# Magnitude-Modulated Equivariant Adapter for Parameter-Efficient Fine-Tuning of Equivariant Graph Neural Networks

arXiv: https://arxiv.org/abs/2511.06696 · HTML: https://mlsanity.com/paper/2511.06696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [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)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection](https://mlsanity.com/paper/2502.06042/) (2025)
- [AdapterGNN: Parameter-Efficient Fine-Tuning Improves Generalization in GNNs](https://mlsanity.com/paper/2304.09595/) (2023)
- [Equivariant Machine Learning Interatomic Potentials with Global Charge Redistribution](https://mlsanity.com/paper/2503.17949/) (2025)

## Abstract (arXiv)

Pretrained equivariant graph neural networks based on spherical harmonics offer efficient and accurate alternatives to computationally expensive ab-initio methods, yet adapting them to new tasks and chemical environments still requires fine-tuning. Conventional parameter-efficient fine-tuning (PEFT) techniques, such as Adapters and LoRA, typically break symmetry, making them incompatible with those equivariant architectures. ELoRA, recently proposed, is the first equivariant PEFT method. It achieves improved parameter efficiency and performance on many benchmarks. However, the relatively high degrees of freedom it retains within each tensor order can still perturb pretrained feature distributions and ultimately degrade performance. To address this, we present Magnitude-Modulated Equivariant Adapter (MMEA), a novel equivariant fine-tuning method which employs lightweight scalar gating to modulate feature magnitudes on a per-order and per-multiplicity basis. We demonstrate that MMEA preserves strict equivariance and, across multiple benchmarks, consistently improves energy and force predictions to state-of-the-art levels while training fewer parameters than competing approaches. These results suggest that, in many practical scenarios, modulating channel magnitudes is sufficient to adapt equivariant models to new chemical environments without breaking symmetry, pointing toward a new paradigm for equivariant PEFT design.