# Orthogonal Yet Coupled: Decoupling Geometric Components for Model Merging

arXiv: https://arxiv.org/abs/2609.37564 · HTML: https://mlsanity.com/paper/2609.37564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 54 of its 60 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 54)

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- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (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)
- [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)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [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)
- [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)
- [LMMs-Eval: Reality Check on the Evaluation of Large Multimodal Models](https://mlsanity.com/paper/2407.12772/) (2024)
- [Magicoder: Empowering Code Generation with OSS-Instruct](https://mlsanity.com/paper/2312.02120/) (2023)
- [Model Merging in LLMs, MLLMs, and Beyond: Methods, Theories, Applications and Opportunities](https://mlsanity.com/paper/2408.07666/) (2024)

## Abstract (arXiv)

Merging pretrained models has emerged as an effective approach for consolidating diverse capabilities into a single unified model. However, prevailing merging methods typically treat each task vector as an indivisible merging unit, overlooking the heterogeneous geometric changes encoded within it. This treatment can induce cross-component coupling: when merging decisions are derived from statistics of the complete task vector, the geometric characteristics of one component may influence how another is selected, weighted, or combined, potentially degrading the quality of the merged model. To address this issue, we propose DiGA, a Disentangled Geometry-Aware model merging framework. Using the pretrained weights as a shared geometric reference, DiGA orthogonally decomposes each task vector into components corresponding to distinct geometric attributes. Rather than merging the task vectors as a whole, DiGA aggregates corresponding components independently within their respective subspaces and subsequently recombines them into a unified update. This component-wise formulation preserves the geometric identity of each component and prevents the characteristics of one component from interfering with the aggregation of another. Furthermore, DiGA can be incorporated into a broad range of existing model merging methods. Extensive experiments across diverse models, tasks, and merging methods demonstrate that DiGA improves merged-model performance and reduces capability degradation. Our repository is on https://github.com/wzj1718/DiGA.