  Prefix-tuning, or more generally continuous prompt tuning, has become an
essential paradigm of parameter-efficient transfer learning. Using a large
pre-trained language model (PLM), prefix-tuning can obtain strong performance
by training only a small portion of parameters. In this paper, we propose to
understand and further develop prefix-tuning through the kernel lens.
Specifically, we make an analogy between \textit{prefixes} and \textit{inducing
variables} in kernel methods and hypothesize that \textit{prefixes} serving as
\textit{inducing variables} would improve their overall mechanism. From the
kernel estimator perspective, we suggest a new variant of prefix-tuning --
\textit{inducer-tuning}, which shares the exact mechanism as prefix-tuning
while leveraging the residual form found in adapter-tuning. This mitigates the
initialization issue in prefix-tuning. Through comprehensive empirical
experiments on natural language understanding and generation tasks, we
demonstrate that inducer-tuning can close the performance gap between
prefix-tuning and fine-tuning.
