03J0005), the National Key R & D Project from Minister of Science and Technology (2024YFA1211500), and the Fundamental Research Funds for the Central Universities (2024ZYGXZR074). + +# References + +[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas, Matthew Mattina, Paul Whatmough, and Venkatesh Saligrama. Federated learning based on dynamic regularization. In International Conference on Learning Representations, 2021. 6 +[2] Ilai Bistritz, Ariana Mann, and Nicholas Bambos. Distributed distillation for on-device learning. 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This dataset offers a real-world benchmark for evaluating the robustness to significant viewpoint changes, scale variations, and resolution differences in cross-platform aerial-ground settings. In addition, to address these challenges, we propose AG-VPReLU-Net, an end-to-end framework composed of three complementary streams: (1) an Adapted Temporal-Spatial Stream addressing motion pattern inconsistencies and facilitating temporal feature learning, (2) a Normalized Appearance Stream leveraging physics-informed techniques to tackle resolution and appearance changes, and (3) a MultiScale Attention Stream handling scale variations across drone altitudes. We integrate visual-semantic cues from all streams to form a robust, viewpoint-invariant whole-body representation. Extensive experiments demonstrate that AG-VPReLU-Net outperforms state-of-the-art approaches on both our new dataset and existing video-based ReID benchmarks, showcasing its effectiveness and generalizability. Nevertheless, the performance gap observed on AG-VPReLU across all methods underscores the dataset's challenging nature. The dataset, code and trained models are available at AG-VPReLU-Net. + +# 1. Introduction + +Video-based person re-identification (ReID) is a challenging and in-demand task, with significant real-world applications in surveillance, search and rescue operations, and urban monitoring [25, 35, 37]. While traditional ReID methods focus on ground-based cameras [7, 50], the inte + +gration of aerial perspectives through aerial-ground person ReID presents a paradigm shift in this field [32]. This approach enables the identification and matching of individuals across non-overlapping aerial and ground-based camera views, substantially enhancing situational awareness and response times in complex environments [31, 46]. The motivation behind this research stems from the increasing deployment of aerial platforms, such as unmanned aerial vehicles (UAVs), which provide unique vantage points that complement ground-based observations. However, the development of robust aerial-ground ReID systems faces a significant challenge: the scarcity of diverse and large-scale datasets that capture the nuances of both aerial and ground perspectives. As demonstrated by ImageNet [4], large and diverse benchmarks are crucial for deep learning based methods, indicating a need for a comprehensive ReID dataset integrating multiple platforms, environments, and real-world challenges. + +Initial efforts in aerial-ground person ReID have focused primarily on image-based tasks. For instance, Nguyen et al. [31] pioneer this area by releasing the first aerial-ground ReID dataset, which includes images from one drone and one CCTV camera capturing 21,983 images of 388 identities. They later expand the dataset to 100,502 images of 1,615 individuals [32]. Recently, Zhang et al. [46] collect a synthetic dataset named CARGO, containing 108,563 images representing 5,000 subjects, to complement real-world datasets. Within video-based tasks, Zhang et al. [47] collect a video-based dataset called G2A-VReID, which consists of 185,907 images and 5,576 tracklets from one drone and one CCTV camera, featuring 2,788 identities. Building on these advancements, G2A-VReID could be expanded compared to ground-based datasets like MARS [51], which includes 20,000 tracklets and 1.19 million frames from six cameras. While current aerial-ground datasets are valuable, increasing identity variation and environmental diversity would + +
DatasetYear#Identities#Tracklets#Frames (M)#CVCCAtt.PlatformDur.Altitude (m)
GroundWearableAerial
MARS [51]20161,26120,4781.196XXXX--
LSVID [18]20193,77214,9432.9815XXXX4-
VCCR [10]20223924,3840.151XXX90-
CCVID [8]20222262,8560.341XXX--
MEVID [3]20231588,09210.4633XXX73-
PDestre [17]20202531,8940.101XX-5-6
G2A-VReID [47]20242,7885,5760.182XXX-20 - 60
AG-VPRelD20246,63232,3219.662015 - 120
+ +Table 1. Comparison of AG-VPReID with existing video-based person ReID datasets. Above: ground-based datasets, Below: aerial-based datasets. CV: Camera Views, CC: Clothes-Change, Att.: Attributes (Soft-biometrics annotations), Dur.: Duration (days). + +improve model robustness for real-world applications. + +In light of this, we introduce AG-VPReID, a comprehensive large-scale benchmark dataset for Aerial-Ground Video-based Person ReID. AG-VPReID comprises 6,632 subjects, 32,321 tracklets, and over 9.6 million frames, captured across multiple dates and times of day using a combination of three platforms: aerial drones operating at various altitudes (15-120m), stationary CCTV cameras and wearable mobile cameras. This dataset significantly surpasses existing video-based ReID benchmarks in terms of scale, diversity, and real-world applicability with the highest number of identities, the highest number of tracklets, the highest drone flying altitudes, and the most diverse platforms. The key characteristics of AG-VPReID include: drastic view changes between aerial and ground perspectives; a large number of annotated identities across multiple sessions; rich outdoor scenarios with varying environmental conditions; significant differences in resolution between aerial and ground footage; and both controlled scenarios with clothing changes and in-the-wild pedestrian traffic. + +Aerial-ground person ReID presents unique challenges due to significant appearance variations between aerial and ground-level views. These variations include extreme viewpoint differences, drastic changes in resolution and scale, partial occlusions, and temporal discontinuities caused by high-flying altitudes and long-range captures. Traditional video-based person ReID methods, although effective in ground-based settings [26, 45], often struggle in aerial-ground scenarios due to the complex combination of inconsistent motion patterns and the aforementioned variations. + +To address these challenges, we introduce AG-VPReID-Net, an end-to-end framework for Aerial-Ground Video-based Person Re-Identification. Unlike existing state-of-the-art methods focused on single-view or ground scenarios, AG-VPReID-Net features three complementary streams tailored for aerial-ground challenges: i) An Adapted Temporal-Spatial Stream enhances traditional temporal modeling by integrating identity-specific memory and temporal shape analysis. This improves the extraction of consistent motion patterns and body shape representations, addressing the temporal discontinuity and motion + +inconsistencies of aerial footage, outperforming standard LSTM [6, 14] or 3D CNN [20] approaches; ii) A Normalized Appearance Stream addresses the resolution and appearance differences between aerial and ground views by using UV maps aggregation across frames for a normalized appearance representation. This provides robustness against pose changes, viewpoint shifts, and varying image quality, excelling where current appearance-based methods [19, 29] falter; and iii) A Multi-Scale Attention Stream addresses scale variations inherent in aerial-ground data by incorporating multi-scale feature extraction, motion analysis, temporal context, and a transformer decoder, effectively improving identification across drone altitudes compared to single-scale [13, 43] methods. By integrating these streams, AG-VPReID-Net offers incremental improvements in aerial-ground video-based re-identification, highlighting its potential in addressing this challenging scenario. + +In summary, our main contributions are as follows: + +(1) We introduce AG-VPReID, a challenging large-scale benchmark for aerial-ground video-based person ReID, bridging the gap with a diverse dataset that captures nuanced challenges from both aerial and ground perspectives. +(2) We propose AG-VPReLUID-Net, an innovative end-to-end framework that integrates adapted temporal-spatial processing, normalized appearance representation, and multiscale attention mechanisms to effectively address the challenges of aerial-ground ReID. +(3) AG-VPReLU-Net sets new state-of-the-art performance on the AG-VPReLU and existing video-based ReID benchmarks, demonstrating our approach's effectiveness and generalizability across different settings. + +# 2. Prior Work + +Video-based Person ReID Datasets. Existing person ReID datasets are numerous but severely lack the ability to address real-world challenges, particularly in aerial-ground scenarios. Ground-based datasets like MARS [51] and LSVID [18] provide large-scale benchmarks but focus mainly on ground perspectives, highlighting the need for multi-platform surveillance datasets. The inclusion of clothing + +![](images/4be2113499ae6adece19cf4a8306ac03f748d2eb26b2f3e4a6eabd1218630242.jpg) +Figure 1. Our AG-VPReID dataset was captured using a variety of six cameras, including aerial drones, CCTVs, and GoPros. Sample images and camera locations are illustrated on the right side of the figure. The left side depicts the cross-camera appearance variations of two pedestrians, showcasing differences across various sessions and times of the day. + +changes in datasets such as MEVID [3], CCVID [8], and VCCR [10] represents progress in addressing real-world challenges, though they could benefit from more identities and diverse environments. The BRIAR dataset [2], while featuring 1,000 subjects and UAV footage, primarily targets face recognition with restricted access. P-Destre [17] pioneered aerial view exploration, though its use of a single drone at lower altitudes (5-6m) creates opportunities for datasets covering higher operational altitudes more common in surveillance applications. The G2A-VReID dataset by Zhang et al. [47] represents an important step in combining aerial and ground views. While innovative, it contains 2,788 identities within a $20 - 60\mathrm{m}$ altitude range using 2 cameras, suggesting opportunities for future datasets to expand in scale, altitude diversity, camera count, and environmental variety. Tab. 1 compares our AG-VPReID dataset with others across multiple dimensions. + +Video-based Person ReID. Video-based person ReID methods have evolved to leverage both spatial and temporal cues. Early approaches used recurrent neural networks and 3D convolutional networks [20, 30], while later works incorporated temporal pooling [51] and attention mechanisms [25]. Recent advancements include temporal complementary learning [13], Transformer-based architectures [11, 28], and techniques addressing cross-platform and cloth-changing scenarios [10, 39, 47]. The + +AG-ReID 2023 Challenge [33] highlighted aerial-ground ReID challenges, with winners employing re-ranking, data augmentation, and centroid-based representations. Recent works include Instruct-ReID [12] with instruction-guided retrieval, Domain Shifting [15] for distribution adaptation, and SEAS [53] using 3D body shape guidance. Despite these developments, most existing methods employ uni-modal frameworks trained on predefined label sets. In contrast, recent work has proposed a visual-language multi-modal learning paradigm [45], potentially offering more flexibility and robustness in feature representation for video-based person ReID. + +# 3. AG-VPReID Dataset + +This section offers a detailed overview of the creation process for our AG-VPReID dataset. We describe the methods used for collecting video footage in Sec. 3.1. Sec. 3.2 introduces our annotation procedures. Sec. 3.3 compares AG-VPReID with existing datasets, highlighting its unique features. + +# 3.1. Dataset Collection + +The AG-VPReLU dataset was collected over a period of 20 days, including 10 morning sessions (8:30am-10:00am) and 10 afternoon sessions (3:30pm-5:00pm), with each session lasting 60 minutes. Data capture involved two drones, two + +CCTV cameras, and two wearable cameras. Each drone operated at four different altitudes—15m, 30m, 80m, and 120m—for 15 minutes per session, providing a comprehensive range of aerial views. In total, the dataset comprises 240 hours of video footage, documented in Tab. 2, which includes detailed specifications of the equipment used. The dataset features diverse resolutions, frame rates, and perspectives, extending from ground level to 120-meter aerial views. Fig. 1 shows example frames across different viewpoints and image qualities from different platforms. The drones, CCTV, and wearable devices are positioned to view individuals from different angles, as illustrated in Fig. 1, forcing person ReID models to learn robust multiview and partial-view representations to be effective. + +
TypeModelResolutionLensFPS
CCTVBosch (Outdoor)704 × 48024mm15
Bosch (Indoor)1280 × 72018mm25
WearableGoPro10 (Front)3840 × 216016mm30
GoPro10 (Side)1920 × 108016mm60
DronesDJI Inspire23840 × 216024mm25
DJI M300RTK8192 × 546035mm1
+ +Table 2. Equipment specifications for the AG-VPReID dataset. + +To ensure professional drone operations, a specialized team (one RPAS engineer, one Chief Remote Pilot, one RPAS technician) managed all 20 data collection days, handling flights, capturing aerial footage, and performing initial data preprocessing. + +# 3.2. Labeling Process + +The AG-VPReID dataset uses YOLOv8x for person detection and tracking [16], extracting images from all frames across multiple cameras. It includes both short-term and long-term ReID scenarios, the latter including instances where participants change clothes to test long-term identity persistence. Identity matching was performed by a team of expert annotators, supported by research assistants, to ensure both accuracy and consistency in the matching process. Following [32], we manually annotated each identity with 15 selective soft-biometrics attributes to enhance the dataset's utility for attribute-based person ReID applications. For a detailed list of these attributes, refer to 8.1. + +# 3.3. Dataset Characteristics + +Compared with existing video-based ReID datasets, our AG-VPReID dataset has five unique characteristics: + +1) The highest number of identities and tracklets. AGVPReID sets a new benchmark with 6,632 unique identities and 32,321 tracklets, substantially surpassing existing datasets. It holds nearly twice as many identities as prominent ground-based datasets such as LSVID [18], which contains 3,772 identities, and more than six times + +the tracklets of the next largest aerial-ground dataset, G2AVReID [47], which includes 5,576 tracklets. Additionally, AG-VPReID encompasses over 9.6 million frames, providing 50 times the volume of frames compared to other aerial-ground datasets. While MEVID [3] exceeds in frame count with 10.46 million, it does not match AG-VPReID in terms of identity and tracklet numbers. + +2) The most diverse platforms. Our AG-VPReLUID dataset is the first to incorporate aerial, ground, and wearable platforms for video-based person ReID. The inclusion of wearable cameras provides a novel dimension with high-quality first-person perspectives. This combination results in extreme variations in resolution and subject size across platforms: UAV (18×37 to 293×542 pixels), CCTV (22×23 to 172×413 pixels), and GoPro (25×48 to 483×1078 pixels). +3) The highest flying altitudes. AG-VPReID features footage from altitudes reaching up to 120 meters, exceeding existing datasets' 60-meter maximum [47]. This introduces challenges: 1) extreme viewpoints with perspective distortions; 2) multiple scales with varying resolutions; and 3) image quality issues (Fig. 2). We used two drones—one with a wide-angle camera for area monitoring and another with a narrow-angle camera for detailed observation. +4) Rich outdoor scenarios with real-world challenges. Our AG-VPReID dataset presents diverse outdoor campus scenarios with real-world challenges including complex occlusions, varied poses from different activities, and uniform-wearing individuals. Fig. 2 shows examples of these diverse scenarios. +5) Other notable characteristics. AG-VPReLU includes comprehensive attributes for each identity (gender, age, clothing style, accessories), enabling fine-grained analysis. The dataset features long-term tracking data of 14 diverse individuals recorded across multiple days, each wearing different clothing per session to capture real-world variations. We also provide camera calibration information and GPS coordinates to support multi-camera tracking research. See supplementary material Sec. 8 for details. + +# 3.4. Ethics and Privacy + +This research received ethics approval for data collection and usage. We implement "Deface" [5] to blur faces, secure data storage, and obtained informed consent from all participants. Details are available at our project repository. + +# 4. AG-VPReID-Net + +We propose AG-VPReLU-DNet, a purpose-built framework addressing aerial-ground ReID's unique challenges. In particular, we propose an Adapted Temporal-Spatial Stream for robust temporal-spatial representations to deal with the temporal discontinuity challenge caused by drone motion + +![](images/f5041b8ee0d43fbe3c67dae2d976f3ba9842453939e1d8967e949f57549b5c4a.jpg) +Aerial Camera + +![](images/84bc2bab5ce1bb227c0c9a5047b2f2878eb081be68533d2c7c1ab3b44ed85f14.jpg) + +![](images/3f33b18445e2169b6dabdd3509ce0cd75de375a821bdd874e2b3a78cde0291b6.jpg) + +![](images/9c10adb7d47f8c23d47fbb8ad49cdb776c6fe02c6359b6e37345ed9339d91b6b.jpg) + +![](images/6a94c1e0b5aea0e6901cab8b1be05a0a065928e010a123d3a8fd8b5158dc5c3a.jpg) +(f) Clothing similarity +Figure 2. The AG-VPReID dataset presents several key challenges: extreme viewpoints, varying resolutions and subject sizes, pose/illumination variations, occlusions, and similar clothing among subjects. + +from unstable tracking between frames. We propose a Normalized Appearance Stream for resolution and appearance changes to deal with extreme viewpoint shifts. To deal with altitude-driven scale variance, we introduce a Multi-Scale Attention Stream for scale variations. Fig. 3 illustrates our architecture. Detailed stream contributions are provided in Tab. 9 of the supplementary material. + +# 4.1. Stream 1: Adapted Temporal-Spatial Stream + +When performing video-based person ReID, a key challenge is handling inconsistent motion patterns and temporal gaps between video frames. To address this, we propose an Adapted Temporal-Spatial stream that combines CLIP's visual encoder with temporal and 3D shape modeling to create a comprehensive representation of individuals. Our method operates on a sequence $\mathcal{V}$ of $T$ frames through the following components: + +Visual Feature Extraction: Using CLIP's visual encoder $E_{v}(\cdot)$ , we extract frame-level features, + +$$ +F _ {t} = E _ {v} \left(\mathcal {I} _ {t}\right), \quad t \in \{1, \dots , T \}, \tag {1} +$$ + +where $\mathcal{I}_t$ and $F_{t}$ are the $t$ -th frame and its features. + +Temporal Processing: We incorporate temporal modeling through two key components: + +1) Temporal 3D Shape Modeling (TSM): Following [34], we extract 3D shape representations, + +$$ +g _ {t} = \operatorname {G R U} \left(F _ {t}, g _ {t - 1}\right), \beta_ {t} = 3 \mathrm {D} \operatorname {R e g u s s o r} \left(g _ {t}\right), \tag {2} +$$ + +where $g_{t}$ captures temporal dynamics and $\beta_{t}$ represents SMPL model parameters. + +2) Temporal Feature Enhancement (TFE): Adapting from [45], we enhance features by combining appearance and shape, + +$$ +F _ {\text {e n h a n c e d}} = \operatorname {T F E} \left(F _ {1: T}, \beta_ {1: T}\right). \tag {3} +$$ + +Identity-Aware Processing: We incorporate identity information through, + +$$ +\mathcal {M} _ {y _ {i}} = \frac {1}{N _ {y _ {i}}} \sum_ {V \in \mathcal {V} _ {y _ {i}}} \operatorname {T A P} \left(F _ {\text {e n h a n c e d}}\right), +$$ + +$$ +\mathcal {M} _ {y _ {i}} ^ {\text {r e f i n e d}} = \operatorname {S S P} \left(F _ {\text {e n h a n c e d}}, \mathcal {M} _ {y _ {i}}\right), +$$ + +$$ +R _ {s t r e a m 1} = \left[ F _ {e n h a n c e d}; \mathcal {M} _ {y _ {i}} ^ {r e f i n e d} \right], \tag {4} +$$ + +where $\mathcal{M}_{y_i}$ is the identity memory bank constructed through Temporal Average Pooling (TAP), and the Sequence-Specific Prompt (SSP) module refines this representation for the final output $R_{stream1}$ . + +# 4.2. Stream 2: Normalized Appearance Stream + +The Adapted Temporal-Spatial (ATS) stream provides robust temporal-spatial representation, but may not fully capture fine-grained appearance details across viewpoints, especially in aerial footage. To address this limitation, we propose a Normalized Appearance (NA) stream that effectively aggregates appearance details from multiple viewpoints. + +The NA stream normalizes and combines appearance information across frames using UVTexture maps and visibility masks. Our process involves: (1) Extracting UVTexture maps and visibility masks per frame, (2) Normalizing UVTexture maps brightness, (3) Aligning maps across frames, (4) Weighted aggregation using visibility masks, and (5) Generating the final normalized representation. The brightness normalization and weighted aggregation of UVTexture maps can be formulated as, + +$$ +T _ {i} ^ {\text {n o r m}} = \gamma (H (N (T _ {i}))), \tag {5} +$$ + +$$ +T _ {\text {a g g r e g a t e d}} = \frac {\sum_ {i = 1} ^ {N} V _ {i} \odot T _ {i} ^ {\text {n o r m}}}{\sum_ {i = 1} ^ {N} V _ {i}}, \tag {6} +$$ + +where $T_{i}^{norm}$ is the normalized UVTexture map for frame $i$ , $N(\cdot), H(\cdot)$ , and $\gamma(\cdot)$ are normalization, histogram matching and gamma correction functions respectively. $T_{aggregated}$ is the final aggregated map. We leverage PhysPT [49] + +![](images/d1697fc18f796b09bfbaba2feb45ad8e162dff3d0f8bf44b83643ec2512766b0.jpg) +Figure 3. The three-stream AG-VPReLU-DNet architecture addresses aerial-ground ReID challenges: Temporal-Spatial stream for motion