LunaTP: Enabling Efficient and Scalable Tensor Product for Equivariant MLIPs

Equivariant machine learning interatomic potentials (MLIPs) have revolutionized atomistic modeling, but accurate treatment of complex materials and molecular systems demands expensive models. This limits simulation length- and time-scales, with tensor products a key computational bottleneck. The recent emergence of foundation-scale MLIPs further exacerbates this challenge. We present Branch Interatomic Potential (BranchIP), a single-model framework for learned adaptive tensor product computation, trained with a novel distillation loss. In our experiments on two systems of physical interest, a heterogeneous catalysis system and a proton-conducting solid acid electrolyte, BranchIP accelerates MLIPs across model sizes by up to $2.4\times$ while reducing memory usage by up to $2.6\times$. This is achieved while maintaining physical fidelity. Furthermore, the learned adaptive computation provides model interpretability by revealing which interactions demand deeper computation and showing how computational depth relates to chemical complexity and dynamics.

Foundation MLIPs demonstrate broad applicability across diverse material systems and have emerged as a powerful and transformative paradigm in chemical and computational materials science. Equivariant MLIPs achieve state-of-the-art accuracy in a wide range of benchmarks by incorporating equivariant inductive bias. However, the reliance on tensor products and high-degree representations makes them computationally costly. This raises a fundamental question: as quantum mechanical-based datasets continue to expand, can we develop a more compact model to thoroughly exploit high-dimensional atomic interactions? In this work, we present MatRIS (Materials Representation and Interaction Simulation), an invariant MLIP that introduces attention-based modeling of three-body interactions. MatRIS leverages a novel separable attention mechanism with linear complexity $O(N)$, enabling both scalability and expressiveness. MatRIS delivers accuracy comparable to that of leading equivariant models on a wide range of popular benchmarks (Matbench-Discovery, MatPES, MDR phonon, Molecular dataset, etc). Taking Matbench-Discovery as an example, MatRIS achieves an F1 score of up to 0.847 and attains comparable accuracy at a lower training cost. The work indicates that our carefully designed invariant models can match or exceed the accuracy of equivariant models at a fraction of the cost, shedding light on the development of accurate and efficient MLIPs.

Machine-learned interatomic potentials extend atomistic simulations beyond the length- and timescales accessible to electronic-structure methods. However, the computational cost of equivariant architectures limits the local correlations they can represent in practice and therefore their achievable accuracy. Here we introduce FlashCart, which makes higher-order correlations affordable by combining generated GPU kernels with an architecture that recursively builds equivariant features and compresses them to a fixed width at each step. We express tensor products in independent Cartesian components and symbolically simplify them and their derivatives, producing fused kernels that often outperform optimized spherical counterparts. We then show that increasing correlation order improves accuracy more efficiently than increasing width, depth, or tensor rank. On SPICE-MACE-OFF, FlashCart models advance the measured accuracy-efficiency frontier: a model with $5.6$ million parameters achieves lower energy and force errors and $10\times$ faster inference than a transformer with $189$ million parameters.