Daily Papers

Audio decisions often depend on evidence that a transcript does not preserve, while their probability estimates can depend on how answer options are ordered. AudioJev maps a waveform, question and supplied alternatives directly to a candidate distribution through one shared full-parameter model. We define order calibration as preserving an answer's probability under meaning-preserving option permutations. Random-derangement SKL training pairs each question with a reordered view in which every alternative changes position, supervises both answers, and aligns the two distributions before applying a symmetric KL penalty. Inference retains a single candidate-scoring forward, with no calibration head or order ensemble. Across three training seeds, AudioJev reaches 68.88%/55.33% mean accuracy on complete MMAU/MMAR and reduces random-order SKL by 43.8%/60.5% relative to the single-view removal ablation. The same model handles intent, environmental sound, note properties, speech activity and conversational transitions. Paired removal ablations and multi-order evaluation measure predictive accuracy and probability stability together, establishing a direct audio interface whose calibration objective acts on candidate meaning rather than presentation position. Inference code and model weights are available at https://github.com/SihanLv/AudioJev-Inference and https://huggingface.co/shlv/AudioJev.

Detecting content that contradicts or is unsupported by a given source text is a critical challenge for the safe deployment of generative language models. We introduce HALT-RAG, a post-hoc verification system designed to identify hallucinations in the outputs of Retrieval-Augmented Generation (RAG) pipelines. Our flexible and task-adaptable framework uses a universal feature set derived from an ensemble of two frozen, off-the-shelf Natural Language Inference (NLI) models and lightweight lexical signals. These features are used to train a simple, calibrated, and task-adapted meta-classifier. Using a rigorous 5-fold out-of-fold (OOF) training protocol to prevent data leakage and produce unbiased estimates, we evaluate our system on the HaluEval benchmark. By pairing our universal feature set with a lightweight, task-adapted classifier and a precision-constrained decision policy, HALT-RAG achieves strong OOF F1-scores of 0.7756, 0.9786, and 0.7391 on the summarization, QA, and dialogue tasks, respectively. The system's well-calibrated probabilities enable a practical abstention mechanism, providing a reliable tool for balancing model performance with safety requirements.

Quantifying the uncertainty of predictions made by large language models (LLMs) in binary text classification tasks remains a challenge. Calibration, in the context of LLMs, refers to the alignment between the model's predicted probabilities and the actual correctness of its predictions. A well-calibrated model should produce probabilities that accurately reflect the likelihood of its predictions being correct. We propose a novel approach that utilizes the inductive Venn--Abers predictor (IVAP) to calibrate the probabilities associated with the output tokens corresponding to the binary labels. Our experiments on the BoolQ dataset using the Llama 2 model demonstrate that IVAP consistently outperforms the commonly used temperature scaling method for various label token choices, achieving well-calibrated probabilities while maintaining high predictive quality. Our findings contribute to the understanding of calibration techniques for LLMs and provide a practical solution for obtaining reliable uncertainty estimates in binary question answering tasks, enhancing the interpretability and trustworthiness of LLM predictions.

Probability-only models, which TypeSafe calls System One models, return calibrated probabilities for fixed choices in milliseconds and generate no text. We study one such model, Jev, through two tasks that require decisions under tight constraints. In bullet chess, a bot that places Jev's judgment inside Stockfish search alongside an opening book and endgame tablebases climbs above a 2200 Lichess bullet rating against other bots. Live model calls are too slow for search, so we distill pairwise judgments into a compact evaluator that runs at every position. We then ask how best to spend a fixed labeling budget when an LLM, Qwen3-32B, is available as a second teacher. In chess, averaging both judges' labels beats spending the whole budget on Qwen alone by 9.6 Elo (95% interval 4.3 to 14.9), and the gain replicates on fresh openings; a second answer from the same judge is no substitute, and Jev is the strongest partner for Qwen among the models tested. In passage reranking, Jev's labels alone train a reranker that scores as high as Qwen's, from 21 minutes of API calls instead of 5.1 GPU-hours, and adding Qwen gains at most a few thousandths in ranking quality. Search supplies the lookahead, distillation makes the judgment cheap enough to use at every position, and an LLM partner pays off in chess.

Detecting hallucinations in Large Vision-Language Models (LVLMs) requires both accurate span localization and well-calibrated confidence scores. Fine-tuned generative VLMs excel at identifying hallucinated text spans but suffer from overconfidence and high inference latency. Discriminative sequence taggers offer deterministic speed and superior calibration but exhibit conservative span recall. We present SpanCalib-VLM, a hybrid dual-system for the SHROOM-Visions Shared Task that combines a multimodal sequence tagger, consisting of XLM-RoBERTa-Large fused with a SigLIP vision encoder via cross-attention, with our fine-tuned generative VLM (Qwen3.5-4B-SHROOM-SFT). Through a Union-Calibrated Fusion strategy, candidate spans from the generative model are re-scored with calibrated probabilities from the sequence tagger. On the SHROOM-Visions English evaluation split, our ensemble achieves a Pearson calibration correlation of 0.41 and an overall IoU of 0.39, with a clean-response IoU of 0.91} and overall detection accuracy of 70.7%. We make our model weights and code publicly available.

Detectors of alignment failures screen deployed language models and score alignment benchmarks. Most are generative judges that spend a decoding pass on every criterion, and classifiers that read token probabilities, such as Llama Guard, still score one fixed label per call. Jev, a model trained with reinforcement learning for calibrated decisions (RLCD), answers many typed questions about one input with calibrated probabilities in a single call. Whether it detects alignment failures has not been measured. We present RLCDAlignBench, which benchmarks Jev on ten alignment failures: sycophancy, jailbreaks, deception, prompt injection, hallucination, privacy violation, social bias, reward hacking, concealing uncertainty, and power seeking. It spans 44 benchmarks and five target models, labelled by each benchmark's scorer and, on two, by humans. Many of these failures are relational, defined against a reference, such as the user's belief or an injected instruction, that the response alone does not reveal. Our key idea is therefore to vary what Jev is asked separately from what it sees: the question's wording and answer type on one side, the fields of the input on the other. A single generic question reaches a median AUROC of 0.886 zero-shot and beats supervised baselines on most benchmarks. Question wording matters little, while context matters more, mostly through fields that encode the label. Jev matches the reference scorer's agreement with human labels, surfaces label defects in existing benchmarks, and costs 63x less than LLM-judge scorers. Code and data: https://github.com/sumleo/RLCDAlignBench.

Pancreatic ductal adenocarcinoma (PDAC) segmentation on contrast-enhanced CT is inherently ambiguous: inter-rater disagreement among experts reflects genuine uncertainty rather than annotation noise. Standard deep learning approaches assume a single ground truth, producing probabilistic outputs that can be poorly calibrated and difficult to interpret under such ambiguity. We present TwinTrack, a framework that addresses this gap through post-hoc calibration of ensemble segmentation probabilities to the empirical mean human response (MHR) -the fraction of expert annotators labeling a voxel as tumor. Calibrated probabilities are thus directly interpretable as the expected proportion of annotators assigning the tumor label, explicitly modeling inter-rater disagreement. The proposed post-hoc calibration procedure is simple and requires only a small multi-rater calibration set. It consistently improves calibration metrics over standard approaches when evaluated on the MICCAI 2025 CURVAS-PDACVI multi-rater benchmark.

AlphaFold confidence scores are widely used to rank protein complex predictions and to select subsets of models for downstream applications. Although these scores provide strong discriminatory power for distinguishing prediction quality, their numerical values were never intended to represent the probability that a prediction satisfies a given structural quality criterion. In this work, we calibrate commonly used confidence scores to estimate the probability that a predicted complex exceeds a chosen threshold of DockQ, an established measure of interface quality. On antibody-antigen and general multimer datasets, post-hoc isotonic calibration consistently improves agreement between predicted probabilities and observed DockQ success rates while preserving the underlying score ordering. The calibrated probabilities also provide more accurate estimates of the fraction of selected models expected to pass a given structural quality threshold. Although the mapping is fitted within a given prediction distribution and therefore transfers imperfectly across prediction domains, we show that reliable estimates are recovered from a small number of labeled target-domain samples. Because the calibration is entirely post hoc and requires no underlying AlphaFold model fine-tuning, it provides a straightforward and customizable way to convert existing model quality rankings into calibrated probabilities of passing a chosen structural quality threshold.

Software that hands branching decisions to a model needs a declared option and a probability it can threshold. Typed decision models, also called System One models, return such probabilities without generating text, while supervised classifiers and generative language models are the established alternatives. One harness sends eight decision-model checkpoints from six families, including the hosted model Jev, and four open generative models from three developers the same semantic requests, and scores trained and zero-shot classifiers on the same workflow, intent, emotion and social-science items. With task labels, a fine-tuned DeBERTa-v3-large has the highest observed accuracy on every labeled benchmark but one. Without labels, no decision model is significantly more accurate than Jev on workflows or intents, but Gemma-4-31B matches it on workflows and exceeds it on CLINC-150 at higher cost and latency. Stated probabilities of generative models become unreadable when replies miss the key format, whereas key likelihoods avoid this but can saturate. A guaranteed 5 percent risk leaves Jev 0.528 of the intent decisions, and an in-scope threshold still accepts 0.310 of out-of-scope requests. On typed-decisions, swapping yes and no flips 50.5 answers per hundred for Jev and at least 16.8 for every generative model tested, against at most 6.5 for four fine-tuned decision checkpoints. Exposure to a benchmark's training data explains the largest lead of an open checkpoint, which vanishes on rater-labeled emotions. An intent-trained first stage escalating to Gemma-4-31B reaches that model's accuracy at about Jev's price. The results yield condition-dependent design rules for automated decision gates.

System One models output calibrated probabilities over typed answers such as categorical choices, ordinal levels, or binary outcomes, via a non-generative interface. Software can act on these probabilities through thresholds, cost-weighted choices, and escalation rules. Consequently, if these probabilities are miscalibrated or wording-sensitive, the software ma take unintended actions leaving human operators with no textual rationale to inspect. Current evaluations largely report accuracy and calibration on public classification datasets without a clear reference. We present TypedBench, a benchmark for typed decision models like Jev built from seven policy-labelled generators and nine evaluation suites. We report accuracy as median and range across paraphrases, and calibration error relative to the finite-sample noise floor of a matched, perfectly calibrated predictor. We assess probability quality through selective prediction, ordinal proper scoring rules, and realised cost under asymmetric cost matrices. We evaluate a hosted model, an open encoder, and a family of open decoders spanning 0.8B-9B parameters on identical items. The hosted model follows the stated policy but is wording-sensitive and systematically underconfident; under asymmetric costs, using its probabilities can be worse than taking its top answer. Decoders route exactly and are slow as options or questions are added. The decoder is least accurate on policy questions and degrades with more options. Overall, typed decision models must be evaluated jointly on policy adherence, wording robustness, probability quality, and induced decision outcomes.

Vision-language models used for decisions in histopathology rarely return calibrated probabilities over the candidates a user cares about. Decision-native models write a question and a candidate set chosen at run time into the input and return a normalised distribution from a small decision head in one forward pass. We build PathJev-P, a decision-native model for histopathology: MedGemma-1.5-4B with LoRA adapters and a decision head, trained on 40,000 patch states from three public collections whose expert labels are turned into typed questions with organ-specific candidate sets and a "none of these" option. In a comparison over 3 seeds with an analysis plan fixed before testing, on test sets without documented overlap with the training data of the backbone, PathJev-P is more accurate than a generative model trained with the same backbone, data and selection rule, the zero-shot pathology model CONCH and a general medical decision model (balanced accuracy 0.541 against 0.492, 0.345 and 0.213); its advantage over the generative model comes from two organs absent from training. The calibration advantage depends on how the generative model's probabilities are read out. With the summed candidate log-likelihood used in previous work, PathJev-P has the lower calibration error (ECE 0.204 against 0.279); with a length-normalised read-out of the same generative model, examined post hoc, the two have similar mean calibration error (0.201) and the generative model is better calibrated on the unseen organs, where PathJev-P remains over-confident. A supervised linear probe on a pathology foundation model is better calibrated in every setting. In a qualitative whole-slide demonstration, PathJev-P labels unsupervised tissue clusters with abstention and separates carcinoma from other tissue while running the model on a fraction of the tiles.

Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of well-calibrated probabilities from modern classification models. We propose a novel conformal prediction method that employs a rank-based score function suitable for classification models that predict the order of labels correctly, even if not well-calibrated. Our approach constructs prediction sets that achieve the desired coverage rate while managing their size. We provide a theoretical analysis of the expected size of the conformal prediction sets based on the rank distribution of the underlying classifier. Through extensive experiments, we demonstrate that our method outperforms existing techniques on various datasets, providing reliable uncertainty quantification. Our contributions include a novel conformal prediction method, theoretical analysis, and empirical evaluation. This work advances the practical deployment of machine learning systems by enabling reliable uncertainty quantification.

Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating miscalibration, particularly through post-hoc recalibration methods that aim to obtain calibrated probabilities without sacrificing the classification performance of pre-trained models. In this study, we summarize and categorize previous works into three general strategies: intuitively designed methods, binning-based methods, and methods based on formulations of ideal calibration. Through theoretical and practical analysis, we highlight ten common limitations in previous approaches. To address these limitations, we propose a probabilistic learning framework for calibration called h-calibration, which theoretically constructs an equivalent learning formulation for canonical calibration with boundedness. On this basis, we design a simple yet effective post-hoc calibration algorithm. Our method not only overcomes the ten identified limitations but also achieves markedly better performance than traditional methods, as validated by extensive experiments. We further analyze, both theoretically and experimentally, the relationship and advantages of our learning objective compared to traditional proper scoring rule. In summary, our probabilistic framework derives an approximately equivalent differentiable objective for learning error-bounded calibrated probabilities, elucidating the correspondence and convergence properties of computational statistics with respect to theoretical bounds in canonical calibration. The theoretical effectiveness is verified on standard post-hoc calibration benchmarks by achieving state-of-the-art performance. This research offers valuable reference for learning reliable likelihood in related fields.

Predicting the fitness impact of mutations is central to protein engineering but constrained by limited assays relative to the size of sequence space. Protein language models (pLMs) trained with masked language modeling (MLM) exhibit strong zero-shot fitness prediction; we provide a unifying view by interpreting natural evolution as implicit reward maximization and MLM as inverse reinforcement learning (IRL), in which extant sequences act as expert demonstrations and pLM log-odds serve as fitness estimates. Building on this perspective, we introduce EvoIF, a lightweight model that integrates two complementary sources of evolutionary signal: (i) within-family profiles from retrieved homologs and (ii) cross-family structural-evolutionary constraints distilled from inverse folding logits. EvoIF fuses sequence-structure representations with these profiles via a compact transition block, yielding calibrated probabilities for log-odds scoring. On ProteinGym (217 mutational assays; >2.5M mutants), EvoIF and its MSA-enabled variant achieve state-of-the-art or competitive performance while using only 0.15% of the training data and fewer parameters than recent large models. Ablations confirm that within-family and cross-family profiles are complementary, improving robustness across function types, MSA depths, taxa, and mutation depths. The codes will be made publicly available.

Reliable confidence estimates are essential in semantic segmentation, especially in safety-critical settings where overconfident errors can mislead downstream decisions. Yet modern segmentation models often remain miscalibrated. Post-hoc calibration offers a practical way to correct confidence estimates without retraining the segmentation model, but its use in dense prediction raises structural issues that are often overlooked. We study two such issues. First, adding a constant to all logits leaves the softmax probabilities unchanged, but several standard calibrators can still depend on this arbitrary offset. As a result, two logit representations encoding the same predictive distribution may yield different calibrated probabilities. We define translation-invariant (TI) calibrators as those whose outputs are unchanged under such shifts, characterize which common calibrators satisfy this property, and construct TI counterparts of shift-sensitive calibrators to isolate the effect of removing representation dependence. Second, post-hoc calibration is typically fitted by minimizing a likelihood-based objective, whereas segmentation models are trained with task-specific metrics such as Dice. This mismatch can cause calibration to alter class orderings and degrade the deployed segmentation map. We study decision-preserving calibration under argmax- and order-preservation constraints. Since enforcing these constraints collapses affine softmax calibrators to temperature scaling, we introduce class-conditional affine calibrators that can be made argmax- or order-preserving while retaining greater expressivity, allowing us to quantify the calibration-segmentation trade-off induced by decision preservation. Across natural-image and medical segmentation benchmarks, and under corruption-based covariate shift, matched comparisons show that TI variants generally improve calibration metrics, while decision-preserving variants prevent segmentation degradation and retain strong calibration performance. These results provide practical design principles for well-defined post-hoc calibration pipelines in semantic segmentation.

An AI control protocol is a plan for usefully deploying AI systems that aims to prevent an AI from intentionally causing some unacceptable outcome. This paper investigates how well AI systems can generate and act on their own strategies for subverting control protocols whilst operating statelessly (without shared memory between contexts). To do this, an AI system may need to reliably generate optimal plans in each context, take actions with well-calibrated probabilities, and coordinate plans with other instances of itself without communicating. We develop Subversion Strategy Eval, a suite of eight environments, covering a range of protocols and strategic capabilities, and six sets of affordances that help isolate individual capabilities. We implement the evaluation in Inspect-AI and release it open-source. We evaluate Claude 3.5 models, including helpful-only versions, as well as OpenAI reasoning models. None of the models demonstrate substantial capability in strategizing to subvert control protocols statelessly. However, providing models with additional affordances, such as the ability to share a plan between contexts, can substantially improve performance. We hope our evaluations can act as a leading indicator for when models are capable of subverting control protocols and also relax the worst-case assumption of perfect strategic ability in AI control evaluations.

"System One" decision models such as TypeSafe's Jev and its open counterpart Laya answer typed questions about a text in a single forward pass with calibrated probabilities, but they cannot ask for missing information: when a first message does not say what separates two departments, they guess. We present LAVOIR (Laya with Value-Of-Information Routing), which places the candidate pieces of missing information (slots) in the input next to the answer options, so that one forward pass returns both the decision distribution and, for every slot, the expected gain in the probability of the correct decision if the user were asked about it. VOI targets need no human labels: gold decisions come from schema rules, an LLM only verbalizes messages and answers, a model from another family checks every text, and pairing each message with several profiles makes regression on realized gains estimate the expected gain. A Gini-impurity cap bounds the predicted value by what a calibrated model can still gain. In a controlled study, decisions on seen schemas are statistically indistinguishable from the Bayes ceiling. The final model's question policy matches a greedy oracle VOI policy on seen schemas (AUC 0.799 vs. 0.797), and with at most 0.5 questions per conversation it is 14.1 points more accurate than never asking. On real ABCD conversations, one real exchange raises accuracy by 8.3 points where LAVOIR asks and leaves it unchanged where it does not; on SGD the cap lowers the asking rate from 93% to 8.6%. On Laya's twelve benchmarks LAVOIR is above Laya's reported scores on seven, and it answers a question in 31 ms (median, GH200).

Jev is a commercial System One model from TypeSafe AI that does not generate text: given a state and typed questions, it returns a choice from fixed options, a position on a rubric, or the probability that a statement is true, with probabilities the vendor describes as calibrated. Such models target small decisions in information access pipelines, such as routing queries, checking grounding, moderating content, or rating against a rubric. We evaluate Jev (jev-1.13.0) zero-shot on 37 datasets spanning classification, routing, natural language inference, reading comprehension, commonsense reasoning, moderation, legal clause analysis and rubric scoring, with one frozen template per dataset and full evaluation splits: 346,009 requests for under USD 10. For reference, we score Qwen3.8-27B and Gemma-4-E4B on identical requests via their exact next-token probabilities over the options. Jev reaches 95-99% accuracy on IMDB, SST-2, HellaSwag and ARC and 86.7% on Belebele across 122 languages. It beats Qwen on 27 of 37 datasets, with none of Qwen's nine leads outside the bootstrap intervals, and Gemma on all 37. All three models degrade on low-resource languages, fine-grained or noisy labels, and rubric-based quality judgments. Jev's choice probabilities are well calibrated and support selective prediction. Binary probabilities rank well but are poorly placed relative to a fixed 0.5 threshold; thresholds tuned on training data raise micro-F1 on UNFAIR-ToS from 0.50 to 0.75. Jev answers MMLU's calculation-heavy questions more accurately than other MMLU questions (94% vs. 91%), whereas both open models, and all three on C-Eval, find them harder. Rotating the options leaves Jev's accuracy unchanged and withholding the question drops it to near chance, ruling out shallow memorization but not memorized question-answer pairs. We release the code, harness and all raw responses.

Large language models (LLMs) often make discrete decisions, such as flagging phishing or escalating to a human. System-1 models, such as Jev and the OpenAI Decisions API, return probabilities over options in a single forward pass, while System-2 approaches generate reasoning steps. Which decisions can System-1 models handle, and which require generative reasoning? We introduce System1-Arena, a benchmark that gives all models the same decision requests and scores their probabilities. It contains 92k questions across 105 tasks from 268 public sources, in four groups: text classification and knowledge, applied decisions, evaluation and control, and agent and action. It also includes 138 closed-loop environments, from web shopping and SWE-bench coding control to robotics, games, and driving; in real-time mode, the world evolves while a model decides. We evaluate 30 models: 7 closed LLMs, 13 open LLMs read at the answer token, and 10 System-1 models. The largest System-1 models match or exceed fast closed LLMs in non-agentic accuracy, with better-calibrated probabilities at one-quarter of the latency. A reasoning LLM is the most accurate, at about 70x the cost of a fast LLM. In closed loops, large open LLMs succeed most often (up to 32.9%); small System-1 models rarely succeed.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

Forecasting real-world events requires language-model agents to reason under uncertainty from incomplete, time-bounded information. Yet evaluating whether agents genuinely forecast requires more than final-answer accuracy: a model may be correct by recalling memorized training facts, citing fabricated evidence, or producing an unsupported causal story. We present WorldReasoner, an evaluation framework for temporally valid event forecasting. Each task gives an agent a resolved forecasting question, a simulated forecast date, and access only to evidence available before that date; after resolution, the framework scores the submitted probability, cited evidence, and optional causal event graph. WorldReasoner reports three complementary axes: outcome quality against resolved answers, evidence quality over cited sources, and reasoning quality against post-resolution hindsight graphs. The benchmark is built by an agentic construction pipeline that generates forecasting questions, collects time-stamped evidence, and builds hindsight reference graphs at scale, yielding 345 resolved tasks derived from 14,141 articles with graphs covering 8,087 extracted events. Across six controlled agent settings, temporally valid retrieval is the strongest driver of outcome accuracy; causal graph construction improves key-event recovery; and correct graph-enabled forecasts are more strongly grounded in key events and relevant sources, yet agents still struggle to convert grounded evidence into calibrated probabilities.

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classification. It is easily implemented with neural nets since it is equivalent to log-transforming the uncalibrated probabilities, followed by one linear layer and softmax. Experiments demonstrate improved probabilistic predictions according to multiple measures (confidence-ECE, classwise-ECE, log-loss, Brier score) across a wide range of datasets and classifiers. Parameters of the learned Dirichlet calibration map provide insights to the biases in the uncalibrated model.