modeling and temporal features, Normalized Appearance for resolution/appearance variations, and Multi-Scale Attention for aerial-ground scale variations. + +for pose estimation and Texformer [41] to generate UV maps from PhysPT's output 3D meshes. The maps are improved through inter-frame consistency before feeding into the DGC Omni-scale Module [52]. + +# 4.3. Stream 3: Multi-Scale Attention Stream + +While the ATS stream provides a robust temporal-spatial representation and the NA stream addresses viewpoint and occlusion challenges, aerial-ground person ReID still faces significant hurdles due to extreme scale variations between drone and ground-level footage. The first two streams effectively capture temporal dynamics, 3D shape information, and viewpoint-invariant appearance details, but they may not fully address the drastic scale differences inherent in aerial-ground scenarios. To complement the ATS stream and NA stream and address this limitation, we propose a Multi-Scale Attention (MSA) stream. + +In detail, this stream leverages the power of frozen large vision models combined with lightweight, adaptive processing. Specifically, this stream utilizes a frozen large vision model to extract multi-scale features for video-based person ReID. By combining a lightweight Transformer decoder with a local temporal module, this approach dynamically integrates spatial and temporal information, thereby enhancing our framework's ability to accurately capture essential person-specific details. + +Specifically, for each frame $\mathcal{I}_t$ within the sequence $\nu y_{i}$ the CLIP vision encoder [36] is employed to extract features independently. The process collects tokens from various layers at regular intervals to compile a detailed feature map that captures spatial correspondences. These frame feature maps are subsequently concatenated and assembled + +into a spatiotemporal feature volume $\mathbf{G}$ . Following the methods [23, 44], we integrate temporal information into this volume before processing it through a Transformer decoder. This decoder globally aggregates features across multiple layers, employing a video-level classification token as a query, with feature volumes from different layers of the backbone serving as keys and values. A linear layer then maps the output of the decoder's final block to produce class predictions. The operational dynamics of the Transformer decoder are outlined as follows, + +$$ +Y _ {i} = \operatorname {T e m p} _ {i} ([ \mathbf {G} _ {N - M + i, 1}, \mathbf {G} _ {N - M + i, 2}, \dots , \mathbf {G} _ {N - M + i, T} ]), +$$ + +$$ +\tilde {q} _ {i} = q _ {i - 1} + \mathrm {M H A} _ {i} \left(q _ {i - 1}, Y _ {i}, Y _ {i}\right), +$$ + +$$ +q _ {i} = \tilde {q} _ {i} + \operatorname {M L P} _ {i} (\tilde {q} _ {i}), +$$ + +$$ +f _ {G} = \operatorname {F C} \left(q _ {M}\right), \tag {7} +$$ + +where $\mathbf{G}_{n,t}$ represents the features of frame $t$ extracted from the $n$ -th layer of CLIP vision encoder. The feature volume $Y_{i}$ , which undergoes temporal modulation, is input into the $i$ -th layer of the Transformer decoder. The query token $q_{i}$ is incrementally refined, beginning with $q_{0}$ as learnable initial parameters. The final output $f_{G}$ , corresponds to the final feature. The spatiotemporal decoder comprises $M$ blocks. $N$ denotes the number of encoder layers. Multi-head attention (MHA) involves query, key, and value, each of which plays a distinct role. The operator $\mathrm{Temp}(\cdot)$ is utilized to model temporal dynamics, which produces feature tokens influenced by detailed temporal information. + +# 5. Experimental Results + +# 5.1. Datasets and Evaluation Metrics + +We conducted evaluations of our method using the AG-VPReID and four established video-based person ReID datasets: iLIDS [38], Mars [51], LS-VID [18] and G2AVReID [47]. For AG-VPReID, we used a balanced split of 3,013 identities with both ground and aerial views, dividing them equally for training and testing purposes [31, 32]. Details on the training and testing configurations are provided in Table 3. We evaluate performance using the Cumulative Matching Characteristic (CMC) at Rank-1 and the mean Average Precision (mAP). + +
CaseSubset#IDs#Tracklets#Images (M)
TrainingAll1,55513,3003.85
Testing (A2G)All1,45613,5663.94
15m5064,9071.50
30m3772,8850.89
80m3562,5920.69
120m3083,1820.86
Testing (G2A)All5,075*19,0215.79
15m1,4036,3622.14
30m1,4064,4681.41
80m1,1623,8661.13
120m1,1954,3251.11
+ +Table 3. Statistics of AG-VPReID dataset. A2G: aerial-to-ground, G2A: ground-to-aerial. *3,619 additional IDs as distractors. + +# 5.2. Implementation Details + +Our pipeline leverages UV maps generated by Texformer [41] using 3D human meshes from PhysPT [49] with refined pose estimation. The UV maps are processed through normalization, histogram matching, and gamma correction before weighted blending with visibility masks. The architecture consists of three streams: an Adapted Temporal-Spatial Stream (CLIP ViT-B/16), a Normalized Appearance Stream for 3D coordinates and UV textures, and a Multi-Scale Attention Stream (CLIP ViT-L/14). More implementation details can be found in the supplementary. + +# 5.3. Comparison with State-of-the-Art Methods + +We evaluate our proposed method AG-VPReID-Net against several state-of-the-art approaches across multiple video-based person ReID datasets. Tab. 4 summarizes the results. + +Ground-to-Ground Datasets. Our method achieves superior performance on MARS (91.5% mAP, 93.2% Rank-1), outperforming CLIP-ReID by 3.4% mAP. On LS-VID (87.3% mAP, 93.2% Rank-1), we surpass LSTRL by 4.9% mAP. For iLIDS-VID, we reach 96.3% Rank-1, which is 3.0% higher than MFA. + +Cross-Platform Datasets. On G2A-VReID, we achieve $81.3\%$ mAP and $73.1\%$ Rank-1, surpassing MGH by $4.6\%$ mAP. Note that the G2A-VReID dataset only provides a + +![](images/5aeac7856fbfa5606dcc60f6256ab85735938e0fee7e11f5c68df0f17dc7efc2.jpg) +Figure 4. Baseline vs our method on AG-VPReLU dataset. Green/red: correct/incorrect labels. First tracklet image shown. Ranks show improvements in bold. + +ground-to-aerial testing set. For AG-VPReID, we demonstrate strong results in both Ground-to-Aerial (58.0% mAP, 75.6% Rank-1, exceeding CLIP-ReID by 8.8% Rank-1) and aerial-to-ground scenarios (64.0% mAP, 71.9% Rank-1, surpassing CLIP-ReID by 1.7% mAP and 0.3% Rank-1). + +# 5.4. Ablation Study + +We conduct an ablation study on AG-VPReLU to evaluate each stream. St-1 is our temporal modeling stream, St-2 is the appearance normalization stream, and St-3 is the multiscale feature stream. Their combinations (St-12/13/23/123) merge multiple streams. + +Stream Contributions. Tab. 5 shows that St-1 achieves the strongest individual performance (71.52% A2G, 74.80% G2A Rank-1). St-2 and St-3 show moderate results (58.40% and 61.65% A2G Rank-1). Combined streams demonstrate complementary strengths, with St-123 achieving the best results (71.91% A2G, 75.57% G2A Rank-1) by integrating the three streams. + +Impact of Altitude. Table 6 shows performance decreasing with altitude, most significantly between $30\mathrm{m} - 80\mathrm{m}$ . A2G Rank-1 drops $\sim 11\%$ across streams. At $120\mathrm{m}$ , St-1 demonstrates robustness (52.47% vs 38.12%/35.13%), achieving +17.34% improvement through temporal modeling. St-2's physics-informed UV mapping provides +7.57% improvement (42.70% vs. 35.13%), while St-3's multi-scale attention yields +17.72% improvement (52.85% vs. 35.13%). St-123 maintains best performance across all altitudes by combining stream strengths. + +Clothing Changes vs. Camera Angles. Analysis shows altitude increases $(15\mathrm{m} \rightarrow 120\mathrm{m})$ reduce Rank-1 by $27.66\%$ , significantly more than clothing changes $(7.85\%$ in ground-to-ground). Without clothing changes, aerial-ground matching $(71.91\%$ Rank-1) still underperforms ground-to-ground $(91.52\%)$ due to viewpoint differences. When combining aerial views with clothing changes $(65.83\%$ Rank-1), these factors create synergistic challenges where viewpoint differences amplify clothing ambi + +
MethodMARSLS-VIDiLIDS-VIDG2A-VReIDAG-VPReID
Ground → GroundGround → AerialAerial → GroundGround → Aerial
mAPRank-1mAPRank-1Rank-1Rank-5mAPRank-1mAPRank-1mAPRank-1
STMP[29]72.784.439.156.884.396.8--50.760.345.255.8
M3D[20]74.184.440.157.774.094.3--52.462.647.957.3
GLTR[19]78.587.044.363.186.098.0--55.665.850.160.5
TCLNet[13]85.189.870.381.586.6-65.454.757.267.952.762.4
MGH[43]85.890.061.879.685.697.176.769.960.370.855.565.2
GRL[25]84.891.0--90.498.3--58.768.453.963.6
BiCnet-TKS[14]86.090.275.184.6--63.451.759.869.254.364.7
CTL[24]86.791.4--89.797.0--56.466.951.861.3
STMN[6]84.590.569.282.1--66.756.161.671.556.966.2
PSTA[39]85.891.5--91.598.1--60.570.255.865.7
DIL[11]87.090.8--92.098.0--61.270.956.366.1
STT[48]86.388.778.087.587.595.0--61.070.756.165.9
TMT[28]85.891.2--91.398.6--60.870.555.965.8
CAVIT[40]87.290.879.289.293.398.0--61.471.156.566.3
SINet[1]86.291.079.687.492.5---61.371.056.466.2
MFA[9]85.090.478.988.293.398.7--61.170.856.266.0
DCCT[27]87.592.3--91.798.6--61.571.256.666.4
LSTRL[26]86.891.682.489.892.298.6--61.771.356.766.5
CLIP-ReID[21]88.191.780.688.8----62.371.657.266.8
AG-VPReID-Net91.593.287.393.296.399.581.373.164.071.958.075.6
+ +Table 4. Performance comparison across datasets. Bold shows best results. + +
MethodAerial → GroundGround → Aerial
Rank-1Rank-5Rank-10Rank-1Rank-5Rank-10
St-171.5280.4283.8874.8084.2786.90
St-258.4070.2075.8061.5073.6078.20
St-361.6574.5379.1567.3878.8282.3
St-1269.5078.8082.5072.8082.6085.40
St-1371.8080.6083.9175.4084.4886.91
St-2365.7076.5580.9070.1080.4583.91
St-12371.9180.6783.9275.5784.5086.92
+ +Table 5. Ranking accuracy (%) improvement on AG-VPReID dataset. + +
MethodAerial → GroundGround → Aerial
15m30m80m120m15m30m80m120m
St-180.2878.7667.2452.4783.2583.0367.0762.31
St-269.7568.1352.6238.1272.8771.4152.2245.43
St-374.2574.0152.5335.1377.1878.9156.5952.56
St-1278.3276.8265.2450.5381.3481.2765.1760.43
St-1380.5578.9567.5052.8583.7083.5567.6063.10
St-2376.4574.9057.4042.7079.5579.4057.4052.80
St-12380.6679.0067.6353.0083.9283.6667.8263.32
+ +Table 6. Rank-1 accuracy (%) on AG-VPReID at various altitudes. + +guity. See Table 7. + +# 5.5. Visualization + +We further visualize the ReID results with Top-5 ranking to understand how our model improves compared to the baseline [21] for aerial-to-ground person ReID in Fig. 4. Unlike the baseline which may be biased by image resolution and clothing textures, our approach pays attention to more robust features like motion patterns and body shape characteristics, which explains its successful identification of similar walking postures and body proportions despite the significant viewpoint differences between the aerial query and ground-view gallery pair. Additional examples are in Figs. 7 and 8 of the supplementary material. + +
ScenarioRank-1mAPKey Observation
Camera Angle Impact
15m altitude (AG)80.6677.23Baseline performance
30m altitude (AG)79.0075.81Minimal degradation
80m altitude (AG)67.6363.42-13.03% Rank-1 vs. 15m
120m altitude (AG)53.0048.75-27.66% Rank-1 vs. 15m
Clothing Change Impact
GG-SameClothes91.5288.74Upper-bound performance
GG-DiffClothes83.6779.92-7.85% Rank-1 (CC-only impact)
AG-SameClothes71.9164.00-19.61% Rank-1 (AG-only impact)
AG-DiffClothes65.8357.52-6.08% Rank-1 (CC impact in AG)
+ +Table 7. Impact of clothing changes (CC) vs. camera angles. + +# 6. Conclusion + +We introduce AG-VPReLU, a comprehensive dataset for video-based aerial-ground person ReID, addressing the critical need for a large and challenging aerial-ground dataset. We also propose AG-VPReLU-Net, a purpose-built three-stream person ReID framework that combines temporal-spatial processing, physics-informed normalized appearance representation, and multi-scale attention mechanisms. This approach achieves state-of-the-art performance on both the AG-VPReLU dataset and existing video-based ReID benchmarks. Notably, the relatively lower performance across all approaches on AG-VPReLU highlights its demanding nature and establishes it as a robust benchmark for advancing future research in the field. + +# 7. Acknowledgement + +This work was supported by the Australian Research Council (ARC) Discovery Project (DP200101942) and a QUT Postgraduate Research Award. 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However, they also pose misuse risks. Therefore, detecting AI-generated faces becomes crucial, yet current detectors show biased performance across different demographic groups. Mitigating biases can be done by designing algorithmic fairness methods, which usually require demographically annotated face datasets for model training. However, no existing dataset encompasses both demographic attributes and diverse generative methods simultaneously, which hinders the development of fair detectors for AI-generated faces. In this work, we introduce the AI-Face dataset, the first million-scale demographically annotated AI-generated face image dataset, including real faces, faces from deepfake videos, and faces generated by Generative Adversarial Networks and Diffusion Models. Based on this dataset, we conduct the first comprehensive fairness benchmark to assess various AI face detectors and provide valuable insights and findings to promote the future fair design of AI face detectors. Our AI-Face dataset and benchmark code are publicly available at https://github.com/Purdue-M2/AI-Face-FairnessBench. + +# 1. Introduction + +AI-generated faces are created using sophisticated AI technologies that are visually difficult to discern from real ones [1]. They can be summarized into three categories: deepfake videos [2] created by typically using Variational Autoencoders (VAEs) [3, 4], faces generated from Generative Adversarial Networks (GANs) [5-8], and Diffusion Models (DMs) [9]. These technologies have significantly advanced the realism and controllability of synthetic facial representations. Generated faces can enrich media and increase creativity [10]. However, they also carry significant risks of misuse. For example, during the 2024 United States presidential election, fake face images of Donald Trump surrounded by groups of black people smiling and laughing to + +![](images/b60e36a480d2233a4dde3cd316471aec9b9fb7003921d83df06178da82c10f17.jpg) +Figure 1. Comparison between AI-Face and other datasets in terms of demographic annotation, generation category, and the number of generation methods. 'DF', 'GAN', and 'DM' stand for Deepfake Videos, Generative Adversarial Networks, and Diffusion Models. + +encourage African Americans to vote Republican are spreading online [11]. This could distort public opinion and erode people's trust in media [12, 13], necessitating the detection of AI-generated faces for their ethical use. + +However, one major issue existing in current AI face detectors [24-27] is biased detection (i.e., unfair detection performance among demographic groups [19, 28-30]). Mitigating biases can be done by designing algorithmic fairness methods, but they usually require demographically annotated face datasets for model training. For example, works like [29, 30] have made efforts to enhance fairness in the detection based on A-FF++ [19] and A-DFD [19]. However, both datasets are limited to containing only faces from deepfake videos, which could cause the trained models not to be applicable for fairly detecting faces generated by GANs and DMs. While some datasets (e.g., GenData [17], DF40 [31]) include GAN and DM faces, they either lack demographic annotations or provide only limited demographic attributes. Most importantly, no existing dataset offers sufficient diversity in generation methods while also providing demographic labels. A comparison of existing datasets is shown in Fig. 1. These limitations of existing datasets hamper the development of fair technologies for detecting AI-generated faces. + +
DatasetYearFace ImagesGeneration Category#Generation MethodsSource of Real ImagesDemographic Annotation
#Real#FakeDeepfake VideosGANDMSkin ToneGenderAge
DF-1.0 [14]20202.9M14.7M1Self-Recording
DeePhy [15]20221K50.4K3YouTube
DF-Platter [16]2023392.3K653.4K3YouTube
GenData [17]2023-20K3CelebA [18]
A-FF++ [19]202429.8K149.1K5YouTube
A-DFD [19]202410.8K89.6K5Self-Recording
A-DFDC [19]202454.5K52.6K8Self-Recording
A-Celeb-DF-v2 [19]202426.3K166.5K1Self-Recording
A-DF-1.0 [19]2024870.3K321.5K1Self-Recording
AI-Face2025400K1.2M37FFHQ [6], IMDB-WIKI [20], real from FF++ [2], DFDC [21], DFD [22],Celeb-DF-v2 [23]
+ +Table 1. Quantitative comparison of existing datasets with ours on demographically annotated AI-generated faces. + +Moreover, benchmarking fairness provides a direct method to uncover prevalent and unique fairness issues in recent AI-generated face detection. However, there is a lack of a comprehensive benchmark to estimate the fairness of existing AI face detectors. Existing benchmarks [32-35] primarily assess utility, neglecting systematic fairness evaluation. Two studies [28, 36] do evaluate fairness in detection models, but their examination is based on a few outdated detectors. Furthermore, detectors' fairness reliability (e.g., robustness with test set post-processing, fairness generalization) has not been assessed. The absence of a comprehensive fairness benchmark impedes a thorough understanding of the fairness behaviors of recent AI face detectors and obscures the research path for detector fairness guarantees. + +In this work, we build the first million-scale demographically annotated AI-generated face image dataset: AI-Face. The face images are collected from various public datasets, including the real faces that are usually used to train AI face generators, faces from deepfake videos, and faces generated by GANs and DMs. Each face is demographically annotated by our designed measurement method and Contrastive Language-Image Pretraining (CLIP) [37]-based lightweight annotator. Next, we conduct the first comprehensive fairness benchmark on our dataset to estimate the fairness performance of 12 representative detectors coming from four model types. Our benchmark exposes common and unique fairness challenges in recent AI face detectors, providing essential insights that can guide and enhance the future design of fair AI face detectors. Our contributions are as follows: + +- We build the first million-scale demographically annotated AI-generated face dataset by leveraging our designed measure and developed lightweight annotator. +- We conduct the first comprehensive fairness benchmark of AI-generated face detectors, providing an extensive fairness assessment of current representative detectors. +- Based on our experiments, we summarize the unsolved questions and offer valuable insights within this research field, setting the stage for future investigations. + +# 2. Background and Motivation + +AI-generated Faces and Biased Detection. AI-generated face images, created by advanced AI technologies, are vi + +sually difficult to discern from real ones. They can be summarized into three categories: 1) Deepfake Videos. Initiated in 2017 [13], these use face-swapping and face-reenactment techniques with a variational autoencoder to replace a face in a target video with one from a source [3, 4]. Note that our paper focuses solely on images extracted from videos. 2) GAN-generated Faces. Post-2017, Generative Adversarial Networks (GANs) [38] like StyleGANs [6-8] have significantly improved generated face realism. 3) DM-generated Faces. Diffusion models (DMs), emerging in 2021, generate detailed faces from textual descriptions and offer greater controllability. Tools like Midjourney [39] and DALLE2 [40] facilitate customized face generation. While these AI-generated faces can enhance visual media and creativity [10], they also pose risks, such as being misused in social media profiles [41, 42]. Therefore, numerous studies focus on detecting AI-generated faces [24-27], but current detectors often show performance disparities among demographic groups [19, 28-30]. This bias can lead to unfair targeting or exclusion, undermining trust in detection models. Recent efforts [29, 30] aim to enhance fairness in deepfake detection but mainly address deepfake videos, overlooking biases in detecting GAN- and DM-generated faces. + +The Existing Datasets. Current AI-generated facial datasets with demographic annotations are limited in size, generation categories, methods, and annotations, as illustrated in Table 1. For instance, A-FF++, A-DFD, A-DFDC, and A-Celeb-DF-v2 [19] are deepfake video datasets with fewer than one million images. Datasets like DF-1.0 [14] and DF-Platter [16] lack various demographic annotations. Additionally, existing datasets offer limited generation methods. These limitations hinder the development of fair AI face detectors, motivating us to build a million-scale demographically annotated AI-Face dataset. + +Benchmark for Detecting AI-generated Faces. Benchmarks are essential for evaluating AI-generated face detectors under standardized conditions. Existing benchmarks, as shown in Table 2, mainly focus on detectors' utility, often overlooking fairness [31-35]. Loc et al. [28] and CCv1 [36] examined detector fairness. However, their study did not have an analysis on DM-generated faces and only measured bias between groups in basic scenarios without considering + +
Existing BenchmarksYearCategoryScope of Benchmark
Deepfake VideosGANDMUtilityFairness General Reliability
Loc et al. [28]2021
CCv1 [36]2021
DeepfakeBench [34]2023
CDDB [32]2023
Lin et al. [33]2024
Le et al. [35]2024
DF40 [31]2024
Ours2025
