LOFT: Low-Rank Orthogonal Fine-Tuning via Task-Aware Support Selection

arXiv:2605.11872v2 Announce Type: replace Abstract: Orthogonal parameter-efficient fine-tuning (PEFT) adapts pretrained weights through structure-preserving multiplicative transformations, but existing methods often conflate two distinct design choices: the subspace in which adaptation occurs and the transformation applied within that subspace. This paper introduces LOFT, a low-rank orthogonal fine-tuning framework that explicitly separates these two components. By viewing orthogonal adaptation as a multiplicative subspace rotation, LOFT provides a unified formulation that recovers the multiplicative core of representative orthogonal PEFT methods, including coordinate-, butterfly-, Householder- (with a learnable support) and principal-subspace-based variants (up to scaling and relaxation). More importantly, this perspective exposes support selection as a central design axis rather than a byproduct of a particular parameterization. We develop a first-order analysis showing that useful adaptation supports should be informed by the downstream training signal, motivating practical task-aware support selection strategies. Across language understanding, visual transfer, mathematical reasoning, and multilingual out-of-distribution adaptation, LOFT with task-aware supports improves performance at matched trainable-parameter and transform settings under a shared protocol. This suggests that, under a fixed transform and budget, the choice of support affects performance, making systematic support selection an important direction for improving orthogonal PEFT.