This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems. While neural networks achieve remarkable predictive performance, their ability to generalize and to quantify uncertainty remains only partly understood. This thesis approaches this challenge from both methodological and theoretical angles: unifying Bayesian inference, function-space modeling, and large-deviation theory under a common probabilistic perspective. On the methodological side, the thesis introduces the Deep Variational Implicit Process (DVIP), a scalable Bayesian framework that extends implicit processes to deep architectures. Complementing this, two post-hoc methods -- the Variational Linearized Laplace Approximation (VaLLA) and the Fixed-Mean Gaussian Process (FMGP) -- are proposed to equip pretrained deterministic networks with calibrated uncertainty estimates. The theoretical contributions focus on one of the central open questions in modern machine learning: why do large, over-parameterized neural networks generalize so well? To address this, the thesis develops a unified probabilistic framework that connects three key mechanisms -- diversity, smoothness, and stochasticity -- within the language of PAC-Bayesian and large-deviation theory.

翻译：本论文探讨如何运用贝叶斯原理深化对现代深度学习系统的理解。尽管神经网络在预测性能上表现卓越，但其泛化能力与不确定性量化机制仍存在诸多未解之谜。本文从方法革新与理论构建双重维度展开研究：将贝叶斯推断、函数空间建模与大偏差理论统一于概率论框架下。在方法论层面，提出深度变分隐式过程（DVIP）这一可扩展贝叶斯框架，将隐式过程延伸至深度架构；同时提出两种后处理方法——变分线性化拉普拉斯近似（VaLLA）与固定均值高斯过程（FMGP），为预训练确定性网络配备校准的不确定性估计。理论贡献聚焦于现代机器学习核心难题：大型过参数化神经网络为何具备卓越泛化能力？为解答该问题，本文构建统一概率框架，在PAC-贝叶斯与大偏差理论语境中建立多样性、平滑性与随机性三大关键机制的内在关联。