图像分类器中单连通决策区域的经验证据

摘要

理解决策区域的拓扑结构对于解释深度神经网络的内部工作原理至关重要。前期实验研究表明这些区域具有路径连通性。本文进一步探究一个更强的拓扑问题：决策区域内的闭合环路能否在不离开该区域的情况下持续收缩。为此，我们提出了一种迭代四边形网格填充方法，该方法可构造出以给定环路为边界的有限分辨率标签保持曲面，且该曲面完全位于同一决策区域内。我们进一步将该构造与自然Coons曲面片建立关联，以量化其与环路标准几何插值的偏差。通过在多个现代图像分类模型上评估该方法，我们获得了支持以下假设的实验证据：深度神经网络中的决策区域不仅具有路径连通性，而且具有单连通性。

English

Understanding the topology of decision regions is central to explaining the inner workings of deep neural networks. Prior empirical work has provided evidence that these regions are path connected. We study a stronger topological question: whether closed loops inside a decision region can be contracted without leaving that region. To this end, we propose an iterative quad-mesh filling procedure that constructs a finite-resolution label-preserving surface bounded by a given loop and lying entirely within the same decision region. We further connect this construction to natural Coons patches in order to quantify its deviation from a canonical geometric interpolation of the loop. By evaluating our method across several modern image-classification models, we provide empirical evidence supporting the hypothesis that decision regions in deep neural networks are not only path connected, but also simply connected.

图像分类器中单连通决策区域的经验证据

Empirical Evidence for Simply Connected Decision Regions in Image Classifiers

摘要

Support