How Do Answer Tokens Read Reasoning Traces? Self-Reading Patterns in Thinking LLMs for Quantitative Reasoning

Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal "overthinking," leading to performance degradation. In this work, we quantify inference-time effort by identifying deep-thinking tokens -- tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that deep-thinking ratio (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@n, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@n matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.

Test-time reasoning has become a significant field of study since the introduction of chain-of-thought reasoning in large language models (LLMs). However, the mechanisms of this reasoning process are still under-explored -- from the same input prompt, and even the same partial solution, LLMs can produce varied answers if sampled multiple times. We propose to leverage question-asking as an inference-time intervention that articulates information about the model's hidden state. To achieve that, we present a student-teacher setting where a student asks questions to a teacher. We train a probe on the student's hidden state before and after asking a question and find it is predictive of the trajectory's final correctness, even before generating the teacher's answer. This suggests there is a meaningful signal from the self-diagnosis that occurs during question generation rather than information transfer from the teacher. We then frame question-asking as a sequential decision problem, using this probe as a quality score, and define a gating policy to ask questions that maximize likelihood of correctness. We find that the success of question-asking as an intervention is largely dependent on the model's self-consistency. Our empirical results show a gap between detection and recovery; while our gating policy captures model correctness and uncertainty, interventions are equally likely to harm correct trajectories as they are to recover incorrect ones. This gap between diagnosis and correction has broader implications on language models' capacity for self-refinement under uncertainty.

Strong reasoning depends not only on model knowledge but also on how effectively cognitive behaviors are deployed during generation. Existing methods often rely on explicit behavior-level control, making them insufficiently adaptive when failures and required corrections vary across reasoning states, tasks, and models. To this end, we propose Latent Reward Steering (LRS), an adaptive inference-time framework that promotes cognitive behaviors by optimizing the sparse-autoencoder (SAE) latent states that implicitly carry them. Rather than relying on predefined cognitive behaviors or steering directions derived from them, LRS trains a latent reward model on reasoning traces by final answer correctness to estimate the quality of intermediate latent states. During inference, reward gradients provide state-specific correction directions for fragile latent states, while a reward and confidence gate restricts intervention to states the reward signal flags as fragile. Experiments on multiple reasoning LLM backbones and benchmarks show that \ours consistently improves performance over various baselines, and post-hoc analyses further indicate that \ours implicitly promotes good cognitive behaviors that fix the original reasoning errors. Code is available at: https://github.com/jiakanglee/Latent-Reward-Steering.