为可解释的对称神经网络提供数学基础，让模型决策更透明。
Mathematical Foundation of Interpretable Equivariant Surrogate Models
- 用非交换性度量对称算子间的距离，建立可解释性框架。
- 提出基于用户偏好定义的复杂度指标，灵活衡量解释程度。
- 适用于卷积神经网络等经典场景，提升图像分类可解释性。
本文提出了一个严格的数学框架，用于神经网络的可解释性，以及更广泛的对称算子（群等变算子，GEOs）的可解释性，其基础是群等变非扩张算子（GENEOs）的变换。核心思想是通过测量特定图的非交换性来量化GEOs之间的距离。此外，论文根据用户偏好定义了GEOs的可解释性，引入复杂度度量。研究还探讨了该框架的正式性质，并展示了其在图像分类等经典机器学习场景中的应用，例如卷积神经网络。
原文摘要 · Abstract (English)
This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs) based on Group Equivariant Non-Expansive Operators (GENEOs) transformations. The central concept involves quantifying the distance between GEOs by measuring the non-commutativity of specific diagrams. Additionally, the paper proposes a definition of interpretability of GEOs according to a complexity measure that can be defined according to each user preferences. Moreover, we explore the formal properties of this framework and show how it can be applied in classical machine learning scenarios, like image classification with convolutional neural networks.
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