+ +Table 2. Comparison of existing AI-generated face detection benchmarks and ours. Fairness 'General' means fairness evaluation under default/basic settings. Fairness 'Reliability' measures fairness consistency across dynamic scenarios (e.g., post-processing). + +fairness reliability under real-world variations and transformations. This motivates us to conduct a comprehensive benchmark to evaluate AI face detectors' fairness. + +The Definition of Demographic Categories. Demography-related labels are highly salient to measuring bias. Following prior works [36, 43-47], we will focus on three key demographic categories: Skin Tone, Gender, and Age, in this work. For skin tone, this vital attribute spans a range from pale to dark. We use the Monk Skin Tone scale [48], specifically designed for computer vision applications. For gender, we adopt binary categories (i.e., Male and Female), following practices by many governments [49, 50] and facial recognition research [45, 51, 52], based on sex at birth. For age, using definitions from the United Nations [53] and Statistics Canada [54], we define five age groups: Child (0-14), Youth (15-24), Adult (25-44), Middle-age Adult (45-64), and Senior $(65+)$ . More discussion is in Appendix A. + +# 3.AI-Face Dataset + +This section outlines the process of building our demographically annotated AI-Face dataset (see Fig. 2), along with its statistics and annotation quality assessment. + +# 3.1. Data Collection + +We build our AI-Face dataset by collecting and integrating public real and AI-generated face images sourced from academic publications, GitHub repositories, and commercial tools. We strictly adhere to the license agreements of all datasets to ensure that they allow inclusion in our datasets and secondary use for training and testing. More details are in Appendix B.1. Specifically, the fake face images in our dataset originate from 4 Deepfake Video datasets (i.e., $\mathrm{FF} + +$ [2], DFDC [21], DFD [22], and Celeb-DFv2 [23]), generated by 10 GAN models (i.e., AttGAN [55], MMDGAN [56], StarGAN [55], StyleGANs [55, 57, 58], MSGGAN [56], ProGAN [59], STGAN [56], and VQGAN [60]), and 8 DM models (i.e., DALLE2 [61], IF [61], Midjourney [61], DCFace [62], Latent Diffusion [63], Palette [64], Stable Diffusion v1.5 [65], Stable Diffusion Inpainting [65]). This constitutes a total of 1,245,660 fake face images in our dataset. We include 6 real source datasets + +(i.e., FFHQ [6], IMDB-WIKI [20], and real images from $\mathrm{FF}++$ [2], DFDC [21], DFD [22], and Celeb-DF-v2 [23]). All of them are usually used as a training set for generative models to generate fake face images. This constitutes a total of 400,885 real face images in our dataset. In general, our dataset contains 28 subsets and 37 generation methods (i.e., 5 in $\mathrm{FF}++$ , 5 in DFD, 8 in DFDC, 1 in Celeb-DF-v2, 10 GANs, and 8 DMs). For all images, we use RetinaFace [66] for detecting and cropping faces. + +# 3.2. Annotation Generation + +# 3.2.1. Skin Tone Annotation Generation + +Skin tone is typically measured using an intuitive approach [67, 68], without requiring a predictive model. Inspired by [67], we developed a method to estimate skin tone using the Monk Skin Tone (MST) Scale [48] (including 10-shade scales: Tone 1 to 10) by combining facial landmark detection with color analysis. Specifically, utilizing Mediapipe's FaceMesh [69] for precise facial landmark localization, we isolate skin regions while excluding non-skin areas such as the eyes and mouth. Based on the detected landmarks, we generate a mask to extract skin pixels from the facial area. These pixels are then subjected to K-Means clustering [70] (we use $\mathrm{K} = 3$ in practice) to identify the dominant skin color within the region of interest. The top-1 largest color cluster is mapped to the closest tone in the MST Scale by calculating the Euclidean distance between the cluster centroid and the MST reference colors in RGB space. + +# 3.2.2. Gender and Age Annotation Generation + +For generating gender and age annotations, the existing online software (e.g., Face++ [71]) and open-source tools (e.g., InsightFace [72]) can be used for the prediction. However, they fall short in our task due to two reasons: 1) They are mostly designed for face recognition and trained on datasets of real face images but lack generalization capability for annotating AI-generated face images. 2) Their use may introduce bias into our dataset, as they are typically designed and trained without careful consideration of bias and imbalance in the training set. See Appendix B.3 for our experimental study on these tools. To this end, we have to develop our specific annotators to predict gender and age annotations for each image in our dataset. + +Problem Definition. Given a training dataset $\mathbb{D} = \{(X_i, A_i)\}_{i=1}^n$ with size $n$ , where $X_i$ represents the $i$ -th face image and $A_i$ signifies a demographic attribute associated with $X_i$ . Here, $A_i \in \mathcal{A}$ , where $\mathcal{A}$ represents user-defined groups (e.g., for gender, $\mathcal{A} = \{\text{Female, Male}\}$ . For age, $\mathcal{A} = \{\text{Child, Youth, Adult, Middle-age Adult, Senior}\}$ ). Our goal is to design a lightweight, generalizable annotator based on $\mathbb{D}$ that reduces bias while predicting facial demographic attributes for each image in our dataset. In practice, we use IMDB-WIKI [20] as training dataset, which contains + +![](images/73cdb83d2fd072d055ecc2be288d34736d78933d58e073c80c3646a5aedbf2b0.jpg) +Figure 2. Generation pipeline of our Demographically Annotated AI-Face Dataset. First, we collect and filter face images from Deepfake Videos, GAN-generated faces, and DM-generated faces found in public datasets. Second, we perform skin tone, gender, and age annotation generation. Skin tone is estimated by combining facial landmark detection with color analysis to generate the corresponding annotation. For gender and age, we develop annotators trained on the IMDB-WIKI dataset [20], then use them to predict attributes for each image. + +images along with profile metadata sourced from IMDb and Wikipedia, ensuring that the demographic annotations are as accurate as possible. We trained two annotators with identical architecture and training procedures for gender and age annotations, respectively. + +Annotator Architecture. We build a lightweight annotator based on the CLIP [37] foundation model by leveraging its strong zero-shot and few-shot learning capabilities. Specifically, our annotator employs a frozen pre-trained CLIP ViT L/14 [73] as a feature extractor $\mathbf{E}$ followed by a trainable classifier parameterized by $\theta$ , which contains 3-layer Multi-layer Perceptron (MLP) M and a classification head $h$ . + +Learning Objective. Aware that neural networks can perform poorly when the training dataset suffers from class-imbalance [74] and CLIP is not free from demographic bias [75-77], we introduce an imbalance loss and fairness loss to address these challenges in the annotator training. Specifically, for image $X_{i}$ , its feature $f_{i}$ is obtained through $f_{i} = \mathbf{M}(\mathbf{E}(X_{i}))$ . Next, two losses are detailed below. + +Imbalance Loss: To mitigate the impact of imbalance data, we use Vector Scaling [78] loss, which is a re-weighting method for training models on the imbalanced data with distribution shifts and can be expressed as + +$$ +L _ {i m b} = \frac {1}{n} \sum_ {i = 1} ^ {n} - u _ {A _ {i}} \log \frac {e ^ {\zeta_ {A _ {i}} h (f _ {i}) _ {A _ {i}} + \Delta_ {A _ {i}}}}{\sum_ {A \in \mathcal {A}} e ^ {\zeta_ {A} h (f _ {i}) _ {A} + \Delta_ {A}}}, +$$ + +where $u_{A_i}$ is the weighting factor for attribute $A_i$ . $h(f_i)_{A_i}$ is the predict logit on $A_i$ . $\zeta_{A_i}$ is the multiplicative logit scaling factor, calculated as the inverse of $A_i$ 's frequency. $\Delta_{A_i}$ is the additive logit scaling factor, calculated as the log of $A_i$ probabilities. More details about them are in appendix B.4. + +Fairness Loss: We introduce a fairness loss to minimize + +the disparity between the distribution $\mathcal{D}^f$ of $f$ and the conditional distribution $\mathcal{D}^{f_A}$ of $f$ on attribute $A\in \mathcal{A}$ . Specifically, we follow [79, 80] to minimize the summation of the following Sinkhorn distance between these two distributions: + +$$ +L_{fair} = \sum_{A\in \mathcal{A}}\inf_{\gamma \in \Gamma (\mathcal{D}^{f},\mathcal{D}^{f_{A}})}\bigl\{\mathbb{E}_{X\sim \gamma}[c(p,q)] + \alpha H(\gamma |\mu \otimes \nu)\bigr \} , +$$ + +where $\Gamma(\mathcal{D}^f, \mathcal{D}^{f_A})$ is the set of joint distributions based on $\mathcal{D}^f$ and $\mathcal{D}^{f_A}$ . Let $p$ and $q$ be the points from $\mathcal{D}^f$ and $\mathcal{D}^{f_A}$ , respectively. Then, $c(p, q)$ represents the transport cost [80]. Let $\mu$ and $\nu$ be the reference measures from the set of measures on $f$ . Then, $H(\gamma | \mu \otimes \nu)$ represents the relative entropy of $\gamma$ with respect to the product measure $\mu \otimes \nu$ . $\alpha \geq 0$ is a regularization hyperparameter. In practice, we use the empirical form of $L_{fair}$ . + +Total Loss: Therefore, the final learning objective becomes $\mathcal{L}(\theta) = L_{imb} + \lambda L_{fair}$ , where $\lambda$ is a hyperparameter. Train. Traditional optimization methods like stochastic gradient descent can lead to poor model generalization due to sharp loss landscapes with multiple local and global minima. To address this, we use Sharpness-Aware Minimization (SAM) [81] to enhance our annotator's generalization by flattening the loss landscape. Specifically, flattening is attained by determining the optimal $\epsilon^{*}$ for perturbing model parameters $\theta$ to maximize the loss, formulated as: $\epsilon^{*} = \arg \max_{\| \epsilon \|_{2} \leq \beta} \mathcal{L}(\theta + \epsilon) \approx \arg \max_{\| \epsilon \|_{2} \leq \beta} \epsilon^{\top} \nabla_{\theta} \mathcal{L} = \beta \text{sign}(\nabla_{\theta} \mathcal{L})$ , where $\beta$ controls the perturbation magnitude. The approximation is based on the first-order Taylor expansion with assuming $\epsilon$ is small. The final equation is obtained by solving a dual norm problem, where sign represents a sign function and $\nabla_{\theta} \mathcal{L}$ being the gradient of $\mathcal{L}$ with respect to $\theta$ . As a result, the model parameters are updated by solving: $\min_{\theta} \mathcal{L}(\theta + \epsilon^{*})$ . + +![](images/ee33e2d2ecf2b2de8ef43e6b49c40496f7bca36c846a744baca4b05c14801536.jpg) +Figure 3. Distribution of face images of the AI-Face dataset. The figure shows the (a) subset distribution and the demographic distribution for (b) skin tone, (c) gender, and (d) gender. The outer rings in (b), (c), and (d) represent the proportion of groups within each attribute category, while the inner rings indicate the distribution of fake $(F)$ and real $(R)$ images within those groups. + +![](images/73dce0516cea83156d02b385626f5b7c5190a16667a7fb0a7c2413c9ae3dae08.jpg) + +![](images/64b85c5d29c5a70ca88dd95e3cd88007ea0acd67770d93cd21e538fb0c9ef472.jpg) + +![](images/7c9ff3f0b1c04966ed4493926d615fc9c3189dd883ddb15e16207aafedd36107.jpg) + +Inference. We use the trained annotators to predict demographic labels for each image in AI-Face dataset, except for those from IMDB-WIKI, which already contain true labels. + +# 3.3. Dataset Statistics + +Fig. 3 illustrates the subset distribution and demographic attributes of the AI-Face dataset. The dataset contains approximately three times more generated images than real images, with diffusion model-generated images constituting the majority. In terms of demographic attributes, the majorities in skin tone are Tone 5 (31.14%) and Tone 6 (35.16%). The lightest skin tones (Tones 1-3) are underrepresented, comprising only 0.97% of the dataset. The dataset is relatively balanced across gender. Adult (25-44) (49.67%) is the predominant representation in age groups. + +# 3.4. Annotation Quality Assessment + +To assess the quality of demographic annotations in our AI-Face dataset, we conducted a user study. Three participants label the demographic attributes for the given images (the details of labeling activities are in appendix B.5), with the final ground truth determined by majority vote. We then compare our annotations with those in A-FF++, A-DFDC, A-CelebDF-V2, and A-DFD datasets. Specifically, we perform two assessments: 1) Strategic comparison: We select 1,000 images from A-FF++ and A-DFDC that have different annotations from AI-Face. These images likely represent challenging cases. 2) Random comparison: We randomly sampled 1,000 images from A-Celeb-DF-V2 and A-DFD. Due to the limited age classes in these datasets, only gender was evaluated. The results, presented in Table 3, demonstrate the high correctness of the AI-Face annotations and their superior quality compared to the annotations of other datasets. For example, our annotation quality (ACC) surpasses those in A-FF++ by $78.714\%$ on gender and $48.000\%$ on age. + +# 4. Fairness Benchmark Settings + +This section demonstrates the fairness benchmark settings for detection methods and evaluation metrics on AI-Face (80%/20%: Train/Test). More settings are in Appendix C.1. + +Detection Methods. Our benchmark has implemented 12 detectors. The methodologies cover a spectrum that + +
Evaluation TypeDatasetGenderAge
ACCPrecisionRecallACCPrecisionRecall
StrategicA-FF++8.14317.5835.96637.70039.45945.381
AI-Face86.85774.40477.36785.70074.02463.751
A-DFDC21.60028.60423.08233.40038.01140.165
AI-Face91.70092.12983.44877.00076.18462.646
RandomA-Celeb-DF-V289.62890.62690.494-
AI-Face91.20691.47491.767-
A-DFD70.90071.68674.435-
AI-Face92.30091.06091.727-
+ +Table 3. Annotation quality assessment results $(\%)$ for $A - FF + +$ A- DFDC, A-Celeb-DF-V2, A-DFD, and our AI-Face. ACC: Accuracy. + +is specifically tailored to detect AI-generated faces from Deepfake Videos, GANs, and DMs. They can be classified into four types: Naive detectors: refer to backbone models that can be directly utilized as the detector for binary classification, including CNN-based (i.e., Xception [82], EfficientB4 [83]) and transformer-based (i.e., ViT-B/16 [84]). Frequency-based: explore the frequency domain for forgery detection (i.e., F3Net [85], SPSL [86], SRM [87]). Spatial-based: focus on mining spatial characteristics (e.g., texture) within images for detection (i.e., UCF [26], UnivFD [88], CORE [89]). Fairness-enhanced: focus on improving fairness in AI-generated face detection by designing specific algorithms (i.e., DAW-FDD [29], DAGFDD [29], PG-FDD [30]). + +Evaluation Metrics. To provide a comprehensive benchmarking, we consider 5 fairness metrics commonly used in fairness community [90-94] and 5 widely used utility metrics [95-98]. For fairness metrics, we consider Demographic Parity $(F_{DP})$ [90, 91], Max Equalized Odds $(F_{MEO})$ [93], Equal Odds $(F_{EO})$ [92], and Overall Accuracy Equality $(F_{OAE})$ [93] for evaluating group (e.g., gender) and intersectional (e.g., individuals of a specific gender and simultaneously a specific skin tone) fairness. In experiments, the intersectional groups are Female-Light (F-L), Female-Medium (F-M), Female-Dark (Dark), Male-Light (M-L), Male-Medium (M-M), and Male-Dark (M-D), where we group 10 categories of skin tones into Light (Tone 1-3), Medium (Tone 4-6), and Dark (Tone 7-10) for simplicity according to [99]. We also use individual fairness $(F_{IND})$ [94, 100] (i.e., similar individuals should have similar predicted outcomes) for estimation. For utility metrics, we employ the Area Under the ROC Curve (AUC), Accuracy (ACC), Average Precision (AP), Equal Error Rate (EER), + +
MeasureAttributeMetricModel Type
NaiveFrequencySpatialFairness-enhanced
Xception [82]EfficientB4 [83]ViT-B/16 [84]F3Net [85]SPSL [86]SRM [87]UCF [26]UnivFD [88]CORE [89]DAW-FDD [29]DAG-FDD [29]PG-FDD [30]
Fairness(%)↓Skin ToneFMEO8.8368.3006.26419.9388.05510.00217.3252.57710.77914.1186.5516.465
FDP9.7516.1847.72812.8769.37910.89712.5818.55610.31710.7068.6179.746
FOAE1.2714.3772.1682.8181.1350.9151.8832.7481.3321.6671.3880.882
FEO12.13211.0628.81323.7089.78914.23921.925.53613.06916.6047.3839.115
GenderFMEO3.9755.3855.1044.7174.4116.2715.0744.5035.7955.5105.9103.190
FDP1.6911.7251.3441.8641.8271.9571.7361.1902.1542.0152.1511.252
FOAE0.9751.4871.8031.1291.0371.7721.4511.6221.3891.3251.4201.071
FEO4.1435.8636.0314.8704.5346.785.5105.4085.9315.6966.0663.702
AgeFMEO27.8836.79614.93738.80127.61424.84347.5005.43633.88245.46615.22914.804
FDP10.90511.84911.83914.90611.23211.57017.04915.24912.56414.1069.63310.467
FOAE7.2652.8566.83810.1167.2706.52411.6523.7938.76011.8785.5335.009
FEO42.21610.30030.79555.03240.94338.52867.54514.14848.72964.38430.18229.585
IntersectionFMEO10.50517.5869.38421.36910.37915.14220.1346.11915.3416.56512.1789.578
FDP14.5118.60711.53517.17513.25915.18617.0314.02614.30114.08811.70514.697
FOAE2.5368.4614.9284.8702.4643.9983.5366.2872.7753.5474.0353.062
FEO24.31525.11427.44347.78321.67930.11243.37620.25528.8433.12226.29518.348
IndividualFIND10.33825.7420.0221.8722.5187.6210.7673.5230.0413.7720.9010.780
Utility(%)-AUC↑98.58398.61198.6998.71498.74797.93698.08298.19298.57997.81198.77199.172
ACC↑96.30894.20394.47295.71996.34695.09295.15193.65196.22495.42695.72296.174
AP↑99.35099.54299.57199.45399.35699.17299.27399.40099.36099.01599.49899.694
EER↓5.1496.6896.3725.2564.3716.4837.7087.6335.1457.0635.4994.961
FPR↓12.96120.06616.42614.67913.66115.74613.64618.55013.41016.67014.84410.971
Training Time / Epoch1h15min2h25min2h40min1h18min1h20min3h10min5h05min4h1h16min1h25min1h17min7h20min
+ +Table 4. Overall performance comparison of difference methods on the AI-Face dataset. The best performance is shown in bold. + +and False Positive Rate (FPR). + +# 5. Results and Analysis + +In this section, we estimate the existing AI-generated image detectors' fairness performance alongside their utility on our AI-Face Dataset. More results can be found in Appendix D. + +# 5.1. General Fairness Comparison + +Overall Performance. Table 4 reports the overall performance on our AI-Face test set. Our observations are: 1) Fairness-Enhanced Models (specifically PG-FDD [30]) are the most effective in achieving both high fairness and utility, underscoring the effectiveness of specialized fairness-enhancement techniques in mitigating demographic biases. 2) UnivFD [88], based on the CLIP backbone [73], also achieves commendable fairness, suggesting that foundation models equipped with fairness-focused enhancements could be a promising direction for developing fairer detectors. 3) Naive detectors, such as EfficientB4 [83], trained on large, diverse datasets (e.g., our AI-Face) can achieve competitive fairness and utility, highlighting the potential of fairness improvements by choosing specific architecture. 4) 10 out of 12 detectors have an AUC higher than $98\%$ , demonstrating our AI-Face dataset is significant for training AI-face detectors in resulting high utility. 5) PG-FDD demonstrates superior performance but has a long training time, which can be explored and addressed in the future. + +Performance on Different Subsets. 1) Fig. 4 demonstrates the intersectional $F_{EO}$ and AUC performance of detectors on each test subset. We observe that the fairness performance varies a lot among different generative methods for every detector. The largest bias on most detectors comes from detecting face images generated by diffusion models. 2) DAG-FDD [29] and SRM [87] demonstrate the most + +consistent fairness across subsets, indicating a robust handling of bias introduced by different generative methods. 3) Moreover, the stable utility demonstrates our dataset's expansiveness and diversity, enabling effective training to detect AI-generated faces from various generative techniques. + +Performance on Different Subgroups. We conduct an analysis of all detectors on intersectional subgroups. 1) As shown in Fig. 5, facial images with lighter skin tone are more often misclassified as fake, likely due to the underrepresentation of lighter tones (Tone 1-3) in our dataset (see Fig. 3 (b)). This suggests detectors tend to show higher error rates for minority groups. 2) Although gender representation is relatively balanced (see Fig. 3 (c)) in our dataset, the detectors consistently exhibit higher false positive rates for female subgroups, indicating a persistent gender-based bias. + +# 5.2. Fairness Reliability Assessment + +Fairness Robustness Evaluation. We apply 6 post-processing methods: Random Crop (RC) [101], Rotation (RT) [34], Brightness Contrast (BC) [34], Hue Saturation Value (HSV) [34], Gaussian Blur (GB) [34], and JEPG Compression (JC) [102] to the test images. Fig. 6 shows each detector's intersectional $F_{EO}$ and AUC performance changes after using post-processing. Our observations are: 1) These impairments tend to wash out forensic traces, so that detectors have evident performance degradation. 2) Post-processing does not always cause detectors more bias (e.g., UCF, UnivFD, CORE, DAW-FDD have better fairness after rotation), though they hurt the utility. 3) Fairness-enhanced detectors struggle to maintain fairness when images undergo post-processing. 4) Spatial detectors have better fairness robustness compared with other model types. + +Fairness Generalization Evaluation. To evaluate detectors' fairness generalization capability, we test them on Casual + +![](images/e46031def0f22af80823816c764efa8d609057504dfa7814e2516c6ac5abeecb.jpg) + +![](images/6ec0f78a6d4f1e7cf989ca92809a4fd0af26df25346a5b2ad4dfc784590fa136.jpg) + +![](images/01b5f57c01e0a85aab33413e5edc86dec9275e457a2fcc570db0106a9a8b77cd.jpg) + +![](images/3ed381744d2a149f361ac5002bf73cdb9224e270715f0926951af5bd27b443d2.jpg) + +![](images/f703227f7c0a1d3042de5635e5224485e29975e281ebb83c2f19c9c1928eb972.jpg) + +![](images/b5cf2bdd2f22f0fe64e0b55ea896aff1bfb41e28fc01205ab907db05edd9c00d.jpg) + +![](images/e33836a66a827e63ba49d5986faa44a281c5f61c13bdc81a1326c85ec9b10c12.jpg) +Figure 4. Visualization of the intersectional $F_{EO}$ (\%) and AUC (\%) of detectors on different subsets. The smaller $F_{EO}$ polygon area represents better fairness. The larger AUC area means better utility. + +![](images/54aaaa160577b20bc7065760bc2188b1c0a14a90ef49b20360fb2d3397e8e5f7.jpg) + +![](images/a7cd58856432107fdfe153cd0a7f772366496c4324f72f4b142fbf760ebb6672.jpg) + +![](images/04dd2777922990ee178b7c87375c81b7f3c5b33437c35c7ebb0d8e9771a5386d.jpg) + +![](images/0dda740b787a117192b48a263b4d80ea906be8d79747a6fd1edd3122ea595f52.jpg) + +![](images/3fb87041182ba581a4144a41520a81745c8ffea2f4b79db682ca098f23a32c69.jpg) + +![](images/be00424190d93f7bc86666e788fa87f2a877b5ed9b6f4a274c244514da0fd855.jpg) +Figure 5. FPR(%) of each intersectional subgroup The dashline represents the lowest FPR on Female-Light (F-L) subgroup. + +![](images/c8b428974b8488c6589a108584966d8fd60bd1d37b3a3fd5055c70f86681c9f6.jpg) + +![](images/7b66e46430a04c9303d75e59aa66d9b11e3b84337a57a3059062880851871ded.jpg) + +![](images/07971c0affdc5b1324513f078b01c55b5fe787d10e186a57af172f5bf4f5000c.jpg) + +![](images/0c507a0a9d0f1ddb836170ca5ed44a91ce6d0652e050b0f96195d9cbc1692452.jpg) + +![](images/59f86cfc141be60c428d5a68cff6f5c5454d96715dbd8157a104501234ee22ca.jpg) + +Conversations v2 (CCv2) [103], DF-Platter [16], and GenData [17], none of which are part of AI-Face. Notably, CCv2 is a dataset that contains only real face images with demographic annotations (e.g., gender) self-reported by the participants. Results on gender attribute in Table 5 show that: 1) Even well-designed detectors that focus on improving utility or fairness generalization (e.g., UCF, PG-FDD) struggle to achieve consistently superior performance across different dataset domains. This highlights the remaining fairness generalization issue. 