Stability and Generalization of Quantum Neural Networks
This work addresses the lack of theoretical foundations for QNNs, which is crucial for researchers in quantum machine learning, though it is incremental as it applies classical stability tools to a quantum context.
The paper tackles the theoretical understanding of quantum neural networks (QNNs) by using algorithmic stability to establish generalization bounds, including high-probability and optimization-dependent bounds, and explores the effects of quantum noise on near-term devices, with numerical experiments validating the findings.
Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their generalization properties, are less developed and primarily focus on the uniform convergence approach. In this paper, we exploit an advanced tool in classical learning theory, i.e., algorithmic stability, to study the generalization of QNNs. We first establish high-probability generalization bounds for QNNs via uniform stability. Our bounds shed light on the key factors influencing the generalization performance of QNNs and provide practical insights into both the design and training processes. We next explore the generalization of QNNs on near-term noisy intermediate-scale quantum (NISQ) devices, highlighting the potential benefits of quantum noise. Moreover, we argue that our previous analysis characterizes worst-case generalization guarantees, and we establish a refined optimization-dependent generalization bound for QNNs via on-average stability. Numerical experiments on various real-world datasets support our theoretical findings.