Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.
Figures & tables
Figure 1: Overview of the reward signal generation pipeline
TriviaQA + NQ (ID)
GSM8k (OOD)
Method
ECE (%) ↓
AUROC (%) ↑
Spearman ↑
ECE (%) ↓
AUROC (%) ↑
Base
41.99
51.89
0.03
32.22
53.79
Base+CoT
34.17
66.18
0.17
22.25
62.17
Brier
15.70
83.36
0.52
33.28
66.89
Entropy-based (ours)
7.2
81.53
0.67
3.15
66.73
Table 1: Performance metrics across methods on in-domain (TriviaQA + Natural Questions) and out-of-domain (GSM8k) datasets.
Reliable deployment of large language models (LLMs) requires accurate uncertainty estimation. Existing methods are predominantly answer-first, producing confidence only after generating an answer, which measure the correctness of a specific response and limits practical usability. We study a confidence-first paradigm, where the model outputs its confidence before answering, interpreting this score as the model's probability of answering the question correctly under its current policy. We propose CoCA(Co-optimized Confidence and Answers), a GRPO reinforcement learning framework that jointly optimizes confidence calibration and answer accuracy via segmented credit assignment. By assigning separate rewards and group-relative advantages to confidence and answer segments, CoCA enables stable joint optimization and avoids reward hacking. Experiments across math, code, and factual QA benchmarks show improved calibration and uncertainty discrimination while preserving answer quality, thereby enabling a broader range of downstream applications.
Changcheng Li, Jiancan Wu, Hengheng Zhang +5
University of Science and Technology of China · Huawei Inc.
Large language models are informing decisions with ever-higher stakes. As the consequences of their errors grow, a central question becomes harder to ignore: how much can we trust an individual answer? Yet recognizing when to defer remains difficult because language models can present incorrect conclusions with fluent explanations and an authoritative tone. Uncertainty quantification seeks to address this disconnect by estimating the reliability of individual predictions. However, many existing methods require repeated generations or separately trained components, and their scalar estimates do not reveal where uncertainty arises or how it evolves during reasoning. Recent work has also shown that generation length can be strongly associated with uncertainty estimates and correctness, raising the question of how much of an estimator's predictive power comes from uncertainty-specific information rather than output length alone. Mechanistic interpretability offers a way to address these limitations by connecting human-interpretable concepts to intermediate model states. Building on this capability, we introduce the U-Space, a low-dimensional subspace that makes a model's evolving uncertainty measurable and interpretable. We identify semantic anchors for doubt and certainty, map their unembedding directions back into the residual space, and combine their contrasts into an orthogonal basis. The U-Lens projects each token state onto these basis vectors, yielding an interpretable token-level uncertainty map that can be inspected directly or aggregated into a scalar uncertainty score. Our approach requires no correctness labels, repeated generations, or training. Across reasoning benchmarks, its confidence score outperforms established baselines under both standard and length-controlled evaluation and transfers more reliably than supervised estimators. Code: https://github.com/s2labres/U-Space.
Tobias Braun, Nils Loose, Alexander Herzog +4
Technische Universität Darmstadt · University College London · Universität zu Lübeck +2
Uncertainty Quantification is a large and growing subfield of large language model behavioral analysis. Primarily to recognize and combat hallucination, the field has largely focused on measuring and improving calibration, the accuracy of uncertainty judgments to task efficacy. In this work, we investigate the relatively underexplored question of how similar large language model uncertainty is to human uncertainty. We investigate the presence and strength of human-similar uncertainty signals, deemed uncertainty alignment, in large language model overt behavior and internal activation patterns. We identify whether the models show evidence of simultaneous alignment and calibration on a variety of datasets covering both multiple choice and open ended factual recall. And we characterize the effect of instruct fine-tuning on each of these facets.
Kyle Moore, Jesse Roberts, Daryl Watson +2
1Vanderbilt University · 2Tennessee Technological University