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2025/Kernel-based Unsupervised Embedding Alignment for Enhanced Visual Representation in Vision-language Models/full.md

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+# Kernel-based Unsupervised Embedding Alignment for Enhanced Visual Representation in Vision-language Models
+
+Shizhan Gong  $^{1}$  Yankai Jiang  $^{2}$  Qi Dou  $^{1}$  Farzan Farnia  $^{1}$
+
+# Abstract
+
+Vision-language models, such as CLIP, have achieved significant success in aligning visual and textual representations, becoming essential components of many multi-modal large language models (MLLMs) like LLaVA and OpenFlamingo. However, numerous studies have identified CLIP's limited fine-grained perception as a critical drawback, leading to substantial failures in downstream MLLMs. In contrast, vision-centric foundation models like DINOv2 demonstrate remarkable capabilities in capturing fine details from images. In this work, we propose a novel kernel-based method to align CLIP's visual representation with that of DINOv2, ensuring that the resulting embeddings maintain compatibility with text embeddings while enhancing perceptual capabilities. Our alignment objective is designed for efficient stochastic optimization. Following this image-only alignment fine-tuning, the visual encoder retains compatibility with the frozen text encoder and exhibits significant improvements in zero-shot object recognition, fine-grained spatial reasoning, and localization. By integrating the aligned visual encoder, downstream MLLMs also demonstrate enhanced performance. The code and models are available at https://github.com/peterant330/KUEA.
+
+# 1. Introduction
+
+Vision-language Models (VLMs) have made significant strides and transformed the field of computer vision. A
+
+$^{1}$ Department of Computer Science and Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China  $^{2}$ Shanghai Artificial Intelligence Laboratory, Shanghai, China. Correspondence to: Shizhan Gong <szgong22@cse.cuhk.edu.hk>, Yankai Jiang <jiangyankai@pjlab.org.cn>, Qi Dou <qidou@cuhk.edu.hk>, Farzan Farnia <farnia@cse.cuhk.edu.hk>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+notable example is CLIP (Radford et al., 2021) and its variants (Zhai et al., 2023; Sun et al., 2023), which are trained on extensive datasets of paired text and images to link images with their corresponding textual descriptions. These models demonstrate exceptional generalizability and zero-shot performance on various downstream tasks, including classification (Saha et al., 2024), segmentation (Yu et al., 2023), and object detection (Vidit et al., 2023). Beyond functioning as a standalone tool, CLIP's vision encoder has been incorporated into several Multi-modal Large Language Models (MLLMs), such as LLaVA (Liu et al., 2024), OpenFlamingo (Awadalla et al., 2023), BLIP-2 (Li et al., 2023a), and Qwen-VL (Bai et al., 2023), serving as an integral component for visual feature extraction.
+
+However, because CLIP is trained with global supervision from image captions, it struggles to learn finer pixel-level details such as color (Thrush et al., 2022) and spatial relationship (Liu et al., 2023; Kamath et al., 2023). This limitation affects CLIP's performance on vision-focused tasks and can also impair the fine-grained perception capabilities of downstream MLLMs. Numerous studies have highlighted these issues (Yuksekgonul et al., 2023; Guo et al., 2024). For instance, Jiang et al. (2023) examined feature visualization from deeper layers and found that it emphasizes global image properties while neglecting intricate details. Similarly, Tong et al. (2024) reported that current MLLMs struggle with simple visual pattern questions, such as counting, color identification, and viewpoint recognition.
+
+Vision-only self-supervised learning protocols, such as DINO (Caron et al., 2021) and MAE (He et al., 2022), produce vision-centric representations that are highly effective for visual grounding. Researchers are exploring these models to address the inherent limitations of CLIP. Some studies have combined multiple models as vision encoders for MLLMs (Jiang et al., 2023; Tong et al., 2024; Shi et al., 2024; Shen et al., 2024). However, this approach introduces considerable computational overhead. Other methods focus on using vision-only self-supervised learning to fine-tune the CLIP encoder (Wu et al., 2023; Covert et al., 2025), which can enhance its localization abilities. Nevertheless, these fine-tuning techniques risk disrupting the alignment between image and text representations, potentially under
+
+![](images/87d4ec661a0906eea4109281f738c53763668ad98f0e7299628982ec48461230.jpg)  
+Figure 1. Main claim of this work. We propose a kernel-based alignment framework, which is able to enhance the visual representation of CLIP via image-only fine-tuning. Moreover, the improvement can be transferred to downstream multi-modal large language models.
+
+mining CLIP's zero-shot performance. Additionally, there are efforts to integrate region-based task loss (Zhong et al., 2022; Wan et al., 2024) or distillation loss from vision models (Salehi et al., 2023) during CLIP's training, which requires re-training the models and incurs high computational costs. Most critically, all these methods produce visual embeddings that differ significantly from the original CLIP embeddings, leading to incompatibility with downstream models trained on the original embeddings. Consequently, all downstream models (e.g., MLLMs) would need to be re-tuned from scratch to align visual-text embeddings. The cost makes these solutions impractical in real applications.
+
+In this paper, we present an innovative approach to address the limitations of CLIP embeddings by aligning them with embeddings from vision-centric models. Our method involves fine-tuning CLIP's vision branch to align with the representations of target models, such as DINOv2 (Oquab et al., 2024), while maintaining compatibility with CLIP's text embeddings, which is totally frozen and untouched (see Fig. 1). Given the significant differences between the feature spaces of target models and CLIP, a direct alignment of the visual representations could disrupt the alignment with text representations. Instead, we propose to align the embeddings in the kernel space, which preserves the integrity of the original feature space while allowing for flexible adjustments of similarities among samples based on their visual details. As a result, this alignment could enhance the vision encoder's ability to recognize fine-grained visual patterns. In addition, we design an optimization objective that can be handled by stochastic optimization, enabling our framework to scale effectively to real-world datasets with minimal computational hardware requirements.
+
+We examine the enhancements achieved through the proposed alignment in both vision-centric tasks and visual question answering (VQA). Experiments conducted on multiple CLIP-benchmark (LAION-AI, 2022) and probing bench (Covert et al., 2025) reveal that the CLIP after alignment demonstrates improved accuracy in zero-shot classi
+
+fication and dense prediction tasks, without requiring finetuning of the text encoder. Subsequently, we integrate the aligned CLIP vision encoder into two pre-trained MLLMs, LLaVA (Liu et al., 2024) and OpenFlamingo (Awadalla et al., 2023), evaluating their performance across several standard VQA benchmarks. This also results in significant enhancements over the original CLIP, even without finetuning the large language model (LLM) component. Our main contributions can be summarized as follows.
+
+- We introduce a kernel-based alignment method that effectively aligns two sets of embeddings while preserving the integrity of the original representation space.  
+- We implement the alignment using CLIP and DINOv2. With minimal image-only fine-tuning, the aligned CLIP visual encoder shows substantial improvements while preserving compatibility with the text encoder and ensuring zero-shot generalizability.  
+- Evaluation across various vision-language benchmarks shows that the enhancements in visual representations can be effectively inherited to downstream MLLMs.
+
+# 2. Related Work
+
+Kernel Methods in Representation Learning. Kernel methods (Hofmann et al., 2008) are algorithms that use the kernel trick, which allows linear algorithms to work in high-dimensional feature spaces without explicit data transformation. It is widely used in deep representation learning. For example, He & Ozay (2022) utilized kernel-based metrics for evaluating the similarity between two embeddings. Several work (Allen-Zhu & Li, 2020; He & Ozay, 2022; Zhou et al., 2024) leveraged kernel functions for knowledge distillation. Dehdashtian et al. (2024) proposed to de-bias CLIP's image and text representations in reproducing kernel Hilbert spaces for better fairness. Kernel methods have also been applied to evaluating the fidelity (Binkowski et al., 2018), diversity (Friedman & Dieng, 2022; Jalali et al.,
+
+2023; Rezaei et al., 2024; Ospanov & Farnia, 2024; Jalali et al., 2024; Ospanov et al., 2024a;b), and novelty (Zhang et al., 2024a;b) of generative models. Our method can be interpreted as aligning visual representations of CLIP and other vision models in the kernel space, through kernel trick.
+
+Fine-tuning Vision-Language Models. Fine-tuning of VLMs has been widely applied to improve the model performance on specific downstream dataset (Zhou et al., 2022; Zhang et al., 2022; Gao et al., 2024) or domain-specific applications (Cao et al., 2024; Gong et al., 2024). Beyond the accuracy gain, studies have also discovered that well-designed fine-tuning scheme can promote some desired properties of the model, such as adversarial robustness (Mao et al., 2022; Schlarmann et al., 2024), fairness (Shen et al., 2023), and visual interpretability (Gong et al., 2025). In this work, we leverage fine-tuning to enhance the general visual ability of the VLMs. Instead of focusing on single datasets, we show the enhancement exhibit good generalizability.
+
+Enhancement of CLIP Visual Representations. Several studies have proposed methods to address the limitations of CLIP's visual embeddings and enhance its fine-grained capabilities. For instance, Salehi et al. (2023) trained the CLIP encoder using multi-task losses supervised by pseudo labels generated from other vision encoders. Similarly, Jiang et al. (2023) and Tong et al. (2024) complemented CLIP with DINOv2 as the vision encoder for downstream MLLMs. Shi et al. (2024) and Shen et al. (2024) further expanded this approach to incorporate a wider variety of vision encoders. Currently, there are limited explorations focusing on the fine-tuning phase. Covert et al. (2025) applied masked fine-tuning to CLIP's vision encoder to enhance its localization capabilities. However, their fine-tuned vision encoders became incompatible with the text encoder and downstream LLMs. The method most closely related to ours is DIVA (Wang et al., 2025), which refines CLIP representations using only images with the help of diffusion models. Comparing to DIVA, our method demands significantly less computation and achieves better zero-shot performance.
+
+# 3. Method
+
+# 3.1. Kernel Function and Kernel Matrix
+
+Consider a function  $k: \mathbb{R}^d \times \mathbb{R}^d \to \mathbb{R}$  that assigns a similarity score  $k(\mathbf{x}, \mathbf{y}) \in \mathbb{R}$  to every pair of vectors  $\mathbf{x}, \mathbf{y} \in \mathbb{R}^d$ . The function  $k$  qualifies as a kernel function if and only if, for any set of samples  $\mathbf{x}_1, \dots, \mathbf{x}_n \in \mathbb{R}^d$ , the resulting kernel matrix  $\mathbf{K} = [k(\mathbf{x}_i, \mathbf{x}_j)]_{1 \leq i,j \leq n}$  is positive semi-definite. This kernel matrix well captures the pairwise similarities among the samples. Common examples of kernel functions include Gaussian kernel, cosine kernel, and polynomial kernel. In this work, we mainly focus on the polynomial kernel
+
+with coefficient  $\gamma$ , constant offset  $c$ , and degree  $d$ :
+
+$$
+k _ {\text {p o l y n o m i a l} (\gamma , c, d)} \left(\mathbf {x}, \mathbf {y}\right) := \left(\gamma \mathbf {x} ^ {T} \mathbf {y} + c\right) ^ {d}. \tag {1}
+$$
+
+We call a kernel function normalized if  $k(\mathbf{x}, \mathbf{x}) = 1$  for any vector  $\mathbf{x} \in \mathbb{R}^d$ . A kernel function can be normalized via:
+
+$$
+\tilde {k} (\mathbf {x}, \mathbf {y}) = \frac {k (\mathbf {x} , \mathbf {y})}{\sqrt {k (\mathbf {x} , \mathbf {x}) k (\mathbf {y} , \mathbf {y})}}. \tag {2}
+$$
+
+Note that for each valid kernel function  $k$ , there exists a feature map  $\phi : \mathbb{R}^d \to \mathbb{R}^s$  such that for every input vectors  $\mathbf{x}, \mathbf{y}$ , the following holds:
+
+$$
+k (\mathbf {x}, \mathbf {y}) = \langle \phi (\mathbf {x}), \phi (\mathbf {y}) \rangle , \tag {3}
+$$
+
+where  $\langle \cdot, \cdot \rangle$  denotes the inner product in  $\mathbb{R}^s$ .  $s$  is usually much greater than  $d$ , indicating that  $\phi$  maps the input features into a higher-dimensional kernel space.
+
+# 3.2. Kernel-based Embedding Alignment
+
+CLIP consists of two components: an image encoder  $f_{\theta}$  and a text encoder  $f_{\varphi}$ . These encoders transform each language-image pair  $(T_i, I_i)$  into their respective representations  $f_{\theta}(I_i), f_{\varphi}(T_i) \in \mathbb{R}^d$ . The target model  $g$  is a vision encoder (e.g., DINOv2) that generates the representation  $g(I_i) \in \mathbb{R}^{d'}$  for the image  $I_i$ . While CLIP effectively achieves visual-language alignment, it struggles to capture fine-grained visual details, an area where the target model excels. As noted by Tong et al. (2024), samples that carry similar semantic meanings but differ in visual details exhibit high similarity in the CLIP feature space, while showing low similarity in the DINOv2 feature space. The value of kernel function is a measure of similarity between two samples. The kernel matrix of the target model reflects how samples are arranged in feature spaces based on their visual similarities, whereas the kernel matrix of CLIP only captures semantic similarities. Consequently, it is a natural idea to align the kernel matrix of CLIP with that of the target model, as it can encourage the arrangement of samples in the feature space to better represent their visual patterns, thus alleviating the limitations of CLIP (as illustrated in Fig. 1). Due to the large sample size, directly minimizing the distance between the two kernel matrices can be computationally infeasible. To address this, we propose the following optimization objective for alignment fine-tuning:
+
+$$
+\min  _ {\theta} \underset {I _ {i}, I _ {j} \sim \mathcal {D} _ {\text {t r a i n}}} {\mathbb {E}} \left[ \left(k _ {1} \left(f _ {\theta} \left(I _ {i}\right), f _ {\theta} \left(I _ {j}\right)\right) - k _ {2} \left(g \left(I _ {i}\right), g \left(I _ {j}\right)\right)\right) ^ {2} \right], \tag {4}
+$$
+
+where  $k_{1}$  and  $k_{2}$  are the kernel functions for CLIP and the target model, which may take different forms or with different parameters to reflect the variation in the feature space. According to Hoeffding's inequality (Hoeffding, 1994), the empirical estimate of the objective function is an unbiased estimator, and the following proposition implies that the gradient w.r.t  $\theta$  can also be computed through limited samples.
+
+Table 1. Accuracy evaluation on zero-shot image classification benchmarks of CLIP models w/wo alignment. Projection means training a linear layer to map DINOv2 representations into the CLIP feature space. Feature means directing aligning the representation pairs subjecting to a linear transformation. DIVA refers to the method proposed by Wang et al. (2025). Kernel is our proposed method.  
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Alignment Strategies</td><td rowspan="2">ImageNet</td><td colspan="11">Zero-shot Datasets</td><td rowspan="2">Average Zero-shot</td></tr><tr><td>CIFAR10</td><td>CIFAR100</td><td>CalTech</td><td>FER</td><td>OxfordPeds</td><td>DTD</td><td>RESISC</td><td>EuroSAT</td><td>PCAM</td><td>ImageNet-S</td><td>ImageNet-O</td></tr><tr><td rowspan="4">ViT-B-16</td><td>CLIP</td><td>67.72</td><td>89.98</td><td>65.61</td><td>82.17</td><td>46.35</td><td>89.04</td><td>44.95</td><td>58.19</td><td>55.89</td><td>50.70</td><td>48.28</td><td>42.30</td><td>61.22</td></tr><tr><td>projection</td><td>68.96</td><td>96.24</td><td>75.30</td><td>73.67</td><td>27.19</td><td>80.70</td><td>34.26</td><td>33.27</td><td>40.44</td><td>50.02</td><td>54.73</td><td>30.00</td><td>54.17</td></tr><tr><td>feature</td><td>67.84</td><td>90.47</td><td>66.46</td><td>82.19</td><td>46.36</td><td>89.02</td><td>45.00</td><td>58.29</td><td>56.04</td><td>50.79</td><td>48.31</td><td>42.60</td><td>61.41</td></tr><tr><td>kernel</td><td>67.84</td><td>91.13</td><td>67.38</td><td>82.20</td><td>46.82</td><td>89.23</td><td>45.43</td><td>57.73</td><td>56.85</td><td>54.02</td><td>48.18</td><td>43.50</td><td>62.04</td></tr><tr><td rowspan="5">ViT-L-14</td><td>CLIP</td><td>74.90</td><td>95.20</td><td>71.08</td><td>83.30</td><td>50.00</td><td>93.21</td><td>55.21</td><td>63.35</td><td>62.65</td><td>52.00</td><td>59.59</td><td>32.25</td><td>65.26</td></tr><tr><td>projection</td><td>70.42</td><td>95.10</td><td>74.14</td><td>80.31</td><td>24.51</td><td>80.02</td><td>37.02</td><td>37.03</td><td>32.48</td><td>50.02</td><td>56.04</td><td>28.05</td><td>54.07</td></tr><tr><td>feature</td><td>75.16</td><td>95.77</td><td>75.13</td><td>83.58</td><td>49.62</td><td>93.35</td><td>55.73</td><td>63.13</td><td>63.11</td><td>51.34</td><td>58.08</td><td>34.20</td><td>65.73</td></tr><tr><td>DIVA</td><td>74.84</td><td>95.10</td><td>70.96</td><td>84.01</td><td>49.47</td><td>93.57</td><td>55.05</td><td>63.48</td><td>62.93</td><td>53.79</td><td>59.53</td><td>32.05</td><td>65.45</td></tr><tr><td>kernel</td><td>75.52</td><td>96.27</td><td>77.04</td><td>84.32</td><td>50.31</td><td>93.40</td><td>55.74</td><td>63.83</td><td>63.83</td><td>52.68</td><td>59.67</td><td>34.90</td><td>66.54</td></tr><tr><td rowspan="5">ViT-L-14-336</td><td>CLIP</td><td>75.82</td><td>94.49</td><td>71.11</td><td>83.42</td><td>49.04</td><td>93.70</td><td>55.64</td><td>63.73</td><td>61.46</td><td>60.68</td><td>61.03</td><td>32.75</td><td>66.10</td></tr><tr><td>projection</td><td>71.26</td><td>94.87</td><td>77.35</td><td>72.33</td><td>23.35</td><td>79.39</td><td>39.20</td><td>42.06</td><td>35.06</td><td>50.02</td><td>57.53</td><td>28.65</td><td>54.53</td></tr><tr><td>feature</td><td>75.36</td><td>95.45</td><td>74.16</td><td>83.45</td><td>50.24</td><td>93.79</td><td>56.22</td><td>64.37</td><td>61.22</td><td>59.82</td><td>60.40</td><td>32.55</td><td>66.52</td></tr><tr><td>DIVA</td><td>75.54</td><td>93.74</td><td>70.73</td><td>83.63</td><td>50.07</td><td>93.32</td><td>55.48</td><td>63.19</td><td>60.13</td><td>59.52</td><td>56.90</td><td>31.65</td><td>65.30</td></tr><tr><td>kernel</td><td>76.30</td><td>95.95</td><td>74.92</td><td>83.53</td><td>50.21</td><td>93.79</td><td>56.33</td><td>64.43</td><td>61.93</td><td>59.65</td><td>61.31</td><td>35.60</td><td>67.13</td></tr></table>
+
+Proposition 3.1. Assume that both  $k_{1}$  and  $k_{2}$  take values in the range  $[-1,1]$ . Let  $(I_{m_1}, I_{m_2})$  for  $1 \leq m \leq M$  represent  $M$  pairs of images independently sampled from the data distribution. Assume  $k_{1}(f_{\theta}(I_{m_1}), f_{\theta}(I_{m_2}))$  is  $L$ -Lipschitz w.r.t.  $\theta$  for any sampled pairs. Define the sample-wise gradient as
+
+$$
+\begin{array}{l} t (\theta ; I _ {m _ {1}}, I _ {m _ {2}}) \\ := \nabla_ {\theta} \left(k _ {1} \left(f _ {\theta} \left(I _ {m _ {1}}\right), f _ {\theta} \left(I _ {m _ {2}}\right)\right) - k _ {2} \left(g \left(I _ {m _ {1}}\right), g \left(I _ {m _ {2}}\right)\right)\right) ^ {2}, \\ \end{array}
+$$
+
+and the true expected gradient is defined as  $\mathbb{E}[t(\theta)]\coloneqq$ $\nabla_{\theta}\mathbb{E}_{I_i,I_j\sim \mathcal{D}_{train}}\left[\left(k_1(f_\theta (I_i),f_\theta (I_j)) - k_2(g(I_i),g(I_j))\right)^2\right].$
+
+Then, for every  $0 < \epsilon < 8L$ , we have
+
+$$
+\begin{array}{l} P \left(\left\| \frac {1}{M} \sum_ {m = 1} ^ {M} t \left(\theta ; I _ {m _ {1}}, I _ {m _ {2}}\right) - \mathbb {E} [ t (\theta) ] \right\| _ {2} \geq \epsilon\right) \\ \leq \exp \left(- \frac {M \epsilon^ {2}}{5 1 2 L ^ {2}} + \frac {1}{4}\right) \tag {5} \\ \end{array}
+$$
+
+As a result, we can utilize stochastic optimization methods, such as mini-batch gradient descent, to solve the problem efficiently. In each iteration, we sample a batch of data pairs and minimize the difference in kernel functions specifically for those pairs. This approach enables the alignment framework to scale effectively to datasets of real-world size.
+
+# 3.3. Regularization for Visual-language Alignment
+
+To ensure the alignment with the text branch is preserved, we introduce a regularization to prevent the aligned features
+
+from straying too far from their original direction. This term is represented by the  $L_{2}$  distance between the visual representations before and after the alignment fine-tuning. The final optimization objective is expressed as follows:
+
+$$
+\begin{array}{l} \min  _ {\theta} w \cdot \mathbb {E} _ {I _ {i}, I _ {j} \sim \mathcal {D} _ {\text {t r a i n}}} \left[ \left(k _ {1} \left(f _ {\theta} (I _ {i}), f _ {\theta} (I _ {j})\right) \right. \right. \tag {6} \\ \left. - k _ {2} \big (g (I _ {i}), g (I _ {j}) \big)\right) ^ {2} \biggr ] + \mathbb {E} _ {I _ {i} \sim \mathcal {D} _ {\mathrm {t r a i n}}} \left[ \left\| f _ {\theta} (I _ {i}) - f _ {\theta_ {0}} (I _ {i}) \right\| _ {2} ^ {2} \right], \\ \end{array}
+$$
+
+where  $\theta_0$  is the parameters of the pre-trained CLIP and is frozen during the alignment phase.  $w$  is a coefficient balancing the two loss terms. The regularization term ensures that the alignment process does not cause the aligned embeddings to deviate significantly from the original embeddings. The following proposition illustrates how this regularization helps preserve the language-image alignment.
+
+Proposition 3.2. (Schlarmann et al., 2024) For every language-image pair  $(T, I)$ , if  $\| f_{\theta}(I) - f_{\theta_0}(I) \|_2 \leq \lambda$  holds, then we will have
+
+$$
+\begin{array}{l} \left| \cos \big (f _ {\theta_ {0}} (I), g (T) \big) - \cos \big (f _ {\theta} (I), g (T) \big) \right| \\ \leq \frac {2 \lambda}{\max  \left\{\| f _ {\theta} (I) \| _ {2} , \| f _ {\theta_ {0}} (I) \| _ {2} \right\}} \\ \end{array}
+$$
+
+The proposition shows this regularization helps preserve the language-image alignment without the need of incorporating any text data during the fine-tuning phase.
+
+Table 2. Summary of zero-shot image-to-text and text-to-image retrieval performance on Flickr30K (Young et al., 2014) and COCO benchmark (Chen et al., 2015) datasets. Our alignment will not sacrifice the image-text alignment property of the original CLIP.  
+
+<table><tr><td rowspan="3"></td><td rowspan="3">Vision Encoder</td><td colspan="6">Image-to-Text Retrieval</td><td colspan="6">Text-to-Image Retrieval</td></tr><tr><td colspan="3">Flickr30K</td><td colspan="3">MSCOCO</td><td colspan="3">Flickr30K</td><td colspan="3">MSCOCO</td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td rowspan="2">ViT-B-16</td><td>w/o align</td><td>77.90</td><td>94.30</td><td>97.40</td><td>48.36</td><td>72.68</td><td>81.76</td><td>60.64</td><td>83.82</td><td>90.36</td><td>31.80</td><td>55.91</td><td>66.97</td></tr><tr><td>w/ align</td><td>78.10</td><td>94.10</td><td>97.50</td><td>48.06</td><td>72.86</td><td>81.78</td><td>60.92</td><td>84.30</td><td>90.62</td><td>32.12</td><td>56.51</td><td>67.15</td></tr><tr><td rowspan="3">ViT-L-14</td><td>w/o align</td><td>81.40</td><td>96.20</td><td>98.70</td><td>50.64</td><td>74.20</td><td>82.96</td><td>63.62</td><td>86.36</td><td>91.86</td><td>34.51</td><td>59.21</td><td>69.37</td></tr><tr><td>DIVA</td><td>78.70</td><td>94.80</td><td>98.30</td><td>49.88</td><td>74.06</td><td>82.82</td><td>59.80</td><td>83.36</td><td>89.40</td><td>34.21</td><td>58.76</td><td>68.97</td></tr><tr><td>w/ align</td><td>83.00</td><td>96.90</td><td>99.00</td><td>51.72</td><td>75.52</td><td>83.30</td><td>64.78</td><td>87.20</td><td>92.32</td><td>35.98</td><td>61.08</td><td>71.02</td></tr><tr><td rowspan="3">ViT-L-14-336</td><td>w/o align</td><td>83.00</td><td>96.60</td><td>99.00</td><td>52.12</td><td>76.12</td><td>83.82</td><td>64.78</td><td>87.92</td><td>93.06</td><td>35.65</td><td>60.30</td><td>70.66</td></tr><tr><td>DIVA</td><td>80.20</td><td>95.90</td><td>98.30</td><td>52.34</td><td>76.48</td><td>84.16</td><td>61.20</td><td>84.72</td><td>90.80</td><td>35.77</td><td>60.29</td><td>70.44</td></tr><tr><td>w/ align</td><td>84.60</td><td>96.80</td><td>99.10</td><td>53.48</td><td>77.64</td><td>85.30</td><td>67.08</td><td>88.98</td><td>93.62</td><td>37.61</td><td>62.48</td><td>72.46</td></tr></table>
+
+Table 3. Accuracy evaluation on counting, spatial reasoning, and caption recognition tasks of CLIP models w/wo alignment.  
+
+<table><tr><td></td><td>Vision Encoder</td><td>svhn</td><td>gtsrb</td><td>clevr distance</td><td>clevr counts</td></tr><tr><td rowspan="6">Zero-shot</td><td>ViT-B-16</td><td>31.31</td><td>43.34</td><td>22.37</td><td>21.21</td></tr><tr><td>+align</td><td>27.40</td><td>44.35</td><td>22.40</td><td>21.30</td></tr><tr><td>ViT-L-14</td><td>57.02</td><td>50.55</td><td>20.21</td><td>19.43</td></tr><tr><td>+align</td><td>59.63</td><td>52.53</td><td>23.39</td><td>21.11</td></tr><tr><td>ViT-L-14-336</td><td>56.03</td><td>52.41</td><td>18.93</td><td>20.05</td></tr><tr><td>+align</td><td>57.65</td><td>53.43</td><td>20.91</td><td>20.90</td></tr><tr><td rowspan="6">Linear Probe</td><td>ViT-B-16</td><td>45.02</td><td>57.13</td><td>31.19</td><td>23.68</td></tr><tr><td>+align</td><td>49.27</td><td>58.30</td><td>30.92</td><td>24.02</td></tr><tr><td>ViT-L-14</td><td>65.20</td><td>72.94</td><td>22.97</td><td>41.25</td></tr><tr><td>+align</td><td>69.39</td><td>74.51</td><td>30.82</td><td>49.67</td></tr><tr><td>ViT-L-14-336</td><td>61.49</td><td>70.17</td><td>28.43</td><td>53.07</td></tr><tr><td>+align</td><td>70.02</td><td>71.77</td><td>34.65</td><td>55.32</td></tr></table>
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Models. The above framework is actually flexible enough to align any two sets of embeddings. In this study, we primarily examine the alignment of visual representations from CLIP and vision-focused models. We experiment with several versions of CLIP, including ViT-B-16, ViT-L-14, and ViT-L-14-336, all pre-trained by OpenAI. For the vision-centric target model, we employ DINOv2 (Oquab et al., 2024) with ViT-L-14 as the backbone, after registration (Darcet et al., 2024). This setup allows for aligned embedding pairs to originate from models with different architectures or to correspond to images of varying resolutions, demonstrating the flexibility and generalizability of our proposed framework.
+
+Training data. We utilize the training set of ImageNet-1K (Deng et al., 2009) as our training data, which contains 1.28M images. Compared to the original training process
+
+of CLIP, the incremental alignment step is quite lightweight and can be performed on image-only datasets.
+
+Training Schemes. The kernel we use is the normalized polynomial kernel of degree 3, which has been commonly adopted by several well-known studies in the literature (Stein et al., 2023; Kang et al., 2023). We also explore different kernel choices in the ablation studies. For DINOv2, we set the hyper-parameter of kernel to  $\gamma = 1 / dim_{emb}$  and  $c = 1$ , while for CLIP, they are set as trainable. More detailed settings for each experiment can be found in the Appendix B.1. With two 4090 GPUs, the alignment of ViT-L-14 takes around 30 hours, which is efficient and hardware-friendly compared to the pre-training phase of CLIP.
+
+# 4.2. Improvements on Vision-centric Tasks
+
+We begin with vision-centric tasks, which can be done by CLIP alone, to verify whether alignment with DINOv2 embeddings can enhance the visual representation of CLIP.
+
+Zero-shot Object Recognition. We first test the zero-shot accuracy of the aligned CLIP model on standard object recognition benchmarks. We experiments on a diverse benchmarks composed of 12 datasets, including (1) common objects: ImageNet (Deng et al., 2009), CIFAR-10, CIFAR-100 (Krizhevsky et al., 2009), Caltech101 (Fei-Fei et al., 2004); (2) fine-grained objects: OxfordPets (Parkhi et al., 2012), DTD (Cimpoi et al., 2014), FER2013 (Goodfellow et al., 2013); (3) domain-specific applications: PCAM (Veeling et al., 2018), RESISC45 (Cheng et al., 2017), EuroSAT (Helber et al., 2018); and (4) out-of-distribution benchmarks: ImageNet-O (Hendrycks et al., 2021), ImageNet-Sketch (Wang et al., 2019). We adopt the standard CLIP-Benchmark (LAION-AI, 2022) as the pipeline for evaluation. The results are presented in Table 1. For zero-shot object recognition, performance depends on both perceptual ability and compatibility with the text encoder. After aligning with DINOv2 representations, we
+
+Table 4. Results on probing benchmark. We report macroaveraged recall for both local probing and global probing.  
+
+<table><tr><td colspan="2">Vision Encoder</td><td>local</td><td>global</td></tr><tr><td rowspan="2">ViT-B-16</td><td>w/o align</td><td>44.63</td><td>52.61</td></tr><tr><td>w/ align</td><td>45.25</td><td>52.94</td></tr><tr><td rowspan="2">ViT-L-14</td><td>w/o align</td><td>46.40</td><td>54.51</td></tr><tr><td>w/ align</td><td>47.44</td><td>55.33</td></tr><tr><td rowspan="2">ViT-14-336</td><td>w/o align</td><td>46.05</td><td>55.13</td></tr><tr><td>w/ align</td><td>46.65</td><td>56.09</td></tr></table>
+
+observe improvements across most datasets. Specifically, the average zero-shot accuracy increases by  $0.82\%$ ,  $1.28\%$ , and  $1.03\%$  with alignment for ViT-B, ViT-L, and ViT-L-336, respectively. This indicates that our proposed alignment enhances visual representation while maintaining compatibility with the CLIP text encoder. The improvements are particularly notable for images with low resolution (e.g., CIFAR) or tiny objects (e.g., EuroSAT), highlighting enhanced fine-grained perception capabilities. Through experiments with different CLIP backbones, we find that these improvements are architecture-agnostic, consistently boosting classification accuracy. Furthermore, the enhancements hold for both the ImageNet dataset and zero-shot datasets, demonstrating that alignment does not compromise the generalizability of CLIP. Even when fine-tuned on relatively small training data, the model still exhibits strong zero-shot performance on out-of-distribution datasets.
+
+To demonstrate the superiority of the proposed kernel-based alignment, we compare our method with two straightforward baselines: (1) a linear projector trained to map the DINOv2 representation into the CLIP representation space, and (2) replacing kernel-based alignment with feature-based alignment (details available in Appendix B.2). However, we observe limited improvements or even significant drops in zero-shot accuracy. The representation spaces of DINOv2 and CLIP can vary significantly, making it challenging to directly align them while preserving compatibility with the text embeddings. In contrast, our kernel-based alignment focuses on aligning the relative relationships among samples, which helps maintain the macro-structure of the feature space. We also compare our approach with DIVA (Wang et al., 2025), and the results indicate that our method achieves better zero-shot performance. Furthermore, DIVA and our proposed alignment are orthogonal, they can be combined for complementary benefits.
+
+In Appendix C.2, we extend our framework to three additional models that incorporate an intermediate embedding layer linking modalities, albeit with implementations differing from CLIP: SigLIP (Zhai et al., 2023), DFN (Fang et al., 2023), and MetaCLIP (Xu et al., 2024). We also
+
+![](images/8052676566bbf8a96b41d05d12e2c9bd6cefa7454548dd3ea9ad2a0b28239587.jpg)  
+Figure 2. Visualization of CLIP encoder's attention maps. Attention maps can show more fine-grained details after alignment.
+
+explore replacing DINOv2 with other vision models, such as MLCD (An et al., 2024). The results show improved zero-shot accuracy for all these pairs, demonstrating the generalizability of the proposed framework.
+
+Image-to-text and Text-to-image Retrievals. To further demonstrate that the proposed alignment framework does not compromise the image-text alignment or the generalizability of CLIP, we present zero-shot image-to-text and text-to-image retrieval performance in Table 2. These experiments were conducted on both the Flicker30K (Young et al., 2014) and MSCOCO (Chen et al., 2015) datasets. The results indicate that CLIP maintains strong performance in both retrieval tasks even after alignment. This reinforces our assertion that the image-text alignment is effectively preserved, despite the improvements in visual capability.
+
+As highlighted in the literature (Tong et al., 2024), the CLIP encoder often struggles with specific tasks, including counting, spatial relationship inference, and caption recognition, which serves as a major motivation for our work. To investigate how alignment with DINOv2 can alleviate these issues, we conduct experiments on four related benchmarks: (1) SVHN (Netzer et al., 2011), which composed of natural scene images with digits and numbers; (2) GTSRB (Stallkamp et al., 2012), a datasets for recognition of German traffic sign; (3) CLEVR Distance (Johnson et al., 2017), which composed of images with multiple objects and the task is to determine the distance between the closest objects; and (4) CLEVR Counts, a benchmark that requires the model to count the number of objects within the images. We again follow the evaluation protocol of CLIP-Benchmark, which formulates all four benchmarks as classification tasks. We assess the improvements through both zero-shot classification and linear probing. The results, presented in Table 3, indicate that alignment significantly enhances CLIP's performance on text or spatial-related tasks, particularly after linear probing. For example, when using ViT-L-14, alignment improves the average accuracy by  $1.58\%$  for zero-shot classi
+
+Table 5. Evaluation of LLaVA on vision-language benchmarks. The performance can be improved by using the CLIP after alignment as the visual encoder, and it can be further improved through parameter-efficient fine-tuning (peft) of the LLM.  
+
+<table><tr><td></td><td>Vision Encoder</td><td>AI2D</td><td>text-ocr</td><td>text-pure</td><td>pope</td><td>tallyQA</td><td>vsr</td><td>RefCOCOg</td><td>RefCOCO+</td><td>RefCOCO</td><td>vqa-v2</td><td>llava-wild</td><td>llava-coco</td><td>Average</td></tr><tr><td rowspan="4">ViT-L</td><td>baseline</td><td>52.91</td><td>55.37</td><td>41.16</td><td>84.64</td><td>60.39</td><td>51.47</td><td>13.89</td><td>12.73</td><td>15.16</td><td>75.07</td><td>44.13</td><td>75.07</td><td>48.50</td></tr><tr><td>+align</td><td>53.66</td><td>55.70</td><td>41.53</td><td>84.92</td><td>60.39</td><td>51.50</td><td>14.15</td><td>12.89</td><td>15.37</td><td>75.10</td><td>44.67</td><td>76.60</td><td>48.87</td></tr><tr><td>+peft</td><td>53.63</td><td>54.54</td><td>41.82</td><td>84.35</td><td>57.19</td><td>53.93</td><td>56.06</td><td>52.74</td><td>61.27</td><td>74.71</td><td>44.30</td><td>64.84</td><td>58.28</td></tr><tr><td>+both</td><td>54.79</td><td>55.03</td><td>42.13</td><td>84.37</td><td>59.87</td><td>58.02</td><td>56.47</td><td>52.82</td><td>62.25</td><td>74.87</td><td>43.70</td><td>65.33</td><td>59.14</td></tr><tr><td rowspan="4">ViT-L-336</td><td>baseline</td><td>53.27</td><td>57.82</td><td>48.63</td><td>85.45</td><td>61.45</td><td>51.47</td><td>55.19</td><td>51.97</td><td>60.49</td><td>76.40</td><td>42.97</td><td>75.60</td><td>60.06</td></tr><tr><td>+align</td><td>52.95</td><td>57.94</td><td>48.53</td><td>85.57</td><td>61.25</td><td>51.47</td><td>55.66</td><td>52.78</td><td>60.54</td><td>76.34</td><td>48.40</td><td>79.07</td><td>60.88</td></tr><tr><td>+peft</td><td>52.69</td><td>57.79</td><td>48.50</td><td>85.41</td><td>61.91</td><td>54.14</td><td>56.76</td><td>53.81</td><td>61.98</td><td>75.88</td><td>44.13</td><td>69.13</td><td>60.18</td></tr><tr><td>+both</td><td>52.78</td><td>58.18</td><td>48.87</td><td>85.70</td><td>62.21</td><td>56.22</td><td>57.68</td><td>55.74</td><td>63.37</td><td>75.93</td><td>44.90</td><td>78.83</td><td>61.70</td></tr></table>
+
+fication and  $5.51\%$  for linear probing. Compared to common object recognition, tasks like caption recognition, counting, and spatial reasoning rely more heavily on the quality of the visual representation. This is where vision-centric models such as DINOv2 significantly outperform CLIP. After alignment, the CLIP representation demonstrates enhanced visual capabilities, resulting in better performance on these tasks. Additionally, we include results from MMVP-VLM (Tong et al., 2024) in Appendix C.4, which provides insights from a more diverse but relatively smaller benchmark.
