Li Shen

Ganzhao Yuan, Wei-Shi Zheng, Li Shen et al.

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized optimization as special cases. This paper proposes and analyzes a new Generalized Matrix Splitting Algorithm (GMSA) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Our algorithm is derived from a novel triangle operator mapping, which can be computed exactly using a new generalized Gaussian elimination procedure. We establish the global convergence, convergence rate, and iteration complexity of GMSA for convex problems. In addition, we also discuss several important extensions of GMSA. Finally, we validate the performance of our proposed method on three particular applications: nonnegative matrix factorization, $\ell_0$ norm regularized sparse coding, and $\ell_1$ norm regularized Dantzig selector problem. Extensive experiments show that our method achieves state-of-the-art performance in term of both efficiency and efficacy.

Shen Li, Jianqing Xu, Jiaying Wu et al.

Synthetic face recognition (SFR) aims to generate synthetic face datasets that mimic the distribution of real face data, which allows for training face recognition models in a privacy-preserving manner. Despite the remarkable potential of diffusion models in image generation, current diffusion-based SFR models struggle with generalization to real-world faces. To address this limitation, we outline three key objectives for SFR: (1) promoting diversity across identities (inter-class diversity), (2) ensuring diversity within each identity by injecting various facial attributes (intra-class diversity), and (3) maintaining identity consistency within each identity group (intra-class identity preservation). Inspired by these goals, we introduce a diffusion-fueled SFR model termed $\text{ID}^3$. $\text{ID}^3$ employs an ID-preserving loss to generate diverse yet identity-consistent facial appearances. Theoretically, we show that minimizing this loss is equivalent to maximizing the lower bound of an adjusted conditional log-likelihood over ID-preserving data. This equivalence motivates an ID-preserving sampling algorithm, which operates over an adjusted gradient vector field, enabling the generation of fake face recognition datasets that approximate the distribution of real-world faces. Extensive experiments across five challenging benchmarks validate the advantages of $\text{ID}^3$.

Huanjin Yao, Jiaxing Huang, Wenhao Wu et al.

In this work, we aim to develop an MLLM that understands and solves questions by learning to create each intermediate step of the reasoning involved till the final answer. To this end, we propose Collective Monte Carlo Tree Search (CoMCTS), a new learning-to-reason method for MLLMs, which introduces the concept of collective learning into ``tree search'' for effective and efficient reasoning-path searching and learning. The core idea of CoMCTS is to leverage collective knowledge from multiple models to collaboratively conjecture, search and identify effective reasoning paths toward correct answers via four iterative operations including Expansion, Simulation and Error Positioning, Backpropagation, and Selection. Using CoMCTS, we construct Mulberry-260k, a multimodal dataset with a tree of rich, explicit and well-defined reasoning nodes for each question. With Mulberry-260k, we perform collective SFT to train our model, Mulberry, a series of MLLMs with o1-like step-by-step Reasoning and Reflection capabilities. Extensive experiments demonstrate the superiority of our proposed methods on various benchmarks. Code will be available at https://github.com/HJYao00/Mulberry