Bowei Zhu

Hongxu Chen, Yanghao Wang, Bowei Zhu et al.

Recent flow matching (FM) methods improve the few-shot adaptation of vision-language models, by modeling cross-modal alignment as a continuous multi-step flow. In this paper, we argue that existing FM methods are inherently constrained by incompatible geometric priors on pre-trained cross-modal features, resulting in suboptimal adaptation performance. We first analyze these methods from a polar decomposition perspective (i.e., radial and angular sub-manifolds). Under this new geometric view, we identify three overlooked limitations in them: 1) Angular dynamics distortion: The radial-angular coupling induces non-uniform speed on the angular sub-manifold, leading to regression training difficulty and extra truncation errors. 2) Radial dynamics neglect: Feature normalization discards modality confidence, failing to distinguish out-of-distribution and in-distribution data, and abandoning crucial radial dynamics. 3) Context-agnostic unconditional flow: Dataset-specific information loss during pre-trained cross-modal feature extraction remains unrecovered. To resolve these issues, we propose warped product flow matching (WP-FM), a unified Riemannian framework that reformulates alignment on a warped product manifold. Within this framework, we derive direct product flow matching (DP-FM) by introducing a constant-warping metric, which yields a decoupled cylindrical manifold (i.e., direct product manifold). DP-FM enables independent radial evolution and constant-speed angular geodesic transport, effectively eliminating angular dynamics distortion while preserving radial consistency. Meanwhile, we incorporate classifier-free guidance by conditioning the flow on the pre-trained VLMs' hidden states to inject missing dataset-specific information. Extensive results across 11 benchmarks have demonstrated that DP-FM achieves a new state-of-the-art for multi-step few-shot adaptation.

Hongxu Chen, Runshi Li, Bowei Zhu et al.

Low-rank adaptations (LoRA) are widely used to fine-tune large models across various domains for specific downstream tasks. While task-specific LoRAs are often available, concerns about data privacy and intellectual property can restrict access to training data, limiting the acquisition of a multi-task model through gradient-based training. In response, LoRA merging presents an effective solution by combining multiple LoRAs into a unified adapter while maintaining data privacy. Prior works on LoRA merging primarily frame it as an optimization problem, yet these approaches face several limitations, including the rough assumption about input features utilized in optimization, massive sample requirements, and the unbalanced optimization objective. These limitations can significantly degrade performance. To address these, we propose a novel optimization-based method, named IterIS: 1) We formulate LoRA merging as an advanced optimization problem to mitigate the rough assumption. Additionally, we employ an iterative inference-solving framework in our algorithm. It can progressively refine the optimization objective for improved performance. 2) We introduce an efficient regularization term to reduce the need for massive sample requirements (requiring only 1-5% of the unlabeled samples compared to prior methods). 3) We utilize adaptive weights in the optimization objective to mitigate potential unbalances in LoRA merging process. Our method demonstrates significant improvements over multiple baselines and state-of-the-art methods in composing tasks for text-to-image diffusion, vision-language models, and large language models. Furthermore, our layer-wise algorithm can achieve convergence with minimal steps, ensuring efficiency in both memory and computation.

Hongxu Chen, Zhen Wang, Taoran Mei et al.

Concept Erasure, which aims to prevent pretrained text-to-image models from generating content associated with semantic-harmful concepts (i.e., target concepts), is getting increased attention. State-of-the-art methods formulate this task as an optimization problem: they align all target concepts with semantic-harmless anchor concepts, and apply closed-form solutions to update the model accordingly. While these closed-form methods are efficient, we argue that existing methods have two overlooked limitations: 1) They often result in incomplete erasure due to "non-zero alignment residual", especially when text prompts are relatively complex. 2) They may suffer from generation quality degradation as they always concentrate parameter updates in a few deep layers. To address these issues, we propose a novel closed-form method ErasePro: it is designed for more complete concept erasure and better preserving overall generative quality. Specifically, ErasePro first introduces a strict zero-residual constraint into the optimization objective, ensuring perfect alignment between target and anchor concept features and enabling more complete erasure. Secondly, it employs a progressive, layer-wise update strategy that gradually transfers target concept features to those of the anchor concept from shallow to deep layers. As the depth increases, the required parameter changes diminish, thereby reducing deviations in sensitive deep layers and preserving generative quality. Empirical results across different concept erasure tasks (including instance, art style, and nudity erasure) have demonstrated the effectiveness of our ErasePro.

Bowei Zhu, Shaojie Li, Mingyang Yi et al.

Prior work (Klochkov $\&$ Zhivotovskiy, 2021) establishes at most $O\left(\log (n)/n\right)$ excess risk bounds via algorithmic stability for strongly-convex learners with high probability. We show that under the similar common assumptions -- - Polyak-Lojasiewicz condition, smoothness, and Lipschitz continous for losses -- - rates of $O\left(\log^2(n)/n^2\right)$ are at most achievable. To our knowledge, our analysis also provides the tightest high-probability bounds for gradient-based generalization gaps in nonconvex settings.

Bowei Zhu, Shaojie Li, Yong Liu

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error and optimization error, present 1/n-rates in strongly-convex-strongly-concave (SC-SC) settings. Existing studies mainly focus on minimax problems with specific algorithms for optimization error, with only a few studies on generalization performance, which limit better excess risk bounds. In this paper, we study the generalization bounds measured by the gradients of primal functions using uniform localized convergence. We obtain a sharper high probability generalization error bound for nonconvex-strongly-concave (NC-SC) stochastic minimax problems. Furthermore, we provide dimension-independent results under Polyak-Lojasiewicz condition for the outer layer. Based on our generalization error bound, we analyze some popular algorithms such as empirical saddle point (ESP), gradient descent ascent (GDA) and stochastic gradient descent ascent (SGDA). We derive better excess primal risk bounds with further reasonable assumptions, which, to the best of our knowledge, are n times faster than exist results in minimax problems.