+
+Localization Ability. We further evaluate the localization ability of CLIP visual encoders w/wo alignment. Specifically, we utilize the probing benchmark introduced by Covert et al. (2025). This evaluation involves freezing the visual encoder and training a classification head to predict the union of labels for each patch (local probing) or the entire image (global probing) using a binary cross-entropy loss. The experiments are conducted on the MSCOCO dataset (Lin et al., 2014). Following the original setup, we report the macro-averaged recall to account for class imbalances. The results, shown in Table 4, reveal that after alignment with DINOv2, the CLIP visual encoder demonstrates improved localization ability, achieving higher recall for both local and global probing. This enhancement can be attributed to the strong perceptual capabilities of the DINOv2 encoder, which are transferred to CLIP encoder via alignment. Furthermore, the improvements are consistent across different CLIP encoder architectures. While the gains may not be as significant compared to those reported by Covert et al. (2025), their approach disrupts the connection with text representations, leading to a loss of CLIP's zero-shot capability. In contrast, our method enhances performance without compromising the textual alignment.
+
+We visualize the attention maps from the penultimate layer of the CLIP visual encoder for several examples in Fig 2.
+
+The attention maps are generally similar w/wo alignment, as the regularization term prevents significant changes in the model's weights. However, we still observe that the attention maps after alignment are sharper and highlight more fine-grained features. This indicates that the aligned model is better at capturing details from the input image, resulting in improved localization ability.
+
+# 4.3. Improvements on MLLMs
+
+We then show that the enhancements in visual representation can be transferred to downstream tasks. Specifically, we replace the vision encoder of several MLLMs with the aligned CLIP encoder and evaluate improvements on relevant benchmarks. The LLM component can either be entirely frozen or fine-tuned. Importantly, our alignment maintains the similarity of visual representations before and after the process, eliminating the need for an additional vision-language alignment step. As a result, fine-tuning can be conducted efficiently using techniques such as LoRA (Hu et al., 2022).
+
+Evaluation on LLaVA. We first conduct experiments on LLaVA-1.5-7B (Liu et al., 2024). We utilize diverse benchmarks which comprises of multiple tasks including (1) open-ended visual question answering: VQAv2 (Goyal et al., 2017) and TextVQA (Singh et al., 2019); (2) localization: RefCOCO, RefCOCO+, RefCOCOg (Kazemzadeh et al., 2014; Yu et al., 2016); and (3) closed-set prediction: VSR (Liu et al., 2023), TallyQA (Acharya et al., 2019), POPE (Li et al., 2023b), and AI2D (Kembhavi et al., 2016). We also perform GPT-aided evaluation, LLaVA-bench (Liu et al., 2024). We replace the visual encoder with our aligned version and experiment with both ViT-L-14 and ViT-L-14-336 versions of CLIP encoder. To better illustrate the enhancements, we further fine-tune the LLM component of the models. We skip the feature alignment step and conduct only visual instruction tuning using LoRA. For the training data,
+
+![](images/fd5f5909374c2b66103b56c913a926dbadd1ca444c7f8b6c10ebfa46013318eb.jpg)  
+Figure 3. Ablation studies. Average zero-shot accuracy across 11 datasets are reported as evaluation metrics: (a) Effects of training epochs; (b) Effects of the regularization term; (c) Effects of the coefficients of alignment; (d) Effects of different kernel functions.
+
+![](images/e58bde59ffcd9bc78ed57f9afb6e6ed4a063b164228d43dccc660928905b1e5d.jpg)
+
+![](images/e44c17b9e48aedf73fdddd63629cfef9002b4cc15d988466d9cd777b2b8d013a.jpg)
+
+![](images/03479de2152dd09e36a5cc2f0e4831fa1cd950268b974958b3f504f223df7fd6.jpg)
+
+Table 6. Evaluation results on OpenFlamingo across seven vision-language datasets using 0, 4, and 16 in-context examples. The performance can be improved by using the CLIP visual encoder after alignment as the visual encoder, without fine-tuning the LLM part. We report CIDEr for COCO and Flicker-30K, ROC AUC for Hateful Memes, and VQA accuracy for the rest.  
+
+<table><tr><td>Shots</td><td>Vision Encoder</td><td>COCO</td><td>Flickr-30K</td><td>VQAv2</td><td>OK-VQA</td><td>TextVQA</td><td>VizWiz</td><td>Hateful Memes</td><td>Average</td></tr><tr><td rowspan="2">0</td><td>CLIP</td><td>74.40</td><td>54.15</td><td>43.54</td><td>28.72</td><td>25.42</td><td>17.80</td><td>51.03</td><td>42.15</td></tr><tr><td>+align</td><td>76.01</td><td>54.42</td><td>43.71</td><td>29.04</td><td>25.92</td><td>17.91</td><td>52.86</td><td>42.84</td></tr><tr><td rowspan="2">4</td><td>CLIP</td><td>82.56</td><td>58.72</td><td>45.40</td><td>31.81</td><td>29.03</td><td>23.05</td><td>48.24</td><td>45.54</td></tr><tr><td>+align</td><td>83.95</td><td>60.03</td><td>45.57</td><td>31.82</td><td>29.43</td><td>23.12</td><td>49.22</td><td>46.16</td></tr><tr><td rowspan="2">16</td><td>CLIP</td><td>90.42</td><td>62.68</td><td>45.59</td><td>32.12</td><td>29.83</td><td>35.22</td><td>50.62</td><td>49.45</td></tr><tr><td>+align</td><td>90.89</td><td>63.85</td><td>45.73</td><td>32.43</td><td>30.33</td><td>35.74</td><td>48.85</td><td>49.69</td></tr></table>
+
+we utilize the LLaVA-1.5 data mixture (Liu et al., 2024), which contains 665k examples and is the tuning dataset for the original LLaVA. We also report metrics from performing the same fine-tuning on the original model to control for the effects of fine-tuning. The results, shown in Table 5, indicate improvements even when the vision encoder is simply replaced with our aligned version, without fine-tuning the LLM component. This suggests that the alignment lead to improvement while preserving the compatibility of CLIP with the LLM component. The improvements are further amplified when we fine-tune the LLM component, resulting in an average score increase of  $1.66\%$ , for model with ViT-L-14-336 as the visual encoder. This is particularly evident in the localization benchmarks, with  $3.05\%$  improvement on average. Furthermore, the enhancements cannot be solely attributed to LLM fine-tuning, as fine-tuning LLM alone does not yield such great gains. These experiments demonstrate that our proposed alignment enhances visual capabilities, especially fine-grained perception, and these improvements can be effectively transferred to downstream applications.
+
+Evaluation on OpenFlamingo. We extend the evaluation to another popular MLLM, OpenFlamingo (Awadalla et al., 2023). We follow the evaluation pipeline of the original paper, which test the in-context-learning ability of the MLLMs in several VQA benchmarks, including COCO (Chen et al., 2015), Flicker-30K (Young et al., 2014), VQAv2 (Goyal et al., 2017), OK-VQA (Marino et al., 2019), TextVQA (Singh et al., 2019), VizWiz (Gurari et al., 2018),
+
+and Hateful Memes (Kiela et al., 2020). For each dataset, we sample a few in-context demonstrations from the training split uniformly at random, and prompt the model to give answers to the test samples. We use the OpenFlamingo-3B (Instruct) version of the model. The results are shown in Table 6. For all experiments, we replace the visual encoder to our aligned version, without fine-tuning the LLM part. We discover the alignment improves most of the metrics, showing the generalization of our proposed framework.
+
+# 4.4. Ablation Studies
+
+We study the impact of various design choices through ablation studies, focusing on factors such as training epochs, loss function design, and the kernel functions utilized. Zeroshot object recognition accuracy serves as our evaluation metric, with results illustrated in Fig.3. Key takeaways include: (1) the method demonstrates optimal performance with a very short training duration; (2) the regularization term is crucial for preserving visual-language alignment; (3) the performance remains stable regardless of the coefficient  $w$ ; and (4) different kernels all contribute positively, with the polynomial kernel yielding the best results. A more comprehensive analysis can be found in Appendix C.7.
+
+# 5. Limitations & Conclusion
+
+In this study, we introduce a novel kernel-based embedding alignment strategy designed to align two sets of embeddings.
+
+Our evaluations on vision-centric tasks and MLLM benchmarks demonstrate that this alignment enhances the visual capabilities of CLIP, with benefits that inherit to downstream applications. Unlike most existing research which enhances the visual encoder but requires re-tuning of the LLM, our approach opens up a new research avenue to facilitate improvements through lightweight adaptation, making these advancements more accessible to a broader community.
+
+Due to the lack of computational resources, we align the embedding on a relatively small-scale dataset, and only evaluate the performance on small MLLMs. It can be left as a future work to conduct the fine-tuning on a larger scale datasets (Gadre et al., 2024) and verify the effects on MLLMs with larger size (e.g., 70B). Another limitation is that this work focuses on the alignment between CLIP and DINOv2. There are MLLMs that utilize vision encoders other than CLIP (Chen et al., 2024), and other of vision-centric models (Bao et al., 2022) available. We would extend the current pipeline to help align other embeddings pairs and bring improvements to more MLLMs.
+
+# Acknowledgements
+
+The work of Farzan Farnia is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by CUHK Direct Research Grants with CUHK Project No. 4055164 and 4937054. Also, this work is supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. T45-401/22-N). Finally, the authors would like to thank the anonymous reviewers for their insightful suggestions and feedback.
+
+# Impact Statement
+
+Our work enhances the capabilities of multi-modal large language models by improving visual perception through the alignment of visual representations. As shown in the experiments, we improve the performance on both general-purpose computer vision benchmarks and domain-specific applications including remote sensing and medical diagnosis. Therefore, Our method has the potential to significantly advance applications in areas such as autonomous systems and assistive technologies. This progress can lead to more accurate and context-aware AI systems, ultimately benefiting industries like healthcare, transportation, and education.
+
+# References
+
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+
+# A. Proofs of Propositions
+
+# A.1. Proof of Proposition 3.1.
+
+This is a conclusion derived from Vector Bernstein Inequality (Gross, 2011; Kohler & Lucchi, 2017), which shows that if  $X_{1}, \dots, X_{M}$  are independent vector-valued random variables with common dimension  $d$  and that each one is centered, uniformly bounded and also the variance is bounded above:
+
+$$
+\mathbb {E} \left[ x _ {m} \right] = 0 \text {a n d} \| X _ {m} \| _ {2} \leq \mu \text {a s w e l l a s} \mathbb {E} \left[ \| X _ {m} \| ^ {2} \right] \leq \sigma^ {2}. \tag {7}
+$$
+
+Let
+
+$$
+Z = \frac {1}{M} \sum_ {m = 1} ^ {M} X _ {m}, \tag {8}
+$$
+
+then we have for  $0 < \epsilon < \sigma^2 /\mu$
+
+$$
+P \left(\| Z \| _ {2} \geq \epsilon\right) \leq \exp \left(- \frac {M \epsilon^ {2}}{8 \sigma^ {2}} + \frac {1}{4}\right). \tag {9}
+$$
+
+By plugging in  $X_{m}$  with  $t(\theta ;I_{m_1},I_{m_2}) - \mathbb{E}[t(\theta)]$ , we have
+
+$$
+\underset {I _ {m _ {1}}, I _ {m _ {2}} \sim \mathcal {D} _ {\mathrm {d a t a}}} {\mathbb {E}} [ t (\theta ; I _ {m _ {1}}, I _ {m _ {2}}) ] - \mathbb {E} [ t (\theta) ] = 0, \tag {10}
+$$
+
+$$
+\left\| t \left(\theta ; I _ {m _ {1}}, I _ {m _ {2}}\right) - \mathbb {E} [ t (\theta) ] \right\| _ {2} \leq 8 L, \tag {11}
+$$
+
+$$
+\mathbb {E} [ \| t (\theta ; I _ {m _ {1}}, I _ {m _ {2}}) - \mathbb {E} [ t (\theta) ] \| _ {2} ^ {2} ] \leq 6 4 L ^ {2}. \tag {12}
+$$
+
+Therefore, we have:
+
+$$
+P \left(\left\| \frac {1}{M} \sum_ {m = 1} ^ {M} t \left(\theta ; I _ {m _ {1}}, I _ {m _ {2}}\right) - \mathbb {E} [ t (\theta) ] \right\| _ {2} \geq \epsilon\right) \leq \exp \left(- \frac {M \epsilon^ {2}}{5 1 2 L ^ {2}} + \frac {1}{4}\right). \tag {13}
+$$
+
+# A.2. Proof of Proposition 3.2.
+
+The proposition and the proof are adapted from (Schlarmann et al., 2024). We have
+
+$$
+\left| \cos \left(f _ {\theta_ {0}} (I), g (T)\right) - \cos \left(f _ {\theta} (I), g (T)\right) \right| = \left| \left\langle \frac {g (T)}{\| g (T) \| _ {2}}, \frac {f _ {\theta_ {0}} (I)}{\| f _ {\theta_ {0}} (I) \| _ {2}} - \frac {f _ {\theta} (I)}{\| f _ {\theta} (I) \| _ {2}} \right\rangle \right| \leq \left\| \frac {f _ {\theta_ {0}} (I)}{\| f _ {\theta_ {0}} (I) \| _ {2}} - \frac {f _ {\theta} (I)}{\| f _ {\theta} (I) \| _ {2}} \right\| _ {2}.
+$$
+
+For which we can get the two upper bounds:
+
+$$
+\left\| \frac {f _ {\theta_ {0}} (I)}{\| f _ {\theta_ {0}} (I) \| _ {2}} - \frac {f _ {\theta} (I)}{\| f _ {\theta} (I) \| _ {2}} \right\| _ {2} \leq \frac {1}{\| f _ {\theta} (I) \| _ {2}} \left[ \| f _ {\theta} (I) \| _ {2} - \| f _ {\theta_ {0}} (I) \| _ {2} \right] + \| f _ {\theta_ {0}} (I) - f _ {\theta} (I) \| _ {2}, \tag {14}
+$$
+
+$$
+\left\| \frac {f _ {\theta_ {0}} (I)}{\| f _ {\theta_ {0}} (I) \| _ {2}} - \frac {f _ {\theta} (I)}{\| f _ {\theta} (I) \| _ {2}} \right\| _ {2} \leq \frac {1}{\| f _ {\theta_ {0}} (I) \| _ {2}} \left[ \| f _ {\theta} (I) \| _ {2} - \| f _ {\theta_ {0}} (I) \| _ {2} \right] + \| f _ {\theta_ {0}} (I) - f _ {\theta} (I) \| _ {2}. \tag {15}
+$$
+
+According the triangle inequality:
+
+$$
+\left| \left| \right| f _ {\theta_ {0}} (I) \right| _ {2} - \left| \left| \right| f _ {\theta} (I) \right| _ {2} | \leq \left| \left| \right| f _ {\theta_ {0}} (I) - f _ {\theta} (I) \right| _ {2}, \tag {16}
+$$
+
+therefore, the upper bound holds:
+
+$$
+\left| \cos \left(f _ {\theta_ {0}} (I), g (T)\right) - \cos \left(f _ {\theta} (I), g (T)\right) \right| \leq \min  \left(\frac {2}{\| f _ {\theta} (I) \| _ {2}}, \frac {2}{\| f _ {\theta_ {0}} (I) \| _ {2}}\right) \| f _ {\theta_ {0}} (I) - f _ {\theta} (I) \| _ {2}. \tag {17}
+$$
+
+Remarks. This proposition demonstrates that minimizing the  $L_{2}$  distance between the visual representations before and after the alignment fine-tuning help directly preserve the visual-text alignment. This is different from previous work such as Xuhong et al. (2018); Li et al. (2020), which penalizes the  $L_{2}$ -norm of parameter changes during the fine-tuning phase. While their method effectively prevents overfitting to the target domain in transfer learning, our direct feature-based penalty measure aims to maintain zero-shot compatibility while enhancing fine-grained visual capabilities.
+
+# B. More Implementation Details
+
+# B.1. Hyper-parameters Setup.
+
+Here we provide more information on the implementation details. Specifically, the hyper-parameters used for the alignment fine-tuning is listed in Table 7. All the experiments are conducted on NVIDIA GeForce RTX 4090 GPUs.
+
+Table 7. Detailed hyper-parameter setups.  
+
+<table><tr><td>Hyper-parameters</td><td>ViT-B-16</td><td>ViT-L-14</td><td>ViT-L-14-336</td></tr><tr><td>coefficient w</td><td>0.5</td><td>0.5</td><td>1.0</td></tr><tr><td>number of GPUs</td><td>2</td><td>2</td><td>4</td></tr><tr><td>batch size</td><td>128</td><td>64</td><td>32</td></tr><tr><td>training epochs</td><td>2</td><td>2</td><td>4</td></tr><tr><td>optimizer</td><td colspan="3">AdamW (Loshchilov, 2017)</td></tr><tr><td>weight decay</td><td colspan="3">1e-4</td></tr><tr><td>β</td><td colspan="3">(0.9, 0.999)</td></tr><tr><td>learning rate</td><td colspan="3">1e-5</td></tr><tr><td>Scheduler</td><td colspan="3">CosineAnnealingLR</td></tr><tr><td>warm-up steps</td><td>1400</td><td>2800</td><td>5600</td></tr></table>
+
+# B.2. Illustration on Feature-based Alignment.
+
+A vanilla way to align the CLIP embedding  $f_{\theta}(I_i)$  with the embedding of the target model  $g(I_i)$  is to minimize the  $L_2$  distance between  $f_{\theta}(I_i)$  and  $g(I_i)$  subject to a linear transformation  $\mathbf{R} \in \mathbb{R}^{d \times d'}$ :
+
+$$
+\min  _ {\theta , \mathbf {R}} \underset {I _ {i} \sim \mathcal {D} _ {\text {t r a i n}}} {\mathbb {E}} [ w \| f _ {\theta} (I _ {i}) - \mathbf {R} g (I _ {i}) \| _ {2} ^ {2} + \| f _ {\theta} (I _ {i}) - f _ {\theta_ {0}} (I _ {i}) \| _ {2} ^ {2} ]. \tag {18}
+$$
+
+We call this method feature-based embedding alignment. This approach also makes sense and leads to certain improvements compared with the original visual embeddings of CLIP. However, the representation space of CLIP and the target model often vary significantly, which can hardly be adjusted via linear transformation. As a result, it is an sub-optimal solution. On the contrary, our kernel-based embedding alignment provides a more flexible solution. Firstly, comparing with absolute position within the feature space, the relative position among samples is more important. We would like the embeddings of two samples with similar visual characteristics to be close to each other. Using kernel function as supervision can directive promote this effects. Secondly, kernel function measures the similarity in the high-dimensional kernel space. Alignment of embeddings within the kernel space will not lead to drastic changes of the embeddings in the original feature space, making the image embeddings after alignment still compatible with text encoder and downstream modules. Moreover, our kernel-based alignment can actually be interpreted as aligning the representations in the kernel space. The feature transformation  $\phi$  for common kernels are usually non-linear. It renders more flexibility compared to the feature-based alignment which only use linear transformation.
+
+# B.3. Implementation Details for LLM's Fine-tuning.
+
+In this section, we elaborate on the implementation details of the LLM fine-tuning of LLaVA, which we used to further demonstrate the enhancement of the vision encoder with alignment. We employ the official implementation from LLaVA for LoRA fine-tuning. The training is conducted on a mixture of LLaVA-1.5 data for one epoch, using the following LoRA configuration:  $r = 128$  and  $\alpha = 256$ . The training is executed in bf16 format across four NVIDIA GeForce RTX 4090 GPUs, with a batch size of 1 per device. To address the small batch size, we apply a gradient accumulation step of 32. The optimizer used is AdamW (Loshchilov, 2017), set with a learning rate of 2e-4 and a weight decay of 0.
+
+# C. Additional Experimental Results
+
+# C.1. Loss Curve for the Alignment Term.
+
+We visualize the alignment loss (with moving average smoothing) during the fine-tuning phase in Fig. 4. We discover the loss term is stably decreasing during the fine-tuning phase, showing that the alignment term is indeed effectively optimized to improve the similarity between CLIP and DINOv2 representations.
+
+![](images/767e77bca0575c8cbd39732a4aa0a06b87abbe4c5bfaa5467cb9173b317c59e9.jpg)  
+Figure 4. Visualization of the alignment loss curve. The alignment loss is stably decreasing during the alignment fine-tuning phase.
+
+# C.2. Results for VLMs other than CLIP.
+
+To evaluate the generalization of our proposed framework, we conducted experiments on three additional models that feature an intermediate embedding layer connecting modalities, but with implementations distinct from CLIP: SigLIP (Zhai et al., 2023), DFN (Fang et al., 2023), and MetaCLIP (Xu et al., 2024). For all the VLMs, we utilized the ViT-L-14 version, maintaining the same implementation details as those for CLIP ViT-L-14. We assessed zero-shot accuracy across 12 datasets as our evaluation metric, with results presented in Table 8. The findings indicate that our alignment fine-tuning enhances zero-shot performance for all three models, yielding average increases of  $0.45\%$ ,  $0.48\%$ , and  $0.87\%$  respectively. These results highlight the generalizability of our framework, demonstrating that the alignment is applicable to VLMs beyond CLIP. Despite ongoing advancements in CLIP research, our proposed alignment remains adaptable and beneficial for these more advanced VLMs.
+
+Table 8. Accuracy evaluation on zero-shot image classification benchmarks of vision-language models w/wo alignment. We experiments with ViT-L-14 version of SigLIP (Zhai et al., 2023), DFN (Fang et al., 2023), and MetaCLIP (Xu et al., 2024).  
+
+<table><tr><td rowspan="2">Vision Encoder</td><td rowspan="2">ImageNet</td><td colspan="11">Zero-shot Datasets</td><td rowspan="2">Average Zero-shot</td></tr><tr><td>CIFAR10</td><td>CIFAR100</td><td>CaTech</td><td>FER</td><td>OxfordPets</td><td>DTD</td><td>RESISC</td><td>EuroSAT</td><td>PCAM</td><td>ImageNet-S</td><td>ImageNet-O</td></tr><tr><td>SigLip</td><td>82.02</td><td>96.87</td><td>84.27</td><td>86.01</td><td>49.90</td><td>95.31</td><td>71.06</td><td>72.59</td><td>62.65</td><td>50.55</td><td>74.02</td><td>29.60</td><td>70.26</td></tr><tr><td>+align</td><td>82.18</td><td>96.88</td><td>84.89</td><td>86.11</td><td>49.16</td><td>95.42</td><td>71.06</td><td>72.84</td><td>65.54</td><td>50.11</td><td>73.92</td><td>31.90</td><td>70.71</td></tr><tr><td>DFN</td><td>81.50</td><td>98.32</td><td>88.15</td><td>85.57</td><td>42.70</td><td>95.58</td><td>66.06</td><td>73.25</td><td>64.94</td><td>63.18</td><td>68.33</td><td>39.30</td><td>71.40</td></tr><tr><td>+align</td><td>81.28</td><td>98.12</td><td>87.82</td><td>85.49</td><td>44.27</td><td>95.39</td><td>66.70</td><td>73.76</td><td>65.44</td><td>62.90</td><td>68.40</td><td>42.35</td><td>71.88</td></tr><tr><td>MetaCLIP</td><td>75.58</td><td>95.67</td><td>77.72</td><td>85.74</td><td>37.96</td><td>93.81</td><td>62.34</td><td>68.52</td><td>60.41</td><td>70.35</td><td>65.05</td><td>28.90</td><td>67.86</td></tr><tr><td>+align</td><td>76.60</td><td>96.42</td><td>80.11</td><td>85.49</td><td>40.39</td><td>93.68</td><td>62.82</td><td>69.25</td><td>60.35</td><td>69.76</td><td>65.12</td><td>32.65</td><td>68.73</td></tr></table>
+
+# C.3. Results for Other Target Models.
+
+We also investigate the potential of replacing DINOv2 with alternative vision encoders to demonstrate the flexibility of our proposed framework. Specifically, we employed MLCD (An et al., 2024) as the target model, with results displayed in Table 9. The findings suggest that switching the target model from DINOv2 to other vision encoders can lead to significant improvements, highlighting the generalizability of our framework. As vision-centric self-supervised learning progresses and larger image datasets are developed, we expect to see the emergence of even more powerful vision encoders in the future. Our research establishes a foundation for utilizing these advanced encoders to enhance the performance of vision-language models and potentially benefit downstream MLLMs.
+
+Table 9. Accuracy evaluation on zero-shot image classification benchmarks of CLIP models w/wo alignment. We use MLCD instead of DINOv2 as the target model for alignment. The results show the alignment still show improvement when using different target model.  
+
+<table><tr><td rowspan="2">Vision Encoder</td><td rowspan="2">ImageNet</td><td colspan="11">Zero-shot Datasets</td><td rowspan="2">Average Zero-shot</td></tr><tr><td>CIFAR10</td><td>CIFAR100</td><td>CalTech</td><td>FER</td><td>OxfordPets</td><td>DTD</td><td>RESISC</td><td>EuroSAT</td><td>PCAM</td><td>ImageNet-S</td><td>ImageNet-O</td></tr><tr><td>ViT-L-14</td><td>74.90</td><td>95.20</td><td>71.08</td><td>83.30</td><td>50.00</td><td>93.21</td><td>55.21</td><td>63.35</td><td>62.65</td><td>52.00</td><td>59.59</td><td>32.25</td><td>65.26</td></tr><tr><td>+align</td><td>75.32</td><td>96.03</td><td>74.90</td><td>83.86</td><td>49.67</td><td>93.43</td><td>55.59</td><td>64.62</td><td>63.44</td><td>52.28</td><td>59.99</td><td>34.70</td><td>66.26</td></tr><tr><td>ViT-L-14-336</td><td>75.82</td><td>94.49</td><td>71.11</td><td>83.42</td><td>49.04</td><td>93.70</td><td>55.64</td><td>63.73</td><td>61.46</td><td>60.68</td><td>61.03</td><td>32.75</td><td>66.10</td></tr><tr><td>+align</td><td>76.18</td><td>95.90</td><td>76.70</td><td>83.53</td><td>49.00</td><td>94.06</td><td>56.60</td><td>63.90</td><td>61.54</td><td>60.66</td><td>61.57</td><td>36.30</td><td>67.25</td></tr></table>
+
+# C.4. Results on MMVP-VLM benchmarks.
+
+We conduct experiments on the MMVP-VLM benchmarks (Tong et al., 2024). The benchmark consists of "CLIP-blind pair" images, which the CLIP vision encoder recognizes as similar, despite notable visual differences. It is designed to test whether the CLIP model can differentiate between these pairs. The pairs encompass a range of visual patterns, including orientation and direction, the presence of specific features, state and condition, quantity and count, positional and relational context, color and appearance, structural and physical characteristics, text, and viewpoint and perspective. The results are detailed in Table 10. Findings indicate that the proposed alignment improves accuracy by  $2.97\%$ ,  $2.96\%$ , and  $2.22\%$  for three variants of CLIP models. These results demonstrate that aligning with DINOv2 helps address the limitations of CLIP in these challenging cases.
+
+Table 10. Performance of CLIP on various visual patterns of MMVP-VLM benchmark. Alignment with DINOv2 embeddings greatly overcomes CLIP's original shortcomings in terms of perceiving visual details. Symbols for visual patterns as (Tong et al., 2024) are inherited:  $\bullet$ : Orientation and Direction,  $\mathbf{Q}$ : Presence of Specific Features,  $\mathbf{\Phi}$ : State and Condition,  $\uparrow \uparrow$ : Quantity and Count,  $\mathbf{\Phi}$ : Positional and Relational Context,  $\mathbf{\Phi}$ : Color and Appearance,  $\mathbf{\Phi}$ : Structural and Physical Characteristics,  $\mathbf{A}$ : Texts,  $\mathbf{\Phi}$ : Viewpoint and Perspective.  
+
+<table><tr><td colspan="2">Vision Encoder</td><td>Q</td><td>G</td><td>↑3</td><td>1</td><td>P</td><td>A</td><td>0</td><td>Average</td></tr><tr><td rowspan="2">ViT-B-16</td><td>w/o align</td><td>6.67</td><td>0.00</td><td>26.67</td><td>13.33</td><td>13.3</td><td>20.00</td><td>13.33</td><td>20.00</td></tr><tr><td>w/ align</td><td>6.67</td><td>0.00</td><td>20.00</td><td>13.33</td><td>20.00</td><td>26.67</td><td>26.67</td><td>26.67</td></tr><tr><td rowspan="2">ViT-L-14</td><td>w/o align</td><td>6.67</td><td>13.33</td><td>20.00</td><td>13.33</td><td>6.67</td><td>53.33</td><td>26.67</td><td>13.33</td></tr><tr><td>w/ align</td><td>13.33</td><td>20.00</td><td>20.00</td><td>20.00</td><td>6.67</td><td>53.33</td><td>33.33</td><td>20.00</td></tr><tr><td rowspan="2">ViT-L-14-336</td><td>w/o align</td><td>0.00</td><td>20.00</td><td>40.00</td><td>20.00</td><td>6.67</td><td>20.00</td><td>33.33</td><td>19.26</td></tr><tr><td>w/ align</td><td>6.67</td><td>26.67</td><td>40.00</td><td>13.33</td><td>6.67</td><td>40.00</td><td>26.67</td><td>21.48</td></tr></table>
+
+# C.5. Results on MMVP benchmarks.
+
+We also conducted experiments on the MMVP benchmarks (Tong et al., 2024), which are similar to the MMVP-VLM benchmark but evaluate through VQA on MLLMs. For this experiment, we used LLaVA-1.5-7B with CLIP ViT-L-14-336 as the visual encoder. The results are shown in Table 11. We found that the proposed alignment framework significantly
+
+enhances the performance of LLaVA, leading to a marked reduction in error rates for these challenging cases. Improvements were observed simply by replacing the vision encoder with the aligned version, and the gains were even more pronounced when we fine-tuned the LLM component as well. These results further confirm that the enhanced visual capabilities of CLIP can be effectively transferred to downstream MLLMs.
+
+Table 11. Performance of LLaVA on MMVP benchmark. The performance improves when we replace the visual encoder with the aligned version. This indicates that alignment enhances visual capabilities, and this effect can be carried over to downstream tasks.  
+
+<table><tr><td>Vision Encoder</td><td>CLIP</td><td>CLIP+align</td><td>CLIP+align+peft</td></tr><tr><td>Accuracy (%)</td><td>23.33</td><td>24.67</td><td>34.00</td></tr></table>
+
+# C.6. Additional Baselines
+
+In this section, we compare our method with two additional baselines, which also entail integrating knowledge from multiple experts to build a stronger visual encoder.
+
+Comparison with AM-RADIO (Ranzinger et al., 2024). AM-RADIO distills knowledge from multiple teacher models into a student model, delivering strong performance across various downstream tasks. However, the original AM-RADIO model is trained on DataComp-1B, a dataset consisting of 13 billion samples. This training process requires computational resources comparable to the pre-training of CLIP, making it highly resource-intensive. In contrast, our proposed kernel-based alignment method achieves strong accuracy and generalizability through fine-tuning on relatively small datasets, such as ImageNet-1k, over just a few epochs. To provide a clearer comparison, we follow the AM-RADIO training protocol and train a model on ImageNet-1k using CLIP and DINOv2 as teacher models (both employing ViT-L-14 backbones), with another ViT-L-14 as the student model. We then evaluate its zero-shot classification performance, as shown in Table 12. The results reveal that AM-RADIO struggles to generalize to out-of-distribution datasets under this setup. In contrast, our alignment method achieves both strong performance and superior generalizability, even with limited data and computational resources.
+
+Table 12. Comparison between our alignment fine-tuning and AM-RADIO. Our method represent better performance when the training data is limited.  
+
+<table><tr><td rowspan="2">Vision Encoder</td><td rowspan="2">ImageNet</td><td colspan="11">Zero-shot Datasets</td><td rowspan="2">Average Zero-shot</td></tr><tr><td>CIFAR10</td><td>CIFAR100</td><td>CaTech</td><td>FER</td><td>OxfordPeds</td><td>DTD</td><td>RESISC</td><td>EuroSAT</td><td>PCAM</td><td>ImageNet-S</td><td>ImageNet-O</td></tr><tr><td>AM-RADIO</td><td>75.38</td><td>95.04</td><td>71.48</td><td>78.47</td><td>25.66</td><td>83.62</td><td>45.37</td><td>38.48</td><td>31.35</td><td>50.02</td><td>51.34</td><td>69.45</td><td>58.21</td></tr><tr><td>Ours</td><td>75.52</td><td>96.27</td><td>77.04</td><td>84.32</td><td>50.31</td><td>93.40</td><td>55.74</td><td>63.83</td><td>63.83</td><td>52.68</td><td>59.67</td><td>34.90</td><td>66.54</td></tr></table>
+
+Comparison with Additive-MoF (Tong et al., 2024). We also compare our method with Additive-MoF, a straightforward approach to combining visual representations from different visual encoders for MLLM applications. This comparison is conducted on vision-language benchmarks using the LLaVA implementation, with the results presented in Table 13. While Additive-MoF achieves better performance in certain tasks, such as object detection, it performs suboptimally in others, such as open-ended visual question answering. As highlighted in the original paper (Tong et al., 2024), simply combining CLIP and DINOv2 features involves an inherent trade-off between visual grounding accuracy and instruction-following capability. In contrast, our alignment fine-tuning approach enhances visual capabilities while maintaining strong alignment with the textual embedding space. Additionally, our framework does not require full re-tuning of the LLM component, making it particularly beneficial in resource-limited settings.
+
+Table 13. Comparison between Additive-MoF and ours on vision-language benchmarks. Our alignment fine-tuning approach achieves enhanced visual capabilities without compromising alignment to the textual embedding space  
+
+<table><tr><td>Vision Encoder</td><td>A12D</td><td>text-ocr</td><td>text-Pure</td><td>pope</td><td>tallyQA</td><td>vSR</td><td>RefCOCOg</td><td>RefCOCO+</td><td>RefCOCO</td><td>vqa-v2</td><td>IIava-wild</td><td>IIava-coco</td><td>Average</td></tr><tr><td>Additive-MoF</td><td>51.36</td><td>45.93</td><td>18.66</td><td>86.58</td><td>63.18</td><td>51.47</td><td>68.44</td><td>65.34</td><td>69.69</td><td>75.12</td><td>41.54</td><td>74.50</td><td>59.32</td></tr><tr><td>Ours</td><td>53.95</td><td>58.89</td><td>50.51</td><td>86.05</td><td>62.14</td><td>52.55</td><td>58.68</td><td>57.74</td><td>65.79</td><td>76.97</td><td>52.20</td><td>78.90</td><td>62.86</td></tr></table>
+
+# C.7. Analysis of Ablation Studies
+
+We conduct several ablation studies to examine the effects of several design choices in our framework. The experiments are performed with CLIP ViT-L-14, and average zero-shot accuracy across 11 datasets are used as evaluation metrics.
+
+![](images/ce9e95666d3a9ae7966573e038ab3265914e0651788b4bf08d687605de526e36.jpg)  
+Figure 5. Ablation studies. Average zero-shot accuracy across 11 datasets are reported as evaluation metrics: (a) Effects of training epochs; (b) Effects of the regularization term; (c) Effects of the coefficients of alignment; (d) Effects of different kernel functions.
+
+![](images/8b085cb06c83d404bab5783b4904fd1985155d9e1d8663e98c40b012a57769e7.jpg)
+
+![](images/675aeef6af4cffb96c01f432b0fd2a6b3bb8ad62942bebbfb5ef005543dd9ef1.jpg)
+
+![](images/b8d247e68c04e3017b43b190e5655b6b2e7f29ab13bb59f81b713b6ccd336f13.jpg)
+
+Effects of Training Epochs. We experiments with fine-tuning for more epochs to see how it affects the performance. The results are shown in Fig. 5 (a). We find that the performance stabilizes after training for 2 epochs. Further training leads to no improvements. This finding highlights the effectiveness of our proposed method, which achieves strong performance with a minimal training time.
+
+Effects of Regularization. We also conducted an ablation study on the regularization term in Eq. 6, specifically fine-tuning the CLIP model using only the kernel alignment term. The results are shown in Fig. 5 (b). Without this regularization term, we observe a significant drop in performance, with zero-shot accuracy even worse than that of the original CLIP model. This indicates that the regularization is crucial for maintaining alignment with the text embeddings. Only when both terms are utilized does the alignment phase achieve an effective balance between fine-grained visual capability and compatibility with text semantics.
+
+Effects of Coefficients. We then tested various coefficients  $w$  for the alignment term in Eq. 6, experimenting with values of 0.1, 0.5, 1.0, 5.0, and 10.0. The results are presented in Fig. 5 (c). We found that performance remains relatively stable across these coefficient changes. In our experiments, a coefficient of 1.0 yielded the best performance, effectively balancing alignment with the DINOv2 representation and compatibility with the text encoder.
+
+Selection of Kernel Function. For the main experiment, we employed a normalized polynomial kernel for alignment and also tested the Gaussian kernel and cosine kernel, with results shown in Fig. 5 (d). Our findings indicate that all three kernels lead to performance improvements, with the polynomial kernel achieving the best results. The Gaussian kernel encounters gradient vanishing issues, complicating the optimization process, while the cosine kernel lacks additional parameters to flexibly address differences in feature dimensions and structures, making them sub-optimal compared to the polynomial kernel. One potential avenue for future improvement is to explore more diverse kernel functions or to combine multiple kernel functions as a compositional kernel for alignment.
+
+Effects of the dataset size. We investigate how the size of the fine-tuning dataset impacts model performance. To this end,
+
+we perform ablation studies using  $25\%$  and  $50\%$  of the ImageNet dataset for fine-tuning. The results, presented in Table 14, indicate that our alignment fine-tuning consistently enhances model performance, even when only  $25\%$  of the samples are used, demonstrating the method's efficiency. Furthermore, the performance improvement grows as the amount of fine-tuning data increases, highlighting the potential for further gains when larger datasets are utilized.
+
+Table 14. Ablation study in terms of fine-tuning data size. We conduct the alignment fine-tuning with different proportions of ImageNet data. The model demonstrates consistent performance gain, and the performance improves as more data is incorporated.  
