SIMAP：一种用于神经网络的单纯形映射层
SIMAP: A simplicial-map layer for neural networks
AI总结：
本文提出SIMAP层，作为深度学习模型中替代经典稠密最终层的可解释模块，通过基于固定最大单纯形和矩阵乘法算法高效计算重心细分，增强了SMNNs的可解释性与结构连通性保持能力。
摘要：
本文提出了SIMAP，一种集成到深度学习模型中的新型层，旨在增强输出的可解释性。SIMAP层是Simplicial-Map Neural Networks (SMNNs)的增强版本，SMNNs是一种基于支撑集和单纯形映射（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。本文提出的方法创新之处有两点：首先，SIMAP层可与其他深度学习架构结合，作为替代经典稠密最终层的可解释层。其次，与SMNNs不同，其支撑集基于固定的最大单纯形，重心细分通过基于矩阵的乘法算法高效计算。
英文摘要：
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.
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