Using Symmetry-Equivariant Neural Networks (ENNs) to Uncover Symmetry-Implied Missing Information

In this talk, we demonstrate how Symmetry-Equivariant Neural Networks (ENNs) can identify sources of symmetry breaking in diverse physical data and uncover symmetry-implied missing information unbeknownst to the researcher. Symmetry and symmetry-breaking is crucial for understanding complex physical systems (e.g. phase transitions in materials and the discovery of the neutrino). Physical systems adhere to Curie's Principle–stating that when effects show certain asymmetry, this asymmetry must be found in the causes that give rise to them. ENNs are built to preserve symmetry and thus obey the same principles [3].<br/>Recorded data can appear to deviate from strict symmetry constraints, so recent studies emphasize the importance of relaxing equivariance to balance model bias with capturing complex patterns [4-6]. Here, we present a complementary approach showing that fully equivariant models can be used for real-world problems where symmetry may be broken due to some noise, external forces, or other asymmetries in the environment. We benchmark our against state-of-the-art approximately equivariant networks in [4]. These methods can be applied to materials science, where approximate symmetry commonly arises due to structural defects, strain, or phase transitions. Understanding and characterizing these deviations from perfect symmetry are crucial for investigating material properties and behavior.<br/><br/>[1] T. E. Smidt, “Euclidean Symmetry and Equivariance in Machine Learning,” Trends in Chemistry 3, 82 (2021).<br/>[2] M. Geiger and T. Smidt, “e3nn: Euclidean Neural Networks,” http://arxiv.org/abs/2207.09453.<br/>[3] T. E. Smidt, M. Geiger, and B. K. Miller, Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks, Phys. Rev. Research 3, L012002 (2021).<br/>[4] R. Wang, R. Walters, and R. Yu, “Approximately Equivariant Networks for Imperfectly Symmetric Dynamics,” https://arxiv.org/abs/2201.11969 (2022).<br/>[5] M. Finzi, G. Benton, and A.G. Wilson, ''Residual Pathway Priors for Soft Equivariance Constraints,'' doi: 10.48550/arXiv.2112.01388 (2021).<br/>[6] S. d'Ascoli, H. Touvron, M. Leavitt, A. Morcos, G. Biroli, and L. Sagun, ''ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases,'' doi: 10.48550/arXiv.2103.10697 (2021).