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Uncertainty Estimation and Generalization Bounds for Modern Deep Learning (PhD Thesis) https://arxiv.org/abs/2606.13818 2026-06-17 <computed>

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

Author: Luis A. Ortega Andrés — Department of Computer Science, Autonomous University of Madrid

Supervisor: Daniel Hernández Lobato

arXiv: 2606.13818v1 [cs.LG] (2026-06-11) — PhD Thesis

Abstract

Investigates how Bayesian principles can deepen understanding of modern deep learning systems. On the methodological side, introduces DVIP (Deep Variational Implicit Process), VaLLA (Variational Linearized Laplace Approximation), and FMGP (Fixed-Mean Gaussian Process). On the theoretical side, develops a unified PAC-Bayesian/large-deviation framework connecting diversity, smoothness, and stochasticity as mechanisms for generalization. Provides quantitative distribution-dependent explanation for double-descent.

Key Concepts