Trainable and Explainable Simplicial Map Neural Networks
This work addresses limitations in topology-based neural networks for researchers in machine learning, though it appears incremental as it builds on existing SMNN frameworks.
The paper tackles the bottlenecks of simplicial map neural networks (SMNNs), such as lack of training and high-dimensional data issues, by introducing a training procedure and a projection-based method, resulting in improved generalization and explainability.
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high-dimensional datasets. First, SMNNs have precomputed fixed weight and no SMNN training process has been defined so far, so they lack generalization ability. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere. In addition, the explainability capacity of SMNNs and an effective implementation are also newly introduced in this paper.