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.

Recent advances in neural network pruning have shown how it is possible to reduce the computational costs and memory demands of deep learning models before training. We focus on this framework and propose a new pruning at initialization algorithm that leverages the Neural Tangent Kernel (NTK) theory to align the training dynamics of the sparse network with that of the dense one. Specifically, we show how the usually neglected data-dependent component in the NTK's spectrum can be taken into account by providing an analytical upper bound to the NTK's trace obtained by decomposing neural networks into individual paths. This leads to our Path eXclusion (PX), aforesight pruning method designed to preserve the parameters that mostly influence the NTK's trace. PX is able to find lottery tickets (i.e. good paths) even at high sparsity levels and largely reduces the need for additional training. When applied to pre-trained models it extracts subnetworks directly usable for several downstream tasks, resulting in performance comparable to those of the dense counterpart but with substantial cost and computational savings. Code available at: https://github.com/iurada/px-ntk-pruning.