  Large language models (LLMs) are expected to respond accurately but often
exhibit deficient reasoning or generate hallucinatory content. To address
these, studies prefixed with ``Self-'' such as Self-Consistency, Self-Improve,
and Self-Refine have been initiated. They share a commonality: involving LLMs
evaluating and updating itself to mitigate the issues. Nonetheless, these
efforts lack a unified perspective on summarization, as existing surveys
predominantly focus on categorization without examining the motivations behind
these works.
  In this paper, we summarize a theoretical framework, termed Internal
Consistency, which offers unified explanations for phenomena such as the lack
of reasoning and the presence of hallucinations. Internal Consistency assesses
the coherence among LLMs' latent layer, decoding layer, and response layer
based on sampling methodologies. Expanding upon the Internal Consistency
framework, we introduce a streamlined yet effective theoretical framework
capable of mining Internal Consistency, named Self-Feedback. The Self-Feedback
framework consists of two modules: Self-Evaluation and Self-Update. This
framework has been employed in numerous studies.
  We systematically classify these studies by tasks and lines of work;
summarize relevant evaluation methods and benchmarks; and delve into the
concern, ``Does Self-Feedback Really Work?'' We propose several critical
viewpoints, including the ``Hourglass Evolution of Internal Consistency'',
``Consistency Is (Almost) Correctness'' hypothesis, and ``The Paradox of Latent
and Explicit Reasoning''. Furthermore, we outline promising directions for
future research. We have open-sourced the experimental code, reference list,
and statistical data, available at
\url{https://github.com/IAAR-Shanghai/ICSFSurvey}.
