SIMAP: A simplicial-map layer for neural networks
This work addresses the need for more interpretable AI systems, particularly in domains requiring transparent decision-making, though it appears incremental as an enhanced version of existing Simplicial-Map Neural Networks.
The paper tackles the problem of enhancing interpretability in deep learning models by introducing SIMAP, a novel layer that substitutes classic dense final layers, resulting in an explainable neural network based on simplicial maps and support sets.
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.