Model merging aims to integrate the strengths of multiple fine-tuned models into a unified model while preserving task-specific capabilities. Existing methods, represented by task arithmetic, are typically classified into global- and local-aware methods. However, global-aware methods inevitably cause parameter interference, while local-aware methods struggle to maintain the effectiveness of task-specific details in the merged model. To address these limitations, we propose a Consensus-Aware Localized Merging (CALM) method which incorporates localized information aligned with global task consensus, ensuring its effectiveness post-merging. CALM consists of three key components: (1) class-balanced entropy minimization sampling, providing a more flexible and reliable way to leverage unsupervised data; (2) an efficient-aware framework, selecting a small set of tasks for sequential merging with high scalability; (3) a consensus-aware mask optimization, aligning localized binary masks with global task consensus and merging them conflict-free. Experiments demonstrate the superiority and robustness of our CALM, significantly outperforming existing methods and achieving performance close to traditional MTL.
Task arithmetic enables efficient model editing by representing task-specific changes as vectors in parameter space. Task arithmetic typically assumes that the source and target models are initialized from the same pre-trained parameters. This assumption limits its applicability in cross-model transfer settings, where models are independently pre-trained on different datasets. To address this challenge, we propose a method based on few-shot orthogonal alignment, which aligns task vectors to the parameter space of a differently pre-trained target model. These transformations preserve key properties of task vectors, such as norm and rank, and are learned using only a small number of labeled examples. We evaluate the method using two Vision Transformers pre-trained on YFCC100M and LAION400M, and test on eight classification datasets. Experimental results show that our method improves transfer accuracy over direct task vector application and achieves performance comparable to few-shot fine-tuning, while maintaining the modularity and reusability of task vectors. Our code is available at https://github.com/kawakera-lab/CrossModelTransfer.
Large Language Models (LLMs) have shown impressive zero-shot performance across a variety of Natural Language Processing tasks, including document re-ranking. However, their effectiveness degrades on unseen tasks and domains, largely due to shifts in vocabulary and word distributions. In this paper, we investigate Task Arithmetic, a technique that combines the weights of LLMs pre-trained on different tasks or domains via simple mathematical operations, such as addition or subtraction, to adapt retrieval models without requiring additional fine-tuning. Our method is able to synthesize diverse tasks and domain knowledge into a single model, enabling effective zero-shot adaptation in different retrieval contexts. Extensive experiments on publicly available scientific, biomedical, and multilingual datasets show that our method improves state-of-the-art re-ranking performance by up to 18% in NDCG@10 and 15% in P@10. In addition to these empirical gains, our analysis provides insights into the strengths and limitations of Task Arithmetic as a practical strategy for zero-shot learning and model adaptation. We make our code publicly available at https://github.com/DetectiveMB/Task-Arithmetic-for-ZS-IR.
Task arithmetic is a straightforward yet highly effective strategy for model merging, enabling the resultant model to exhibit multi-task capabilities. Recent research indicates that models demonstrating linearity enhance the performance of task arithmetic. In contrast to existing methods that rely on the global linearization of the model, we argue that this linearity already exists within the model's submodules. In particular, we present a statistical analysis and show that submodules (e.g., layers, self-attentions, and MLPs) exhibit significantly higher linearity than the overall model. Based on these findings, we propose an innovative model merging strategy that independently merges these submodules. Especially, we derive a closed-form solution for optimal merging weights grounded in the linear properties of these submodules. Experimental results demonstrate that our method consistently outperforms the standard task arithmetic approach and other established baselines across different model scales and various tasks. This result highlights the benefits of leveraging the linearity of submodules and provides a new perspective for exploring solutions for effective and practical multi-task model merging.
Task arithmetic has emerged as a promising approach for editing models by representing task-specific knowledge as composable task vectors. However, existing methods rely on network linearization to derive task vectors, leading to computational bottlenecks during training and inference. Moreover, linearization alone does not ensure weight disentanglement, the key property that enables conflict-free composition of task vectors. To address this, we propose TaLoS which allows to build sparse task vectors with minimal interference without requiring explicit linearization and sharing information across tasks. We find that pre-trained models contain a subset of parameters with consistently low gradient sensitivity across tasks, and that sparsely updating only these parameters allows for promoting weight disentanglement during fine-tuning. Our experiments prove that TaLoS improves training and inference efficiency while outperforming current methods in task addition and negation. By enabling modular parameter editing, our approach fosters practical deployment of adaptable foundation models in real-world applications.
