ICML 2025

AtlasD: Automatic Local Symmetry Discovery
Manu Bhat 1 Jonghyun Park 1 Jianke Yang 1 Nima Dehmamy 2 Robin Walters 3 Rose Yu 1
Abstract
Existing symmetry discovery methods predomi-
nantly focus on global transformations across the
entire system or space, but they fail to consider
the symmetries in local neighborhoods. This may
result in the reported symmetry group being a
misrepresentation of the true symmetry. In this
paper, we formalize the notion of local symme-
try as atlas equivariance. Our proposed pipeline,
automatic local symmetry discovery (AtlasD),
recovers the local symmetries of a function by
training local predictor networks and then learn-
ing a Lie group basis to which the predictors are
equivariant. We demonstrate AtlasD is capable
of discovering local symmetry groups with multi-
ple connected components in top-quark tagging
and partial differential equation experiments. The
discovered local symmetry is shown to be a use-
ful inductive bias that improves the performance
of downstream tasks in climate segmentation and
vision tasks. Our code is publicly available at
https://github.com/Rose-STL-Lab/AtlasD.
1. Introduction
Equivariant neural networks (Bronstein et al., 2021), a fam-
ily of models that exploit symmetry as an inductive bias
for neural network architectures, have received increasing
attention in deep learning due to their training efficiency
and improved generalization (Krizhevsky et al., 2017; Wor-
rall & Welling, 2019; Zaheer et al., 2017). The key idea
behind these models is that many real-world situations ex-
hibit inherent symmetries—transformations such as rotation,
translation, and scaling, which leave the essential properties
of a system unchanged. This has enabled a wide range of
applications, leading to empirical success (Winkels & Co-
hen, 2018; Brown & Lunter, 2018; Cohen & Welling, 2016;
Cohen et al., 2018). Despite its achievements, equivariant
1University of California San Diego
2IBM Research
3Northeastern University.
Correspo...