Mengyuan Zhang

Mengyuan Zhang, Kai Liu

Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues. First, they usually adopt a two-stage framework and isolate the processes of affinity learning, multi-view information fusion and clustering. Second, they assume the data lies in a linear subspace which may fail in practice as most real-world datasets may have non-linearity structures. To address the above issues, in this paper we propose a novel Enriched Robust Multi-View Kernel Subspace Clustering framework where the consensus affinity matrix is learned from both multi-view data and spectral clustering. Due to the objective and constraints which is difficult to optimize, we propose an iterative optimization method which is easy to implement and can yield closed solution in each step. Extensive experiments have validated the superiority of our method over state-of-the-art clustering methods.

Mengyuan Zhang, Kai Liu

Sparse logistic regression is for classification and feature selection simultaneously. Although many studies have been done to solve $\ell_1$-regularized logistic regression, there is no equivalently abundant work on solving sparse logistic regression with nonconvex regularization term. In this paper, we propose a unified framework to solve $\ell_1$-regularized logistic regression, which can be naturally extended to nonconvex regularization term, as long as certain requirement is satisfied. In addition, we also utilize a different line search criteria to guarantee monotone convergence for various regularization terms. Empirical experiments on binary classification tasks with real-world datasets demonstrate our proposed algorithms are capable of performing classification and feature selection effectively at a lower computational cost.

Mengyuan Zhang, Kai Liu

Multi-task learning aims to boost the generalization performance of multiple related tasks simultaneously by leveraging information contained in those tasks. In this paper, we propose a multi-task learning framework, where we utilize prior knowledge about the relations between features. We also impose a penalty on the coefficients changing for each specific feature to ensure related tasks have similar coefficients on common features shared among them. In addition, we capture a common set of features via group sparsity. The objective is formulated as a non-smooth convex optimization problem, which can be solved with various methods, including gradient descent method with fixed stepsize, iterative shrinkage-thresholding algorithm (ISTA) with back-tracking, and its variation -- fast iterative shrinkage-thresholding algorithm (FISTA). In light of the sub-linear convergence rate of the methods aforementioned, we propose an asymptotically linear convergent algorithm with theoretical guarantee. Empirical experiments on both regression and classification tasks with real-world datasets demonstrate that our proposed algorithms are capable of improving the generalization performance of multiple related tasks.

Mengyuan Zhang, Kai Liu

We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with a novel support set projection operation on the singular values of the intermediate update. We show that our algorithms are able to achieve a convergence rate of $O(\frac{1}{t^2})$, which is exactly same as Nesterov's optimal convergence rate for first-order methods on smooth and convex problems. Strict sparsity can be expected and the support set of singular values during each update is monotonically shrinking, which to our best knowledge, is novel in momentum-based algorithms.

Jinpeng Wang, Chao Li, Ting Ye et al.

Reinforcement Learning with Verifiable Rewards (RLVR) demonstrates significant potential in enhancing the reasoning capabilities of Large Language Models (LLMs). However, existing RLVR methods are often constrained by issues such as coarse-grained rewards, reward noise, and inefficient exploration, which lead to unstable training and entropy collapse. To address this challenge, we propose the Intrinsic Confidence-Driven Group Relative Preference Optimization method (ICPO). The intuition behind it lies in the fact that the probabilities of an LLM generating different responses can inherently and directly reflect its self-assessment of the reasoning process. Inspired by the idea of preference modeling, ICPO calculates a preference advantage score for each response by comparing the relative generation probabilities of multiple responses under the same input prompt, and integrates this score with verifiable rewards to guide the exploration process. We have discovered that the preference advantage score not only alleviates the issues of coarse-grained rewards and reward noise but also effectively curbs overconfident errors, enhances the relative superiority of undervalued high-quality responses, and prevents the model from overfitting to specific strategies. Comprehensive experiments across four general-domain benchmarks and three mathematical benchmarks demonstrate that ICPO steadily boosts reasoning compared to GRPO.