A Topology Layer for Machine Learning

Abstract

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: the topological layer can (i) regularize data reconstruction or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.

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• Artificial Text Detection via Examining the Topology of Attention Maps
• Optimizing persistent homology based functions
• Path homologies of deep feedforward networks
• PLLay: Efficient Topological Layer based on Persistence Landscapes
• Fuzzy c-Means Clustering for Persistence Diagrams
• Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
• Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks
• A Topological Framework for Deep Learning
• Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
• Topological Node2vec: Enhanced Graph Embedding via Persistent Homology
• Accelerating Iterated Persistent Homology Computations with Warm Starts
• Pull-back Geometry of Persistent Homology Encodings
• ICLR 2021 Challenge for Computational Geometry & Topology: Design and Results
• Topological Deep Learning: Classification Neural Networks