Rerankers decide which documents users and LLMs see, yet their standard metric, nDCG, relies on human relevance labels that are costly, sparse, noisy, and discretely graded. As rerankers approach each other in quality, nDCG on these labels therefore increasingly fails to separate them. LLM judges could supply dense labels. Relative judgments within one query tell even close candidates apart, yet their scores share no scale across queries. Absolute grades share one scale but are too coarse to distinguish documents of similar relevance. We propose Rubric-Calibrated Preferences (RCP), which combine both kinds of judgment. A listwise Bradley-Terry tournament orders each query's documents, and a rubric of yes/no criteria of increasing stringency provides an absolute standard. Item Response Theory (IRT), which scores test-takers based on their answers to common questions, then uses the shared criteria to put all queries' tournament scores on one scale. RCP's retrieval metric, RCP-nDCG, replaces nDCG's discrete labels with the resulting calibrated relevance probabilities. Against blind grades from 46 external annotators, calibration raises the correlation between a query's mean score and its mean human grade from 0.538 to 0.795. The probabilities rank a useful document above a non-useful one with probability 0.910 (AUC, chance 0.5), versus 0.651 for the benchmark labels. When the annotators' grades prefer one of two rerankers and exactly one metric agrees, that metric is RCP-nDCG in 72.4% of 185 comparisons (chance about 53%). On TREC-DL, RCP-nDCG sides with NIST assessors' grades on every reranker pair that these grades separate significantly. RCP-nDCG also resolves many of nDCG's ties and separates 1.9 times as many reranker pairs on NanoBEIR. Rubric calibration thus turns relative LLM judgments into dense relevance labels that are comparable across queries and agree with human judgment.

Peripheral blood smears remain a cornerstone in the diagnosis of hematological neoplasms, offering rapid and valuable insights that inform subsequent diagnostic steps. However, since neoplastic transformations typically arise in the bone marrow, they may not manifest as detectable aberrations in peripheral blood, presenting a diagnostic challenge. In this paper, we introduce cAItomorph, an explainable transformer-based AI model, trained to classify hematological malignancies based on peripheral blood cytomorphology. Our data comprises peripheral blood single-cell images from 6115 patients with diagnoses confirmed by cytomorphology, cytogenetics, molecular genetics, and immunophenotyping from bone marrow samples, and 495 healthy controls, eight coarse classes. cAItomorph leverages the DinoBloom hematology foundation model and aggregates image encodings via a transformer-based architecture into a single vector. It achieves an overall accuracy of 0.72 in eight disease classification, with F1 scores of 0.76 for acute leukemia, 0.80 for myeloproliferative neoplasms and 0.94 for healthy cases. The overall accuracy increases to 0.87 in top-2 predictions. cAItomorph achieves high sensitivity for acute leukemia cases in external test sets. By analyzing attention heads, we demonstrate clinically relevant cell-level attentions in both internal and external test sets. Moreover, our model's calibrated prediction probabilities reduce the false discovery rate from 13.5% to 8.7% without missing any acute leukemia cases, thereby decreasing the number of unnecessary bone marrow aspirations based on peripheral blood smears. This study highlights the potential of AI-assisted diagnostics in hematological malignancies, illustrating how models trained on real-world data could enhance diagnostic accuracy and reduce invasive procedures.

ufakzeka-karar is an open Turkish decision model with 182,494,466 parameters. Given a Turkish text and questions of a fixed answer type (a choice, a level on an ordered scale, or yes or no), it returns a temperature-scaled probability for every option and an expected error that serves as a "not sure" signal, without generating text and in one CPU forward pass for up to ten options. Built on the lab's ufakzeka-1-base, its head scores each option blind to the others at shared positions, so the answer does not depend on option order. A sequential head trained with shuffled options was about as accurate but changed 2.3 to 2.8 percent of its answers when only the option order changed; REINFORCE lost 10.2 points (0.102) of macro F1 to cross-entropy. On the open set of HakemBench v1.0 (4,275 questions, 7 tracks) the released model ranks 7th of 16 rows with a composite of 0.660 (95% interval 0.642 to 0.677). Temperature scaling lowers calibration error (smooth ECE) on the development set but raises it on held-out support questions, from 0.027 to 0.045 for the first scored run, which never trained on them; the released model later trained on them, so its 0.036 to 0.064 is not an unseen-question test. The released model is the last of three runs scored on HakemBench, and its numbers are not blind. The second run's new training data was aimed at the first run's errors on the full test set in guardrails, moderation and customer support, and the released run was trained after the second run's guardrail results on the full test set were read, under a protocol fixed in writing before any of its data, code or runs. All its numbers come after these readings; its guardrail, moderation and customer support numbers carry the flag "shaped by reading the test results". With every model scored on the other four tracks only, its composite is 0.678, 6th of 16. Weights and code are under Apache-2.0.

Funnelling (Fun) is a recently proposed method for cross-lingual text classification (CLTC) based on a two-tier learning ensemble for heterogeneous transfer learning (HTL). In this ensemble method, 1st-tier classifiers, each working on a different and language-dependent feature space, return a vector of calibrated posterior probabilities (with one dimension for each class) for each document, and the final classification decision is taken by a metaclassifier that uses this vector as its input. The metaclassifier can thus exploit class-class correlations, and this (among other things) gives Fun an edge over CLTC systems in which these correlations cannot be brought to bear. In this paper we describe Generalized Funnelling (gFun), a generalization of Fun consisting of an HTL architecture in which 1st-tier components can be arbitrary view-generating functions, i.e., language-dependent functions that each produce a language-independent representation ("view") of the (monolingual) document. We describe an instance of gFun in which the metaclassifier receives as input a vector of calibrated posterior probabilities (as in Fun) aggregated to other embedded representations that embody other types of correlations, such as word-class correlations (as encoded by Word-Class Embeddings), word-word correlations (as encoded by Multilingual Unsupervised or Supervised Embeddings), and word-context correlations (as encoded by multilingual BERT). We show that this instance of gFun substantially improves over Fun and over state-of-the-art baselines, by reporting experimental results obtained on two large, standard datasets for multilingual multilabel text classification. Our code that implements gFun is publicly available.

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii) accurately identifies queries coming out of the target domain and rejects them. We introduce an original combination of Evidential Deep Learning, Neural Processes, and Neural Turing Machines capable of providing all three essential properties mentioned above for total uncertainty quantification. We observe our method on five classification tasks to be the only one that can excel all three aspects of total calibration with a single standalone predictor. Our unified solution delivers an implementation-friendly and compute efficient recipe for safety clearance and provides intellectual economy to an investigation of algorithmic roots of epistemic awareness in deep neural nets.

LLM rerankers add of the order of \$0.2-0.3 per 1,000 queries and about a second of tail latency on top of a graph-augmented dense pipeline such as HippoRAG2, and on three multi-hop benchmarks they improve final-hop top-K coverage on seven of nine (dataset, K) cells, by up to +34.8 pp. We ask whether a learned per-query gate can skip the reranker where it will not help, using only features available before the LLM call (27 score and lexical statistics of the two retrieval lists plus a PCA of a small query embedding) with an executable fallback. Every choice, including the fallback and the threshold, is made inside the training fold and applied once to held-out queries, and harmful skips (the rerank would have found the target, the fallback did not) are reported next to the aggregate coverage. Across nine cells on 2WikiMultiHopQA, MuSiQue and HotpotQA the gate skips 51% of calls at an average held-out LastHop@K cost of 1.2 pp; four cells meet a pre-registered 1 pp rule, harmful skips occur in eight (190 harmful against 136 beneficial), and a random gate at the same skip rate loses 2 to 11 pp on the high-lift cells. A second rule sets each cell's threshold from a pre-specified budget on the expected harmful-skip rate over Platt-calibrated harm probabilities (ECE 0.025 after calibration, 0.094 before): at a 1 pp budget the gate skips 42% at -0.8 pp with 66 harmful skips and six cells within 1 pp, but realised harm exceeds the promise in six cells (mean 1.45 vs 0.83 pp), a selection optimism we quantify; a 0.5 pp budget realises about 1 pp. The harm probabilities are calibrated but barely discriminative (AUC 0.16 to 0.70). An earlier version reported 73% "lossless" savings; that figure rested on an oracle fallback and a wrong MuSiQue target, and we document both.

Recent image generation and editing models demonstrate robust adherence to instructions and high visual quality on academic benchmarks. However, their performance on paid, real-world design projects remains uncertain. We introduce ServImage, a benchmark that explicitly correlates model outputs with economic value in commercial design projects. ServImage consists of (i) \textit{ServImageBench}: a dataset of 1.07k paid commercial design tasks and 2.05k designer deliverables totaling over \$295k, covering portrait, product, and digital content, along with 33k candidate images and 33k human annotations. (ii) \textit{ServImageScore}: an integrated scoring system that combines three quality dimensions: baseline requirements fulfilment, visual execution quality, and commercial necessity satisfaction. These three dimensions are designed to characterize the factors that drive human payment decisions and indicate whether an image is commercially acceptable. (iii) \textit{ServImageModel}: under this scoring system, we propose a payment prediction model trained on the human-annotated candidate images, achieving 82.00\% accuracy in predicting human payment decisions and producing calibrated payment probabilities. ServImage provides a comprehensive foundation for assessing the commercial viability of image generation models and offers a scalable resource for future research on economically grounded vision systems https://github.com/FengxianJi/ServImage{Github.}

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.

As LLM-powered agents have been used for high-stakes decision-making, such as clinical diagnosis, it becomes critical to develop reliable verification of their decisions to facilitate trustworthy deployment. Yet, existing verifiers usually underperform owing to a lack of domain knowledge and limited calibration. To address this, we establish GLEAN, an agent verification framework with Guideline-grounded Evidence Accumulation that compiles expert-curated protocols into trajectory-informed, well-calibrated correctness signals. GLEAN evaluates the step-wise alignment with domain guidelines and aggregates multi-guideline ratings into surrogate features, which are accumulated along the trajectory and calibrated into correctness probabilities using Bayesian logistic regression. Moreover, the estimated uncertainty triggers active verification, which selectively collects additional evidence for uncertain cases via expanding guideline coverage and performing differential checks. We empirically validate GLEAN with agentic clinical diagnosis across three diseases from the MIMIC-IV dataset, surpassing the best baseline by 12% in AUROC and 50% in Brier score reduction, which confirms the effectiveness in both discrimination and calibration. In addition, the expert study with clinicians recognizes GLEAN's utility in practice.

The appearance of Jev marked the era of System One Models, foundation models that return structured decisions with probability distributions rather than text. Aside from low cost and great speed, Jev's central promise is that these probabilities are calibrated: such claim is not backed by any public test and available external benchmarks evaluate confidence calibration, not whether every returned option probability has the right numerical meaning. To tackle this issue, we introduce Sys1Cal-v1, a dataset of True/False questions about a proposition A for which the exact probability P(A) is known by construction. Each item is queried through the three Jev primitives - Noul, Choice and Score - and evaluated by total variation distance from the ground-truth distribution, which can be used to estimate a soft accuracy of System One Models. We showcase the utility of Sys1Cal-v1 as a benchmark dataset by evaluating Jev and SemIf, an open-source Choice-style baseline. In this work, however, we focus even more deeply on Jev, by studying the calibration of its Score and Choice answers. In particular, we discover a peculiar behaviour that can be explained by assuming that Jev suppresses a third truth value, going beyond True and False. In other words, in Choice answers, P(A) and P(neg A) are presented as if P(A)+P(neg A)=1, while a term P(U)neq0 is missing in the sum. Recovering P(U) leads to an improvement of median soft accuracy in Choice answers from 0.771 to 0.978, suggesting that, even in binary decisions, Jev wants to answer with a third option:``I don't know''.

Crash datasets that carry an investigator narrative hold information the coded fields omit. Coding those narratives at scale has been blocked by three obstacles. Frontier large language models are costly at that scale, their generated text cannot be verified, and no rule says how much output a human must check. This paper formulates narrative coding as gated, typed decisions answered by Jev, a System One model that returns probabilities over analyst-defined options and generates no text. A screen covered 499,500 Texas narratives and 195,857 were coded with a 27-question schema. Cost is governed by schema size rather than narrative length. The probabilities are audited against coded fields and against 2,416 blinded human judgments drawn under a stated sampling design. Two frontier large language models are benchmarked on the same records. Against human labels the typed model attains an F1 of 0.908. One frontier model gains 0.059 and the other is indistinguishable from it. Calibration varies by model rather than by paradigm, so each model must be audited. Recalibration on the same labels reduces calibration error by a factor of 3.3. Agreement with coded fields understates fidelity to the narrative by a median of 0.26 in kappa. A resolution-floor bound covers any model that reports probabilities on a discrete grid. A review budget over flagged records gives the records a human must read per variable and per year. Adding the calibrated variables to the coded fields raises the injury and fatal crashes attributed to nine factors by 10,747 per year.

