Catastrophic forgetting is a pervasive issue for pre-trained language models (PLMs) during continual learning, where models lose previously acquired knowledge when sequentially trained on a series of tasks. The model's ability to retain old tasks is referred to as stability, while its adaptability to new tasks is called plasticity. Therefore, the key to solving this problem is to find a trade-off between the plasticity and stability of the model. To address this issue, in this paper, we propose a novel method to achieve a balance between model stability and plasticity, thereby mitigating catastrophic forgetting. More specifically, our proposed approach leverages parameter isolation and a subsequent combination strategy. Initially, in the training stage, the model adapts to each downstream task via a parameter isolation method to prevent potential interference among different tasks. We then combine all trained parameters, which contain acquired knowledge, using the task arithmetic method and finally apply them to the backbone model. Empirical evaluations on continual language learning benchmarks substantiate the effectiveness of our approach, revealing a marked enhancement over existing state-of-the-art approaches.
Model merging aggregates Large Language Models (LLMs) finetuned on different tasks into a stronger one. However, parameter conflicts between models leads to performance degradation in averaging. While model routing addresses this issue by selecting individual models during inference, it imposes excessive storage and compute costs, and fails to leverage the common knowledge from different models. In this work, we observe that different layers exhibit varying levels of parameter conflicts. Building on this insight, we average layers with minimal parameter conflicts and use a novel task-level expert routing for layers with significant conflicts. To further reduce storage costs, inspired by task arithmetic sparsity, we decouple multiple fine-tuned experts into a dense expert and several sparse experts. Considering the out-of-distribution samples, we select and merge appropriate experts based on the task uncertainty of the input data. We conduct extensive experiments on both LLaMA and Qwen with varying parameter scales, and evaluate on real-world reasoning tasks. Results demonstrate that our method consistently achieves significant performance improvements while requiring less system cost compared to existing methods.
Multi-task model merging offers an efficient solution for integrating knowledge from multiple fine-tuned models, mitigating the significant computational and storage demands associated with multi-task training. As a key technique in this field, Task Arithmetic (TA) defines task vectors by subtracting the pre-trained model ($\theta_{\text{pre}}$) from the fine-tuned task models in parameter space, then adjusting the weight between these task vectors and $\theta_{\text{pre}}$ to balance task-generalized and task-specific knowledge. Despite the promising performance of TA, conflicts can arise among the task vectors, particularly when different tasks require distinct model adaptations. In this paper, we formally define this issue as knowledge conflicts, characterized by the performance degradation of one task after merging with a model fine-tuned for another task. Through in-depth analysis, we show that these conflicts stem primarily from the components of task vectors that align with the gradient of task-specific losses at $\theta_{\text{pre}}$. To address this, we propose Task Arithmetic in Trust Region (TATR), which defines the trust region as dimensions in the model parameter space that cause only small changes (corresponding to the task vector components with gradient orthogonal direction) in the task-specific losses. Restricting parameter merging within this trust region, TATR can effectively alleviate knowledge conflicts. Moreover, TATR serves as both an independent approach and a plug-and-play module compatible with a wide range of TA-based methods. Extensive empirical evaluations on eight distinct datasets robustly demonstrate that TATR improves the multi-task performance of several TA-based model merging methods by an observable margin.
In continual learning, where task data arrives in a sequence, fine-tuning on later tasks will often lead to performance degradation on earlier tasks. This is especially pronounced when these tasks come from diverse domains. In this setting, how can we mitigate catastrophic forgetting of earlier tasks and retain what the model has learned with minimal computational expenses? Inspired by other merging methods, and L2-regression, we propose Sequential Fine-tuning with Averaging (SFA), a method that merges currently training models with earlier checkpoints during the course of training. SOTA approaches typically maintain a data buffer of past tasks or impose a penalty at each gradient step. In contrast, our method achieves comparable results without the need to store past data, or multiple copies of parameters for each gradient step. Furthermore, our method outperforms common merging techniques such as Task Arithmetic, TIES Merging, and WiSE-FT, as well as other penalty methods like L2 and Elastic Weight Consolidation. In turn, our method offers insight into the benefits of merging partially-trained models during training across both image and language domains.
