An Asymptotic Theory of Chain-of-Thought in In-Context Learning

Chain-of-Thought (CoT) reasoning has become a foundation for eliciting multi-step reasoning in large language models, but recent studies show that its benefits do not scale monotonically with chain length: while longer CoT generally enables a model to tackle harder problems, on a given problem, accuracy typically increases with CoT length up to a point, after which it declines. We identify a major cause of this phenomenon: as the CoT grows, the model's attention to critical insights produced earlier in the trace gradually weakens, making those insights progressively less accessible when they are most needed. Therefore, we propose \textbf{InsightReplay}, a stateful reasoning approach in which the model periodically extracts critical insights from its reasoning trace and replays them near the active generation frontier, keeping them accessible as the reasoning scales. Extensive experiments on a $\mathbf{2}\!\times\!\mathbf{3}\!\times\!\mathbf{4}$ benchmark grid, covering model scales $\{\text{8B}, \text{30B}\}$, model families $\{\text{Qwen3.5}, \text{DeepSeek-R1-Distill-Qwen}, \text{Gemma-4}\}$, and reasoning benchmarks $\{\text{AIME}, \text{HMMT}, \text{GPQA Diamond}, \text{LiveCodeBench v5}\}$, show that 3-round InsightReplay yields accuracy gains across \textbf{all 24 settings}, with an averaged improvement of $\mathbf{+1.65}$ points over standard CoT, and a largest single-setting gain of $\mathbf{+9.2}$ points on R1-Distill-32B's LiveCodeBench v5 subset. Our results suggest that the effectiveness of test-time scaling depends not only on how much a model reasons, but also on whether critical intermediate insights remain accessible throughout long reasoning trajectories.

In-context reinforcement learning (ICRL) refers to the ability of RL agents to adapt to new tasks at inference time without parameter updates by conditioning on additional context. Recent empirical studies further demonstrate that Chain-of-Thought (CoT) generation can amplify this ICRL capability. This paper is the first to provide a theoretical understanding on how CoT interacts with ICRL. We conduct our analysis in a policy evaluation setup with linear Transformer. We prove that with specific Transformer parameters, the CoT generation process is equivalent to repeatedly executing temporal difference learning updates. Additionally, we provide finite sample convergence analysis showing that the policy evaluation error decreases geometrically with CoT length and eventually saturates at a statistical floor determined by the context length. We also prove that the desired Transformer parameters are a global minimizer of the pretraining loss, providing a theoretical understanding on the empirical emergence of those parameters.

Chain-of-thought (CoT) reasoning is the dominant paradigm for inference-time scaling in language models, yet the causal influence of individual steps on the final answer poorly understood. We estimate each step's causal importance via early exit and use this measure to study how answers form across the reasoning traces of several model families. Across diverse tasks, we find that reasoning typically crosses a \emph{commitment boundary} -- a sharp transition from transient intermediate guesses to a stable, high-confidence answer. This transition often happens in a single step, well before the model's reasoning block ends, and is followed by \emph{epiphenomenal} CoT steps that leave the final answer probability unaltered. Using attention probes, we show that answer-formation stages can be linearly decoded from intermediate reasoning steps with high accuracy and generalize robustly to unseen reasoning tasks. We exploit this signal to early-exit reasoning blocks at the commitment boundary, reducing the length of CoTs up to 55% on average with negligible impact on model performance.