ELoRA: Low-Rank Adaptation for Equivariant GNNs

Abstract

Pre-trained interatomic potentials have become a new paradigm for atomistic materials simulations, enabling accurate and efficient predictions across diverse chemical systems. Despite their promise, fine-tuning is often required for complex tasks to achieve high accuracy. Traditional parameter-efficient fine-tuning approaches are effective in NLP and CV. However, when applied to SO(3) equivariant pre-trained interatomic potentials, these methods will inevitably break equivariance—a critical property for preserving physical symmetries. In this paper, we introduce ELoRA (Equivariant Low-Rank Adaptation), a novel fine-tuning method designed specifically for SO(3) equivariant Graph Neural Networks (GNNs), the backbones in multiple pre-trained interatomic potentials. ELoRA adopts a path-dependent decomposition for weights updating which offers two key advantages: (1) it preserves SO(3) equivariance throughout the fine-tuning process, ensuring physically consistent predictions, and (2) it leverages low-rank adaptations to significantly improve data efficiency. We prove that ELoRA maintains equivariance and demonstrate its effectiveness through comprehensive experiments. On the rMD17 organic dataset, ELoRA achieves a 25.5% improvement in energy prediction accuracy and a 23.7% improvement in force prediction accuracy compared to full-parameter fine-tuning. Similarly, across 10 inorganic datasets, ELoRA achieves average improvements of 12.3% and 14.4% in energy and force predictions, respectively. Code will be made publicly available at https://github.com/hyjwpk/ELoRA.