mlsanityData to 7 Oct 2026

Any-dimensional equivariant neural networks

arXiv 2306.06327 ↗First posted 10 Jun 2023cs.LG math.RT stat.MLcited by 8

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 17 of its 61 references that are in the map. First posted on arXiv 10 Jun 2023.

Builds on

17 of 61 references.

References · 17

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  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  3. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
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  10. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  11. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
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5 more
  1. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  2. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  3. 2020Building powerful and equivariant graph neural networks with structural message-passingcited by 95
  4. 2022What is an equivariant neural network?cited by 21
  5. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 16

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 2; 2026: 3.

8 papers.

  1. 2024Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networkscited by 7
  2. 2024Graph neural networks and non-commuting operatorscited by 5
  3. 2024From Learning to Optimize to Learning Optimization Algorithmscited by 2
  4. 2025Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equationscited by 1
  5. 2026Any-Dimensional Invariant Universalitycited by 1
  6. 2025Axial Neural Networks for Dimension-Free Foundation Modelscited by 0
  7. 2026Graded Representation Theory of Equivariant Neural Networkscited by 0
  8. 2026Warm-starting PDE solvers with any-dimensional machine learningcited by 0