Wenzheng Hu | Searcharxiv

arXiv2026

Logarithmically Coupled \(p\)-Laplacian Systems: From Discrete Ground States to Rigidity and Critical Continuous Limits

This paper introduces a new coupled \(p\)-Laplacian system with logarithmic nonlinearities, on locally finite graphs and, in the critical case \(p=N>4\), on \(\mathbb R^N\) via a regularised formulation. The logarithmic coupling renders the energy functional ill-defined on the natural Sobolev space. To address this non-separable singularity, we develop an exponent calibration technique that converts the logarithmic terms into strictly lower-order power estimates. This technique underpins the existence proofs in two distinct settings-and is essential in the continuous critical setting, where the failure of the \(L^\infty\)-embedding renders classical methods inapplicable. The same technique is also used to recover compactness, thereby completing the passage from the regularised problem to the original ill-posed equation.In the discrete setting, we further develop a rigidity theory for ground states, which yields an explicit Hessian factorisation dictated by the Nehari constraint. The compactness restoration and limit theorem, the convergence rates, and the existence results in both settings together form a discrete-continuous double loop, from ill-posedness through compactness and rigidity to asymptotics, providing a unified variational framework for logarithmically coupled systems.

math.AP↗

arXiv2023

CATRO: Channel Pruning via Class-Aware Trace Ratio Optimization

Deep convolutional neural networks are shown to be overkill with high parametric and computational redundancy in many application scenarios, and an increasing number of works have explored model pruning to obtain lightweight and efficient networks. However, most existing pruning approaches are driven by empirical heuristic and rarely consider the joint impact of channels, leading to unguaranteed and suboptimal performance. In this paper, we propose a novel channel pruning method via Class-Aware Trace Ratio Optimization (CATRO) to reduce the computational burden and accelerate the model inference. Utilizing class information from a few samples, CATRO measures the joint impact of multiple channels by feature space discriminations and consolidates the layer-wise impact of preserved channels. By formulating channel pruning as a submodular set function maximization problem, CATRO solves it efficiently via a two-stage greedy iterative optimization procedure. More importantly, we present theoretical justifications on convergence of CATRO and performance of pruned networks. Experimental results demonstrate that CATRO achieves higher accuracy with similar computation cost or lower computation cost with similar accuracy than other state-of-the-art channel pruning algorithms. In addition, because of its class-aware property, CATRO is suitable to prune efficient networks adaptively for various classification subtasks, enhancing handy deployment and usage of deep networks in real-world applications.

cs.LG↗