Task vectors, which are derived from the difference between pre-trained and fine-tuned model weights, enable flexible task adaptation and model merging through arithmetic operations such as addition and negation. However, existing approaches often rely on heuristics with limited theoretical support, often leading to performance gaps comparing to direct task fine tuning. Meanwhile, although it is easy to manipulate saved task vectors with arithmetic for different purposes, such compositional flexibility demands high memory usage, especially when dealing with a huge number of tasks, limiting scalability. This work addresses these issues with a theoretically grounded framework that explains task vector arithmetic and introduces the task vector bases framework. Building upon existing task arithmetic literature, our method significantly reduces the memory cost for downstream arithmetic with little effort, while achieving competitive performance and maintaining compositional advantage, providing a practical solution for large-scale task arithmetic.
Task Arithmetic has emerged as a simple yet effective method to merge models without additional training. However, by treating entire networks as flat parameter vectors, it overlooks key structural information and is susceptible to task interference. In this paper, we study task vectors at the layer level, focusing on task layer matrices and their singular value decomposition. In particular, we concentrate on the resulting singular vectors, which we refer to as Task Singular Vectors (TSV). Recognizing that layer task matrices are often low-rank, we propose TSV-Compress (TSV-C), a simple procedure that compresses them to 10% of their original size while retaining 99% of accuracy. We further leverage this low-rank space to define a new measure of task interference based on the interaction of singular vectors from different tasks. Building on these findings, we introduce TSV-Merge (TSV-M), a novel model merging approach that combines compression with interference reduction, significantly outperforming existing methods.
Machine unlearning aims to selectively remove specific knowledge from a model. Current methods, such as task arithmetic, rely on fine-tuning models on the forget set, generating a task vector, and subtracting it from the original model. However, we argue the effectiveness of this approach is highly sensitive to hyperparameter selection, necessitating careful validation to identify the best model among many fine-tuned candidates. In this paper, we propose a novel method that leverages all given fine-tuned models rather than selecting a single one. By constructing task vectors from models trained with varied hyperparameters and merging only the components of the task vectors with consistent signs, we perform unlearning by negating the merged task vector from the original model. Given that existing methods also utilize multiple fine-tuned models, our approach delivers more effective unlearning without incurring additional computational costs. We demonstrate the effectiveness of our method on both vision-language models and standard image classification models, showing improved unlearning performance with minimal degradation on the retain set, outperforming state-of-the-art techniques.
Federated Learning has emerged as a promising paradigm for collaborative machine learning, while preserving user data privacy. Despite its potential, standard FL lacks support for diverse heterogeneous device prototypes, which vary significantly in model and dataset sizes -- from small IoT devices to large workstations. This limitation is only partially addressed by existing knowledge distillation techniques, which often fail to transfer knowledge effectively across a broad spectrum of device prototypes with varied capabilities. This failure primarily stems from two issues: the dilution of informative logits from more capable devices by those from less capable ones, and the use of a single integrated logits as the distillation target across all devices, which neglects their individual learning capacities and and the unique contributions of each. To address these challenges, we introduce TAKFL, a novel KD-based framework that treats the knowledge transfer from each device prototype's ensemble as a separate task, independently distilling each to preserve its unique contributions and avoid dilution. TAKFL also incorporates a KD-based self-regularization technique to mitigate the issues related to the noisy and unsupervised ensemble distillation process. To integrate the separately distilled knowledge, we introduce an adaptive task arithmetic knowledge integration process, allowing each student model to customize the knowledge integration for optimal performance. Additionally, we present theoretical results demonstrating the effectiveness of task arithmetic in transferring knowledge across heterogeneous devices with varying capacities. Comprehensive evaluations of our method across both CV and NLP tasks demonstrate that TAKFL achieves SOTA results in a variety of datasets and settings, significantly outperforming existing KD-based methods Code is released at https://github.com/MMorafah/TAKFL
Model merging offers an effective strategy to combine the strengths of multiple finetuned models into a unified model that preserves the specialized capabilities of each. Existing methods merge models in a global manner, performing arithmetic operations across all model parameters. However, such global merging often leads to task interference, degrading the performance of the merged model. In this work, we introduce Localize-and-Stitch, a novel approach that merges models in a localized way. Our algorithm works in two steps: i) Localization: identify tiny ($1\%$ of the total parameters) localized regions in the finetuned models containing essential skills for the downstream tasks, and ii) Stitching: reintegrate only these essential regions back into the pretrained model for task synergy. We demonstrate that our approach effectively locates sparse regions responsible for finetuned performance, and the localized regions could be treated as compact and interpretable representations of the finetuned models (tasks). Empirically, we evaluate our method on various vision and language benchmarks, showing that it outperforms existing model merging methods under different data availability scenarios. Beyond strong empirical performance, our algorithm also facilitates model compression and preserves pretrained knowledge, enabling flexible and continual skill composition from multiple finetuned models with minimal storage and computational overhead. Our code is available at https://github.com/uiuctml/Localize-and-Stitch.
