# CORAM: Coherent Orthogonal Rotation for Model Merging

arXiv: https://arxiv.org/abs/2608.17366 · HTML: https://mlsanity.com/paper/2608.17366/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 25 of 25)

- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [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)
- [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)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [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)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [MMSI-Bench: A Benchmark for Multi-Image Spatial Intelligence](https://mlsanity.com/paper/2505.23764/) (2025)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Model merging with SVD to tie the Knots](https://mlsanity.com/paper/2410.19735/) (2024)
- [No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces](https://mlsanity.com/paper/2502.04959/) (2025)
- [Model Stock: All we need is just a few fine-tuned models](https://mlsanity.com/paper/2403.19522/) (2024)
- [What Matters for Model Merging at Scale?](https://mlsanity.com/paper/2410.03617/) (2024)
- [Localize-and-Stitch: Efficient Model Merging via Sparse Task Arithmetic](https://mlsanity.com/paper/2408.13656/) (2024)
- [MergeBench: A Benchmark for Merging Domain-Specialized LLMs](https://mlsanity.com/paper/2505.10833/) (2025)

## Abstract (arXiv)

Merging finetuned models combines specialized capabilities without joint training or access to the original data. Most methods operate by linear arithmetic in Euclidean weight space, which cannot carry the geometry of the update. Orthogonal Model Merging (OrthoMerge) uses a single orthogonal transform for each weight matrix, but such a transform cannot change singular values. We propose CORAM, which partitions each target matrix into row slices, represents every expert slice by its singular value decomposition in the corresponding base-model SVD frame, and merges the task-specific factors on their corresponding manifolds. Because manifold averaging contracts the merged update, CORAM applies an amplification coefficient λ=kappahatc. The scale chat is estimated from the expert and merged update norms and is approximately √N for N experts with comparable update magnitudes. The restoration strength kappa is selected from the dispersion of expert updates without evaluating candidate merged models. This rule remains within 0.72 points of the best swept value on all evaluated suites. CORAM also includes spread slicing to distribute highly updated rows across slices and a residual pathway for non-target layers. Across four suites covering three model families, 3B to 9B scales, and language and vision-language experts, CORAM improves over OrthoMerge by 0.25 to 1.35 points and matches or exceeds the strongest weight-space baselines.