# Truncated automatic sparse differentiation for machine learning interatomic potentials

arXiv: https://arxiv.org/abs/2609.20510 · HTML: https://mlsanity.com/paper/2609.20510/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 52 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Open Materials 2024 (OMat24) Inorganic Materials Dataset and Models](https://mlsanity.com/paper/2410.12771/) (2024)
- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (2023)
- [The dark side of the forces: assessing non-conservative force models for atomistic machine learning](https://mlsanity.com/paper/2412.11569/) (2024)
- [PET-MAD, a lightweight universal interatomic potential for advanced materials modeling](https://mlsanity.com/paper/2503.14118/) (2025)
- [HIP: Hessian Interatomic Potentials without derivatives](https://mlsanity.com/paper/2509.21624/) (2025)
- [Pushing the limits of unconstrained machine-learned interatomic potentials](https://mlsanity.com/paper/2601.16195/) (2026)
- [PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials](https://mlsanity.com/paper/2601.07742/) (2026)
- [Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation](https://mlsanity.com/paper/2501.17737/) (2025)
- [Projected Hessian Learning: Fast Curvature Supervision for Accurate Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2603.04523/) (2026)
- [Fixed-sparsity matrix approximation from matrix-vector products](https://mlsanity.com/paper/2402.09379/) (2024)
- [Higher-order Reverse Automatic Differentiation with emphasis on the third-order](https://mlsanity.com/paper/1309.5479/) (2013)

## Abstract (arXiv)

Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.