In recent years, task arithmetic has garnered increasing attention. This approach edits pre-trained models directly in weight space by combining the fine-tuned weights of various tasks into a unified model. Its efficiency and cost-effectiveness stem from its training-free combination, contrasting with traditional methods that require model training on large datasets for multiple tasks. However, applying such a unified model to individual tasks can lead to interference from other tasks (lack of weight disentanglement). To address this issue, Neural Tangent Kernel (NTK) linearization has been employed to leverage a "kernel behavior", facilitating weight disentanglement and mitigating adverse effects from unrelated tasks. Despite its benefits, NTK linearization presents drawbacks, including doubled training costs, as well as reduced performance of individual models. To tackle this problem, we propose a simple yet effective and efficient method that is to finetune the attention modules only in the Transformer. Our study reveals that the attention modules exhibit kernel behavior, and fine-tuning the attention modules only significantly improves weight disentanglement. To further understand how our method improves the weight disentanglement of task arithmetic, we present a comprehensive study of task arithmetic by differentiating the role of the representation module and task-specific module. In particular, we find that the representation module plays an important role in improving weight disentanglement whereas the task-specific modules such as the classification heads can degenerate the weight disentanglement performance. (The code is available at https://github.com/kyrie-23/task_arithmetic_tangent)
Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate its scalibility.
Model merging and task arithmetic have emerged as promising scalable approaches to merge multiple single-task checkpoints to one multi-task model, but their applicability is reduced by significant performance loss. Previous works have linked these drops to interference in the weight space and erasure of important task-specific features. Instead, in this work we show that the information required to solve each task is still preserved after merging as different tasks mostly use non-overlapping sets of weights. We propose TALL-masks, a method to identify these task supports given a collection of task vectors and show that one can retrieve >99% of the single task accuracy by applying our masks to the multi-task vector, effectively compressing the individual checkpoints. We study the statistics of intersections among constructed masks and reveal the existence of selfish and catastrophic weights, i.e., parameters that are important exclusively to one task and irrelevant to all tasks but detrimental to multi-task fusion. For this reason, we propose Consensus Merging, an algorithm that eliminates such weights and improves the general performance of existing model merging approaches. Our experiments in vision and NLP benchmarks with up to 20 tasks, show that Consensus Merging consistently improves existing approaches. Furthermore, our proposed compression scheme reduces storage from 57Gb to 8.2Gb while retaining 99.7% of original performance.
Modular deep learning is the state-of-the-art solution for lifting the curse of multilinguality, preventing the impact of negative interference and enabling cross-lingual performance in Multilingual Pre-trained Language Models. However, a trade-off of this approach is the reduction in positive transfer learning from closely related languages. In response, we introduce a novel method called language arithmetic, which enables training-free post-processing to address this limitation. Extending the task arithmetic framework, we apply learning via addition to the language adapters, transitioning the framework from a multi-task to a multilingual setup. The effectiveness of the proposed solution is demonstrated on three downstream tasks in a MAD-X-based set of cross-lingual schemes, acting as a post-processing procedure. Language arithmetic consistently improves the baselines with significant gains, especially in the most challenging case of zero-shot application. Our code and models are available at https://github.com/mklimasz/language-arithmetic .
