Explainability in Simplicial Map Neural Networks

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation capability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high dimensions. First, no SMNN training process has been defined so far. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we propose a SMNN training procedure based on a support subset of the given dataset and a method based on projection to a hypersphere as a replacement for the convex polytope construction. In addition, the explainability capacity of SMNNs is also introduced for the first time in this paper.