# CT-Merging: Consensus Directions and Task-Specific Scaling for LoRA Adapter Merging

arXiv: https://arxiv.org/abs/2607.20561 · HTML: https://mlsanity.com/paper/2607.20561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [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)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [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)
- [Accurate and Efficient Low-Rank Model Merging in Core Space](https://mlsanity.com/paper/2509.17786/) (2025)
- [RobustMerge: Parameter-Efficient Model Merging for MLLMs with Direction Robustness](https://mlsanity.com/paper/2502.17159/) (2025)
- [DC-Merge: Improving Model Merging with Directional Consistency](https://mlsanity.com/paper/2603.06242/) (2026)

## Abstract (arXiv)

LoRA merging methods increasingly operate on the low-rank structure of task updates, yet how the common subspace is estimated and how coefficients are assigned after recomposition are rarely compared directly. We propose CT-Merging, which estimates common directions from averaged task subspace projectors and assigns a separate residual scale to each task. Projector averaging selects directions supported across task subspaces without weighting them by singular magnitude, while task-specific scaling removes component-wise magnitude variation and preserves scale differences across tasks. On the released KnOTS CLIP adapters, CT-Merging achieves the best average and worst-task normalized accuracy on both backbones, improving over the strongest baseline by up to 2.56 and 6.65 points, respectively. On the DC-Merge adapter benchmark, it achieves the best average normalized accuracy in eight of nine backbone and task-count settings. Ablations show that projector averaging outperforms summed-update SVD and that task-specific scaling improves worst-task accuracy over global isotropic scaling.