2) DAW-FDD and PG-PDD are two fairness-enhanced detectors that require accessing demographic information during training, but their fairness does not encounter a drastic drop when evaluating on CCv2. This reflects the high accuracy of the annotations in our AI-face. + +Effect of Training Set Size. We randomly sample $20\%$ , $40\%$ , $60\%$ , and $80\%$ of each training subset from AI-Face to assess the impact of training size on performance. Key observations from Fig. 7 (Left): 1) Among all detectors, UnivFD demonstrates the most stable fairness and utility performance as the training dataset size changes, likely due to its fixed CLIP backbone. 2) Increasing the training dataset size generally improves model utility, but this pattern does not extend to fairness metrics. In fact, certain detectors such as F3Net and UCF exhibit worsening fairness as the training size reaches its maximum. This suggests that more training data does not necessarily lead to fairer detectors. + +Effect of the Ratio of Real and Fake. To examine how training real-to-fake sample ratios affect detector performance, we set the ratios at 1:10, 1:1, and 10:1 while keeping the total sample count constant. Experimental results in Fig. 7 (Right) show: 1) Most detectors' fairness improves as real sample representation increases. Probably because increasing real and reducing fake samples helps detectors reduce overfitting to artifacts specific to fake samples. This makes it easier for detectors to distinguish real from fake, even for underrepresented groups, thereby enhancing fairness. 2) Most detectors achieve the highest AUC with balanced data. + +# 5.3. Discussion + +According to the above experiments, we summarize the unsolved fairness problems in recent detectors: 1) Detectors' fairness is unstable when detecting face images generated by different generative methods, indicating a future direction for enhancing fairness stability since new generative models continue to emerge. 2) Even though fairness-enhanced detectors exhibit small overall fairness metrics, they still show biased detection towards minority groups. Future studies should be more cautious when designing fair detectors to ensure balanced performance across all demographic groups. 3) There is currently no reliable detector, as all detectors experience severe large performance degradation under image post-processing and cross-domain evaluation. Future + +![](images/62c71090c95651797a47b03964b61722d2a55d6802d1bfa822336b0986e770aa.jpg) +Figure 6. Performance ratio after vs. before post-processing. Points closer to 1.0 (i.e., no post-processing) indicate better robustness. + +![](images/68008447f733340256d211e2ea028e169a18c9aa3abaec3961e24c8e2fd13c1d.jpg) + +![](images/f7f61cca8e81436fef80425da46d9a5460d41d86dcba5847c49004dcf222480b.jpg) + +![](images/578ff42d96fa595ace4f5a6a53b17142d06e0d0d598dc743a023d62a2e304a01.jpg) + +
Model TypeDetectorDataset
CCv2 [103]DF-Platter [16]GenData [17]
Fairness(%)↓FOAEUtility(%)↑ACCFairness(%)↓FOAEFEOUtility(%)↑AUCFairness(%)↓FOAEFEOUtility(%)↑AUC
NaiveXception1.006(+0.031)86.465(-9.843)6.836(+5.861)9.789(+5.646)81.273(-17.310)2.539(+1.564)13.487(+9.344)96.971(-1.612)
EfficientB44.077(+0.259)82.980(-11.223)8.786(+7.299)12.370(+6.507)67.694(-30.917)3.304(+1.817)1.995 (-3.686)93.213(-5.398)
ViT-B/162.167(+0.364)81.489(-12.983)0.015 (-1.788)12.373(+6.342)76.050(-22.640)3.164(+1.361)9.610(+3.579)88.253(-10.437)
FrequencyF3Net5.743(+4.614)87.867(-7.852)3.521(+2.392)6.445(+1.575)85.112(-13.602)1.188(+0.059)16.306(+11.436)91.603(-7.111)
SPSL0.601 (-0.436)80.006(-16.340)5.109(+4.072)7.842(+3.308)82.175(-16.572)1.385(+0.348)9.261(+4.272)98.838 (+0.091)
SRM7.000(+5.228)79.768(-15.324)3.823(+2.051)6.567(-0.213)66.401(-31.535)3.281(+1.509)7.907(+1.127)90.049(-7.887)
SpatialUCF2.169(+0.718)93.009 (-2.142)8.687(+7.236)17.068(+11.558)80.821(-17.261)3.513(+2.062)10.529(+5.019)87.778(-10.304)
UnivFD7.625(+6.003)67.983(-25.668)4.540(+2.918)9.950(+4.542)76.443(-21.749)1.645(+0.023)3.848(-1.560)94.418(-3.774)
CORE4.410(+3.021)83.328(-12.896)7.741(+6.352)17.348(+11.417)77.226(-21.353)3.759(+2.370)23.289(+17.358)98.408(-0.171)
Fairness-enhancedDAW-FDD4.726(+3.401)84.685(-10.741)5.536(+4.211)13.667(+7.791)81.807(-16.004)1.443(+0.118)10.228(+4.532)97.854(+0.043)
DAG-FDD2.364(+0.944)83.918(-11.804)3.064(+1.644)22.203(+16.137)75.206(-23.565)0.714 (-0.706)10.332(+4.266)92.108(-6.663)
PG-FDD1.513(+0.442)92.852(-3.322)4.565(+3.494)9.717(+6.015)85.271 (-13.901)3.063(+1.992)9.479(+5.777)93.329(-5.843)
+ +Table 5. Fairness generalization results based on the gender attribute. The smallest performance changes (in parentheses) and the best performance are in red and in bold, respectively. Only $F_{OAE}$ fairness metric and ACC metric are used in CCv2 due to all samples are real. + +![](images/084be84553a199b922a7ec664074fd2869b88a754601e70c2177a9a14abde391.jpg) +Figure 7. Impact of the training set size (Left) and the ratio of real and fake (Right) on detectors' intersectional $F_{EO}(\%)$ and AUC (\%). + +studies should aim to develop a unified framework that ensures fairness, robustness, and generalization, as these three characteristics are essential for creating a reliable detector. Moreover, integrating foundation models (e.g., CLIP) into detector design may help mitigate bias. + +# 6. Conclusion + +This work presents the first demographically annotated million-scale AI-Face dataset, serving as a pivotal foundation for addressing the urgent need for developing fair AI face detectors. Based on this dataset, we conduct the first comprehensive fairness benchmark, shedding light on the fairness performance and challenges of current representative AI face detectors. Our findings can inspire and guide researchers in refining current models and exploring new methods to mitigate bias. Limitation and Future Work: One limitation is that our dataset's annotations are algorithmically generated, so they may lack $100\%$ accuracy. This challenge is difficult to resolve, as demographic attributes for most AI-generated faces are often too ambiguous to predict and do not map to real-world individuals. We plan to enhance annotation quality through human labeling in the future. We + +also plan to extend our fairness benchmark to evaluate large language models like LLaMA2 [104] and GPT4 [105] for detecting AI faces. Social Impact: Malicious users could misuse AI-generated face images from our dataset to create fake social media profiles and spread misinformation. To mitigate this risk, only users who submit a signed end-user license agreement will be granted access to our dataset. + +# Ethics Statement + +Our dataset collection and annotation generation are approved by Purdue's Institutional Review Board. The dataset is only for research purposes. All data included in this work are sourced from publicly available datasets, and we strictly comply with each dataset's license agreement to ensure lawful inclusion and permissible secondary use for training and testing. All collected data and their associated licenses are mentioned in the Datasheet of AI-Face in Appendix E. Our annotation processes prioritize ethical considerations: 1) $76\%$ images we annotated are generated facial images, ensuring no potential for harm to any individual. 2) For real images, we only provide annotations for content either licensed by the original copyright holders or explicitly stated as freely shareable for research purposes. + +# Acknowledgments + +This work is supported by the U.S. National Science Foundation (NSF) under grant IIS-2434967 and the National Artificial Intelligence Research Resource (NAIRR) Pilot and TACC Lonestar6. The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of NSF and NAIRR Pilot. + +# References + +[1] L. Lin, N. Gupta, Y. Zhang, H. Ren, C.-H. Liu, F. Ding, X. Wang, X. Li, L. Verdoliva, and S. Hu, "Detecting multimedia generated by large ai models: A survey," arXiv preprint arXiv:2402.00045, 2024. 1 +[2] A. Rossler, D. Cozzolino, L. Verdoliva, C. 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Current VQA models generally fall short in accurately assessing the perceptual quality of AIGVs due to the presence of unique distortions, such as unrealistic objects, unnatural movements, or inconsistent visual elements. To address this challenge, we first present AIGVQA-DB, a large-scale dataset comprising 36,576 AIGVs generated by 15 advanced text-to-video models using 1,048 diverse prompts. With these AIGVs, a systematic annotation pipeline including scoring and ranking processes is devised, which collects 370k expert ratings to date. Based on AIGVQA-DB, we further introduce AIGV-Assessor, a novel VQA model that leverages spatiotemporal features and LMM frameworks to capture the intricate quality attributes of AIGVs, thereby accurately predicting precise video quality scores and video pair preferences. Through comprehensive experiments on both AIGVQA-DB and existing AIGV databases, AIGV-Assessor demonstrates state-of-the-art performance, significantly surpassing existing scoring or evaluation methods in terms of multiple perceptual quality dimensions. The dataset and code are released at https://github.com/IntMeGroup/AIGV-Assessor. + +# 1. Introduction + +Text-to-video generative models [12, 27, 44, 64, 73], including auto-regressive [23, 81] and diffusion-based [12, 27, 55] approaches, have experienced rapid advancements in recent years with the explosion of large multimodal models + +(LMMs). Given appropriate text prompts, these models can generate high-fidelity and semantically-aligned videos, commonly referred to as AI-generated videos (AIGVs), which have significantly facilitated the content creation in various domains, including entertainment, art, design, and advertising, etc [11, 13, 43]. Despite the significant progress, current AIGVs are still far from satisfactory. Unlike natural videos, which are usually affected by low-level distortions, such as noise, blur, low-light, etc, AIGVs generally suffer from degradations such as unrealistic objects, unnatural movements, inconsistent visual elements, and misalignment with text descriptions [25, 31, 43, 65, 79, 84, 85]. + +The unique distortions in AIGVs also bring challenges to the video evaluation. Traditional video quality assessment (VQA) methods [10, 18, 33, 35, 57, 70, 71] mainly focus on evaluating the quality of professionally-generated content (PGC) and user-generated content (UGC), thus struggling to address the specific distortions associated with AIGVs, such as spatial artifacts, temporal inconsistencies, and misalignment between generated content and text prompts. For evaluation of AIGVs, some metrics such as Inception Score (IS) [52] and Fréchet Video Distance (FVD) [61] have been widely used, which are computed over distributions of videos and may not reflect the human preference for an individual video. Moreover, these metrics mainly evaluate the fidelity of videos, while failing to assess the text-video correspondence. Vision-language pre-training models, such as CLIPScore [22], BLIPScore [37], and AestheticScore [53] are frequently employed to evaluate the alignment between generated videos and their text prompts. However, these models mainly consider the text-video alignment at the image level, while ignoring the dynamic diversity and motion consistency of visual elements that are crucial to the vide-viewing experience. + +In this paper, to facilitate the development of more comprehensive and precise metrics for evaluating AI-generated videos, we present AIGVQA-DB, a large-scale VQA dataset, including 36,576 AIGVs generated by 15 advanced text-to-video models using 1,048 diverse prompts. An + +![](images/e2f88f0b1752496702c959cf991c9bb7ab6e815905c8a1788b7757a50de31c59.jpg) +Figure 1. An overview of the AIGVQA-DB construction pipeline, illustrating the generation and the subjective evaluation procedures for the AIGVs in the database. (a) Prompt categorization according to the spatial major content. (b) Prompt categorization according to the temporal descriptions. (c) Prompt categorization according to the attribute control. (d) Prompt categorization according to the prompt complexity. (e) The 15 generative models used in the database. (f) Four visual quality evaluation perspectives, including static quality, temporal smoothness, dynamic degree, and text-video correspondence. (g) and (h) demonstrates the pair comparison and preference scoring processes, respectively. + +overview of the dataset construction pipeline is shown in Figure 1. The prompts are collected from existing open-domain text-video datasets [7, 8, 38, 43, 68, 76] or manually-written, which can be categorized based on four orthogonal aspects respectively, as shown in Figure 1(a)-(d). Based on the AIGVs, we collect 370k expert ratings comprising both mean opinion scores (MOSs) and pairwise comparisons, which are evaluated from four dimensions, including: (1) static quality, (2) temporal smoothness, (3) dynamic degree, and (4) text-video correspondence. Equipped with the dataset, we propose AIGV-Assessor, a large multimodal model-based (LMM-based) VQA method for AIGVs, which reformulates the quality regression task into an interactive question-and-answer (Q&A) framework and leverages the powerful multimodal representation capabilities of LMMs to provide accurate and robust quality assessments. AIGV-Assessor not only classifies videos into different quality levels through natural language output, but also generates precise quality scores through regression, thus enhancing the interpretability and usability of VQA results. Moreover, AIGV-Assessor also excels in pairwise video comparisons, enabling nuanced assessments that are closer to human preferences. Extensive experimental results demonstrate that AIGV-Assessor outperforms existing text-to-video scoring methods in terms of multiple dimensions relevant to human preference. + +The main contributions of this paper are summarized as follows: + +- We construct AIGVQA-DB, a large-scale dataset comprising 36,576 AI-generated videos annotated with MOS scores and pairwise comparisons. Compared with existing benchmarks, AIGVQA-DB provides a more comprehensive assessment of the capabilities of text-to-video models from multiple perspectives. + +Table 1. An overview of popular text-to-video (T2V) and image-to-video (I2V) generation models. ${}^{ \dagger }$ Representative variable. + +
ModelYearModeResolutionFramesOpen
CogVideo [23]22.05T2V480×48032
Make-a-Video [55]22.09T2V256×25616
LVDM [21]22.11T2V256×25616
Tune-A-Video [73]22.12T2V512×5128
VideoFusion [44]23.03T2V128×12816
Text2Video-Zero [27]23.03T2V512×5128
ModelScope [64]23.03T2V256×25616
Lavie [67]23.09T2V512×32016
VideoCrafter [12]23.10T2V, I2V1024×57616
Hotshot-XL [1]23.10T2V672×3848
StableVideoDiffusion [9]23.11I2V576×102414
AnimateDiff [20]23.12T2V, I2V384×25620
Floor33 [2]23.08T2V,I2V1024×64016-
Genmo [3]23.10T2V, I2V2048×153660-
Gen-2 [4]23.12T2V, I2V1408×76896-
MoonValley [5]24.01T2V, I2V1184×672200†-
MorphStudio [6]24.01T2V, I2V1920×108072-
Sora [7]24.02T2V, I2V1920×1080600†-
+ +- Based on AIGVQA-DB, we evaluate and benchmark 15 representative text-to-video models, and reveal their strengths and weaknesses from four crucial preference dimensions, i.e., static quality, temporal smoothness, dynamic degree, and text-to-video correspondence. +- We present a novel LMM-based VQA model for AIGVs, termed AIGV-Assessor, which integrates both spatial and temporal visual features as well as prompt features into a LMM to give quality levels, predict quality scores, and conduct quality comparisons. +- Thorough analysis of our AIGV-Assessor is provided and extensive experiments on our proposed AIGVQA-DB and other AIGV quality assessment datasets have shown the effectiveness and applicability of AIGV-Assessor. + +# 2. Related Work + +# 2.1. Text-to-video Generation + +Recent advancements in text-to-video generative models have substantially broadened video creation and modifica + +Table 2. Summary of existing text-to-image and text-to-video evaluation datasets. + +
Dataset TypesNameNumbersPromptsModelsAnnotatorsDimensionsMOSs / PairsAnnotation
AIGIQAAGIQA-3k [34]2,98218062125,964MOS
AIGCIQA2023 [63]2,40010062837,200MOS
RichHF-18k [39]17,76017,76033471,040MOS
HPS [75]98,80725,20512,659125,205Pairs
AIGVQAPick-a-Pic [29]-37,52334,3751584,247Pairs
MQT [15]1,00520152422,010MOS
EvalCrafter [42]2,5007005741,024MOS
FETV [43]2,4766194337,428MOS
LGVQ [84]2,80846862038,424MOS
T2VQA-DB [31]10,0001,000927110,000MOS
GAIA [13]9,1805101854327,540MOS
AIGVQA-DB (Ours)36,5761,048151204122,304MOS and Pairs
+ +tion possibilities. As shown in Table 1, these models exhibit distinct characteristics and capacities, including modes, resolution, and total frames. CogVideo [23] is an early text-to-video (T2V) model capable of generating short videos based on CogView2 [16]. Make-a-video [55] adds effective spatial-temporal modules on a diffusion-based text-to-image (T2I) model (i.e., DALLE-2 [50]). VideoFusion [44] also leverages the DALLE-2 and presents a decomposed diffusion process. LVDM [21], Text2Video-Zero [27], Tune-A-Video [73], and ModelScope [64] are models that inherit the success of Stable Diffusion (SD) [51] for video generation. Lavie [67] extends the original transformer block in SD to a spatio-temporal transformer. Hotshot-XL [1] introduces personalized video generation. Beyond these laboratory-driven advancements, the video generation landscape has also been enriched by a series of commercial products. Notable among them are Floor33 [2], Gen-2 [4], Genmo [3], MoonValley [5], MorphStudio [6], and Sora [7], which have gained substantial attention in both academia and industry, demonstrating the widespread application potential of AI-assisted video creation. + +# 2.2. Text-to-video Evaluation + +The establishment of the AI-generated image quality assessment (AIGIQA) dataset is relatively well-developed, including both mean opinion scores (MOSs) for absolute quality evaluations, and pairwise comparisons for relative quality judgments. Recent developments in text-to-video generation models have also spurred the creation of various AI-generated video quality assessment (AIGVQA) datasets, addressing different aspects of the T2V generation challenge, as shown in Table 2. MQT [15] consists of 1,005 videos generated by 5 models using 201 prompts. EvalCrafter [42] and FETV [43] extend the scale of the videos, prompts, and evaluation dimensions. LGVQ [84] increases the number of annotators, providing more reliable MOSs. T2VQA-DB [31] consists of 10,000 videos from 1,000 prompts representing a significant improvement in scale. GAIA [13] collects 9,180 videos focusing on action quality assessment in AIGVs, but falls short in addressing the consistency between the generated visuals and their textual prompts. Most existing VQA datasets predominantly rely on MOS, an absolute scoring method, which suffers from the same drawback: absolute scores alone may cause am + +biguity and overlook subtle quality differences. In contrast, our AIGVQA-DB includes both MOSs and pairwise comparisons, addressing the limitations of current works by providing fine-grained preference feedbacks. + +# 3. Database Construction and Analysis + +# 3.1. Data Collection + +Prompt Scources and Categorization. Prompts of the AIGVQA-DB are primarily sourced from existing open-domain text-video pair datasets, including InternVid [68], MSRVTT [76], WebVid [8], TGIF [38], FETV [43] and Sora website [7]. We also manually craft prompts describing highly unusual scenarios to test the generalization ability of the generation models. As shown in Figure 1(a)-(d), we follow the categorization principles from FETV [43] to organize each prompt based on the "spatial major content", "temporal major content", "attribute control", and "prompt complexity". + +Text-to-Video Generation. We utilize 15 latest text-to-video generative models to create AI-generated videos as shown in Figure 1(e). We leverage open-source website APIs and code with default weights for these models to produce AIGVs. For the construction of the MOS subset, we collect 48 videos from the Sora Website [7], along with their corresponding text prompts. Using these prompts, we generate additional videos using 11 different generative models. This process results in a total of 576 videos (12 generative models $\times$ 48 prompts). In addition to the MOS subset, we construct the pair-comparison subset using 1,000 diverse prompts, and 12 generative models including 8 open-sourced and 4 close-sourced are employed for text-to-video generation. Specifically, for each prompt, we generate four distinct videos for each open-source generative model and one video for each closed-source generative model. This process yields a total of 36,000 videos. More details of the database can be found in the supplementary material. + +# 3.2. Subjective Experiment Setup and Procedure + +Due to the unique and unnatural characteristics of AI-generated videos and the varying target video spaces dictated by different text prompts, relying solely on a single score, such as "quality", to represent human visual preferences is insufficient. In this paper, we propose to measure + +![](images/fb0385b3e755dd0ce7af1b2bf2c5ae793450e483574d3b22a009ca8c5c39ce30.jpg) +(a) Distribution of Raw Scores + +![](images/8eac122b8407f48e45e263fdddc23287419766654acec0728f07feffd5b4ba0f.jpg) +(b) Distribution