  Large Language Models (LLMs) can improve their responses when instructed to
do so, a capability known as self-correction. When these instructions lack
specific details about the issues in the response, this is referred to as
leveraging the intrinsic self-correction capability. The empirical success of
self-correction can be found in various applications, e.g., text detoxification
and social bias mitigation. However, leveraging this self-correction capability
may not always be effective, as it has the potential to revise an initially
correct response into an incorrect one. In this paper, we endeavor to
understand how and why leveraging the self-correction capability is effective.
We identify that appropriate instructions can guide LLMs to a convergence
state, wherein additional self-correction steps do not yield further
performance improvements. We empirically demonstrate that model uncertainty and
activated latent concepts jointly characterize the effectiveness of
self-correction. Furthermore, we provide a mathematical formulation indicating
that the activated latent concept drives the convergence of the model
uncertainty and self-correction performance. Our analysis can also be
generalized to the self-correction behaviors observed in Vision-Language Models
(VLMs). Moreover, we highlight that task-agnostic debiasing can benefit from
our principle in terms of selecting effective fine-tuning samples. Such initial
success demonstrates the potential extensibility for better instruction tuning
and safety alignment.
