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Fine-tuning in the tangent space of a pre-trained model (linear fine-tuning) has proven effective, as it produces task vectors that are naturally disentangled and resistant to interference. However, linearized models suffer from limited expressivity during training and incur higher computational costs at inference time, which restrict their practical applicability. In this work, we bridge the gap between linear and standard non-linear fine-tuning. We show that linearity with respect to weight perturbations, a property defined in parameter space, can be enforced through constraints in activation space during training. Concretely, we distill hidden representations from a curvature-regularized linearized teacher into a non-linear student trained via conventional fin","title":"Distilling Linearized Behavior into Non-Linear Fine-Tuning for Effective Task Arithmetic","url":"https://arxiv.org/abs/2605.18993","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.18993v2 Announce Type: replace-cross \nAbstract: Task vector composition has emerged as a promising paradigm for editing pre-trained models, enabling model merging through addition and unlearning through subtraction. Fine-tuning in the tangent space of a pre-trained model (linear fine-tuning) has proven effective, as it produces task vectors that are naturally disentangled and resistant to interference. However, linearized models suffer from limited expressivity during training and incur higher computational costs at inference time, which restrict their practical applicability. In this work, we bridge the gap between linear and standard non-linear fine-tuning. We show that linearity with respect to weight perturbations, a property defined in parameter space, can be enforced through constraints in activation space during training. 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