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Recognizing the substantial computational cost of backpropagation (BP), non-BP methods have emerged as attractive alternatives for efficient learning on emerging neuromorphic systems. However, existing non-BP approaches still face critical…

Longitudinal low-dose CT follow-ups vary in noise, reconstruction kernels, and registration quality. These differences destabilize subtraction images and can trigger false new lesion alarms. We present TopoGate, a lightweight model that…

Semantic segmentation in marine environments is crucial for the autonomous navigation of unmanned surface vessels (USVs) and coastal Earth Observation events such as oil spills. However, existing methods, often relying on deep CNNs and…

This paper consider solving a class of nonconvex-strongly-convex distributed stochastic bilevel optimization (DSBO) problems with personalized inner-level objectives. Most existing algorithms require computational loops for hypergradient…

We study the minimization of smooth, possibly nonconvex functions over the positive orthant, a key setting in Poisson inverse problems, using the exponentiated gradient (EG) method. Interpreting EG as Riemannian gradient descent (RGD) with…

In distributed and federated learning algorithms, communication overhead is often reduced by performing multiple local updates between communication rounds. However, due to data heterogeneity across nodes and the local gradient noise within…

A fundamental challenge in neurosymbolic systems is applying continuous gradient-based optimization to discrete logical domains. While fuzzy relaxations provide differentiability, they often lack a formal structural alignment with classical…

Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation…

Electronic health records contain rich textual data which possess critical predictive information for machine-learning based diagnostic aids. However many traditional machine learning methods fail to simultaneously integrate both vector…

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

In this paper, we present a novel localized Generative Adversarial Net (GAN) to learn on the manifold of real data. Compared with the classic GAN that {\em globally} parameterizes a manifold, the Localized GAN (LGAN) uses local coordinate…

We provide a theoretical analysis of the representation learning problem aimed at learning the latent variables (design matrix) $\Theta$ of observations $Y$ with the knowledge of the coefficient matrix $X$. The design matrix is learned…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

Reinforcement Learning, particularly through policy gradient methods, has played a central role in enabling reasoning capabilities of Large Language Models. However, the optimization stability of policy gradients in this setting remains…

In this paper, we study the numerical simulation of stochastic differential equations (SDEs) on the special orthogonal Lie group $\text{SO}(n)$. We propose a geometry-preserving numerical scheme based on the stochastic tangent space…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

We develop here an algorithmic framework for constructing consistent multiscale Laplacian eigenfunctions (vectors) on data. Consequently, we address the unsupervised machine learning task of finding scalar functions capturing consistent…

Safety alignment of large language models remains brittle under domain shift and noisy preference supervision. Most existing robust alignment methods focus on uncertainty in alignment data, while overlooking optimization-induced fragility…

Conventional algorithms in autonomous exploration face challenges due to their inability to accurately and efficiently identify the spatial distribution of convex regions in the real-time map. These methods often prioritize navigation…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…