Trainable and Explainable Simplicial Map Neural Networks

arXiv:2306.00010v2 Announce Type: replace
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 …

abstract adversarial adversarial examples application approximation arxiv bottlenecks cs.ai cs.lg datasets examples however map math.at networks neural networks process robustness topology training type universal