With the prevalence of pre-trained language models (PLMs) and the pre-training-fine-tuning paradigm, it has been continuously shown that larger models tend to yield better performance. However, as PLMs scale up, fine-tuning and storing all the parameters is prohibitively costly and eventually becomes practically infeasible. This necessitates a new branch of research focusing on the parameter-efficient adaptation of PLMs, which optimizes a small portion of the model parameters while keeping the rest fixed, drastically cutting down computation and storage costs. In general, it demonstrates that large-scale models could be effectively stimulated by the optimization of a few parameters. Despite the various designs, here we discuss and analyse the approaches under a more consistent and accessible term 'delta-tuning', where 'delta' a mathematical notation often used to denote changes, is borrowed to refer to the portion of parameters that are 'changed' during training. We formally describe the problem and propose a unified categorization criterion for existing delta-tuning methods to explore their correlations and differences. We also discuss the theoretical principles underlying the effectiveness of delta-tuning and interpret them from the perspectives of optimization and optimal control. Furthermore, we provide a holistic empirical study on over 100 natural language processing tasks and investigate various aspects of delta-tuning. With comprehensive study and analysis, our research demonstrates the theoretical and practical properties of delta-tuning in the adaptation of PLMs. Training a deep neural network can be costly but training time is reduced when a pre-trained network can be adapted to different use cases. Ideally, only a small number of parameters needs to be changed in this process of fine-tuning, which can then be more easily distributed. In this Analysis, different methods of fine-tuning with only a small number of parameters are compared on a large set of natural language processing tasks.
