March 2026

arXiv:2603.19657v1 Announce Type: new Abstract: In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower bound on the critical sample complexity required for reliable model selection. More specifically, we show that distinguishing a $k$-component mixture from a simpler model necessitates a sample size scaling of $Omega(Delta^{-(4k-4)})$. We then propose a thresholding-based estimation algorithm that evaluates […]

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arXiv:2603.19629v1 Announce Type: new Abstract: Learned priors based on deep generative models offer data-driven regularization for seismic inversion, but training them requires a dataset of representative subsurface models — a resource that is inherently scarce in geoscience applications. Since the training objective of most generative models can be cast as maximum likelihood on a finite dataset, any such model risks converging to the empirical distribution — effectively memorizing the training examples rather than learning the underlying geological distribution. […]

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arXiv:2603.19440v1 Announce Type: new Abstract: Precision medicine aims to tailor therapeutic decisions to individual patient characteristics. This objective is commonly formalized through dynamic treatment regimes, which use statistical and machine learning methods to derive sequential decision rules adapted to evolving clinical information. In most existing formulations, these approaches produce a single optimal treatment at each stage, leading to a unique decision sequence. However, in many clinical settings, several treatment options may yield similar expected outcomes, and focusing on […]

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arXiv:2603.19439v1 Announce Type: new Abstract: Several graph data mining, signal processing, and machine learning downstream tasks rely on information related to the eigenvectors of the associated adjacency or Laplacian matrix. Classical eigendecomposition methods are powerful when the matrix remains static but cannot be applied to problems where the matrix entries are updated or the number of rows and columns increases frequently. Such scenarios occur routinely in graph analytics when the graph is changing dynamically and either edges and/or […]

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arXiv:2603.19422v1 Announce Type: new Abstract: We propose a principled framework for unsupervised domain adaptation under covariate shift in kernel Generalized Linear Models (GLMs), encompassing kernelized linear, logistic, and Poisson regression with ridge regularization. Our goal is to minimize prediction error in the target domain by leveraging labeled source data and unlabeled target data, despite differences in covariate distributions. We partition the labeled source data into two batches: one for training a family of candidate models, and the other […]

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Learning systems are typically optimized by minimizing loss or maximizing reward, assuming that improvements in these signals reflect progress toward the true objective. However, when feedback reliability is unobservable, this assumption can fail, and learning algorithms may converge stably to incorrect solutions. This failure arises because single-step feedback does not reveal whether an experience is informative or persistently biased. When information is aggregated over learning trajectories, however, systematic differences between reliable and unreliable regimes can emerge. We propose […]

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Developing efficient CUDA kernels is a fundamental yet challenging task in the generative AI industry. Recent researches leverage Large Language Models (LLMs) to automatically convert PyTorch reference implementations to CUDA kernels, significantly reducing the engineering efforts. State-of-the-art LLMs, such as GPT-5.2 and Claude-Sonnet-4.5, still struggle in this specific task. To address this challenge, we propose DRTriton, a scalable learning framework for training LLMs to convert PyTorch codes into highly optimized Triton kernels, which are then compiled to CUDA […]

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