Understanding Reasoning in LLMs through Strategic Information Allocation under Uncertainty

Large language models (LLMs) often produce confident yet incorrect answers, which can lead to risky failures in real-world applications. We study whether post-training can make a model's self-assessment explicit: when the model is uncertain, can it be trained to signal so within its own response? A central design question is where in the response this signal should be exposed -- during reasoning, while the answer is still being formed, or at the end, once the answer has been produced. We study both. For end-of-reasoning self-assessment, we train the model to verbalize a confidence score for its response, with the aim of high confidence on correct answers and low confidence on incorrect ones. For during-reasoning self-assessment, we train the model to emit the marker <uncertain> whenever its current reasoning state appears unreliable. Across factual reasoning tasks, both forms sharply reduce overconfident errors while improving answer quality, and both can be used as triggers for retrieval augmented generation (RAG) to improve the final response. We further analyze their internal mechanisms: end-of-reasoning verbalized confidence sharpens a confidence-related structure already present in the pretrained model, whereas during-reasoning <uncertain> emission teaches the model to mark high-risk reasoning steps, with parameter changes concentrated in the model's late layers.

Large Language Models (LLMs) have achieved significant breakthroughs across various domains, but they can still produce unreliable or misleading outputs. For responsible LLM applications, uncertainty quantification techniques are used to estimate a model's uncertainty about its outputs, indicating the likelihood that those outputs may be problematic. For LLM reasoning tasks, it is essential to estimate uncertainty not only in the final answer but also in the intermediate reasoning process, particularly to identify where uncertainty arises. Such information may enable more fine-grained and targeted interventions during inference. In this study, we investigate which metrics can effectively localize uncertain places within an LLM reasoning trajectory. Our study reveals that uncertain intermediate continuations are more likely to occur at tokens that are highly sensitive to perturbations in the embeddings of preceding tokens. In our experiments, we show that such perturbation-based metrics achieve stronger performance in localizing uncertain intermediate steps than baseline methods, including probability-based, sampling-based, and Bayesian-based approaches. Meanwhile, our proposed metrics also enjoy good simplicity and efficiency.

Large Language Models (LLMs) achieve strong performance through extended inference-time deliberation, yet how their reasoning failures arise remains poorly understood. By analyzing model-generated reasoning trajectories, we find that errors are not uniformly distributed but often originate from a small number of early transition points, after which reasoning remains locally coherent but globally incorrect. These transitions coincide with localized spikes in token-level entropy, and alternative continuations from the same intermediate state can still lead to correct solutions. Based on these observations, we introduce GUARD, a targeted inference-time framework that probes and redirects critical transitions using uncertainty signals. Empirical evaluations across multiple benchmarks confirm that interventions guided by these failure dynamics lead to more reliable reasoning outcomes. Our findings highlight the importance of understanding when and how reasoning first deviates, complementing existing approaches that focus on scaling inference-time computation.