  With the increasingly powerful performances and enormous scales of pretrained
models, promoting parameter efficiency in fine-tuning has become a crucial need
for effective and efficient adaptation to various downstream tasks. One
representative line of fine-tuning methods is Orthogonal Fine-tuning (OFT),
which rigorously preserves the angular distances within the parameter space to
preserve the pretrained knowledge. Despite the empirical effectiveness, OFT
still suffers low parameter efficiency at $\mathcal{O}(d^2)$ and limited
capability of downstream adaptation. Inspired by Givens rotation, in this
paper, we proposed quasi-Givens Orthogonal Fine-Tuning (qGOFT) to address the
problems. We first use $\mathcal{O}(d)$ Givens rotations to accomplish
arbitrary orthogonal transformation in $SO(d)$ with provable equivalence,
reducing parameter complexity from $\mathcal{O}(d^2)$ to $\mathcal{O}(d)$. Then
we introduce flexible norm and relative angular adjustments under soft
orthogonality regularization to enhance the adaptation capability of downstream
semantic deviations. Extensive experiments on various tasks and pretrained
models validate the effectiveness of our methods.
