arXiv:2509.15888v1 Announce Type: cross Abstract: Adapting billion-parameter language models to a downstream task is still costly, even with parameter-efficient fine-tuning (PEFT). We re-cast task adaptation as output-distribution alignment: the objective is to steer the output distribution toward the task distribution directly during decoding rather than indirectly through weight updates. Building on this view, we introduce Steering Vector Decoding (SVD), a lightweight, PEFT-compatible, and theoretically grounded method. We start with a short warm-start fine-tune and extract a task-aware steering vector from the Kullback-Leibler (KL) divergence gradient between the output distribution of the warm-started and pre-trained models. This steering vector is then used to guide the decoding process to steer the model's output distribution towards the task distribution. We theoretically prove that SVD is first-order equivalent to the gradient step of full fine-tuning and derive a globally optimal solution for the strength of the steering vector. Across three tasks and nine benchmarks, SVD paired with four standard PEFT methods improves multiple-choice accuracy by up to 5 points and open-ended truthfulness by 2 points, with similar gains (1-2 points) on commonsense datasets without adding trainable parameters beyond the PEFT adapter. SVD thus offers a lightweight, theoretically grounded path to stronger task adaptation for large language models.