Orthogonal Model Merging

TL;DR

This paper introduces Orthogonal Model Merging (OrthoMerge), a novel approach for merging finetuned large language models on the Riemannian manifold to better preserve geometric properties and improve task performance.

Contribution

OrthoMerge is the first method to perform model merging on the orthogonal group manifold, preserving geometric structure and extending to various finetuning techniques.

Findings

OrthoMerge effectively mitigates catastrophic forgetting.

It maintains model performance across diverse tasks.

The method outperforms linear merging approaches.

Abstract

Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model. However, prevailing model merging methods rely on linear arithmetic in Euclidean space, which often destroys the intrinsic geometric properties of pretrained weights, such as hyperspherical energy. To address this, we propose Orthogonal Model Merging (OrthoMerge), a method that performs merging operations on the Riemannian manifold formed by the orthogonal group to preserve the geometric structure of the model's weights. By mapping task-specific orthogonal matrices learned by Orthogonal Finetuning (OFT) to the Lie algebra, OrthoMerge enables a principled yet efficient integration that takes into account both the direction and intensity of adaptations. In addition to directly leveraging orthogonal matrices obtained by OFT, we further extend this approach to general models finetuned with non-OFT methods (i.e., low-rank finetuning, full finetuning) via an Orthogonal-Residual Decoupling strategy. This technique extracts the orthogonal components of expert models by solving the orthogonal Procrustes problem, which are then merged on the manifold of the orthogonal group, while the remaining linear residuals are processed through standard additive merging. Extensive empirical results demonstrate the effectiveness of OrthoMerge in mitigating catastrophic forgetting and maintaining model performance across diverse tasks.