Equivariant Learning and Symmetry Discovery

The field of equivariant learning is rapidly advancing, with a focus on developing methods that can learn and respect symmetries in data. Recent work has explored the use of quadratic forms to learn equivariant functions, as well as the automatic discovery of one-parameter subgroups of SO(n). Additionally, there has been a push to improve the efficiency and expressiveness of equivariant models, such as the development of the Clebsch-Gordan Transformer. Noteworthy papers in this area include the introduction of adaptive canonicalization, which addresses the issue of discontinuities in canonicalization, and the development of the SIM(3)-equivariant shape completion network, which achieves state-of-the-art results on 3D shape completion tasks. Other notable works include the Explicit Discovery of Nonlinear Symmetries from Dynamic Data, which proposes a method for determining the number of infinitesimal generators with nonlinear terms and their explicit expressions, and the Geometric Learning of Canonical Parameterizations of 2D-curves, which presents a method for modding out symmetries based on the notion of section of a principal fiber bundle.

Sources

Learning Equivariant Functions via Quadratic Forms

Automatic Discovery of One Parameter Subgroups of $SO(n)$

Clebsch-Gordan Transformer: Fast and Global Equivariant Attention

Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks

Geometric Learning of Canonical Parameterizations of $2D$-curves

Equivariance by Local Canonicalization: A Matter of Representation

Learning Generalizable Shape Completion with SIM(3) Equivariance

To Augment or Not to Augment? Diagnosing Distributional Symmetry Breaking

Explicit Discovery of Nonlinear Symmetries from Dynamic Data

An efficient quantum algorithm for computing $S$-units and its applications

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