Dist2Cycle: A Simplicial Neural Network for Homology Localization

Alexandros Keros, Vidit Nanda, Kartic Subr

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher dimensional topological features of data, features to which graphs, encoding only pairwise relationships, remain oblivious. While attempts have been made to extend Graph Neural Networks (GNNs) to a simplicial complex setting, the methods do not inherently exploit, or reason about, the underlying topological structure of the network. We propose a graph convolutional model for learning functions parametrized by the k-homological features of simplicial complexes. By spectrally manipulating their combinatorial k-dimensional Hodge Laplacians, the proposed model enables learning topological features of the underlying simplicial complexes, specifically, the distance of each k-simplex from the nearest "optimal" k-th homology generator, effectively providing an alternative to homology localization.
Original languageEnglish
Title of host publicationProceedings of The Thirty-Sixth AAAI Conference on Artificial Intelligence
Number of pages9
Publication statusAccepted/In press - 1 Dec 2022
Event36th AAAI Conference on Artificial Intelligence - Virtual Conference
Duration: 22 Feb 20221 Mar 2022
https://aaai.org/Conferences/AAAI-22/

Conference

Conference36th AAAI Conference on Artificial Intelligence
Abbreviated titleAAAI 2022
Period22/02/221/03/22
Internet address

Keywords

  • ML
  • Graph-based machine learning, KRR
  • Geometric, Spatial, and Temporal Reasoning

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