Confidence Calibration

Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs are just unsupervised clustering algorithms. We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run $k$ ensembles or stochastic trajectories at $k\times$ compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.

Calibration is commonly evaluated by comparing model confidence with its empirical correctness, implicitly treating reliability as a function of the confidence score alone. However, this view can hide substantial structure: models may be systematically overconfident on some kinds of inputs and underconfident on others, causing global reliability diagnostics to obscure localised calibration failures. To address this, we formulate the problem of discovering hidden miscalibration regimes without assuming access to predefined data slices. We define the corresponding miscalibration field and propose a diagnostic framework for estimating it. Our approach learns a calibration-aware representation of the input space and estimates signed local miscalibration by kernel smoothing in the learned geometry. Across four real-world LLM benchmarks and twelve LLMs, we find that input-dependent calibration heterogeneity is prevalent. We further show that the discovered fields are actionable: they support local confidence correction and reduce calibration error in systematically miscalibrated regions where confidence-based methods such as isotonic regression and temperature scaling are less effective.

The Metacognitive Probe is an exploratory five-task, 15-slot diagnostic that decomposes an LLM's confidence behaviour into five behaviourally-distinct dimensions: confidence calibration (T1-CC), epistemic vigilance (T2-EV), knowledge boundary (T3-KB), calibration range (T4-CR), and reasoning-chain validation (T5-RCV). It is evaluated on N=8 frontier models and N=69 humans. The instrument is motivated by Flavell (1979) and Nelson and Narens (1990) but operates on observable confidence-correctness alignment; it is not a validated cross-species metacognition scale, and the pre-specified human developmental hypothesis was falsified. Composite benchmarks (MMLU, BIG-Bench, HELM, GPQA) ask whether a model produces a correct response. They are silent on whether the model knows when its response is wrong. A model can score 80 on a composite calibration benchmark and still be wildly overconfident in narrow pockets the aggregate cannot surface. The Metacognitive Probe surfaces those pockets. Our headline is a 47-point within-model dissociation in Gemini 2.5 Flash: panel-best within-task calibration (T1-CC = 88; Spearman rho = +0.551, 95% CI [+0.14, +0.80], p = 0.005) and panel-worst cross-task difficulty prediction (T4-CR = 41; sigma_conf = 1.4 across twelve factoids).

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on the choice of martingale updates, and many existing constructions do not exploit prior information about plausible data-generating distributions or mean values. We propose a Bayes-assisted framework that uses a Bayesian working predictive model to adaptively construct confidence sequences. For each candidate mean and time point, the predictive distribution selects, among valid one-step martingale factors, the update maximising predictive expected log-growth; validity is therefore preserved even when the prior or working model is misspecified. We prove that if the predictive distribution is Wasserstein-consistent, the resulting procedure is asymptotically log-optimal, matching the per-sample log-growth of an oracle procedure with access to the true distribution. We instantiate the framework using robust predictives based on Dirichlet-process mixtures and Bayesian exponentially tilted empirical likelihood. Experiments on synthetic data, sequential best-arm identification for LLM evaluation, and prediction-powered inference show that informative priors can substantially reduce confidence-sequence width and sampling effort while retaining anytime-valid coverage.

Large language models are increasingly used as surrogate models for low-data optimization, but their optimizer-facing prediction and its uncertainty remain poorly understood. We study the surrogate belief elicited from an LLM under sparse observations, showing that it depends strongly on prompt text and query protocol. We introduce an uncertainty-alignment criterion that measures whether model uncertainty tracks residual ambiguity among sample-consistent functions. Across controlled inference tasks and Bayesian optimization studies, we find that structural prompts act as effective priors, POINTWISE and JOINT querying induce different beliefs, and sequential evidence leads to non-monotonic, order-sensitive confidence updates. These effects change downstream acquisition decisions and regret, showing that elicitation protocol is part of the LLM surrogate specification, not a formatting detail.

Large Language Model ensembles improve reasoning accuracy, but only up to a performance boundary beyond which additional deliberation degrades accuracy. We introduce DASE (Deliberative Adaptive Stopping Ensemble), a stopping heuristic for iterative ensemble deliberation that commits early on genuine consensus and applies a global-frequency fallback on fragmented evidence. We make three contributions. (1) DASE produces a commit-type routing partition that generalises across benchmarks and is complementary to verbalized single-call confidence. On GPQA-Extended (N=546, 70B ensemble), the partition yields a 39.5 pp routing gap (right-wall 81.1% vs. left-wall 41.5%). On AIME 2010-2023 (N=261, 120B ensemble, 3 seeds), right-wall commits reach 98.3% accuracy vs. left-wall 72.8% (25.5 pp gap), statistically equivalent to Opus 4.6 Standard verbalized confidence at matched coverage (25.7 pp gap; bootstrap p=0.873); the two mechanisms disagree on 37% of routing assignments. (2) Adaptive stopping, not injection bandwidth, drives accuracy. On AIME-300, bandwidth accounts for only 0.3 pp (ns). On GPQA-Extended at the 120B tier, sparse injection ($\approx15$ tokens/worker/round) achieves 70.9% with a 30.7 pp routing gap; dense injection ($\approx600$ chars/worker/round) achieves 72.2% but with halved right-wall coverage and a narrower 18.9 pp gap. (3) Injection-based methods exhibit an inverted-U accuracy-vs-inference trajectory; this pattern is hypothesis-generating.

