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Symmetry Breaking and Equivariant Neural Networks
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Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons (E-MLPs), offering an alternative to the noise-injection method. The relevance of symmetry breaking is then discussed in various application domains: physics, graph representation learning, combinatorial optimization and equivariant decoding.
Forward citations
Cited by 3 Pith papers
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Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks
On symmetric graphs, an exact-k GNN explanation cannot be simultaneously single-valued, minimal, and symmetry-respecting, so any report naming one edge from an automorphism orbit is an arbitrary tie-break.
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SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models
SymmCD generates crystals by diffusing over the asymmetric unit and a binary site-symmetry representation, then deterministically replicating to obtain a full symmetric crystal.
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When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approach
Orbit-based feature augmentation, which assigns distinct random values within each orbit of an ILP's symmetry group, lets GNNs distinguish symmetric variables and improves solution-prediction accuracy on bin packing, ...
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