An Explanation of Intrinsic Self-Correction via Linear Representations and Latent Concepts

We provide an explanation for the performance gains of intrinsic self-correction, a process where a language model iteratively refines its outputs without external feedback. More precisely, we investigate how prompting induces interpretable changes in hidden states and thus affects the output distributions. We hypothesize that each prompt-induced shift lies in a linear span of some linear representation vectors, naturally separating tokens based on individual concept alignment. Building around this idea, we give a mathematical formulation of self-correction and derive a concentration result for output tokens based on alignment magnitudes. Our experiments on text detoxification with zephyr-7b-sft reveal a substantial gap in the inner products of the prompt-induced shifts and the unembeddings of the top-100 most toxic tokens vs. those of the unembeddings of the bottom-100 least toxic tokens, under toxic instructions. This suggests that self-correction prompts enhance a language model's capability of latent concept recognition. Our analysis offers insights into the underlying mechanism of self-correction by characterizing how prompting works explainably. For reproducibility, our code is available.

RL-STaR: Theoretical Analysis of Reinforcement Learning Frameworks for Self-Taught Reasoner

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks in a stepwise manner. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (2) conditions for convergence to an optimal reasoning policy; (3) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps; and (4) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement. This framework aims to bridge empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.