Xuemei Chen

Noreen Jamil, Xuemei Chen, Alex Cloninger

The Hildreth's algorithm is a row action method for solving large systems of inequalities. This algorithm is efficient for problems with sparse matrices, as opposed to direct methods such as Gaussian elimination or QR-factorization. We apply the Hildreth's algorithm, as well as a randomized version, along with prioritized selection of the inequalities, to efficiently detect the highest priority feasible subsystem of equations. We prove convergence results and feasibility criteria for both cyclic and randomized Hildreth's algorithm, as well as a mixed algorithm which uses Hildreth's algorithm for inequalities and Kaczmarz algorithm for equalities. These prioritized, sparse systems of inequalities commonly appear in constraint-based user interface (UI) layout specifications. The performance and convergence of these proposed algorithms are evaluated empirically using randomly generated UI layout specifications of various sizes. The results show that these methods offer improvements in performance over standard methods like Matlab's LINPROG, a well-known efficient linear programming solver, and the recent developed Kaczmarz algorithm with prioritized IIS detection.

Xuemei Chen, Owen Deen

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is the sum of the $\ell_1$-norm and nuclear norm. In this paper we detail the iterative algorithms and its associated computations for solving this convex optimization problem. We present various efficient implementation strategies, with attention to practical cases where $H$ is circulant, separable, or block structured. Notably, we propose a preconditioning technique that drastically improved the performance of our algorithms in terms of efficiency, accuracy, and robustness. While this paper serves as an illustrative algorithm implementation manual, we also provide theoretical guarantee for our preconditioning strategy. Numerical results demonstrate the effectiveness of the proposed approach.

Yuqi Ma, Huamin Wang, Hangchi Shen et al.

Recently, brain-inspired spiking neural networks (SNNs) have attracted great research attention owing to their inherent bio-interpretability, event-triggered properties and powerful perception of spatiotemporal information, which is beneficial to handling event-based neuromorphic datasets. In contrast to conventional static image datasets, event-based neuromorphic datasets present heightened complexity in feature extraction due to their distinctive time series and sparsity characteristics, which influences their classification accuracy. To overcome this challenge, a novel approach termed Neuromorphic Momentum Contrast Learning (NeuroMoCo) for SNNs is introduced in this paper by extending the benefits of self-supervised pre-training to SNNs to effectively stimulate their potential. This is the first time that self-supervised learning (SSL) based on momentum contrastive learning is realized in SNNs. In addition, we devise a novel loss function named MixInfoNCE tailored to their temporal characteristics to further increase the classification accuracy of neuromorphic datasets, which is verified through rigorous ablation experiments. Finally, experiments on DVS-CIFAR10, DVS128Gesture and N-Caltech101 have shown that NeuroMoCo of this paper establishes new state-of-the-art (SOTA) benchmarks: 83.6% (Spikformer-2-256), 98.62% (Spikformer-2-256), and 84.4% (SEW-ResNet-18), respectively.

Xuemei Chen, Alexander Powell

A randomized subspace action algorithm is investigated for fusion frame signal recovery problems. It is noted that Kaczmarz bounds provide upper bounds on the algorithm's error moments. The main question of which probability distributions on a random fusion frame lead to provably fast convergence is addressed. In particular, it is proven which distributions give minimal Kaczmarz bounds, and hence give best control on error moment upper bounds arising from Kaczmarz bounds. Uniqueness of the optimal distributions is also addressed.