Protein language models are increasingly used to guide experimental and clinical decisions, yet it is often unclear whether a confident prediction reflects recognition of biological evidence or retrieval of a statistical default. We examine this distinction for a near-universal biological rule, that proteins begin with methionine, by tracing the computational pathway through which ESM2-8M produces this prediction. The model does not detect methionine at the masked position. Instead, it retrieves a methionine-favouring signal from a reference representation at the beginning-of-sequence token via a position-specific query assembled across layers, with the final output emerging through competition with context-dependent circuits. To understand how positional information reaches the readout, we introduce a norm-direction decomposition of attention scores within rotary frequency bands. Positional encoding operates through coupled changes in query norm and angular alignment distributed across these bands. On sequences whose true N-terminus is not methionine, where the biological question matters, the model predicts methionine anyway. This is not a correct prediction produced by an unexpected mechanism, but the output of a positional-prior retrieval circuit that matches the statistical average and fails where biology diverges from it. Distinguishing the two requires resolution at the level of individual circuits, frequency bands, and query composition, suggesting that mechanistic verification will be necessary, and challenging, for predictions where the biological stakes are higher. Even for the simplest biological rule, the model's prediction is mediated by a distributed computational circuit rather than direct recognition, suggesting that increasing task complexity will further obscure the relationship between model confidence and underlying biological evidence.

Incorporating specific knowledge into large language models via retrieval-augmented generation (RAG) is a widespread technique that fuels many of today's industry AI applications. A fundamental problem is to assess if the context retrieved by some similarity search provides indeed supporting facts, or instead misguides the generator with irrelevant information. It is critical to associate meaningful confidence measures about the factuality of the retrieval process with the generated answers. We present a new, two-staged approach to predict fact faithfulness of the output of retrieval-augmented generations. First, we employ conformal prediction to select only those retrieved chunks who have a high chance to come from the correct source. This approach in itself can improve answer quality by up to 6% in some of the studied datasets, however, the associated statistical guarantees do not hold generally, since the assumption of sample exchangeability depends on the retriever setup. We present diagnostic metrics to assess whether a setup is suitable. Second, we quantify confidence in the consistency of a generated final answer with a given retrieved context, using an attention-based factuality classifier. This approach can detect inconsistent answers with a chance of up to 77%. Our work helps to establish a novel type of certified RAG systems for a broad range of natural language industry applications.

Confidence calibration has been dominated by the Expected Calibration Error (ECE), a linear metric that counts calibration offset equally regardless of the confidence level at which it occurs. We show that ECE can remain small even under arbitrarily large overconfidence risk, so we propose Calibrated Size Ratio (CSR) instead, an interpretable metric that equals 1 under perfect calibration, from which we derive the risk probability $P_{\mathrm{risk}}$ that quantifies the statistical evidence for overconfidence. We further argue that overconfidence risk assessment must be complemented by a measure of discriminative value: whether the assigned confidences actively distinguish correct from incorrect predictions. We show that confidence-weighted accuracy $\mathrm{cwA}$ is the natural such complement, and that confidence-weighting extends to all standard classification metrics. In particular, we prove that the confidence-weighted AUC (cwAUC) captures the information about calibration while the classical AUC cannot. We validate the proposed indicators on several synthetic confidence distributions under multiple controlled calibration profiles and find that CSR separates risky from non-risky assignments. We also test the metrics on fifteen real datasets, with and without post-hoc calibration, and find that standard methods can yield risky confidence profiles.

When language models lack relevant knowledge for a given query, they frequently generate plausible responses that can be hallucinations, rather than admitting being agnostic about the answer. Retraining models to reward admitting ignorance can lead to overly conservative behaviors and poor generalization due to scarce evaluation benchmarks. We propose a post hoc framework, Conformal Abstention (CA), adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. Importantly, the abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we improve selective answering significantly with 75 percent conditional correctness.

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

We present MEMRES, an agentic system for Python dependency resolution that introduces a multi-level confidence cascade where the LLM serves as the last resort. Our system combines: (1) a Self-Evolving Memory that accumulates reusable resolution patterns via tips and shortcuts; (2) an Error Pattern Knowledge Base with 200+ curated import-to-package mappings; (3) a Semantic Import Analyzer; and (4) a Python 2 heuristic detector resolving the largest failure category. On HG2.9K using Gemma-2 9B (10 GB VRAM). MEMRES resolves 2503 of 2890 (86.6%, 10-run average) snippets, combining intra-session memory with our confidence cascade for the remainder. This already exceeds PLLM's 54.7% overall success rate by a wide margin.