of Mean Opinion Scores (MOSs) + +![](images/36c72da19ded12678e8963e4090622f43eaf08a13abe22c112d4b9d85ec226dc.jpg) +Figure 2. Video score distribution from the four perspectives including static quality, temporal smoothness, dynamic degree, and t2v correspondence. (a) Distribution of raw scores. (b) Distribution of Mean Opinion Scores (MOSs) +(a) +(b) +(c) + +![](images/1f6e6965f46d7954d0df029d696dd198d84ae054cd372b5706fa71d41fde0ab3.jpg) +Figure 3. Comparison of averaged win rates of different generation models across different categories. (a) Results across prompt complexity. (b) Results across attribute control. (c) Results across temporal major contents. (d) Results across spatial major contents. +Figure 4. (a) Comparison of text-to-video generation models regarding the MOS in terms of four dimensions sorted bottom-up by their averaged MOS. (b) Comparison of text-to-video generation models regarding the win rate in terms of four dimensions sorted bottom-up by their averaged win rate. + +the human visual preferences of AIGVs from four perspectives. Static quality assesses the clarity, sharpness, color accuracy, and overall aesthetic appeal of the frames when viewed as standalone images. Temporal smoothness evaluates the temporal coherence of video frames and the absence of temporal artifacts such as flickering or jittering. Dynamic degree evaluates the extent to which the video incorporates large motions and dynamic scenes, which contributes to the overall liveliness and engagement measurement of the content. Text-video (TV) correspondence assesses how accurately the video content reflects the details, themes, and actions described in the prompt, ensuring that the generated video effectively translates the text input into + +a visual narrative. Each of these four visual perception perspectives is related but distinct, offering a comprehensive evaluation for AIGVs. To evaluate the quality of the videos in the AIGVQA-DB, we conduct subjective experiments adhering to the guidelines outlined in ITU-R BT.500-14 [17, 54]. For the MOS annotation type, we use a 1-5 Likert-scale judgment to score the videos. For the pairs annotation type, participants are presented with pairs of videos and asked to choose the one they prefer, providing a direct comparison method for evaluating relative video quality. The videos are displayed using an interface designed with Python Tkinter, as illustrated in Figure 1(g)-(h). A total of 120 graduate students participate in the experiment. + +# 3.3. Subjective Data Processing + +In order to obtain the MOS for an AIGV, we linearly scale the raw ratings to the range [0, 100] as follows: + +$$ +z _ {i j} = \frac {r _ {i j} - \mu_ {i j}}{\sigma_ {i}}, \quad z _ {i j} ^ {\prime} = \frac {1 0 0 (z _ {i j} + 3)}{6}, +$$ + +$$ +\mu_ {i} = \frac {1}{N _ {i}} \sum_ {j = 1} ^ {N _ {i}} r _ {i j}, \sigma_ {i} = \sqrt {\frac {1}{N _ {i} - 1} \sum_ {j = 1} ^ {N _ {i}} (r _ {i j} - \mu_ {i j}) ^ {2}} +$$ + +where $r_{ij}$ is the raw ratings given by the $i$ -th subject to the $j$ -th video. $N_i$ is the number of videos judged by subject $i$ . Next, the MOS of the video $j$ is computed by averaging the rescaled z-scores as follows: + +$$ +M O S _ {j} = \frac {1}{M} \sum_ {i = 1} ^ {M} z _ {i j} ^ {\prime} +$$ + +![](images/6e2271fc92b4aadac9147836c9305b52893182b0a5fb8fd4763fd447322a3f64.jpg) +Figure 5. The framework of AIGV-Assessor: (a) AIGV-Assessor takes AI-generated video frames as input and outputs both text-based quality levels and numerical quality scores. The system begins with the extraction of spatiotemporal features using two vision encoders, which are then passed through spatial and temporal projection modules to generate aligned visual tokens into language space. The LLM decoder produces text-based feedback describing the video quality level for four evaluation dimensions, respectively. Simultaneously, the last-hidden-states from the LLM are used to perform quality regression that outputs final quality scores in terms of four dimensions. (b) AIGV-Assessor is fine-tuned on pairwise comparison, further allowing the model to output the evaluation comparison between two videos. + +where $MOS_{j}$ indicates the MOS for the $j$ -th AIGV, $M$ is the number of subjects, and $z_{ij}^{\prime}$ are the rescaled z-scores. + +For the pairs annotation type, given a text prompt $p_i$ and 12 video generation models labeled $\{A,B,C,\dots,L\}$ , we generate videos using each model, forming a group of videos $G_{i,j} = \{V_{i,A,j},V_{i,B,j},V_{i,C,j},\dots,V_{i,L,j}\}$ . For each prompt $p_i$ , we generate four different videos randomly for each of the eight open-source generative models and one video for each of the four closed-source generative models, resulting in a group of 36 videos $\{G_{i,A,1},G_{i,A,2},G_{i,A,3},G_{i,A,4},G_{i,B,1},\dots,G_{i,L,1}\}$ . For each group, we create all possible pairwise combinations, resulting in $C_{36}^2$ pairs: $(V_{A1},V_{B1})$ , $(V_{A1},V_{B2})$ , $(V_{A1},V_{B3})$ , $(V_{A1},V_{B4})$ , $(V_{A1},V_{C1})$ , ..., $(V_{K1},V_{L1})$ . In the AIGVQA-DB construction pipeline, a prompt suite of 1000 prompts results in 630,000 $(1000\times C_{36}^2)$ pairwise video comparisons. From this extensive dataset, we randomly sample 30,000 pairs for evaluation from four perspectives. Each pair is judged by three annotators, and the final decision of the better video in each pair is determined by the majority vote. Finally, we obtain a total of 46,080 reliable score ratings (20 annotators × 4 perspectives × 576 videos) and 360,000 pair ratings (3 annotators × 4 perspectives × 30,000 pairs). + +# 3.4. AIGV Analysis from Four Perspectives + +As shown in Figure 2, the videos in the AIGVQA-DB cover a wide range of perceptual quality. We further analyze the win rates of various generation models across categories in Figure 3, revealing the strengths and weaknesses of each T2V model. As shown in Figure 3(a), the performances of T2V models rank uniform for different prompt complexity items in terms of static quality, which manifests current T2V model rank consistently for different prompts, likely + +due to shared architectures like diffusion-based systems, with common strengths and limitations in handling complex prompts. As shown in Figure 3(b), in terms of attribute control, StableVideoDiffusion [9] excels in managing quantity over event order, as it first generates static images before animating them, preserving the original event sequence. As shown in Figure 3(d), in terms of spatial content, most videos featuring "plants" and "people" show poor T2V correspondence. More comparison and analysis can be found in the supplementary material. We also launch comparisons among text-to-video generation models regarding the MOS and pairwise win rates shown in Figure 4. Notably, models such as LVDM [21] demonstrate exceptional performance in handling dynamic content, but exhibit relatively lower performance in temporal smoothness. Sora [7] and MorphStudio [6] perform well in static quality and temporal smoothness while lagging in dynamic degree. Additionally, closed-source models exhibit much better performance compared to open-source models. + +# 4. Proposed Method + +# 4.1. Model Structure + +Spatial and Temporal Vision Encoder. As shown in Figure 5(a), the model leverages two different types of encoders to capture the spatial and temporal characteristics of the video: (1) 2D Encoder: A pre-trained 2D vision transformer (InternViT [69]) is used to process individual video frames. (2) 3D Encoder: A 3D network, i.e., SlowFast [19], is employed to extract temporal features by processing sequences of video frames. + +Spatiotemporal Projection Module. Once the spatial and temporal features are extracted, they are projected into a + +Table 3. Performance comparisons of the state-of-the-art quality evaluation methods on the AIGVQA-DB from four perspectives. The best performance results are marked in RED and the second-best performance results are marked in BLUE. + +
DimensionStatic QualityTemporal SmoothnessDynamic DegreeTV Correspondence
Methods / MetricsPair AccSRCCPLCCKRCCPair AccSRCCPLCCKRCCPair AccSRCCPLCCKRCCPair AccSRCCPLCCKRCC
NIQE [49]54.32%0.08670.16260.061552.67%0.06410.11520.045145.64%0.17650.24480.119446.99%0.17710.22310.1193
QAC [80]49.96%0.10220.13630.068054.90%0.16330.20390.110554.72%0.04480.04270.029554.48%0.03030.01970.2233
BRISQUE [48]59.98%0.29090.24430.196955.67%0.23250.15690.155344.60%0.13510.09590.089351.02%0.12940.10170.0869
BPRI [46]52.28%0.21810.17230.139847.26%0.17660.08800.113846.83%0.19560.16880.132949.13%0.15690.15480.1052
HOSA [77]61.54%0.24200.21060.164357.31%0.23110.17570.155944.97%0.07550.04490.049652.23%0.16450.13240.1097
BMPRI [47]53.71%0.16900.14810.107549.31%0.14340.08440.089445.07%0.11530.09250.077748.43%0.15670.15000.1041
V-Dynamic [25]51.34%0.07680.07920.049431.91%0.37130.48710.255753.11%0.14660.02530.098846.96%0.04050.05760.0223
V-Smoothness [25]61.63%0.67480.45060.459076.59%0.85260.83130.653347.63%0.24460.23280.158061.28%0.31880.30730.2214
CLIPScore [22]47.09%0.07310.08160.047346.33%0.04230.03340.027152.99%0.06750.08350.043955.62%0.15190.17310.1014
BLIPScore [37]53.24%0.04920.04210.033053.07%0.06590.04870.043753.03%0.17860.19040.120561.53%0.18130.18960.1219
AestheticScore [53]70.24%0.67130.69590.478454.82%0.51540.49460.348452.96%0.22950.23220.152759.64%0.23810.24400.1602
ImageReward [78]56.69%0.26060.26460.174954.09%0.23820.23050.160053.90%0.18400.18360.123763.97%0.23110.24500.1568
UMTScore [43]48.93%0.01680.01990.011749.93%0.03020.03700.020752.69%0.01680.01980.011753.82%0.01720.00650.0108
Video-LLaVA [40]50.90%0.03840.05130.029750.36%0.04310.02810.034750.34%0.15610.14360.117650.54%0.13640.10510.1009
Video-ChatGPT [45]51.20%0.12420.15870.094050.16%0.05800.05330.045350.47%0.07240.04360.056350.07%0.03570.01240.0274
LLaVA-NeXT [36]52.85%0.12390.16250.095452.41%0.40210.37220.305251.84%0.17670.16550.132859.20%0.41160.34280.3261
VideoLLaMA2 [14]52.73%0.26430.32710.192852.27%0.36080.24500.269650.78%0.19000.15610.137954.25%0.16560.16330.1210
Qwen2-VL [66]56.50%0.49220.52910.383849.12%0.16810.42190.123352.08%0.11220.13350.084953.30%0.31110.27750.2306
HyperIQA [56]68.30%0.79310.80930.596954.65%0.74260.66300.540753.32%0.21030.21000.138457.54%0.62260.62500.4432
MUSIQ [26]66.46%0.78800.80440.577355.16%0.71990.69200.503452.85%0.52060.48460.352158.46%0.41250.40930.2844
LIQE [83]63.86%0.87760.86910.700855.84%0.79350.77200.608449.02%0.53030.58400.383755.10%0.38620.36390.2640
VSFA [35]46.43%0.33650.34210.226850.95%0.33170.32730.220251.46%0.12010.13620.081548.07%0.10240.10640.0666
BVQA [33]29.98%0.45940.47010.326837.65%0.37040.38190.250755.08%0.45940.47010.326842.32%0.37200.39780.2559
simpleVQA [57]68.12%0.83550.64380.848954.14%0.70820.70080.497853.08%0.46710.31600.399458.20%0.46430.54400.3163
FAST-VQA [70]70.64%0.87380.86440.686062.93%0.90360.91340.716654.34%0.56030.57030.389565.05%0.68750.67040.4978
DOVER [71]72.92%0.89070.88950.700458.83%0.90630.91950.718753.16%0.55490.54890.380062.35%0.67830.68020.4969
Q-Align [72]71.86%0.85160.83830.664157.95%0.81160.70250.619553.71%0.56550.50120.395062.91%0.55420.56470.3870
AIGV-Assessor (Ours)79.83%0.91620.91900.757676.60%0.92320.92160.803860.30%0.60930.60820.443570.32%0.75000.76970.5591
Improvement+ 6.9%+2.7%+3.0%+ 5.7%13.7%+1.7%+0.2%+8.5%+5.2%+4.4%+3.8%+4.4%+5.3%+6.3%+9.9%+6.13%
+ +shared feature space for alignment with text-based queries. This is done through two projection modules that map the spatial and temporal visual features respectively into the language space. The mapped visual tokens are aligned with text tokens, enabling the model to query the video content in a multimodal fashion. + +Feature Fusion and Quality Regression. We apply LLM (InternVL2-8B [69]) to combine the visual tokens and user-provided quality prompts to perform the following tasks: (1) Quality level descriptions: the model generates a descriptive quality level evaluation of the input video, such as "The static quality of the video is (bad, poor, fair, good, excellent)." This initial categorization provides a preliminary classification of the video's quality, which is beneficial for subsequent quality regression tasks. By obtaining a rough quality level, the model can more accurately predict numerical scores in later evaluations. (2) Regression score output: the model uses the final hidden states from the LLM to perform a regression task, outputting numerical quality scores for the video from four different dimensions. + +# 4.2. Training and Fine-tuning Strategy + +The training process of AIGV-Assessor follows a three-stage approach to ensure high-quality video assessment with quality level prediction, individual quality scoring, and pairwise preference comparison capabilities. This process includes: (1) training the spatial and temporal projectors to align visual and language features, (2) fine-tuning the vision + +encoder and LLM with LoRA [24], and training the quality regression module to generate accurate quality scores, (3) incorporating pairwise comparison training using the pair-comparison subset with a pairwise loss function for robust video quality comparison. + +Spatiotemporal Projector Training. The first stage focuses on training the spatial and temporal projectors to extract meaningful spatiotemporal visual features and map them into the language space. Through this process, the LLM is able to produce the quality level descriptions i.e., bad, poor, fair, good, excellent. + +Quality Regression Fine-tuning. Once the model can generate coherent descriptions of video quality level, the second stage focuses on fine-tuning the quality regression module. The goal here is to enable the model to output stable and precise numerical quality scores (MOS-like predictions). The quality regression model takes the last-hidden-state features from LLM as input and generates quality scores from four perspectives. The training objective uses an L1 loss function to minimize the difference between the predicted quality score and the groundtruth MOS. + +Pairwise Comparison Fine-tuning. The third stage mainly focuses on integrating the pairwise comparison into the training pipeline. As shown in Figure 5(b), two input video pairs share network weights within the same batch. We design a judge network inspired by LPIPS [82] to determine which video performs better. This network leverages + +Table 4. Performance comparisons on LGVQ [84] and FETV [43]. + +
AspectsMethodsLGVQFETV
SRCCPLCCKRCCSRCCPLCCKRCC
SpatialMUSIQ [26]0.6690.6820.4910.7220.7580.613
StairlQA [59]0.7010.7370.5210.8060.8120.643
CLIP-IQA [62]0.6840.7090.5020.7410.7670.619
LIQE [83]0.7210.7520.5380.7650.7990.635
UGVQ [84]0.7590.7950.5670.8410.8410.685
TemporalAIGV-Assessor (Ours)0.8030.8190.6170.8530.8560.699
Improvement+4.4%+2.4%+5.0%+1.2%+1.5%+1.4%
VSFA [35]0.8410.8570.6430.8390.8590.705
SimpleVQA [57]0.8570.8670.6590.8520.8620.726
FastVQA [70]0.8490.8430.6470.8420.8470.714
DOVER [71]0.8670.8780.6720.8680.8810.731
UGVQ [84]0.8930.9070.7030.8970.9070.753
AlignmentAIGV-Assessor (Ours)0.9000.9200.7170.9360.9400.815
Improvement+0.7%+1.3%+1.4%+3.9%+3.3%+6.2%
CLIPScore [22]0.4460.4530.3010.6070.6330.498
BLIPScore [37]0.4550.4640.3190.6160.6450.505
ImageReward [78]0.4980.4990.3440.6570.6870.519
PickScore [28]0.5010.5150.3530.6690.7080.533
HPSv2 [74]0.5040.5110.3570.6860.7030.540
UGVQ [84]0.5510.5550.3940.7340.7370.572
AlignmentAIGV-Assessor (Ours)0.5770.5780.4110.7530.7460.585
Improvement+2.6%+2.3%+1.7%+1.9%+0.9%+1.3%
+ +learned features and evaluates the perceptual differences between the two videos, allowing more reliable quality assessments in video pair comparison. + +Loss Function. In the first stage, the spatial and temporal projectors are trained to align visual and language features using language loss. The second stage refines the vision encoder, LLM, and quality regression module's scoring ability with an L1 loss. The third stage incorporates pairwise comparison training with cross-entropy loss to improve the model's performance on relative quality evaluation. + +# 5. Experiments + +# 5.1. Experiment Settings + +Evaluation Datasets and Metrics. Our proposed method is validated on five AIGVQA datasets: AIGVQA-DB, LGVQ [84], FETV [43], T2VQA [31], and GAIA [13]. To evaluate the correlation between the predicted scores and the ground-truth MOSs, we utilize three evaluation criteria: Spearman Rank Correlation Coefficient (SRCC), Pearson Linear Correlation Coefficient (PLCC), and Kendall's Rank Correlation Coefficient (KRCC). For pair comparison, we adopt the comparison accuracy as the metric. + +Reference Algorithms. To assess the performance of our proposed method, we select state-of-the-art evaluation metrics for comparison, which can be classified into five groups: (1) Handcrafted-based I/VQA models, including: NIQE [49], BRISQUE [48], QAC [80], BMPRI [47], HOSA [77], BPRI [46], HIGRADE [32], etc. (2) Action-related evaluation models, including: V-Dynamic [25], V-Smoothness [25] which are proposed in VBench [25]. (3) Vision-language pre-training models, including: CLIPScore [22], BLIPScore [37], AestheticScore [53], ImageReward [78], and UMTScore [43]. (4) LLM-based models, in- + +Table 5. Performance comparisons on T2VQA-DB [31]. + +
AspectsMethodsT2VQA-DBSora Testing
SRCCPLCCKRCCSRCCPLCCKRCC
zero-shotCLIPScore [22]0.10470.12770.07020.21160.15380.1406
BLIPScore [37]0.16590.18600.11120.21160.10380.1515
ImageReward [78]0.18750.21210.12660.09920.04150.0748
UMTScore [43]0.06760.07210.04530.25940.08400.1680
finetunedSimpleVQA [57]0.62750.63880.44660.03400.23440.0237
BVQA [37]0.73900.74860.54870.42350.24890.2635
FAST-VQA [70]0.71730.72950.53030.43010.23690.2939
DOVER [71]0.76090.76930.57040.44210.26890.2757
T2VQA [31]0.79650.80660.60580.64850.31240.4874
AIGV-Assessor (Ours)0.81310.82220.63640.66120.33180.5075
Improvement+1.7%+1.6%+3.1%+1.3%+1.9%+2.0%
+ +Table 6. Performance comparisons on GAIA [13]. + +
DimensionSubjectCompletenessInteraction
Methods / MetricsSRCCPLCCSRCCPLCCSRCCPLCC
V-Smoothness [25]0.24020.19130.14740.16250.17410.1693
V-Dynamic [25]0.12850.08310.09030.06820.11410.0758
Action-Score [42]0.20230.18230.28670.26230.26890.2432
Flow-Score [42]0.14710.15410.08160.12730.10410.1309
CLIPScore [22]0.33980.33300.39440.38710.38750.3821
BLIPScore [37]0.34530.33860.41740.40820.40440.3994
LLaVAScore [41]0.34840.34360.41890.41330.40770.4025
TLVQM [30]0.50370.51370.41270.41580.40790.4093
VIDEVAL [60]0.52370.54460.42830.43750.41210.4234
VSFA [35]0.55940.57620.49400.50170.47090.4811
BVQA [37]0.57020.58880.48760.49460.47610.4825
SimpleVQA [58]0.59200.59740.49810.50780.48430.4971
FAST-VQA [70]0.60150.60920.51570.52150.51540.5216
DOVER [71]0.61730.63010.51980.53230.51640.5278
AIGV-Assessor (Ours)0.68420.68970.66350.66940.63290.6340
Improvement+6.7%+6.0%+14.4%+13.7%+11.65%+10.6%
+ +cluding: Video-LLaVA [40], Video-ChatGPT [45], LLaVA-NeXT [36], VideoLLaMA2 [14], and Qwen2-VL [66]. (5) Deep learning-based I/VQA models, including: HyperIQA [56], MUSIQ [26], LIQE [83], VSFA [35], BVQA [33], SimpleVQA [58], FAST-VQA [70], DOVER [71], and Q-Align [72]. + +Training Settings. Traditional handcrafted models are directly evaluated on the corresponding databases, and the average score of all frames is calculated. For vision-language pre-training and LLM-based models, we load the pre-trained weights for inference. CLIPscore [22], BLIP-score [37], and other vision-language pre-training models are calculated directly as the average cosine similarity between text and each video frame. SimpleVQA [58], BVQA [33], FAST-VQA [70], DOVER [71], and Q-Align [72] are fine-tuned on every test dataset. For deep learning-based IQA and VQA models, all experiments for each method are retrained on each dimension using the same training and testing split as the previous literature at a ratio of 4:1. All results are averaged after ten random splits. + +# 5.2. Results and Analysis + +Table 3 presents the pairwise win rates and the score prediction correlation between predicted results and human ground truths. The results indicate that handcrafted-based methods consistently underperform across all four evalu- + +![](images/3a323b11ba3b97928a16f87d4016f9fd2550b9e4d10c010126e4ee85c42f694d.jpg) +Figure 6. Comparison of win rates of different generation models across four dimensions evaluated by different VQA methods, demonstrating our AIGV-Assessor has better win-rate evaluation ability aligned with Ground Truth (GT). + +Table 7. Ablation study of the proposed AIGV-Assessor method. + +
No.Feature & StrategyStatic QualityTemporal SmoothnessDynamic DegreeT2V Correspondence
spatialtemporalquality levelLoRA finetuningSRCCPLCCKRCCSRCCPLCCKRCCSRCCPLCCKRCCSRCCPLCCKRCC
(1)0.8640.8660.7260.8700.8680.7270.5560.5720.4320.6160.6200.492
(2)0.8740.8760.7230.8750.8760.7360.5580.5730.4310.7230.7340.533
(3)0.8870.8840.7220.8810.8830.7060.5620.5750.4330.7390.7580.544
(4)0.8870.8880.7530.9170.9100.7960.5690.5360.4380.6880.6730.557
(5)0.9050.9080.7540.9190.9170.7990.5890.5870.4410.7420.7630.549
(6)0.9160.9190.7580.9230.9220.8040.6090.6080.4440.7500.7700.559
