Euclidean Symmetry and Equivariance in Machine Learning

Understanding symmetry’s role in the physical sciences is critical for choosing an appropriate machine learning method. While invariant models are the most prevalent symmetry-aware models, equivariant models can more faithfully represent physical interactions. Until recently, equivariant models had been absent in the literature due to their technical complexity. Now, after two years of active development, fully-equivariant Euclidean neural net- works are ready to take on challenges across the physical sciences.

Euclidean Symmetry and Equivariance in Machine Learning

Understanding symmetry’s role in the physical sciences is critical for choosing an appropriate machine learning method. While invariant models are the most prevalent symmetry-aware models, equivariant models can more faithfully represent physical interactions. Until recently, equivariant models had been absent in the literature due to their technical complexity. Now, after two years of active development, fully-equivariant Euclidean neural net- works are ready to take on challenges across the physical sciences.

Physical angular momentum separation for QED

We study the non-uniqueness problem of the gauge-invariant angular momentum separation for the case of QED, which stems from the recent controversy concerning the proper definitions of the orbital angular momentum and spin operator of the individual parts of a gauge field system. For the free quantum electrodynamics without matter, we show that the basic requirement of Euclidean symmetry selects a unique physical angular momentum separation scheme from the multitude of the possible angular momentum separation schemes constructed using the various gauge-invariant extensions (GIEs). Based on these results, we propose a set of natural angular momentum separation schemes for the case of interacting QED by invoking the formalism of asymptotic fields. Some perspectives on such a problem for the case of QCD are briefly discussed.