# DC-Merge: Improving Model Merging with Directional Consistency

arXiv: https://arxiv.org/abs/2603.06242 · HTML: https://mlsanity.com/paper/2603.06242/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 71 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Builds on (most cited first, 30 of 52)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Generation and Comprehension of Unambiguous Object Descriptions](https://mlsanity.com/paper/1511.02283/) (2015)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [A-OKVQA: A Benchmark for Visual Question Answering using World Knowledge](https://mlsanity.com/paper/2206.01718/) (2022)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)

## Built on by (most cited first, 8 of 8)

- [Data-Aware Model Merging in the Essential Subspace for Multi-Task Knowledge Aggregation](https://mlsanity.com/paper/2606.19164/) (2026)
- [Reading the Gate, Not the Interference: Output-Side Interference Measurement Does Not Track Merge Collapse](https://mlsanity.com/paper/2608.11797/) (2026)
- [From Parameters to Behaviors: A Survey of Model Fusion for Large Language Models](https://mlsanity.com/paper/2609.19553/) (2026)
- [CT-Merging: Consensus Directions and Task-Specific Scaling for LoRA Adapter Merging](https://mlsanity.com/paper/2607.20561/) (2026)
- [AgentPatch: Coarse-to-Fine Weak-Task Repair for Merging Agentic Multimodal Large Language Models](https://mlsanity.com/paper/2608.06699/) (2026)
- [Tracing and Coordinating Cross-Layer Influence for Multimodal Model Merging](https://mlsanity.com/paper/2609.12897/) (2026)
- [Not All Task Vectors Need Equal Rank: Energy-Proportional Allocation for Model Merging](https://mlsanity.com/paper/2609.24517/) (2026)
- [Beyond Uniform Subspaces: Spectrum-Aware and Depth-Adaptive Fusion for Multi-Task Model Merging](https://mlsanity.com/paper/2609.24612/) (2026)

## Abstract (arXiv)

Model merging aims to integrate multiple task-adapted models into a unified model that preserves the knowledge of each task. In this paper, we identify that the key to this knowledge retention lies in maintaining the directional consistency of singular spaces between merged multi-task vector and individual task vectors. However, this consistency is frequently compromised by two issues: i) an imbalanced energy distribution within task vectors, where a small fraction of singular values dominate the total energy, leading to the neglect of semantically important but weaker components upon merging, and ii) the geometric inconsistency of task vectors in parameter space, which causes direct merging to distort their underlying directional geometry. To address these challenges, we propose DC-Merge, a method for directional-consistent model merging. It first balances the energy distribution of each task vector by smoothing its singular values, ensuring all knowledge components are adequately represented. These energy-balanced vectors are then projected onto a shared orthogonal subspace to align their directional geometries with minimal reconstruction error. Finally, the aligned vectors are aggregated in the shared orthogonal subspace and projected back to the original parameter space. Extensive experiments on vision and vision-language benchmarks show that DC-Merge consistently achieves state-of-the-art performance in both full fine-tuning and LoRA settings. The implementation code is available at https://github.com/Tobeginwith/DC-Merge.