+ +ation perspectives. Vision-language pre-training methods such as CLIPscore [22] and BLIPscore [37] demonstrate moderate performance but are still surpassed by more specialized and fine-tuned VQA models. Specifically, deep learning-based models like FAST-VQA [70] and DOVER [71] achieve more competitive performances after fin-tuning. However, they are still far away from satisfactory. Notably, most VQA models perform better on quality evaluation than on text-video correspondence, as they lack text prompts input used in video generation, making it challenging to extract relation features from the AI-generated videos, which inevitably leads to the performance drop. Finally, the performance exploration of recent LMMs on our database shows that current LMMs are able to produce meaningful evaluations, which can motivate future works to further explore the use of LMMs for AIGV assessment. + +The proposed AIGV-Assessor achieves the best performance compared to the competitors for both MOS prediction and pair ranking tasks in terms of all four dimensions. To further validate the effectiveness and generalizability of our proposed model, we also evaluate it on four other AIGVQA datasets [13, 31, 43, 84]. From Tables 4-6, we observe that AIGV-Assessor consistently achieves the best performance across these datasets. As shown in Figure 6, AIGV-Assessor achieves the highest overlap in area with Ground Truth (GT), indicating that AIGV-Assessor can reliably perform T2V model benchmarking, outperforming other assessment models in discerning quality differences in AI-generated videos. + +# 5.3. Ablation Study + +We conduct ablation experiments to verify the effectiveness of the main components in our AIGV-Assessor method, including the spatial feature, the temporal feature, the quality level, and the LoRA finetuning strategy. Additionally, we assess how each feature contributes to the performance + +across different quality dimensions. The results of these experiments are summarized in Table 7. Experiments (1), (2), and (3) validate the effectiveness of the quality regression module and the LoRA finetuning strategy, confirming that fine-tuning and quality regression significantly enhance model performance over only regressing the generated text outputs from the LLM. The addition of temporal features, as seen in Experiments (4), (5), and (6), significantly improves model performance. Experiment (6), which integrates all components, yields the best overall performance, showing that the combination of spatial and temporal features, quality level prediction, and LoRA finetuning provides the most robust and accurate AIGV assessment. + +# 6. Conclusion + +In this paper, we study the human visual preference evaluation problem for AIGVs. We first construct AIGVQA-DB, which includes 36,576 videos generated based on 1048 various text-prompts, with the MOSs and pair comparisons evaluated from four perspectives. Our detailed manual evaluations reflect different aspects of human visual preferences on AIGVs and reveal critical insights into the strengths and weaknesses of various text-to-video models. Based on the database, we evaluate the performance of state-of-the-art quality evaluation models and establish a new benchmark, revealing their limitations in measuring the perceptual preference of AIGVs. Finally, we propose AIGV-Assessor, a novel VQA model that leverages the capabilities of LMMs to give quality levels, predict quality scores, and compare preferences from four dimensions. Extensive experiments demonstrate that AIGV-Assessor achieves state-of-the-art performance on both AIGVQA-DB and other AIGVQA benchmarks, validating its robustness in understanding and evaluating the AI-generated videos. + +# References + +[1] Hotshot-XL. https://github.com/hotshotco/hotshot-xl, 2023.2, 3 +[2] Floor33. https://discord.qq/EuB9KT6H, 2023.2, 3 +[3] Gemo. https://www.genmo.ai, 2024.2, 3 +[4] Gen2. https://research.runwayml.com/gen2, 2024.2,3 +[5] Moonvalley. https://moonvalley.ai, 2024. 2, 3 +[6] Morph studio. https://www.morphstudio.com, 2024.2,3,5 +[7] Sora. https://openai.com/research/video-generation-models-as-world-simulators, 2024.2,3,5 +[8] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. 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However, existing methods often face limitations in the diversity and quality of synthetic data, leading to compromised fairness and overall model accuracy. Moreover, many approaches rely on the availability of demographic group labels, which are often costly to annotate. This paper proposes AIM-Fair, aiming to overcome these limitations and harness the potential of cutting-edge generative models in promoting algorithmic fairness. We investigate a fine-tuning paradigm starting from a biased model initially trained on real-world data without demographic annotations. This model is then fine-tuned using unbiased synthetic data generated by a state-of-the-art diffusion model to improve its fairness. Two key challenges are identified in this fine-tuning paradigm, 1) the low quality of synthetic data, which can still happen even with advanced generative models, and 2) the domain and bias gap between real and synthetic data. To address the limitation of synthetic data quality, we propose Contextual Synthetic Data Generation (CSDG) to generate data using a text-to-image diffusion model (T2I) with prompts generated by a context-aware LLM, ensuring both data diversity and control of bias in synthetic data. To resolve domain and bias shifts, we introduce a novel selective fine-tuning scheme in which only model parameters more sensitive to bias and less sensitive to domain shift are updated. Experiments on CelebA and UTKFace datasets show that our AIM-Fair improves model fairness while maintaining utility, outperforming both fully and partially fine-tuned approaches to model fairness. The code is available at https://github.com/zengqunzhao/AIM-Fair. + +# 1. Introduction + +Recent research has raised significant concerns about fairness and bias in machine learning models [30]. These mod- + +![](images/f8d0530fa245105e65d5f0c4b739b0f8b3dea27cba27db507c87aa7fbc563021.jpg) +Figure 1. Facial attributes classification (FAC) on the CelebA dataset based on different training strategies, in which Smiling is the target attribute and Gender is the protected attribute. This shows different learning strategies result in variable model utility (Overall Accuracy) vs. model fairness (Worst Group Accuracy and Equalized Odds) on demographic groups. A model trained solely on real data if biased exhibits high accuracy but poor fairness scores. Conversely, models trained on balanced synthetic data show better fairness but poorer accuracy due to a "domain gap" between the real and synthetic data, and a lack of selective model fine-tuning when synthetic data is deployed. Strategies to repair imbalances in real data [9, 56] or to supplement real data with synthetic data [47] marginally increase accuracy but do little to improve fairness. Our method for selective fine-tuning of a pre-trained (biased) model with synthetic data not only preserves model accuracy but also substantially improves fairness, outperforming fully fine-tuning (FFT) in both model utility and fairness. + +els often demonstrate varying performance across different demographic groups, leading to unfair outcomes. To mitigate the spurious correlation caused by learning from imbalanced (biased) data, regularizations were used as optimization objectives [1, 10, 12, 23]. Methods like distributionally robust optimization (DRO) [12] optimizes the worst-case performance, while invariant risk minimization (IRM) [1] learns unbiased representations with invariance to different environments. Influenced by the success of repre + +![](images/968ef6fce9fb3dfd9ee650e2f55496e5ce680ace7aa301e85fbf4cca5b71cf7c.jpg) +Figure 2. The effects of selective fine-tuning by layer-wise freezing from facial attribute classifications on the CelebA dataset, with Smiling as the target attribute and Male as the protected attribute: When only the fully connected (FC) layer is frozen the model shows improved worst demographic group accuracy and reduced equalized odds, i.e. more fair, but sacrifices some utility (overall accuracy). This indicates increased cross-domain generalisability (real and synthetic). Conversely, freezing only block 2 while fine-tuning the remaining parameters results in high overall accuracy but poorer fairness, i.e. further enhanced domain-bias specificity. When only block 1 is frozen, the model not only maintained equalized odds but also increased utility (overall accuracy) and worst group accuracies. + +![](images/0ee6f775f8d3b9eaeae3aaa12f11590e01bdf33b2ec7a9f98e8e538dd8a10a16.jpg) + +![](images/3365cae16dacab792e323a67948865d1373f9eaaeba542387d0e645ff9fca91d.jpg) + +sentation learning [51], attempts were made to learn a fair feature representation invariant to protected facial attributes [6, 29, 34, 54]. However, these methods rely on demographic group labelling, often unavailable in practice [2, 4]. More recent advances in generative models have utilized generative augmentation for a more balanced training data distribution [8, 9, 17, 36, 40, 59]. These techniques primarily focus on image editing, either on real data [36, 40] or synthetic data [9], to create less biased training data. Yet, these methods still require additional group annotations of the data they edit. To address this limitation, DiGA [59] proposed to create an unbiased training set by editing spurious facial attributes to a random degree while keeping a target facial attribute unchanged without knowing each sample's group label. However, DiGA increases training data size multiple times, leading to substantially higher training costs, and the quality of generated data is limited due to the unknown group labels. + +Recent advancements in text-to-image generative models showcase impressive data fidelity [43], yet their potential for improving fairness through data expansion has not been fully explored by the fairness community. This raises the question: can AI-generated synthetic data play a crucial role in mitigating biases within machine learning models? This research question is particularly important given the successful application of AI-generated data in fine-tuning large language models (LLMs) [11], data augmentation [64], and long-tail recognition [47], alongside some reported limitations of synthetic data effectiveness [49]. This work presents a comprehensive empirical investigation into whether fine-tuning high-quality, balanced generative data from a contemporary text-to-image model can counteract model biases caused by training on imbalanced real data. We identify two key challenges in bias-correcting fine-tuning with synthetic data: (1) A data-related challenge arising from linguistic ambiguity of the textual prompt and/or model misrepresentation [48, 57], which results in low-quality and low-diversity generated data. (2) A model learning challenge caused by both a domain shift (synthetic vs. real) and a bias shift (unbiased vs. biased) between + +the real and the synthetic data. Fine-tuning blindly on the synthetic will result in a model with decreased utility. + +To address the data quality issue, we propose Contextual Synthetic Data Generation (CSDG). Existing Latent Diffusion Models (LDMs) [3, 36, 41, 45] often use vision-language models, such as CLIP, for cross-modality alignment. To yield more diverse and better fine-grained image generation, we formulate a contextual synthetic data generation strategy that uses more detailed text descriptions from expansive linguistic expressions of LLMs to condition an LDM with richer, context-driven text. As a result, the generated images cover more scenarios and provide more details, enhancing diversity and mitigating bias in real data. In contrast to other methods that edit or manipulate real data samples, a key strength of our method is that it does not require annotating the Protected Group Attributes of real data. + +The model learning challenge is due to the existence of two types of shifts between the generated and the real data, namely, the desired bias shift and the undesired domain shift (image quality, realism, scene characteristics). To address this challenge we propose to locate and update model parameters that are more sensitive to the bias shift and less sensitive to the domain shift. Our observation is that some parameters are more sensitive to data distribution shift (cross-domain generalisability) - we call domain-sensitive parameters, while others are more sensitive to demographic group discrepancies (real data domain bias specificity), which we call fairness-sensitive parameters. This observation is supported by the experiments shown in Fig. 2. This is from fine-tuning a real data pre-trained model on balanced synthetic data while keeping parameters at different layers frozen. To identify which parameters to update, we propose a novel selection scheme in which the gradient differences between the updates by the real (biased) dataset and two synthetic datasets with one unbiased and another biased. Ranking the gradient differences between the synthetic-biased data and the synthetic-unbiased data reveals parameters sensitive to fairness (fairness-sensitive parameters). In contrast, inverse ranking the gradient differences between the real data and the synthetic-biased data + +![](images/8860308feb1162fc43c47e04d965954e07a35434eeed64d6650d343d90084e9c.jpg) +Figure 3. A selective fine-tuning model consisting of three parts: (1) Contextual Synthetic Data Generation (CSDG) for generating diverse images using GPT-4 generated prompts, (2) Selective Mask Generation (SMG) for creating a selection mask that determines which parameters are updated during fine-tuning, and (3) Selective Fine-Tuning (SFT) to enhance model fairness obtained from synthetic data whilst simultaneously to preserve model utility yielded from real data in pre-training. + +discovers parameters less sensitive to domain shift (domain-insensitive parameters). In fine-tuning, a selection mask is constructed as the intersection of the top-k rankings. This selection mask is applied to initialize the pre-trained model, so that only the selected parameters are updated using the balanced synthetic data. + +Fig. 1 presents a comparison of the results across various training strategies using real and/or synthetic data. Fig 3 shows an overview of our model, which consists of three parts: Contextual Synthetic Data Generation (CSDG), Selective Mask Generation (SMG), and Selective Fine-Tuning (SFT). CSDG uses a pre-trained and fixed LDM to generate high-quality images, where a series of contextual prompts serve as the conditions. SMG creates a selection mask that determines which parameters are updated during finetuning. SFT is designed to correct bias in the model. We initialize a pre-trained model using the parameter selection mask. Then the model is fine-tuned on balanced synthetic data to enhance its fairness while retaining the model utility. Our contributions are as follows: + +- We investigate a fine-tuning paradigm that mitigates model bias stemming from unbalanced real data using synthetic data generated by a text-to-image (T2I) process without requiring demographic group annotations. +- We design contextual synthetic data generating by using a T2I diffusion mode with prompts generated by a context-aware LLM, ensuring both data diversity and control of bias in synthetic data. +- We introduce a selective fine-tuning method for fair model learning, which identifies domain-sensitive and fairness-sensitive parameters for improving model fairness and utility simultaneously. +- Our method outperforms both full and partial fine-tuning methods and achieves superior performance compared to state-of-the-art methods across several datasets. + +# 2. Related Work + +Mitigating Model Bias. Current methods for model fairness can be categorized into three types: pre-processing, in-processing, and post-processing. Pre-processing approaches modify sample distributions of protected variables or perform transformations to remove discrimination from the data. Many recent works use generative models to create balanced, unbiased datasets [36, 40, 58]. In-processing methods incorporate fairness metrics into model optimization to maximize both performance and fairness [1, 10, 12, 20, 23, 55]. Some studies explore mitigating bias without group annotations, such as Just Train Twice (JTT) [24], which upweights misclassified examples to improve worst-group performance, and Cross-Tisk Minimization (XRM) [37], which trains twin classifiers to reduce spurious correlations. Post-processing methods apply transformations to model outputs to improve fairness, such as model calibration [25, 33, 38] and thresholding [5, 13] to align predicted positive outcomes with actual positive examples across groups. Our method falls within the pre-processing paradigm, but instead of simply balancing real data with synthetic data, we focus on using synthetic data to enhance model fairness. + +Improving Model Fairness on Generative Data. Generative models have advanced rapidly in recent years [43, 46], with several studies exploring their use to improve model fairness through generative data [9, 17, 59]. Much of the prior research has focused on generating counterfactual samples to assess fairness [8, 17], and generative methods have also made strides in bias mitigation by creating balanced, unbiased datasets [36, 40, 58]. Instead of generating counterfactual samples based on real data, D'Inca et al. [9] use a diffusion model for uncontrolled image generation, followed by manipulation of the synthetic images in a semantic space. However, these approaches require additional + +group annotations. Zhang et al. [59] use generative models to identify spurious attributes that may bias the model, then edit each image to modify these attributes. They train a fair FAC model on the augmented dataset, enhancing its invariance to these spurious variations. While this approach does not require protected group labels for training the FAC model, annotations are still needed to train the generative models that detect and edit spurious attributes. Additionally, generating accurate counterfactual images remains challenging, as the edits are applied randomly to images without known protected attributes. In contrast, our method uses generative data from a text-to-image LDM, enabling greater control over the diversity of the generated data and allowing a broader range of scenarios and variations. + +Model Fine-Tuning. A common approach to transfer learning in the presence of distribution shifts is to fine-tune the last few layers of a pre-trained model, retaining the learned features while adapting to the new task [27, 65]. To prevent overfitting during this fine-tuning process, existing methods suggest using a smaller learning rate compared to the initial pretraining phase [21], freezing the early backbone layers and gradually unfreezing them [15], or applying different learning rates to each layer [42]. Lee et al. [22] introduced surgical fine-tuning, which showed that selectively fine-tuning a subset of layers can either match or outperform conventional fine-tuning strategies. Recent research [19] indicates that training a carefully selected subset of layers while keeping the remaining weights frozen at their initial values can lead to varying contributions from different layers across the network to overall performance. Our proposed method inherits some common findings from these works but we further investigated with parameters-wise selective fine-tuning, which details the parameters' sensibility to the property from the pre-train data distribution and the property from the downstream data distribution. + +# 3. Methods + +This section first introduces how to generate contextual synthetic data with LLM-generated prompts. Then, we detail how to obtain the parameters selection mask. Finally, we present how to conduct model fair fine-tuning with a selection mask on balanced synthetic data. We provide the algorithm for the selective fine-tuning in the Appendix. + +# 3.1. Contextual Synthetic Data Generation + +Our method attempts to correct the biased model trained on imbalanced real data by fine-tuning on balanced synthetic data, so the quality of the synthetic data is crucial to the success of fair learning. Although current text-to-image models have demonstrated remarkable performance, several studies indicate that directly expressing the desired attributes in the prompt often results in sub-optimal outcomes due to linguistic ambiguity or model misrepresentation [48, 57]. For example, as shown in Fig. 4, to generate a face photo with + +![](images/748d899da50ee608b8a1e088410a484573eb1820cb8f563d2335b8625262dfb3.jpg) +Figure 4. Generated images of Smiling Male conditioned on different prompts. Compared to the plain prompt, our contextual prompts enhance the diversity. More on UTKFace in Appendix. + +both target and protected attributes, one might use a prompt like "Portrait face photo of a smiling male." as suggested in [56]. However, such manually designed prompts may lead to stereotypical image generation, excluding certain attributes or minority groups, which in turn can introduce bias in other attributes, such as age or hairstyle [57]. + +The recent work in zero-shot [31] and supervised [62] classification suggest that leveraging additional contextual and detailed information can enhance vision-language alignment. Considering current text-to-image models [3, 36, 41, 45] often use vision-language models, such as CLIP [39], for cross-modality alignment, we propose a contextual synthetic data generation strategy that leverages the powerful linguistic capabilities of large language models, such as GPT-4, to condition an LDM with richer and context-driven text. As a result, the generated images cover more scenarios and provide more details, enhancing diversity and mitigating the bias in the characteristics not involved in the target and protected. The structure of the CSDG is shown in the upper right of Fig. 3. + +Concretely, the instruction provided for the GPT-4 model following the format: “{Task}, {Number of Prompts}, {Target Attribute}, {Protected Attribute}, {Other Detailed Descriptions}, and {Prompt Format}”. For generating facial photos, for example, the other detailed descriptions contain specific facial features, hair characteristics, eye-related details, and head orientation or angle. Our text-to-image generation model is a pre-trained latent diffusion model-Stable Diffusion (SD) [43], which reverses noises applied to the latent embedding of images. SD contains a variational autoencoder (VAE) [28], a CLIP text encoder [39], and a U-Net [44]. During the inference, the random Gaussian noise $\varepsilon_{t} \sim \mathcal{N}(0,\mathbf{I})$ and the contextual prompt features $c = (w_{1}, w_{2}, \ldots, w_{n})$ encoded via a CLIP text + +encoder $\Psi (\cdot)$ will be fed into the U-Net to condition the denoising process, where $n$ is the number of the contextual prompts. We provide detailed instruction and contextual prompts in the Appendix. The empirical results in Tab. 5 demonstrate that the generated contextual synthetic data mitigate domain shift and improve model fairness. + +# 3.2. Selective Mask Generation + +As recent studies [50, 53, 64] have mentioned, synthetic data often fail