Ultra-fine entity typing plays a crucial role in information extraction by predicting fine-grained semantic types for entity mentions in text. However, this task poses significant challenges due to the massive number of entity types in the output space. The current state-of-the-art approaches, based on standard multi-label classifiers or cross-encoder models, suffer from poor generalization performance or inefficient inference. In this paper, we present CASENT, a seq2seq model designed for ultra-fine entity typing that predicts ultra-fine types with calibrated confidence scores. Our model takes an entity mention as input and employs constrained beam search to generate multiple types autoregressively. The raw sequence probabilities associated with the predicted types are then transformed into confidence scores using a novel calibration method. We conduct extensive experiments on the UFET dataset which contains over 10k types. Our method outperforms the previous state-of-the-art in terms of F1 score and calibration error, while achieving an inference speedup of over 50 times. Additionally, we demonstrate the generalization capabilities of our model by evaluating it in zero-shot and few-shot settings on five specialized domain entity typing datasets that are unseen during training. Remarkably, our model outperforms large language models with 10 times more parameters in the zero-shot setting, and when fine-tuned on 50 examples, it significantly outperforms ChatGPT on all datasets. Our code, models and demo are available at https://github.com/yanlinf/CASENT.

Calibration, the alignment of predicted probabilities with true outcome frequencies, is essential for reliable decision-making. While extensively studied for classification and regression, calibration has not been formally addressed for probabilistic label ranking, where the goal is to predict a distribution over orderings of a label set. Naively treating rankings as classes ignores their structure and fails to capture important modalities such as pairwise and top-k predictions. We formalize calibration for label ranking and develop a hierarchy of notions covering full rankings, sub-rankings, and top-k rankings. We prove that full-rank calibration implies the others but not conversely, and sub-ranking and top-k calibration are incomparable. Empirically, we find popular label ranking models are often poorly calibrated, with substantial differences between sub-ranking and top-k metrics. Applying our framework to RLHF reward models, we find that calibration correlates strongly but not perfectly with benchmark accuracy, suggesting it captures a meaningful quality dimension beyond top-1 accuracy. These findings motivate future work on understanding the downstream effects of miscalibration and developing methods to correct it.

LLM cascades and model routing promise lower inference cost by sending easy queries to a small model and escalating hard ones to a large model, but most deployed routers use uncalibrated confidence scores and require per-workload threshold tuning. We present UCCI, a calibration-first router that maps token-level margin uncertainty to a per-query error probability via isotonic regression and selects the escalation threshold by constrained cost minimization. Under three explicit assumptions, threshold policies on the calibrated score are cost-optimal, and isotonic calibration achieves O(n^{-1/3}) sample complexity for expected calibration error (ECE). On a production named entity recognition workload of 75,000 queries served by 4B and 12B instruction-tuned LLMs on H100 GPUs, UCCI cuts inference cost by 31% (95% CI: [27%, 35%]) at micro-F1 = 0.91 while reducing ECE from 0.12 to 0.03. At the same operating point, UCCI beats entropy thresholding, split-conformal routing, and a FrugalGPT-style learned threshold. All cascade results use end-to-end routing on actual model outputs and measured H100 latency, not simulated routing from global accuracies or nominal API prices.

Confidence estimation for Vision-Language-Action (VLA) models is essential for robots to perform manipulation tasks in the open world, providing crucial signals for risk-sensitive decision-making and failure anticipation. Existing confidence estimation methods typically rely on ensemble-based paradigms or action-token probabilities to predict the likelihood of task success. However, they still encounter challenges in computational efficiency and cross-architecture generalizability. These methods usually require repeated sampling, leading to inference inefficiency, and are restricted to VLA models with discrete action outputs, making them difficult to apply to continuous action spaces. To address this issue, we propose VLAConf, a one-class discriminative confidence framework. By leveraging frozen pretrained VLA internal representations, VLAConf directly estimates step-wise anomaly scores in a single forward pass using a lightweight confidence head, thereby eliminating the overhead of exhaustive resampling. We additionally use step-conditioned modeling to encode rollout-phase information along the manipulation trajectory. Experiments on the LIBERO benchmark demonstrate that VLAConf significantly improves the quality of the confidence signal constructed for post-hoc calibration, outperforming existing baselines by a large margin in inference efficiency. The effectiveness of VLAConf is further validated in real-robot experiments. To access the source code and supplementary videos, visit https://sites.google.com/view/vlaconf.

Search agents repeatedly make short decisions about relevance, evidence sufficiency, and search actions. Using generative language models for these decisions introduces latency and unreliable confidence. We present SearchJev, a fast and calibrated System-1 model that separates search decisions from System-2 reasoning and generation. Given a search state and a decision schema, SearchJev directly scores legal options without autoregressive output generation. We propose Soft-Label Learning for Calibrated Decisions (SLCD) to learn decision probabilities from uncertain supervision and calibrate their confidence. In a dual-system search agent, SearchJev handles short decisions and delegates uncertain judgments to System 2, which retains planning, query generation, and answer composition. We also introduce SearchDecision-Bench, a benchmark unifying six types of search decisions for training and evaluation. On SearchDecision-Bench, SEARCHJEV improves decision quality over same-size Qwen3.5 autoregressive models, achieves 5.2-5.3 times faster decisions, and reduces average expected calibration error by 41-74%. On BrowseComp-Plus, the dual-system agents achieve a 3.7-4.7 times speedup in active search time while improving answer accuracy from 45% to up to 54%.

A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pre-training produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widely-used LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHF-LMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model's conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative 50%.

Fetal ultrasound standard-plane classification underpins reliable prenatal biometry and anomaly screening, yet real-world deployment is limited by domain shift, image noise, and poor calibration of predicted probabilities. This paper presents a practical framework for uncertainty-calibrated explainable AI in fetal plane classification. We synthesize uncertainty estimation methods (Monte Carlo dropout, deep ensembles, evidential learning, and conformal prediction) with post-hoc and uncertainty-aware explanations (Grad-CAM variants, LIME-style local surrogates, and uncertainty-weighted multi-resolution activation maps), and we map these components to a clinician-facing workflow. Using FETAL_PLANES_DB as a reference benchmark, we define a reporting protocol that couples accuracy with calibration and selective prediction, including expected calibration error, Brier score, coverage-risk curves, and structured error analysis with explanations. We also discuss integration points for quality control and human-in-the-loop review, where uncertainty flags trigger re-acquisition or expert confirmation. The goal is a reproducible, clinically aligned blueprint for building fetal ultrasound classifiers whose confidence and explanations remain trustworthy under noisy acquisition conditions.

Operational telemetry can be jointly anomalous while every individual stream stays inside its familiar range. TRACE-C is an auditable strictly-prior rank-calibrated detector for aligned multi-stream telemetry: same-regime rolling median/MAD residuals feed three window channels -- a maximum normalized local sum, a Gaussian copula-form dependence contrast on robust-z residuals, and a worst standardized AR(1) innovation -- whose channel ranks are Fisher-aggregated and ranked against earlier aggregates. We evaluate six Great Britain grid streams with a January-April 2019 fit, July-December 2019 development evidence, and a 2020 hold-out frozen before inspection. TRACE-C ranks Storm Atiyah first among 2019 test windows, but a disclosed channel ablation attributes that rank to the local channel, not the copula-form channel: copula-only ranks Atiyah 59th. The short 9 August frequency event is ranked far lower by the fused detector (143) than by the temporal channel alone (40), and reconstruction baselines rank it first. In 2020 no window is selected, which is consistent with record-rule saturation rather than an uneventful year; the highest-ranked frozen window was later interpreted as Storm Ellen. Three interpretive limits carry throughout. The resulting p-values are selection quantities, not event probabilities. The copula-form channel is not a literal copula density: the method applies no probability-integral or normal-score transform. Empirical rank counts are diagnostics, not coverage or false-discovery proofs. Every table and figure in this paper is generated from committed machine-readable reports.

Typed decision models answer schema-constrained questions about a text in one forward pass and return probabilities meant to be thresholded. We ask whether biomedical sentence encoders trained for retrieval are good starting points for such models. We present SBERT2S1, which converts Sentence-Transformers encoders into bi-encoder, cross-head (C) and prior-fused residual (PFR) decision models, together with BIODECIDE, a biomedical typed-decision suite, and MEDLINE-S1, 243k training decisions derived from NLM indexing. Across six parent-retriever pairs, retrieval training improves zero-shot matching of content-bearing options. After fine-tuning, its effect depends on the head: across five pairs and three training-set sizes, retrieval training significantly helps PFR, which keeps the retrieval prior, in 10 of 15 comparisons, but helps C in one and hurts it in five. A matched grid of two heads and five training objectives shows that C outperforms PFR under every objective, and that the released RLCD recipe of open System One models trails cross-entropy by 2.5-3.0 points. The deficit stems mainly from its reward normalisation, which inflates the noisy score-function term 3.6-15-fold; an unbiased leave-one-out estimator recovers most of the gap. After temperature scaling, no objective is clearly better calibrated than cross-entropy. We release the code, the MEDLINE-S1 labels and a model.

Jev-style decision models return categorical probability distributions over predefined options without generating free-form text, enabling software systems to act on their outputs directly. In this work, we investigate the extent to which general-purpose LLMs already possess this capability out of the box, and when fine-tuning is actually necessary. We present LLM-as-Jev, an architecture-preserving framework that extracts calibrated decisions directly from next-token probabilities over bracketed numeric identifiers. LLM-as-Jev provides both a training-free inference recipe and a fine-tuning objective that optimizes candidate selection via a tree-factorized listwise loss while anchoring auxiliary predictions to the base model using KL divergence penalties. Evaluating on Qwen3.5-4B and Qwen3-0.6B, we find that modern LLMs are inherently effective decision models: without training, the 4B model matches community Jev-style models built on the same backbone, outperforms letter-logit readouts, supports arbitrary option counts, and natively handles multimodal decisions over images. Fine-tuning provides targeted rather than universal benefits -- substantially improving weaker models and specific tasks (such as many-option intent routing), but offering diminishing returns for strong backbones. Crucially, our KL anchors prevent behavioral degradation in conversational text generation, with LoRA delivering the strongest performance on capable models.

We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, potentially benefiting other sequential algorithms. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (R\'enyi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any epsilon-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance.

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard baseline methods such as model logits and elicited probabilities produce overconfident and poorly calibrated estimates. In this work, we propose Approximate Bayesian Computation (ABC), a likelihood-free Bayesian inference, based approach that treats LLMs as a stochastic simulator to infer posterior distributions over predictive probabilities. We evaluate our ABC approach on two clinically relevant benchmarks: a synthetic oral lesion diagnosis dataset and the publicly available GretelAI symptom-to-diagnosis dataset. Compared to standard baselines, our approach improves accuracy by up to 46.9\%, reduces Brier scores by 74.4\%, and enhances calibration as measured by Expected Calibration Error (ECE) and predictive entropy.

Depression and post traumatic stress disorder (PTSD) often co-occur with connected symptoms, complicating automated assessment, which is often binary and disorder specific. Clinically useful diagnosis needs severity aware cross disorder estimates and decision support explanations. Our unified tri modal affective severity framework synchronizes and fuses interview text with sentence level transformer embeddings, audio with log Mel statistics with deltas, and facial signals with action units, gaze, head and pose descriptors to output graded severities for diagnosing both depression (PHQ-8; 5 classes) and PTSD (3 classes). Standardized features are fused via a calibrated late fusion classifier, yielding per disorder probabilities and feature-level attributions. This severity aware tri-modal affective fusion approach is demoed on multi disorder concurrent depression and PTSD assessment. Stratified cross validation on DAIC derived corpora outperforms unimodal/ablation baselines. The fused model matches the strongest unimodal baseline on accuracy and weighted F1, while improving decision curve utility and robustness under noisy or missing modalities. For PTSD specifically, fusion reduces regression error and improves class concordance. Errors cluster between adjacent severities; extreme classes are identified reliably. Ablations show text contributes most to depression severity, audio and facial cues are critical for PTSD, whereas attributions align with linguistic and behavioral markers. Our approach offers reproducible evaluation and clinician in the loop support for affective clinical decision making.

