arXiv:2509.24882v1 Announce Type: cross Abstract: Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic…
arXiv:2509.25153v1 Announce Type: cross Abstract: When and how can an attention mechanism learn to selectively attend to informative tokens, thereby enabling detection of weak, rare, and sparsely located features? We address these questions theoretically in a sparse-token classification model in…
arXiv:2509.24710v1 Announce Type: new Abstract: Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an…
arXiv:2405.18176v5 Announce Type: replace Abstract: This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic approach for generating prediction intervals with any ML model. SEMF extends the Expectation-Maximization algorithm, traditionally used in unsupervised learning, to a supervised context,…
arXiv:2509.24912v1 Announce Type: new Abstract: Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($sigma to 0$). In this work, we propose an alternative perspective: their success…
arXiv:2411.16663v2 Announce Type: replace Abstract: Working with systems of partial differential equations (PDEs) is a fundamental task in computational science. Well-posed systems are addressed by numerical solvers or neural operators, whereas systems described by data are often addressed by PINNs…
arXiv:2509.24914v1 Announce Type: new Abstract: We study empirical risk minimization in a single-head tied-attention layer trained on synthetic high-dimensional sequence tasks, given by the recently introduced attention-indexed model. Using tools from random matrix theory, spin-glass physics, and approximate message passing,…
arXiv:2502.16816v3 Announce Type: replace Abstract: We present the first finite-sample analysis of policy evaluation in robust average-reward Markov Decision Processes (MDPs). Prior work in this setting have established only asymptotic convergence guarantees, leaving open the question of sample complexity. In…
arXiv:2509.24920v1 Announce Type: new Abstract: The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition, offering a natural…
arXiv:2507.08150v2 Announce Type: replace Abstract: Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in a balanced manner. We propose CLEAR, a calibration method with two distinct parameters,…
