arXiv:2501.18879v2 Announce Type: replace-cross Abstract: Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial…
arXiv:2009.05908v4 Announce Type: replace-cross Abstract: Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks. Specifically,…
arXiv:2407.18707v2 Announce Type: replace-cross Abstract: Infinitely wide or deep neural networks (NNs) with independent and identically distributed (i.i.d.) parameters have been shown to be equivalent to Gaussian processes. Because of the favorable properties of Gaussian processes, this equivalence is commonly…
arXiv:2503.15704v5 Announce Type: replace Abstract: The performance of sequential Monte Carlo (SMC) samplers heavily depends on the tuning of the Markov kernels used in the path proposal. For SMC samplers with unadjusted Markov kernels, standard tuning objectives, such as the…
arXiv:2509.12691v1 Announce Type: cross Abstract: This paper introduces a novel framework for estimation theory by introducing a second-order diagnostic for estimator design. While classical analysis focuses on the bias-variance trade-off, we present a more foundational constraint. This result is model-agnostic,…
arXiv:2509.12783v1 Announce Type: cross Abstract: Neurons communicate through spikes, and spike timing is a crucial part of neuronal processing. Spike times can be recorded experimentally both intracellularly and extracellularly, and are the main output of state-of-the-art neural probes. On the…
arXiv:2509.12406v1 Announce Type: cross Abstract: Scientific machine learning increasingly uses spectral methods to understand physical systems. Current spectral learning approaches provide only point estimates without uncertainty quantification, limiting their use in safety-critical applications where prediction confidence is essential. Parametric matrix…
arXiv:2509.12527v1 Announce Type: cross Abstract: Large language models often produce plausible but incorrect outputs. Existing heuristics such as HallBayes lack formal guarantees. We develop the first comprehensive theory of emph{information-lift certificates} under selective classification. Our contributions are: (i) a PAC-Bayes…
arXiv:2509.12401v1 Announce Type: cross Abstract: Physics-aware deep learning (PADL) has gained popularity for use in complex spatiotemporal dynamics (field evolution) simulations, such as those that arise frequently in computational modeling of energetic materials (EM). Here, we show that the challenge…
arXiv:2509.12387v1 Announce Type: cross Abstract: Modern deep learning models excel at pattern recognition but remain fundamentally limited by their reliance on spurious correlations, leading to poor generalization and a demand for massive datasets. We argue that a key ingredient for…
