# Purifying Task Vectors in Knowledge-Aware Subspace for Model Merging

arXiv: https://arxiv.org/abs/2510.14697 · HTML: https://mlsanity.com/paper/2510.14697/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 67 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 30 of 49)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (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)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (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)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)

## Built on by (most cited first, 3 of 3)

- [Plato's Form: Toward Backdoor Defense-as-a-Service for LLMs with Prototype Representations](https://mlsanity.com/paper/2602.06887/) (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 task-specific abilities from individually fine-tuned models into a single model without extra training. In recent model merging methods, task vector has become a fundamental building block, as it can encapsulate the residual information from finetuning. However, the merged model often suffers from notable performance degradation due to the conflicts caused by task-irrelevant redundancy in task vectors. Existing efforts in overcoming redundancy by randomly dropping elements in the parameter space involves randomness and lacks knowledge awareness. To address these challenges, in this study, we propose Purifying TAsk Vectors (PAVE) in knowledge-aware subspace. Concretely, we sample some training examples from each task, and feed them into their corresponding fine-tuned models to acquire the covariance matrices before linear layers. We then perform a context-oriented singular value decomposition, which accentuates the weight components most relevant to the target knowledge. As a result, we can split fine-tuned model weights into task-relevant and redundant components in the knowledge-aware subspace, and purify the task vector by pruning the redundant components. To induce fair pruning efforts across models, we further introduce a spectral rank allocation strategy by optimizing a normalized activated pruning error. The task vector purification by our method as a plug-and-play scheme is applicable across various task vector-based merging methods to improve their performance. In experiments, we demonstrate the effectiveness of PAVE across a diverse set of merging methods, tasks, and model architectures.