🤖 AI Summary
This work addresses the fundamental trade-off between adversarial robustness and generalization in quantum machine learning models under both trainable and non-trainable data encoding schemes. We first derive a parameter-dependent Lipschitz bound, theoretically revealing how trainable encodings regulate model stability, and rigorously prove that fixed encodings cannot adjust the Lipschitz constant—establishing their insufficiency for robustness control. We propose a joint optimization training strategy regularized by the Lipschitz bound and derive explicit, parameterized upper bounds on both adversarial robustness and generalization error. Numerical experiments demonstrate that our method significantly improves model accuracy under adversarial perturbations and enhances out-of-distribution generalization performance. This work establishes an interpretable, controllable paradigm for designing robust quantum machine learning models.
📝 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. Based on these theoretical results, we propose a practical strategy for training robust and generalizable quantum models by regularizing the Lipschitz bound in the cost. Moreover, we show that, for fixed and nontrainable 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.
Published by the American Physical Society
2024