发现图像分类器的决策区域不仅是连通的，而且是单连通的。
Empirical Evidence for Simply Connected Decision Regions in Image Classifiers
- 用四边形网格填充法构造保标签表面，验证区域可收缩
- 多模型实验支持决策区域为单连通的假设
- 适用于研究神经网络几何性质的学者
理解决策区域的拓扑结构对解释深度神经网络的工作机制至关重要。已有研究提供了决策区域路径连通的实证证据。本文探讨更强的拓扑问题：决策区域内闭合环路能否在不离开该区域的前提下被收缩。为此，提出一种迭代四边形网格填充方法，构建由给定环路界定且完全位于同一决策区域内的有限分辨率保标签表面。进一步将此构造与自然柯恩斯补片关联，量化其相对于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，提供实证支持，表明深度神经网络的决策区域不仅路径连通，而且是单连通的。
原文摘要 · Abstract (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.
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