+
+<table><tr><td rowspan="2">Proportion</td><td rowspan="2">ImageNet</td><td colspan="11">Zero-shot Datasets</td><td rowspan="2">Average Zero-shot</td></tr><tr><td>CIFAR10</td><td>CIFAR100</td><td>CaTech</td><td>FER</td><td>OxfordPets</td><td>DTD</td><td>RESISC</td><td>EuroSAT</td><td>PCAM</td><td>ImageNet-S</td><td>ImageNet-O</td></tr><tr><td>0%</td><td>74.90</td><td>95.20</td><td>71.08</td><td>83.30</td><td>50.00</td><td>93.21</td><td>55.21</td><td>63.35</td><td>62.65</td><td>52.00</td><td>59.59</td><td>32.25</td><td>65.26</td></tr><tr><td>25%</td><td>75.08</td><td>95.84</td><td>74.13</td><td>83.89</td><td>50.59</td><td>93.40</td><td>55.32</td><td>64.33</td><td>61.54</td><td>52.02</td><td>59.96</td><td>35.30</td><td>66.03</td></tr><tr><td>50%</td><td>75.34</td><td>95.87</td><td>76.05</td><td>83.91</td><td>50.29</td><td>93.59</td><td>55.90</td><td>64.41</td><td>64.00</td><td>52.53</td><td>59.98</td><td>34.75</td><td>66.48</td></tr><tr><td>100%</td><td>75.52</td><td>96.27</td><td>77.04</td><td>84.32</td><td>50.31</td><td>93.40</td><td>55.74</td><td>63.83</td><td>63.83</td><td>52.68</td><td>59.67</td><td>34.90</td><td>66.54</td></tr></table>

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2025/KinDEL_ DNA-Encoded Library Dataset for Kinase Inhibitors/fc2388dc-2aed-439e-b69c-7502bf634cf6_origin.pdf

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2025/KinDEL_ DNA-Encoded Library Dataset for Kinase Inhibitors/full.md

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+# KinDEL: DNA-Encoded Library Dataset for Kinase Inhibitors
+
+Benson Chen  $^{*1}$  Tomasz Danel  $^{*1}$  Gabriel H. S. Dreiman  $^{1}$  Patrick J. McEnaney  $^{1}$  Nikhil Jain  $^{1}$  Kirill Novikov  $^{1}$  Spurti Umesh Akki  $^{1}$  Joshua L. Turnbull  $^{1}$  Virja Atul Pandya  $^{1}$  Boris P. Belotserkovskii  $^{1}$  Jared Bryce Weaver  $^{1}$  Ankita Biswas  $^{1}$  Dat Nguyen  $^{1}$  Kent Gorday  $^{1}$  Mohammad Sultan  $^{1}$  Nathaniel Stanley  $^{1}$  Daniel M Whalen  $^{1}$  Divya Kanichar  $^{1}$  Christoph Klein  $^{1}$  Emily Fox  $^{1}$  R. Edward Watts
+
+# Abstract
+
+DNA-Encoded Libraries (DELs) represent a transformative technology in drug discovery, facilitating the high-throughput exploration of vast chemical spaces. Despite their potential, the scarcity of publicly available DEL datasets presents a bottleneck for the advancement of machine learning methodologies in this domain. To address this gap, we introduce KinDEL, one of the largest publicly accessible DEL datasets and the first one that includes binding poses from molecular docking experiments. Focused on two kinases, Mitogen-Activated Protein Kinase 14 (MAPK14) and Discoidin Domain Receptor Tyrosine Kinase 1 (DDR1), KinDEL includes 81 million compounds, offering a rich resource for computational exploration. Additionally, we provide comprehensive biophysical assay validation data, encompassing both on-DNA and off-DNA measurements, which we use to evaluate a suite of machine learning techniques, including novel structure-based probabilistic models. We hope that our benchmark, encompassing both 2D and 3D structures, will help advance the development of machine learning models for data-driven hit identification using DELs.
+
+# 1. Introduction
+
+DNA-Encoded Libraries (DEL) have emerged as a powerful tool in drug discovery, enabling highly efficient screens of small molecule libraries against therapeutically relevant targets (Yuen & Franzini, 2017; Gironda-Martínez et al., 2021; Kunig et al., 2021; Peterson & Liu, 2023). These massive libraries are efficiently constructed through combinatorial
+
+*Equal contribution 1Insitro, South San Francisco, CA 94080, USA. Correspondence to: Benson Chen <benatorc@gmail.com>, Tomasz Danel <tomek@insitro.com>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+![](images/fdc0bd3a6ce8c43173e0f26c0358616d1f593495bb2f62412665aa4eaf333801.jpg)  
+Figure 1: (Top) DELs are synthesized in a sequential manner; at every step, the DNA codon specifies the next building block (synthon) to be attached. (Bottom) An example of a fully synthesized DEL molecule, with the building blocks and codons colored-coded for visualizability. Typically, there is also a linker that connects the molecule to the DNA, which here is a 6-carbon chain.
+
+synthesis of chemical building blocks, or synthons, with each resulting molecule being assigned a DNA barcode (see Figure 1). DELs are then used in selection experiments where they are mixed with proteins of interest bound to a matrix. Multiple rounds of washing are conducted to remove any weak binders, and the DNA tags of surviving molecules are sequenced as a measure of binding affinity. Data generated through these experiments are intrinsically noisy with various sources of bias arising from the DEL synthesis and selection processes, suggesting that modern machine learning methods may be needed to learn signal from the data. Unfortunately, there is still a lack of large, publicly available DEL datasets and benchmarking tasks to drive this important research area.
+
+The growing interest in utilizing DEL data for modeling is evidenced by the many recent efforts to advance this area (Iqbal et al., 2024; Blevins et al., 2024; Gu et al., 2024). One of the primary reasons for this interest is that selection experiments using DELs alleviate some of the data limitations typical of the field; most chemistry problems in the machine learning domain lack consistent and sufficiently
+
+high-quality labels. In particular, DELs can contain billions of compounds, and require fewer resources to run compared to more traditional high-throughput screens (Peterson & Liu, 2023). However, the process of DEL synthesis and selection introduces various sources of bias that can add noise to the observed data. For instance, DEL experiments measure the affinity of molecules while they are attached to a DNA barcode (hence, on-DNA binding). In contrast, during a real therapeutic campaign, drug-like molecules are tested without a DNA tag (off-DNA), meaning the DEL data is biased by the DNA and the molecule's attachment to it. Moreover, uncertainties in reaction yields and biases in polymerase chain reaction (PCR) amplification add additional noise to the process. These difficulties have fueled an increasing enthusiasm within the community for developing structured computational models to more effectively interpret the data signals.
+
+Despite these challenges, several efforts have demonstrated successful applications of machine learning to DEL data (McCloskey et al., 2020). These early successes suggest that there is still much to explore in this domain. Currently, most methods have focused purely on discriminative modeling, which plays a crucial role in drug discovery campaigns by ranking prospective compounds in order to select potential hits. These prediction methods typically utilize established architectures, building upon both molecular fingerprints and more sophisticated graph convolutional networks (Duvenaud et al., 2015). More recently, efforts have been made to pose the problem in a probabilistic manner, directly incorporating experimental uncertainty in the model structure (Chen et al., 2024). These models leverage the fact that, while individual data points may be noisy, it is generally expected that groups of molecules with the same synthons or substructures will show enrichment, or signal, when analyzed collectively. Additionally, DEL data can be employed for generative modeling, providing weak supervision to navigate the complex chemical landscape, which is valuable for lead optimization steps of drug discovery.
+
+To demonstrate the advantages of DEL data and promote development of the methods described above, we release KinDEL (Kinase Inhibitor DNA-Encoded Library) as library of 81 million small molecules tested against two kinase targets, MAPK14 and DDR1. Our dataset, distinguished by its high consistency across experimental replicates (see Appendix B), provides a large amount of supervised data for the machine learning community to develop methods for solving small molecule chemistry problems in drug discovery.
+
+In addition to the KinDEL dataset, we provide a set of benchmark tasks validated using biophysical assay data, which we also release publicly. A major challenge in driving research in this area has been the dearth of benchmark
+
+tasks to demonstrate the efficacy of using DEL data in deriving therapeutic insights. By releasing these benchmarks, we aim to facilitate the comparison of various modeling techniques currently applied to DELs. To seed these benchmarks, we survey computational methods from the literature and build predictive models, validated through biophysical data from compounds independently resynthesized both on- and off-DNA. Since DEL data primarily captures on-DNA binding events, but our interest lies in off-DNA binding affinity, these additional data are crucial for assessing the models' generalizability to diverse biophysical data. Our studies show that models built on DEL data can effectively characterize both on- and off-DNA affinities, highlighting the usefulness of DEL data in drug discovery. We hope that KinDEL serves as a public resource that can facilitate the iterative refinement of chemical models by providing supervised data in densely sampled chemical spaces. Data and code for our benchmarks can be found at https://github.com/insitro/kindel.
+
+# 2. Dataset
+
+We first introduce a high level summary of the dataset generation, and then provide an overview of the data that we publicly release. The data generation is divided into roughly three experimental processes, which are the synthesis of the DEL, the subsequent selection experiments against proteins of interest, and the biophysical assays to collect validation data. Specific experimental details can be found in Appendix A.
+
+# 2.1. Data Generation
+
+DEL Synthesis The DEL is built as a trisynthon library with 378 synthons in the A position, 1128 synthons in the B position, and 191 synthons in the C position. The synthesis is a sequential process, with each synthon specified by the DNA tag and added one at a time. Notably, each molecule does not have only a single encoding; instead, multiple encodings of DNA map to the same final molecular structure. These redundant encodings help mitigate potential biases during the subsequent DNA sequencing step. Rather than counting the total number of amplified DNA associated with a single molecule (which is subject to PCR noise), we count the number of different redundant encodings observed for each molecule. This library was designed to enhance scaffold uniqueness and chemical diversity, thereby exploring a broader region of chemical space. A simplified diagram of synthesis can be found in Figure 1.
+
+DEL Selection DEL Selection was performed by combining the DEL with the target proteins, which were immobilized on beads, as well as a negative control without any protein. Multiple rounds of washes removed any weak binders in the solution. The molecules were then extracted via elution,
+
+![](images/e5524faa8d003fdb8c2c8c80008aa503f831b3b983c56f463e999264137a21e4.jpg)  
+(a) Panning experiment
+
+![](images/1c222d42b7f373564f6999bc6029fda8e285645350ffb8ffa7663b3b4fb7b430.jpg)  
+(b) Data structure  
+Figure 2: KinDEL data acquisition process. (a) DEL selection experiments are conducted by combining the DEL with the protein target of interest immobilized onto Streptavidin beads. After multiple rounds of washing, the tight binders are eluted off of the protein, and their corresponding DNA are sequenced to obtain the count data. (b) Molecules in the dataset are represented as separate synthons A, B, and C and the combined product. The labels for each compound include the pre-selection counts measured before panning and read counts for the targets and the matrix measured in triplicate.
+
+and the subsequent samples were then amplified via PCR and sequenced to obtain the count data. Each selection was performed in triplicate with each protein. This process is visualized in Figure 2.
+
+Biophysical Assay Validation Additional biophysical data on a small subset of molecules were collected both on- and off-DNA (see Appendix C for more details on how these molecules were selected). For on-DNA data, we use Fluorescence Polarization (FP), which utilizes polarized light to quantify binding affinity by measuring the dissociation constant  $(K_{D})$ . For off-DNA data, we use Surface Plasmon Resonance (SPR), which also relies on light to measure the dissociation constant. The reason we collect both types of data is because on-DNA  $K_{D}$  data reveals insights about the actual binding of the molecule in the DEL selection experiment, while off-DNA  $K_{D}$  focuses on interactions of the molecules without a DNA barcode, which is the relevant setting for an actual drug candidate.
+
+# 2.2. Data Overview
+
+DEL Data KinDEL contains count data for more than 81M unique molecules used in selection experiments with two proteins MAPK14 and DDR1. Typically, DEL experiments are run with a negative control without the protein, so that non-specific binding events (such as binding directly to
+
+bead) can be captured. In our dataset we provide three (3) replicates of data for each of the control and the protein target conditions. As mentioned earlier, raw DNA counts can be noisy due to PCR amplification bias (Aird et al., 2011; Kebschull & Zador, 2015), so we use the sequence count information as data, which measures the number of unique DNA sequences observed for each molecule.
+
+Pre-selection Data Additionally, we provide data about the sequenced library itself, called pre-selection data, which provides a rough estimate of the relative abundance of each molecule prior to any experimental run. During the synthesis of the DNA-encoded library, not all molecules are produced in equal amounts. Variability can arise from differences in synthesis efficiency, coupling yields, or synthesis errors. Additionally, some molecules may precipitate or adhere to storage containers, resulting in loss and lower observed counts. Due to the size of the library, it is too costly to sequence the library deeply enough for an extremely accurate pre-selection estimate. However, because there is always some amount of synthesis noise, for instance using impure reactants or having incomplete reaction yields, achieving a precise measurement of the pre-selection data is not imperative. While this data is typically used to normalize counts, sequencing inaccuracies can lead to error propagation, especially for low-abundance molecules.
+
+![](images/d876877842130956da1773a3a445abb32b8a479c5fe57b6ba8933cf3730e3dd0.jpg)
+
+![](images/fca643da1bb46fd8bd6f0c4a6f1041bd5d405e8a5145755898b15c64c44680a0.jpg)
+
+![](images/3f6f73a99789ca2b045b4449183ad3d5f4a439a6aedd93ba8011ca21e364f422.jpg)
+
+![](images/b263e138db25f690e9ba0383300569e2a1465edd6b91c453c4aa5e7903806ae4.jpg)
+
+![](images/bb5bbbe70e2dfa1463c04c38fa95279cc64bffebc8d158d3b71e783725f7cb84.jpg)
+
+![](images/719485a5f444d204f1f1b4689e5fb6109c6bf2c512c3ab66277a014adad3d3bd.jpg)  
+Figure 4: The 3D cube visualization of the dataset, where each axis corresponds to a different synthon in the DEL. Points in the plot are the most enriched compounds (measured using Poisson enrichment). The linear patterns can be interpreted as enriched disynthons, i.e. combinations of two synthons that often bind to the protein target.
+
+![](images/6982964bb0876d9ff4cd692fc924cc87ea73de34e8a395fe712c3360578a6b97.jpg)  
+Figure 3: The distributions of chemical properties in the KinDEL dataset. These selected properties are often used to assess the druglikeness of molecules. The light blue areas mark the 10th and 90th percentiles computed for all the FDA approved oral new chemical entities, as reported by Shultz (2018). QED: quantitative estimate of druglikeness (Bickerton et al., 2012).
+
+![](images/dd8faedf4942283f01305189994f44b9addbc93a4e1a32d90036319ba5902b53.jpg)
+
+![](images/e999342b0c93d7da28dfb3d1f29bf52d79305b4105417c9ad95a958f3c4142a9.jpg)
+
+Biophysical Assay Data We have collected data from 30-50 molecules using the aforementioned biophysical assays, FP and SPR, to validate our models. For molecules on-DNA, we have resynthesized molecules both from within and from outside our library. For off-DNA compounds, we have only resynthesized molecules that are within the DEL itself. These molecules were primarily selected from the top hits predicted from models trained on the DEL data.
+
+Figure 3 illustrates various properties of the molecules in our dataset, comparing them to those of typical drug-like molecules. From this, we can see that KinDEL is well-posed within typical drug-like distributions according to an analysis by (Shultz, 2018). Notably, over  $30\%$  of the molecules in our library fall within the property ranges of already approved drugs, as outlined by Schultz. While certain synthon combinations may result in compounds that fall outside these preferred ranges, DEL molecules primarily serve to provide initial hits for drug discovery campaigns. These initial hits undergo iterative refinement during the hit-to-lead optimization process.
+
+# 3. Benchmarking
+
+# 3.1. Experimental Setup
+
+One primary use case of DEL data is building predictive models of binding affinity. To that end, we investigate commonly used models in DEL literature as benchmark models
+
+![](images/dab551d81fa4b25004cb8544f747c81da5f1bca78fc547b387a67e13d129e699.jpg)  
+(a) MAPK14
+
+![](images/785c25e563491e2960f9f08139eb6e03b9300814e56d0d0d446bed97e3376245.jpg)  
+(b) DDR1
+
+and compare their performance in modeling binding affinity. In this benchmark, all models were trained using the top 1M compounds with the highest counts from our KinDEL dataset. We publish the full library to enable construction of further benchmarks.
+
+Held-out Test Set The observed count data in DEL experiments are an approximation of the true on-DNA binding affinity  $(K_{D})$ . The count data are influenced by multiple sources of noise (see Section 4). We ultimately wish to rank molecules by binding affinity, so we use compounds with measured  $K_{D}$  (from biophysical assays) as a test set. Performance on these compounds assesses if the models correctly rank compounds by  $K_{D}$ . This can be viewed as measuring how well models can remove the noise inherent to DELs.
+
+For both our targets, MAPK14 and DDR1, the selected compounds contained in the DEL library were resynthesized on- and off-DNA to create an in-library held-out test set. For hit finding, we would like to be able to predict off-DNA  $K_{D}$ . This is challenging because the DEL data comes from DNA bound molecules, and is biased by the DNA. The on-DNA  $K_{D}$  more closely aligns with DEL data since the molecules in the training data are bound to the same DNA in the same way. A few additional compounds were added from outside the library (and tagged with DNA) to create an additional held-out test set that we refer to as "Extended". The  $K_{D}$  data from these biophysical assays are also released with our dataset. A UMAP visualization of the DEL including the in-library and external test set compounds is depicted in Figure 5.
+
+Data Splits We split our datasets using three strategies, ensuring that all held-out compounds are placed in the test set and not used for training. The first type of data split is a random split, where a randomly selected  $10\%$  of compounds
+
+![](images/7cfad8a40162d8aae8005136b3c39360c96776d7c5772fc1f81d72b0c30dc408.jpg)  
+Figure 5: UMAP visualization of KinDEL constructed using Tanimoto distances between compounds. The compounds selected for the held-out testing set are depicted as orange diamonds (in-library) and green triangles (external).
+
+![](images/46a4d69deeeed58d06a9b95ebbb7bf14f371b73b742f89bb17fc0c2fc9005a93.jpg)  
+Figure 6: Three data splitting strategies used to construct the testing set.
+
+are placed in the validation set, and another randomly selected  $10\%$  are placed in the test set. The second type of data split is a disynthon split, where we sample disynthon structures (molecules with the same 2 synthons), and put all compounds containing these sampled structures in the same subset using the same 80-10-10 ratio between the training, validation, and test sets. This data partitioning method is more challenging for the machine-learning models because some synthon combinations tend to have a binding profile distinct from the individual synthons they consist of (see Figure 4). The third approach is a cluster split based on compound similarity. The details about the clustering algorithm can be found in Appendix E. The types of data splits are illustrated in Figure 6. Each dataset is split five times for each splitting strategy, and the reported performance of the models is aggregated over five training runs.
+
+Evaluation Metrics Models trained on DEL data typically predict an enrichment score, which can be regarded as a measure of binding affinity. To evaluate different baselines, we compare how well each method's predicted enrichment scores correlate with experimental  $K_{D}$  values for the molecules in the held-out test set. Since different models
+
+are trained with different losses, this is a consistent way to compare model performance. Here, we use Spearman correlation, because we are primarily concerned with the ability of a model to rank order molecules by their binding affinity.
+
+# 3.2. Benchmark Models
+
+In this benchmark, we compare models commonly used for DEL data in the literature. These methods follow a similar paradigm, in which the models try to learn the protein binding signal in the target data by subtracting out noise from the control data. Two baselines are included to gauge the alignment in the actual data, between the DEL counts and validation  $K_{D}$  values. The first baseline, count enrichment, computes an enrichment score by subtracting the average control counts from the average target counts. The second baseline, Poisson enrichment, computes a ratio of fitted Poisson distributions of the target and control data (Gerry et al., 2019).
+
+Next, we compare ML models trained on the data to predict the aforementioned Poisson enrichment using a mean-squared error (MSE) loss. These models include: random forest (RF) (Breiman, 2001), XGBoost (Chen & Guestrin, 2016), k-nearest neighbors (kNN) (Fix & Hodges, 1989), and a deep neural network (DNN) using Morgan fingerprints (radius=2, length=2048) (Rogers & Hahn, 2010) from RDKit (Landrum, 2010) as input features. We also tested two molecular graph models, Graph Isomorphism Network (GIN) (Xu et al., 2018) and Chemprop DMPNN (Heid et al., 2023). DEL-Compose (Chen et al., 2024) is a probabilistic model that uses Morgan fingerprints as input and predicts the parameters of a zero-inflated Poisson distribution to maximize the likelihood of the observed count data. We train two variants of DEL-Compose, one with only full molecule structures (DEL-Compose $^{(M)}$ ), and one with synthon structures (DEL-Compose $^{(S)}$ ). The hyperparameters of all the models used in this study are presented in Appendix D.
+
+The architectures of the neural network models follow the implementation in the original publications. The DNN architecture contains multiple linear layers with ReLU activation, batch normalization, and dropouts after each layer except for the last one (see Appendix D). All neural networks were trained using the Adam optimizer until convergence with early stopping when the validation loss does not improve for more than 5 epochs.
+
+# 3.3. Benchmark Results
+
+Tables 1 and 2 show the performance of various models on MAPK14 and DDR1, respectively. The number of data points  $(n)$  in each held-out test set is also reported in the tables. The Counts and Poisson enrichment baselines serve as an estimate of the alignment between DEL screening
+
+Table 1: Model performance evaluation for MAPK14. The test loss column contains values of the loss function computed on test split. The performance for the on- and off-DNA "In-Library" is the negative Spearman correlation between model predictions and experimental  $K_{D}$  for compounds resynthesized from the DEL. The performance for on-DNA "Extended" set includes additional compounds resynthesized on-DNA but not in the original DEL.  
+
+<table><tr><td rowspan="2">Split</td><td rowspan="2">Model</td><td rowspan="2">Test Loss ↓</td><td colspan="2">In-Library</td><td rowspan="2">Extended on-DNA Spearman&#x27;s ρ ↑ n = 30 Spearman&#x27;s ρ ↑ n = 33 Spearman&#x27;s ρ ↑ n = 41</td></tr><tr><td>on-DNA Spearman&#x27;s ρ ↑ n = 30</td><td>off-DNA Spearman&#x27;s ρ ↑ n = 33</td></tr><tr><td></td><td>Counts</td><td>-</td><td>0.778</td><td>0.353</td><td>-</td></tr><tr><td></td><td>Poisson</td><td>-</td><td>0.737</td><td>0.166</td><td>-</td></tr><tr><td rowspan="8">random</td><td>RF</td><td>0.064 ± 0.003</td><td>0.694 ± 0.030</td><td>0.370 ± 0.111</td><td>0.453 ± 0.028</td></tr><tr><td>XGBoost</td><td>0.056 ± 0.002</td><td>0.477 ± 0.009</td><td>0.345 ± 0.036</td><td>0.196 ± 0.074</td></tr><tr><td>kNN</td><td>0.072 ± 0.002</td><td>0.649 ± 0.041</td><td>0.466 ± 0.103</td><td>0.464 ± 0.040</td></tr><tr><td>DNN</td><td>0.139 ± 0.010</td><td>0.582 ± 0.062</td><td>0.514 ± 0.071</td><td>0.351 ± 0.058</td></tr><tr><td>GIN</td><td>0.062 ± 0.004</td><td>0.511 ± 0.038</td><td>0.492 ± 0.139</td><td>0.174 ± 0.067</td></tr><tr><td>Chemprop</td><td>0.121 ± 0.008</td><td>0.693 ± 0.039</td><td>0.504 ± 0.093</td><td>0.462 ± 0.063</td></tr><tr><td>DEL-Compose(M)</td><td>3.017 ± 0.005</td><td>0.448 ± 0.054</td><td>0.756 ± 0.011</td><td>0.569 ± 0.048</td></tr><tr><td>DEL-Compose(S)</td><td>3.192 ± 0.167</td><td>0.420 ± 0.050</td><td>0.760 ± 0.018</td><td>-</td></tr><tr><td rowspan="8">cluster</td><td>RF</td><td>0.063 ± 0.015</td><td>0.697 ± 0.033</td><td>0.313 ± 0.071</td><td>0.472 ± 0.048</td></tr><tr><td>XGBoost</td><td>0.059 ± 0.013</td><td>0.486 ± 0.032</td><td>0.378 ± 0.091</td><td>0.176 ± 0.069</td></tr><tr><td>kNN</td><td>0.080 ± 0.018</td><td>0.575 ± 0.034</td><td>0.435 ± 0.094</td><td>0.421 ± 0.032</td></tr><tr><td>DNN</td><td>0.065 ± 0.011</td><td>0.565 ± 0.089</td><td>0.592 ± 0.065</td><td>0.284 ± 0.114</td></tr><tr><td>GIN</td><td>0.072 ± 0.015</td><td>0.411 ± 0.209</td><td>0.369 ± 0.054</td><td>0.123 ± 0.171</td></tr><tr><td>Chemprop</td><td>0.131 ± 0.047</td><td>0.713 ± 0.013</td><td>0.532 ± 0.070</td><td>0.485 ± 0.036</td></tr><tr><td>DEL-Compose(M)</td><td>3.038 ± 0.053</td><td>0.440 ± 0.045</td><td>0.730 ± 0.009</td><td>0.583 ± 0.032</td></tr><tr><td>DEL-Compose(S)</td><td>3.339 ± 0.114</td><td>0.369 ± 0.050</td><td>0.766 ± 0.012</td><td>-</td></tr><tr><td rowspan="8">disynthon</td><td>RF</td><td>0.154 ± 0.016</td><td>0.157 ± 0.138</td><td>0.505 ± 0.062</td><td>0.302 ± 0.096</td></tr><tr><td>XGBoost</td><td>0.148 ± 0.015</td><td>0.377 ± 0.054</td><td>0.482 ± 0.045</td><td>0.212 ± 0.126</td></tr><tr><td>kNN</td><td>0.165 ± 0.014</td><td>0.402 ± 0.074</td><td>0.266 ± 0.078</td><td>0.367 ± 0.043</td></tr><tr><td>DNN</td><td>0.160 ± 0.017</td><td>0.275 ± 0.135</td><td>0.429 ± 0.118</td><td>0.184 ± 0.146</td></tr><tr><td>GIN</td><td>0.153 ± 0.011</td><td>0.090 ± 0.084</td><td>0.483 ± 0.151</td><td>-0.080 ± 0.071</td></tr><tr><td>Chemprop</td><td>0.216 ± 0.007</td><td>0.390 ± 0.091</td><td>0.506 ± 0.093</td><td>0.228 ± 0.121</td></tr><tr><td>DEL-Compose(M)</td><td>3.177 ± 0.028</td><td>0.120 ± 0.070</td><td>0.716 ± 0.052</td><td>0.421 ± 0.054</td></tr><tr><td>DEL-Compose(S)</td><td>3.351 ± 0.040</td><td>0.128 ± 0.049</td><td>0.748 ± 0.024</td><td>-</td></tr></table>
+
+results and experimental  $K_{D}$  computed directly from the sequence count data, measuring how well the DEL data itself predicts the  $K_{D}$  in the follow-up assays. For DDR1, we see that DEL-Compose, which views the data from a probabilistic perspective, is the most performant model in all but the "Extended on-DNA" set. For MAPK14, relatively simple models (RF and kNN) perform best for the in-library on-DNA validation while DEL-Compose performs better off-DNA. Recall that off-DNA is the task more reflective of the setting for selecting actual drug candidates. Interestingly, we find that DEL-Compose rank orders the validation compounds off-DNA better than using enrichment metrics of the DEL data itself (Counts, Poisson). This is true for both targets, and on all three splits of the data. As mentioned earlier, DEL data is only indirectly correlated to off-DNA data, so this demonstrates that these structure-based models may have regularization properties that can denoise the DEL data. Most models perform similarly in the cluster split compared to the random split, indicating that the cluster split created based on fingerprint cluster is not too much more challenging. However, we observe that almost all models perform
+
+worse on the disynthon split compared to the random split. In particular, this change in performance is quite significant for the MAPK14 data, which might suggest that these models are overfitting to certain features. The disynthon split is a more challenging task, since we remove structures entirely from the training data, and the models have to infer based on chemical structures (out-of-distribution inference). Overall, these results demonstrate that models trained on DEL data can be used for hit selection, since models can predict enrichment scores that correlate well with on- and off-DNA biophysical data.
+
+# 4. Discussion
+
+Data Applicability and Limitations Our data and benchmarking tasks were designed to evaluate the ability to predict compounds within the DEL. Although we incorporated challenging splits of the data, such as disynthon splits, we have not evaluated the usefulness of this particular data for truly out-of-distribution sets. While we do include an extended held-out set with molecules from outside of the
+
+Table 2: Model performance evaluation for DDR1. The test loss column contains values of the loss function computed on test split. The performance for the on- and off-DNA "In-Library" is the negative Spearman correlation between model predictions and experimental  $K_{D}$  for compounds resynthesized from the DEL. The performance for on-DNA "Extended" set includes additional compounds resynthesized on-DNA but not in the original DEL.  
+
+<table><tr><td rowspan="2">Split</td><td rowspan="2">Model</td><td rowspan="2">Test Loss ↓</td><td colspan="2">In-Library</td><td>Extended on-DNA Spearman&#x27;s ρ ↑ n = 49</td></tr><tr><td>on-DNA Spearman&#x27;s ρ ↑ n = 39</td><td>off-DNA Spearman&#x27;s ρ ↑ n = 49</td><td>Spearman&#x27;s ρ ↑ n = 54</td></tr><tr><td></td><td>Counts</td><td>-</td><td>0.695</td><td>0.355</td><td>-</td></tr><tr><td></td><td>Poisson</td><td>-</td><td>0.779</td><td>0.441</td><td>-</td></tr><tr><td rowspan="8">random</td><td>RF</td><td>0.685 ± 0.011</td><td>0.578 ± 0.034</td><td>0.267 ± 0.022</td><td>0.608 ± 0.021</td></tr><tr><td>XGBoost</td><td>0.519 ± 0.011</td><td>0.553 ± 0.032</td><td>0.252 ± 0.031</td><td>0.587 ± 0.025</td></tr><tr><td>kNN</td><td>0.748 ± 0.010</td><td>0.599 ± 0.025</td><td>0.316 ± 0.026</td><td>0.508 ± 0.036</td></tr><tr><td>DNN</td><td>1.261 ± 0.057</td><td>0.703 ± 0.025</td><td>0.335 ± 0.009</td><td>0.668 ± 0.033</td></tr><tr><td>GIN</td><td>0.454 ± 0.012</td><td>0.572 ± 0.044</td><td>0.283 ± 0.028</td><td>0.579 ± 0.037</td></tr><tr><td>Chemprop</td><td>1.391 ± 0.043</td><td>0.729 ± 0.017</td><td>0.335 ± 0.004</td><td>0.680 ± 0.021</td></tr><tr><td>DEL-Compose(M)</td><td>2.873 ± 0.003</td><td>0.731 ± 0.016</td><td>0.509 ± 0.024</td><td>0.646 ± 0.024</td></tr><tr><td>DEL-Compose(S)</td><td>2.918 ± 0.057</td><td>0.689 ± 0.048</td><td>0.483 ± 0.044</td><td>-</td></tr><tr><td rowspan="8">cluster</td><td>RF</td><td>0.641 ± 0.190</td><td>0.586 ± 0.025</td><td>0.273 ± 0.017</td><td>0.615 ± 0.019</td></tr><tr><td>XGBoost</td><td>0.589 ± 0.164</td><td>0.569 ± 0.024</td><td>0.262 ± 0.009</td><td>0.599 ± 0.013</td></tr><tr><td>kNN</td><td>0.887 ± 0.189</td><td>0.581 ± 0.061</td><td>0.329 ± 0.063</td><td>0.489 ± 0.049</td></tr><tr><td>DNN</td><td>0.519 ± 0.150</td><td>0.708 ± 0.015</td><td>0.330 ± 0.022</td><td>0.673 ± 0.014</td></tr><tr><td>GIN</td><td>0.633 ± 0.142</td><td>0.524 ± 0.081</td><td>0.137 ± 0.047</td><td>0.599 ± 0.047</td></tr><tr><td>Chemprop</td><td>1.507 ± 0.363</td><td>0.732 ± 0.028</td><td>0.326 ± 0.014</td><td>0.690 ± 0.023</td></tr><tr><td>DEL-Compose(M)</td><td>2.891 ± 0.079</td><td>0.737 ± 0.041</td><td>0.467 ± 0.025</td><td>0.540 ± 0.037</td></tr><tr><td>DEL-Compose(S)</td><td>2.993 ± 0.065</td><td>0.686 ± 0.027</td><td>0.482 ± 0.019</td><td>-</td></tr><tr><td rowspan="8">disynthon</td><td>RF</td><td>1.151 ± 0.151</td><td>0.481 ± 0.120</td><td>0.330 ± 0.081</td><td>0.557 ± 0.082</td></tr><tr><td>XGBoost</td><td>0.989 ± 0.131</td><td>0.523 ± 0.071</td><td>0.241 ± 0.031</td><td>0.572 ± 0.046</td></tr><tr><td>kNN</td><td>1.109 ± 0.088</td><td>0.663 ± 0.043</td><td>0.363 ± 0.038</td><td>0.523 ± 0.036</td></tr><tr><td>DNN</td><td>0.977 ± 0.104</td><td>0.572 ± 0.063</td><td>0.265 ± 0.051</td><td>0.598 ± 0.055</td></tr><tr><td>GIN</td><td>0.966 ± 0.090</td><td>0.410 ± 0.020</td><td>0.070 ± 0.031</td><td>0.546 ± 0.023</td></tr><tr><td>Chemprop</td><td>1.690 ± 0.192</td><td>0.558 ± 0.061</td><td>0.310 ± 0.038</td><td>0.579 ± 0.037</td></tr><tr><td>DEL-Compose(M)</td><td>3.184 ± 0.025</td><td>0.663 ± 0.022</td><td>0.463 ± 0.023</td><td>0.492 ± 0.049</td></tr><tr><td>DEL-Compose(S)</td><td>3.110 ± 0.041</td><td>0.563 ± 0.084</td><td>0.429 ± 0.069</td><td>-</td></tr></table>
+
+DEL, this extended set is limited in size. We envision that models trained on this data can be used to make predictions for molecules from purchased catalogues, but such applications will require further exploration, especially being cognizant of problems in this space such as domain of applicability (Weaver & Gleeson, 2008).
+
+One limitation of DEL data is that it only measures on-DNA binding events, and on- and off-DNA binding are only loosely correlated (Hackler et al., 2019). While we have shown in our experiments that machine learning models can have nice regularization properties and learn some correlations to off-DNA binding, DEL data needs to be combined with additional 3-D structural data to fully understand these different binding modalities. To that end, we also publicly release docked 3-D poses of our library molecules to the target proteins to aid future model development by the community (see Appendix F). Additionally, DEL screens are sometimes run with an additional experimental condition to distinguish potential allosteric binders from orthosteric binders (Gironda-Martínez et al., 2021). This is usually
+
+achieved by running the experiment with a known inhibitor doped in at high concentrations. Because our data lacks this condition, it can be difficult to discern non-specific binding modes. We also recognize that one limitation of the dataset is that the two targets we provide are kinases. In order to make this dataset more broadly applicable for modeling DEL data, we additionally release our data on another well studied target, Bovine Carbonic Anhydrase (BCA), using the same library.
+
+Challenges and Future Directions DEL data is powerful in that it specifically densely samples particular chemical spaces, which can be leveraged to learn more powerful representations. However, DEL data suffers from experimental noise. In particular, there are unobserved factors such as synthesis noise that makes it difficult to separate out signal from noise in the data (Zhu et al., 2021). Additionally, since our observations are sequencing read counts rather than actual binding affinity, the measurements also suffer from PCR bias (Aird et al., 2011). While we have presented several benchmark methods that try to learn a denoised
+
+enrichment from structure-based models, how best to do this is still an open question in the field, and we hope that our dataset release will enable the development of more denoising methods.
+
+Furthermore, our benchmark primarily focuses on building purely predictive models, which encapsulates most of the published work in this field currently. However, KinDEL holds significant potential for use in generative frameworks. Many generative modeling approaches in the small-molecule space lack sufficient supervised data to learn interesting sampling distributions. However, this is exactly the data that DEL provides, densely sampling around particular synthon or di-synthon structures. Therefore, we hope that DEL data combined with provided docking poses can be used to train or fine-tune generative models on specific protein targets.
+
+# 5. Related Work
+
+# 5.1. Current datasets
+
+To the best of the authors' knowledge, only a limited number of DEL datasets have been released publicly. While KinDEL is not the largest library tested, our dataset is evaluated on two distinct targets in the Kinase family and contains comprehensive and consistently replicated raw experimental data (see Appendix B) in addition to orthogonal, non-DEL based binding affinity data for validation.
+
+Iqbal et al. (2024) released three DEL datasets tested against two targets, Casein Kinase  $1\alpha/\delta$ . Their libraries span a range of chemical size and diversity, and they demonstrated the efficacy of a suite of machine learning methods to model binding affinities. Like our work, they experimentally validated some of their machine learning derived molecule predictions with biophysical assay data. However, they only tested off-DNA binding affinities, whereas we have synthesized our compounds both on- and off-DNA. Having both kinds of data is important because on-DNA data bridges the gap between DEL data and off-DNA data. Additionally, they have not investigated probabilistic models in their benchmarking tasks, which we find to be empirically useful.
+
+Another recent dataset release is from Leash Bio, who released their data as a Kaggle competition (Blevins et al., 2024). Their dataset has a single DEL screened against on three different proteins, but their data has been preprocessed from raw count to a binary label. This process is often used to denoise DEL data, but it removes information from the data. We show through our experiments that it is possible to learn over discrete count data through probabilistic approaches.
+
+Gerry et al. (2019) and Hou et al. (2023) have released libraries tested against well-studied targets Horseradish Per
+
+oxidase and members of the Carbonic Anhydrase family. In both cases, the DELs were synthesized with specific chemotypes known to bind to their targets. As a result, evaluation in each is primarily limited to comparing relative enrichment for compounds containing known binders. These papers serve as excellent case-studies but with their targeted library construction and limited library size  $\sim 100\mathrm{k}$  (Gerry et al., 2019) and  $\sim 7\mathrm{M}$  (Hou et al., 2023), they are unlikely to serve as generalizable benchmarks for DEL ML methods.
