SIMAP: A simplicial-map layer for neural networks
Rocio Gonzalez-Diaz Miguel A. Gutiérrez-Naranjo Eduardo Paluzo-Hidalgo
In this paper, we present SIMAP, a novel layer integrated into deep learning
models, aimed at enhancing the interpretability of the output. The SIMAP layer
is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an
explainable neural network based on support sets and simplicial maps (functions
used in topology to transform shapes while preserving their structural
connectivity). The novelty of the methodology proposed in this paper is
two-fold: Firstly, SIMAP layers work in combination with other deep learning
architectures as an interpretable layer substituting classic dense final
layers. Secondly, unlike SMNNs, the support set is based on a fixed maximal
simplex, the barycentric subdivision being efficiently computed with a
matrix-based multiplication algorithm.