The interplay of robustness and generalization in quantum machine learning

TL;DR

This paper explores the relationship between robustness and generalization in variational quantum models, proposing a regularization approach based on Lipschitz bounds and demonstrating its application in time series analysis.

Contribution

It introduces a theoretical framework linking robustness and generalization in quantum models, emphasizing trainable data encoding strategies and practical regularization methods.

Findings

Lipschitz bounds quantify robustness and generalization in quantum models.

Regularization based on these bounds improves model robustness and generalization.

Application to time series analysis demonstrates practical benefits.

Abstract

While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for variational quantum models, which were recently proposed as function approximators in supervised learning. We discuss recent results quantifying both robustness and generalization via Lipschitz bounds, which explicitly depend on model parameters. Thus, they give rise to a regularization-based training approach for robust and generalizable quantum models, highlighting the importance of trainable data encoding strategies. The practical implications of the theoretical results are demonstrated with an application to time series analysis.