+
+The AIRCHECK database facilitates the public release of large-scale DEL datasets, notably including a 3-billion-molecule library screened against WDR91 (Wellnitz et al., 2024). However, chemical structures are masked with fingerprints in these commercial-sized libraries, which inherently limits the range of applicable modeling approaches.
+
+# 5.2. Computational Methods on DEL Data
+
+Computational efforts on DEL data have evolved over time. One of the major concerns with DEL data is its intrinsic noisiness. Firstly, the synthesis of a DEL is optimized for scale, and not precision, which results in uncertainty in the composition of the library. For instance, DEL synthesis will result in forming partial or truncated products (Gironda-Martínez et al., 2021; Binder et al., 2022), which has some causal effect on the observed data that cannot easily be measured. Additionally, the final data measurement is obtained by sequencing PCR-amplified DNA barcodes; however, the PCR process itself does not uniformly sample from the surviving members of the selection experiment (Aird et al., 2011).
+
+Computational methodology for DEL data is still a nascent area, largely due to a lack of publicly available data. Current works typically directly apply fingerprint and graph neural network approaches that are popular within property prediction models. Due to the noisiness intrinsic to the data, many methods bin the labeled data into a binary classification to avoid overfitting on the raw data. For instance, McCloskey et al. (2020) trained classification models on disynths using variants of typical graph neural networks. This approach was applied by Ahmad et al. (2023) to find first-in-class WD Repeat Domain 91 ligands, using molecules from buyable catalogues. Torng et al. (2023) follows up on this work and uses Weave GCN for hit identification of CA-IX. However, the true binding process is observed on a discrete scale, so more recent works have focused on building probabilistic models of binding. Lim et al. (2022) proposed a new uncertainty-based loss function for training regression models, and demonstrated the efficacy of their method using various graph neural network models. (Shmilovich et al., 2023) takes this process one step further and incorporates 3-D docked poses to leverage the scale of DEL data by us
+
+ing multiple-instance learning to learn over poses. Other works exploit compositionality of DELs as inductive biases of the models. (Binder et al., 2022) tries to explicitly model the partial products, while (Chen et al., 2024) computes a hierarchical representation of DEL molecules and incorporates a probabilistic loss. (Koziarski et al., 2024) explores generative models of DEL molecules using GFlowNets. Many of these developments are relatively new, and we hope that KinDEL will enable the further development of these methodologies in the field.
+
+# 6. Conclusion
+
+DELs have emerged as a high-throughput technology that enables screenings of large combinatorial small molecule libraries. However, DEL data has many sources of intrinsic noise stemming from synthesis and selection experiments, necessitating the right machine learning tools to extract the correct signal in the data. We introduce KinDEL as a 81M molecule dataset with selection data from two targets, MAPK14 and DDR1, in order to highlight the ability to model DEL data to find potent binders. Our DEL is built with chemical diversity in mind, and many of the molecules in the library have properties within the range of approved drugs. We additionally release biophysical data for molecules synthesized both on- and off-DNA to validate our models trained on DEL data. We hope that our public data release and benchmarking will engender more interest in DEL data as an important chemical modality for machine learning research in the future.
+
+# Impact Statement
+
+The broader impact of this work includes the potential to accelerate the identification of novel therapies, ultimately benefiting public health. However, as with many datasets in the chemical and biological sciences, there is a potential risk of misuse, such as designing harmful substances. While there are inherent societal implications with advancing drug discovery, we do not anticipate any specific ethical concerns that must be highlighted beyond the established consequences of advancing machine learning techniques in this domain.
+
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+
+# A. Experimental Protocols
+
+# A.1. DEL Synthesis
+
+Library Design The design of DNA-encoded libraries (DELs) often grapples with limited diversity and availability of bifunctional building blocks compared to their monofunctional counterparts. In order to expand structural diversity of the first two synthons of a three-step linear library, we implemented a hybrid design that combines trifunctional and monofunctional building blocks within one step of synthesis, to form a bifunctional synthon, by using DEL synthesis on solid supports. This strategy significantly expands the chemical space and diversity of our DELs, offering a robust pathway to discovering novel compounds with enhanced biological activity.
+
+Library Build The DEL is built as a trisynthon library, comprised of 378 synthons in the A position, 1128 synthons in the B position (the terminal, capping step), and 191 synthons in the C position. This resulted in a DNA encoded library comprised of roughly 81 million unique members. The first two steps are done either by acylation with N-protected (Boc or Fmoc) amino acid, followed by deprotection, or by immobilization of the DNA to a solid support (DEAE sepharose resin) followed by a series of chemical transformations: acylation with trifunctional building block (Boc-amino acid with protected side chain: Fmoc-amine, ester or ketone), deprotection (if necessary) of the side chain protecting group, reaction (amide coupling, reductive amination/alkylation) with the monofunctional building block (amine, aldehyde or acid), and lastly eluting the DNA off the DEAE sepharose and cleavage of the Boc group. In the final step, the downstream amino groups were reacted with monofunctional acids or aldehydes. Each of the steps described herein is encoded by the attached DNA strand allowing for ready deconvolution of the sequence of chemical steps taken for any given member.
+
+# A.2. DEL Selection
+
+The DEL selection was performed using an Agilent Bravo for all handling steps. To immobilize the protein 1 nanomole of the protein of interest (Avi-tagged MAPK14 or DDR1). were incubated through gentle aspiration through streptavidin-coated beads housed within PhyTips (Cat. #PTV-92-20-05). This was performed in technical triplicate for each protein. Following immobilization, any unbound proteins were washed away using Buffer A (45 mM HEPES, 45 mM Tris-HCl, 150 mM NaCl, 5 mM MgCl $_2$ , pH 8.1).
+
+Subsequently, the immobilized proteins were incubated through gentle aspiration and dispersion over a period of 30 minutes with the Naive DEL library (at 500K copies of each member) in solution of Buffer A supplemented with  $0.1\mathrm{mg / ml}$  sheared salmon sperm DNA to minimize non-specific binding. To eliminate noise and unbound library compounds, the Phynexus tips were washed six independent times with Buffer B (45 mM HEPES, 45 mM Tris-HCl, 425 mM NaCl, 5 mM  $\mathrm{MgCl}_2$ , pH 8.1,  $0.03\%$  Tween).
+
+Post-washing procedure. Any compounds remaining (the binders) were eluted by  $5\mathrm{x}$  aspiration through the tip of hot water at  $90^{\circ}\mathrm{C}$ . The material eluted is termed 'Elution Round 1'. Following this the used Phytips were disposed, and fresh streptavidin PhyTip were used to capture a fresh 1 nanomole of avi-tagged protein of interest, and the process described above repeated, but, the Naive DEL Library is instead the  $90\%$  of the eluent from Round 1 (Elution Round 1) as the source of library. This procedure is repeated a final time with the Elution Round 2 sample to generate an Elution Round 3 sample.
+
+From the  $10\%$  of eluates conserved from round 2 and the round 3 eluate were taken  $5\mu \mathrm{L}$  of sample that was subsequently PCR amplified in  $50~\mu \mathrm{L}$  reactions using New England BioLabs 2x Q5 mastermix (Cat. #M0492S) and custom designed barcode primers to differentiate both the round, target and experiment. Following this  $1\mu \mathrm{L}$  of the amplified material is transferred to a  $25~\mu \mathrm{L}$  PCR reaction with Q5 and custom P5 and P7 primers to install the relevant sequencing primers. The PCR mixture is purified using a QIAquick PCR Purification Kit (Cat. #28104), this sample is then further purified to remove any DNA products of incorrect size using a PippenHT. The purified samples are submitted to next-generation sequencing utilizing the Novaseq platform with a 2x150 BP S4 kit. The sequencing depth (number of read counts/sequence counts) is 514.5M/65.8M for MAPK14, 296.5M/49.8M for DDR1, and 440.7M/52M for BCA in all three replicates.
+
+# A.3. Biophysical Assays
+
+# A.3.1. MOLECULAR BIOLOGY
+
+hMAPK14-1 (1-360, WT) gene was cloned into pET-28a expression vector (Novagen) by polymerase chain reaction (PCR). An N-terminal His-TEV-Avi tag was added by using the forward primer  $5^{\prime}$ -CTTTAAGAAGGAGATATACCATGGGCCATCATCACCATCACCAC-3' and the reverse primer  $5^{\prime}$ -
+
+TTCGTGCCATTCAATTTCTG-3'. The forward primer included the restriction site NcoI. The hMAPK14 (1-360, WT) gene was cloned using the forward primer 5'-CTCAGAAAATTGAATGGCACGAAATGTCTCAGGAGAGGCCCACG-3' and the reverse primer 5'-GTGGTGGTGGTGGTGGTGCTCGAGTTAGGACTCCATCTCTTCTTGGTCA-3'. The reverse primer included the restriction site XhoI. This generated plasmid pET28a-His-TEV-avi-hMAPK14-1 (1-360, WT).
+
+hMAPK14-2 (1-360, WT) gene was cloned into pET-28a expression vector (Novagen) by PCR. An N-terminal His-TEV tag was added by using the forward primer  $5^{\prime}$ -CTTTAAGAAGGAGATATACCATGGGCCATCATCACCATCACCAC-3' and the reverse primer  $5^{\prime}$ -GCCCTGGAAGTACAGGTTCTC-3'. The forward primer included the restriction site NcoI. The hMAPK14 (1-360, WT) gene was cloned using the forward primer  $5^{\prime}$ -GAGAACCTGTACTTCCAGGGCATGTCTCAGGAGAGGCCACG-3' and the reverse primer  $5^{\prime}$ -GTGGTGGTGGTGGTGGTGCTCGAGTTAGGACTCCATCTCTTCTTGGTCA-3'. The reverse primer included the restriction site XhoI. This generated plasmid pET28a-His-TEV-hMAPK14-2 (1-360, WT).
+
+hDDR1-1 (593-913,  $\Delta 730 - 735$  ) gene was cloned into pFastBac1 expression vector by PCR. An N-terminal His-TEV tag was added by using the forward primer  $5^{\prime}$  -GGTCCGAAGCGCGCGGAATTCACCATGCACCATCACCATCACCAC $3^{\prime}$  and the reverse primer  $5^{\prime}$  -ACCTTGGAAGTACAGGTTCTC-  $3^{\prime}$ . The forward primer included the restriction site EcoRI. The hDDR1-1 (593-913,  $\Delta 730 - 735$  ) gene was cloned using the forward primer  $5^{\prime}$  -GAGAACCTGTACTTCCAAGGTCCTGGTGCTGTGGGTGACGGT-  $3^{\prime}$  and the reverse primer  $5^{\prime}$  -GGCTCTAGATTCGAAAGCGGCCGCTTACACAGTGTCAGAGCGTC-  $3^{\prime}$ . The reverse primer included the restriction site NotI. This generated plasmid pFastBac1-His-TEV-hDDR1-1 [593-913 ( $\Delta 730 - 735$ ), WT].
+
+hDDR1-2 (593-913,  $\Delta 730 - 735$  ) gene was cloned into pFastBac1 expression vector by PCR. An N-terminal His-TEV-Avi tag was added by using the forward primer  $5^{\prime}$  -GGTCCGAAGCGCGCGGAATTCACCATGCATCATCACCATCACCAC3' and the reverse primer  $5^{\prime}$  -TTCGTGCCATTCAATTTTCTG-3'. The forward primer included the restriction site EcoRI. The hDDR1-2 (593-913,  $\Delta 730 - 735$  ) gene was cloned using the forward primer  $5^{\prime}$  -CTCAGAAAATTGAATGGCACGAACCTGGTGCTGTGGGTGACGGT-3' and the reverse primer  $5^{\prime}$  -GGCTCTAGATTCGAAAGCGGCCGCTTACACAGTGTCAGAGCGTC-3'. The reverse primer included the restriction site NotI. This generated plasmidpFastBac1-His-TEV-Avi-hDDR1-2 [593-913 ( $\Delta 730 - 735$ ), WT].
+
+BCA2-1 (1-260, WT) gene was cloned into pET28a expression vector by PCR. An N-terminal His-TEV-Avi tag was added by using the forward primer 5'-CTTTAAGAAGGAGATATACCATGGGCCATCATCACCATCACCAC3' and the reverse primer 5'-TTCGTGCCATTCAATTTTCTG-3'. The forward primer included the restriction site NcoI. The BCA2-1 (1-260, WT) gene was cloned using the forward primer 5'-CTCAGAAAATTGAATGGCACGAAATGAGCCATCATTGGGGCTATGGCAAAC-3' and the reverse primer 5'-GTGGTGGTGGTGGTGGTGCTCGAGTTATTTCGGAAAGCCGCGCACT-3'. The reverse primer included the restriction site XhoI. This generated plasmid pET28a-His-TEV-Avi-BCA2(1-260,WT).
+
+All cloning was performed using the Beyotime Seamless Cloning kit (D7010M). All plasmids were amplified using  $\mathrm{DH5}\alpha$  cells followed by DNA extraction. Insertion of the genes were verified by sequencing.
+
+# A.3.2. PROTEIN PRODUCTION
+
+# MAPK14
+
+MAPK14 plasmid [either pET28a-His-TEV-avi-hMAPK14-1 (1-360, WT) or pET28a-His-TEV-hMAPK14-2 (1-360, WT)] was transformed into BL21-Gold (DE3) competent cells (Agilent, 230132) and plated on LB/agar/kanamycin  $(50\mu \mathrm{g} / \mathrm{mL})$  medium then left to grow at  $37^{\circ}\mathrm{C}$ . Fresh colonies from transformed BL21-Gold cells were picked and used to inoculate 100 mL of LB medium (10 g tryptone, 10 g NaCl, 5 g yeast extract per liter water) supplemented with  $(50\mu \mathrm{g} / \mathrm{mL})$  kanamycin and cultured overnight at 250 rpm  $37^{\circ}\mathrm{C}$ . The overnight culture was added to 2 L LB/kanamycin  $(50\mu \mathrm{g} / \mathrm{mL}))$  and grown at 250 rpm  $37^{\circ}\mathrm{C}$  until OD600 reached 0.600. Isopropyl β-D-1-thiogalactopyranoside (IPTG) was then added (final concentration 0.3 mM) and the culture was left to continue to grow at  $16^{\circ}\mathrm{C}$ , 250 rpm overnight.
+
+Cells were harvested the following day at  $8,000~\mathrm{rpm}$  at  $4^{\circ}\mathrm{C}$  and stored at  $-20^{\circ}\mathrm{C}$ . Cell pellets were resuspended in lysis buffer (50 mM Tris, 500 mM NaCl, 1 mM TCEP, 10% glycerol, pH 8.0 and 0.5 μL Benzonase) and lysed using a high pressure cell homogenizer. Lysate was centrifuged at 13,000 rpm for 30 minutes at  $4^{\circ}\mathrm{C}$ , twice, to remove cell debris. Lysate supernatant was then applied to 6 mL of Ni-Resin (which had been pre-equilibrated with lysis buffer) and the lysate/Ni mixture was incubated for 1 hr at  $4^{\circ}\mathrm{C}$ . Resin was then loaded into a column and the column was washed with wash buffer (50 mM Tris, 500 mM NaCl, 1 mM TCEP, 10% glycerol, pH 8.0) and eluted with elution buffer (50 mM Tris, 500 mM NaCl, 1 mM
+
+TCEP,  $10\%$  glycerol, pH 8.0 and  $250~\mathrm{mM}$  imidazole). Eluted protein was cleaved with TEV protease at a 1:10 (w/w) ratio and dialyzed against dialysis buffer (50 mM Tris, 100 mM NaCl, 1 mM TCEP, 7.5 mM MgCl2, pH 8.0) at  $4^{\circ}\mathrm{C}$  overnight.
+
+Protein was loaded onto a Ni-resin column, pre-equilibrated with lysis buffer and the cleaved protein was collected in the flow-through (cleaved-tag left on the column). In the case of Avi-tagged protein (MAPK14-1), the dialyzed protein was incubated at  $18^{\circ}\mathrm{C}$  for 4 hrs with ATP  $(1\mathrm{mM})$ , Biotin  $(0.5\mathrm{mM})$ , and BirA  $(200\mathrm{nM})$ , prior to loading onto Ni-resin to remove cleaved hexahistidine tags.
+
+Protein was collected and concentrated with a  $10\mathrm{kDa}$  Millipore Amicon Ultra-15 centrifugal filter unit. Concentrated protein was loaded onto a Superdex 200 column pre-equilibrated with SEC buffer. Protein was collected according to UV-vis signal and follow-up SDS-PAGE verification. Protein fractions were pooled and concentrated with a  $10\mathrm{kDa}$  Millipore Amicon Ultra-15 centrifugal filter unit and exchanged into a final buffer containing  $10\mathrm{mM}$  HEPES,  $200\mathrm{mMNaCl}$ ,  $1\mathrm{mM}$  TCEP at  $\mathrm{pH}7.5$ . A final purified protein yield of  $19\mathrm{mg/L}$  cell culture was obtained.
+
+# DDR1
+
+DDR1 plasmid (either pFastBac1-His-TEV-Avi-hDDR1-2 [593-913 ( $\Delta$ 730-735), WT] or pFastBac1-His-TEV-hDDR1-1 [593-913 ( $\Delta$ 730-735), WT]) was transformed into DH10Bac competent cells (Agilent) and plated on LB/agar plates containing  $50\mu \mathrm{g} / \mathrm{mL}$  kanamycin,  $7\mu \mathrm{g} / \mathrm{mL}$  gentamicin,  $10\mu \mathrm{g} / \mathrm{mL}$  tetracycline,  $100\mu \mathrm{g} / \mathrm{mL}$  X-gal and  $40\mu \mathrm{g} / \mathrm{mL}$  IPTG then left to grow at  $37^{\circ}\mathrm{C}$  for 48 hours. Fresh colonies from transformed DH10Bac competent cells were picked and used to inoculate  $5\mathrm{mL}$  of LB medium ( $10\mathrm{g}$  tryptone,  $10\mathrm{gNaCl}$ ,  $5\mathrm{g}$  yeast extract per liter water) supplemented with  $50\mu \mathrm{g} / \mathrm{mL}$  kanamycin,  $7\mu \mathrm{g} / \mathrm{mL}$  gentamicin,  $10\mu \mathrm{g} / \mathrm{mL}$  tetracycline and cultured overnight at  $37^{\circ}\mathrm{C}$ . An aliquot of each cell culture was verified to contain the recombinant bacmid by PCR analysis.
+
+Transfection. In a 6-well plate, Sf9 cells were grown in  $2\mathrm{mL}$  cultures to a cell density of  $2\times 106$  cells/mL in SF900II medium at  $27^{\circ}\mathrm{C}$ . The culture medium was then exchanged with fresh SF900II medium followed by inoculation with the recombinant bacmid:lipid (Cellfectin II reagent) complexes. The bacmid infected cells were incubated at  $27^{\circ}\mathrm{C}$  for 5 days. The cell culture medium was collected as P1 virus and cell pellet was used for western blot analysis.
+
+P2 baculovirus generation and scale-up protein expression. Sf9 cells were grown in a  $50~\mathrm{mL}$  culture medium to a cell density of  $2\times 106$  cells/mL followed by infection with P1 virus in the ratio 1:200. Incubate the P1 infected Sf9 cells at  $27^{\circ}C$  for 3 days. The cell culture medium was collected as P2 virus and the cell pellet from  $1\mathrm{mL}$  cell culture was used for western blot analysis. For scale-up expression, Sf9 cells were grown in a  $12\mathrm{L}$  culture medium to a cell density of  $2\times 106$  cells/mL followed by infection with P2 virus in the ratio 1:200. For N-Avi tagged hDDR1-2, BirA was co-expressed (infection ratio 1:500, biotin  $40~\mu \mathrm{M}$ ) with the P2 infected Sf9 cells. The P2 infected Sf9 cells were incubated at  $27^{\circ}C$  for 3 days.
+
+Cells were harvested after 3 days at  $8,000\mathrm{rpm}$  at  $4^{\circ}\mathrm{C}$  and stored at  $-20^{\circ}\mathrm{C}$ . Cell pellets were resuspended in lysis buffer (50 mM HEPES, 300 mM NaCl, 2 mM TCEP, 10 mM  $\mathrm{MgCl}_2$ , 10% saccharose, cocktail, 100U/mL Benzonase, pH 8.0) and Protease Inhibitor Cocktail Tablet was added until a final concentration of 1 tablet/L. Cells were sonicated to lyse in repeating periods of 3 seconds on, 3 seconds off for 10 minutes. This cycle was then repeated for an additional 10 minutes. A color change of cell lysate was used to help indicate if cell lysis was sufficient, if no color change from pre-lysed cells was observed, cell lysis was allowed to continue. Cell lysate was centrifuged at 13,000 rpm for 30 minutes at  $4^{\circ}\mathrm{C}$ , twice, to remove cell debris. Lysate supernatant was then applied to 6 mL of Ni-Resin (which had been pre-equilibrated with lysis buffer) and the lysate/Ni resin mixture was incubated for 1 hr at  $4^{\circ}\mathrm{C}$ . Resin was then loaded into a column and the column was washed with wash buffer (50 mM HEPES, 300 mM NaCl, 2 mM TCEP, 10 mM  $\mathrm{MgCl}_2$ , pH 8.0) and eluted with elution buffer (50 mM HEPES, 300 mM NaCl, 2 mM TCEP, 10 mM  $\mathrm{MgCl}_2$ , pH 8.0, 50 mM imidazole). Eluted protein was cleaved with TEV protease at a 1:10 (w/w) ratio and dialyzed against dialysis buffer (50 mM HEPES, 300 mM NaCl, 2 mM TCEP, 10 mM  $\mathrm{MgCl}_2$ , pH 8.0) at  $4^{\circ}\mathrm{C}$  overnight.
+
+Protein was loaded onto a Ni-resin column, pre-equilibrated with lysis buffer and the cleaved protein was collected in the flow-through (cleaved-tag left on the column). Protein was collected and concentrated with a  $30\mathrm{kDa}$  Millipore Amicon Ultra-15 centrifugal filter unit. Concentrated protein was loaded onto a Superdex 200 column pre-equilibrated with SEC buffer. Protein was collected according to UV-vis signal and follow-up SDS-PAGE verification. Protein fractions were pooled and concentrated with a  $30\mathrm{kDa}$  Millipore Amicon Ultra-15 centrifugal filter unit and exchanged into a final buffer containing  $20\mathrm{mM}$  HEPES,  $200\mathrm{mMNaCl}$ ,  $1\mathrm{mM}$  TCEP,  $5\%$  glycerol at  $\mathsf{pH}7.5$ . A final purified protein yield of  $1.8\mathrm{mg / L}$  cell culture was obtained.
+
+# BCA2
+
+The BCA plasmid, pET28a-His-TEV-Avi-BCA2(1-260,WT), was transformed into BL21-Gold (DE3) competent cells (Agilent, 230132) and plated on LB/agar/kanamycin  $(50\mu \mathrm{g} / \mathrm{mL})$  medium then left to grow at  $37^{\circ}\mathrm{C}$ . Fresh colonies from transformed BL21-Gold cells were picked and used to inoculate  $100~\mathrm{mL}$  of LB medium (10 g tryptone, 10 g NaCl, 5 g yeast extract per liter water) supplemented with  $50~\mu \mathrm{g} / \mathrm{mL}$  kanamycin and cultured overnight at 220 rpm  $37^{\circ}\mathrm{C}$ . The overnight culture was added to 10 L LB/kanamycin  $(50~\mu \mathrm{g} / \mathrm{mL})$  and grown at 180 rpm  $37^{\circ}\mathrm{C}$  until OD600 reached 0.600. Isopropyl  $\beta$ -D-1-thiogalactopyranoside (IPTG) was then added (final concentration  $0.3\mathrm{mM}$ ) and the culture was left to continue to grow at  $16^{\circ}\mathrm{C}$ , 160 rpm overnight.
+
+Cells were harvested the following day at  $8,000~\mathrm{rpm}$  at  $4^{\circ}\mathrm{C}$  and stored at  $-20^{\circ}\mathrm{C}$ . Cell pellets were resuspended in lysis buffer (50 mM Tris, 500 mM NaCl, 1 mM TCEP, 1 mM PMSF, 10% glycerol, pH 8.0 and 100 U/mL Benzonase) and lysed using a high pressure cell homogenizer. Lysate was centrifuged at 13,000 rpm for 30 minutes at  $4^{\circ}\mathrm{C}$ , twice, to remove cell debris. Lysate supernatant was then applied to 5 mL of Ni-Resin (which had been pre-equilibrated with lysis buffer) and the lysate/Ni mixture was incubated for 1 hr at  $4^{\circ}\mathrm{C}$ . Resin was then loaded into a column and the column was washed with wash buffer (50 mM Tris, 500 mM NaCl, 1 mM TCEP, 10% glycerol, pH 8.0) and eluted with elution buffer (50 mM Tris, 500 mM NaCl, 1 mM TCEP, 10% glycerol, pH 8.0 and 250 mM imidazole). Eluted protein was cleaved with TEV protease at a 1:10 (w/w) ratio and dialyzed against dialysis buffer (50 mM Tris, 100 mM NaCl, 1 mM TCEP, 7.5 mM MgCl2, 5% glycerol, pH 8.0) at  $4^{\circ}\mathrm{C}$  overnight.
+
+The dialyzed protein was incubated at  $18^{\circ}\mathrm{C}$  for 4 hrs with ATP (1 mM), Biotin (0.5 mM), and BirA (200 nM), prior to loading onto Ni-resin to remove cleaved hexahistidine tags. Protein was loaded onto a Ni-resin column, pre-equilibrated with lysis buffer and the cleaved protein was collected in the flow-through (cleaved-tag left on the column).
+
+Protein was collected and concentrated with a  $30\mathrm{kDa}$  Millipore Amicon Ultra-15 centrifugal filter unit. Concentrated protein was loaded onto a Superdex 75 column pre-equilibrated with SEC buffer. Protein was collected according to UV-vis signal and follow-up SDS-PAGE verification. Protein fractions were pooled and concentrated with a  $30\mathrm{kDa}$  Millipore Amicon Ultra-15 centrifugal filter unit and exchanged into a final buffer containing  $25\mathrm{mM}$  HEPES,  $200\mathrm{mMNaCl}$ ,  $1\mathrm{mM}$  TCEP at  $\mathsf{pH}7.5$ . A final purified protein yield of  $8.38\mathrm{mg / L}$  cell culture was obtained.
+
+BCA used for fluorescence polarization assay was obtained from Sigma-Aldrich (Product No. C2522).
+
+# A.3.3. BIOPHYSICAL METHODS
+
+# Fluorescence Polarization
+
+Annealing of DNA tagged DEL molecules. DEL small molecule hits are attached to the DNA oligo, Za (GCAGGCGGAGACCTGCAGTCTG). Fluorescein (Integrated DNA Technologies, /3FluorT/) tagged complementary DNA oligo Za' (CAGACTGCAGGTCTCCGCCTG/3FluorT/) was annealed to Za-tagged DEL compounds using a thermocycler (Bio-Rad, 1851148).
+
+Assay setup. In a 384 well black small volume microplate (Greiner Bio-One, 784900), the annealed compounds were dispensed using Echo650 (Labcyte) at a constant final concentration of  $4\mathrm{nM}$  in  $137\mathrm{mMNaCl}$ ,  $2.7\mathrm{mM}$  KCl,  $9.8\mathrm{mM}$  Phosphate buffer,  $0.01\%$  Tween-20. MAPK14-2, DDR1-1, and BCA were each serially diluted 1:1 starting from a top dose of  $50\mu \mathrm{M}$  in  $137\mathrm{mMNaCl}$ ,  $2.7\mathrm{mM}$  KCl,  $9.8\mathrm{mM}$  Phosphate buffer,  $0.01\%$  Tween-20 for a total 16-point dilution and were transferred to the 384 well black small volume microplate containing the annealed compounds using Agilent Bravo G5563A. The final assay concentration was  $2\mathrm{nM}$  the annealed compound and  $25\mu \mathrm{M}$  top dose of the protein. The final assay volume was  $10\mu \mathrm{L}$ . The serially diluted protein was incubated with the annealed DEL compounds and then the fluorescence polarization was measured using PerkinElmer EnVision 2105 in milli-P (mP), where  $mP = 1000\times (S - GP) / (S + GP)$  ( $S$  and  $P$  are background subtracted fluorescence count rates, and  $G$  is an instrument and assay dependent factor). The dose-response curves ( $mP$  vs. [Protein]) were fit in GraphPad Prism using the equation,  $Y = Bmax\times X / (K_{D} + X) + NS\times X + Background$ , where  $Y$  is  $mP$ ,  $X$  is [Protein],  $Bmax$  is the maximum specific binding in the same units as  $Y$ ,  $K_{D}$  is the equilibrium dissociation constant, in the same units as  $X$ ,  $NS$  is the slope of nonspecific binding in  $Y$  units divided by  $X$  units, Background is the amount of nonspecific binding with no added radioligand.
+
+![](images/9ff1ebd7d658130de68b7b3234bed59525aa1b7f5b93bd627712d7227f675b10.jpg)  
+(a) Correlation between experimental replicates for MAPK14.
+
+![](images/2fd8de0da3ccf0df2198f724c4f556891dbb93c7afd2d0cb204eb23af93e6c93.jpg)
+
+![](images/14e5cabe72d95c4c4c36913cf598f7637972819fc21d22ca4e5815d4f4866ff5.jpg)
+
+![](images/0d00da1c2eb69fbbd54bfe5f932dadbd6df268764f49658a4160068640f7c603.jpg)  
+(b) Correlation between experimental replicates for DDR1.
+
+![](images/fd8716086ff09428698baef6f6f5f6403fb604cd0010914618321962aafdd67e.jpg)
+
+![](images/aac8f6930c08533ac5a5608f6fe7fc2d03eaa54ecc9632f1ae7f2ce3c38537c5.jpg)
+
+![](images/231023c5ddff75f313acf58fb593c6e20c1a5fb463d851c908f2ca76a5a31486.jpg)  
+(c) Correlation between experimental replicates for BCA.
+
+![](images/ee582c0171438cdac6965ffa0dbd1e02f3c32c99a7a0c63e25db7c40f460e511.jpg)
+
+![](images/e09ea1544f651e20cacb00665fd8411b62ece173384872e7d7ae38e0ea5dd0e2.jpg)
+
+![](images/182da6586248877d88745da119c613ad8f09d435dcba18208931c4e22dac8a86.jpg)  
+(d) Correlation between experimental replicates for the control.
+
+![](images/d84eef7d0030526f5d96f4b02ba037b05019406172f71d3dc1572141bab0daaa.jpg)  
+Figure 7: Correlation between experimental replicates. Binding to each target and the control was measured in three replicates, which are included in the published dataset.
+
+![](images/19139d30970bf3d5d56967b35a1330f889d802e2b212974b3d9198ca50d88145.jpg)
+
+# Surface Plasmon Resonance
+
+Compounds were tested using Surface Plasmon Resonance (SPR) using a Biacore T200 and a Biacore S200 (Cytiva Life Sciences). N-terminally biotinylated DDR1 [593-913 ( $\Delta$ 730-735)], MAPK14 (1-360), and BCA2-1 (1-260, WT) were immobilized to a streptavidin coated SPR chip (Series S SA, Cytiva, 29699621). Approximately 4400 RU of hDDR1-2, 4900 RU of MAPK14-1, and 3300 RU of BCA2-1 were immobilized for dose response assays using 1xHBS-P+ (10 mM HEPES, 150 mM NaCl, 0.05% v/v Surfactant P20; pH 7.4). 1xHBS-P+ was prepared by mixing 10xHBS-P+ (Cytiva, BR100671) with HPLC-grade water (Fisher Scientific, W51).
+
+Compounds were diluted in the SPR running buffer which consisted of 1xHBS-P+ supplemented with  $5\%$  DMSO (VWR, 76177-938). Multi-cycle kinetics was used to determine compound affinities. Compounds were injected in a series of increasing concentrations with a  $30~\mu \mathrm{L / min}$  flow rate, a  $60~s$  contact time and a  $300~s$  dissociation time. Compound sensorgrams were processed and fit using Biacore Evaluation software, with DMSO correction applied during sensorgram processing. Binding and dissociation curves for each compound were globally fit to obtain an on- and off-rate kinetic constant ( $\mathrm{k_a}$  and  $\mathrm{k_d}$ , respectively) which were used to determine the overall binding constant ( $\mathrm{K_D}$ ) for each compound.
+
+# B. Experimental Replicability
+
+DEL experiments suffer from the substantial noise that stems from the large scale of combinatorial libraries screened simultaneously within a single tube. Key sources of this noise include inconsistent control over the quantities of each compound in the mixture, synthesis-related challenges such as the introduction of side products and low synthetic yields, as well as errors during DNA sequencing. Figure 7 illustrates the strong correlation between experimental replicates in our DEL experiments, underscoring the reproducibility of the panning procedures we conducted.
+
+# C. Validation Set Selection
+
+We selected validation compounds to cover a range of  $K_{D}$  values and chemical diversity, allowing us to better assess the models' ability to rank molecules across diverse binding affinities. To achieve this, we used an ensemble of models described in Section 3, and then clustered the molecules based on chemical similarity via Butina clustering using Morgan fingerprints. This constituted the molecules in the "in-library" set. Figure 8 shows the distributions of the  $\mathrm{pK}_{D}$  values of the selected compounds. We also surveyed literature for tool compounds, which we also re-synthesized on-DNA. This made up the additional molecules found in the "extended" set.
+
+![](images/8a883f1e4b517adbe27b868bfae6abf3f6cbb4a7aa95c6cc906794d4c75948d7.jpg)  
+(a) MAPK14 on-DNA
+
+![](images/63f8631d05b71fa80eb76ef273da1336df428f7b21f0859226d8889e196cdbab.jpg)  
+(b) MAPK14 off-DNA
+
+![](images/a76cea3123d3330775033fc4ea1e14335ce6de525c5699fb921e1e66a33dbeb4.jpg)  
+(c) DDR1 on-DNA  
+Figure 8: Distributions of  $\mathbf{pK}_D$  values in the in-library held-out sets.
+
+![](images/8fd5021763e0c8cb3e0ceec3d739f092d3d9b9df250fce5c1950009359adfb0d.jpg)  
+(d) DDR1 off-DNA
+
+# D. Model Hyperparameters
+
+This section describes the hyperparameters used to train the models presented in this study. Random Forest and XGBoost used 100 decision trees trained with the squared error criterion, and the depth of decision trees was not restricted. The k-Nearest Neighbors model used 5 nearest neighbors.
+
+The final architecture of the DNN model consisted of 5 linear layers with the ReLU activation functions except for the last one. Batch norm and dropout layers (with the probability of zeroing an element equal to  $20\%$ ) were applied after each layer before the activation layers. The hidden dimension size was set to 512 for all layers.
+
+The GIN model has 5 GIN convolutional layers with hidden dimension size equal to 256. The graph convolutional layers are followed by the global average pooling layer and two linear layers with a ReLU activation layer between them. The first linear layer reduces the dimensionality from 256 to 128 before the second layer produces the model prediction.
+
+Chemprop uses three layers of bond message passing with the hidden dimension of 300. Then, the information is aggregated using a global average pooling layer, and one linear layer is used to make predictions. The model is trained using the default Chemprop optimization procedure, which employs the Adam optimizer with a Noam learning rate scheduler and 2 epochs of warmup.
+
+The DEL-Compose model was used in two modes of molecule encoding: synthon-based encoding (denoted DEL-Compose $^{(S)}$ ) and full molecule encoding (denoted DEL-Compose $^{(M)}$ ). The full molecule encoding uses four linear layers with ReLU activation functions to learn the encoding of the molecule based on its Morgan fingerprint. The synthon-based mode embeds each synthon separately using the same 4-layer MLP. Next, combinations of synthon embeddings (AB, BC, AC, ABC) are further processed by 2-layer MLPs, and finally all embeddings are aggregated using a 4-head attention pooling. The output distribution was set to zero-inflated Poisson distribution. The learning rate used to train DEL-Compose was 5e-5, and the batch size was 64.
+
+# E. Dataset Splitting
+
+It is often difficult to ensure that information from the test set does not leak into train. One popular method is calculating Bemis-Murcko scaffolds (Bemis & Murcko, 1996) for each compound in a dataset and assigning compounds to a split by scaffold. Unfortunately, this method often fails for DEL data. Below we calculate Bemis-Murcko scaffolds for the top million compounds in the MAPK14 dataset using rdkit (Landrum, 2010). There are  $\sim 300,000$  unique scaffolds calculated for these compounds, implying many compounds have a unique scaffold (see Fig. 9a). Additionally the common scaffolds are often trivial (see Fig. 9b). The most common scaffold is a simple benzene, and the next five most common are also extremely common molecular building blocks. Given these shortcomings, we do not use a scaffold split.
+
+An alternative method is a similarity split based on clustering with fingerprints. A classic method for this is Butina Clustering (Butina, 1999). Unfortunately, it does not scale well to large datasets. We have developed an internal method that scales to large datasets. Our two step method first uses UMAP (McInnes et al., 2018) to reduce 1024 ECFP4 fingerprints (Rogers & Hahn, 2010) to length 10 float vectors. Then HDBSCAN (McInnes et al., 2017) is used to cluster compounds, in a GPU implementation from NVIDIA (cuml) this runs in a few hours on a single Tesla T4. Clusters are assigned to splits using a waterfall method, at each step assigning the largest remaining cluster to the smallest current split. The following settings were used:
+
+UMAP(n_components=10, metric="jaccard", n_neighbors=30, min_dist=0.0, n_epochs=1000)
+
+HDBSCAN(min_cluster_size=10, min_samples=None, metric='euclidean', prediction_data=True, cluster_selection_method='eom')
+
+![](images/761204ae0e924fb790f2eb08e95c509ede805a3d08558b867da5bc83450c76c6.jpg)  
+(a) Number of occurrences for the 100 most common scaffolds in the top one million compounds for MAPK14. The number of compounds assigned to each scaffold declines rapidly, and many scaffolds are unique.
+
+![](images/c9fca6028d3d95cacd1adb2c79f45c996a4000666e79fb2a1bc954bb88643430.jpg)  
+10061 counts
+
+![](images/5acfa47a42081c365b98e12653eedf6de593c47eafb49b2f865c58c65a01ed97.jpg)  
+2476 counts
+
+![](images/dd22b81f2d5a238a0b576264d4791e6b90d83dc11474a810903d8697482d02a8.jpg)  
+1927 counts
+
+1894 counts  
+![](images/d3aff103dbc979ec985941736a648b150d255bd03aa0a4e7cd561f9caea299b6.jpg)  
+(b) The top six most frequent scaffolds are common structures that are not pharmacologically "interesting".
