Equivariance by Local Canonicalization: A Matter of Representation

• URL: http://arxiv.org/abs/2509.26499v1
• Date: Tue, 30 Sep 2025 16:41:18 GMT
• Title: Equivariance by Local Canonicalization: A Matter of Representation
• Authors: Gerrit Gerhartz, Peter Lippmann, Fred A. Hamprecht,
• Abstract summary: We present a framework to transfers existing tensor field networks into the more efficient local canonicalization paradigm.<n>Within this framework, we systematically compare different equivariant representations in terms of theoretical complexity, empirical runtime, and predictive accuracy.
• Score: 11.697651699958755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Equivariant neural networks offer strong inductive biases for learning from molecular and geometric data but often rely on specialized, computationally expensive tensor operations. We present a framework to transfers existing tensor field networks into the more efficient local canonicalization paradigm, preserving equivariance while significantly improving the runtime. Within this framework, we systematically compare different equivariant representations in terms of theoretical complexity, empirical runtime, and predictive accuracy. We publish the tensor_frames package, a PyTorchGeometric based implementation for local canonicalization, that enables straightforward integration of equivariance into any standard message passing neural network.

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