用自旋玻璃理论分析神经网络结构，揭示传统指标未捕捉的隐藏特性。
A Spin Glass Characterization of Neural Networks
- 构建基于自旋玻璃的模型，通过副本重叠度描述单个神经网络结构
- 发现该方法能有效关联网络的拟合能力、泛化性能与鲁棒性
- 适用于模型检测、安全验证等场景，可发现潜在漏洞
本文基于自旋玻璃中的复制对称性破缺（RSB）现象，提出一种统计力学框架来刻画前馈神经网络（FNN）。通过将给定的FNN转化为霍普菲尔德型自旋玻璃模型，利用模拟副本样本间的重叠度作为其特征描述符。研究了该自旋玻璃描述与常见网络性质（如数据拟合、容量、泛化和鲁棒性）之间的联系，并进行了实证验证。与以往关注模型集合的解析研究不同，该方法可计算单个网络实例的特征，揭示出传统指标（如损失或准确率）无法捕捉的非平凡结构特性。初步结果表明，其在模型检查、安全验证及隐藏漏洞检测等方面具有应用潜力。
原文摘要 · Abstract (English)
This work presents a statistical mechanics characterization of neural networks, motivated by the replica symmetry breaking (RSB) phenomenon in spin glasses. A Hopfield-type spin glass model is constructed from a given feedforward neural network (FNN). Overlaps between simulated replica samples serve as a characteristic descriptor of the FNN. The connection between the spin-glass description and commonly studied properties of the FNN -- such as data fitting, capacity, generalization, and robustness -- has been investigated and empirically demonstrated. Unlike prior analytical studies that focus on model ensembles, this method provides a computable descriptor for individual network instances, which reveals nontrivial structural properties that are not captured by conventional metrics such as loss or accuracy. Preliminary results suggests its potential for practical applications such as model inspection, safety verification, and detection of hidden vulnerabilities.
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