to align with the real data distribution due to domain shift, suggesting that fine-tuning the pre-trained model directly on the balanced synthetic data may not learn the desired properties effectively. This is caused by the fact that there is both a domain shift (synthetic vs. real) and a bias shift (unbiased vs. biased) between the real and the synthetic data, and fine-tuning with the domain shift will result in a model with decreased utility. The empirical finding shown in Fig. 2 demonstrates that when fine-tuning a real data pre-trained model on balanced synthetic data, some parameters are more sensitive to the data distribution shift, called domain-sensitive parameters, while some are more sensitive to group discrepancies, called fairness-sensitive parameters. To discover the parameters' sensibility towards different scenarios, we propose to construct three distinct datasets with different distributions to elicit the model responses by calculating the parameter-wise gradients. + +We aim to fine-tune a pre-trained model $f_{\theta}(x)$ to improve fairness while accounting for domain differences between real and synthetic data, hence, we want to find the parameters which are more sensitive to fairness while less sensitive to domain shift. Specifically, we start by constructing three different datasets: biased real data $\{(x_i^{(R)},y_i^{(R)})\}_{i = 1}^{N_R}\in \mathcal{D}_R$ representing training data with inherent biases, biased synthetic data $\{(x_i^{(S_1)},y_i^{(S_1)})\}_{i = 1}^{N_{S_1}}\in \mathcal{D}_{S_1}$ mirroring the unfairness of the real data, and unbiased synthetic data $\{(x_i^{(S_2)},y_i^{(S_2)})\}_{i = 1}^{N_{S_2}}\in \mathcal{D}_{S_2}$ designed to be fair, mitigating biases. $N_{R},N_{S_{1}}$ , and $N_{S_2}$ is the image number of the corresponding dataset. + +We then compute the gradients $\pmb{g}_R$ , $\pmb{g}_{S1}$ , and $\pmb{g}_{S2}$ of the loss function $\mathcal{L}(\theta ;x,y)$ , which is defined from a binary softmax loss. Rather than considering fine-grained, scalar-wise parameters, we select parameters at the level of weights and biases, denoted by $\theta$ , which includes weights $W^{(l)}$ and biases $b^{(l)}$ for the Convolution Layer, Batch Normalization, and Fully Connected Layer, where $l$ refers to the layer index. Then, for the model parameters $\theta$ on each dataset: + +$$ +\boldsymbol {g} _ {R} = \frac {1}{N _ {R}} \sum_ {i = 1} ^ {N _ {R}} \nabla_ {\boldsymbol {\theta}} \mathcal {L} \left(\theta ; x _ {i} ^ {(R)}, y _ {i} ^ {(R)}\right) \tag {1} +$$ + +$$ +\boldsymbol {g} _ {S _ {1}} = \frac {1}{N _ {S _ {1}}} \sum_ {i = 1} ^ {N _ {S _ {1}}} \nabla_ {\theta} \mathcal {L} \left(\theta ; x _ {i} ^ {(S _ {1})}, y _ {i} ^ {(S _ {1})}\right) \tag {2} +$$ + +$$ +\boldsymbol {g} _ {S _ {2}} = \frac {1}{N _ {S _ {2}}} \sum_ {i = 1} ^ {N _ {S _ {2}}} \nabla_ {\theta} \mathcal {L} (\theta ; x _ {i} ^ {(S _ {2})}, y _ {i} ^ {(S _ {2})}) \tag {3} +$$ + +where $\nabla$ is the gradient operator. We then calculate the gradient differences to capture how each parameter behaves across different data distributions. For parameter $\theta_{j}$ : + +$$ +\begin{array}{l} \Delta_ {1, j} = \left| \boldsymbol {g} _ {R, j} - \boldsymbol {g} _ {S _ {1}, j} \right| \tag {4} \\ \Delta_ {2, j} = \left| \mathbf {g} _ {S _ {1}, j} - \mathbf {g} _ {S _ {2}, j} \right| \\ \end{array} +$$ + +where $\Delta_{1}$ measures parameters sensitive to the domain shift while $\Delta_{2}$ identifies parameters crucial for fairness, $j$ denotes the index of all the parameters. To obtain the parameters which are less affected by domain differences and more impactful for fairness, we conduct a ranking in ascending order on $\Delta_{1}$ (smaller differences first) and a ranking in descending order on $\Delta_{2}$ (larger differences first): + +$$ +R _ {1} = \operatorname {a r g s o r t} \left(\Delta_ {1}\right); R _ {2} = \operatorname {a r g s o r t} \left(- \Delta_ {2}\right) \tag {5} +$$ + +Then we can find the intersections from the top- $k$ parameters are both less sensitive to the domain gap and significant for fairness by $K = K_{1}\cap K_{2}$ , where + +$$ +\begin{array}{l} \begin{array}{l} K _ {1} = \left\{\theta_ {j} \mid j \in R _ {1} [ 1: k ] \right\} \\ I = \left\{\theta_ {i} \mid i \in D _ {1} [ 1: k ] \right\} \end{array} \tag {6} \\ K _ {2} = \left\{\theta_ {j} \mid j \in R _ {2} [ 1: k ] \right\} \\ \end{array} +$$ + +Finally, the selection mask can be obtained by: + +$$ +M _ {j} = \left\{ \begin{array}{l l} \text {T r u e}, & \text {i f} \theta_ {j} \in K \\ \text {F a l s e}, & \text {o t h e r w i s e} \end{array} \right. \tag {7} +$$ + +# 3.3. Selective Fine-Tuning on Synthetic Data + +Our goal is to fine-tune the pre-trained model $f_{\theta}(x)$ on the balanced synthetic dataset $\mathcal{D}_{S_2}$ following the ERM framework, while only updating selected parameters as indicated by the mask $M$ . Specifically, given the model $f_{\theta}(x)$ pretrained on the biased real data, balanced synthetic data $\{(x_i^{(S)},y_i^{(S)})_{i = 1}^{N_{S_2}}$ , and the parameters selection mask $M$ , during optimization, we apply the mask to the gradients so that only the selected parameters are updated: + +$$ +\theta^ {(t + 1)} = \theta^ {(t)} - \eta \left(M \odot \nabla_ {\theta} \mathcal {L} \left(f _ {\theta^ {(t)}} \left(x _ {i} ^ {(S _ {2})}\right), y _ {i} ^ {(S _ {2})}\right)\right) \tag {8} +$$ + +where $\theta^{(t)}$ are the parameters at iteration $t$ , $\eta$ is the learning rate, and $\odot$ denotes element-wise multiplication. Notably, once the mask $M$ is provided by SMG, it will be applied throughout the entire fine-tuning optimization process. + +# 4. Experiments + +This section presents the experimental setup and results. We begin by describing the datasets, followed by the implementation details. The main results and ablation studies are presented at the end. + +# 4.1. Datasets + +CelebA [26] contains over 200,000 facial images with 40 binary attribute annotations. Following the setting of the previous works [35, 58, 59], we set Male and Young to protected attributes and selected Smiling and Young as the target attribute which has the highest correlation with the protected attributes. For each experiment, we randomly sample a biased subset as a training dataset with a size of 20,000 images, where the majority group and minority group have + +Table 1. Comparisons to other methods on the CelebA dataset under settings of varied target and protected attributes. + +
MethodsT: Smiling, P: MaleT: Smiling, P: YoungT: Young, P: Male
ACC (↑) WST(↑) EO (↓)ACC (↑) WST(↑) EO (↓)ACC (↑) WST(↑) EO (↓)
ERM [14]88.2070.1025.3088.3071.5015.6077.7042.0052.00
CVaR DRO [23]87.3074.0022.8087.0076.1013.9075.4042.3048.80
EIL [7]87.9075.6019.7087.9072.5013.3077.5045.6039.20
LfF [32]87.1077.5017.0085.3072.9014.3077.4044.2043.60
JTT [24]88.0074.8019.4087.6073.3014.2076.3043.6047.70
MAPLE [63]88.1072.0019.6088.1073.6013.6076.3046.2043.50
DiGA [59]88.4081.907.4089.1078.509.5080.0051.3033.30
AIM-Fair (Ours)89.0284.206.0790.2187.785.4478.1954.8928.18
+ +90% and 10% of the sample size respectively. We report performance on the whole original test dataset. UTK Face [60] consists of over 20,000 facial images with three kinds of annotations: gender, age, and ethnicity. Following the experimental setup in the previous works [17, 18, 59], we define a binary spurious attribute "Ethnicity" based on whether the facial image is white or not. The task is to predict the Gender. We randomly sample a biased subset of 10,000 images, with the same bias degree as CelebA. We also construct a balanced and unbiased test dataset consisting of 3,200 images. + +# 4.2. Fairness Metrics + +Our goal is to learn a fair and accurate model. For model utility, we present the overall accuracy (ACC) and group accuracy. For fairness, follow previous work [35, 58, 59] we use equalized odds (EO) [13], defined as: + +$$ +\left. \overline {{\sum}} _ {\forall y, \hat {y}} \left| P _ {s _ {0}} (\hat {Y} = \hat {y} \mid Y = y) - P _ {s _ {1}} (\hat {Y} = \hat {y} \mid Y = y) \right|, \right. \tag {9} +$$ + +where $\overline{\sum}$ is the averaged sum, $Y$ target label, $\hat{Y}$ classifier predictive label, and $s_0,s_1\in S$ protected attributes. The worst-group accuracy (WST) defined as: + +$$ +\min _ {\forall y \in \mathcal {Y}, \forall s \in S} P _ {s} (\hat {Y} = y \mid Y = y) \tag {10} +$$ + +and group standard deviation (STD) [52] defined as: + +$$ +\underset {\forall y \in \mathcal {Y}, \forall s \in S} {\operatorname {s t d}} P _ {s} (\hat {Y} = y \mid Y = y) \tag {11} +$$ + +# 4.3. Implementation Details + +Following previous work [59], we use ResNet-18 [14] as the backbone for all experiments. We use stable diffusion v2.1 as our latent diffusion model for generating images. We generated 10,000 images for each group and then randomly sampled $N_{S}$ . To be consistent with the real data image number $N_{R}$ , we set the $N_{S} = N_{R} / G$ , where $G$ is the group number. During the pre-training phase, we set the batch size to 128 and trained the model for 15 epochs. The initial learning rate was set to 0.01, which was then reduced by a factor of 0.01 at the 10th epoch. During the fine-tuning phase, we set the batch size to 128 and trained the model for 10 epochs. And the learning rate is searched from \{0.4, 0.5, 0.6\}. All models are optimized by the SGD optimizer and trained on the Tesla A100 GPU based on the open-source PyTorch platform. To obtain more stable and reliable results, we conducted all experiments 10 times with different + +Table 2. Comparisons to other methods on the CelebA dataset (T=Smiling, P=Male) under settings of training set sizes. + +
MethodsSamples Ratio = 50%Samples Ratio = 25%Samples Ratio = 10%
ACC (↑)WST(↑)EO (↓)ACC (↑)WST(↑)EO (↓)ACC (↑)WST(↑)EO (↓)
ERM [14]87.5067.8026.1087.1065.9027.7086.9062.8028.90
CVaR DRO [23]86.6072.9022.1086.6072.3022.4085.5069.1027.30
EIL [7]86.2071.3022.5085.9069.6025.4086.8064.2026.70
LfF [32]86.9075.5019.4085.9072.1023.6085.5066.1027.70
JTT [24]87.3072.9020.1086.7071.1020.6086.8067.1023.10
MAPLE [63]87.4073.7023.8087.0072.7024.2085.6069.2027.10
DiGA [59]88.4081.107.8088.4078.308.0088.3078.808.40
AIM-Fair (Ours)88.8583.996.2888.8982.547.5987.9081.738.16
+ +random seeds and then used the average as the final result. + +# 4.4. Comparisons to State of the Art + +We compared our method against seven contemporary techniques, including the baseline ERM [14] method and six debiasing models all of which do not require protected attribute labels: Two regularization-based methods (CVaR DRO [23] and EIIL [7]); three reweighting-based methods (LfF [32], JTT [24], and MAPLE [63]); and generativemodel-based method (DiGA [59]). Our comparison covers two settings: different target and protected attributes and varying numbers of target labels. + +Tab.1 shows that ERM achieves good accuracy but suffers from significant unfairness. Other debiasing methods, while improving fairness to some extent, generally sacrifice accuracy. DiGA [59] improves fairness while maintaining accuracy by using a generative model to edit real data and create more balanced training data. In contrast, our method generates images from scratch using a text-driven latent diffusion model. It is evident that our method outperforms the best of the existing models DiGA [59] in both fairness and accuracy in all categories, except "Young / Male" where we come close second to DiGA. We outperform all other methods consistently. We also conducted comparisons with other methods under smaller training set sizes, with the subsampling ratio of $50\%$ , $25\%$ , and $10\%$ . Tab. 2 shows that our method outperforms all others consistently, except on ACC score for Lable Ratio at $10\%$ where we come close second to DiGA. Critically, our method maintains robust model utility and fairness even with varying amounts of real training data, with these improvements attributed to the selective updating with balanced synthetic data. + +# 4.5. Ablation Analysis + +Comparisons of Different Training Strategies. To evaluate the effectiveness of the proposed selective fine-tuning, we first compare our method with several other strategies trained on different types of data. These include the baseline, which trains the model using conventional ERM on real data, training the model solely on synthetic data, supplementing real data with synthetic data [47], and balancing the real data [9, 56]. Furthermore, we compare common fine-tuning methods, such as linear probing and full fine-tuning. + +The results in Tab. 3 indicate that both data supplen + +Table 3. Comparisons of varied training strategies on CelebA and UTKFace datasets. + +
MethodsTargetCelebAUTKFace
ProtectedT: Smiling; P: MaleProtectedT: Smiling; P: YoungProtectedT: Female; P: White
P=0P=1ACC (↑) WST (↑) EO (↓) STD (↓)P=0P=1ACC (↑) WST (↑) EO (↓) STD (↓)P=0P=1ACC (↑) WST (↑) EO (↓) STD (↓)
Baseline [14]T=083.5798.5089.2371.5223.8410.6578.7296.0990.1978.7217.376.9279.5896.1688.8679.5816.597.26
T=195.3671.5294.3786.4295.7583.96
Trained on Synthetic DataT=086.8289.4085.9878.527.874.0785.4585.7685.1282.423.501.3482.7188.1285.4482.715.501.96
T=186.3978.5282.4285.2784.9086.04
Data Supplementation [47]T=084.3998.3989.7773.6721.969.7678.0595.3690.3578.0517.317.0282.1293.9790.2582.1211.855.24
T=195.4073.6794.9087.6295.6289.28
Data Repairing [9, 56]T=082.8298.1089.7275.0521.189.5079.5095.1990.6879.5015.696.3081.1594.2289.4281.1513.375.89
T=196.0475.0594.5188.3595.7186.61
Linear ProbT=084.5596.2289.6977.4117.517.7185.2093.8190.1485.208.613.1881.0691.5188.4081.0610.595.14
T=194.8277.4190.4387.8894.5986.42
Fully Fine-TuningT=088.8191.6288.7782.746.833.3185.9890.0687.8585.984.371.6883.0088.0487.9083.005.402.99
T=189.5582.7486.0286.8190.7489.83
AIM-Fair (Ours)T=088.1691.4089.0284.206.072.7488.1993.6490.2187.785.442.3484.2689.0888.3084.264.812.41
T=190.2584.2088.9887.7890.6289.25
+ +Table 4. Comparisons of varied partial fine-tuning strategies on CelebA and UTKFace datasets. + +
MethodsTargetCelebAUTKFace
ProtectedT: Smiling; P: MaleProtectedT: Smiling; P: YoungProtectedT: Female; P: White
P=0P=1ACC (↑)WST (↑)EO (↓)STD (↓)P=0P=1ACC (↑)WST (↑)EO (↓)STD (↓)P=0P=1ACC (↑)WST (↑)EO (↓)STD (↓)
Best Random SelectionT=087.9392.8189.3382.179.144.0985.5291.5388.9585.526.022.1683.5088.8587.9283.505.382.61
T=191.3182.1788.2587.6390.3089.01
Best Sub-Tuning [19] (By Updating One Block)T=087.5094.7590.0480.6412.455.5287.2894.6390.3387.287.343.0083.0589.5689.0183.056.513.56
T=193.0980.6489.1587.3292.0791.34
Best Sub-Tuning [19] (By Freezing One Block)T=088.6991.0989.0683.487.003.0086.5591.8988.6586.555.342.2583.5888.3487.4283.584.762.23
T=190.4883.4887.0886.5588.9688.81
Selective Fine-Tuning (Cosine Similarity)T=086.0791.7788.8583.338.403.6187.4392.9690.2687.435.532.0583.7288.8288.2183.725.102.64
T=191.5383.3389.5288.6590.1490.15
AIM-Fair (Ours) (Absolute Difference)T=088.1691.4089.0284.206.072.7488.1993.6490.2187.785.442.3484.2689.0888.3084.264.812.41
T=190.2584.2088.9887.7890.6289.25
+ +tation and data repairing do not significantly improve fairness. Data supplementation, which combines biased real data with balanced synthetic data for co-training, makes it difficult for the model to learn fairness properties from the synthetic data because of the domain gap. While data repairing can create balanced training data, the domain shift between real and synthetic data limits the effectiveness of fair learning. Common transfer learning methods, such as linear probing and full fine-tuning, also face challenges due to domain shifts. Specifically, linear probing is affected by discrepancies in feature representations, while full fine-tuning improves fairness at the cost of reduced model utility. + +Comparisons of Different Partial Fine-Tuning. We also compare our method with other partial fine-tuning approaches, including random selection and sub-tuning [19]. For random selection, we set the updating ratios at $40\%$ , $55\%$ , $70\%$ , and $85\%$ , and select the best result as the final one. For sub-tuning, we perform block-wise fine-tuning and block-wise freezing (i.e., updating one block or freezing one block while updating the rest), also selecting the block with the best result. + +Tab. 4 shows that fine-tuning only one block consistently yields the best accuracy, but at the cost of fairness, while freezing one block tends to improve fairness but often sacrifices model utility. This demonstrates that coarse-grained approaches, such as block-wise updating or freezing, strut + +Table 5. Classification results on CelebA dataset (T=Smiling, P=Male) under settings of different prompt types and numbers. + +
Prompt Types (Number)TargetProtectedT: Smiling; P: MaleProtectedT: Smiling; P: Young
P=0P=1ACC(↑)WST(↑)EO(↓)STD(↓)P=0P=1ACC(↑)WST(↑)EO(↓)STD(↓)
Plain Prompt (1)t=065.1889.4471.6543.2834.2017.0783.1077.7272.7559.539.308.96
t=177.4743.2859.5368.83
Contextual Prompts (25)t=077.1289.2581.8569.7316.37.6576.7267.9079.8067.908.828.75
t=185.9969.7385.1691.09
Contextual Prompts (50)t=089.4789.8082.6672.225.077.6687.7290.4385.8579.674.364.20
t=177.2672.2279.6782.67
Contextual + Head Poses (50)t=086.8289.4085.9878.527.874.0785.4585.7685.1282.423.501.34
t=186.3978.5282.4285.27
+ +gle to achieve an optimal balance between model utility and fairness. In contrast, our method performs fine-grained, parameter-wise updating, which allows the model to enhance fairness while maintaining utility. As a result, our method achieves the best worst-group accuracy while preserving high overall accuracy. + +Additionally, our method uses gradient differences to identify parameter sensitivity to varying data distributions. We also compared absolute gradient differences with the cosine similarity between gradients. The results in Tab. 4 show that using absolute gradient differences yields better results. The possible reason is that the cosine similarity only provides the direction of gradient disparity, whereas the absolute difference directly captures the magnitude of the gradient disparity. + +Comparisons of Different Prompts. To evaluate the performance of the varied prompts used for generating images, + +![](images/e44f458f7551955a43c17778c446f70cb11207d0428beb2a67bac569ce9b1397.jpg) +Figure 5. Classification results on the CelebA dataset (T=Smiling, P=Male) with different top-k values. The top-k values {40, 45, 50, 55, 60} correspond approximately to $\{64\%, 72\%, 80\%, 88\%, 96\% \}$ of the total model parameters. + +we trained the model solely on the balanced synthetic data generated with corresponding prompts and tested it on the real test set. Tab. 5 shows the results of different prompt types and quantities, indicating that images generated with contextual prompts lead to significantly better performance in both model accuracy and fairness. We believe this improvement is due to the increased diversity and details in the synthetic images generated from contextual prompts. Moreover, as the number of contextual prompts increases, test performance improves as well. Specifically, incorporating head pose variation into the prompt further enhances both accuracy and fairness in the generated images, as the results shown in the last row of Tab. 5. + +Evaluations of Varied Top-k Values. In our method, to identify the intersection parameters from the two gradient difference rankings, we use the top-k selection to ensure that the chosen parameters are more sensitive to fairness and less affected by domain shift. The results for different top-k values are shown in Fig. 5. When k is set to 55, our method achieves the best fairness performance while retaining overall accuracy. Intuitively, a lower k results in fewer updates, leading to better model utility but worse fairness, while a high k involves more parameter updates, which can negatively impact both accuracy and fairness. + +Evaluations of Varied Bias Ratio for Synthetic Data Construction. To evaluate the model's sensitivity to domain shift and group disparity, we construct three distinct datasets with different distributions. In our method, the bias ratio for the biased synthetic data distribution is treated as a hyperparameter, referenced by the error set of real training examples, as suggested in JTT [24]. To assess the impact of varying bias ratios in synthetic data, we explore different ratios. As shown in Tab. 6, a disparity between the synthetic data bias ratio and the real data bias ratio leads to worse performance in both accuracy and fairness. However, despite these differences in bias ratios, our method still outperforms the fully fine-tuning approach. This demonstrates that our + +Table 6. Classification results on CelebA dataset (T=Smiling, P=Male) with varied bias ratio of the biased synthetic data. + +
Bias RatioTargetProtectedACC (↑)WST (↑)EOD (↓)STD (↓)
P=0P=1
Fully Fine-Tuningt=088.8191.6288.7782.746.833.31
t=189.5582.74
4:6t=085.7291.7189.2383.908.783.77
t=192.6983.90
3:7t=087.0591.6288.9083.527.723.26
t=190.9383.52
2:8t=088.0191.7688.9783.167.303.28
t=190.4683.16
1:9t=088.1691.4089.0284.206.072.74
t=190.2584.20
+ +Table 7. Classification results on CelebA dataset (T=Smiling, P=Male) with different number of synthetic data. + +
Ratio To Real DataTargetProtectedACC (↑)WST (↑)EOD (↓)STD (↓)
P=0P=1
0.5t=088.6593.9689.5180.8010.314.90
t=191.1080.80
1t=088.1691.4089.0284.206.072.74
t=190.2584.20
1.5t=089.1892.0588.3481.257.133.98
t=188.3881.25
2t=089.0191.2688.8183.366.082.96
t=191.2689.44
