Probing the effects of broken symmetries in machine learning
This work addresses the computational and design constraints of enforcing exact symmetries in ML models for atomic-scale physics, showing that approximate symmetry may suffice, which is incremental but relevant for researchers in computational chemistry and materials science.
The study investigated the impact of using machine learning models that only approximately obey rotational symmetry, rather than enforcing exact symmetry, on predicting properties of water in gas, liquid, and solid phases. It found negligible effects in bulk interpolative regimes and stability in extrapolative gas-phase predictions, with symmetry artifacts being noticeable but manageable.
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms. Incorporating symmetries -- rotations in particular -- constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that non-symmetric models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We put a model that obeys rotational invariance only approximately to the test, in realistic scenarios involving simulations of gas-phase, liquid, and solid water. We focus specifically on physical observables that are likely to be affected -- directly or indirectly -- by symmetry breaking, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables.