Training robust and generalizable quantum models

TL;DR

This paper develops theoretical bounds for the robustness and generalization of quantum machine learning models, emphasizing the importance of trainable data encodings and providing strategies for improving model reliability.

Contribution

It introduces parameter-dependent Lipschitz bounds for quantum models with trainable encodings, linking data encoding norms to robustness and generalization, and proposes regularization strategies.

Findings

Trainable encodings significantly improve robustness and generalization.

Lipschitz bounds can be controlled through encoding parameters.

Numerical results validate the theoretical bounds and strategies.

Abstract

Adversarial robustness and generalization are both crucial properties of reliable machine learning models. In this paper, we study these properties in the context of quantum machine learning based on Lipschitz bounds. We derive parameter-dependent Lipschitz bounds for quantum models with trainable encoding, showing that the norm of the data encoding has a crucial impact on the robustness against data perturbations. Further, we derive a bound on the generalization error which explicitly involves the parameters of the data encoding. Our theoretical findings give rise to a practical strategy for training robust and generalizable quantum models by regularizing the Lipschitz bound in the cost. Further, we show that, for fixed and non-trainable encodings, as those frequently employed in quantum machine learning, the Lipschitz bound cannot be influenced by tuning the parameters. Thus, trainable encodings are crucial for systematically adapting robustness and generalization during training. The practical implications of our theoretical findings are illustrated with numerical results.