Adaptive Filtration Learning via Explainable Neural Topological Layers

Nishikawa et al. (2023) propose learning filtrations for PH using neural networks, but the resulting features are often black-box in nature. This research idea pushes further, aiming for "explainable topological learning": neural network layers that, while optimizing filtrations for downstream tasks, simultaneously generate human-interpretable explanations of what topological changes (e.g., birth/death of cycles) correspond to in original data space. This could draw on recent advances in explainable AI and feature attribution, perhaps by linking learned filtration parameters to data attributes or by providing visualizations of the topological evolution during learning. Such a framework could be invaluable in scientific domains—chemistry, neuroscience, or genomics—where understanding "why" a topological feature matters is as important as detecting it. This approach would bridge the gap between topological machine learning and transparent, trustworthy AI.

References:

1. Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds. Naoki Nishikawa, Yuichi Ike, K. Yamanishi (2023). Neural Information Processing Systems.