# GFFMERGE: Efficient Merging of Graph Neural Force Fields and Beyond

arXiv: https://arxiv.org/abs/2606.03232 · HTML: https://mlsanity.com/paper/2606.03232/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 49 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Twin-Merging: Dynamic Integration of Modular Expertise in Model Merging](https://mlsanity.com/paper/2406.15479/) (2024)
- [EMR-Merging: Tuning-Free High-Performance Model Merging](https://mlsanity.com/paper/2405.17461/) (2024)
- [Representation Surgery for Multi-Task Model Merging](https://mlsanity.com/paper/2402.02705/) (2024)
- [GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation](https://mlsanity.com/paper/2001.08184/) (2020)
- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Network](https://mlsanity.com/paper/2209.11588/) (2022)
- [GraphReach: Position-Aware Graph Neural Network using Reachability Estimations](https://mlsanity.com/paper/2008.09657/) (2020)
- [FRIGATE: Frugal Spatio-temporal Forecasting on Road Networks](https://mlsanity.com/paper/2306.08277/) (2023)
- [Graph Neural Networks in Modern AI-aided Drug Discovery](https://mlsanity.com/paper/2506.06915/) (2025)
- [GRAFENNE: Learning on Graphs with Heterogeneous and Dynamic Feature Sets](https://mlsanity.com/paper/2306.03447/) (2023)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have revolutionized Neural Force Fields for atomistic simulations, achieving near-quantum accuracy at reduced cost, yet adapting these models to new chemical systems requires expensive retraining of foundation models. Inspired by model merging in vision and language processing, we introduce GFFMERGE, the first principled framework for closed-form model merging in GNNs. We exploit the linear structure of message-passing layers and formulate merging as a convex embedding-alignment problem with an analytical solution. Through the first systematic benchmarking of model merging for GNNs, we show that existing methods designed for vision and language catastrophically fail on force field regression, while GFFMERGE recovers performance approaching gold standard joint training. Across molecular (MD17, MD22), solid-state (LiPS20), and large-scale graph benchmarks, GFFMERGE and GNNMERGE (its generic GNN counterpart) achieve 5-27× speedups while enabling modular composition of specialized models. Remarkably, our closed-form solution alone outperforms all baseline methods before fine-tuning and provides superior initialization for faster, data-efficient convergence.