Different Tunes Played with Equal Skill: Exploring a Unified Optimization Subspace for Delta Tuning

Delta tuning (DET, also known as parameter-efficient tuning) is deemed as the new paradigm for using pre-trained language models (PLMs). Up to now, various DETs with distinct design elements have been proposed, achieving performance on par with fine-tuning. However, the mechanisms behind the above success are still under-explored, especially the connections among various DETs. To fathom the mystery, we hypothesize that the adaptations of different DETs could all be reparameterized as low-dimensional optimizations in a unified optimization subspace, which could be found by jointly decomposing independent solutions of different DETs. Then we explore the connections among different DETs by conducting optimization within the subspace. In experiments, we find that, for a certain DET, conducting optimization simply in the subspace could achieve comparable performance to its original space, and the found solution in the subspace could be transferred to another DET and achieve non-trivial performance. We also visualize the performance landscape of the subspace and find that there exists a substantial region where different DETs all perform well. Finally, we extend our analysis and show the strong connections between fine-tuning and DETs.