Task arithmetic in large-scale pre-trained models enables agile adaptation to diverse downstream tasks without extensive retraining. By leveraging task vectors (TVs), users can perform modular updates through simple arithmetic operations like addition and subtraction. Yet, this flexibility presents new security challenges. In this paper, we investigate how TVs are vulnerable to backdoor attacks, revealing how malicious actors can exploit them to compromise model integrity. By creating composite backdoors that are designed asymmetrically, we introduce BadTV, a backdoor attack specifically crafted to remain effective simultaneously under task learning, forgetting, and analogy operations. Extensive experiments show that BadTV achieves near-perfect attack success rates across diverse scenarios, posing a serious threat to models relying on task arithmetic. We also evaluate current defenses, finding they fail to detect or mitigate BadTV. Our results highlight the urgent need for robust countermeasures to secure TVs in real-world deployments.
The use of language models (LMs) has increased considerably in recent years, and the biases and stereotypes in training data that are reflected in the LM outputs are causing social problems. In this paper, inspired by the task arithmetic, we propose the ``Bias Vector'' method for the mitigation of these LM biases. The Bias Vector method does not require manually created debiasing data. The three main steps of our approach involve: (1) continual training the pre-trained LMs on biased data using masked language modeling; (2) constructing the Bias Vector as the difference between the weights of the biased LMs and those of pre-trained LMs; and (3) subtracting the Bias Vector from the weights of the pre-trained LMs for debiasing. We evaluated the Bias Vector method on the SEAT across three LMs and confirmed an average improvement of 0.177 points. We demonstrated that the Bias Vector method does not degrade the LM performance on downstream tasks in the GLUE benchmark. In addition, we examined the impact of scaling factors, which control the magnitudes of Bias Vectors, with effect sizes on the SEAT and conducted a comprehensive evaluation of our debiased LMs across both the SEAT and GLUE benchmarks.
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.
Model merging has recently gained attention as an economical and scalable approach to incorporate task-specific weights from various tasks into a unified multi-task model. For example, in Task Arithmetic (TA), adding the fine-tuned weights of different tasks can enhance the model's performance on those tasks, while subtracting them leads to task forgetting. Although TA is highly effective, interference among task still hampers the performance of the merged model. Existing methods for handling conflicts between task generally rely on empirical selection, resulting in suboptimal performance. In this paper, we introduce an Adaptive Weight Disentanglement method. We begin by theoretically proving that task vectors employed in model merging should be orthogonal to minimize interference among tasks. Guided by this insight, we initialize redundant vectors such that, when subtracted from the original task vectors, the resulting vectors exhibit increased orthogonality. Additionally, we impose an norm constraint on the redundant vectors to preserve the performance of the task-specific models. Experimental results demonstrate the effectiveness of our proposed technique: it successfully extracts redundant vectors, and after their subtraction, the task vectors not only retain robust performance but also achieve superior fusion outcomes. Our code is available at \href{https://github.com/FarisXiong/AWD.git}{https://github.com/FarisXiong/AWD.git}.
Task Arithmetic is a model merging technique that enables the combination of multiple models' capabilities into a single model through simple arithmetic in the weight space, without the need for additional fine-tuning or access to the original training data. However, the factors that determine the success of Task Arithmetic remain unclear. In this paper, we examine Task Arithmetic for multi-task learning by framing it as a one-shot Federated Learning problem. We demonstrate that Task Arithmetic is mathematically equivalent to the commonly used algorithm in Federated Learning, called Federated Averaging (FedAvg). By leveraging well-established theoretical results from FedAvg, we identify two key factors that impact the performance of Task Arithmetic: data heterogeneity and training heterogeneity. To mitigate these challenges, we adapt several algorithms from Federated Learning to improve the effectiveness of Task Arithmetic. Our experiments demonstrate that applying these algorithms can often significantly boost performance of the merged model compared to the original Task Arithmetic approach. This work bridges Task Arithmetic and Federated Learning, offering new theoretical perspectives on Task Arithmetic and improved practical methodologies for model merging.
