# When is Task Vector Provably Effective for Model Editing? A Generalization Analysis of Nonlinear Transformers

arXiv: https://arxiv.org/abs/2504.10957 · HTML: https://mlsanity.com/paper/2504.10957/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Placed in Machine unlearning, one of 12 directions in LLM safety and security.
- Builds on 70 of its 79 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Placed in

- LLM safety and security / [Machine unlearning](https://mlsanity.com/safety/machine-unlearning/)

## Builds on (most cited first, 30 of 70)

- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Visual Prompt Tuning](https://mlsanity.com/paper/2203.12119/) (2022)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [What learning algorithm is in-context learning? Investigations with linear models](https://mlsanity.com/paper/2211.15661/) (2022)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [Dataless Knowledge Fusion by Merging Weights of Language Models](https://mlsanity.com/paper/2212.09849/) (2022)
- [Trained Transformers Learn Linear Models In-Context](https://mlsanity.com/paper/2306.09927/) (2023)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)

## Built on by (most cited first, 30 of 38)

- [FlyLoRA: Boosting Task Decoupling and Parameter Efficiency via Implicit Rank-Wise Mixture-of-Experts](https://mlsanity.com/paper/2510.08396/) (2025)
- [MergeBench: A Benchmark for Merging Domain-Specialized LLMs](https://mlsanity.com/paper/2505.10833/) (2025)
- [SoK: Machine Unlearning for Large Language Models](https://mlsanity.com/paper/2506.09227/) (2025)
- [UltraEdit: Training-, Subject-, and Memory-Free Lifelong Editing in Language Models](https://mlsanity.com/paper/2505.14679/) (2025)
- [ICM-Fusion: In-Context Meta-Optimized LoRA Fusion for Multi-Task Adaptation](https://mlsanity.com/paper/2508.04153/) (2025)
- [Stable and Explainable Personality Trait Evaluation in Large Language Models with Internal Activations](https://mlsanity.com/paper/2601.09833/) (2026)
- [Merge to Mix: Mixing Datasets via Model Merging](https://mlsanity.com/paper/2505.16066/) (2025)
- [Adaptive Helpfulness-Harmlessness Alignment with Preference Vectors](https://mlsanity.com/paper/2504.20106/) (2025)
- [Adaptive Task Vectors for Large Language Models](https://mlsanity.com/paper/2506.03426/) (2025)
- [CoT Vectors: Transferring and Probing the Reasoning Mechanisms of LLMs](https://mlsanity.com/paper/2510.00579/) (2025)
- [On Fairness of Task Arithmetic: The Role of Task Vectors](https://mlsanity.com/paper/2505.24262/) (2025)
- [Merging Smarter, Generalizing Better: Enhancing Model Merging on OOD Data](https://mlsanity.com/paper/2506.09093/) (2025)
- [Understanding and Enforcing Weight Disentanglement in Task Arithmetic](https://mlsanity.com/paper/2604.17078/) (2026)
- [How Can Mamba Learn In Context with Outliers and Generalize Provably?](https://mlsanity.com/paper/2510.00399/) (2025)
- [Model Merging via Multi-Teacher Knowledge Distillation](https://mlsanity.com/paper/2512.21288/) (2025)
- [Inference-time Unlearning Using Conformal Prediction](https://mlsanity.com/paper/2602.03787/) (2026)
- [Bus-Conditioned Zero-Shot Trajectory Generation via Task Arithmetic](https://mlsanity.com/paper/2602.13071/) (2026)
- [Cross-Model Transfer of Task Vectors via Few-Shot Orthogonal Alignment](https://mlsanity.com/paper/2505.12021/) (2025)
- [Pseudo2Real: Task Arithmetic for Pseudo-Label Correction in Automatic Speech Recognition](https://mlsanity.com/paper/2510.08047/) (2025)
- [Weight Weaving: Parameter Pooling for Data-Free Model Merging](https://mlsanity.com/paper/2510.13921/) (2025)
- [Attesting Model Lineage by Consisted Knowledge Evolution with Fine-Tuning Trajectory](https://mlsanity.com/paper/2601.11683/) (2026)
- [Multi-task Code LLMs: Data Mix or Model Merge?](https://mlsanity.com/paper/2601.21115/) (2026)
- [A Theoretical Framework for LLM Fine-tuning Using Early Stopping for Non-random Initialization](https://mlsanity.com/paper/2602.13942/) (2026)
- [Visual prompting reimagined: The power of the Activation Prompts](https://mlsanity.com/paper/2604.06440/) (2026)
- [Decouple before Integration: Test-time Synthesis of SFT and RLVR Task Vectors](https://mlsanity.com/paper/2605.00610/) (2026)
- [On the Blessing of Pre-training in Weak-to-Strong Generalization](https://mlsanity.com/paper/2605.05710/) (2026)
- [Suppression Sticks, Locality Is Fragile: A Closed-Loop Target-and-Control Audit of Task-Vector Negation in VLA Policies](https://mlsanity.com/paper/2608.04692/) (2026)
- [Efficient Multi-Source Knowledge Transfer by Model Merging](https://mlsanity.com/paper/2508.19353/) (2025)
- [Variational Task Vector Composition](https://mlsanity.com/paper/2509.18208/) (2025)
- [Subtract the Corruption: Training-Data-Free Corrective Machine Unlearning using Task Arithmetic](https://mlsanity.com/paper/2511.18660/) (2025)

## Abstract (arXiv)

Task arithmetic refers to editing the pre-trained model by adding a weighted sum of task vectors, each of which is the weight update from the pre-trained model to fine-tuned models for certain tasks. This approach recently gained attention as a computationally efficient inference method for model editing, e.g., multi-task learning, forgetting, and out-of-domain generalization capabilities. However, the theoretical understanding of why task vectors can execute various conceptual operations remains limited, due to the highly non-convexity of training Transformer-based models. To the best of our knowledge, this paper provides the first theoretical characterization of the generalization guarantees of task vector methods on nonlinear Transformers. We consider a conceptual learning setting, where each task is a binary classification problem based on a discriminative pattern. We theoretically prove the effectiveness of task addition in simultaneously learning a set of irrelevant or aligned tasks, as well as the success of task negation in unlearning one task from irrelevant or contradictory tasks. Moreover, we prove the proper selection of linear coefficients for task arithmetic to achieve guaranteed generalization to out-of-domain tasks. All of our theoretical results hold for both dense-weight parameters and their low-rank approximations. Although established in a conceptual setting, our theoretical findings were validated on a practical machine unlearning task using the large language model Phi-1.5 (1.3B).