ReLU神经网络、多面体分解与持续同调
代数拓扑
2023-07-03 v1 机器学习
最优化与控制
摘要
ReLU神经网络导致输入空间的有限多面体分解及相应的有限对偶图。我们表明,尽管该对偶图是输入空间的粗量化,但它足够鲁棒,可与持续同调结合,从样本中检测输入空间内流形的同调信号。该性质对多种为与上述拓扑应用无关广泛目的训练的网络均成立。我们发现此特征令人惊讶且有趣;希望它也将有用。
引用
@article{arxiv.2306.17418,
title = {ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog},
author = {Yajing Liu and Christina M Cole and Chris Peterson and Michael Kirby},
journal= {arXiv preprint arXiv:2306.17418},
year = {2023}
}
备注
Accepted by Proceedings of the 2 nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML) at the 40 th In- ternational Conference on Machine Learning