+
+![](images/e9ea7244d4bdeaea7071c9e4f9dd8b8f4433c1f6b415c5104125c99a849c28d7.jpg)  
+1859 counts
+
+![](images/56d5f1840f602d8dd5c943119fe5c6ecfb312795e532e79f51c74e0c452de746.jpg)  
+1670 counts  
+Figure 9: Bemis-Murcko scaffolds in KinDEL. The high number of unique scaffolds and the simplicity of the most common scaffolds indicate that a scaffold-based split is not challenging enough for our benchmark.
+
+![](images/5142d134d919097dd39204f196d775151114da988667bcef961e22a03bb21906.jpg)  
+(a) DDR1
+
+![](images/b2ca68b1f6a6d0af95974cf54b92b8aa86a429bccf5099cbc535fa1172bcee86.jpg)  
+(b) MAPK14  
+Figure 10: Example ligands from the KinDEL datasets docked to our selected kinases; (a) example pose of a library member docked to a DFG-out conformation of DDR1 (PDB: 6FEX), forming extensive hinge interactions. Beta-1 and -2 hidden for clarity; (b) example pose of a library member docked to a DFG-out conformation of MAPK14 (PDB: 3KQ7), bridging the activation loop and C-alpha glutamate.
+
+# F. Molecular Docking Procedure
+
+Tautomer and protonation state selection was performed using Epik Classic (Shelley et al., 2007) from Schrödinger Suite 2024-4 at pH 7.4. For each library member, a random subset of stereoisomers was enumerated using rdkit 2023.09.2 (up to 32), then 4 conformers per stereoisomer were generated using ETKDGv3 (Wang et al., 2020). Up to 8 of the lowest-energy conformers under the UFF force field (Rappé et al., 1992) (max 1 per stereoisomer) were retained, for compounds with UFF parameters for all atoms (otherwise, up to 8 random conformers). Docking was performed using the Vina scoring function (Trott & Olson, 2010) in Uni-Dock 1.1.2 (Yu et al., 2023) with exhaustiveness 128 and max_step 20, saving the top three poses per receptor. All of these 234k ligand states were docked against all six receptor models, using a fixed 20 Å docking box centered on the orthosteric pocket.
+
+One receptor model represents the major conformation of DDR1 in available experimental structures, the DFG-out, C-helix-in PDB: 6FEX (Richter et al., 2018). Five receptor models were chosen to represent most experimental structures of MAPK14, with a variety of activation loop and P-loop conformations, PDB: 3KQ7, 3S3I, 5WJJ, 5XYY, and 6SFI (Cheng et al., 2009; Aiguadé et al., 2012; Kaieda et al., 2018; Wang et al., 2017; Rohm et al., 2019). All receptors were prepared using the Protein Preparation Wizard from Schrödinger Suite 2023-4, capping termini with neutral ends, and aligned into a common frame.
+
+Docked poses are provided in SDF format with "molecule_hash" and "receptor" properties. Example poses are shown in Figure 10, where the hinge binding motif that is characteristic for kinases can be observed.

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2025/Knowledge Retention in Continual Model-Based Reinforcement Learning/full.md

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+# Knowledge Retention in Continual Model-Based Reinforcement Learning
+
+Haotian Fu  $^{*1}$  Yixiang Sun  $^{*1}$  Michael Littman  $^{1}$  George Konidaris  $^{1}$
+
+# Abstract
+
+We propose DRAGO, a novel approach for continual model-based reinforcement learning aimed at improving the incremental development of world models across a sequence of tasks that differ in their reward functions but not the state space or dynamics. DRAGO comprises two key components: Synthetic Experience Rehearsal, which leverages generative models to create synthetic experiences from past tasks, allowing the agent to reinforce previously learned dynamics without storing data, and Regaining Memories Through Exploration, which introduces an intrinsic reward mechanism to guide the agent toward revisiting relevant states from prior tasks. Together, these components enable the agent to maintain a comprehensive and continually developing world model, facilitating more effective learning and adaptation across diverse environments. Empirical evaluations demonstrate that DRAGO is able to preserve knowledge across tasks, achieving superior performance in various continual learning scenarios.
+
+# 1. Introduction
+
+Model-based Reinforcement Learning (MBRL) aims to enhance decision-making by developing a world model that captures the underlying dynamics of the environment. A robust world model allows an agent to predict future states, plan actions, and adapt to new situations with minimal real-world trial and error. For MBRL to be effective in dynamic, real-world applications, the world model must incrementally learn and adapt, continually integrating new information as the agent encounters diverse environments and tasks.
+
+Imagine an agent initially exploring a small, confined part of a complex world, like a home-assistance robot learning to navigate a kitchen. At first, the robot masters dynamics
+
+specific to that environment, such as avoiding countertops and maneuvering around chairs. When deployed to a new household, it must adapt to unfamiliar layouts while retaining its understanding of prior environments. Over time, as the robot encounters diverse settings—homes with varying furniture arrangements, hospitals with strict privacy constraints, or factories with evolving machinery—it must incrementally integrate new dynamics without forgetting earlier knowledge. This process aligns with the principles of continual learning, where agents progressively acquire new skills across tasks while preserving past experiences (Lange et al., 2022). However, real-world constraints often prohibit storing raw interaction data from prior tasks due to: 1. Storage limitations: Robots or embodied agents cannot indefinitely retain growing datasets (Hadsell et al., 2020). 2. Privacy regulations: Healthcare or service robots handling sensitive data may be restricted from archiving task-specific interactions (Kemker et al., 2018). 3. On-device deployment: Deployed AI systems (e.g., smartphones) often rely on pre-trained models where the original training data is proprietary or privacy-sensitive.
+
+In principle, continual MBRL would enable agents to learn a generalizable world model supporting a universal set of tasks. If data from all previous tasks are available, multitask learning strategies (Fu et al., 2022) could solve this by leveraging shared dynamics. However, in storage- or privacy-constrained settings, agents lack access to prior task data, rendering such approaches infeasible. In practice, we actually always have bounded storage. If we consider the hardest case, where no previous data is available: as shown in Figure 1 and our experiments, naive MBRL suffers catastrophic forgetting, overwriting critical dynamics (e.g., a robot forgetting kitchen layouts after learning living rooms). To address this, we need strategies that retain essential knowledge without storing past data, enabling agents to build increasingly complete world models across tasks.
+
+Specifically, we propose DRAGO, a novel continual MBRL approach designed to address catastrophic forgetting and incomplete world models in the absence of prior task data. DRAGO consists of two key components: Synthetic Experience Rehearsal and Regaining Memories Through Exploration. Synthetic Experience Rehearsal uses a continually learned generative model to enable the agent to simulate and learn from synthetic experiences that resemble those
+
+![](images/46aeec0035f967c1f23ce4f11f7a266db5713230b704eb892f6f9acbad77c0a9.jpg)  
+Figure 1. Comparison between the world model learned by naive continual MBRL and MBRL without forgetting. Each task requires the agent to move from the corner of one room to a specific point in the same room. Shaded areas represent the world model's coverage after finishing each task. Naively continually training MBRL (Left) tends to suffer the catastrophic forgetting problem—the agent forgets almost everything about the first room after training in the second room (our experimental results support this claim). Our project identifies a method (Right) that helps the world model preserve the knowledge of previous tasks even when the old data is no longer available.
+
+![](images/9d913d0d16c24c20d5ca936c63136eed06b6e89496fe9e99f5911b629bece628.jpg)
+
+from prior tasks. This process allows the agent to synthesize representative transitions that resemble prior experience, reinforcing its understanding of previously learned dynamics without requiring access to past data. In the Regaining Memories Through Exploration component, we introduce an intrinsic reward mechanism that encourages the agent to actively explore states where the previous transition model performs well. This exploration bridges the gap between tasks by discovering connections within the environment, leading to a more comprehensive and cohesive world model. To sum up, we make the following contributions:
+
+1. We introduce DRAGO, a new approach for continual model-based reinforcement learning that addresses catastrophic forgetting while incrementally learning a world model across sequential tasks without retaining any past data.  
+2. We propose a generative replay mechanism that synthesizes "old" transitions using a learned generative model alongside a frozen copy of the previously trained world model.  
+3. We design an intrinsic reward signal that nudges the agent toward revisiting states that the old model explained well—effectively "reconnecting" current experiences with previously learned transitions.  
+4. Through experiments on MiniGrid and DeepMind Control Suite domains, we show that DRAGO substantially improves knowledge retention compared to standard continual MBRL baselines and achieves higher transfer performance, allowing faster adaptation to entirely new (but related) tasks. Code is available at https://github.com/YixiangSun/drago.
+
+# 2. Background
+
+In reinforcement learning, an agent interacts with an environment modeled as a Markov Decision Process (MDP). An MDP is defined by a tuple  $< S, \mathcal{A}, T, r, \gamma >$ , where  $S$  is the state space,  $\mathcal{A}$  is the action space,  $T(s' \mid s, a)$  represents the transition dynamics,  $r(s, a)$  is the reward function, and  $\gamma \in [0,1)$  denotes the discount factor. Throughout this paper,  $T$  is the parametric transition model (the learned dynamics predictor) and  $p$  denotes a probability or distribution.
+
+In continual model-based reinforcement learning, the agent is presented with a sequence of tasks  $\mathcal{T}_1,\mathcal{T}_2,\ldots ,\mathcal{T}_n$ . We assume the agent knows when the task switches. Each task  $\mathcal{T}_i$  is associated with its own MDP,  $\mathcal{M}_i = (\mathcal{S},\mathcal{A},T,r_i,\rho_i,\gamma)$ , where  $r_i(s,a)$  is the task-specific reward function, and  $\rho_{i}(s)$  denotes the initial state distribution for task  $\mathcal{T}_i$ . Importantly, all tasks share the same transition function  $T(s^{\prime}\mid s,a)$ , which defines the probability of reaching state  $s^\prime \in S$  from state  $s\in S$  after taking action  $a\in \mathcal{A}$ . In this paper, we consider the case where, in each task, the agent tends to be exposed to distinct aspects of the transition dynamics and different termination states.
+
+The objective in continual MBRL is to efficiently solve the sequence of tasks, while learning a world model  $T_{\psi}(s' \mid s, a)$ , parameterized by  $\psi$ , that captures the shared dynamics across all tasks, allowing the agent to adapt to the task-specific objectives defined by  $r_i$  and  $\rho_i$ . A challenge arises because, during training on a new task  $\mathcal{T}_i$ , the agent in our setting only has access to the replay buffer  $\mathcal{B}_i = \{(s, a, s')\}$ .
+
+# 3. DRAGO
+
+The central question in this paper is: how do we aggregate the knowledge from previous tasks and learn a increasingly complete world model without forgetting, while trying to solve a sequence of tasks using MBRL? As shown in previous works (Fu et al., 2022), the agent can easily learn a general world model in a multitask/meta-learning way as long as the access to previous tasks' memories is given. Thus, a straightforward way is to figure out an approach that is able to regain the old memories that had to be discarded. We propose DRAGO, a continual MBRL approach is composed of two main components: dreaming and rehearsing old memories while training on new tasks ( $\S 3.1$ ), and regaining memories via actively exploration ( $\S 3.2$ ). Then we introduce the overall algorithm in  $\S 3.3$ .
+
+# 3.1. Synthetic Experience Rehearsal
+
+To help the agent retain knowledge from previous tasks without direct access to past data, we introduce a method called Synthetic Experience Rehearsal. This approach enables the agent to internally generate and learn from synthetic experiences that resemble those from prior tasks, effectively reinforcing its understanding of the environment's dynamics and mitigating catastrophic forgetting.
+
+The concept of Synthetic Experience Rehearsal draws inspiration from how humans and animals replay and consolidate memories during sleep (Wilson & McNaughton, 1994). Just as dreaming allows for the consolidation of memories and learning in biological systems, our method helps the agent retain and reinforce knowledge of previous dynamics by generating and learning from synthetic experiences. Imagine a robot that has navigated through several rooms in a building. As it progresses to new rooms, it may begin to forget the layouts and navigation strategies of earlier ones due to limited memory capacity and the inability to revisit those rooms. By internally generating and rehearsing synthetic experiences that mimic its interactions in earlier rooms, the robot can maintain and reinforce its knowledge of how to navigate them. This internal rehearsal helps it integrate past experiences with new ones, ensuring a more comprehensive understanding of the entire environment.
+
+Our method leverages a generative model (which is also continually learned) to produce synthetic data that aids in training the dynamics model, thereby preventing forgetting of previously learned dynamics. Note that for real-world tasks, retaining the model (neural nets) usually costs much less than retaining all the training transitions, especially when the task number grows larger and larger.
+
+Specifically, we employ a generative model  $G$  that encodes and decodes both states and actions, capturing the joint distribution of state-action pairs encountered in previous tasks.
+
+Including actions is crucial, especially in continuous action spaces where randomly sampled actions may not correspond to meaningful behaviors. Throughout the continual learning process, we also keep one copy of the old world model learned after finishing the last task (one for all previous tasks, not one for each). Then after generating the state-action pair, we feed it into this frozen old model  $T_{\mathrm{old}}$  and generate a synthetic next state. The synthetic data used for training the model is generated through the following steps:
+
+$$
+\hat {s} ^ {\prime} = T _ {\text {o l d}} (\hat {s}, \hat {a}), (\hat {s}, \hat {a}) \sim p _ {G} (s, a; \theta), \tag {1}
+$$
+
+where  $p_G(s, a; \theta)$  is the distribution modeled by the generative model  $G_{\theta}$  with parameters  $\theta$ .  $T_{\mathrm{old}}$  is the frozen old world model, capturing the dynamics up to a previous task.
+
+We can express the likelihood of the entire dataset, including both real data  $\mathcal{D}_i$  for current task  $\mathcal{T}_i$  and synthetic data  $\hat{\mathcal{D}}$ , given the parameters  $\psi$  and  $\theta$ , as follows:
+
+$$
+p (\mathcal {D} _ {i}, \hat {\mathcal {D}} \mid \psi , \theta) =
+$$
+
+$$
+\prod_ {(s, a, s ^ {\prime}) \in \mathcal {D} _ {i}} p \left(s ^ {\prime} \mid s, a; \psi\right) \prod_ {(\hat {s}, \hat {a}, \hat {s} ^ {\prime}) \in \hat {\mathcal {D}}} p _ {G} (\hat {s}, \hat {a}; \theta) p \left(\hat {s} ^ {\prime} \mid \hat {s}, \hat {a}; \psi\right), \tag {2}
+$$
+
+where  $p(s' \mid s, a; \psi)$  is the likelihood of observing  $s'$  given  $s$  and  $a$  under the transition model  $T_{\psi}$ ,  $p_G(\hat{s}, \hat{a}; \theta)$  is the likelihood of generating synthetic state-action pairs from the generative model  $G_{\theta}$ . This joint likelihood captures the dependencies of the synthetic data on both the generative model parameters  $\theta$  and the frozen transition model  $T_{\mathrm{old}}$ .
+
+The posterior distribution over the transition model parameters  $\psi$  and the generative model parameters  $\theta$  is given by Bayes' theorem:
+
+$$
+p (\psi , \theta \mid \mathcal {D} _ {i}, \hat {\mathcal {D}}) \propto p (\mathcal {D} _ {i}, \hat {\mathcal {D}} \mid \psi , \theta) p (\psi) p (\theta), \tag {3}
+$$
+
+where  $p(\psi)$  and  $p(\theta)$  are the prior distributions over the parameters.
+
+Taking the negative logarithm of the posterior (and ignoring constants independent of  $\psi$  and  $\theta$ ), we obtain the joint loss function:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} (\psi , \theta) = - \log p (\mathcal {D} _ {i}, \hat {\mathcal {D}} \mid \psi , \theta) - \log p (\psi) - \log p (\theta) \\ = -\log p(\psi) - \log p(\theta)\underbrace{-\sum_{(s,a,s^{\prime})\in\mathcal{D}_{i}}\log p(s^{\prime}\mid s,a;\psi)}_{\text{Loss on current task data}} \\ - \underbrace {\sum_ {(\hat {s} , \hat {a})} \log p _ {G} (\hat {s} , \hat {a} ; \theta) - \sum_ {(\hat {s} , \hat {a})} \log p \left(\hat {s} ^ {\prime} \mid \hat {s} , \hat {a} ; \psi\right)} _ {\text {S y n t h e t i c d a t a l i k e l i h o o d}}. \tag {4} \\ \end{array}
+$$
+
+The dynamics model is trained by minimizing the prediction loss over the combined dataset:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {d y n}} (\psi) = \mathbb {E} _ {(s, a, s ^ {\prime}) \sim \mathcal {D} _ {i}} \left[ \| s ^ {\prime} - T _ {i} (s, a; \psi) \| ^ {2} \right] \tag {5} \\ + \lambda \mathbb {E} _ {(\hat {s}, \hat {a}) \sim p _ {G} (s, a; \theta)} \left[ \left\| T _ {\mathrm {o l d}} (\hat {s}, \hat {a}) - T _ {i} (\hat {s}, \hat {a}; \psi) \right\| ^ {2} \right], \\ \end{array}
+$$
+
+where  $\lambda$  is a weighting factor controlling the importance of the synthetic data loss. While this enables the agent to learn from synthetic old experience, the generative model itself (minimizing  $-\sum \log p_{G}(\hat{s},\hat{a};\theta)$  in Eqn 4) also requires accumulating the knowledge of different tasks as the training goes on. Retaining such a generative model for every task will also introduces huge additional cost.
+
+Continual learning for the generative model. To prevent forgetting within the generative model itself, we adopt a continual training strategy. We generate synthetic state-action pairs using the previous generative model  $G_{i-1}$ :
+
+$$
+(\tilde {s}, \tilde {a}) = G _ {i - 1} (\tilde {z}), \tilde {z} \sim p (z),
+$$
+
+and combine these with real data from the current task to form the training dataset for the new generative model:  $\mathcal{D}_{\mathrm{gen}} = \mathcal{D}_i\cup \tilde{\mathcal{D}}$  , where  $\tilde{\mathcal{D}} = \{(\tilde{s},\tilde{a})\}$  . The new generative model  $G_{i}$  - we use Variational AutoEncoder (VAE) (Kingma & Welling, 2014) - is then trained by minimizing the loss over  $\mathcal{D}_{\mathrm{gen}}$  ..
+
+$$
+\begin{array}{l} \mathcal {L} _ {\text {g e n}} \left(\theta_ {i}\right) = \mathbb {E} _ {(s, a) \sim \mathcal {D} _ {\text {g e n}}} \left[ - \mathbb {E} _ {z \sim q _ {\theta_ {i}} (z | s, a)} \left[ \log p _ {\theta_ {i}} (s, a \mid z) \right] \right. \tag {6} \\ \left. + \operatorname {K L} \left(q _ {\theta_ {i}} (z \mid s, a) \| p (z)\right) \right]. \\ \end{array}
+$$
+
+This continual learning procedure ensures that the generative model retains its ability to produce state-action pairs representative of all previous tasks.
+
+Our method is general and can be applied with other types of generative models. Additionally, integrating more sophisticated generative models, such as diffusion models, could further enhance the quality of synthetic experiences and improve knowledge retention in high-dimensional environments. We leave this for future work.
+
+# 3.2. Regaining Memories Through Exploration
+
+While generating synthetic data via a generative model helps mitigate forgetting, it may not fully capture the richness of real experiences and it is subject to model error. In the meantime, to eventually build a complete world model, we would like to find a way that can "connect" knowledge gained from different tasks if they are disjoint. Thus, to further enhance the agent's retention of prior knowledge and make the world model more complete, we propose an intrinsic reward mechanism that encourages the agent to actively explore states where the previous transition model performs well, effectively "regaining" forgotten memories through real interaction with the environment, and fill in the gap between knowledge of different tasks.
+
+Our approach is inspired by the need to complement the generation-based rehearsal method with actual exploration that bridges the gap between different tasks. The generative model can produce states from prior tasks, but these imagined states might not be naturally encountered or connected
+
+within the current task. Consider the earlier example of a robot exploring different rooms within a building. The method introduced in the last section can generate imagined states from previously visited rooms, but without actual exploration, the robot might not find the doorways or corridors connecting these rooms to its current location. Our intrinsic reward incentivizes the robot to search for these connections, enabling it to discover pathways that link the new room to the old ones. Without exploring the actual environment to find these connections, the agent's world model remains fragmented, lacking a cohesive understanding of how different regions relate. To overcome this, we propose an intrinsic reward that guides the agent to:
+
+- Revisit Familiar States: Encourage exploration of states where the previous model  $T_{i - 1}$  predicts accurately, indicating familiarity from earlier tasks.  
+- Discover New Connections: Incentivize the agent to find paths that connect current and previous task environments, enriching the world model's completeness.  
+- Balance Learning Dynamics: Deter the agent from spending excessive time in regions where the current model  $T_{i}$  already performs well.
+
+Specifically, during training on task  $\mathcal{T}_i$ , we introduce an intrinsic reward  $r_{\mathrm{cont}}^i$  designed to guide the agent towards states that are familiar to the previous transition model  $T_{i-1}$  (trained and froze after task  $\mathcal{T}_{i-1}$ ) but less familiar to the current model  $T_i$ . The intrinsic reward is defined as:
+
+$$
+\begin{array}{l} r _ {\text {c o n t}} ^ {i} \left(s _ {t}, a _ {t}, s _ {t + 1}\right) := \sigma (- \log \left| T _ {i - 1} \left(s _ {t}, a _ {t}\right) - s _ {t + 1} \right|) \tag {7} \\ - \alpha \cdot \sigma (- \log | T _ {i} (s _ {t}, a _ {t}) - s _ {t + 1} |), \\ \end{array}
+$$
+
+where  $\sigma$  denotes the sigmoid function, and  $\alpha$  is a weighting coefficient that balances the two terms.
+
+Intuitively the first term assigns higher rewards when the previous transition model  $T_{i-1}$  predicts the next state  $s_{t+1}$  accurately. This incentivizes the agent to revisit states that were well-understood in previous tasks. The second term penalizes the agent for visiting states where the current model  $T_i$  already has low prediction error. This encourages the agent to explore less familiar areas to improve the current model's understanding.
+
+By actively exploring and connecting different regions, the agent's world model becomes more comprehensive, capturing the dynamics across tasks more effectively. Revisiting familiar states reinforces prior knowledge, reducing the tendency of the model to forget previously learned information. This approach complements the synthetic data generation in Section 3.1 by providing actual experience that reinforces the agent's knowledge.
+
+![](images/8fadb3f34ea0ae8692e8b13f0013006d79cda2a15b6e1cee737bdd75acbbe592.jpg)  
+Figure 2. The two-step process of how DRAGO retain and aggregate the knowledge learned from prior tasks for the world model. Step 1 involves Synthetic Experience Rehearsal, where synthetic state-action pairs are generated from the previous tasks' generative model  $G_{i-1}(z)$ , and next states  $\hat{s}'$  are predicted using the previous transition model  $T_{i-1}$ . Step 2 introduces Regaining Memories through Exploration, where an intrinsic reward  $r_{\text{cont}}^i$  encourages the agent to explore states where the previous transition model  $T_{i-1}$  performs well, while penalizing states that the current model  $T_i$  already predicts accurately. Together, these components allow the agent to retain and transfer knowledge across tasks.
+
+# 3.3. Overall Algorithm
+
+We implement DRAGO on top of TDMPC (Hansen et al., 2022) and the overall algorithm is described in Algorithm 1. Compared to regular TDMPC algorithm, we additionally train an encoder and decoder for the state-action pair as part of the generative model in §3.1. To integrate the intrinsic reward for regaining memories proposed in §3.2, we train an additional reward model, value model, and policy as a "reviewer" that aims to maximize the cumulative intrinsic reward, besides the original "learner" that aims to maximize the cumulative environmental reward. Note that the reviewer and the learner share the same world model, which is also trained using data from both.
+
+During the inference step, DRAGO leverages Model Predictive Path Integral (Williams et al., 2015) as the planning method. Given an initial state and task  $\mathcal{T}_i$ , DRAGO samples  $N$  trajectories with the world model  $T_{i}$  and estimates the total return  $J_{\tau}$  of each sampled trajectory  $\tau$  as:
+
+$$
+J _ {\tau} := \mathbb {E} _ {\tau} \left[ \sum_ {t = 0} ^ {H - 1} \gamma^ {t} R _ {s _ {t}, a _ {t}} + \gamma^ {H} Q \left(s _ {H}, a _ {H}\right) \right], s _ {t + 1} \sim T _ {i} \left(s _ {t}, a _ {t}; \psi\right), \tag {8}
+$$
+
+where  $Q(\cdot)$  is the learned value function. Then a trajectory with the highest return is picked and the agent will execute the first action in the trajectory.
+
+During training, the dynamics model and the generative model are trained together with the reward&value prediction of the learner and reviewer. At the beginning of each new task, for each new test task, we randomly initialize the reward, policy and value models and reuse only the world model (dynamics). Moreover, unlike TDMPC, the gradients from updating Q function and reward model are detached for updating the dynamics model in DRAGO. More implementation details can be found in the appendix.
+
+![](images/a29f2d9b3b153e19275f47fec0934acd3c2e7b043c4fd6514e097bef89f7f300.jpg)  
+Figure 3. Visualization of the evaluated domains. Task names in Blue denote the continual training tasks; Task names in Red denote the test tasks. We train and test all the tasks in the order of left to right as in the figure. E.g., we train the cheetah agent in the order of run, jump and backward. And after training on jump, we test on jump2run and jump&run.
+
+# 4. Experiments
+
+We evaluated DRAGO on three continual learning domains. For each domain, we let the agent train on a sequence of tasks, where the tasks share the same transition dynamics but different reward functions. Although the transition dynamics are the same, the training tasks are designed in a way such that to solve each task only part of the state space's transition dynamics needs to be learned and different tasks involve learning transition dynamics corresponding to different parts of the state space with a small overlap. We evaluate the agent's continual learning performance on test tasks by measuring the agent's training performance on them, using the retained world model as an initiation. The test tasks require the combination of knowledge from more than one previously learned tasks. For example, to better transfer on Cheetah jump2run the agent is expected to still remember the knowledge learned in Cheetah run even after continual training on Cheetah jump. These transfer tasks
+
+are designed to test the agent's ability to retain knowledge from previous tasks, as solving them requires understanding multiple tasks.
+
+MiniGrid. We evaluated the performance of DRAGO in the MiniGrid (Chevalier-Boisvert et al., 2023) domain using a sequence of four tasks, each set in one of the four rooms of a  $27 \times 27$  gridworld. In each task, the agent starts from a fixed corner of one room, with the objective of reaching a specified goal position within that room. The obstacles vary across tasks and the agent can only access other rooms by passing through a door located at the center of the gridworld, which creates a bottleneck that the agent must learn to navigate effectively in transfer tasks. Each task requires exploring a small and mostly non-overlapping portion of the world, ensuring that knowledge from one task does not directly overlap with others. To assess transfer performance, we evaluated the models learned at different stages of the continual learning process (i.e., after completing 2, 3, and 4 tasks). The evaluation was conducted on four new tasks that require the agent to move between different rooms (e.g., start in room 1 and move to the goal position in room 2). The tasks are designed such that solving them requires understanding multiple rooms.
+
+Deepmind Control Suite. We also evaluated the performance of DRAGO in the Cheetah and Walker domains from the Deepmind Control Suite (Tassa et al., 2018). For each domain, we define a sequence of tasks that share the same dynamics but with different task goals, which requires the agent to learn different parts of the state space of dynamics. Similarly, to assess transfer performance, we evaluated the models learned at different stages of the continual learning process. The evaluation was conducted on several new tasks that require the agent to quickly change to different locomotion modes from another mode (jump, run, etc.), except for two tasks: jump and runforward & jump and runbackward, where the agent will get the maximum reward if it runs forward/backward and jumps at the same time.
+
+We compared to baselines including: Training TDMPC from scratch for each task, continual TDMPC, where we initialize the world model with the one learned in the previous task at the beginning of the new task and train it with the task reward, and EWC, a regularization-based continual learning method as we introduced in the related work section. We use TDMPC as the base model-based reinforcement learning (MBRL) algorithm for all the baselines. More experimental results can be found in appendix E & D.
+
+# 4.1. Qualitative Results
+
+In Figure 4, we also visualize the prediction accuracy of the learned world models across the whole gridworld, comparing just naively continually training TDMPC and our method. The prediction score is calculated based on the
+
+states predictions' mean square error (MSE). The results are aligned with our intuition. Without other counter-forgetting techniques, world models easily forget almost everything learned in previous tasks and are only accurate in the transition space related to the current task. By contrast, DRAGO is able to retain most of the knowledge learned in previous tasks and have a increasingly complete world model as training continues, leading to the performance gain on new tasks shown in Figure 5. Note that DRAGO's performance without Synthetic Experience Rehearsal (so only has the Regaining Memories Through Exploration Component) drops a bit compared to the full version, but it still exhibits better knowledge retention to some extent in post-task3 and post-task4, compared to naive continual TDMPC. As we also show in the ablation study, combining two components of DRAGO eventually achieves the best overall performance.
+
+# 4.2. Overall Performance
+
+As shown in Figure 5, we find that the proposed method DRAGO achieves the best overall performance compared to all the other approaches across three domains. The results demonstrate its advantage in continual learning settings by effectively retaining knowledge from previous tasks and transferring it to new ones. We can also see that naively continual Model-based RL may suffer from severe plasticity loss: Continual TDMPC constantly performs worse than learning from scratch baseline. Equipped with EWC, it can achieve better overall performance but still not as good as DRAGO. But DRAGO does not fully alleviate the plasticity loss, in Cheetah Jump and runbackward (Last plot in the mid row of Figure 5), learning from scratch still has the best performance, but we can see that DRAGO still improves a lot compared to Continual TDMPC.
+
+# 4.3. Ablation Study
+
+This section evaluates the essentiality of DRAGO's components. Specifically, we evaluate DRAGO's performance without Synthetic Experience Rehearsal and Regaining Memories Through Exploration (reviewer) separately in four transfer tasks of Cheetah and MiniGrid. As we show in Figure 7, while DRAGO w/o. Rehearsal achieves similar performance with the full version in Cheetah-jumpandrunforward, the full DRAGO still has the best overall performance across domains. If we compare the performance with Continua TDMPC shown in Figure 5, one single component of DRAGO consistently improves continual learning performance. These results highlight the complementary roles of both components and demonstrate that each contributes significantly to mitigating forgetting and enhancing transfer capabilities in continual model-based RL settings.
+
+![](images/0857120e97d27496138f3a5eb8f593bf3fa1ab6a6038c92973f98692a0d56708.jpg)
+
+![](images/81d46c69937e02418cd0c19d3d22ebef968570a10700afd75e139112cb180b77.jpg)
+
+![](images/8821ea28c6c48a3c6f30ceeee3882d28b4fbf00c995aff2668e576c810d2b78a.jpg)
+
+![](images/9278a05e26c5797c70cc09558d0c4e586ae17f8ec51fec53eed50e06b134f4f0.jpg)
+
+![](images/31b25ca0a09afbcd708555321524521b23130bffc5049de375a210ab8e5d0c64.jpg)
+
+![](images/4b9e68b5f41da89dd7d852efe305176f105b0c7b0335f3f40a06830a41fe5cbe.jpg)
+
+![](images/418ef6980dc08917a83aba50555c6c2a55a7d0f8bf3eaaeab72564b3aa64747c.jpg)
+
+![](images/4d21cfb2d61a47ca93d71179fe7460092fc86e959d2e5a3becfc96853eaedbdc.jpg)
+
+![](images/dceae8de9dc200cf73544043bf67c3d7e60ff6196f6d115d94ff4add99799997.jpg)  
+Figure 4. DRAGO reduces the catastrophic forgetting from previous tasks, illustrated by the prediction score of the learned world models across the entire gridworld after each task. Light color indicates higher prediction accuracy. The heatmaps compare the performance of naive continual training of TDMPC (top row), DRAGO without Synthetic Experience Rehearsal (mid row), with our proposed full DRAGO method (bottom row) after Tasks 1 to 4. The results show that continual MBRL suffers from significant forgetting, maintaining accuracy only in regions relevant to the current task, whereas DRAGO effectively retains knowledge from previous tasks.
+
+![](images/f9b2dafa4806d38a4d9b391a6399b4ae8c9d01509e11f771a07fa7aecce12864.jpg)
+
+![](images/02e1a944f3528abbb4e6300c75dbaeff29b48cceba31940f29eed67a373d78b1.jpg)
+
+![](images/f3d097815bb1d00a5065c7a705d514eccd7461d33b9f8c8ca770b204af559d93.jpg)
+
+![](images/36515edc97c2ee65bf9e8c27afa62999a24a93b2319ca28998a675d8285a8421.jpg)
+
+![](images/9adf32f9e8fbb6eb90d2dc8ef6d8a0fdb65504da25b18cd7d083016f49d7d168.jpg)
+
+![](images/7548f0e211aecbc6b783d89ce8c80c5254401d70940b81b2fadeb5b8c396f795.jpg)
+
+![](images/7aca332433e407c8c35fe091ac483f144df9a2d9ed045c9fca26da4821913fed.jpg)
+
+![](images/f0e550ba62f2a91332596e4d29b67a2693e123cae5db380e7889b2cd044ef09a.jpg)
+
+![](images/7425d3f9b174bf4f469bb79965825cfda0518f662c6717a1c4d1e42d5d6a1c2b.jpg)
+
+![](images/b42760bb2bc029eeb57647f9c2a24366fd72f2b2df295e08508e89802a036f04.jpg)
+
+![](images/4057ab4db220c92ff13faf40f700a0f9b590a0e8aff38c7dda7c720a3250bab4.jpg)
+
+![](images/ba10927d6dc418f8bc5e3cbcc5d91d1da4719a9f8ecc4649f2de78b67f86dea9.jpg)  
+Figure 5. We evaluate the continual learning transfer performance on 12 tasks (3 domains, 4 tasks each) that are not seen during the agent's previous training. Each plot corresponds to a single test task, and the agent's performance is tracked as it learns that task from scratch, using the retained world model. For each test task of MiniGrid, the agent starts in one room and have to move to the goal in another room. E.g., Transfer 3to4 after 4 means that after sequentially training on four tasks, the agent is tested on a new task where it starts in room 3 and the target position is in room 4. For each test task of Cheetah & Walker, the agent has to start from a state in one locomotion mode and the goal is to switch to another mode. E.g., Jump2runforward after Jump means that after training on Cheetah-Jump, the agent is tested on a new task where it starts in one state of the jumping mode, and the goal is to run forward.
+
+![](images/8d326bc37d1b349783e5a2797d16930d060e57d0bee0361fd7f1fbfccf537131.jpg)
+
+![](images/5a6ee51acf1a2964057b9e2baaf0d6d1f567fdd6c120906ed871268c9488e5d9.jpg)
+
+![](images/8d11ec5561ff4a8516eaec8e9f23b22f1040819002505b264675ae79b8f2eb3e.jpg)
+
+![](images/4a5c3c00ba022c302d69fe5f4c8d6c14857cc2578830d3fd8c90297c550f26ad.jpg)  
+Figure 6. Comparison of DRAGO with (1) Replay-based MBRL, which stores a bounded replay buffer for past tasks (using the same memory size as DRAGO's generative model), and (2) Pseudo-rehearsal MBRL (Ketz et al., 2019), which generates old data via a pretrained VAE model, without continual training of the generative model as well as our intrinsic reward mechanism. Each plot shows Minigrid transfer performance (average return vs. environment steps) on a new task after sequentially training on earlier tasks. DRAGO consistently achieves higher or faster-improving returns, suggesting stronger knowledge retention and quicker adaptation to the transfer tasks.
+
+![](images/f68795d040910c799dc94080310bdec5f135f9145a9d332425acc4ab8ee55430.jpg)
+
+![](images/eb35a6380fcfb96cf1bab11b22a58d6a4ca3b015d393a25609cec39d7730fb1f.jpg)
+
+![](images/10267b92c32eecaf4040a99938539ddeaa3e8c9ab5cc73e9c38b63ef51481fd5.jpg)
+
+![](images/3384fb3c0132c7d777dfbb24408ffa41f4dab39536b67521d8f194f3a40836f8.jpg)  
+Figure 7. Ablation study results on four transfer tasks in the Cheetah and MiniGrid domains, comparing the performance of DRAGO without individual components (Synthetic Experience Rehearsal and Regaining Memories Through Exploration) to the full method. While removing Rehearsal results in competitive performance in the Cheetah-jumpandrunforward task, the full version of DRAGO achieves superior overall performance across all tasks.
+
+![](images/45f78283ba095b41ab5c64755c554c47b4defdeaa4c0255143a76ef28780b549.jpg)
+
+![](images/a9c73bf39eb4e81ce883a74df822f42873fd278a5c1860b29e97214196943636.jpg)
+
+![](images/ecdc57089d7d07f1a12cca9fc44d88ba4a187268f2c9410aa442b3b6bdc502f0.jpg)
+
+# 4.4. Few-shot Transfer Performance
+
+We also evaluated the agent's few-shot transfer performance during the continual learning process and compared the results of DRAGO with the other baselines. The setting is useful and common in real world tasks, especially for robotics, where the number of steps to interact with the environment is limited. Specifically, for each test task in Cheetah and Walker domains, we let the agent train by interacting with the environment for only 20 episodes and evaluate its average cumulative reward after training. As shown in Table 1, DRAGO outperforms the other baselines in 6 out of 8 tasks. In the two tasks where DRAGO does not outperform, it remains competitive, highlighting its robustness and efficiency in continual learning scenarios.
