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Symmetry can occur in many forms. For physical systems in 3D, we have the freedom to choose any coordinate
system and therefore any physical property must transform predictably under elements of Euclidean symmetry (3D rotations, translations and inversion). For algorithms involving the nodes and edges of graphs, we have symmetry under permutation of how the nodes
and edges are ordered in computer memory. Unless coded otherwise, machine-learned models make no assumptions about the symmetry of a problem and will be sensitive to e.g. an arbitrary choice of coordinate system or ordering of nodes and edges in an array.
In this talk, I will break down the variety of methods used in machine learning to overcome this from data augmentation to canonicalization to symmetry-based methods. I hope to give an intuitive overview for the types of mathematical concepts and operations
that arise in these methods, present recent advances in this area, and show applications of these methods in science and engineering. I will also discuss properties of the various approaches in terms of smoothness of representation, data efficiency, and generalization.
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