# BranchIP: Learning Adaptive Equivariant Computation for Interatomic Potentials

arXiv: https://arxiv.org/abs/2610.02013 · HTML: https://mlsanity.com/paper/2610.02013/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 25 of 25)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [BranchyNet: Fast Inference via Early Exiting from Deep Neural Networks](https://mlsanity.com/paper/1709.01686/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [DeeBERT: Dynamic Early Exiting for Accelerating BERT Inference](https://mlsanity.com/paper/2004.12993/) (2020)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [BlockDrop: Dynamic Inference Paths in Residual Networks](https://mlsanity.com/paper/1711.08393/) (2017)
- [Dynamic Channel Pruning: Feature Boosting and Suppression](https://mlsanity.com/paper/1810.05331/) (2018)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Channel Gating Neural Networks](https://mlsanity.com/paper/1805.12549/) (2018)
- [Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products](https://mlsanity.com/paper/2401.10216/) (2024)
- [Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size](https://mlsanity.com/paper/2304.10061/) (2023)
- [An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networks](https://mlsanity.com/paper/2501.13986/) (2025)
- [High-performance training and inference for deep equivariant interatomic potentials](https://mlsanity.com/paper/2504.16068/) (2025)
- [ADMP-GNN: Adaptive Depth Message Passing GNN](https://mlsanity.com/paper/2509.01170/) (2025)
- [A Cartesian-3j Framework for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2512.16882/) (2025)
- [Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2607.02499/) (2026)
- [Efficient and Accurate Spatial Mixing of Machine Learned Interatomic Potentials for Materials Science](https://mlsanity.com/paper/2502.19081/) (2025)
- [Early-Exit Graph Neural Networks](https://mlsanity.com/paper/2505.18088/) (2025)
- [Smooth Dynamic Cutoffs for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2601.21147/) (2026)
- [Mixture of Experts Framework in Machine Learning Interatomic Potentials for Atomistic Simulations](https://mlsanity.com/paper/2604.26143/) (2026)
- [LAMMPS-KOKKOS: Performance Portable Molecular Dynamics Across Exascale Architectures](https://mlsanity.com/paper/2508.13523/) (2025)

## Abstract (arXiv)

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× while reducing memory usage by up to 2.6×. 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.