+
+# 5. Related Work
+
+Continual reinforcement learning (CRL) aims to develop agents that can learn from a sequence of tasks, retaining knowledge from previous tasks while efficiently adapting to new ones (Khetarpal et al., 2022; Abel et al., 2023; Anand & Precup, 2023; Baker et al., 2023). Many recent papers investigate the plasticity loss in continual learning (Lyle et al., 2023; Abbas et al., 2023; Dohare et al., 2024). This paper focuses more on how we better retain and aggregate knowledge learned from previous tasks in Continual MBRL, which is related to another central challenge in CRL,
+
+catastrophic forgetting, where learning new tasks causes the agent's performance on earlier tasks to degrade due to the overwriting of important knowledge (McCloskey & Cohen, 1989). To address catastrophic forgetting, several strategies have been proposed: Regularization-Based Methods (Kirkpatrick et al., 2016; Li & Hoiem, 2016; Zenke et al., 2017; Nguyen et al., 2017; Yu et al., 2020a): these approaches introduce constraints during training to prevent significant changes to parameters important for previous tasks. Elastic Weight Consolidation (EWC) (Kirkpatrick et al., 2016) is a prominent example that uses the Fisher Information Matrix to estimate parameter importance and penalize updates accordingly. However regularization-based methods often struggles in practice, especially in reinforcement learning scenarios, due to challenges in accurately estimating parameter importance and scalability issues with large neural networks (Huszár, 2017; Farquhar & Gal, 2018). Replay-Based methods (Riemer et al., 2019; Rolnick et al., 2019; Oh et al., 2022; Henning et al., 2021; Lampinen et al., 2021): these methods typically assume unbounded storage, which is usually not feasible in practice. Our work is therefore focused on the hardest case — alleviating the catastrophic forgetting problem and learn a complete world model without prior data. Generative replay-based methods (Shin et al., 2017; Triki et al., 2017; Rao et al., 2019) share some similar high-level idea with our work. However, none of them has been applied on MBRL or World Models. In terms of Continual MBRL specifically, Fu et al. (2022) show that the
+
+<table><tr><td>Average Reward</td><td>DRAGO</td><td>EWC</td><td>Continual TDMPC</td><td>Scratch</td></tr><tr><td>Cheetah jump2run</td><td>106.78 ± 32.01</td><td>54.72 ± 62.72</td><td>93.96 ± 39.29</td><td>26.54 ± 2.67</td></tr><tr><td>Cheetah jump&amp;run</td><td>248.92 ± 15.38</td><td>156.98 ± 99.68</td><td>128.58 ± 100.14</td><td>182.77 ± 28.58</td></tr><tr><td>Cheetah jump2back</td><td>331.85 ± 11.05</td><td>29.93 ± 7.15</td><td>73.98 ± 38.45</td><td>45.15 ± 4.92</td></tr><tr><td>Cheetah jump&amp;back</td><td>147.30 ± 34.29</td><td>117.92 ± 1.20</td><td>140.82 ± 28.00</td><td>129.75 ± 20.44</td></tr><tr><td>Walker walk2run</td><td>332.38 ± 20.07</td><td>287.02 ± 37.80</td><td>229.14 ± 33.71</td><td>52.11 ± 3.41</td></tr><tr><td>Walker run2back</td><td>145.98 ± 17.96</td><td>150.19 ± 2.77</td><td>128.56 ± 9.47</td><td>60.49 ± 9.40</td></tr><tr><td>Walker back2run</td><td>229.79 ± 9.77</td><td>254.09 ± 70.29</td><td>241.39 ± 42.64</td><td>40.76 ± 18.34</td></tr><tr><td>Walker stand2run</td><td>265.50 ± 8.40</td><td>177.02 ± 62.48</td><td>182.71 ± 30.74</td><td>64.02 ± 31.54</td></tr></table>
+
+Table 1. Comparison of few-shot transfer performance on eight test tasks in Cheetah and Walker. We report the mean and standard deviation of the cumulative reward at the end of training. Bold value indicates the best result.
+
+agent can benefit from a joint world model for adapting to new individual tasks. Similarly, Nagabandi et al. (2019) propose a meta-learning approach where a dynamics model is trained to adapt quickly to new tasks by learning a prior over models. Hypernetwork-based methods (Huang et al., 2021) have been proposed to minimize forgetting while learning task-specific parameters in the multitask setting. Liu et al. (2024) introduces locality-sensitive sparse encoding to learn world models incrementally in a single task online setting. Kessler et al. (2023) investigate how different experience replay methods will affect the performance of MBRL. Related work for model-based RL in general can be found in Appendix B.
+
+# 6. Conclusion
+
+We proposed DRAGO, a novel approach for continual MBRL that effectively mitigates catastrophic forgetting and enhances the transfer of knowledge across sequential tasks. By integrating Synthetic Experience Rehearsal and Regaining Memories Through Exploration, DRAGO retains and consolidates knowledge from previous tasks without requiring access to past data, resulting in a progressively more complete world model. Our empirical evaluations demonstrate that DRAGO performs well in terms of knowledge retention and transferability, making it a promising solution for complex continual learning scenarios. Future work will explore extending DRAGO to larger-scale environments and more diverse task distributions.
+
+# 7. Limitations
+
+We only maintain one generative model throughout the continual training process, and this could potentially have mode collapse problem as the number of the tasks grows. The generative model is expected to capture the distribution of all prior tasks, which also relies on its own generated data. Thus the forgetting issue of the generative model will appear as its memory becomes "blurry" when the task number grows. To some extent, mixing the synthetic data with real world data will help mitigate this (note that the real world data can also come from the data collected by our reviewer,
+
+which connects to the previous tasks), but the question of how we can better do continual learning for generative models remains and we leave it for future works. The current tasks tested in the paper are not highly complex, and there is a limited number of tasks, which can be the reason why we do not observe this problem in our setting. Developing continual generative models can be much more challenging, but also rewarding towards the goal of real continual agent.
+
+# Impact Statement
+
+This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
+
+# Acknowledgement
+
+This work was supported by the Office of Naval Research (ONR) under grant #N00014-22-12592. Partial funding was also provided by The Robotics and AI Institute. The authors would like to thank David Abel, Lijing Yu, and Jingwen Zhang for their help and feedbacks on this project. This work was conducted using computational resources and services at the Center for Computation and Visualization, Brown University.
+
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+
+Algorithm 1 DRAGO (Training process for each task)  
+Require:  $\psi, \psi^{-}, \theta, \phi, \phi^{-}$ : randomly initialized network parameters  
+ $T_{old}, E_{old}, G_{old}$ : transition network and VAE up to the previous task  
+ $\eta, \tau, \lambda, \mathcal{B}^l, \mathcal{B}^r$ : learning rate, coefficients, learner buffer, reviewer buffer  
+1:  $T_{\psi} \gets T_{old}$  {load transition model from the previous task}  
+2:  $E_{\theta} \gets E_{old}$  {load VAE encoder from the previous task}  
+3:  $G_{\theta} \gets G_{old}$  {load VAE decoder from the previous task}  
+4: while not tired do  
+5: // Collect episode with learner and reviewer models from  $s_0 \sim p_0$ :  
+6: for step  $t = 0, \dots, \tau$  do  
+7:  $a_t \sim \Pi_\theta^l(\cdot|s_t)$  {Sample with learner model}  
+8:  $(s_{t+1}, r_t) \sim ENV(s_t, a_t)$  {Step environment}  
+9:  $\mathcal{B}^l \gets \mathcal{B}^l \cup (s_t, a_t, r_t, s_{t+1})$  {Add to learner buffer}  
+10: end for  
+11: for step  $t = 0, \dots, \tau$  do  
+12:  $a_t \sim \Pi_\theta^r(\cdot|s_t)$  {Sample with reviewer model}  
+13:  $(s_{t+1}, -) \sim ENV(s_t, a_t)$  {Step environment}  
+14:  $r_t = \text{calculate\_intrinsic\_reward}(s_t, a_t, s_{t+1})$  {Equation 7}  
+15:  $\mathcal{B}^r \gets \mathcal{B}^r \cup (s_t, a_t, r_t, s_{t+1})$  {Add to reviewer buffer}  
+16: end for  
+17: update_learning_and_reviewer( $\mathcal{B}^l, \mathcal{B}^r, \theta, \phi, \psi, \eta, \tau, \lambda$ ) {Algorithm 2}  
+18: update_vae( $\theta, G_{old}, \mathcal{B}^l$ ) {Algorithm 3}  
+19: update_transition_from_synthetic_data( $\psi, T_{old}, G_{old}$ ) {Algorithm 4}  
+20: end while
+
+# A. Algorithm Details
+
+The DRAGO algorithm combines synthetic experience rehearsal and exploration-driven memory regaining to facilitate continual learning in model-based reinforcement learning (MBRL). This section provides a detailed, step-by-step breakdown of DRAGO, outlining how it maintains and updates both the dynamics and generative models throughout a sequence of tasks. For the first task, DRAGO exclusively trains the learner model and the rehearsal encoder-decoder pair using only online data.
+
+# A.0.1. INITIALIZATION
+
+For each task  $\mathcal{T}_i$ , DRAGO begins by randomly initializing the policy networks  $\pi^{l,r}i$ , the Q networks  $Q_{i}^{l,r}$ , and the reward networks  $R_{i}^{l,r}$  for both the learner and reviewer models. These components are initialized separately, but they share a common transition network  $T_{i}$ .
+
+The transition network  $T_{i}$ , along with the synthetic experience rehearsal encoder  $E_{i}$  and decoder  $G_{i}$ , are initially randomly initialized for the first task. For subsequent tasks, these networks are loaded with the weights from the previous task's networks  $(T_{i-1}, E_{i-1}, \text{and } D_{i-1})$ . Notably, these previously trained components  $(T_{i-1}, E_{i-1}, \text{and } D_{i-1})$  are employed as fixed modules for generating synthetic data, thereby supporting the rehearsal process without further updates.
+
+# A.0.2. DATA COLLECTION
+
+During each episode, both the learner agent and reviewer agent interact with the environment for the same number of time steps. The experiences  $(s,a,s^{\prime},r)$  encountered by each agent are stored in separate replay buffers:  $\mathcal{B}_i^l$  for the learner and  $\mathcal{B}_i^r$  for the reviewer. While the learner agent's rewards are directly sourced from the environment, the reviewer agent's intrinsic rewards are computed using the methodology outlined in Equation 7. This intrinsic reward mechanism drives the reviewer's exploration and memory regaining.
+
+Algorithm 2 update_learner_and reviewer  
+Require:  $\mathcal{B}^l,\mathcal{B}^r$  :Learner and reviewer buffers  $\psi ,\psi^{-},\theta ,\phi ,\phi^{-}$  : Network parameters  $\eta ,\tau ,\lambda$  : Learning rate, coefficients   
+1:  $\{s_t^l,a_t^l,r_t^l,s_{t + 1}^l\}_{t:t + H}\sim \mathcal{B}^l$  {Sample trajectory from learner buffer}   
+2:  $\{s_t^r,a_t^r,r_t^r,s_{t + 1}^r\}_{t:t + H}\sim \mathcal{B}^r$  {Sample trajectory from reviewer buffer}   
+3:  $r_{t:t + H}^{l^{\prime}}\gets$  calculate reviewerreward  $(r_{t:t + H}^{l})$    
+4:  $J_{\theta},J_{\phi},J_{\psi}\gets 0,0,0$  {Initialize loss accumulation}   
+5:  $\hat{q}_1^l = Q_\theta^l (s_1^l,a_1^l)$    
+6:  $\hat{q}_1^r = Q_\theta^r (s_1^r,a_1^r)$    
+7:  $\hat{q}_1^{\prime} = Q_\theta^r (s_1^{\prime},a_1^{\prime})$    
+8:  $L_{Q} = \mathcal{L}_{\mathrm{value}}(\hat{q}_1^l) + \mathcal{L}_{\mathrm{value}}(\hat{q}_1^r) + \mathcal{L}_{\mathrm{value}}(\hat{q}_1^{\prime})$  {Calculate value loss at the first observation}   
+9:  $\hat{r}_1^l = R_\phi^l (\hat{s}_1^l,a_1^l)$    
+10:  $\hat{r}_1^r = R_\phi^r (\hat{s}_1^r,a_1^r)$    
+11:  $\hat{r}_1^{l'} = R_\phi^r (\hat{s}_1^l,a_1^l)$    
+12:  $L_{R} = \mathcal{L}_{\mathrm{reward}}(\hat{r}_{1}^{l}) + \mathcal{L}_{\mathrm{reward}}(\hat{r}_{1}^{r}) + \mathcal{L}_{\mathrm{reward}}(\hat{r}_{1}^{l'})$  {Calculate reward loss at the first observation}   
+13:  $J_{\theta}\gets J_{\theta} + L_{Q} + L_{R}$  {Only update reward and value functions at the first step}   
+14:  $\hat{s}_1^l = s_1^l,\hat{s}_1^r = s_1^r$  {Initialize the estimated first observations}   
+15: for  $i = t,\ldots ,t + H$  do   
+16:  $\hat{s}_{i + 1}^{l} = t_{\psi}(\hat{s}_{i}^{l},a_{i}^{l})$    
+17:  $\hat{s}_{i + 1}^{r} = t_{\psi}(\hat{s}_{i}^{r},a_{i}^{r})$    
+18:  $\hat{a}_i^l = \pi_\phi^l (\hat{s}_i^l,s_i^l)$    
+19:  $\hat{a}_i^r = \pi_\phi^r (\hat{s}_i^r,s_i^r)$    
+20:  $J_{\phi}\gets J_{\phi} + \lambda^{i - t}(\mathcal{L}_{\pi}(\hat{a}_i^l) + \mathcal{L}_{\pi}(\hat{a}_i^r))$    
+21:  $J_{\psi}\leftarrow J_{\psi} + \lambda^{i - t}(\mathcal{L}_{\mathrm{dynamics}}(\hat{s}_{i + 1}^{l}) + \mathcal{L}_{\mathrm{dynamics}}(\hat{s}_{i + 1}^{r}))$    
+22: end for   
+23:  $\phi \gets \phi -\frac{\eta}{H}\nabla_{\phi}J_{\phi}$  {Update online network}   
+24:  $\psi \gets \psi -\frac{\eta}{H}\nabla_{\psi}J_{\psi}$  {Update online network}   
+25:  $\phi^{-}\gets (1 - \tau)\phi^{-} + \tau \phi$  {Update target network}   
+26:  $\psi^{-}\gets (1 - \tau)\psi^{-} + \tau \psi$  {Update target network}
+
+Algorithm 3 update_vae  
+Require:  $\theta$ : VAE parameters  
+ $G_{old}$ : Previously trained VAE decoder  
+ $\mathcal{B}^l$ : Replay buffer of the learner  
+1:  $h \sim \mathcal{N}(0,1)$   
+2:  $(s^{\mathrm{synth}}, a^{\mathrm{synth}}) \gets G_{old}(h)$   
+3:  $h^{\mathrm{synth}} \gets E_\theta(s^{\mathrm{synth}}, a^{\mathrm{synth}})$   
+4:  $(\hat{s}^{\mathrm{synth}}, \hat{a}^{\mathrm{synth}}) \gets G_\theta(h^{\mathrm{synth}})$   
+5:  $\{s_t^l, a_t^l, r_t^l, s_{t+1}^l\}_{t:t+H} \sim \mathcal{B}^l$   
+6:  $h \gets E_\theta(s_1^l, a_1^l)$   
+7:  $(\hat{s}, \hat{a}) \gets G_\theta(h)$   
+8:  $J_\theta = J_\theta + \mathcal{L}_{gen}(\hat{s}, \hat{a}) + \mathcal{L}_{gen}(\hat{s}^{\mathrm{synth}}, \hat{a}^{\mathrm{synth}})$   
+9:  $\theta \gets \theta - \frac{\eta}{H} \nabla_\theta J_\theta$   
+{update VAE parameters}
+
+Algorithm 4 update_transition_from_synthetic_data   
+Require:  $\psi$  Transition network parameters  $T_{\mathrm{old}}$  : Previously trained transition network  $G_{\mathrm{old}}$  : Previously trained VAE decoder   
+1:  $h\sim \mathcal{N}(0,1)$    
+2:  $(s^{\mathrm{synth}},a^{\mathrm{synth}})\gets G^{\mathrm{old}}(h)$  {Generate synthetic observations and actions}   
+3:  $s' = T^{\mathrm{old}}(s^{\mathrm{synth}},a^{\mathrm{synth}})$  {generate next observation from old transition model}   
+4:  $\hat{s}^{\prime} = T_{\psi}(s^{\mathrm{synth}},a^{\mathrm{synth}})$    
+5:  $J_{\psi}\gets J_{\psi} + \mathcal{L}_{\mathrm{dynamics}}(\hat{s}',s')$    
+6:  $\psi \gets \psi -\frac{\eta}{H}\nabla_{\theta}J_{\psi}$  {Update online network}
+
+# A.0.3. INFERENCE
+
+The inference process in DRAGO is inspired by TD-MPC (Hansen et al., 2022), utilizing the Cross-Entropy Method (CEM) (Rubinstein, 1997) for action selection. During this process, a fixed number of trajectories of predetermined length are sampled and simulated using the current transition model  $T_{i}$ . For each trajectory, the cumulative return is calculated. The trajectories with the highest returns, referred to as elite trajectories, are selected to reshape the distribution of the initial actions. This iterative process is repeated for a fixed number of iterations, ultimately yielding a refined distribution over actions, which informs the final action selection. All the hyperparameters related to the CEM algorithms is the same with TD-MPC (Hansen et al., 2022).
+
+# A.0.4. UPDATING
+
+DRAGO updates after each episode of rollouts for the same iterations as the number of rollout time-steps. The updates tries to minimize the training objective, which is the sum of several losses weighted temporally by a discount factor  $\lambda$ . Below is a detailed description of the loss functions used in the updates:
+
+The transition model is updated using data from both the learner agent and the reviewer agent, as well as the synthetic observation-action pairs generated by the previous VAE decoder  $(G_{i - 1})$  and the subsequent observations generated by the previous transition model  $(T_{i - 1})$ . This process maintains the transition model's accuracy for transitions encountered in previous tasks, thereby mitigating catastrophic forgetting of the world model. Given an observation  $s$ , an action  $a$ , and a target next state  $s'$ , the loss function calculates the mse between the predicted next observation using the transition model  $T$  and the next state provided:
+
+$$
+\mathcal {L} _ {\mathrm {d y n a m i c s}} = c _ {1} \| T _ {\psi} (s, a) - s ^ {\prime} \| _ {2} ^ {2}
+$$
+
+However, synthetic data updates for  $T_{i}$  only occur at fixed intervals of steps to cope with the noise arising from inaccuracies in  $G_{i-1}$  and  $T_{i-1}$ . This periodic updating strategy helps avoid noisy updates that can result from relying on outdated or inaccurate synthetic data.
+
+Continual learning of the VAE  $(E_{i}$  and  $G_{i})$  occurs concurrently with the agent's updates. Data for this learning comes from both the state-action pairs obtained from the learner model's rollouts and the generated state-action pairs from  $G_{i - 1}$ . The associated loss function for the VAE  $\mathcal{L}_{gen}$  is shown in Equation 6.
+
+The reward function  $R$  which estimates the immediate reward from a given observation. The reward model enables the agent to estimate total return from a trajectory, and stabilizes the update for Q functions. It is updated using the following loss function:
+
+$$
+\mathcal {L} _ {\text {r e w a r d}} = c _ {2} \| R _ {\phi} \left(z _ {i}, a _ {i}\right) - r _ {i} \| _ {2} ^ {2}
+$$
+
+Additionally, the  $Q$  functions for both agents are updated using the TD-objective shown as follows:
+
+$$
+\mathcal {L} _ {\text {v a l u e}} = c _ {3} \left\| Q _ {\phi} \left(s _ {i}, a _ {i}\right) - \left(r _ {i} + \gamma Q _ {\phi^ {-}} \left(s _ {i + 1}, \pi_ {\phi} \left(s _ {i + 1}\right)\right)\right) \right\| _ {2} ^ {2}
+$$
+
+$Q$  and  $R$  update only using the first steps of the horizons sampled, rather than using the complete horizon as in the original TD-MPC algorithm. This reduces the risk of noisy updates resulting from inaccuracies in the initial transition model.
+
+The policy networks for both learner and reviewer agents are updated to maximize the expected  $Q$  value using
+
+$$
+\mathcal {L} _ {\pi} = - Q _ {\phi} (s, \pi_ {\phi} (s))
+$$
+
+In the above loss functions,  $c_{1}, c_{2}, c_{3}$  are hyper parameters as weights for each losses.
+
+# A.1. Hyperparameters
+
+<table><tr><td>Hyperparameter</td><td>Value (minigrid, cheetah, walker)</td></tr><tr><td>action repeat</td><td>1, 4, 2</td></tr><tr><td>discount factor</td><td>0.99</td></tr><tr><td>batch size</td><td>512</td></tr><tr><td>maximum steps</td><td>100, 1000, 1000</td></tr><tr><td>planning horizon</td><td>10, (25, 15), 15</td></tr><tr><td>policy fraction</td><td>0.05</td></tr><tr><td>temperature</td><td>0.5</td></tr><tr><td>momentum</td><td>0.1</td></tr><tr><td>reward loss coef</td><td>0.5</td></tr><tr><td>value coef</td><td>0.1</td></tr><tr><td>consistency loss coef</td><td>2</td></tr><tr><td>vae recon loss coef</td><td>1</td></tr><tr><td>vae kl loss coef</td><td>0.02</td></tr><tr><td>temporal loss discount (ρ)</td><td>0.5</td></tr><tr><td>learning rate</td><td>1e-3</td></tr><tr><td>sampling technique</td><td>PER(0.6, 0.4)</td></tr><tr><td>target networks update freq</td><td>40, 2, 2</td></tr><tr><td>temperature (τ)</td><td>0.01</td></tr><tr><td>cost coef for reviewer reward (α)</td><td>0.5</td></tr><tr><td>vae latent dim</td><td>64, 256, 256</td></tr><tr><td>vae encoding dim</td><td>128</td></tr><tr><td>mlp latent dim</td><td>512</td></tr><tr><td>gumble softmax temp</td><td>1.0</td></tr><tr><td>steps per synthetic data rehearsal</td><td>10, 20</td></tr></table>
+
+Table 2. Here we list the hyperparameters used for MiniGrid World, DM-Control cheetah, and DM-Control walker. Unlisted hyperparameters are all identical to the default parameters in TD-MPC.
+
+# B. Related Work (Model-Based Reinforcement Learning)
+
+Model-based reinforcement learning (MBRL) focuses on learning a predictive model of the environment's dynamics (Sutton, 1991). Learning world models (Ha & Schmidhuber, 2018; Hafner et al., 2019) specifically enables agents to accumulate knowledge about the environment's dynamics and generalize to new tasks or situations. By utilizing this model to simulate future states, agents can plan and make informed decisions without excessive real-world interactions. Most MBRL approaches can be categorized into two main categories in terms of how the learned model is used. The first category consists of methods that use the learned model to generate additional data and explicitly train a policy (Sutton, 1991; Pong et al., 2018; Ha & Schmidhuber, 2018; Sekar et al., 2020; Hafner et al., 2020; 2021; 2023), these approaches leverage the learned dynamics model to simulate experiences, which are then used to augment real data for policy optimization; the second category includes methods that learn the dynamics model and use it directly for planning to assign credit to actions (Ebert et al., 2018; Zhang et al., 2018; Janner et al., 2019; Hafner et al., 2019; Lowrey et al., 2019; Kaiser et al., 2020; Yu et al., 2020b; Schrittwieser et al., 2020; Nguyen et al., 2021; Zhang et al., 2024). These methods perform online planning by simulating future trajectories using the learned model to select actions without explicitly learning a policy. Recent approaches (Hansen et al., 2022; 2024) combine both techniques and achieves superior performance on various continuous control tasks. TD-MPC2 (Hansen et al., 2024) especially demonstrates the possibility of train a single world model on multiple tasks at once using MBRL.
+
+# C. Tasks Specifications
+
+Here we describe the specifications of the tasks included in this paper:
+
+For MiniGrid World domain, all the tasks are to reach a goal. The pre-training tasks are dense-reward, and all fine-tuning tasks are sparse-reward.
+
+- Room1to2: In this task we initialize the agent inside room 1 (top left, [11, 8]) and the goal inside room 2 (top right, [14, 9]).  
+- Room1to3: In this task we initialize the agent inside room 1 (top left, [8, 11]) and the goal inside room 3 (bottom left, [9, 14]).  
+- Room3to4: In this task we initialize the agent inside room 3 (bottom left, [11, 18]) and the goal inside room 4 (bottom right, [14, 17]).
+
+For Deep Mind Control domain, all the pre-training tasks are from TD-MPC2 (Hansen et al., 2024), and the new fine-tune tasks are described below:
+
+- cheetah jump2run: In this task we initialize the observation as a random state when the agent is performing the task "jump", then initialize the objective to be "cheetah run".  
+- cheetah jump2back: In this task, we initialize the observation as a random state when the agent is performing "jump", then initialize the objective to be "cheetah run backwards".  
+- walker walk2run: In this task, we initialize the observation as a random state when the agent is performing the task "walk", then initialize the objective to be "walker run".  
+- walker run2back: In this task, we initialize the observation as a random state when the agent is performing the task "run," then initialize the objective to be "walker run backwards".  
+- walker back2run: In this task, we initialize the observation as a random state when the agent is performing "run backwards", then initialize the objective to be "walker run".  
+- walker stand2run: In this task, we initialize the observation as a random state when the agent is performing the task "stand", then initialize the objective to be "walker run".  
+- cheetah jump&run In this tasks we encourage the agent to move forward in a high speed while their feet are both above the ground for a longer period of time. We averaged the rewards from cheetah run and cheetah jump with a lower threshold for speed and height.  
+- cheetah jump&back In this tasks we encourage the agent to move backwards in a high speed while their feet are both above the ground for a longer period of time. We averaged the rewards from cheetah run backwards and cheetah jump with a lower threshold for speed and height.
+
+# D. Additional Results of Continual Training
+
+We investigate whether the two components we proposed have side effect on the continual training tasks, where each two of them has relatively small overlap of transition dynamics and covers different state space. As shown in Table 3, DRAGO achieves similar performance with Continual TDMPC in all the training tasks, which is the MBRL baseline it is built upon, demonstrating that the proposed approaches will not deteriorate the training performance or induce more plasticity loss.
+
+<table><tr><td>Episode Reward</td><td>Cheetah run</td><td>Cheetah jump</td><td>Cheetah backward</td></tr><tr><td>DRAGO</td><td>652.53</td><td>587.24</td><td>624.09</td></tr><tr><td>Continual TDMPC</td><td>675.31</td><td>646.30</td><td>580.59</td></tr><tr><td>Walker run</td><td>Walker walk</td><td>Walker backward</td><td>Walker stand</td></tr><tr><td>708.74</td><td>954.56</td><td>953.8</td><td>972.46</td></tr><tr><td>693.61</td><td>959.31</td><td>956.42</td><td>982.69</td></tr></table>
+
+Table 3. Average Episode Return of the Continual training tasks after training for 1M steps.
+
+# E. More Ablation Study Results
+
+When trying the continual learning version for TDMPC, we find two interesting results. As shown in Figure 8 left, since we only transfer the dynamics model not the Q function, we thought excluding the Q value estimation in the planning process may yield better transfer results, but the result is the opposite. Without using the Q value in the planning process causes a performance drop. Moreover, in the original TDMPC implementation, a multi-step ahead prediction loss is used for updating the Q function and reward model, in the continual learning setting, we find that one-step prediction is better in complex environments like Deep Mind Control Suite as shown in the results of Cheetah-jump, which is the second one in Cheetah's continual training tasks.
+
+We also investigate the influence of the frequency of synthetic experience rehearsal, the results are shown in Figure 8's second subfigure (from left to right).
+
+In Figure 8's third subfigure, we show that if we also load Cheetah run's policy&value&reward, our method can reach even better results. However, this in practice requires prior knowledge that jump2run's reward function is similar to that of cheetah run. So it's not a scalable approach for now.
+
+In Figure 8's last subfigure, we show a comparison of the effect of the planning horizon to the performance of DRAGO on Cheetah jump2back.
+
+![](images/41574bb0861810bde8600da23de16f32705676b4ff9dad72bad7c05968901980.jpg)  
+Figure 8. More ablation study results for continual TDMPC and DRAGO.
+
+![](images/87c6b956097220c0ecac2c03190644101c0dfb5bd6369cd73e3ce07f648e28b9.jpg)
+
+![](images/27a74a5feb1505bbfece4aabcd603e4e21b957a049a98a9ec75a9849ff828000.jpg)
+
+![](images/d5b85de920e403da2050c2132e5bea1513178ed08748aeb1c8c0a9c29f48dd3a.jpg)
+
+In Table 4, we compare with another baseline: Continual TDMPC + Curiosity, where we add the curiosity-based intrinsic reward to the continual TDMPC policy to increase exploration. We can see that DRAGO still outperforms this new continual MBRL baseline in all the four tasks. We should note that while this is a reasonable baseline, the comparison is a little unfair for our method as DRAGO can also be combined with any exploration method in a straightforward way. Specifically, while we have a separate reviewer model that aims to maximize our proposed intrinsic reward, our learner model that aims to solve each specific task can also be directly added with any intrinsic reward method like curiosity to encourage exploration, which does not contradict with the intrinsic reward of the separate reviewer.
+
+We also try directly calculating the intrinsic reward of the reviewer and adding to the total reward of the learner, thus we do not need an additional reviewer model. As shown in Table 5, we see a large drop of performance for the continual training
+
+<table><tr><td>Average Reward</td><td>DRAGO</td><td>Curiosity + Continual TDMPC</td><td>EWC</td><td>Continual TDMPC</td><td>Scratch</td></tr><tr><td>Cheetah jump2run</td><td>106.78 ± 32.01</td><td>88.36 ± 25.81</td><td>54.72 ± 62.72</td><td>93.96 ± 39.29</td><td>26.54 ± 2.67</td></tr><tr><td>Cheetah jump&amp;run</td><td>248.92 ± 15.38</td><td>165.35 ± 67.01</td><td>156.98 ± 99.68</td><td>128.58 ± 100.14</td><td>182.77 ± 28.58</td></tr><tr><td>Cheetah jump2back</td><td>331.85 ± 11.05</td><td>133.81 ± 23.07</td><td>29.93 ± 7.15</td><td>73.98 ± 38.45</td><td>45.15 ± 4.92</td></tr><tr><td>Cheetah jump&amp;back</td><td>147.30 ± 34.29</td><td>138.77 ± 45.55</td><td>117.92 ± 1.20</td><td>140.82 ± 28.00</td><td>129.75 ± 20.44</td></tr></table>
+
+tasks, and this performance gap becomes larger and larger as the agent encounters more tasks, since it is encouraged to visit more and more possibly irrelevant states. Directly adding our intrinsic reward to the external reward and training only one single learner model makes it hard for the agent to complete the original task goal. If we only have one agent model (one policy), the intrinsic reward can have a side effect that 1. discourages the agent to visit places that it is already familiar with, thus hinders it to find the optimal solution to solve the task. 2. Encourages it to visit places that the previous mode is familiar with, which could be completely irrelevant for solving the current task. By having a separate reviewer policy that maximizes the intrinsic reward, we decouple the objectives. The learner policy focuses on maximizing the external reward to solve the current task effectively, while the reviewer policy explores states that help in retaining knowledge and connecting different regions of the state space. This separation allows both policies to operate without hindering each other's performance.
+
+![](images/7bf5f1f494fedbdfce3f9ef68edd2d4b78ca5bdc4f5b236fe14ea9579cb6a6f8.jpg)  
+Figure 9. Prediction score heatmaps for replay-based method (limited storage). The heatmaps illustrates the accuracy of the dynamics model during continual learning by keeping a fixed part of the previous replay buffer (capped to a similar memory size as our generative model). Compared to DRAGO's performance in Figure 4, this method does not achieve the same qualitative result.
+
+![](images/0e9c05dcb4517cbd3ebb7a77683abe21365205e0f4a4fdfc905a5de0b13347ac.jpg)
+
+![](images/155ae52e759c2f098182b614417e8aae5bda6d72e81fe7a795ec021c28199664.jpg)
+
+![](images/1230eca7a638ab3c6783df312a3289c6aa183ca255b6411921dc2be3a1a80c22.jpg)
+
+Table 4. Comparison of few-shot transfer performance on four test tasks in Cheetah. We report the mean and standard deviation of the cumulative reward at the end of training.  
+
+<table><tr><td>Episode Reward</td><td>Cheetah run</td><td>Cheetah jump</td><td>Cheetah backward</td></tr><tr><td>DRAGO</td><td>652.53</td><td>587.24</td><td>624.09</td></tr><tr><td>DRAGO (Learner w. reviewer reward)</td><td>583.13</td><td>403.70</td><td>330.73</td></tr></table>
+
+Table 5. Average Episode Return of the Continual training tasks after training for 1M steps.
+
+While in all our experiments above we evaluated DRAGO using TDMPC as the MBRL baseline, we also tried to combine DRAGO with another popular model-based RL baseline PETS (Chua et al., 2018), and show the preliminary results on the same MiniGrid tasks but with dense reward (we are not able to make PETS work on sparse reward settings unfortunately) in Table 7. DRAGO-PETS outperforms the baseline in 3 out of 4 tested tasks. Although we select finetune tasks that encourage the agent to perform in the union of sub observation spaces it has seen in previous tasks, we want to showcase the ability of DRAGO to retain knowledge by also comparing the few shot performance of pretrain tasks from only loading the world models of DRAGO and naive continual learning. Here, both world models are from a continual training of all four tasks in the Walker environment, in the order of Walker-Run, Walker-Walk, Walker-Stand, and Walker-Walk-Backwards.
+
+<table><tr><td>Average Reward (Dense)</td><td>DRAGO-PETS</td><td>Continual PETS</td></tr><tr><td>MiniGrid1to3 after3</td><td>233.21 ± 21.07</td><td>150.84 ± 62.37</td></tr><tr><td>MiniGrid1to2 after2</td><td>101.03 ± 116.21</td><td>161.70 ± 44.31</td></tr><tr><td>MiniGrid1to3 after4</td><td>138.26 ± 99.05</td><td>43.04 ± 111.93</td></tr><tr><td>MiniGrid3to4 after4</td><td>234.65 ± 41.71</td><td>147.80 ± 105.84</td></tr></table>
+
+Table 6. Comparison of few-shot transfer performance of PETS based methods on four test tasks in MiniGrid. We report the mean and standard deviation of the cumulative reward at the end of training.  
+
+<table><tr><td>Average Reward</td><td>DRAGO</td><td>Naive TDMPC</td></tr><tr><td>walker-run</td><td>371.46 ± 12.79</td><td>300.52 ± 27.07</td></tr><tr><td>walker-walk</td><td>740.89 ± 54.90</td><td>685.66 ± 43.05</td></tr><tr><td>walker-stand</td><td>871.17 ± 55.07</td><td>463.60 ± 107.12</td></tr></table>
+
+Table 7. Comparison of few-shot performance of DRAGO and naive TDMPC continual learning by loading the world model at the end of pretraining on Walker tasks. We report the mean and standard deviation of the reward at 40k steps into the training.

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+    {
+        "type": "text",
+        "text": "Mingyu Xing  $^{1}$  Lechao Cheng  $^{1}$  Shengeng Tang  $^{1}$  Yaxiong Wang  $^{1}$  Zhun Zhong  $^{1,2}$  Meng Wang",
+        "bbox": [
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+        "text": "Abstract",
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+    {
+        "type": "text",
+        "text": "We introduce Knowledge Swapping, a novel task designed to selectively regulate knowledge of a pretrained model by enabling the forgetting of user-specified information, retaining essential knowledge, and acquiring new knowledge simultaneously. By delving into the analysis of knock-on feature hierarchy, we find that incremental learning typically progresses from low-level representations to higher-level semantics, whereas forgetting tends to occur in the opposite direction—starting from high-level semantics and moving down to low-level features. Building upon this, we propose to benchmark the knowledge swapping task with the strategy of Learning Before Forgetting. Comprehensive experiments on various tasks like image classification, object detection, and semantic segmentation validate the effectiveness of the proposed strategy. The source code is available at https://github.com/xingmingyu123456/KnowledgeSwapping",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The proliferation of deep learning has led to the widespread adoption of pretrained models (Han et al., 2021), which are typically fine-tuned using task-specific data to achieve parameter-efficient adaptation. In the context of streaming tasks, researchers have increasingly explored methods for continuously optimizing and adapting pretrained models to new tasks (Lin et al., 2023; Chen et al., 2024; Zhu et al., 2023), a paradigm referred to as continual learning (Wang et al., 2024). However, in practical applications, as deep models integrate more knowledge, they often encounter additional requirements, such as the need to continuously",
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+    {
+        "type": "text",
+        "text": "$^{1}$ School of Computer Science and Information Engineering, Hefei University of Technology  $^{2}$ School of Computer Science, University of Nottingham. Correspondence to: Lechao Cheng <chenglc@h Fut.edu.cn>, Zhun Zhong <zhunzhong007@gmail.com>.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
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+        "img_path": "images/66ce1fb2c5ad22475beb12c546cd15bdb40245219f85998b41c345f38660a054.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "image_caption": [],
+        "image_footnote": [
+            "Retained Knowledge"
+        ],
+        "bbox": [
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+    },
+    {
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+    {
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+        "img_path": "images/b471aff170cd2d3303d20acfae081727686cd05162725d160e2870bd3d5d3973.jpg",
+        "image_caption": [
+            "Figure 1. Comparisons of three tasks: Continuous Learning, Machine Unlearning, and our Knowledge Swapping."
