Sharper Generalization Bounds for Transformer

TL;DR

This paper derives sharper, architecture-dependent generalization bounds for Transformer models using offset Rademacher complexity, covering various architectures and feature distribution assumptions.

Contribution

It introduces new excess risk bounds for Transformers based on offset Rademacher complexity and extends results to unbounded feature settings.

Findings

Sharper generalization bounds achieved for different Transformer architectures.

Bounds depend on matrix ranks and norms, providing architecture-specific insights.

Extended theoretical results to unbounded and heavy-tailed feature distributions.

Abstract

This paper studies generalization error bounds for Transformer models. Based on the offset Rademacher complexity, we derive sharper generalization bounds for different Transformer architectures, including single-layer single-head, single-layer multi-head, and multi-layer Transformers. We first express the excess risk of Transformers in terms of the offset Rademacher complexity. By exploiting its connection with the empirical covering numbers of the corresponding hypothesis spaces, we obtain excess risk bounds that achieve optimal convergence rates up to constant factors. We then derive refined excess risk bounds by upper bounding the covering numbers of Transformer hypothesis spaces using matrix ranks and matrix norms, leading to precise, architecture-dependent generalization bounds. Finally, we relax the boundedness assumption on feature mappings and extend our theoretical results to settings with unbounded (sub-Gaussian) features and heavy-tailed distributions.