On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning

Abstract

The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobolev space as an expanded hypothesis space. This enhanced bound remains valid even in single output settings, outperforming existing Koopman based bounds. The resulting framework maintains key advantages such as flexibility and independence from network width, offering a more precise theoretical understanding of multitask deep learning in the context of kernel methods.

Accepted at the 11th International Conference on Machine Learning, Optimization, and Data Science (LOD), Castiglione della Pescaia, Italy, September 21-24, 2025. To appear in Lecture Notes in Computer Science (LNCS), volume 16467