+        ],
+        "image_footnote": [
+            "Removed Knowledge",
+            "New Knowledge"
+        ],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "block or forget certain sensitive content. Recent works, such as machine unlearning (Liu et al., 2024c; Wang et al., 2025; Zhang et al., 2024b), have begun to address the unilateral forgetting of specific content within pretrained models. Nonetheless, approaches that simultaneously enable the learning of new knowledge and the forgetting of specific content remain underexplored.",
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+    {
+        "type": "text",
+        "text": "Inspired by this insight, we propose a novel task termed Knowledge Swapping, which enables the selective forgetting of specific categories of knowledge while preserving others, tailored to the requirements of new tasks. As depicted in Figure 1, continual learning (Cheng et al., 2024a;b; Zhang et al., 2024a; Huang et al., 2024a;b; Wu et al., 2025) aims to integrate new task knowledge into an existing pretrained model. Current mainstream approaches (Li et al., 2024; Wang et al., 2022b) often involve attaching a new adapter for each task and fine-tuning it, yet the need to forget outdated or less relevant knowledge remains an underexplored challenge. Recent advancements (Liu et al., 2024b; Wang et al., 2025) in machine unlearning have demonstrated that isolating or removing specific knowledge from a pretrained model necessitates an explicit unlearning process. In contrast, our proposed Knowledge Swapping task facili-",
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+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            227,
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "1",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "tates the learning of new tasks while simultaneously forgetting less important prior knowledge or sensitive data that requires protection, thereby preserving the core capabilities of the pretrained model.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We further delve into how to perform knowledge swapping more effectively by leveraging empirical insights. Intuitively, this process can be divided into two stages: forgetting specific knowledge and learning novel knowledge. A natural assumption might be that the model should first forget less important or potentially detrimental priors in order to \"free up\" the capacity for new information. We conduct a set of straightforward experiments to analyze, in isolation, how incremental learning and targeted forgetting each influence model parameters. Our findings indicate that incremental learning typically progresses from low-level representations to higher-level semantic features, whereas forgetting tends to occur in the opposite direction—starting from high-level semantics and moving down to low-level features. This contrast provides valuable insights for designing strategies for knowledge swapping task. Specifically, if we perform targeted forgetting first, we may complete the forgetting of high-level semantics before any major adjustments occur in the low-level feature space. Once we begin introducing new content afterward, these low-level changes may no longer align with the previously forgotten high-level semantic representations, thereby creating potential conflicts. Conversely, if we first learn the new task (thus updating the low-level feature distribution), and only then conduct targeted forgetting, the process is more likely to remain confined to higher-level semantics. As a result, the updated low-level distributions are less likely to be perturbed during the forgetting stage, which helps to maintain the integrity of previously acquired knowledge. We empirically show learning new tasks first, followed by selective forgetting of specific knowledge, leads to significantly better results. Our contributions are summarized as follows:",
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+    {
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+        "list_items": [
+            "- We propose the concept of Knowledge Swapping, a novel task that facilitates the learning of new tasks while simultaneously forgetting less important prior knowledge and preserving essential pretrained capabilities.",
+            "- We uncover that incremental learning progresses from low-level to higher-level semantic features, whereas targeted forgetting begins at high-level semantics and works downward. This directional contrast provides key insights into how to design effective knowledge swapping procedures.",
+            "- Building upon the insight from feature-hierarchy interplay, we propose to achieve knowledge swapping by sequential learning-then-forgetting principle. Comprehensive experiments also demonstrate that the pro"
+        ],
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+    {
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+        "text": "posed strategy significantly improves overall performance.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "2.1. Continual Learning",
+        "text_level": 1,
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Continual learning, also known as lifelong learning, aims to enable models to learn new tasks incrementally while mitigating catastrophic forgetting. Existing approaches can be broadly categorized into Regularization-Based Methods (Kirkpatrick et al., 2017; Li & Hoiem, 2017; Zhu et al., 2021; Liu & Liu, 2022; Wang et al., 2023), Memory-Based Methods (Rebuffi et al., 2017; Ashok et al., 2022; Chaudhry et al., 2021; Zhou et al., 2022; Sun et al., 2023; Yang et al., 2023), and Architecture-Based Methods (Rusu et al., 2016; Douillard et al., 2022; Wang et al., 2022a; Lu et al., 2024).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Regularization-based methods introduce constraints in the loss function to retain past knowledge. For instance, EWC (Kirkpatrick et al., 2017) distills knowledge from old models to new ones for prediction consistency. Memory-based methods maintain an external memory to store or generate past knowledge. BMKP (Sun et al., 2023) introduces a bilevel memory framework, where a working memory adapts to new tasks and a long-term memory retains compact knowledge representations. Architecture-based methods expand the model to accommodate new tasks. Progressive Neural Networks(Rusu et al., 2016) expands the model using gradient boosting and compresses it via knowledge distillation. ArchCraft (Lu et al., 2024) leverages neural architecture search (NAS) to balance stability and plasticity, generating architectures that enhance knowledge retention with minimal parameter overhead. Our proposed method shares the goal of balancing retention and learning with continual learning approaches. However, knowledge swapping introduces an additional challenge of selective forgetting, which is not explicitly addressed in traditional continual learning methods.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.2. Machine Unlearning",
+        "text_level": 1,
+        "bbox": [
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+            676,
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+            691
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Machine unlearning (Koh & Liang, 2017; Kurmanji et al., 2024; Liu et al., 2024a) focuses on efficiently removing specific data or knowledge from a trained model without requiring full retraining, which is crucial for data privacy compliance. One of the earliest approaches is fine-tuning, which exploits catastrophic forgetting by retraining the model on a retention dataset, though it may leave residual traces of forgotten data. This method forms the foundation for subsequent unlearning techniques. Building on this, Influence Functions (Koh & Liang, 2017) emerged, whistimates the influence of individual data points on model parameters, providing a more precise and computationally efficient method for data removal without retraining the entire model. Later,",
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+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            323,
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "more sophisticated methods are introduced. NegGrad+ (Kurmanji et al., 2024) balances the loss on the forgotten set and the retention dataset, offering a more controlled trade-off in the unlearning process. To further refine the removal of specific knowledge, L1-Sparse (Liu et al., 2024a) introduces the use of L1-regularization to zero out parameters associated with forgotten data, effectively eliminating their influence on the model. Additionally, Relabeling techniques, such as Saliency Unlearning (Feldman, 2020) disrupts the model's memory of forgotten data by altering its labels, focusing on modifying key parameters that store the data's influence. Unlike conventional unlearning methods, which primarily focus on individual data points, our proposed framework introduces a novel approach for category-level forgetting. By integrating the processes of learning, retention, and forgetting into a unified system, this framework offers more flexibility and control over knowledge management, marking a significant advancement in this area of research.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Knowledge Swapping",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Task Definition",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "We introduce a novel task, referred to as Knowledge Swapping, which aims to selectively regulate a model's knowledge by employing specific swapping mechanisms to achieve three primary objectives: (1) forgetting userspecified knowledge, (2) retaining core knowledge, and (3) simultaneously learning new knowledge.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Let  $\\mathcal{D}_p = (X_p,Y_p)$  be the pretraining dataset on which an initial model  $M_0$  has been trained. We define three additional sets:",
+        "bbox": [
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Retaining Set:  $\\mathcal{D}_r = (X_r, Y_r)$ , which contains the knowledge that must be preserved.",
+            "- Forgetting Set:  $\\mathcal{D}_f = (X_f, Y_f)$ , containing the knowledge that the model needs to forget.",
+            "- Learning Set:  $\\mathcal{D}_l = (X_l, Y_l)$ , comprising new knowledge to acquire."
+        ],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In general, both  $\\mathcal{D}_r$  and  $\\mathcal{D}_f$  are subsets of the pretraining dataset  $\\mathcal{D}_p$ , i.e.,  $\\mathcal{D}_r, \\mathcal{D}_f \\subseteq \\mathcal{D}_p$ , while  $\\mathcal{D}_l$  could represent an entirely new task or domain.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Objectives: We seek to train an updated model  $M_{1}$  such that:",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. For each  $x_r \\in X_r$ ,  $M_1$  correctly predicts its label  $y_r$ . Formally,  $P\\big(M_1(x_r) = y_r\\big) \\approx 1$ ,  $\\forall x_r \\in X_r$ . (Retention)",
+            "2. For each  $x_{f}\\in X_{f}$ ,  $M_1$  does not correctly predict its label  $y_{f}$ . Formally,  $P\\big(M_1(x_f) = y_f\\big)\\approx 0,\\quad \\forall x_f\\in X_f$ . (Forgetting)"
+        ],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. For each  $x_{l} \\in X_{l}$ ,  $M_{1}$  correctly predicts its label  $y_{l}$ . Formally,  $P\\big(M_1(x_l) = y_l\\big) \\approx 1$ ,  $\\forall x_{l} \\in X_{l}$  (Learning)",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here,  $P(\\cdot)$  denotes the probability of the corresponding event under the trained model. The objectives are then to promote or discourage each of these criteria accordingly.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. To Forget Before Learning, or to Learn Before Forgetting?",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Revisiting that we have already provided a comprehensive definition of the knowledge swapping task, we note that—based on its criteria—it can be naturally divided into two core phases: forgetting and learning. This highlights a pivotal question: should a model first forget certain existing knowledge before learning new information (which seems intuitively appealing), or should it learn new content first and then perform forgetting? The way we answer this sequence dilemma directly informs how we design a robust knowledge swapping benchmark. Although intuitively, forgetting old knowledge first appears to free up capacity for accommodating the new, is this really the optimal approach? To explore this, we conduct two sets of experiments on dense prediction tasks such as semantic segmentation, each corresponding to one of these two learning orders. We then examine how the neural network's parameters, across various layers, evolve under each approach (see Figure 2).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Knock-on Feature Hierarchy In this section, we directly evaluate the weight norms and parameter differences at each stage of the process. Specifically,  $L \\to F$  denotes Learning Before Forgetting, while  $F \\to L$  indicates Learning After Forgetting. The superscript  $W$  represents the weight norms at different stages under each sequence. We aggregate results from multiple image segmentation tasks and observe that when following the  $L \\to F$  sequence, the majority of parameter updates occur in the latter layers of the neural network—those responsible for generating semantic-level features. Conversely, in the  $F \\to L$  sequence, the principal changes are concentrated in the earlier layers, which produce low-level features. Based on these results, we found:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Discovery-I: Incremental learning typically progresses from low-level representations to higher-level semantic features, whereas forgetting tends to occur in the opposite direction—starting from high-level semantics and moving down to low-level features.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Remark. What is the practical significance of this seemingly intuitive finding? Clearly, its hierarchical feature implications offer valuable insights for designing knowledge swapping strategies. Specifically, if we conduct targeted forgetting first, we may erase high-level semantic parameters before making any substantial adjustments to the low-level feature parameter space. However, once we subsequently",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/6eb6bde45338fe565778f1f548379c3f43b442fd344ce7386df3bf06aa08c484.jpg",
+        "image_caption": [
+            "(a) Learning Before Forgetting  $(L\\to F)$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            84,
+            830,
+            251
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/5d307344405c3fe0e9200551ab3aa46cec42b0e5992cdc71eaf6bc6fd60a9fd3.jpg",
+        "image_caption": [
+            "(b) Learning After Forgetting  $(F\\to L)$",
+            "Figure 2.  $\\mathcal{L}_2$  norm for each parameter under  $L\\to F$  and  $F\\rightarrow L$ . The superscript  $W$  denotes the weight norm value at the current stage. The figure illustrates that (a) during the Learning Before Forgetting phase, changes in parameter norms are predominantly concentrated in layers responsible for high-level semantic representations. Conversely, (b) in the Learning After Forgetting phase, parameter norm changes primarily occur in layers associated with low-level feature representations."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "introduce new content, further modifications to the low-level parameters can cause inconsistencies in the high-level semantics (breaking the forgetting pipeline owing to altering low-level parameters), potentially leading to conflicts. By contrast, if we begin by learning a new task (thereby updating the low-level parameters) and then perform targeted forgetting, the forgetting process is more likely confined to the high-level semantic parameters.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Principle: Learning Before Forgetting. Recall that we demonstrate that initiating the forgetting process before learning disrupts the intended forgetting due to alterations in low-level feature learning. This raises the question: does conducting the learning process before forgetting similarly interfere with previously acquired knowledge? We also measure the average gradient changes across two primary sequences,  $L \\rightarrow F$  and  $F \\rightarrow L$ , as shown in Figure 4. The superscript  $G$  means the log average gradient at the current stage. First, parameter changes during the learning phases ( $L^G \\rightarrow F$  and  $F \\rightarrow L^G$ ) are consistently more significant, indicating that the Learning process is relatively challenging; second, in the  $L \\rightarrow F^G$  phase, the final updates to forgetting gradients remain consistently small, suggesting",
+        "bbox": [
+            84,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "that Learning Before Forgetting is more stable.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Benchmark",
+        "text_level": 1,
+        "bbox": [
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+            614
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            496,
+            625,
+            599,
+            638
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As illustrated in Figure 3, we employ the Low-Rank Adaptation (LoRA) technique (Hu et al., 2021) to fine-tune the pretrained model  $M_0$  (Sec. 4.2). Additionally, we leverage group sparse regularization to constrain the selective learning and forgetting of specific knowledge (Sec. 4.3).",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. LoRA-Based Fine-Tuning",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Building on the findings in (Geva et al., 2020), which demonstrate that the linear layers within Transformers encapsulate a substantial amount of the model's knowledge, we employ the Low-Rank Adaptation (LoRA) technique (Hu et al., 2021) to fine-tune only these linear layers. Let  $\\mathbf{X}$  denote the input to the Feed-Forward Network (FFN) of the  $k$ -th Transformer block after the  $t$ -th gradient update. The weights and biases of the first linear layer are represented by  $W_{k1}^{t}$  and  $b_{k1}^{t}$ , respectively, while those of",
+        "bbox": [
+            495,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            323,
+            56,
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+            71
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/454a88b82cdab7ce214d080f2954a2479817bde03220d39d21f4f676167b36bc.jpg",
+        "image_caption": [
+            "Figure 3. Benchmark Framework. First, we decouple knowledge swapping into separate learning and forgetting processes. We observed that the learning process progresses from low-level features to high-level features, while the forgetting process proceeds in the opposite direction—from high-level features to low-level features. Therefore, a two-stage strategy of Learning Before Forgetting is adopted. In general, we adopt LoRA to fine-tune the linear layers in each Transformer block, with all other parameters frozen to enable selective regulation of the model knowledge."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            88,
+            80,
+            883,
+            280
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/f47201d74a0ca57d2803745a9d73f4d66239ae2c046841f6d2c0895fd6765047.jpg",
+        "image_caption": [
+            "Figure 4. Logarithm of the Average Gradient. We compute the logarithm of cumulative average gradient changes at different stages in the  $L \\to F$  and  $F \\to L$  processes. We observe two key phenomena: first, parameter changes during the learning phases ( $L^G \\to F$  and  $F \\to L^G$ ) are consistently more significant, indicating that the Learning process is relatively challenging; second, in the  $L \\to F^G$  phase, the final updates to forgetting gradients remain consistently small, suggesting that Learning Before Forgetting is more stable."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            124,
+            380,
+            849,
+            561
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the second linear layer are denoted by  $\\pmb{W}_{k2}^{t}$  and  $\\pmb{b}_{k2}^{t}$ . The computation performed by the FFN can be expressed as:",
+        "bbox": [
+            84,
+            656,
+            473,
+            686
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {F F N} _ {k} ^ {t} (\\boldsymbol {X}) = \\operatorname {R e L U} \\left(\\boldsymbol {X} \\boldsymbol {W} _ {k 1} ^ {t} + \\boldsymbol {b} _ {k 1} ^ {t}\\right) \\boldsymbol {W} _ {k 2} ^ {t} + \\boldsymbol {b} _ {k 2} ^ {t}. \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Using LoRA, the weights are decomposed into their original pretrained components and learnable low-rank adaptations:",
+        "bbox": [
+            84,
+            724,
+            475,
+            755
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {W} _ {k 1} ^ {t} = \\boldsymbol {W} _ {k 1} ^ {0} + \\Delta \\boldsymbol {W} _ {k 1} ^ {t}, \\quad \\Delta \\boldsymbol {W} _ {k 1} ^ {t} = \\boldsymbol {A} _ {k 1} ^ {t} \\boldsymbol {B} _ {k 1} ^ {t}. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            124,
+            763,
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+            782
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {W} _ {k 2} ^ {t} = \\boldsymbol {W} _ {k 2} ^ {0} + \\Delta \\boldsymbol {W} _ {k 2} ^ {t}, \\quad \\Delta \\boldsymbol {W} _ {k 2} ^ {t} = \\boldsymbol {A} _ {k 2} ^ {t} \\boldsymbol {B} _ {k 2} ^ {t}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            125,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In these equations,  $\\pmb{W}_{k1}^{0}$  and  $\\pmb{W}_{k2}^{0}$  represent the original pretrained weights, while  $\\Delta W_{k1}^{t}$  and  $\\Delta W_{k2}^{t}$  are the low-rank updates at time step  $t$ , parameterized by the matrices  $\\pmb{A}$  and  $\\pmb{B}$ . This approach ensures efficient adaptation by focusing solely on the linear layers of the Transformer, which are hypothesized to store the majority of the model's knowledge.",
+        "bbox": [
+            84,
+            814,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Although the biases  $\\pmb{b}_{k1}^{t}$  and  $\\pmb{b}_{k2}^{t}$  may also be fine-tuned, they typically involve fewer parameters compared to the weights. By restricting updates to low-rank matrices, LoRA enables efficient fine-tuning with reduced computational and storage overhead while preserving the knowledge embedded in the original pretrained weights.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Sparse Constraint",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We employ Group Coefficient Regularization to selectively retain specific knowledge within the Feed-Forward Network (FFN) modules. Specifically, we adopt the Lasso strategy (Liu et al., 2015; Wen et al., 2016; Yuan & Lin, 2006) for group sparse regularization. Lasso achieves the selective retention of knowledge by zeroing out the  $A$  and  $B$  matrices of irrelevant FFN modules within LoRA, thereby enabling",
+        "bbox": [
+            495,
+            787,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            323,
+            56,
+            651,
+            71
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/e0a1c7bf07e052447069672801a80db9136dbc63921146305ab0de191997b5ec.jpg",
+        "table_caption": [
+            "Table 1. Image classification results on Imagenet100 under Learning Before Forgetting.  $L$  and  $F$  are short for Learning and Forgetting, respectively.  ${\\mathrm{{Acc}}}_{r},{\\mathrm{{Acc}}}_{l}$  and  ${\\mathrm{{Acc}}}_{f}$  represent the accuracy of the retaining set,the learning set,and the forgetting set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Stages</td><td colspan=\"3\">Cub</td><td colspan=\"3\">Resisc45</td><td colspan=\"3\">Oxford-pet</td><td colspan=\"3\">Plantvillage</td></tr><tr><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td></tr><tr><td colspan=\"13\">Learning Set: 5 classes, Forgetting Set: 5 classes, Retaining Set: 95 classes</td></tr><tr><td>Start</td><td>88.08</td><td>0</td><td>84.4</td><td>88.08</td><td>0.2</td><td>84.4</td><td>88.08</td><td>0.4</td><td>84.4</td><td>88.08</td><td>0</td><td>84.4</td></tr><tr><td>F</td><td>86.63</td><td>0</td><td>0.4</td><td>86.63</td><td>0.4</td><td>0.4</td><td>86.63</td><td>0.4</td><td>0.4</td><td>86.63</td><td>0</td><td>0.4</td></tr><tr><td>F → L</td><td>86.94</td><td>94.04</td><td>80.8</td><td>87.62</td><td>99</td><td>70.8</td><td>88.48</td><td>93.6</td><td>77.2</td><td>88.06</td><td>99.13</td><td>74.8</td></tr><tr><td>L</td><td>86.67</td><td>94.04</td><td>82.44</td><td>87.93</td><td>98.8</td><td>82.0</td><td>87.83</td><td>94.4</td><td>82.8</td><td>87.97</td><td>99.56</td><td>82.4</td></tr><tr><td>L → F</td><td>86.4</td><td>91.66</td><td>0</td><td>86.77</td><td>99.2</td><td>0</td><td>87.01</td><td>93.6</td><td>0</td><td>87.26</td><td>99.78</td><td>0</td></tr><tr><td colspan=\"13\">Learning Set: 10 classes, Forgetting Set: 10 classes, Retaining Set: 90 classes</td></tr><tr><td>Start</td><td>87.75</td><td>0</td><td>89.2</td><td>87.75</td><td>0.1</td><td>89.2</td><td>87.75</td><td>1.8</td><td>89.2</td><td>87.75</td><td>0</td><td>89.2</td></tr><tr><td>F</td><td>85.22</td><td>0</td><td>0</td><td>85.22</td><td>0.2</td><td>0</td><td>85.2</td><td>2</td><td>0</td><td>85.22</td><td>0</td><td>0</td></tr><tr><td>F → L</td><td>86.84</td><td>96.27</td><td>82</td><td>87.2</td><td>98.7</td><td>82</td><td>88</td><td>96</td><td>83</td><td>87.66</td><td>98.55</td><td>82.2</td></tr><tr><td>L</td><td>85.06</td><td>95.03</td><td>83.6</td><td>86.84</td><td>98.9</td><td>84.4</td><td>87.0</td><td>95.8</td><td>85.2</td><td>87.35</td><td>98.86</td><td>85.4</td></tr><tr><td>L → F</td><td>84.68</td><td>93.78</td><td>0</td><td>85.97</td><td>98.7</td><td>0.6</td><td>86.22</td><td>95.2</td><td>0.2</td><td>85.48</td><td>98.65</td><td>0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "targeted learning and forgetting. The Lasso regularization loss  $\\mathcal{L}_{\\mathrm{re}}$  is defined as:",
+        "bbox": [
+            84,
+            349,
+            473,
+            378
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e}} = \\sum_ {k = 1} ^ {n} \\left(\\| \\boldsymbol {A} _ {k} \\| _ {F} ^ {2} + \\| \\boldsymbol {B} _ {k} \\| _ {F} ^ {2}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            169,
+            383,
+            475,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\| \\cdot \\| _F$  denotes the Frobenius norm, calculated as the square root of the sum of the squared elements of a matrix, and  $n$  represents the number of FFN groups.",
+        "bbox": [
+            84,
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+            474
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Remark. Sparse constraints enhance parameter efficiency by limiting non-zero parameters, reducing computational and storage overhead, and accelerating inference. In knowledge swapping tasks, they enable the selective retention of crucial parameters for the current task while suppressing redundant ones, thereby preventing conflicts between new and existing knowledge. Additionally, parameter sparsification mitigates interference from irrelevant variables during learning and forgetting (similar idea in model pruning), allowing the model to focus on important information. Specifically, Lasso regularization penalizes the Frobenius norms of matrices, promoting group sparsification that selectively retains and forgets at the module level and maintains stability in low-level feature parameters when introducing new knowledge. Consequently, the model preserves new knowledge while maintaining the stability of existing representations. Overall, sparse constraints effectively manage parameters in knowledge swapping, enabling efficient adaptation to new tasks and maintaining previously acquired knowledge, thereby supporting scalable continual learning.",
+        "bbox": [
+            84,
+            481,
+            475,
+            784
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Training and Inference Protocol",
+        "text_level": 1,
+        "bbox": [
+            84,
+            800,
+            344,
+            814
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the learning phase, the objective is for the model to acquire new knowledge while retaining essential existing knowledge. Accordingly, the loss function for this phase is defined as follows.",
+        "bbox": [
+            84,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {r e t a i n}} = \\mathcal {L} \\left(f \\left(\\boldsymbol {X} _ {r}\\right), \\boldsymbol {Y} _ {r}\\right), \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            192,
+            888,
+            473,
+            906
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {l e a r n}} = \\mathcal {L} \\left(f \\left(\\boldsymbol {X} _ {l}\\right), \\boldsymbol {Y} _ {l}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            609,
+            348,
+            885,
+            364
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {a l l}} = \\mathcal {L} _ {\\text {r e t a i n}} + \\beta \\mathcal {L} _ {\\text {l e a r n}} + \\alpha \\mathcal {L} _ {\\text {r e}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            578,
+            371,
+            885,
+            387
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $(\\mathbf{X}_r,\\mathbf{Y}_r)$  denotes the data from the retention set,  $(\\mathbf{X}_l,\\mathbf{Y}_l)$  denotes the data from the learning set, and  $\\alpha$  and  $\\beta$  are hyperparameters that balance the contributions of the different loss components.",
+        "bbox": [
+            496,
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+            455
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the forgetting phase, the goal is to eliminate specific knowledge while retaining both the original and newly acquired knowledge. This involves minimizing  $\\mathcal{L}(f(\\boldsymbol{X}_r),\\boldsymbol{Y}_r)$  and  $\\mathcal{L}(f(\\boldsymbol{X}_l),\\boldsymbol{Y}_l)$ , while maximizing  $\\mathcal{L}(f(\\boldsymbol{X}_f),\\boldsymbol{Y}_f)$ . However, directly maximizing the negative loss (i.e., minimizing  $-\\mathcal{L}(f(\\boldsymbol{X}_f),\\boldsymbol{Y}_f))$  can result in unbounded loss growth, leading to optimization instability. To address this issue, we introduce a boundary constraint (BND) to stabilize the loss. The final loss function for the forgetting phase is defined as:",
+        "bbox": [
+            496,
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+            599
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {f o r g e t}} = \\operatorname {R e L U} (\\mathrm {B N D} - \\mathcal {L} (f (\\boldsymbol {X} _ {f}), \\boldsymbol {Y} _ {f})), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            547,
+            611,
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+            628
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {a l l}} = \\mathcal {L} _ {\\text {r e t a i n}} + \\mathcal {L} _ {\\text {l e a r n}} + \\beta \\mathcal {L} _ {\\text {f o r g e t}} + \\alpha \\mathcal {L} _ {\\text {r e}}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            545,
+            638,
+            885,
+            656
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where BND defines the forgetting boundary, and  $(X_{f},Y_{f})$  represents the data from the forgetting set.",
+        "bbox": [
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+            693
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            496,
+            712,
+            629,
+            729
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            496,
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+            753
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "All experiments are conducted on a hardware setup comprising  $2 \\times$  RTX 4090 GPUs, with the software environment configured as Python 3.12, PyTorch 2.5.1, and CUDA 12.4. The AdamW optimizer is employed for all training and forgetting phases.",
+        "bbox": [
+            495,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For image classification tasks, the learning set includes: CUB-200-2011 (Wah et al., 2011), Oxford-IIIT Pet (Parkhi et al., 2012), RESISC45 (Cheng et al., 2017) and PlantVillage (Geetharamani & Pandian, 2019). Both the retention",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            323,
+            56,
+            651,
+            71
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/fbc555cc2d7c889cedc6ad4e1f48b4377b8df8db681a278083689a5e82339408.jpg",
+        "image_caption": [
+            "The forgotten classes are lamp and scope. The learned class is cow. The retained classes are all remaining classes."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            109,
+            88,
+            359,
+            217
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a29d0ec0e273b96b045e327f854446a6d5283de817572ec8305dc9f8f6adee11.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            361,
+            88,
+            609,
+            217
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/60bd93b6b1f2635a64565a7c51452f3dc09813f6ad62cc519d7f9c71d1973512.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            217
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8a2bcbaf00c83ca0b18b3b4fe4a7581864cb6c42f12e439347f14f3c89202ba6.jpg",
+        "image_caption": [
+            "Pretrained"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            109,
+            237,
+            359,
+            382
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/1bf15f8e96c91fff381c403fb60c383fda2f75712636490651146e04ed4b53e8.jpg",
+        "image_caption": [
+            "Learning"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            361,
+            237,
+            609,
+            382
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4a42a7f3905a49d64e2787628d9c84b44981b36df0342180e929293c0460819b.jpg",
+        "image_caption": [
+            "Forgetting After Learning",
+            "Figure 5. Qualitative results on semantic segmentation. The forgotten classes are marked with red dotted lines, and the learned class is marked with dark green dotted lines."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            611,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "set and the forgetting set are selected from ImageNet-100. During the training phase, the hyperparameters are set to  $\\alpha = 0.05$  and  $\\beta = 0.2$ , while BND = 105 in the forgetting phase. The classification performance is evaluated using accuracy as the primary metric.",
+        "bbox": [
+            84,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For object detection tasks, the learning set consists of CUB-200-2011 and Stanford Dogs (Dataset, 2011). Both the retention set and the forgetting set are sourced from the COCO (Lin et al., 2014) dataset. The learning phase employs  $\\alpha = 0.01$  and  $\\beta = 0.9$ , while the forgetting phase uses  $\\mathrm{BND} = 15$ ,  $\\alpha = 0.01$ , and  $\\beta = 0.2$ . The detection capability is assessed using the mean Average Precision (mAP) metric.",
+        "bbox": [
+            84,
+            526,
+            475,
+            647
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For semantic segmentation tasks, the learning set includes: Pascal VOC (Hoiem et al., 2009), COCO, Oxford-IIIT Pet (Parkhi et al., 2012), and DeepGlobe Land (Demir et al., 2018). These datasets cover a diverse range of segmentation domains. The learning phase is configured with  $\\alpha = 0.01$  and  $\\beta = 0.9$  while the forgetting phase is set to BND  $= 115$ ,  $\\alpha = 0.01$ , and  $\\beta = 0.2$ . The segmentation accuracy is evaluated using the mean Intersection over Union (mIoU) metric.",
+        "bbox": [
+            84,
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+            776
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Classification Results",
+        "text_level": 1,
+        "bbox": [
+            84,
+            791,
+            269,
+            806
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We use VIT-B16 model pretrained on ImageNet100 as the base model. As shown in Table 1, under the Learning Before Forgetting setting, the accuracy of the learning set consistently increases from approximately  $0\\%$  to over  $90\\%$ , demonstrating effective knowledge acquisition. Concur",
+        "bbox": [
+            84,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "rently, the forgetting phase appears to be more straightforward, as the accuracy of the forgetting set decreases from approximately  $80\\%$  to  $0\\%$ , indicating successful forgetting. Besides, the retaining set can also be well preserved even though there exist limited negative impacts on the whole phase. We further evaluate the reverse order (Learning After Forgetting) in the same setting. We observe that although the accuracy of the forgetting set initially drops significantly during the forgetting phase, the subsequent learning phase induces substantial changes in the model's lower-level parameters. This renders the previously forgotten higher-level parameters ineffective, resulting in an increase in the accuracy of the forgetting set during the later stages. These findings confirm the validity of our hypothesis.",
+        "bbox": [
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+            443,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Semantic Segmentation Results",
+        "text_level": 1,
+        "bbox": [
+            496,
+            671,
+            750,
+            686
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We select the pretrained Mask2Former(Cheng et al., 2021) model on ADE20K as the pretraining model. The results in Table 2 demonstrate that under the Learning Before Forgetting strategy, the mIoU of the retention set remains stable, ensuring effective memory retention. In contrast, the mIoU of the forgetting set decreases from  $68.31\\%$  to nearly  $0\\%$ , indicating complete forgetting. Concurrently, the learning set achieves a high mIoU, confirming successful knowledge acquisition. Figure 5 further illustrates this process, where the classes lamp and sconce are successfully forgotten and blended into the wall, while the learned class cow remains well retained even after the forgetting phase. In contrast, under the Learning After Forgetting setting (Table 2), al",
+        "bbox": [
+            495,
+            694,
+            888,
+            891
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            323,
+            56,
+            651,
+            71
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/9b19728dd4a9ab97cf345b1eeaa1211bdd737415d5107fa42792dfa25425c268.jpg",
+        "table_caption": [
+            "Table 2. Semantic segmentation results on four datasets. For each dataset, the learning set and forgetting set include randomly selected 5 classes. The retaining set includes all other classes from ADE20K."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">procedure</td><td colspan=\"3\">VOC</td><td colspan=\"3\">Oxford-pet</td><td colspan=\"3\">COCO</td><td colspan=\"3\">Deep globe Land</td></tr><tr><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td></tr><tr><td>Start</td><td>50.51</td><td>0</td><td>68.31</td><td>50.51</td><td>0</td><td>68.31</td><td>50.51</td><td>0</td><td>68.31</td><td>50.51</td><td>0</td><td>68.31</td></tr><tr><td>F</td><td>50.36</td><td>0</td><td>2.26</td><td>50.61</td><td>0</td><td>3.48</td><td>50.24</td><td>0</td><td>2.41</td><td>50.66</td><td>0</td><td>3.65</td></tr><tr><td>F → L</td><td>50.7</td><td>85.45</td><td>49.42</td><td>50.28</td><td>59.45</td><td>53.67</td><td>51.03</td><td>90.87</td><td>54.47</td><td>50.38</td><td>54.33</td><td>60.25</td></tr><tr><td>F → L → F</td><td>50.98</td><td>88.07</td><td>0.15</td><td>50.17</td><td>61.85</td><td>0.33</td><td>50.64</td><td>94.64</td><td>0.39</td><td>50.87</td><td>63.86</td><td>0.27</td></tr><tr><td>L</td><td>50.2</td><td>84.97</td><td>60.67</td><td>48.92</td><td>62.21</td><td>65.5</td><td>50.54</td><td>93.46</td><td>61.85</td><td>50.96</td><td>59.8</td><td>64.61</td></tr><tr><td>L → F</td><td>50.57</td><td>85.43</td><td>0.12</td><td>49.87</td><td>69.55</td><td>0.08</td><td>50.35</td><td>93.36</td><td>0.71</td><td>49.54</td><td>58.34</td><td>0.4</td></tr><tr><td>L → F → L</td><td>50.5</td><td>95.83</td><td>45.51</td><td>50.97</td><td>86.98</td><td>53.87</td><td>50.41</td><td>97.27</td><td>50.03</td><td>50.54</td><td>69.18</td><td>57.25</td></tr></table>",
+        "bbox": [
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+            233
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/1115b0cbb74ffac4d64ed33bdefb866bba14194aef80c3ff997b8d0d983b3b2f.jpg",
+        "image_caption": [
+            "Figure 6.  $\\mathcal{L}_2$  norm of weights in  $F\\to L\\to F$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            133,
+            247,
+            836,
+            421
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "though both the retention and learning sets perform well, the mIoU of the forgetting set increases after learning due to significant changes in low-level parameters, rendering previously tuned high-level forgetting parameters ineffective. Figure 7 highlights this issue, showing that mountain, which is initially erased and blended into sand, re-emerges after learning, demonstrating the instability of this approach.",
+        "bbox": [
+            84,
+            446,
+            475,
+            551
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4. Object Detection Results",
+        "text_level": 1,
+        "bbox": [
+            84,
+            569,
+            292,
+            583
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For the object detection task, we use DINO (Zhang et al., 2022) pretrained on the COCO dataset as the base model. The forgetting set consists of five randomly selected classes: person, teddy bear, toilet, bench, and bed, while all remaining classes form the retention set. The learning sets consist of 5 classes: Black-footed Albatross, Laysan Albatross, Sooty Albatross, Groove-billed Ani, and Brewer Blackbird for CUB-200-2011 and Chihuahua, Maltese Dog, Basset, American Staffordshire Terrier, and Norwich Terrier for Stanford Dogs, respectively.",
+        "bbox": [
+            84,
+            592,
+            475,
+            743
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/33d233742d210508609c7dd26db57d7be6c478da4ceced44c54bf01935df7ede.jpg",
+        "table_caption": [
+            "Table 3. Object Detection Results on COCO."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">procedure</td><td colspan=\"3\">Cub</td><td colspan=\"3\">Stanford Dogs</td></tr><tr><td>mAPr↑</td><td>mAPl↑</td><td>mAPf↓</td><td>mAPr↑</td><td>mAPl↑</td><td>mAPf↓</td></tr><tr><td>Start</td><td>55.4</td><td>0</td><td>44.5</td><td>55.4</td><td>0</td><td>44.5</td></tr><tr><td>F</td><td>54.9</td><td>16.8</td><td>3.4</td><td>54.8</td><td>9.7</td><td>3.4</td></tr><tr><td>F → L</td><td>55</td><td>65.4</td><td>7.7</td><td>54.6</td><td>78.5</td><td>11.1</td></tr><tr><td>L</td><td>55.3</td><td>64.3</td><td>37.6</td><td>54.5</td><td>67.5</td><td>37.5</td></tr><tr><td>L → F</td><td>55.5</td><td>62.2</td><td>0.5</td><td>55</td><td>80.1</td><td>0.6</td></tr></table>",
+        "bbox": [
+            89,
+            763,
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+            847
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The quantitative results in Table 3 demonstrate the effectiveness of our Learning Before Forgetting strategy, as the mAP of the retention set remains stable at around  $55\\%$ , the for",
+        "bbox": [
+            84,
+            859,
+            478,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/e448c30299874e4747b2b49c70994c1dd247c49b570179b406a8692b03afef99.jpg",
+        "image_caption": [
+            "Figure 7. Semantic segmentation results for Learning After Forgetting on ADE20K."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            516,
+            450,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "getting set drops from  $44.5\\%$  to below  $1\\%$ , and the learning set improves from 0 to a satisfactory level, confirming the success of our approach. In contrast, it also shows that in the Learning After Forgetting  $(F \\rightarrow L)$  setting, the forgetting set retains a relatively high mAP, indicating ineffective forgetting. This supports our hypothesis that learning progresses from low-level to high-level features, while forgetting follows the opposite direction, from high-level to low-level features.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.5. Insights and Discussion",
+        "text_level": 1,
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To further validate the effectiveness of our strategy, we conduct an additional experiment involving a Forget-Learn-Forget sequence. As shown in Table 2, although the mIoU of the forgetting set remains high after the initial forgetting and subsequent learning phases, it is significantly reduced after the second forgetting phase. This result demonstrates the robustness of the Learn Before Forget strategy. The results  $L \\to F \\to L$  further provide indirect evidence that",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "Knowledge Swapping via Learning and Unlearning",
+        "bbox": [
+            323,
+            56,
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+            71
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "positioning the learning phase at the end influences the content that was previously forgotten. We analyze the  $\\mathcal{L}_2$  norm of model parameters at different stages, as illustrated in Figure 6. The red line represents parameter changes from  $F$  to  $F\\rightarrow L$ , while the black line indicates changes from  $F\\rightarrow L$  to  $F\\rightarrow L\\rightarrow F$ . The results show that learning-induced parameter changes are primarily concentrated in the early layers of the model, whereas forgetting-related changes are more prominent in the later layers. These observations align well with our previous findings.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion and Future Works",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We proposed Knowledge Swapping, a novel task that enables selective regulation of model knowledge by achieving three goals: forgetting user-specified knowledge, retaining essential knowledge, and learning new knowledge. To accomplish this, we introduced a two-stage training strategy based on the Learning Before Forgetting principle, which decouples learning and forgetting to mitigate catastrophic forgetting effectively. We benchmark our Learning Before Forgetting with various experiments. However, our experiments also reveal that the difficulty of learning new knowledge for different categories and forgetting old knowledge varies. An interesting direction for future research is to explore and analyze the difficulty of forgetting specific knowledge and learning new knowledge of categories.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This work has been supported by the New Cornerstone Science Foundation through the XPLORER PRIZE. This work was funded by the National Natural Science Foundation of China (No. 72188101 & No. 62472139 & No. 62302140) and the Fundamental Research Funds for the Central Universities (No. JZ2024HGTB0261 & No. JZ2024HGTA0178). The computation is completed on the HPC Platform of Hefei University of Technology.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Impact Statement",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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2025/Knowledge Swapping via Learning and Unlearning/full.md

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+Mingyu Xing  $^{1}$  Lechao Cheng  $^{1}$  Shengeng Tang  $^{1}$  Yaxiong Wang  $^{1}$  Zhun Zhong  $^{1,2}$  Meng Wang
+
+# Abstract
+
+We introduce Knowledge Swapping, a novel task designed to selectively regulate knowledge of a pretrained model by enabling the forgetting of user-specified information, retaining essential knowledge, and acquiring new knowledge simultaneously. By delving into the analysis of knock-on feature hierarchy, we find that incremental learning typically progresses from low-level representations to higher-level semantics, whereas forgetting tends to occur in the opposite direction—starting from high-level semantics and moving down to low-level features. Building upon this, we propose to benchmark the knowledge swapping task with the strategy of Learning Before Forgetting. Comprehensive experiments on various tasks like image classification, object detection, and semantic segmentation validate the effectiveness of the proposed strategy. The source code is available at https://github.com/xingmingyu123456/KnowledgeSwapping
+
+# 1. Introduction
+
+The proliferation of deep learning has led to the widespread adoption of pretrained models (Han et al., 2021), which are typically fine-tuned using task-specific data to achieve parameter-efficient adaptation. In the context of streaming tasks, researchers have increasingly explored methods for continuously optimizing and adapting pretrained models to new tasks (Lin et al., 2023; Chen et al., 2024; Zhu et al., 2023), a paradigm referred to as continual learning (Wang et al., 2024). However, in practical applications, as deep models integrate more knowledge, they often encounter additional requirements, such as the need to continuously
+
+$^{1}$ School of Computer Science and Information Engineering, Hefei University of Technology  $^{2}$ School of Computer Science, University of Nottingham. Correspondence to: Lechao Cheng <chenglc@h Fut.edu.cn>, Zhun Zhong <zhunzhong007@gmail.com>.
