Scaling Laws and Symmetry, Evidence from Neural Force Fields
This work addresses the problem of efficient scaling in machine learning for geometric tasks like interatomic potentials, suggesting that incorporating symmetry inductive biases is crucial for optimal performance at larger scales, which is incremental but impactful for domain-specific applications.
The study investigated scaling laws for neural force fields, finding that equivariant architectures, especially those with higher-order representations, exhibit better power-law scaling with data, parameters, and compute compared to non-equivariant models, with architecture-dependent exponents influencing performance.
We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute with ``architecture-dependent exponents''. In particular, we observe that equivariant architectures, which leverage task symmetry, scale better than non-equivariant models. Moreover, among equivariant architectures, higher-order representations translate to better scaling exponents. Our analysis also suggests that for compute-optimal training, the data and model sizes should scale in tandem regardless of the architecture. At a high level, these results suggest that, contrary to common belief, we should not leave it to the model to discover fundamental inductive biases such as symmetry, especially as we scale, because they change the inherent difficulty of the task and its scaling laws.