提出新方法高效准确估算量子-经典模型的Lipschitz常数
Efficient and Accurate Estimation of Lipschitz Constants for Hybrid Quantum-Classical Decision Models
- 用凸优化统一建模经典与量子层的交互关系
- 相比已有方法，估计更紧致且计算更快
- 适合关注模型鲁棒性与公平性的研究者
本文提出一种新型框架，用于高效且准确地估算混合量子-经典决策模型中的Lipschitz常数。该方法将经典神经网络与量子变分电路相结合，解决学习理论中的关键问题，如公平性验证、鲁棒训练与泛化能力。通过统一的凸优化形式，将现有经典方法扩展至捕捉经典层与量子层之间的相互作用。该集成策略不仅提供了更紧致的Lipschitz常数上界，还显著提升了计算效率，相较于先前方法具有明显优势。
原文摘要 · Abstract (English)
In this paper, we propose a novel framework for efficiently and accurately estimating Lipschitz constants in hybrid quantum-classical decision models. Our approach integrates classical neural network with quantum variational circuits to address critical issues in learning theory such as fairness verification, robust training, and generalization. By a unified convex optimization formulation, we extend existing classical methods to capture the interplay between classical and quantum layers. This integrated strategy not only provide a tight bound on the Lipschitz constant but also improves computational efficiency with respect to the previous methods.
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