Task Arithmetic in Trust Region: A Training-Free Model Merging Approach to Navigate Knowledge Conflicts

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 (θ pre ) from the fine-tuned task models in parameter space, then adjusting the weight between these task vectors and θ pre to balance task-generalized and taskspecific 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 θ 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 TAbased 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.