Understanding and Enforcing Weight Disentanglement in Task Arithmetic
TL;DR
This paper first proves that TFS is a sufficient condition for weight disentanglement, and finds that TFS also gives rise to an observable geometric consequence: weight vector orthogonality, which positions TFS as the common cause for both the desired functional outcome and a measurable geometric property.
Abstract
Task arithmetic provides an efficient, training-free way to edit pre-trained models, yet lacks a fundamental theoretical explanation for its success. The existing concept of ``weight disentanglement"describes the ideal outcome of non-interfering task composition but does not reveal its underlying cause. Crucially, what intrinsic properties of the pre-trained model ($\theta_0$) or the task vectors ($\tau_t$) enable this disentanglement remains underexplored. In this paper, we introduce Task-Feature Specialization (TFS), a model's ability to allocate distinct internal features to different tasks, as the fundamental principle. We first prove that TFS is a sufficient condition for weight disentanglement. More importantly, we find that TFS also gives rise to an observable geometric consequence: weight vector orthogonality. This positions TFS as the common cause for both the desired functional outcome (disentanglement) and a measurable geometric property (orthogonality). This relationship provides the key insight for our method: since the abstract TFS property is intractable to enforce directly, we can instead promote weight disentanglement by shaping its concrete geometric consequence, orthogonality. Therefore, we propose OrthoReg, a simple and effective regularization method that actively enforces an internal orthogonal structure on weight updates ($\Delta W$) that constitute $\tau_t$ during fine-tuning. And we theoretically prove that OrthoReg promotes disentanglement. Extensive experiments demonstrate that OrthoReg consistently and significantly enhances the performance of various task arithmetic methods. Code is available at \href{https://github.com/RL-MIND/OrthoReg}{https://github.com/RL-MIND/OrthoReg}.