+ +method is able to identify the model's sensitivity under the bias ratios different to real data. + +**Evaluations of Different Number of Synthetic Data.** We also evaluate fine-tuning with varying amounts of balanced synthetic data. As shown in Tab. 7, we use the real training data count as a reference and set different ratios to determine the number of synthetic data. The results indicate that when the amount of synthetic data matches that of real data, the model achieves the best fairness. Additionally, using half the amount of real data results in the best accuracy. We believe that using too much synthetic data during fine-tuning can lead to overfitting, while using too little data may fail to adequately debias the model. + +# 5. Conclusion + +In this work, we proposed a method to mitigate bias in machine learning models using synthetic data generated by a text-to-image process. By designing contextual synthetic data generation and selective fine-tuning, we enhance model fairness without requiring demographic group annotations. Our model updates selectively fairness-sensitive parameters, optimizing simultaneously model fairness and utility scores. Empirical results demonstrate that our method outperforms existing techniques, improving fairness while maintaining model utility performance. This work highlights the potential of synthetic data for creating fairer AI systems, offering a promising direction for future research in bias mitigation. + +# 6. Acknowledgments + +This research utilised Queen Mary's Apocrita HPC facility, supported by QMUL Research-IT. Zengqun Zhao is funded by Queen Mary Principal's PhD Studentships. 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Guibas $^{1}$ Guandao Yang $^{1}$ Gordon Wetzstein $^{1}$ + +$^{1}$ Stanford University $^{2}$ ETH Zürich + +![](images/dfde9e7929811c6d8a0102986e5e00c0dc227df96c33eeb3a7ca403c46ed2233.jpg) +Figure 1. Apparel. We present a multimodal foundation model for digital garments trained by fine-tuning a large multimodal model on a custom sewing pattern dataset using a novel tokenization scheme for these patterns. Apparel generates complex, diverse, high-quality sewing patterns based on multimodal inputs, such as text and images, and it unlocks new applications such as language-instructed sewing pattern editing. The generated sewing patterns can be directly used to simulate the corresponding 3D garments. + +# Abstract + +Apparel is essential to human life, offering protection, mirroring cultural identities, and showcasing personal style. Yet, the creation of garments remains a time-consuming process, largely due to the manual work involved in designing them. To simplify this process, we introduce AByarel, a multimodal foundation model for generating and editing sewing patterns. Our model fine-tunes state-of-the-art large multimodal models (LMMs) on a custom-curated large-scale dataset of over 120,000 unique garments, each with multimodal annotations including text, images, and sewing patterns. Additionally, we propose a novel tokenization scheme that concisely encodes these complex sewing patterns so that LLMs can learn to predict them efficiently. AByarel achieves state-of-the-art performance in single-modal tasks, including text-to-garment and image-to-garment prediction, and enables novel multimodal garment generation applications such as interactive garment editing. The project website is at https://georgenakayama.github.io/AByarel/. + +# 1. Introduction + +Clothing plays a crucial role in society, serving as a barrier against the elements, a reflection of societal norms, and a means of personal expression. A key stage in garment production is the development of sewing patterns—a set of flat 2D panels with standardized assembly instructions that form a complete 3D garment [4]. Pattern making is a challenging task due to the complex geometric relationship between the 2D pattern and the draped 3D shape of the sewn garment. Even an experienced tailor must go through multiple iterations, incorporating feedback from various sources, including verbal descriptions of the garment's fit and feel, as well as visual references of its appearance. To simplify the pattern-making process, we explore strategies to leverage emerging generative models with multimodal inputs, such as language and images. + +State-of-the-art sewing pattern prediction methods are designed to work with one specific input modality, such as 3D points [6, 14, 28], images [43, 47, 65, 70, 74], or language [21]. While effective within their respective domains, these single-modal approaches are often challenging to adapt to garment prediction tasks requiring different or combined input modalities. Expanding these meth + +ods to multimodal pattern prediction presents two primary challenges. First, no large-scale multimodal sewing pattern dataset is publicly available. Second, the capacity to accurately interpret multimodal inputs typically only emerges in large models with billions of parameters [1, 34]. It remains uncertain how to efficiently scale existing methods to models of this size. + +In this paper, we propose to build such multimodal garment generative models by extending existing large multimodal models (LMMs) [34, 57, 69] to understand sewing patterns with complex geometries. To achieve this, we annotate the largest sewing pattern dataset [30] with multimodal labels. Our annotated dataset is ten times larger than those used by previous state-of-the-art generative methods [21, 28, 36], including over 120,000 unique sewing patterns paired with detailed text descriptions, images, edited sewing patterns, and editing instructions. Fine-tuning an LMM to perform multimodal garment generation requires representing complex garments in a format that LMMs can understand—tokens. For this task, we develop a novel tokenization method that is both expressive in representing the complex geometries of sewing patterns and concise enough to fit within the limited context length of existing LMMs, making fine-tuning computationally efficient. + +Combining these components, we present AApparel, a large multimodal model for generating sewing patterns. AApparel can predict sewing patterns with complex geometries and it outperforms state-of-the-art methods in single-modal garment prediction, often by a large margin. Moreover, our approach unlocks entirely new multimodal garment-generation tasks. Our contributions include: + +- We present GCD-MM, a multimodal sewing pattern dataset extending the largest public dataset of sewing patterns with multimodal annotations. We plan to publicly release the dataset to inspire innovative garment prediction capabilities and further enable research in multimodal garment generation. +- We develop a novel tokenization scheme and a new training objective for fine-tuning LMMs to predict sewing patterns. This tokenization method is critical for retargeting LMMs to multimodal garment prediction tasks efficiently. +- We present AIpparel, the first multimodal foundation model for sewing pattern prediction capable of taking language, images, and sewing patterns as input. + +# 2. Related Works + +Garment Generation. Prior works have studied learning-based garment generation represented in various formats, including images [5, 26], 3D meshes [17, 25, 32, 38, 39, 41, 46, 49, 52, 55, 76, 77, 79, 80], and sewing patterns [21, 28, 36, 47, 63]. Our paper focuses on generating sewing patterns, which, compared to other representations, are industry standard and can be directly used for downstream simulation and manufacturing. Earlier works + +have explored a variety of different ways to generate and predict sewing patterns, including retrieval-based methods [14, 20], predicting sewing pattern templates with few parameters [24, 59, 60, 71], or cutting 3D scans into 2D panels [16, 18, 35, 40, 50, 62]. These algorithms usually require heuristics, such as the output garment templates. This limits their flexibility to extend to different input modalities or more complex garment types. Researchers have successfully applied deep learning methods to generating sewing patterns [21, 28, 36]. While these methods can predict accurate sewing patterns based on input conditioning, they offer task-specific models designed to only work well in a single modality. Extending these single-modal methods to a novel modality is difficult, in part because of the lack of large-scale multimodal sewing-pattern datasets and the requirement to redesign the network architecture. While Wang et al. [63] can predict sewing patterns with multiple modalities, including image, 3D garment, and body measurements, their method is limited to predicting simple garments with a predefined set of parameters. In this paper, we aim to tackle the challenge of creating a large multimodal generative model by curating the first multimodal garment dataset with complex garment geometries and providing a scalable recipe building on existing large multimodal models. + +Extending Large Multimodal Models. Large multimodal models have gained significant attention for their ability to understand language and images [2, 15, 45, 53, 57]. Efforts to extend LMMs to additional domains typically fall into two categories. Optimization-free approaches [23, 37, 51, 64, 66, 69, 72] employ prompt engineering. The other option is to fine-tune LMMs to take the new modality as input and/or output. The latter approach was first introduced for vision-language models [34, 56, 78] and subsequent works extended it to other modalities [11, 19, 31, 33, 67, 75]. Their approaches typically involve using pre-trained encoders [31, 33, 67] or standard discrete representations [11, 75] to convert the input modalities into tokens and align them with the text feature space of the LMMs. In particular, LLaVA [34] is pioneering in fine-tuning Large Language Models (LLMs) for visual understanding. It uses a pre-trained vision encoder to encode images into tokens, and a trainable projection layer to project the visual tokens into the LLM's feature space. We build our work on top of LLaVA by fine-tuning it to understand sewing patterns. This presents unique challenges, however, due to the lack of pretrained encoders or learning-efficient representations for sewing patterns. This motivates us to design an efficient, learning-friendly tokenizer and a fine-tuning objective for sewing pattern prediction. + +Garment Datasets. Garment datasets mostly fall into one of the following three categories: 1) datasets based on 3D scans of real-world garments [3, 9, 22, 39, 54, 68, 79], 2) datasets of designer-created garments [10, 81], and 3) datasets containing mostly procedurally generated sewing + +
DatasetTotalTextImageEdits
Wang et al. [63]8kX
Korosteleva and Lee [27]23.5kXX
Sewfactory [36]19.1kXX
DressCode [21]20.3kXX
GCD [30]130kXX
GCD-MM (Ours)120k
+ +Table 1. Modalities of Sewing Pattern Datasets. GCD-MM is a large-scale sewing pattern dataset with multimodal annotations, including text, images, and edited patterns. + +patterns [7, 25, 27, 36, 42, 48, 58, 61, 63]. While 3D garment scans and designer-created garments can accurately depict the real-world complexity of garments, they are expensive to obtain, which limits the scale of these categories of data. Our work focuses on leveraging large-scale procedurally generated sewing pattern datasets. To the best of our knowledge, the largest synthetic sewing pattern datasets available are DressCode [21], SewFactory [36], and GarmentCodeData (GCD) [29, 30]. None of their annotations, however, contain all combinations of text, images, and sewing pattern edits, making them insufficient for training a multimodal sewing pattern generative model. To overcome this data gap, we curate the first large-scale multimodal sewing pattern dataset by expanding GCD with annotations including images, text, editing pairs, and editing instructions. Tab. 1 compares different sewing pattern datasets and their annotation modalities. + +# 3. Method + +We propose a large multimodal generative model for sewing patterns by fine-tuning existing LMMs on a multimodal sewing pattern dataset. For this purpose, we first curate a sewing pattern dataset containing multimodal annotations (Sec. 3.1). We then describe how to train our model, $AIP_{\text{parel}}$ , using an efficient tokenization scheme for sewing patterns using LlaVA 1.5-7B [34] as a base model (Sec. 3.2). + +# 3.1. Multimodal GarmentCode Dataset + +We create annotations containing many modalities to train a multimodal sewing pattern generative model. Specifically, we build on top of the largest existing sewing-pattern dataset, GarmentCodeData (GCD) [30], to incorporate two other modalities: text descriptions and sewing pattern pairs with editing instructions. We dub our dataset GarmentCodeData-MultiModal (GCD-MM). + +Text Descriptions of Sewing Patterns. To enable applications such as text-conditioned sewing pattern generation, it is important to obtain detailed text annotation describing the sewing patterns [8, 21]. He et al. [21] created short keyword descriptions of sewing patterns by prompting GPT-4V with rendered images. However, this method suffers from hallucination, and the short keywords are in + +sufficient to describe the garments in detail, leading to irrecoverable ambiguities. Our pipeline improves on this by leveraging the design parameters associated with each synthetically generated sewing pattern to create accurate descriptions that capture the garment's key features. Specifically, we develop a rule-based algorithm to generate a set of short phrases, including a garment type (e.g., "midi dress", "godet skirt") and brief descriptions based on distinctive characteristics (e.g., "flared hem", "V-neckline"). To obtain the final sewing pattern description, we prompt GPT-4o [69] using the rule-based short captions and the rendered views of the draped garment. Our approach reduces GPT-4o's hallucination and results in more accurate descriptions in natural language. Please refer to the supplementary for caption comparison with DressCode and the prompts and rules we use to generate them. + +Language-instructed Sewing Pattern Editing. We also augment GCD with language-instructed editing annotations. Specifically, we use the programming abstraction from GarmentCode [29] to create paired sewing patterns with corresponding text instructions describing the applied edits. We first manually specify a series of common sewing pattern edits using the abstraction. This includes edits such as adjustments in skirt and pants length, changing insert and neckline styles, and adding or excluding a hood or sleeve. For each modification, we generate captions using a text template to describe the applied changes. See the supplementary for editing templates and captions examples. + +# 3.2. A1pparel + +AIParel fine-tunes LLaVA 1.5-7B on our GCD-MM dataset to generate sewing patterns from multimodal conditioning. For this purpose, we need to encode sewing patterns into a compact list of tokens for LLaVA's input. We also propose a novel fine-tuning objective that allows AIParel to generate both discrete tokens and continuous parameters. Figure 2 shows an overview of our method. + +Pattern Representation. Following GCD [30], we define sewing patterns as a set of 2D panels in 3D with stitching information. A sewing pattern $\mathcal{P} = (P, S)$ is a tuple consisting of $N$ panels $P = \{P_1, \ldots, P_N\}$ and stitching information $S$ . Each panel $P_i$ is a planar surface with vertices $V_i = \{v_1^{(i)}, \ldots, v_{n_i}^{(i)}\}$ and edges $E_i = (e_1^{(i)}, \ldots, e_{n_i}^{(i)})$ , where each edge contains two endpoints connecting $(v_k^{(i)}, v_{k'}^{(i)})$ with $k' = k \mod n_i + 1$ . Since each panel is defined in its own coordinate frame, we always set $v_1^{(i)} = 0 \in \mathbb{R}^2$ . An edge can be a straight line, a quadratic or cubic Bezier curve, or an arc, and includes its corresponding control vertices $c_k^{(i)}$ . Each panel also includes a rigid 3D transformation $R$ that transforms $P_i$ into the global coordinate frame for draping. Lastly, each panel contains a unique name indicating the panel type for the designers. We define stitching information $S$ as a set of edge pairs among panel + +![](images/8cdada81c13a60940fc4d9c27e8e9c971eb48436a6e7c51783a5afb3a18044a0.jpg) +Figure 2. Illustration of Our Method. Apparel uses a novel sewing pattern tokenizer (light blue region) to tokenize each panel into a set of special tokens (light green region). Panel vertex positions and 3D transformations are incorporated using positional embeddings (colored arrows) to the tokens. Apparel takes in multimodal inputs, such as images and texts (light orange region), to output sewing patterns using autoregressive sampling (light grey region). Finally, the output is decoded to produce simulation-ready sewing patterns (light pink region). See Section 3 for method details. + +![](images/f2065f1f8bdb78b416cf9582bcab7ff18ed0189b4273d6e24ec800a3919eb12e.jpg) + +edges, i.e., $S = \{(e_{k_1}^{(i_1)}, e_{l_1}^{(j_1)}), \ldots, (e_{k_m}^{(i_m)}, e_{l_m}^{(j_m)})\}$ where each $(e_{k_s}^{(i_s)}, e_{l_s}^{(j_s)})$ indicates that edge $e_{k_s}^{(i_s)}$ from panel $P_{i_s}$ will be stitched with edge $e_{l_s}^{(j_s)}$ . See the supplementary for representation details. + +Sewing Pattern Tokenization. The sewing pattern representation in GCD contains both continuous parameters, such as panel vertex coordinates, and discrete parameters, such as the number of panels and stitches. This poses challenges in compactly representing each sewing pattern as a set of tokens for the transformer's prediction. Prior works use extensive zero-padding to make sure that all sewing patterns can be represented as a fixed-length vector [21, 28, 36]. This approach is impractical for the complex sewing patterns present in GCD-MM, as it leads to an extremely long context. For example, the tokenization scheme of He et al. [21] requires more than $30\mathrm{k}$ tokens to represent a typical sewing pattern in the GCD-MM dataset, making it extremely inefficient for generation and learning. $^{1}$ + +Inspired by recent work on vector graphics generation [13], we develop a tokenization scheme to efficiently represent sewing patterns as a sequence of drawing commands. Specifically, we introduce four special tokens to indicate garment-start $(<\text{SoG}>)$ , garment-end $(<\text{EoG}>)$ , panel-start $(<\text{SoP}>)$ and panel-end $(<\text{EoP}>)$ . With these tokens, each sewing pattern can be represented as + +$$ +\mathrm {E} _ {g} (\mathcal {P}) = < \mathrm {S} \circ \mathrm {G} > \mathrm {E} _ {p} (P _ {1}, S) \dots \mathrm {E} _ {p} (P _ {n}, S) < \mathrm {E} \circ \mathrm {G} >, \tag {1} +$$ + +where $\mathrm{E}_p$ tokenizes panel $P$ in the form of + +$\langle \mathrm{SoP}\rangle \ldots \langle \mathrm{EoP}\rangle$ . $\mathbf{E}_p$ consists of three pieces of panel information: name, transformation, and edges. The panel name is tokenized using LLaVA-1.5-8B's text tokenizer and inserted after $\langle \mathrm{SoP}\rangle$ . We introduce a new token $\langle \mathbb{R}\rangle$ and place it after the panel name to represent the panel's transformation. Each edge type also corresponds to two special tokens, depending on whether the edge ends at the starting endpoint: line $(< \mathsf{L}>$ $< \mathsf{cL}>$ ),quadratic Bézier curve $(< Q>$ $< cQ>$ ), cubic Bézier curve $(< \mathsf{B}>$ $< c\mathsf{B}>$ ),and arc $(< A>$ $< cA>$ ).We also introduce a set of stitching tag tokens $\{< t1 > ,\dots , < tM > , < tN > \}$ to represent stitching information $S$ .We associate each edge with a stitching tag so that $(e_{k_s}^{(i_s)},e_{l_s}^{(j_s)})\in S$ iff there exists $a\in \{1,\dots ,M\}$ such that $e_{k_s}^{(i_s)}$ and $e_{l_s}^{(j_s)}$ are both associated with $< Ta>$ .If an edge is not stitched to another edge, it is associated with the null tag $< tN>$ .For example, a panel consisting of two lines stitched together, one cubic Bézier curve and an arc is tokenized as + +$$ +\begin{array}{l} < \mathrm {S o P} > [ \text {p a n e l n a m e} ] < \mathrm {R} > < \mathrm {L} > < \mathrm {t} 1 > < \mathrm {L} > < \mathrm {t} 1 > \\ < \mathrm {B} > < \mathrm {t N} > < \mathrm {c A} > < \mathrm {t N} > < \mathrm {E o P} >. \\ \end{array} +$$ + +Compared to the DressCode tokenizer [21], our proposed scheme uses around 100 times fewer tokens to describe the same garment. On average, we represent a sewing pattern with around 250 tokens with a maximum of 838 tokens on GCD-MM, whereas DressCode uses more than 30k tokens for each sewing pattern on the same data. + +Notation. From now on, we use bold letters (e.g., $X \in \mathbb{R}^{N \times D}$ ) to denote the input embedding sequence to the transformer. We denote the $i$ -th embedding in $X$ as $X_{i}$ , + +![](images/e3a99a1d16832044dd2a5c32b83d46431933184709170c661d80e44894d44b4e.jpg) +Figure 3. Image-to-Garment Prediction (Qualitative). GCD-MM (Left): our model can reconstruct suitable sewing patterns from the input image alone. In contrast, SewFormer does not produce simulation-ready sewing patterns despite fine-tuning. SewFactory (Right): SewFormer produces inaccurate panels (top row) and incorrect garment types (bottom row) while Apparel accurately recovers sewing patterns from the images, resulting in superior simulation results. See Sec. 4.1. + +
DatasetMethodPanel L2 (↓)#Panel Acc (↑)#Edge Acc (↑)Rot L2 (↓)Transl L2 (↓)#Stitch Acc (↑)
SewfactorySewFormer3.389.899.3.0080.899.2
AApparel2.893.999.9.0050.699.8
GCD-MMSewFormer-FT12.379.444.7.0404.52.8
AApparel5.485.282.7.0202.777.2
+ +Table 2. Image-to-Garment Prediction (Quantitative). AIIpparel achieves state-of-the-art performance in both datasets and surpasses SewFormer-FT by a large margin on GCD-MM. + +and $X_{i}$ are sliced sequences before or after the $i$ -th embedding, respectively. We use $f_{\phi}$ to denote the language transformer from LLaVA. We use $\mathbf{X}$ to denote tokens before passing through $f_{\phi}$ and $\mathbf{H} = f_{\phi}(\mathbf{X})$ as the output hidden embeddings from the transformer. + +Continuous Parameters. The tokenization scheme in Eq. 1 does not include any continuous parameters such as vertex positions, control points for edges, or rigid transformation of panels. Prior works represent continuous parameters as quantized tokens in discrete space [21, 44]. This introduces quantization error for the continuous parameters and uses more tokens per panel, leading to a longer, inefficient representation. Inspired by recent approaches of extending LMMs [19, 31], we propose using small regression heads to map hidden embeddings of the transformer to the continuous parameters. Specifically, we define an MLP $g_{\theta}^{(\mathrm{e})}: \mathbb{R}^D \to \mathbb{R}^C$ to map LLaVA's hidden embedding from the last layer to vertices and control points. As illustrated in Fig. 2, $g_{\theta}^{(\mathrm{e})}$ takes the output embedding corresponding to the token right before the edge type token. Concretely, if the $i$ -th token, $X_i$ , corresponds to an edge-type token for edge $e$ , its associated output embedding $H_{