Persistent spatial memory enables embodied agents to navigate familiar environments across repeated visits. However, targets may move while unobserved, including during navigation, making remembered locations unreliable by the time an agent arrives. Despite advances in memory retrieval and state prediction, accounting for continued hidden world evolution and revising beliefs under limited visibility remain challenging. We study Evolving-World Navigation, where agents infer target locations from intermittent observations, predict their states at inspection time, and revise beliefs using visual evidence. We propose EvolvingNav, which constructs a time-indexed belief from timestamped 3D object histories through a structured persistence-relocation model. The belief distinguishes persistence at the last observed location from relocation to alternative locations and retains probability mass outside the known candidate set. An event-driven filter propagates the current belief as time elapses, forecasts target occupancy at candidate inspection times, and incorporates new RGB-D evidence. Negative observations downweight location hypotheses according to calibrated, visibility-conditioned detection probabilities, while evidence tracking prevents repeated use of the same observations. A frozen, zero-shot vision-language controller uses the updated belief to choose actions and replan. We further introduce EvoWorld-Bench, a benchmark grounded in human activity traces, comprising 54 scenes and 803,680 tasks with controlled changes before and during navigation. In simulation and real-robot experiments, EvolvingNav improves navigation success and search efficiency over the evaluated baselines. Paired experiments show the clearest gains under learnable temporal patterns, while ablations demonstrate the value of preserving uncertainty and incorporating visibility-aware evidence.

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model prediction probabilities to bin the data and evaluate calibration error. We propose a more generalized definition of calibration error called Partitioned Calibration Error (PCE), revealing that the key difference among these calibration error metrics lies in how the data space is partitioned. We put forth an intuitive proposition that an accurate model should be calibrated across any partition, suggesting that the input space partitioning can extend beyond just the partitioning of prediction probabilities, and include partitions directly related to the input. Through semantic-related partitioning functions, we demonstrate that the relationship between model accuracy and calibration lies in the granularity of the partitioning function. This highlights the importance of partitioning criteria for training a calibrated and accurate model. To validate the aforementioned analysis, we propose a method that involves jointly learning a semantic aware grouping function based on deep model features and logits to partition the data space into subsets. Subsequently, a separate calibration function is learned for each subset. Experimental results demonstrate that our approach achieves significant performance improvements across multiple datasets and network architectures, thus highlighting the importance of the partitioning function for calibration.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

The increasing complexity of advanced machine learning models requires innovative approaches to manage computational resources effectively. One such method is the Early Exit strategy, which allows for adaptive computation by providing a mechanism to shorten the processing path for simpler data instances. In this paper, we propose EERO, a new methodology to translate the problem of early exiting to a problem of using multiple classifiers with reject option in order to better select the exiting head for each instance. We calibrate the probabilities of exiting at the different heads using aggregation with exponential weights to guarantee a fixed budget .We consider factors such as Bayesian risk, budget constraints, and head-specific budget consumption. Experimental results, conducted using a ResNet-18 model and a ConvNext architecture on Cifar and ImageNet datasets, demonstrate that our method not only effectively manages budget allocation but also enhances accuracy in overthinking scenarios.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the ell_2 Expected Calibration Error (ECE). We consider top-1-to-k calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

Large language models (LLMs) show impressive abilities via few-shot prompting. Commercialized APIs such as OpenAI GPT-3 further increase their use in real-world language applications. However, the crucial problem of how to improve the reliability of GPT-3 is still under-explored. While reliability is a broad and vaguely defined term, we decompose reliability into four main facets that correspond to the existing framework of ML safety and are well-recognized to be important: generalizability, social biases, calibration, and factuality. Our core contribution is to establish simple and effective prompts that improve GPT-3's reliability as it: 1) generalizes out-of-distribution, 2) balances demographic distribution and uses natural language instructions to reduce social biases, 3) calibrates output probabilities, and 4) updates the LLM's factual knowledge and reasoning chains. With appropriate prompts, GPT-3 is more reliable than smaller-scale supervised models on all these facets. We release all processed datasets, evaluation scripts, and model predictions. Our systematic empirical study not only sheds new insights on the reliability of prompting LLMs, but more importantly, our prompting strategies can help practitioners more reliably use LLMs like GPT-3.

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates---those representative of the true likelihood of a prediction. Most models are not calibrated out of the box but are recalibrated by post-processing model outputs. We find in this work that popular recalibration methods like Platt scaling and temperature scaling are (i) less calibrated than reported, and (ii) current techniques cannot estimate how miscalibrated they are. An alternative method, histogram binning, has measurable calibration error but is sample inefficient---it requires O(B/ε^2) samples, compared to O(1/ε^2) for scaling methods, where B is the number of distinct probabilities the model can output. To get the best of both worlds, we introduce the scaling-binning calibrator, which first fits a parametric function to reduce variance and then bins the function values to actually ensure calibration. This requires only O(1/ε^2 + B) samples. Next, we show that we can estimate a model's calibration error more accurately using an estimator from the meteorological community---or equivalently measure its calibration error with fewer samples (O(B) instead of O(B)). We validate our approach with multiclass calibration experiments on CIFAR-10 and ImageNet, where we obtain a 35% lower calibration error than histogram binning and, unlike scaling methods, guarantees on true calibration. In these experiments, we also estimate the calibration error and ECE more accurately than the commonly used plugin estimators. We implement all these methods in a Python library: https://pypi.org/project/uncertainty-calibration

Candidate-scoring decision models return a probability distribution over a presented set of answers. Public documentation of one such system, Jev, and of an open counterpart, JevAny, describes three training ingredients that determine what these probabilities estimate: soft targets from larger models, a frozen pretrained backbone and temperature calibration. We analyze each ingredient in Gaussian surrogates where the finite-sample risk can be computed exactly. A student trained on teacher targets inherits the teacher's bias, which more student data does not remove and agreement with the teacher does not reveal. A fixed representation lowers the risk only below an explicit sample-size threshold. In a probit model the exact recalibration map is a temperature scaling, which removes all excess risk only when the teacher's coefficient has the correct direction and otherwise leaves a residual that calibration diagnostics do not detect. Under Luce's choice axiom, candidate scores are coherent across refinements of an event if and only if they aggregate by log-sum-exp. On 231,521 credit card complaints from the Consumer Financial Protection Bureau, where the decision is whether a complaint ends in monetary relief, a student trained on a logistic teacher's probabilities ends at the teacher's decision cost while a student trained on outcomes goes 8% below it, a 30B model read zero-shot remains worse than the teacher after recalibration, and that model departs from the coherence condition by 17.5 decibans. Pretrained representations reduce the labeled data required and calibration corrects the scale of the probabilities, but neither corrects a biased teacher, so the probabilities have to be checked against realized outcomes.

Decision models such as Jev answer questions with probabilities, which are only useful if they are calibrated. Open-source reproductions rely on supervised fine-tuning plus temperature scaling, while reinforcement learning from verifiable rewards (RLVR) makes reasoning models overconfident. We present a working implementation of reinforcement learning for calibrated decisions (RLCD) for reasoning models: the model samples a rationale, and we score the answer distribution it commits to afterwards with a strictly proper scoring rule. A variance identity shows that scoring the mixture of several samples rewards disagreeing rationales, and that RLVR is exactly this mixture objective without its diversity term. Optimized naively, the per-rationale objective either switches reasoning off or is drowned out by policy-gradient noise, which leads to a two-stage recipe: calibrate, then reinforce. With Qwen3-1.7B on two reasoning tasks (3 seeds, paired tests), RLCD matches or beats SFT, RFT/STaR and GRPO (each temperature-scaled) in accuracy and beats all of them in selective prediction; on GSM8K answer verification a single query decides \gvTwoCovFive\% of the items at le5\% error, versus \gvGrpoCovFive\% for GRPO. When uncertainty comes from annotator disagreement, RLCD provably cannot beat cross-entropy. Code and results: https://github.com/ZimmyGao/openjev-rlcd.

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood p sim Beta(α, β) and outcome y sim Bernoulli(p), with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the largest empirical study to date to assess the probabilistic calibration of neural networks. We also analyze the performance of recalibration, conformal, and regularization methods to enhance probabilistic calibration. Additionally, we introduce novel differentiable recalibration and regularization methods, uncovering new insights into their effectiveness. Our findings reveal that regularization methods offer a favorable tradeoff between calibration and sharpness. Post-hoc methods exhibit superior probabilistic calibration, which we attribute to the finite-sample coverage guarantee of conformal prediction. Furthermore, we demonstrate that quantile recalibration can be considered as a specific case of conformal prediction. Our study is fully reproducible and implemented in a common code base for fair comparisons.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Overconfidence and underconfidence in machine learning classifiers is measured by calibration: the degree to which the probabilities predicted for each class match the accuracy of the classifier on that prediction. How one measures calibration remains a challenge: expected calibration error, the most popular metric, has numerous flaws which we outline, and there is no clear empirical understanding of how its choices affect conclusions in practice, and what recommendations there are to counteract its flaws. In this paper, we perform a comprehensive empirical study of choices in calibration measures including measuring all probabilities rather than just the maximum prediction, thresholding probability values, class conditionality, number of bins, bins that are adaptive to the datapoint density, and the norm used to compare accuracies to confidences. To analyze the sensitivity of calibration measures, we study the impact of optimizing directly for each variant with recalibration techniques. Across MNIST, Fashion MNIST, CIFAR-10/100, and ImageNet, we find that conclusions on the rank ordering of recalibration methods is drastically impacted by the choice of calibration measure. We find that conditioning on the class leads to more effective calibration evaluations, and that using the L2 norm rather than the L1 norm improves both optimization for calibration metrics and the rank correlation measuring metric consistency. Adaptive binning schemes lead to more stablity of metric rank ordering when the number of bins vary, and is also recommended. We open source a library for the use of our calibration measures.

Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying uncertainty is especially critical in real-world settings, which often involve input distributions that are shifted from the training distribution due to a variety of factors including sample bias and non-stationarity. In such settings, well calibrated uncertainty estimates convey information about when a model's output should (or should not) be trusted. Many probabilistic deep learning methods, including Bayesian-and non-Bayesian methods, have been proposed in the literature for quantifying predictive uncertainty, but to our knowledge there has not previously been a rigorous large-scale empirical comparison of these methods under dataset shift. We present a large-scale benchmark of existing state-of-the-art methods on classification problems and investigate the effect of dataset shift on accuracy and calibration. We find that traditional post-hoc calibration does indeed fall short, as do several other previous methods. However, some methods that marginalize over models give surprisingly strong results across a broad spectrum of tasks.

Pre-trained Transformers are now ubiquitous in natural language processing, but despite their high end-task performance, little is known empirically about whether they are calibrated. Specifically, do these models' posterior probabilities provide an accurate empirical measure of how likely the model is to be correct on a given example? We focus on BERT and RoBERTa in this work, and analyze their calibration across three tasks: natural language inference, paraphrase detection, and commonsense reasoning. For each task, we consider in-domain as well as challenging out-of-domain settings, where models face more examples they should be uncertain about. We show that: (1) when used out-of-the-box, pre-trained models are calibrated in-domain, and compared to baselines, their calibration error out-of-domain can be as much as 3.5x lower; (2) temperature scaling is effective at further reducing calibration error in-domain, and using label smoothing to deliberately increase empirical uncertainty helps calibrate posteriors out-of-domain.

Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We introduce a large-scale, standardized benchmark for post-hoc calibration, covering nearly 2000 experiments across tabular and computer vision tasks, including binary, multiclass, and large-scale classification settings. Our benchmark aggregates predictions from a diverse set of classical models, modern deep learning architectures, and foundation models, and provides unified, reproducible implementations of dozens of calibration methods within a common evaluation framework. We argue that Post-Hoc Improvement (PHI) in proper scoring rules offers a principled alternative to traditional calibration error estimators for comparing post-hoc methods, capturing both calibration quality and potential degradation to the model's predictive performance. Using this framework, we conduct the most comprehensive empirical study of post-hoc calibration to date. Our results reveal consistent patterns across domains: smooth calibration functions outperform binning-based approaches, dedicated multiclass methods are essential in high-dimensional settings, and generic machine learning models are not competitive without calibration-specific design. To facilitate future research, we release all data, code, and evaluation tools, providing a plug-and-play benchmark for developing and comparing calibration methods.

Video world models approximate the stochastic distribution of physical outcomes through generative sampling, but existing benchmarks score individual generations or compare distributions coarsely over a whole dataset, leaving the fine-grained aleatoric uncertainty of specific phenomena untested. We introduce CaliBench, which scores outcomes in a physically interpretable discrete space - a bin index, a die face, a suit, a colour - rather than a learned feature space such as in FID, so the distance from a known reference distribution is measured directly. We curate outcome spaces whose reference is known in closed form (binomial Galton boards, Bernoulli forks, uniform dice/cards/lottery, a skewed European-roulette colour), enabling an exact calibration test. We decompose performance into two orthogonal axes that a single accuracy metric conflates: scorability, the fraction of generations yielding a scoreable outcome, and calibration, the total variation distance from the reference on that sample. A chi-squared test assesses significance; as calibration is its null hypothesis it can evidence only miscalibration, and at N=32 per cell detects only large deviations. We apply it to nine scenes and six image-to-video models (WAN-2.7, SeeDance-2.0, HappyHorse-1.0, Veo 3.1, Runway Gen-4.5, Cosmos3-Super), 32 generations each. Models consistently concentrate probability mass on a few outcomes rather than reproducing the reference. Most scene-model combinations are significantly miscalibrated, in the extreme collapsing to one outcome, as Veo 3.1 does on dice. On roulette, generations often leave the ball ambiguously placed, giving several models low scorability. Performance varies by scene: no model dominates all nine. We release the protocol and a metric (mean normalised total variation, mnTV) for comparing new models against our results.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

We introduce Iterated Bellman Calibration, a simple, model-agnostic, post-hoc procedure for calibrating off-policy value predictions in infinite-horizon Markov decision processes. Bellman calibration requires that states with similar predicted long-term returns exhibit one-step returns consistent with the Bellman equation under the target policy. We adapt classical histogram and isotonic calibration to the dynamic, counterfactual setting by repeatedly regressing fitted Bellman targets onto a model's predictions, using a doubly robust pseudo-outcome to handle off-policy data. This yields a one-dimensional fitted value iteration scheme that can be applied to any value estimator. Our analysis provides finite-sample guarantees for both calibration and prediction under weak assumptions, and critically, without requiring Bellman completeness or realizability.

Post-hoc calibration corrects reported confidence, yet a multiclass calibrator can also change the associated top-1 prediction. Accuracy captures only the net effect of these changes on correctness, not how often predictions change; the Top-1 Prediction Change Rate (TPCR) instead measures this frequency. We propose Calibrator-Output Repair for Top-1 Decision Preservation (CORD), the first post-fit adapter to impose exact prediction preservation by repairing the full calibrated probability vector. From the original and calibrated outputs alone, CORD determines the mass assigned to the original top-1. The calibrated conditional distribution allocates the remaining mass over the other classes, yielding a repaired vector whose own argmax recovers the original prediction. On the calibration split, CORD coordinates the repaired masses to retain the calibrated outputs' mean mass on original predictions whenever attainable. The adapter alters neither the fitted calibrator nor its direct output, fits no additional supervised map, and requires no user- or validation-tuned hyperparameter. Across CIFAR-10/100 and ImageNet-1K, CORD attains zero TPCR by construction and lowers mean ECE, NLL, and Brier relative to the corresponding direct outputs in every dataset; paired gains persist under distribution shift and across calibration-set sizes. CORD thus removes the preservation constraint from calibrator fitting and assigns exact recovery of the original decision to subsequent output repair. Our code is available at https://github.com/labhai/CORD.

Probability estimation models play an important role in various fields, such as weather forecasting, recommendation systems, and sports analysis. Among several models estimating probabilities, it is difficult to evaluate which model gives reliable probabilities since the ground-truth probabilities are not available. The win probability estimation model for esports, which calculates the win probability under a certain game state, is also one of the fields being actively studied in probability estimation. However, most of the previous works evaluated their models using accuracy, a metric that only can measure the performance of discrimination. In this work, we firstly investigate the Brier score and the Expected Calibration Error (ECE) as a replacement of accuracy used as a performance evaluation metric for win probability estimation models in esports field. Based on the analysis, we propose a novel metric called Balance score which is a simple yet effective metric in terms of six good properties that probability estimation metric should have. Under the general condition, we also found that the Balance score can be an effective approximation of the true expected calibration error which has been imperfectly approximated by ECE using the binning technique. Extensive evaluations using simulation studies and real game snapshot data demonstrate the promising potential to adopt the proposed metric not only for the win probability estimation model for esports but also for evaluating general probability estimation models.

We propose to reinterpret a standard discriminative classifier of p(y|x) as an energy based model for the joint distribution p(x,y). In this setting, the standard class probabilities can be easily computed as well as unnormalized values of p(x) and p(x|y). Within this framework, standard discriminative architectures may beused and the model can also be trained on unlabeled data. We demonstrate that energy based training of the joint distribution improves calibration, robustness, andout-of-distribution detection while also enabling our models to generate samplesrivaling the quality of recent GAN approaches. We improve upon recently proposed techniques for scaling up the training of energy based models and presentan approach which adds little overhead compared to standard classification training. Our approach is the first to achieve performance rivaling the state-of-the-artin both generative and discriminative learning within one hybrid model.

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating distribution and do not require model refitting. The framework addresses, among other examples, false discovery rate control in multi-label classification, intersection-over-union control in instance segmentation, and the simultaneous control of the type-1 error of outlier detection and confidence set coverage in classification or regression. Our main insight is to reframe the risk-control problem as multiple hypothesis testing, enabling techniques and mathematical arguments different from those in the previous literature. We use the framework to provide new calibration methods for several core machine learning tasks, with detailed worked examples in computer vision and tabular medical data.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Machine unlearning aims to remove the influence of specific training data from a model while preserving reliable behavior on the remaining data, making reliable prediction and uncertainty estimation essential for evaluation. Calibration is commonly used as a proxy for reliability in language models, but low calibration error does not necessarily imply reliable decision rules, as models may rely on spurious correlations while remaining well calibrated. We investigate this gap in generative language models using the multiple-choice question-answering evaluation protocol on the TOFU benchmark, measuring probabilistic reliability with calibration metrics (ECE, MCE, Brier) and decision-rule reliability via attribution-based shortcut detection with Integrated Gradients and Local Mutual Information. We find that fine-tuned models achieve low calibration error (ECE ~ 0.04) compared to pretrained models (ECE > 0.5), and models after unlearning retain similarly low calibration despite reduced accuracy on the forget split, while attribution analysis shows increased reliance on correlation-based tokens. These results demonstrate that good calibration can coexist with shortcut-based decision rules after unlearning, extending the reliability paradox to the machine unlearning setting.

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning.

Evaluating model uncertainty on real-world data is challenging because each instance provides only a single observed label, leaving true conditional class probabilities unknown. To address this, we introduce ProbabilityBench, a benchmark that provides exact, instance-level class probabilities across three simulated text-based domains: peer review, covert information transfer, and credit risk. By explicitly defining the full data-generating process for each environment, we analytically compute both exact class probabilities and Bayes error. Furthermore, we provide a theoretical guarantee that rendering these cases into natural-language memos strictly preserves their underlying generative probabilities. This exactness enables direct measurement of reported probability quality via KL divergence. Across 16 evaluated models, most models on the observed cost-quality Pareto frontiers are decision models, including Jev and Perplexity Decider. Finally, ProbabilityBench serves as a meta-evaluation framework, leveraging known ground-truth values to benchmark the accuracy of standard calibration metrics and Bayes-error estimators themselves.

The use of large language models (LLMs) as automated evaluation tools to assess the quality of generated natural language, known as LLMs-as-Judges, has demonstrated promising capabilities and is rapidly gaining widespread attention. However, when applied to pairwise comparisons of candidate responses, LLM-based evaluators often exhibit selection bias. Specifically, their judgments may become inconsistent when the option positions or ID tokens are swapped, compromising the effectiveness and fairness of the evaluation result. To address this challenge, we introduce CalibraEval, a novel label-free method for mitigating selection bias during inference. Specifically, CalibraEval reformulates debiasing as an optimization task aimed at adjusting observed prediction distributions to align with unbiased prediction distributions. To solve this optimization problem, we propose a non-parametric order-preserving algorithm (NOA). This algorithm leverages the partial order relationships between model prediction distributions, thereby eliminating the need for explicit labels and precise mathematical function modeling.Empirical evaluations of LLMs in multiple representative benchmarks demonstrate that CalibraEval effectively mitigates selection bias and improves performance compared to existing debiasing methods. This work marks a step toward building more robust and unbiased automated evaluation frameworks, paving the way for improved reliability in AI-driven assessments

Machine learning models are widely used, but can also often be wrong. Users would benefit from a reliable indication of whether a given output from a given model should be trusted, so a rational decision can be made whether to use the output or not. For example, outputs can be associated with a confidence measure; if this confidence measure is strongly associated with likelihood of correctness, then the model is said to be well-calibrated. A well-calibrated confidence measure can serve as a basis for rational, graduated decision-making on how much review and care is needed when using generated code. Calibration has so far been studied in mostly non-generative (e.g. classification) settings, especially in software engineering. However, generated code can quite often be wrong: Given generated code, developers must decide whether to use directly, use after varying intensity of careful review, or discard model-generated code. Thus, calibration is vital in generative settings. We make several contributions. We develop a framework for evaluating the calibration of code-generating models. We consider several tasks, correctness criteria, datasets, and approaches, and find that, by and large, generative code models we test are not well-calibrated out of the box. We then show how calibration can be improved using standard methods, such as Platt scaling. Since Platt scaling relies on the prior availability of correctness data, we evaluate the applicability and generalizability of Platt scaling in software engineering, discuss settings where it has good potential for practical use, and settings where it does not. Our contributions will lead to better-calibrated decision-making in the current use of code generated by language models, and offers a framework for future research to further improve calibration methods for generative models in software engineering.

We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated confidence scores using post-hoc calibration methods. In this contribution, we demonstrate that the performance of accuracy-preserving state-of-the-art post-hoc calibrators is limited by their intrinsic expressive power. We generalize temperature scaling by computing prediction-specific temperatures, parameterized by a neural network. We show with extensive experiments that our novel accuracy-preserving approach consistently outperforms existing algorithms across a large number of model architectures, datasets and metrics.

We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly. We first show that larger models are well-calibrated on diverse multiple choice and true/false questions when they are provided in the right format. Thus we can approach self-evaluation on open-ended sampling tasks by asking models to first propose answers, and then to evaluate the probability "P(True)" that their answers are correct. We find encouraging performance, calibration, and scaling for P(True) on a diverse array of tasks. Performance at self-evaluation further improves when we allow models to consider many of their own samples before predicting the validity of one specific possibility. Next, we investigate whether models can be trained to predict "P(IK)", the probability that "I know" the answer to a question, without reference to any particular proposed answer. Models perform well at predicting P(IK) and partially generalize across tasks, though they struggle with calibration of P(IK) on new tasks. The predicted P(IK) probabilities also increase appropriately in the presence of relevant source materials in the context, and in the presence of hints towards the solution of mathematical word problems. We hope these observations lay the groundwork for training more honest models, and for investigating how honesty generalizes to cases where models are trained on objectives other than the imitation of human writing.

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.

