Trainable and Explainable Simplicial Map Neural Networks
Abstract
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high-dimensional datasets. First, SMNNs have precomputed fixed weight and no SMNN training process has been defined so far, so they lack generalization ability. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere. In addition, the explainability capacity of SMNNs and an effective implementation are also newly introduced in this paper.
Cite
@article{arxiv.2306.00010,
title = {Trainable and Explainable Simplicial Map Neural Networks},
author = {Eduardo Paluzo-Hidalgo and Miguel A. Gutiérrez-Naranjo and Rocio Gonzalez-Diaz},
journal= {arXiv preprint arXiv:2306.00010},
year = {2024}
}