Pretrained models have revolutionized deep learning by enabling significant performance improvements across a wide range of tasks, leveraging large-scale, pre-learned knowledge representations. However, deploying these models in real-world multi-task learning (MTL) scenarios poses substantial challenges, primarily due to high computational costs and inefficiencies in inference. Traditional approaches such as pruning, quantization, and knowledge distillation have been explored to mitigate these issues, but they often fall short in fully addressing the complexities of multi-task environments. This paper introduces \textbf{\underline{S}}elective \textbf{\underline{T}}ask \textbf{\underline{A}}rithmetic \underline{\textbf{(STA)}}, a training-free framework designed to enhance multi-task performance through task-specific parameter fusion. STA addresses three key challenges: (i) \textbf{Parameter importance diversity: } Recognizing that different tasks relie on distinct parameters, STA employs a loss-sensitive parameter importance metric derived from a first-order Taylor expansion to accurately measure the importance of parameters for each task. (ii) \textbf{Over-reliance on hyperparameter tuning: }By enhancing the sparsity of task vectors through parameter importance metrics, STA reduces the need for extensive hyperparameter tuning, thereby improving the generalization and robustness of the model. (iii) \textbf{Neglect of other abilities in task arithmetic: } Previous works have largely overlooked the potential for more precise task forgetting. STA leverages its parameter importance metric to achieve more controlled and effective task forgetting, minimizing the impact of noisy elements that can degrade model performance. Experimental results demonstrate that STA achieves superior multi-task performance across benchmarks and excellent performance in task forgetting.
Model merging has recently emerged as a cost-efficient paradigm for multi-task learning. Among current approaches, task arithmetic stands out for its simplicity and effectiveness. In this paper, we motivate the effectiveness of task vectors by linking them to multi-task gradients. We show that in a single-epoch scenario, if the optimization is performed via gradient descent, task vectors are after one step mathematically equivalent to the gradients obtained via gradient descent in a multi-task setting, and still approximate these gradients in subsequent epochs. Furthermore, we show that the effectiveness of task vectors is largely driven by the first epoch's gradient. Given this parallel between task vectors and gradients, we propose viewing model merging as a single step in an iterative process that alternates between tuning and merging (ATM). We then propose two ways to utilize ATM. The first is to replace multi-task learning with ATM in scenarios where data sharing is prohibited, such as federated learning. The second is to improve the outcome of any model merging algorithm by applying a few post-hoc iterations of ATM on a small validation dataset, which is commonly available for hyperparameter tuning. Finally, we provide both empirical and theoretical support for the effectiveness of ATM, demonstrating that it minimizes an upper bound on the loss obtained by jointly finetuning all tasks.
Multi-task learning (MTL) leverages a shared model to accomplish multiple tasks and facilitate knowledge transfer. Recent research on task arithmetic-based MTL demonstrates that merging the parameters of independently fine-tuned models can effectively achieve MTL. However, existing merging methods primarily seek a static optimal solution within the original model parameter space, which often results in performance degradation due to the inherent diversity among tasks and potential interferences. To address this challenge, in this paper, we propose a Weight-Ensembling Mixture of Experts (WEMoE) method for multi-task model merging. Specifically, we first identify critical (or sensitive) modules by analyzing parameter variations in core modules of Transformer-based models before and after finetuning. Then, our WEMoE statically merges non-critical modules while transforming critical modules into a mixture-of-experts (MoE) structure. During inference, expert modules in the MoE are dynamically merged based on input samples, enabling a more flexible and adaptive merging approach. Building on WEMoE, we further introduce an efficient-and-effective WEMoE (E-WEMoE) method, whose core mechanism involves eliminating non-essential elements in the critical modules of WEMoE and implementing shared routing across multiple MoE modules, thereby significantly reducing both the trainable parameters, the overall parameter count, and computational overhead of the merged model by WEMoE. Experimental results across various architectures and tasks demonstrate that both WEMoE and E-WEMoE outperform state-of-the-art (SOTA) model merging methods in terms of MTL performance, generalization, and robustness.