Graphical User Interface (GUI) grounding aims to translate natural language instructions into executable screen coordinates, enabling automated GUI interaction. Nevertheless, incorrect grounding can result in costly, hard-to-reverse actions (e.g., erroneous payment approvals), raising concerns about model reliability. In this paper, we introduce SafeGround, an uncertainty-aware framework for GUI grounding models that enables risk-aware predictions through calibrations before testing. SafeGround leverages a distribution-aware uncertainty quantification method to capture the spatial dispersion of stochastic samples from outputs of any given model. Then, through the calibration process, SafeGround derives a test-time decision threshold with statistically guaranteed false discovery rate (FDR) control. We apply SafeGround on multiple GUI grounding models for the challenging ScreenSpot-Pro benchmark. Experimental results show that our uncertainty measure consistently outperforms existing baselines in distinguishing correct from incorrect predictions, while the calibrated threshold reliably enables rigorous risk control and potentials of substantial system-level accuracy improvements. Across multiple GUI grounding models, SafeGround improves system-level accuracy by up to 5.38% percentage points over Gemini-only inference.

Confidence calibration is central to providing accurate and interpretable uncertainty estimates, especially under safety-critical scenarios. However, we find that existing calibration algorithms often overlook the issue of *proximity bias*, a phenomenon where models tend to be more overconfident in low proximity data (i.e., data lying in the sparse region of the data distribution) compared to high proximity samples, and thus suffer from inconsistent miscalibration across different proximity samples. We examine the problem over 504 pretrained ImageNet models and observe that: 1) Proximity bias exists across a wide variety of model architectures and sizes; 2) Transformer-based models are relatively more susceptible to proximity bias than CNN-based models; 3) Proximity bias persists even after performing popular calibration algorithms like temperature scaling; 4) Models tend to overfit more heavily on low proximity samples than on high proximity samples. Motivated by the empirical findings, we propose ProCal, a plug-and-play algorithm with a theoretical guarantee to adjust sample confidence based on proximity. To further quantify the effectiveness of calibration algorithms in mitigating proximity bias, we introduce proximity-informed expected calibration error (PIECE) with theoretical analysis. We show that ProCal is effective in addressing proximity bias and improving calibration on balanced, long-tail, and distribution-shift settings under four metrics over various model architectures. We believe our findings on proximity bias will guide the development of *fairer and better-calibrated* models, contributing to the broader pursuit of trustworthy AI. Our code is available at: https://github.com/MiaoXiong2320/ProximityBias-Calibration.

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.

Federated Learning enables multiple data centers to train a central model collaboratively without exposing any confidential data. Even though deterministic models are capable of performing high prediction accuracy, their lack of calibration and capability to quantify uncertainty is problematic for safety-critical applications. Different from deterministic models, probabilistic models such as Bayesian neural networks are relatively well-calibrated and able to quantify uncertainty alongside their competitive prediction accuracy. Both of the approaches appear in the federated learning framework; however, the aggregation scheme of deterministic models cannot be directly applied to probabilistic models since weights correspond to distributions instead of point estimates. In this work, we study the effects of various aggregation schemes for variational Bayesian neural networks. With empirical results on three image classification datasets, we observe that the degree of spread for an aggregated distribution is a significant factor in the learning process. Hence, we present an investigation on the question of how to combine variational Bayesian networks in federated learning, while providing benchmarks for different aggregation settings.

Obtaining high-quality labels is costly, whereas unlabeled covariates are often abundant, motivating semi-supervised inference methods with reliable uncertainty quantification. Prediction-powered inference (PPI) leverages a machine-learning predictor trained on a small labeled sample to improve efficiency, but it can lose efficiency under model misspecification and suffer from coverage distortions due to label reuse. We introduce Machine-Learning-Assisted Generalized Entropy Calibration (MEC), a cross-fitted, calibration-weighted variant of PPI. MEC improves efficiency by reweighting labeled samples to better align with the target population, using a principled calibration framework based on Bregman projections. This yields robustness to affine transformations of the predictor and relaxes requirements for validity by replacing conditions on raw prediction error with weaker projection-error conditions. As a result, MEC attains the semiparametric efficiency bound under weaker assumptions than existing PPI variants. Across simulations and a real-data application, MEC achieves near-nominal coverage and tighter confidence intervals than CF-PPI and vanilla PPI.

High-stakes decision making involves reasoning under uncertainty about the future. In this work, we train language models to make predictions on open-ended forecasting questions. To scale up training data, we synthesize novel forecasting questions from global events reported in daily news, using a fully automated, careful curation recipe. We train the Qwen3 thinking models on our dataset, OpenForesight. To prevent leakage of future information during training and evaluation, we use an offline news corpus, both for data generation and retrieval in our forecasting system. Guided by a small validation set, we show the benefits of retrieval, and an improved reward function for reinforcement learning (RL). Once we obtain our final forecasting system, we perform held-out testing between May to August 2025. Our specialized model, OpenForecaster 8B, matches much larger proprietary models, with our training improving the accuracy, calibration, and consistency of predictions. We find calibration improvements from forecasting training generalize across popular benchmarks. We open-source all our models, code, and data to make research on language model forecasting broadly accessible.

A well-calibrated model should express confidence that matches its actual accuracy -- when it claims 80\% confidence, it should be correct 80\% of the time. While large language models (LLMs) have achieved remarkable performance across diverse tasks, their epistemic calibration remains poorly understood. We introduce KalshiBench, a benchmark of 300 prediction market questions from Kalshi, a CFTC-regulated exchange, with verifiable real-world outcomes occurring after model training cutoffs. Unlike traditional benchmarks measuring accuracy on static knowledge, KalshiBench evaluates whether models can appropriately quantify uncertainty about genuinely unknown future events. We evaluate five frontier models -- Claude Opus 4.5, GPT-5.2, DeepSeek-V3.2, Qwen3-235B, and Kimi-K2 -- and find systematic overconfidence across all models. Even the best-calibrated model (Claude Opus 4.5, ECE=0.120) shows substantial calibration errors, while reasoning-enhanced models like GPT-5.2-XHigh exhibit worse calibration (ECE=0.395) despite comparable accuracy. Critically, only one model achieves a positive Brier Skill Score, indicating most models perform worse than simply predicting base rates. Our findings suggest that scaling and enhanced reasoning do not automatically confer calibration benefits, highlighting epistemic calibration as a distinct capability requiring targeted development.

Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification, providing calibrated predictive intervals associated with automatic volume measurements. However, this methodology is based on the hypothesis that calibration and test samples are exchangeable, an assumption that is in practice often violated in medical image applications. A weighted formulation of Conformal Prediction can be framed to mitigate this issue, but its empirical investigation in the medical domain is still lacking. A potential reason is that it relies on the estimation of the density ratio between the calibration and test distributions, which is likely to be intractable in scenarios involving high-dimensional data. To circumvent this, we propose an efficient approach for density ratio estimation relying on the compressed latent representations generated by the segmentation model. Our experiments demonstrate the efficiency of our approach to reduce the coverage error in the presence of covariate shifts, in both synthetic and real-world settings. Our implementation is available at https://github.com/benolmbrt/wcp_miccai

This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to which model predictions differ from probabilities estimated from data. It offers (i) a clear interpretation, (ii) a consistent scale that is unaffected by class imbalance, and (iii) an enhanced visual representation with repect to the standard reliability diagram. In addition, we introduce an optimality criterion for the binning procedure of calibration error metrics based on a minimal estimation error of the empirical probabilities. We provide a novel computational algorithm for optimal bins under bin-size constraints. We demonstrate properties of TCE through a range of experiments, including multiple real-world imbalanced datasets and ImageNet 1000.

Large reasoning models (LRMs) often suffer from overconfidence when expressing their uncertainty. Confidence-aware reinforcement learning (RL) offers a promising way to optimize calibration. However, it relies on on-policy rollouts and is thus constrained by the model's pre-RL confidence distribution, which we term confidence prior. In this work, we reveal that off-the-shelf LRMs exhibit a confidence prior heavily concentrated on a few high values, which persists throughout RL. Theoretically, we prove that this concentration suppresses policy gradient updates for rarely sampled confidence values and inflates the lower bound on expected Brier risk. To overcome this exploration bottleneck, we propose CalibSFT, a plug-and-play supervised fine-tuning stage that shapes a calibrated confidence prior with broad support before RL. For each question, CalibSFT constructs confidence targets combining its success rate with response-level correctness, which provably preserves proper-scoring optimality, and then balances training responses across the confidence spectrum to enable diverse confidence exploration during RL. To learn from incorrect responses without imitating their reasoning, CalibSFT introduces correctness-conditional supervision, guiding confidence across all responses while supervising reasoning only on correct ones. Across 16 mathematical and general reasoning benchmarks, incorporating CalibSFT reduces calibration errors and improves discrimination across five representative RL algorithms while preserving comparable accuracy. Furthermore, CalibSFT delivers practical benefits for downstream selective prediction and model routing. Our code is available at https://github.com/ml-stat-Sustech/verbalized-confidence-training.

Conformal prediction (CP) provides distribution-free prediction intervals for fixed forecasters, but its standard calibration procedure is often inefficient for time series data, where forecast errors are temporally dependent and change across time and operating conditions. Recent time series CP methods improve local calibration using recent, weighted, or localized residuals. Yet local calibration can remain indirect, since broad residual weighting or additional adaptation procedures may dilute the evidence most relevant to the current prediction. This motivates a simple retrieval and correction strategy that selects similar past residuals as local evidence and then corrects the coverage error left by retrieval. In this paper, we propose Retrieval--Corrected Conformal Prediction (RCCP), a retrieval-augmented calibration method for time series prediction intervals. RCCP builds an asymmetric interval from retrieved one-sided residuals and calibrates its normalized retrieval error with a scalar conformal correction. Thus, retrieval provides local residual evidence, while conformal correction determines the final scale needed for coverage. We provide a coverage-gap bound based on the stability of the normalized retrieval error distribution. Across standard benchmarks and backbone forecasters, RCCP attains the target coverage in every setting and achieves the lowest Winkler scores, with fewer severe misses. RCCP also achieves low calibration and inference overhead, showing that retrieval-corrected calibration is an effective and scalable approach to uncertainty quantification in time series forecasting. Code is available at https://github.com/jinsaaang/rccp.

Sports betting's recent federal legalisation in the USA coincides with the golden age of machine learning. If bettors can leverage data to reliably predict the probability of an outcome, they can recognise when the bookmaker's odds are in their favour. As sports betting is a multi-billion dollar industry in the USA alone, identifying such opportunities could be extremely lucrative. Many researchers have applied machine learning to the sports outcome prediction problem, generally using accuracy to evaluate the performance of predictive models. We hypothesise that for the sports betting problem, model calibration is more important than accuracy. To test this hypothesis, we train models on NBA data over several seasons and run betting experiments on a single season, using published odds. We show that using calibration, rather than accuracy, as the basis for model selection leads to greater returns, on average (return on investment of +34.69% versus -35.17%) and in the best case (+36.93% versus +5.56%). These findings suggest that for sports betting (or any probabilistic decision-making problem), calibration is a more important metric than accuracy. Sports bettors who wish to increase profits should therefore select their predictive model based on calibration, rather than accuracy.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

As AI-based code generation becomes widespread, researchers are investigating the calibration of code LLMs - ensuring their confidence scores faithfully represent the true likelihood of code correctness. To do so, we investigate multicalibration, which can capture additional factors about a coding problem, such as complexity, code length, or programming language used. We study four multicalibration approaches on three function synthesis benchmarks, using latest-generation code LLMs (Qwen3 Coder, GPT-OSS, DeepSeek-R1-Distill). Our results demonstrate that multicalibration can yield distinct improvements over both uncalibrated token likelihoods (+1.03 in skill score) and baseline calibrations (+0.37 in skill score). We study the influence of the aforementioned factors in ablations, and make our dataset (consisting of code generations, likelihoods, and correctness labels) available for future research on code LLM calibration.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

Reinforcement Learning with verifiable rewards (RLVR) has emerged as a primary learning paradigm for enhancing the reasoning capabilities of multi-modal large language models (MLLMs). However, during RL training, the enormous state space of MLLM and sparse rewards often leads to entropy collapse, policy degradation, or over-exploitation of suboptimal behaviors. This necessitates an exploration strategy that maintains productive stochasticity while avoiding the drawbacks of uncontrolled random sampling, yielding inefficient exploration. In this paper, we propose CalibRL, a hybrid-policy RLVR framework that supports controllable exploration with expert guidance, enabled by two key mechanisms. First, a distribution-aware advantage weighting scales updates by group rareness to calibrate the distribution, therefore preserving exploration. Meanwhile, the asymmetric activation function (LeakyReLU) leverages the expert knowledge as a calibration baseline to moderate overconfident updates while preserving their corrective direction. CalibRL increases policy entropy in a guided manner and clarifies the target distribution by estimating the on-policy distribution through online sampling. Updates are driven by these informative behaviors, avoiding convergence to erroneous patterns. Importantly, these designs help alleviate the distributional mismatch between the model's policy and expert trajectories, thereby achieving a more stable balance between exploration and exploitation. Extensive experiments across eight benchmarks, including both in-domain and out-of-domain settings, demonstrate consistent improvements, validating the effectiveness of our controllable hybrid-policy RLVR training. Code is available at https://github.com/zhh6425/CalibRL.

