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.

翻译：本文提出了一种新型的深度学习模型集成层——SIMAP，旨在提升模型输出的可解释性。SIMAP层是单纯映射神经网络（SMNNs）的增强版本，后者是一种基于支持集和单纯映射（拓扑学中用于在保持结构连通性的同时变换形状的函数）的可解释神经网络。本文提出的方法论创新体现在两个方面：首先，SIMAP层可与其他深度学习架构协同工作，作为可解释层替代传统的全连接输出层；其次，与SMNNs不同，其支持集基于固定最大单纯形，并通过基于矩阵乘法的算法高效计算重心细分。