Abstract: Model-editing techniques using task arithmetic have rapidly gained attention.Through task arithmetic, simply through arithmetic operations on the weights of pre-trained and fine-tuned models create desired models, such as multi-task models, models in which specific tasks are unsolvable, or domain-transferred models.However, task arithmetic faces challenges, such as poor reproducibility and the high cost associated with adjusting coefficients in the arithmetic operations on model parameters, which have limited its practical success. In this paper, we present three key contributions in the context of task addition and task negation within task arithmetic. First, we propose a new metric called $\tau$Jp which is based on the product of the task vector ($\tau$) and the Jacobian of the pre-trained model with respect to its weights. We show that $\tau$Jp has a causal relationship with the interference that occurs from arithmetic operations. Second, we show that introducing regularization to minimize $\tau$Jp significantly mitigates interference between task inference, which leads to the elimination of coefficient tuning and improved accuracy on each task.Third, in the context of incremental learning, we demonstrate that our $\tau$Jp regularization achieves more robust performance in environments where access to future tasks is unavailable, thus validating the scalability of the approach.Finally, we demonstrate that the $\tau$Jp regularizer further reinforces the performance of task arithmetic by leveraging publicly available fine-tuned models, offering practical benefits for real-world applications.Our code is available at https://github.com/katoro8989/tau-Jp_Task_Arithmetic