ReLU 神经网络激活模式的拓扑特征
机器学习
2026-04-20 v2 人工智能
计算几何
代数拓扑
机器学习
摘要
This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary -- in the case of binary classification. Additionally, we compute the homology of the cellular decomposition -- in a regression task -- to draw similar patterns in behavior between the training loss and polyhedral cell-count, as the model is trained.
关键词
引用
@article{arxiv.2510.12700,
title = {Topological Signatures of ReLU Neural Network Activation Patterns},
author = {Vicente Bosca and Tatum Rask and Sunia Tanweer and Andrew R. Tawfeek and Branden Stone},
journal= {arXiv preprint arXiv:2510.12700},
year = {2026}
}