  Context-based fine-tuning methods, including prompting, in-context learning,
soft prompting (also known as prompt tuning), and prefix-tuning, have gained
popularity due to their ability to often match the performance of full
fine-tuning with a fraction of the parameters. Despite their empirical
successes, there is little theoretical understanding of how these techniques
influence the internal computation of the model and their expressiveness
limitations. We show that despite the continuous embedding space being more
expressive than the discrete token space, soft-prompting and prefix-tuning are
potentially less expressive than full fine-tuning, even with the same number of
learnable parameters. Concretely, context-based fine-tuning cannot change the
relative attention pattern over the content and can only bias the outputs of an
attention layer in a fixed direction. This suggests that while techniques like
prompting, in-context learning, soft prompting, and prefix-tuning can
effectively elicit skills present in the pretrained model, they may not be able
to learn novel tasks that require new attention patterns.