+
+Proceedings of the  $42^{nd}$  International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
+
+![](images/66ce1fb2c5ad22475beb12c546cd15bdb40245219f85998b41c345f38660a054.jpg)
+
+![](images/e2a2e19494bf94112bb19ce57886797aba48e879ae2c4f6016ee16bad393d857.jpg)  
+Retained Knowledge
+
+![](images/43931a935edc24835685dbcfe40477f81e936978b3db594fae10ed0bb719e50f.jpg)
+
+Figure 1. Comparisons of three tasks: Continuous Learning, Machine Unlearning, and our Knowledge Swapping.  
+![](images/b471aff170cd2d3303d20acfae081727686cd05162725d160e2870bd3d5d3973.jpg)  
+Removed Knowledge  
+New Knowledge
+
+block or forget certain sensitive content. Recent works, such as machine unlearning (Liu et al., 2024c; Wang et al., 2025; Zhang et al., 2024b), have begun to address the unilateral forgetting of specific content within pretrained models. Nonetheless, approaches that simultaneously enable the learning of new knowledge and the forgetting of specific content remain underexplored.
+
+Inspired by this insight, we propose a novel task termed Knowledge Swapping, which enables the selective forgetting of specific categories of knowledge while preserving others, tailored to the requirements of new tasks. As depicted in Figure 1, continual learning (Cheng et al., 2024a;b; Zhang et al., 2024a; Huang et al., 2024a;b; Wu et al., 2025) aims to integrate new task knowledge into an existing pretrained model. Current mainstream approaches (Li et al., 2024; Wang et al., 2022b) often involve attaching a new adapter for each task and fine-tuning it, yet the need to forget outdated or less relevant knowledge remains an underexplored challenge. Recent advancements (Liu et al., 2024b; Wang et al., 2025) in machine unlearning have demonstrated that isolating or removing specific knowledge from a pretrained model necessitates an explicit unlearning process. In contrast, our proposed Knowledge Swapping task facili-
+
+tates the learning of new tasks while simultaneously forgetting less important prior knowledge or sensitive data that requires protection, thereby preserving the core capabilities of the pretrained model.
+
+We further delve into how to perform knowledge swapping more effectively by leveraging empirical insights. Intuitively, this process can be divided into two stages: forgetting specific knowledge and learning novel knowledge. A natural assumption might be that the model should first forget less important or potentially detrimental priors in order to "free up" the capacity for new information. We conduct a set of straightforward experiments to analyze, in isolation, how incremental learning and targeted forgetting each influence model parameters. Our findings indicate that incremental learning typically progresses from low-level representations to higher-level semantic features, whereas forgetting tends to occur in the opposite direction—starting from high-level semantics and moving down to low-level features. This contrast provides valuable insights for designing strategies for knowledge swapping task. Specifically, if we perform targeted forgetting first, we may complete the forgetting of high-level semantics before any major adjustments occur in the low-level feature space. Once we begin introducing new content afterward, these low-level changes may no longer align with the previously forgotten high-level semantic representations, thereby creating potential conflicts. Conversely, if we first learn the new task (thus updating the low-level feature distribution), and only then conduct targeted forgetting, the process is more likely to remain confined to higher-level semantics. As a result, the updated low-level distributions are less likely to be perturbed during the forgetting stage, which helps to maintain the integrity of previously acquired knowledge. We empirically show learning new tasks first, followed by selective forgetting of specific knowledge, leads to significantly better results. Our contributions are summarized as follows:
+
+- We propose the concept of Knowledge Swapping, a novel task that facilitates the learning of new tasks while simultaneously forgetting less important prior knowledge and preserving essential pretrained capabilities.  
+- We uncover that incremental learning progresses from low-level to higher-level semantic features, whereas targeted forgetting begins at high-level semantics and works downward. This directional contrast provides key insights into how to design effective knowledge swapping procedures.  
+- Building upon the insight from feature-hierarchy interplay, we propose to achieve knowledge swapping by sequential learning-then-forgetting principle. Comprehensive experiments also demonstrate that the pro
+
+posed strategy significantly improves overall performance.
+
+# 2. Related Work
+
+# 2.1. Continual Learning
+
+Continual learning, also known as lifelong learning, aims to enable models to learn new tasks incrementally while mitigating catastrophic forgetting. Existing approaches can be broadly categorized into Regularization-Based Methods (Kirkpatrick et al., 2017; Li & Hoiem, 2017; Zhu et al., 2021; Liu & Liu, 2022; Wang et al., 2023), Memory-Based Methods (Rebuffi et al., 2017; Ashok et al., 2022; Chaudhry et al., 2021; Zhou et al., 2022; Sun et al., 2023; Yang et al., 2023), and Architecture-Based Methods (Rusu et al., 2016; Douillard et al., 2022; Wang et al., 2022a; Lu et al., 2024).
+
+Regularization-based methods introduce constraints in the loss function to retain past knowledge. For instance, EWC (Kirkpatrick et al., 2017) distills knowledge from old models to new ones for prediction consistency. Memory-based methods maintain an external memory to store or generate past knowledge. BMKP (Sun et al., 2023) introduces a bilevel memory framework, where a working memory adapts to new tasks and a long-term memory retains compact knowledge representations. Architecture-based methods expand the model to accommodate new tasks. Progressive Neural Networks(Rusu et al., 2016) expands the model using gradient boosting and compresses it via knowledge distillation. ArchCraft (Lu et al., 2024) leverages neural architecture search (NAS) to balance stability and plasticity, generating architectures that enhance knowledge retention with minimal parameter overhead. Our proposed method shares the goal of balancing retention and learning with continual learning approaches. However, knowledge swapping introduces an additional challenge of selective forgetting, which is not explicitly addressed in traditional continual learning methods.
+
+# 2.2. Machine Unlearning
+
+Machine unlearning (Koh & Liang, 2017; Kurmanji et al., 2024; Liu et al., 2024a) focuses on efficiently removing specific data or knowledge from a trained model without requiring full retraining, which is crucial for data privacy compliance. One of the earliest approaches is fine-tuning, which exploits catastrophic forgetting by retraining the model on a retention dataset, though it may leave residual traces of forgotten data. This method forms the foundation for subsequent unlearning techniques. Building on this, Influence Functions (Koh & Liang, 2017) emerged, whistimates the influence of individual data points on model parameters, providing a more precise and computationally efficient method for data removal without retraining the entire model. Later,
+
+more sophisticated methods are introduced. NegGrad+ (Kurmanji et al., 2024) balances the loss on the forgotten set and the retention dataset, offering a more controlled trade-off in the unlearning process. To further refine the removal of specific knowledge, L1-Sparse (Liu et al., 2024a) introduces the use of L1-regularization to zero out parameters associated with forgotten data, effectively eliminating their influence on the model. Additionally, Relabeling techniques, such as Saliency Unlearning (Feldman, 2020) disrupts the model's memory of forgotten data by altering its labels, focusing on modifying key parameters that store the data's influence. Unlike conventional unlearning methods, which primarily focus on individual data points, our proposed framework introduces a novel approach for category-level forgetting. By integrating the processes of learning, retention, and forgetting into a unified system, this framework offers more flexibility and control over knowledge management, marking a significant advancement in this area of research.
+
+# 3. Knowledge Swapping
+
+# 3.1. Task Definition
+
+We introduce a novel task, referred to as Knowledge Swapping, which aims to selectively regulate a model's knowledge by employing specific swapping mechanisms to achieve three primary objectives: (1) forgetting userspecified knowledge, (2) retaining core knowledge, and (3) simultaneously learning new knowledge.
+
+Let  $\mathcal{D}_p = (X_p,Y_p)$  be the pretraining dataset on which an initial model  $M_0$  has been trained. We define three additional sets:
+
+- Retaining Set:  $\mathcal{D}_r = (X_r, Y_r)$ , which contains the knowledge that must be preserved.  
+- Forgetting Set:  $\mathcal{D}_f = (X_f, Y_f)$ , containing the knowledge that the model needs to forget.  
+- Learning Set:  $\mathcal{D}_l = (X_l, Y_l)$ , comprising new knowledge to acquire.
+
+In general, both  $\mathcal{D}_r$  and  $\mathcal{D}_f$  are subsets of the pretraining dataset  $\mathcal{D}_p$ , i.e.,  $\mathcal{D}_r, \mathcal{D}_f \subseteq \mathcal{D}_p$ , while  $\mathcal{D}_l$  could represent an entirely new task or domain.
+
+Objectives: We seek to train an updated model  $M_{1}$  such that:
+
+1. For each  $x_r \in X_r$ ,  $M_1$  correctly predicts its label  $y_r$ . Formally,  $P\big(M_1(x_r) = y_r\big) \approx 1$ ,  $\forall x_r \in X_r$ . (Retention)  
+2. For each  $x_{f}\in X_{f}$ ,  $M_1$  does not correctly predict its label  $y_{f}$ . Formally,  $P\big(M_1(x_f) = y_f\big)\approx 0,\quad \forall x_f\in X_f$ . (Forgetting)
+
+3. For each  $x_{l} \in X_{l}$ ,  $M_{1}$  correctly predicts its label  $y_{l}$ . Formally,  $P\big(M_1(x_l) = y_l\big) \approx 1$ ,  $\forall x_{l} \in X_{l}$  (Learning)
+
+Here,  $P(\cdot)$  denotes the probability of the corresponding event under the trained model. The objectives are then to promote or discourage each of these criteria accordingly.
+
+# 3.2. To Forget Before Learning, or to Learn Before Forgetting?
+
+Revisiting that we have already provided a comprehensive definition of the knowledge swapping task, we note that—based on its criteria—it can be naturally divided into two core phases: forgetting and learning. This highlights a pivotal question: should a model first forget certain existing knowledge before learning new information (which seems intuitively appealing), or should it learn new content first and then perform forgetting? The way we answer this sequence dilemma directly informs how we design a robust knowledge swapping benchmark. Although intuitively, forgetting old knowledge first appears to free up capacity for accommodating the new, is this really the optimal approach? To explore this, we conduct two sets of experiments on dense prediction tasks such as semantic segmentation, each corresponding to one of these two learning orders. We then examine how the neural network's parameters, across various layers, evolve under each approach (see Figure 2).
+
+Knock-on Feature Hierarchy In this section, we directly evaluate the weight norms and parameter differences at each stage of the process. Specifically,  $L \to F$  denotes Learning Before Forgetting, while  $F \to L$  indicates Learning After Forgetting. The superscript  $W$  represents the weight norms at different stages under each sequence. We aggregate results from multiple image segmentation tasks and observe that when following the  $L \to F$  sequence, the majority of parameter updates occur in the latter layers of the neural network—those responsible for generating semantic-level features. Conversely, in the  $F \to L$  sequence, the principal changes are concentrated in the earlier layers, which produce low-level features. Based on these results, we found:
+
+Discovery-I: Incremental learning typically progresses from low-level representations to higher-level semantic features, whereas forgetting tends to occur in the opposite direction—starting from high-level semantics and moving down to low-level features.
+
+Remark. What is the practical significance of this seemingly intuitive finding? Clearly, its hierarchical feature implications offer valuable insights for designing knowledge swapping strategies. Specifically, if we conduct targeted forgetting first, we may erase high-level semantic parameters before making any substantial adjustments to the low-level feature parameter space. However, once we subsequently
+
+![](images/6eb6bde45338fe565778f1f548379c3f43b442fd344ce7386df3bf06aa08c484.jpg)  
+(a) Learning Before Forgetting  $(L\to F)$
+
+![](images/5d307344405c3fe0e9200551ab3aa46cec42b0e5992cdc71eaf6bc6fd60a9fd3.jpg)  
+(b) Learning After Forgetting  $(F\to L)$  
+Figure 2.  $\mathcal{L}_2$  norm for each parameter under  $L\to F$  and  $F\rightarrow L$ . The superscript  $W$  denotes the weight norm value at the current stage. The figure illustrates that (a) during the Learning Before Forgetting phase, changes in parameter norms are predominantly concentrated in layers responsible for high-level semantic representations. Conversely, (b) in the Learning After Forgetting phase, parameter norm changes primarily occur in layers associated with low-level feature representations.
+
+introduce new content, further modifications to the low-level parameters can cause inconsistencies in the high-level semantics (breaking the forgetting pipeline owing to altering low-level parameters), potentially leading to conflicts. By contrast, if we begin by learning a new task (thereby updating the low-level parameters) and then perform targeted forgetting, the forgetting process is more likely confined to the high-level semantic parameters.
+
+Principle: Learning Before Forgetting. Recall that we demonstrate that initiating the forgetting process before learning disrupts the intended forgetting due to alterations in low-level feature learning. This raises the question: does conducting the learning process before forgetting similarly interfere with previously acquired knowledge? We also measure the average gradient changes across two primary sequences,  $L \rightarrow F$  and  $F \rightarrow L$ , as shown in Figure 4. The superscript  $G$  means the log average gradient at the current stage. First, parameter changes during the learning phases ( $L^G \rightarrow F$  and  $F \rightarrow L^G$ ) are consistently more significant, indicating that the Learning process is relatively challenging; second, in the  $L \rightarrow F^G$  phase, the final updates to forgetting gradients remain consistently small, suggesting
+
+that Learning Before Forgetting is more stable.
+
+# 4. Benchmark
+
+# 4.1. Overview
+
+As illustrated in Figure 3, we employ the Low-Rank Adaptation (LoRA) technique (Hu et al., 2021) to fine-tune the pretrained model  $M_0$  (Sec. 4.2). Additionally, we leverage group sparse regularization to constrain the selective learning and forgetting of specific knowledge (Sec. 4.3).
+
+# 4.2. LoRA-Based Fine-Tuning
+
+Building on the findings in (Geva et al., 2020), which demonstrate that the linear layers within Transformers encapsulate a substantial amount of the model's knowledge, we employ the Low-Rank Adaptation (LoRA) technique (Hu et al., 2021) to fine-tune only these linear layers. Let  $\mathbf{X}$  denote the input to the Feed-Forward Network (FFN) of the  $k$ -th Transformer block after the  $t$ -th gradient update. The weights and biases of the first linear layer are represented by  $W_{k1}^{t}$  and  $b_{k1}^{t}$ , respectively, while those of
+
+![](images/454a88b82cdab7ce214d080f2954a2479817bde03220d39d21f4f676167b36bc.jpg)  
+Figure 3. Benchmark Framework. First, we decouple knowledge swapping into separate learning and forgetting processes. We observed that the learning process progresses from low-level features to high-level features, while the forgetting process proceeds in the opposite direction—from high-level features to low-level features. Therefore, a two-stage strategy of Learning Before Forgetting is adopted. In general, we adopt LoRA to fine-tune the linear layers in each Transformer block, with all other parameters frozen to enable selective regulation of the model knowledge.
+
+![](images/f47201d74a0ca57d2803745a9d73f4d66239ae2c046841f6d2c0895fd6765047.jpg)  
+Figure 4. Logarithm of the Average Gradient. We compute the logarithm of cumulative average gradient changes at different stages in the  $L \to F$  and  $F \to L$  processes. We observe two key phenomena: first, parameter changes during the learning phases ( $L^G \to F$  and  $F \to L^G$ ) are consistently more significant, indicating that the Learning process is relatively challenging; second, in the  $L \to F^G$  phase, the final updates to forgetting gradients remain consistently small, suggesting that Learning Before Forgetting is more stable.
+
+the second linear layer are denoted by  $\pmb{W}_{k2}^{t}$  and  $\pmb{b}_{k2}^{t}$ . The computation performed by the FFN can be expressed as:
+
+$$
+\operatorname {F F N} _ {k} ^ {t} (\boldsymbol {X}) = \operatorname {R e L U} \left(\boldsymbol {X} \boldsymbol {W} _ {k 1} ^ {t} + \boldsymbol {b} _ {k 1} ^ {t}\right) \boldsymbol {W} _ {k 2} ^ {t} + \boldsymbol {b} _ {k 2} ^ {t}. \tag {1}
+$$
+
+Using LoRA, the weights are decomposed into their original pretrained components and learnable low-rank adaptations:
+
+$$
+\boldsymbol {W} _ {k 1} ^ {t} = \boldsymbol {W} _ {k 1} ^ {0} + \Delta \boldsymbol {W} _ {k 1} ^ {t}, \quad \Delta \boldsymbol {W} _ {k 1} ^ {t} = \boldsymbol {A} _ {k 1} ^ {t} \boldsymbol {B} _ {k 1} ^ {t}. \tag {2}
+$$
+
+$$
+\boldsymbol {W} _ {k 2} ^ {t} = \boldsymbol {W} _ {k 2} ^ {0} + \Delta \boldsymbol {W} _ {k 2} ^ {t}, \quad \Delta \boldsymbol {W} _ {k 2} ^ {t} = \boldsymbol {A} _ {k 2} ^ {t} \boldsymbol {B} _ {k 2} ^ {t}. \tag {3}
+$$
+
+In these equations,  $\pmb{W}_{k1}^{0}$  and  $\pmb{W}_{k2}^{0}$  represent the original pretrained weights, while  $\Delta W_{k1}^{t}$  and  $\Delta W_{k2}^{t}$  are the low-rank updates at time step  $t$ , parameterized by the matrices  $\pmb{A}$  and  $\pmb{B}$ . This approach ensures efficient adaptation by focusing solely on the linear layers of the Transformer, which are hypothesized to store the majority of the model's knowledge.
+
+Although the biases  $\pmb{b}_{k1}^{t}$  and  $\pmb{b}_{k2}^{t}$  may also be fine-tuned, they typically involve fewer parameters compared to the weights. By restricting updates to low-rank matrices, LoRA enables efficient fine-tuning with reduced computational and storage overhead while preserving the knowledge embedded in the original pretrained weights.
+
+# 4.3. Sparse Constraint
+
+We employ Group Coefficient Regularization to selectively retain specific knowledge within the Feed-Forward Network (FFN) modules. Specifically, we adopt the Lasso strategy (Liu et al., 2015; Wen et al., 2016; Yuan & Lin, 2006) for group sparse regularization. Lasso achieves the selective retention of knowledge by zeroing out the  $A$  and  $B$  matrices of irrelevant FFN modules within LoRA, thereby enabling
+
+Table 1. Image classification results on Imagenet100 under Learning Before Forgetting.  $L$  and  $F$  are short for Learning and Forgetting, respectively.  ${\mathrm{{Acc}}}_{r},{\mathrm{{Acc}}}_{l}$  and  ${\mathrm{{Acc}}}_{f}$  represent the accuracy of the retaining set,the learning set,and the forgetting set.  
+
+<table><tr><td rowspan="2">Stages</td><td colspan="3">Cub</td><td colspan="3">Resisc45</td><td colspan="3">Oxford-pet</td><td colspan="3">Plantvillage</td></tr><tr><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td><td>Accr↑</td><td>Accl↑</td><td>Accf↓</td></tr><tr><td colspan="13">Learning Set: 5 classes, Forgetting Set: 5 classes, Retaining Set: 95 classes</td></tr><tr><td>Start</td><td>88.08</td><td>0</td><td>84.4</td><td>88.08</td><td>0.2</td><td>84.4</td><td>88.08</td><td>0.4</td><td>84.4</td><td>88.08</td><td>0</td><td>84.4</td></tr><tr><td>F</td><td>86.63</td><td>0</td><td>0.4</td><td>86.63</td><td>0.4</td><td>0.4</td><td>86.63</td><td>0.4</td><td>0.4</td><td>86.63</td><td>0</td><td>0.4</td></tr><tr><td>F → L</td><td>86.94</td><td>94.04</td><td>80.8</td><td>87.62</td><td>99</td><td>70.8</td><td>88.48</td><td>93.6</td><td>77.2</td><td>88.06</td><td>99.13</td><td>74.8</td></tr><tr><td>L</td><td>86.67</td><td>94.04</td><td>82.44</td><td>87.93</td><td>98.8</td><td>82.0</td><td>87.83</td><td>94.4</td><td>82.8</td><td>87.97</td><td>99.56</td><td>82.4</td></tr><tr><td>L → F</td><td>86.4</td><td>91.66</td><td>0</td><td>86.77</td><td>99.2</td><td>0</td><td>87.01</td><td>93.6</td><td>0</td><td>87.26</td><td>99.78</td><td>0</td></tr><tr><td colspan="13">Learning Set: 10 classes, Forgetting Set: 10 classes, Retaining Set: 90 classes</td></tr><tr><td>Start</td><td>87.75</td><td>0</td><td>89.2</td><td>87.75</td><td>0.1</td><td>89.2</td><td>87.75</td><td>1.8</td><td>89.2</td><td>87.75</td><td>0</td><td>89.2</td></tr><tr><td>F</td><td>85.22</td><td>0</td><td>0</td><td>85.22</td><td>0.2</td><td>0</td><td>85.2</td><td>2</td><td>0</td><td>85.22</td><td>0</td><td>0</td></tr><tr><td>F → L</td><td>86.84</td><td>96.27</td><td>82</td><td>87.2</td><td>98.7</td><td>82</td><td>88</td><td>96</td><td>83</td><td>87.66</td><td>98.55</td><td>82.2</td></tr><tr><td>L</td><td>85.06</td><td>95.03</td><td>83.6</td><td>86.84</td><td>98.9</td><td>84.4</td><td>87.0</td><td>95.8</td><td>85.2</td><td>87.35</td><td>98.86</td><td>85.4</td></tr><tr><td>L → F</td><td>84.68</td><td>93.78</td><td>0</td><td>85.97</td><td>98.7</td><td>0.6</td><td>86.22</td><td>95.2</td><td>0.2</td><td>85.48</td><td>98.65</td><td>0</td></tr></table>
+
+targeted learning and forgetting. The Lasso regularization loss  $\mathcal{L}_{\mathrm{re}}$  is defined as:
+
+$$
+\mathcal {L} _ {\mathrm {r e}} = \sum_ {k = 1} ^ {n} \left(\| \boldsymbol {A} _ {k} \| _ {F} ^ {2} + \| \boldsymbol {B} _ {k} \| _ {F} ^ {2}\right), \tag {4}
+$$
+
+where  $\| \cdot \| _F$  denotes the Frobenius norm, calculated as the square root of the sum of the squared elements of a matrix, and  $n$  represents the number of FFN groups.
+
+Remark. Sparse constraints enhance parameter efficiency by limiting non-zero parameters, reducing computational and storage overhead, and accelerating inference. In knowledge swapping tasks, they enable the selective retention of crucial parameters for the current task while suppressing redundant ones, thereby preventing conflicts between new and existing knowledge. Additionally, parameter sparsification mitigates interference from irrelevant variables during learning and forgetting (similar idea in model pruning), allowing the model to focus on important information. Specifically, Lasso regularization penalizes the Frobenius norms of matrices, promoting group sparsification that selectively retains and forgets at the module level and maintains stability in low-level feature parameters when introducing new knowledge. Consequently, the model preserves new knowledge while maintaining the stability of existing representations. Overall, sparse constraints effectively manage parameters in knowledge swapping, enabling efficient adaptation to new tasks and maintaining previously acquired knowledge, thereby supporting scalable continual learning.
+
+# 4.4. Training and Inference Protocol
+
+In the learning phase, the objective is for the model to acquire new knowledge while retaining essential existing knowledge. Accordingly, the loss function for this phase is defined as follows.
+
+$$
+\mathcal {L} _ {\text {r e t a i n}} = \mathcal {L} \left(f \left(\boldsymbol {X} _ {r}\right), \boldsymbol {Y} _ {r}\right), \tag {5}
+$$
+
+$$
+\mathcal {L} _ {\text {l e a r n}} = \mathcal {L} \left(f \left(\boldsymbol {X} _ {l}\right), \boldsymbol {Y} _ {l}\right), \tag {6}
+$$
+
+$$
+\mathcal {L} _ {\text {a l l}} = \mathcal {L} _ {\text {r e t a i n}} + \beta \mathcal {L} _ {\text {l e a r n}} + \alpha \mathcal {L} _ {\text {r e}}, \tag {7}
+$$
+
+where  $(\mathbf{X}_r,\mathbf{Y}_r)$  denotes the data from the retention set,  $(\mathbf{X}_l,\mathbf{Y}_l)$  denotes the data from the learning set, and  $\alpha$  and  $\beta$  are hyperparameters that balance the contributions of the different loss components.
+
+In the forgetting phase, the goal is to eliminate specific knowledge while retaining both the original and newly acquired knowledge. This involves minimizing  $\mathcal{L}(f(\boldsymbol{X}_r),\boldsymbol{Y}_r)$  and  $\mathcal{L}(f(\boldsymbol{X}_l),\boldsymbol{Y}_l)$ , while maximizing  $\mathcal{L}(f(\boldsymbol{X}_f),\boldsymbol{Y}_f)$ . However, directly maximizing the negative loss (i.e., minimizing  $-\mathcal{L}(f(\boldsymbol{X}_f),\boldsymbol{Y}_f))$  can result in unbounded loss growth, leading to optimization instability. To address this issue, we introduce a boundary constraint (BND) to stabilize the loss. The final loss function for the forgetting phase is defined as:
+
+$$
+\mathcal {L} _ {\text {f o r g e t}} = \operatorname {R e L U} (\mathrm {B N D} - \mathcal {L} (f (\boldsymbol {X} _ {f}), \boldsymbol {Y} _ {f})), \tag {8}
+$$
+
+$$
+\mathcal {L} _ {\text {a l l}} = \mathcal {L} _ {\text {r e t a i n}} + \mathcal {L} _ {\text {l e a r n}} + \beta \mathcal {L} _ {\text {f o r g e t}} + \alpha \mathcal {L} _ {\text {r e}}, \tag {9}
+$$
+
+where BND defines the forgetting boundary, and  $(X_{f},Y_{f})$  represents the data from the forgetting set.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+All experiments are conducted on a hardware setup comprising  $2 \times$  RTX 4090 GPUs, with the software environment configured as Python 3.12, PyTorch 2.5.1, and CUDA 12.4. The AdamW optimizer is employed for all training and forgetting phases.
+
+For image classification tasks, the learning set includes: CUB-200-2011 (Wah et al., 2011), Oxford-IIIT Pet (Parkhi et al., 2012), RESISC45 (Cheng et al., 2017) and PlantVillage (Geetharamani & Pandian, 2019). Both the retention
+
+![](images/fbc555cc2d7c889cedc6ad4e1f48b4377b8df8db681a278083689a5e82339408.jpg)  
+The forgotten classes are lamp and scope. The learned class is cow. The retained classes are all remaining classes.
+
+![](images/a29d0ec0e273b96b045e327f854446a6d5283de817572ec8305dc9f8f6adee11.jpg)
+
+![](images/60bd93b6b1f2635a64565a7c51452f3dc09813f6ad62cc519d7f9c71d1973512.jpg)
+
+![](images/8a2bcbaf00c83ca0b18b3b4fe4a7581864cb6c42f12e439347f14f3c89202ba6.jpg)  
+Pretrained
+
+![](images/1bf15f8e96c91fff381c403fb60c383fda2f75712636490651146e04ed4b53e8.jpg)  
+Learning
+
+![](images/4a42a7f3905a49d64e2787628d9c84b44981b36df0342180e929293c0460819b.jpg)  
+Forgetting After Learning  
+Figure 5. Qualitative results on semantic segmentation. The forgotten classes are marked with red dotted lines, and the learned class is marked with dark green dotted lines.
+
+set and the forgetting set are selected from ImageNet-100. During the training phase, the hyperparameters are set to  $\alpha = 0.05$  and  $\beta = 0.2$ , while BND = 105 in the forgetting phase. The classification performance is evaluated using accuracy as the primary metric.
+
+For object detection tasks, the learning set consists of CUB-200-2011 and Stanford Dogs (Dataset, 2011). Both the retention set and the forgetting set are sourced from the COCO (Lin et al., 2014) dataset. The learning phase employs  $\alpha = 0.01$  and  $\beta = 0.9$ , while the forgetting phase uses  $\mathrm{BND} = 15$ ,  $\alpha = 0.01$ , and  $\beta = 0.2$ . The detection capability is assessed using the mean Average Precision (mAP) metric.
+
+For semantic segmentation tasks, the learning set includes: Pascal VOC (Hoiem et al., 2009), COCO, Oxford-IIIT Pet (Parkhi et al., 2012), and DeepGlobe Land (Demir et al., 2018). These datasets cover a diverse range of segmentation domains. The learning phase is configured with  $\alpha = 0.01$  and  $\beta = 0.9$  while the forgetting phase is set to BND  $= 115$ ,  $\alpha = 0.01$ , and  $\beta = 0.2$ . The segmentation accuracy is evaluated using the mean Intersection over Union (mIoU) metric.
+
+# 5.2. Classification Results
+
+We use VIT-B16 model pretrained on ImageNet100 as the base model. As shown in Table 1, under the Learning Before Forgetting setting, the accuracy of the learning set consistently increases from approximately  $0\%$  to over  $90\%$ , demonstrating effective knowledge acquisition. Concur
+
+rently, the forgetting phase appears to be more straightforward, as the accuracy of the forgetting set decreases from approximately  $80\%$  to  $0\%$ , indicating successful forgetting. Besides, the retaining set can also be well preserved even though there exist limited negative impacts on the whole phase. We further evaluate the reverse order (Learning After Forgetting) in the same setting. We observe that although the accuracy of the forgetting set initially drops significantly during the forgetting phase, the subsequent learning phase induces substantial changes in the model's lower-level parameters. This renders the previously forgotten higher-level parameters ineffective, resulting in an increase in the accuracy of the forgetting set during the later stages. These findings confirm the validity of our hypothesis.
+
+# 5.3. Semantic Segmentation Results
+
+We select the pretrained Mask2Former(Cheng et al., 2021) model on ADE20K as the pretraining model. The results in Table 2 demonstrate that under the Learning Before Forgetting strategy, the mIoU of the retention set remains stable, ensuring effective memory retention. In contrast, the mIoU of the forgetting set decreases from  $68.31\%$  to nearly  $0\%$ , indicating complete forgetting. Concurrently, the learning set achieves a high mIoU, confirming successful knowledge acquisition. Figure 5 further illustrates this process, where the classes lamp and sconce are successfully forgotten and blended into the wall, while the learned class cow remains well retained even after the forgetting phase. In contrast, under the Learning After Forgetting setting (Table 2), al
+
+Table 2. Semantic segmentation results on four datasets. For each dataset, the learning set and forgetting set include randomly selected 5 classes. The retaining set includes all other classes from ADE20K.  
+
+<table><tr><td rowspan="2">procedure</td><td colspan="3">VOC</td><td colspan="3">Oxford-pet</td><td colspan="3">COCO</td><td colspan="3">Deep globe Land</td></tr><tr><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td><td>mIoUr↑</td><td>mIoUl↑</td><td>mIoUf↓</td></tr><tr><td>Start</td><td>50.51</td><td>0</td><td>68.31</td><td>50.51</td><td>0</td><td>68.31</td><td>50.51</td><td>0</td><td>68.31</td><td>50.51</td><td>0</td><td>68.31</td></tr><tr><td>F</td><td>50.36</td><td>0</td><td>2.26</td><td>50.61</td><td>0</td><td>3.48</td><td>50.24</td><td>0</td><td>2.41</td><td>50.66</td><td>0</td><td>3.65</td></tr><tr><td>F → L</td><td>50.7</td><td>85.45</td><td>49.42</td><td>50.28</td><td>59.45</td><td>53.67</td><td>51.03</td><td>90.87</td><td>54.47</td><td>50.38</td><td>54.33</td><td>60.25</td></tr><tr><td>F → L → F</td><td>50.98</td><td>88.07</td><td>0.15</td><td>50.17</td><td>61.85</td><td>0.33</td><td>50.64</td><td>94.64</td><td>0.39</td><td>50.87</td><td>63.86</td><td>0.27</td></tr><tr><td>L</td><td>50.2</td><td>84.97</td><td>60.67</td><td>48.92</td><td>62.21</td><td>65.5</td><td>50.54</td><td>93.46</td><td>61.85</td><td>50.96</td><td>59.8</td><td>64.61</td></tr><tr><td>L → F</td><td>50.57</td><td>85.43</td><td>0.12</td><td>49.87</td><td>69.55</td><td>0.08</td><td>50.35</td><td>93.36</td><td>0.71</td><td>49.54</td><td>58.34</td><td>0.4</td></tr><tr><td>L → F → L</td><td>50.5</td><td>95.83</td><td>45.51</td><td>50.97</td><td>86.98</td><td>53.87</td><td>50.41</td><td>97.27</td><td>50.03</td><td>50.54</td><td>69.18</td><td>57.25</td></tr></table>
+
+![](images/1115b0cbb74ffac4d64ed33bdefb866bba14194aef80c3ff997b8d0d983b3b2f.jpg)  
+Figure 6.  $\mathcal{L}_2$  norm of weights in  $F\to L\to F$
+
+though both the retention and learning sets perform well, the mIoU of the forgetting set increases after learning due to significant changes in low-level parameters, rendering previously tuned high-level forgetting parameters ineffective. Figure 7 highlights this issue, showing that mountain, which is initially erased and blended into sand, re-emerges after learning, demonstrating the instability of this approach.
+
+# 5.4. Object Detection Results
+
+For the object detection task, we use DINO (Zhang et al., 2022) pretrained on the COCO dataset as the base model. The forgetting set consists of five randomly selected classes: person, teddy bear, toilet, bench, and bed, while all remaining classes form the retention set. The learning sets consist of 5 classes: Black-footed Albatross, Laysan Albatross, Sooty Albatross, Groove-billed Ani, and Brewer Blackbird for CUB-200-2011 and Chihuahua, Maltese Dog, Basset, American Staffordshire Terrier, and Norwich Terrier for Stanford Dogs, respectively.
+
+Table 3. Object Detection Results on COCO.  
+
+<table><tr><td rowspan="2">procedure</td><td colspan="3">Cub</td><td colspan="3">Stanford Dogs</td></tr><tr><td>mAPr↑</td><td>mAPl↑</td><td>mAPf↓</td><td>mAPr↑</td><td>mAPl↑</td><td>mAPf↓</td></tr><tr><td>Start</td><td>55.4</td><td>0</td><td>44.5</td><td>55.4</td><td>0</td><td>44.5</td></tr><tr><td>F</td><td>54.9</td><td>16.8</td><td>3.4</td><td>54.8</td><td>9.7</td><td>3.4</td></tr><tr><td>F → L</td><td>55</td><td>65.4</td><td>7.7</td><td>54.6</td><td>78.5</td><td>11.1</td></tr><tr><td>L</td><td>55.3</td><td>64.3</td><td>37.6</td><td>54.5</td><td>67.5</td><td>37.5</td></tr><tr><td>L → F</td><td>55.5</td><td>62.2</td><td>0.5</td><td>55</td><td>80.1</td><td>0.6</td></tr></table>
+
+The quantitative results in Table 3 demonstrate the effectiveness of our Learning Before Forgetting strategy, as the mAP of the retention set remains stable at around  $55\%$ , the for
+
+![](images/e448c30299874e4747b2b49c70994c1dd247c49b570179b406a8692b03afef99.jpg)  
+Figure 7. Semantic segmentation results for Learning After Forgetting on ADE20K.
+
+getting set drops from  $44.5\%$  to below  $1\%$ , and the learning set improves from 0 to a satisfactory level, confirming the success of our approach. In contrast, it also shows that in the Learning After Forgetting  $(F \rightarrow L)$  setting, the forgetting set retains a relatively high mAP, indicating ineffective forgetting. This supports our hypothesis that learning progresses from low-level to high-level features, while forgetting follows the opposite direction, from high-level to low-level features.
+
+# 5.5. Insights and Discussion
+
+To further validate the effectiveness of our strategy, we conduct an additional experiment involving a Forget-Learn-Forget sequence. As shown in Table 2, although the mIoU of the forgetting set remains high after the initial forgetting and subsequent learning phases, it is significantly reduced after the second forgetting phase. This result demonstrates the robustness of the Learn Before Forget strategy. The results  $L \to F \to L$  further provide indirect evidence that
+
+positioning the learning phase at the end influences the content that was previously forgotten. We analyze the  $\mathcal{L}_2$  norm of model parameters at different stages, as illustrated in Figure 6. The red line represents parameter changes from  $F$  to  $F\rightarrow L$ , while the black line indicates changes from  $F\rightarrow L$  to  $F\rightarrow L\rightarrow F$ . The results show that learning-induced parameter changes are primarily concentrated in the early layers of the model, whereas forgetting-related changes are more prominent in the later layers. These observations align well with our previous findings.
+
+# 6. Conclusion and Future Works
+
+We proposed Knowledge Swapping, a novel task that enables selective regulation of model knowledge by achieving three goals: forgetting user-specified knowledge, retaining essential knowledge, and learning new knowledge. To accomplish this, we introduced a two-stage training strategy based on the Learning Before Forgetting principle, which decouples learning and forgetting to mitigate catastrophic forgetting effectively. We benchmark our Learning Before Forgetting with various experiments. However, our experiments also reveal that the difficulty of learning new knowledge for different categories and forgetting old knowledge varies. An interesting direction for future research is to explore and analyze the difficulty of forgetting specific knowledge and learning new knowledge of categories.
+
+# Acknowledgements
+
+This work has been supported by the New Cornerstone Science Foundation through the XPLORER PRIZE. This work was funded by the National Natural Science Foundation of China (No. 72188101 & No. 62472139 & No. 62302140) and the Fundamental Research Funds for the Central Universities (No. JZ2024HGTB0261 & No. JZ2024HGTA0178). The computation is completed on the HPC Platform of Hefei University of Technology.
+
+# Impact Statement
+
+This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
+
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