# LunaTP: Enabling Efficient and Scalable Tensor Product for Equivariant MLIPs

arXiv: https://arxiv.org/abs/2610.18393 · HTML: https://mlsanity.com/paper/2610.18393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [Open Materials 2024 (OMat24) Inorganic Materials Dataset and Models](https://mlsanity.com/paper/2410.12771/) (2024)
- [Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products](https://mlsanity.com/paper/2401.10216/) (2024)
- [An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networks](https://mlsanity.com/paper/2501.13986/) (2025)
- [The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Products](https://mlsanity.com/paper/2506.13523/) (2025)
- [MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2603.02002/) (2026)
- [Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space](https://mlsanity.com/paper/2509.14961/) (2025)
- [PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials](https://mlsanity.com/paper/2601.07742/) (2026)
- [Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing](https://mlsanity.com/paper/2510.03046/) (2025)

## Abstract (arXiv)

Equivariant machine learning interatomic potentials (MLIPs) promise atomistic simulations with accuracy approaching that of quantum-mechanical calculations. However, the high computational cost of their core Clebsch--Gordan tensor product (CGTP) convolutions severely limits model scalability and efficiency. In this paper, we rethink the parallel execution of CGTP convolutions and introduce LunaTP. Built on node-centric execution, LunaTP exploits path-group parallelism and multi-level reuse to accelerate CGTP convolutions and higher-order derivative computation while preserving the underlying mathematical formulation. On an NVIDIA H100 GPU, LunaTP achieves kernel speedups of up to 250.0× over e3nn and 17.1× over OpenEquivariance. It also delivers end-to-end training throughput gains of up to 28.7× over e3nn and 3.11× over OpenEquivariance. Finally, LunaTP demonstrates scalability and robust performance across models, workload scales, and GPUs, delivering substantial acceleration for training and atomistic simulation with high-accuracy equivariant MLIPs.