# Not All Task Vectors Need Equal Rank: Energy-Proportional Allocation for Model Merging

arXiv: https://arxiv.org/abs/2609.24517 · HTML: https://mlsanity.com/paper/2609.24517/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [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)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [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)
- [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)
- [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)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Localizing Task Information for Improved Model Merging and Compression](https://mlsanity.com/paper/2405.07813/) (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)
- [Parameter Competition Balancing for Model Merging](https://mlsanity.com/paper/2410.02396/) (2024)
- [Whoever Started the Interference Should End It: Guiding Data-Free Model Merging via Task Vectors](https://mlsanity.com/paper/2503.08099/) (2025)
- [AdaRank: Adaptive Rank Pruning for Enhanced Model Merging](https://mlsanity.com/paper/2503.22178/) (2025)
- [DC-Merge: Improving Model Merging with Directional Consistency](https://mlsanity.com/paper/2603.06242/) (2026)
- [Purifying Task Vectors in Knowledge-Aware Subspace for Model Merging](https://mlsanity.com/paper/2510.14697/) (2025)

## Abstract (arXiv)

Model merging aims to combine multiple fine-tuned models derived from a common pretrained model into a single multi-task model without additional joint training. Recent spectral merging methods improve over simple weight averaging by exploiting low-rank structures of task-specific updates, but they commonly assign the same rank capacity to every task. This uniform allocation ignores that task vectors can have heterogeneous spectral complexity, causing the shared merging space to be used suboptimally. In this paper, we propose Spectral Energy-proportional Rank Allocation (SERA), a simple task-adaptive strategy that allocates ranks according to the singular-value energy structure of each task vector. By assigning richer spectral capacity to complex or isolated tasks and fewer directions to compact tasks, SERA extends SVD-based model merging from uniform-capacity merging to task-dependent capacity allocation. Experiments under standard vision model merging protocols show that SERA improves multi-task merging performance while preserving the same total rank budget as existing spectral merging methods. Further analysis demonstrates that task-level spectral concentration is closely related to the per-task effect of adaptive rank allocation, providing insight into when and why SERA is effective.