Adaptive parameter-efficient fine-tuning via Hessian-informed subset selection

Parameter-efficient fine-tuning (PEFT) is a highly effective approach for adapting large pre-trained models to downstream tasks with minimal computational overhead. At the core, PEFT methods freeze most parameters and only trains a small subset (say $<0.1\%$ of total parameters). Notably, different PEFT methods select different subsets, resulting in varying levels of performance. This variation prompts a key question: how to effectively select the most influential subset to train? We formulate the subset selection as a multi-task problem: maximizing the performance and minimizing the number of trainable parameters. We leverage a series of transformations -- including $\epsilon$-constraint method and second-order Taylor approximation -- to arrive at the classical 0-1 knapsack problem, which we solve through the lens of Pareto optimality. Consequently, we propose AdaPEFT, a Hessian-informed PEFT that adapts to various tasks and models, in which the selected subset empirically transfers across training horizons and model sizes.