圖像分類器中單連通決策區域的實證證據

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运作至关重要。先前的实证研究已提供证据表明这些区域是路径连通的。我们研究一个更强的拓扑问题：决策区域内部的闭环能否在不离开该区域的情况下收缩。为此，我们提出了一种迭代的四边形网格填充方法，该方法构造一个由给定回路界定且完全位于同一决策区域内的有限分辨率标签保持曲面。我们进一步将该构造与自然的Coons曲面片联系起来，以量化其与回路的典型几何插值之间的偏差。通过在多个现代图像分类模型上评估我们的方法，我们提供了支持以下假设的实证证据：深度神经网络中的决策区域不仅是路径连通的，而且是单连通的。

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.

圖像分類器中單連通決策區域的實證證據

Empirical Evidence for Simply Connected Decision Regions in Image Classifiers

摘要

Support