用统计场论解析深度学习的泛化与特征学习机制。
Applications of Statistical Field Theory in Deep Learning
- 以统计场论为框架，建模深度学习中函数分布的复杂性。
- 揭示了模型泛化能力、隐式偏差与特征学习的内在规律。
- 适合对理论深度学习感兴趣的科研人员阅读。
过去十年间，深度学习算法取得了巨大进展，但由于其复杂性，深度学习科学仍处于初级阶段。作为一个实验驱动的领域，自然需要在物理范式中寻求深度学习的理论基础。由于深度学习本质上是关于学习函数及函数分布，而统计场论正是处理复杂函数（场）分布的强大工具，因此成为理想的形式体系。近年来的研究表明，场论能为泛化、隐式偏差和特征学习效应提供有益洞见。本文系统梳理了这一新兴研究方向，旨在为相关领域提供教学性综述。
原文摘要 · Abstract (English)
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep learning within the physics paradigm. As deep learning is largely about learning functions and distributions over functions, statistical field theory, a rich and versatile toolbox for tackling complex distributions over functions (fields) is an obvious choice of formalism. Research efforts carried out in the past few years have demonstrated the ability of field theory to provide useful insights on generalization, implicit bias, and feature learning effects. Here we provide a pedagogical review of this emerging line of research.
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