mlsanityData to 14 Oct 2026

A Unified Framework for Discovering Discrete Symmetries

arXiv 2309.02898 ↗First posted 6 Sep 2023cs.LG cs.CVcited by 7

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Abstract (arXiv)

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear, matrix-valued and non-linear functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the non-linear functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the matrix-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 34 of its 70 references that are in the map. First posted on arXiv 6 Sep 2023.

Builds on

34 of 70 references.

References · 34

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22 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 3.

7 papers.

  1. 2023Latent Space Symmetry Discoverycited by 29
  2. 2024Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structurescited by 4
  3. 2025Discovering Symmetry Groups with Flow Matchingcited by 3
  4. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  5. 2026Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rulescited by 1
  6. 2026Sparse Data Augmentation for Optimization with Provable Guaranteescited by 1
  7. 2026Discovering Symmetries in Neural Network Parameter Spacescited by 0