  Going beyond mimicking limited human experiences, recent studies show initial
evidence that, like humans, large language models (LLMs) are capable of
improving their abilities purely by self-correction, i.e., correcting previous
responses through self-examination, in certain circumstances. Nevertheless,
little is known about how such capabilities arise. In this work, based on a
simplified setup akin to an alignment task, we theoretically analyze
self-correction from an in-context learning perspective, showing that when LLMs
give relatively accurate self-examinations as rewards, they are capable of
refining responses in an in-context way. Notably, going beyond previous
theories on over-simplified linear transformers, our theoretical construction
underpins the roles of several key designs of realistic transformers for
self-correction: softmax attention, multi-head attention, and the MLP block. We
validate these findings extensively on synthetic datasets. Inspired by these
findings, we also illustrate novel applications of self-correction, such as
defending against LLM jailbreaks, where a simple self-correction step does make
a large difference. We believe that these findings will inspire further
research on understanding, exploiting, and enhancing self-correction for
building better foundation models.
