Accelerating SO(2)-Equivariant Materials Models through Low-Precision Emulation

Rotationally equivariant architectures improve the physical fidelity of machine-learned (ML) universal materials models based on graph neural networks (GNNs). However, their scalability is limited by the use of non-trivial, high-precision tensor operations during both training and inference. Adopting the reduced-precision formats of matrix multiplication units (MMUs), e.g., FP8 instead of FP32, provides massive increases in throughput, up to 30× (60×) on NVIDIA Hopper (Blackwell) GPUs, but may lead to drastic loss of accuracy. Here, we introduce tailored ‘emulated’ low-precision operations under the integer Ozaki scheme to accelerate the ‘SO(2)-equivariant’ processing layers of GNNs, which dominate the runtime of (1) many state-of-the-art ML interatomic potentials (MLIPs) and (2) most universal ML Hamiltonian (MLH) models. Our framework, FlashSO(2), outperforms TF32, the most accurate native low-precision MMU format, in throughput, accuracy, and memory footprint at once. At the SO(2) layer level, it reaches 40× (7×) the throughput of MALOQ’s (UMA’s) reference implementation, an MLH (MLIP) model, sustaining up to 236 (232) effective Tflop/s on an NVIDIA GH200, 3.5× the FP32 peak. At the model level, FlashSO(2) helps train MALOQ 3.9× faster than its pure-FP32 version while reducing peak memory by 58% at no loss in accuracy. In molecular dynamics simulations with UMA, the speedup factor is 3.3×, and the peak memory is reduced by 51%. FlashSO(2) thus pushes the speed-accuracy Pareto frontier of equivariant materials models beyond the native low-precision formats and substantially lowers the resources required to exploit their scaling laws.