Group invariant machine learning by fundamental domain projections

David Sheard, Daniel Platt, Benjamin Aslan

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
51 Downloads (Pure)

Abstract

We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), finding an improvement in accuracy versus others in the literature.
Original languageEnglish
Pages (from-to)182-218
Number of pages37
JournalProceedings of Machine Learning Research
Volume197
Publication statusPublished - 2023

Keywords

  • fundamental domain
  • geometric topology
  • group invariant
  • group equivariant
  • geometric deep learning

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