| Summary: | 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 strictly 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 prefixtuning can effectively elicit skills present in the pretrained model, they cannot
learn novel tasks that require new attention patterns.
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