Any-dimensional equivariant neural networks

Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings, the unknown mapping takes inputs in any dimension; examples in...

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Bibliographic Details
Published inarXiv.org
Main Authors Levin, Eitan, Díaz, Mateo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.04.2024
Subjects
Computer architecture
Mapping
Neural networks
Numerical methods
Supervised learning
Topology
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Summary:Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings, the unknown mapping takes inputs in any dimension; examples include graph parameters defined on graphs of any size and physics quantities defined on an arbitrary number of particles. We leverage a newly-discovered phenomenon in algebraic topology, called representation stability, to define equivariant neural networks that can be trained with data in a fixed dimension and then extended to accept inputs in any dimension. Our approach is user-friendly, requiring only the network architecture and the groups for equivariance, and can be combined with any training procedure. We provide a simple open-source implementation of our methods and offer preliminary numerical experiments.
ISSN:2331-8422