A robust decision-making process must take into account uncertainty, especially when the choice involves inherent risks. Because artificial intelligence (AI) systems are increasingly integrated into decision-making workflows, managing uncertainty relies more and more on the metacognitive capabilities of these systems; i.e, their ability to assess the reliability of and regulate their own decisions. Hence, it is crucial to employ robust methods to measure the metacognitive abilities of AI. This paper is primarily a methodological contribution arguing for the adoption of the meta-d' framework as the gold standard for assessing the metacognitive sensitivity of AIs--the ability to generate confidence ratings that distinguish correct from incorrect responses. Moreover, we propose to leverage signal detection theory (SDT) to measure the ability of AIs to spontaneously regulate their decisions based on uncertainty and risk. To demonstrate the practical utility of these psychophysical frameworks, we conduct two series of experiments on three large language models (LLMs)--GPT-5, DeepSeek-V3.2-Exp, and Mistral-Medium-2508.

Predictive confidence serves as a foundational control signal in mission-critical systems, directly governing risk-aware logic such as escalation, abstention, and conservative fallback. While prior federated learning attacks predominantly target accuracy or implant backdoors, we identify confidence calibration as a distinct attack objective. We present the Temperature Scaling Attack (TSA), a training-time attack that degrades calibration while preserving accuracy. By injecting temperature scaling with learning rate-temperature coupling during local training, TSA shifts model confidence while keeping predictive accuracy and common optimization signals close to benign training. We provide a convergence analysis under non-IID settings, showing that the coupling controls the primary update scale while leaving a bounded temperature-induced residual, yielding the standard non-convex FL convergence structure with an additional residual term. Across three benchmarks, TSA substantially shifts calibration (e.g., 145% error increase on CIFAR-100) with <2% accuracy change, and remains effective under robust aggregation and post-hoc calibration defenses. Case studies further show up to a 7.2x increase in missed verifications in healthcare and severe confidence-gating failures in autonomous driving, even when accuracy is unchanged. Overall, our results establish calibration integrity as a critical attack surface in federated learning.

Confidence calibration, the alignment of a model's predicted confidence with its actual accuracy, is crucial for the reliable deployment of Large Language Models (LLMs). However, this critical property remains largely under-explored in multilingual contexts. In this work, we conduct the first large-scale, systematic studies of multilingual calibration across six model families and over 100 languages, revealing that non-English languages suffer from systematically worse calibration. To diagnose this, we investigate the model's internal representations and find that the final layer, biased by English-centric training, provides a poor signal for multilingual confidence. In contrast, our layer-wise analysis uncovers a key insight that late-intermediate layers consistently offer a more reliable and better-calibrated signal. Building on this, we introduce a suite of training-free methods, including Language-Aware Confidence Ensemble (LACE), which adaptively selects an optimal ensemble of layers for each specific language. Our study highlights the hidden costs of English-centric alignment and offer a new path toward building more globally equitable and trustworthy LLMs by looking beyond the final layer.

Test-time strategies have shown remarkable success in improving large language models, but their application to next-token prediction (NTP) autoregressive (AR) image generation remains largely underexplored. Existing test-time scaling (TTS) methods for visual autoregressive models (VAR) rely on frequent partial decoding and external reward models, which are inefficient and often ineffective for NTP-based image generation due to the inherent instability of intermediate decoding results. To address these limitations, we propose ScalingAR, a novel test-time scaling framework tailored for NTP-based AR image generation. ScalingAR introduces token entropy as a confidence signal and operates at two complementary levels: (i) Profile Level, integrates intrinsic uncertainty and conditional utilization into a unified confidence state, and (ii) Policy Level, leverages this state for adaptive trajectory pruning and dynamic guidance scheduling. Without requiring early decoding or auxiliary rewards, ScalingAR achieves significant improvements across diverse benchmarks. Experiments show that ScalingAR (I) improves base models by $12.5\%$ on GenEval and $15.2\%$ on TIIF-Bench, (II) reduces visual token consumption by $62.0\%$ while outperforming baselines, and (III) enhances robustness, mitigating performance degradation by $26.0\%$ in challenging scenarios. These results establish ScalingAR as a robust and efficient test-time scaling solution for autoregressive image generation.

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Verbalized confidence, in which LLMs report a numerical certainty score, is widely used to estimate uncertainty in black-box settings, yet the confidence scale itself (typically 0--100) is rarely examined. We show that this design choice is not neutral. Across six LLMs and three datasets, verbalized confidence is heavily discretized, with more than 78% of responses concentrating on just three round-number values. To investigate this phenomenon, we systematically manipulate confidence scales along three dimensions: granularity, boundary placement, and range regularity, and evaluate metacognitive sensitivity using $meta\text{-}d'$. We find that a 0--20 scale consistently improves metacognitive efficiency over the standard 0--100 format, while boundary compression degrades performance and round-number preferences persist even under irregular ranges. These results demonstrate that confidence scale design directly affects the quality of verbalized uncertainty and should be treated as a first-class experimental variable in LLM evaluation.