Model merging aims to efficiently combine the weights of multiple expert models, each trained on a specific task, into a single multi-task model, with strong performance across all tasks. When applied to all but the last layer of weights, existing methods -- such as Task Arithmetic, TIES-merging, and TALL mask merging -- work well to combine expert models obtained by fine-tuning a common foundation model, operating within a "local" neighborhood of the foundation model. This work explores the more challenging scenario of "non-local" merging, which we find arises when an expert model changes significantly during pretraining or where the expert models do not even share a common foundation model. We observe that standard merging techniques often fail to generalize effectively in this non-local setting, even when accounting for permutation symmetries using standard techniques. We identify that this failure is, in part, due to "variance collapse", a phenomenon identified also in the setting of linear mode connectivity by Jordan et al. (2023). To address this, we propose a multi-task technique to re-scale and shift the output activations of the merged model for each task, aligning its output statistics with those of the corresponding task-specific expert models. Our experiments demonstrate that this correction significantly improves the performance of various model merging approaches in non-local settings, providing a strong baseline for future research on this problem.
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.
Model merging aims to combine multiple expert models into a more capable single model, offering benefits such as reduced storage and serving costs, improved generalization, and support for decentralized model development. Despite its promise, previous studies have primarily focused on merging a few small models. This leaves many unanswered questions about the effect of scaling model size and how it interplays with other key factors -- like the base model quality and number of expert models -- , to affect the merged model's performance. This work systematically evaluates the utility of model merging at scale, examining the impact of these different factors. We experiment with merging fully fine-tuned models using 4 popular merging methods -- Averaging, Task~Arithmetic, Dare, and TIES -- across model sizes ranging from 1B-64B parameters and merging up to 8 different expert models. We evaluate the merged models on both held-in tasks, i.e., the expert's training tasks, and zero-shot generalization to unseen held-out tasks. Our experiments provide several new insights about model merging at scale and the interplay between different factors. First, we find that merging is more effective when experts are created from strong base models, i.e., models with good zero-shot performance. Second, larger models facilitate easier merging. Third merging consistently improves generalization capabilities. Notably, when merging 8 large expert models, the merged models often generalize better compared to the multitask trained models. Fourth, we can better merge more expert models when working with larger models. Fifth, different merging methods behave very similarly at larger scales. Overall, our findings shed light on some interesting properties of model merging while also highlighting some limitations. We hope that this study will serve as a reference point on large-scale merging for upcoming research.
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
Recent advances in large language models (LLMs) have gained interest in speech-text multimodal foundation models, achieving strong performance on instruction-based speech translation (ST). However, expanding language pairs from an existing instruction-tuned ST system is costly due to the necessity of re-training on a combination of new and previous datasets. We propose to expand new language pairs by merging the model trained on new language pairs and the existing model, using task arithmetic. We find that the direct application of task arithmetic for ST causes the merged model to fail to follow instructions; thus, generating translation in incorrect languages. To eliminate language confusion, we propose an augmented task arithmetic method that merges an additional language control model. It is trained to generate the correct target language token following the instructions. Our experiments demonstrate that our proposed language control model can achieve language expansion by eliminating language confusion. In our MuST-C and CoVoST-2 experiments, it shows up to 4.66 and 4.92 BLEU scores improvement, respectively. In addition, we demonstrate the use of our task arithmetic framework can expand to a language pair where neither paired ST training data nor a pre-trained ST model is available. We first synthesize the ST system from machine translation (MT) systems via task analogy, then merge the synthesized ST system to the existing ST model.
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.