用图曲率识别神经网络中的数据瓶颈，助力提升模型鲁棒性。
Analyzing Neural Network Robustness Using Graph Curvature
- 引入神经网络的黎曼曲率概念，量化数据传输路径的拥堵程度。
- 在MNIST上验证：模型脆弱时，瓶颈边出现频率显著升高。
- 为抗干扰训练提供新思路，适合关注模型稳定性的研究者。
本文从图论角度重新审视神经网络（NN）的鲁棒性问题，引入图曲率（如黎曼曲率）分析。该方法已被用于交通流和互联网路由等领域的系统动态分析与瓶颈识别。我们定义了神经黎曼曲率，用于识别那些在数据向输出传递中被频繁使用的瓶颈边。在MNIST数据集上的评估表明，当神经网络对输入扰动更不鲁棒时，这些瓶颈边出现频率更高。这一发现可作为替代性鲁棒训练方法的基础，即通过减少瓶颈边数量来增强模型稳定性。
原文摘要 · Abstract (English)
This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics and identify bottlenecks in many domains, including road traffic analysis and internet routing. We define the notion of neural Ricci curvature and use it to identify bottleneck NN edges that are heavily used to ``transport data" to the NN outputs. We provide an evaluation on MNIST that illustrates that such edges indeed occur more frequently for inputs where NNs are less robust. These results will serve as the basis for an alternative method of robust training, by minimizing the number of bottleneck edges.
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