# Orthogonal Model Merging

arXiv: https://arxiv.org/abs/2602.05943 · HTML: https://mlsanity.com/paper/2602.05943/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 72 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 30 of 63)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [XSTest: A Test Suite for Identifying Exaggerated Safety Behaviours in Large Language Models](https://mlsanity.com/paper/2308.01263/) (2023)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- ["Do Anything Now": Characterizing and Evaluating In-The-Wild Jailbreak Prompts on Large Language Models](https://mlsanity.com/paper/2308.03825/) (2023)
- [OCRBench: On the Hidden Mystery of OCR in Large Multimodal Models](https://mlsanity.com/paper/2305.07895/) (2023)
- [PathVQA: 30000+ Questions for Medical Visual Question Answering](https://mlsanity.com/paper/2003.10286/) (2020)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)

## Built on by (most cited first, 4 of 4)

- [ISO: An RLVR-Native Optimization Stack](https://mlsanity.com/paper/2607.19331/) (2026)
- [M2A: Synergizing Mathematical and Agentic Reasoning in Large Language Models](https://mlsanity.com/paper/2605.09879/) (2026)
- [Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging](https://mlsanity.com/paper/2609.37564/) (2026)
- [SuperAI: Merging Capabilities Across Heterogeneous Foundation Models](https://mlsanity.com/paper/2610.15322/) (2026)

## Abstract (arXiv)

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.