Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing

TL;DR

This paper introduces higher-rank irreducible Cartesian tensors into equivariant message passing neural networks, enhancing flexibility and performance in atomistic simulations while maintaining equivariance properties.

Contribution

It presents a novel integration of irreducible Cartesian tensor products into message-passing neural networks, improving model expressiveness and computational efficiency.

Findings

Achieves comparable or superior performance to existing models.

Proves equivariance and tracelessness of the new tensor layers.

Demonstrates effectiveness across multiple benchmark datasets.

Abstract

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models.