Symmetry From Scratch: Group Equivariance as a Supervised Learning Task
<|reference_start|>Symmetry From Scratch: Group Equivariance as a Supervised Learning Task: In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest. However, this process becomes increasingly over-engineered as models are geared towards specific symmetries/asymmetries hardwired of a particular set of equivariant basis functions. In this work, we introduce symmetry-cloning, a method for inducing equivariance in machine learning models. We show that general machine learning architectures (i.e., MLPs) can learn symmetries directly as a supervised learning task from group equivariant architectures and retain/break the learned symmetry for downstream tasks. This simple formulation enables machine learning models with group-agnostic architectures to capture the inductive bias of group-equivariant architectures.<|reference_end|>
@article{huang2024symmetry,
    title={Symmetry From Scratch: Group Equivariance as a Supervised Learning Task},
    author={Haozhe Huang, Leo Kaixuan Cheng, Kaiwen Chen, Al'an Aspuru-Guzik},
    journal={arXiv preprint arXiv:2410.03989},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.03989},
    primaryClass={cs.LG}
}