We present a comprehensive study of task arithmetic in vision-language models and show that weight disentanglement is the crucial factor that makes it effective. This property arises during pre-training and manifests when distinct directions in weight space govern separate, localized regions in function space associated with the tasks.

Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while negating them leads to task forgetting. Yet, our understanding of the effectiveness of task arithmetic and its underlying principles remains limited. We present a comprehensive study of task arithmetic in vision-language models and show that weight disentanglement is the crucial factor that makes it effective. This property arises during pre-training and manifests when distinct directions in weight space govern separate, localized regions in function space associated with the tasks. Notably, we show that fine-tuning models in their tangent space by linearizing them amplifies weight disentanglement. This leads to substantial performance improvements across multiple task arithmetic benchmarks and diverse models. Building on these findings, we provide theoretical and empirical analyses of the neural tangent kernel (NTK) of these models and establish a compelling link between task arithmetic and the spatial localization of the NTK eigenfunctions. Overall, our work uncovers novel insights into the fundamental mechanisms of task arithmetic and offers a more reliable and effective approach to edit pre-trained models through the NTK linearization.

The scarcity of molecules with desirable properties (i.e., `positive' molecules) is an inherent bottleneck for generative molecule design. To sidestep such obstacle, here we propose molecular task arithmetic: training a model on diverse and abundant negative examples to learn 'property directions' - without accessing any positively labeled data - and moving models in the opposite property directions to generate positive molecules. When analyzed on 33 design experiments with distinct molecular entities (small molecules, proteins), model architectures, and scales, molecular task arithmetic generated more diverse and successful designs than models trained on positive molecules in general. Moreover, we employed molecular task arithmetic in dual-objective and few-shot design tasks. We find that molecular task arithmetic can consistently increase the diversity of designs while maintaining desirable complex design properties, such as good docking scores to a protein. With its simplicity, data efficiency, and performance, molecular task arithmetic bears the potential to become the de facto transfer learning strategy for de novo molecule design.

Model merging combines multiple fine-tuned checkpoints into a single model without additional training, offering an attractive approach to reusing models and efficiently improving performance. However, it remains unclear whether the advantages reported for smaller models and classifiers generalize to LLMs. We present a large-scale, systematic evaluation of six state-of-the-art merging methods, including recent subspace methods, across four open-weight LLMs, twelve fine-tuned checkpoints per base model, and sixteen standard LLM benchmarks. Evaluating through standardized benchmarks, we measure both the probability that a merged model outperforms the base model and relative gains over the best individual checkpoint. Our results show that the oldest and simplest method, Task Arithmetic, is the only approach that reliably yields performance gains on LLMs. Other interference-aware and subspace merging methods typically result in significant performance drops. Our findings indicate that current merging techniques do not directly transfer to modern LLMs. This motivates the design of LLM-specific merging algorithms and merging-aware fine-tuning methods. Code will be released upon acceptance of this paper.

Current methods for editing pre-trained models face significant challenges, primarily high computational costs and limited scalability. Task arithmetic has recently emerged as a promising solution, using simple arithmetic operations--addition and negation--based on task vectors which are the differences between fine-tuned and pre-trained model weights, to efficiently modify model behavior. However, the full potential of task arithmetic remains underexplored, primarily due to limited mechanisms for overcoming optimization stagnation. To address this challenge, we introduce the notion of difference vector, a generalized form of task vectors derived from the historical movements during optimization. Using difference vectors as directed perturbations, we propose the Difference V ector-based Anisotropic Scaling Iterative algorithm (DV -BASI) to enable a continuous optimization process for task arithmetic methods without relying on any additional modules or components. Notably, by leveraging escapability and directional advantages of difference vectors, the average performance on different tasks of the multi-task model merged by DV -BASI may even outperform models individually fine-tuned. Based on this observation, we extend the application of difference vectors to a feasible fine-tuning method for single-task models. On the practical side, DV -BASI allows expressive searching directions with few learnable parameters and forms a scalable framework. We also integrate DV -BASI with task arithmetic methods and advanced optimization techniques to achieve state-of-the-art performance on both supervised and unsupervised evaluation protocols.

Task arithmetic has recently emerged as a promising method for editing pre-trained \textit{open-vocabulary} models, offering a cost-effective alternative to standard multi-task fine-tuning. However, despite the abundance of \textit{closed-vocabulary} models that are not pre-trained with language supervision, applying task arithmetic to these models remains unexplored. In this paper, we deploy and study task addition in closed-vocabulary image classification models. We consider different pre-training schemes and find that \textit{weight disentanglement} -- the property enabling task arithmetic -- is a general consequence of pre-training, as it appears in different pre-trained closed-vocabulary models. In fact, we find that pre-trained closed-vocabulary vision transformers can also be edited with task arithmetic, achieving high task addition performance and enabling the efficient deployment of multi-task models. Finally, we demonstrate that simple linear probing is a competitive baseline to task addition. Overall, our findings expand the applicability of task arithmetic to a broader class of pre-trained models and open the way for more efficient use of pre-trained models in diverse settings.

Large Language Models (LLMs) face significant challenges in distributed healthcare, including consolidating specialized domain knowledge across institutions while maintaining privacy, reducing computational overhead, and preventing catastrophic forgetting during model updates.This paper presents a systematic evaluation of six parameter-space merging techniques applied to two architecturally compatible medical LLMs derived from the Mistral-7B base model. We introduce a novel hierarchical method that combines selective Optimal Transport (OT) alignment for attention layers with cosine similarity-weighted interpolation, designed to address permutation variance while minimizing computational overhead for edge deployment scenarios. Our study evaluates Task Arithmetic, Linear Averaging, DARE-TIES, DELLA, Breadcrumbs, and our Hierarchical approach across five medical benchmarks. Results demonstrate that architecturally compatible models benefit significantly from simple averaging methods, with Task Arithmetic achieving 45.80% accuracy on MedQA, outperforming complex pruning-based approaches. These findings offer critical insights for the deployment of distributed medical AI in resource-constrained IoT environments, where computational efficiency and model compatibility are paramount. Our work establishes that for architecturally compatible models, simple averaging provides a robust and computationally efficient baseline for knowledge consolidation, offering a pragmatic path forward for scalable medical AI systems.