Understanding Generalization in Quantum Machine Learning with Margins

Understanding and improving generalization capabilities is crucial for both classical and quantum machine learning (QML). Recent studies have revealed shortcomings in current generalization theories, particularly those relying on uniform bounds, across both classical and quantum settings. In this work, we present a margin-based generalization bound for QML models, providing a more reliable framework for evaluating generalization. Our experimental studies on the quantum phase recognition (QPR) dataset demonstrate that margin-based metrics are strong predictors of generalization performance, outperforming traditional metrics like parameter count. By connecting this margin-based metric to quantum information theory, we demonstrate how to enhance the generalization performance of QML through a classical-quantum hybrid approach when applied to classical data. Quantum machine learning (QML) presents exciting opportunities to expand the horizons of machine learning beyond classical approaches. Generalization--the ability to learn from examples and make accurate predictions on unseen data--is a core component of intelligence and a critical factor that quantifies the effectiveness of machine learning models in real-world applications. Thus, fundamental challenge in QML, as in classical machine learning, is to understand, characterize, and optimize generalization. Generalization in QML has been studied through various factors, such as the number of parameters (Caro et al., 2022), effective dimension (Abbas et al., 2021), quantum resource theory Bu et al. (2021; 2022; 2023), and quantum information-theoretic quantities Banchi et al. (2021); Caro et al. (2023).