---
title: "Uncertainty Estimation and Generalization Bounds for Modern Deep Learning (PhD Thesis)"
source_url: https://arxiv.org/abs/2606.13818
ingested: 2026-06-17
sha256: <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

- [[deep-variational-implicit-process|DVIP]]
- [[variational-linearized-laplace-approximation|VaLLA]]
- [[fixed-mean-gaussian-process|FMGP]]
- [[pac-bayesian-bounds|PAC-Bayesian 界]]
- [[implicit-processes|隐式过程]]
- [[function-space-modeling|函数空间建模]]
- [[generalization-bounds|泛化界]]
- [[double-descent|双下降]]
- [[deep-gaussian-process|深度高斯过程]]
