# EquiFiLM: Charge-Conditioned Equivariant Force Fields via Feature-wise Linear Modulation

arXiv: https://arxiv.org/abs/2607.05559 · HTML: https://mlsanity.com/paper/2607.05559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 6 Jul 2026.

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

- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Modulating early visual processing by language](https://mlsanity.com/paper/1707.00683/) (2017)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [PET-MAD, a lightweight universal interatomic potential for advanced materials modeling](https://mlsanity.com/paper/2503.14118/) (2025)
- [EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers](https://mlsanity.com/paper/2604.09130/) (2026)
- [MACE-POLAR-1: A Polarisable Electrostatic Foundation Model for Molecular Chemistry](https://mlsanity.com/paper/2602.19411/) (2026)

## Abstract (arXiv)

Foundation machine learning force fields (MLFFs) such as MACE-MP-0 and UMA cover broad chemical space at near density functional theory (DFT) accuracy. However, they assume equilibrium ground-state physics and do not natively handle externally induced changes to the electronic state, such as charging, applied fields, or electronic excitation, which limits their use for driven processes such as photoexcitation and charge injection. We propose EquiFiLM, a lightweight extension that adds continuous external conditioning to any equivariant foundation MLFF via a per-layer Feature-wise Linear Modulation (FiLM) block, learning externally driven changes to the potential energy surface from minimal training data. The block modulates only scalar channels and preserves E(3)-equivariance exactly. We demonstrate the recipe on charged liquid water with the foundation model MACE-MatPES as the backbone, yielding E-MACE. On the four training charges, E-MACE delivers a 3.1× reduction in force RMSE (21.3 to 6.96 meV/mathringA) and a 61× reduction in per-atom energy RMSE (6.1 to 0.1 meV/atom) over a baseline without EquiFiLM trained on the same data, at indistinguishable inference cost. Across seven held-out interpolation and extrapolation charges, force RMSE stays within 18-61 meV/mathringA and energy RMSE within 0.7-5.4 meV/atom. The model runs stable molecular dynamics across the full range tested and predicts the charge-dependent first-shell response of the reduced pair distribution function probed by ultrafast electron diffraction. Adding this conditioning axis to the foundation requires only a few thousand DFT-labeled frames, against the ≈ 108 structures of a charge-aware foundation trained from scratch. The recipe is backbone- and conditioning-agnostic: it applies without architectural change to any equivariant MLFF with scalar interaction-layer channels.