Model merging is a promising lightweight model empowerment technique that does not rely on expensive computing devices (e.g., GPUs) or require the collection of specific training data. Instead, it involves editing different upstream model parameters to absorb their downstream task capabilities. However, uncertified model merging can infringe upon the Intellectual Property (IP) rights of the original upstream models. In this paper, we conduct the first study on the robustness of IP protection methods under model merging scenarios. Specifically, we investigate two state-of-the-art IP protection techniques: Quantization Watermarking and Instructional Fingerprint, along with various advanced model merging technologies, such as Task Arithmetic, TIES-MERGING, and so on. Experimental results indicate that current Large Language Model (LLM) watermarking techniques cannot survive in the merged models, whereas model fingerprinting techniques can. Our research aims to highlight that model merging should be an indispensable consideration in the robustness assessment of model IP protection techniques, thereby promoting the healthy development of the open-source LLM community. Our code is available at https://github.com/ThuCCSLab/MergeGuard.
Aligned language models face a significant limitation as their fine-tuning often results in compromised safety. To tackle this, we propose a simple method RESTA that performs LLM safety realignment. RESTA stands for REstoring Safety through Task Arithmetic. At its core, it involves a simple arithmetic addition of a safety vector to the weights of the compromised model. We demonstrate the effectiveness of RESTA in both parameter-efficient and full fine-tuning, covering a wide range of downstream tasks, including instruction following in Chinese, English, and Hindi, as well as problem-solving capabilities in Code and Math. We also showcase the generalizability of RESTA on three existing safety evaluation benchmarks and a multilingual benchmark dataset proposed as a part of this work, consisting of 550 harmful questions covering 11 categories, each with 5 sub-categories of harm. Overall, RESTA decreases the harmfulness of the compromised model from 18.6% to 5.1% and from 9.2% to 1.5% in parameter-efficient and full fine-tuning, respectively, while maintaining most of the model's performance on the task. We release the source codes at: https://github.com/declare-lab/resta.
Merging various task-specific Transformer-based models trained on different tasks into a single unified model can execute all the tasks concurrently. Previous methods, exemplified by task arithmetic, have been proven to be both effective and scalable. Existing methods have primarily focused on seeking a static optimal solution within the original model parameter space. A notable challenge is mitigating the interference between parameters of different models, which can substantially deteriorate performance. In this paper, we propose to merge most of the parameters while upscaling the MLP of the Transformer layers to a weight-ensembling mixture of experts (MoE) module, which can dynamically integrate shared and task-specific knowledge based on the input, thereby providing a more flexible solution that can adapt to the specific needs of each instance. Our key insight is that by identifying and separating shared knowledge and task-specific knowledge, and then dynamically integrating them, we can mitigate the parameter interference problem to a great extent. We conduct the conventional multi-task model merging experiments and evaluate the generalization and robustness of our method. The results demonstrate the effectiveness of our method and provide a comprehensive understanding of our method. The code is available at https://github.com/tanganke/weight-ensembling_MoE
Merging models fine-tuned from a common, extensively pre-trained large model but specialized for different tasks has been demonstrated as a cheap and scalable strategy to construct a multi-task model that performs well across diverse tasks. Recent research, exemplified by task arithmetic, highlights that this multi-task model can be derived through arithmetic operations on task vectors. Nevertheless, current merging techniques frequently resolve potential conflicts among parameters from task-specific models by evaluating individual attributes, such as the parameters' magnitude or sign, overlooking their collective impact on the overall functionality of the model. In this work, we propose the CONtinuous relaxation of disCRETE (Concrete) subspace learning method to identify a common low-dimensional subspace and utilize its shared information to track the interference problem without sacrificing much performance. Specifically, we model the problem as a bi-level optimization problem and introduce a meta-learning framework to find the Concrete subspace mask through gradient-based techniques. At the upper level, we focus on learning a shared Concrete mask to identify the subspace, while at the inner level, model merging is performed to maximize the performance of the merged model. We conduct extensive experiments on both vision domain and language domain, and the results demonstrate the effectiveness of our method. The code is available at https://github.com/tanganke/subspace_fusion
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.
Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a new uncertainty-based scheme to improve the performance by reducing the mismatch. The connection also reveals implicit assumptions in other schemes such as averaging, task arithmetic, and Fisher-weighted averaging. Our new method gives consistent improvements for large language models and vision transformers, both in terms of performance and robustness to hyperparameters. Code available here.