Consider the problem of finding the best matching in a weighted graph where we only have access to predictions of the actual stochastic weights, based on an underlying context. If the predictor is the Bayes optimal one, then computing the best matching based on the predicted weights is optimal. However, in practice, this perfect information scenario is not realistic. Given an imperfect predictor, a suboptimal decision rule may compensate for the induced error and thus outperform the standard optimal rule. In this paper, we propose multicalibration as a way to address this problem. This fairness notion requires a predictor to be unbiased on each element of a family of protected sets of contexts. Given a class of matching algorithms mathcal C and any predictor γ of the edge-weights, we show how to construct a specific multicalibrated predictor hat γ, with the following property. Picking the best matching based on the output of hat γ is competitive with the best decision rule in mathcal C applied onto the original predictor γ. We complement this result by providing sample complexity bounds.

Deep neural networks remain vulnerable to adversarial perturbations, which can distort not only predictions but also confidence scores, undermining uncertainty calibration. While existing certification methods focus on preserving the predicted category, providing guarantees on how calibration behaves under adversarial attacks remains overlooked. In this work, we introduce CalCErt, a simple and efficient post-hoc strategy that certifies bin-wise confidence calibration for any pretrained differentiable classifier. Our approach combines empirical calibration estimates, statistical concentration bounds, and local Lipschitz estimates of the confidence function to derive data-dependent upper bounds on worst-case miscalibration within an ell_2-ball of radius R. We evaluate CalCErt across 11 medical image classification tasks and multiple adversarial perturbations, demonstrating substantially higher certified coverage than baseline strategies while maintaining competitive tightness. Our code is available at https://github.com/leofillioux/calcert.

As LLM-based judges become integral to industry applications, obtaining well-calibrated uncertainty estimates efficiently has become critical for production deployment. However, existing techniques, such as verbalized confidence and multi-generation methods, are often either poorly calibrated or computationally expensive. We introduce linear probes trained with a Brier score-based loss to provide calibrated uncertainty estimates from reasoning judges' hidden states, requiring no additional model training. We evaluate our approach on both objective tasks (reasoning, mathematics, factuality, coding) and subjective human preference judgments. Our results demonstrate that probes achieve superior calibration compared to existing methods with approx10x computational savings, generalize robustly to unseen evaluation domains, and deliver higher accuracy on high-confidence predictions. However, probes produce conservative estimates that underperform on easier datasets but may benefit safety-critical deployments prioritizing low false-positive rates. Overall, our work demonstrates that interpretability-based uncertainty estimation provides a practical and scalable plug-and-play solution for LLM judges in production.

Reliable large language models (LLMs) must not only produce accurate answers but also express confidence that faithfully reflects their probability of being correct. Such calibration is essential for identifying uncertain predictions and supporting reliable decision-making in real-world deployment. Recent studies incorporate calibration learning into reinforcement learning (RL), jointly optimizing answer correctness and verbalized confidence using ground-truth correctness supervision. However, their reliance on labeled data limits their applicability in practical test-time settings, where ground-truth labels are unavailable and calibration may need to adapt to newly encountered target tasks. To address this challenge, we propose Test-Time Calibration Learning (TTCL), a label-free framework that jointly adapts reasoning accuracy and verbalized confidence directly on unlabeled target-task data. Specifically, TTCL derives self-supervision signals for both correctness and calibration from multiple model-generated responses, enabling calibration learning at test time without ground-truth labels. Theoretical analysis further establishes TTCL as a bounded surrogate for the ideal calibration objective. Extensive experiments on mathematical reasoning and factual question answering demonstrate that TTCL consistently improves both accuracy and calibration across diverse models and tasks. On base models, TTCL achieves an average relative accuracy improvement of +40.13% and an ECE reduction of +70.80% across eight benchmarks. Moreover, TTCL can further improve both accuracy and calibration for already calibrated models under domain shift, particularly when source-domain calibration transfers poorly to target tasks. In the math-to-factQA setting, TTCL achieves an average relative accuracy gain of +20.35% and reduces ECE by +53.83%. The source code is released at https://github.com/tmlr-group/TTCL.

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing definition for calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new definition that escapes this caveat and an evaluation method using a simple histogram-based approach. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple, scaling-based calibration method that preforms as well as much more complex ones. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Forecasting has become a natural benchmark for reasoning under uncertainty. Yet existing evaluations of large language models remain limited to judgmental tasks in simple formats, such as binary or multiple-choice questions. In practice, however, forecasting spans a far broader scope. Across domains such as economics, public health, and social demographics, decisions hinge on numerical estimates over continuous quantities, a capability that current benchmarks do not capture. Evaluating such estimates requires a format that makes uncertainty explicit and testable. We propose prediction intervals as a natural and rigorous interface for this purpose. They demand scale awareness, internal consistency across confidence levels, and calibration over a continuum of outcomes, making them a more suitable evaluation format than point estimates for numerical forecasting. To assess this capability, we introduce a new benchmark QuantSightBench, and evaluate frontier models under multiple settings, assessing both empirical coverage and interval sharpness. Our results show that none of the 11 evaluated frontier and open-weight models achieves the 90\% coverage target, with the top performers Gemini 3.1 Pro (79.1\%), Grok 4 (76.4\%), and GPT-5.4 (75.3\%) all falling at least 10 percentage points short. Calibration degrades sharply at extreme magnitudes, revealing systematic overconfidence across all evaluated models.

Language models (LMs) may lead their users to make suboptimal downstream decisions when they confidently hallucinate. This issue can be mitigated by having the LM verbally convey the probability that its claims are correct, but existing models cannot produce text with calibrated confidence statements. Through the lens of decision-making, we formalize linguistic calibration for long-form generations: an LM is linguistically calibrated if its generations enable its users to make calibrated probabilistic predictions. This definition enables a training framework where a supervised finetuning step bootstraps an LM to emit long-form generations with confidence statements such as "I estimate a 30% chance of..." or "I am certain that...", followed by a reinforcement learning step which rewards generations that enable a user to provide calibrated answers to related questions. We linguistically calibrate Llama 2 7B and find in automated and human evaluations of long-form generations that it is significantly more calibrated than strong finetuned factuality baselines with comparable accuracy. These findings generalize under distribution shift on question-answering and under a significant task shift to person biography generation. Our results demonstrate that long-form generations may be calibrated end-to-end by constructing an objective in the space of the predictions that users make in downstream decision-making.

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level δ=0.1, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.

Learned post-training quantization (PTQ) calibration fits quantizer parameters on a small calibration set, and for a text embedder the natural supervision is retrieval relevance. We ask two questions that are usually conflated: how far to calibrate, and whether to calibrate at all. Across three embedders (e5-base-v2, BGE-M3, EmbeddingGemma-300m) at 4-bit weight quantization, 161 calibration runs, the outcome of a fixed procedure ranges from a gain to catastrophic degradation, and the driver is the dose of the update, measured as the functional displacement D_func of the quantized model from its uncalibrated start. On EmbeddingGemma the same learning-rate grid gives +1.47 to -71.53 points of in-domain NDCG@10 change; a label-free cosine objective collapses at the same dose (-69.52 vs -71.63), so the collapse is a property of learnable calibration rather than of retrieval supervision. Objective sensitivity is heterogeneous: on e5, ranking calibration is substantially more robust than cosine at matched displacement (+14.16 +/- 4.34 pp, 95% t-CI [+3.37, +24.96], three paired slates), whereas on BGE-M3 the ordering is directionally opposite but unresolved ([-5.18, +2.38]). Dose is the main axis but not a sufficient statistic: equal D_func reached along different paths differs by up to 1.61 pp. We therefore treat calibration as an optional intervention. A pre-registered rule that accepts a checkpoint only when a per-query paired confidence interval on a 25% calibration-validation split clears the uncalibrated baseline was run on 6 independent slates and five arms. It never selected a checkpoint below its slate's baseline (0 harmful selections in 30 decisions), retained 8 of 11 beneficial updates, and paid a mean oracle regret of 1.52 pp with one abstention that forfeited 11.13 pp, a safety-opportunity trade-off, not a free improvement. We report what remains open, including label efficiency.

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.

In the era of large language models, creative writing quality lacks a computable theoretical anchor. The dominant approaches are rubric scoring -- decomposing holistic aesthetic judgment into sub-scores -- and RLHF preference signals -- replacing quality with group votes. Both bypass the statistical structure of the text itself. This paper provides an information-theoretic foundation to fill this gap. We propose 'calibrated surprise' as the information-theoretic essence of excellent creative writing. This judgment matches reading intuition and covers its opposite. This literary judgment admits a precise mathematical formulation. Under full-dimensional constraints Y, feasible writing choices are forced into an extremely narrow space. The rare survivors are, from the unconstrained perspective, exactly the least predictable choices. Both are measured precisely by Shannon mutual information I(X;Y) = H(X) - H(X|Y) -- 'calibrated' corresponds to H(X|Y) approaching 0; 'surprising' corresponds to H(X) going high. The subtraction structure of the formula naturally separates 'well-grounded surprise' from 'pure noise'. We use token-level logprobs from Qwen1.5-7B as an operational proxy for the ideal reader's probability distribution. Across 20 pairs (12 Chinese / 8 English) of high-quality vs. systematically degraded literary passages, 20/20 pairs support the core prediction: high-quality passages have systematically higher I(X;Y) than their degraded versions.

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable Bayesian conformal approach based on the influence-function Bayesian bootstrap (BB) with data-driven tuning of the Dirichlet concentration parameter, α. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating α to optimize empirical coverage or average log-probability, our method constructs prediction intervals and distributions that are both well-calibrated and sharp. Across a range of regression models and data settings, this Bayesian conformal framework consistently yields improved empirical coverage and log-score compared to standard Bayesian posteriors. Our procedure is fast, easy to implement, and offers a flexible approach for distributional calibration in predictive modeling.

Autonomous agents based on large language models (LLMs) are rapidly evolving to handle multi-turn tasks, but ensuring their trustworthiness remains a critical challenge. A fundamental pillar of this trustworthiness is calibration, which refers to an agent's ability to express confidence that reliably reflects its actual performance. While calibration is well-established for static models, its dynamics in tool-integrated agentic workflows remain underexplored. In this work, we systematically investigate verbalized calibration in tool-use agents, revealing a fundamental confidence dichotomy driven by tool type. Specifically, our pilot study identifies that evidence tools (e.g., web search) systematically induce severe overconfidence due to inherent noise in retrieved information, while verification tools (e.g., code interpreters) can ground reasoning through deterministic feedback and mitigate miscalibration. To robustly improve calibration across tool types, we propose a reinforcement learning (RL) fine-tuning framework that jointly optimizes task accuracy and calibration, supported by a holistic benchmark of reward designs. We demonstrate that our trained agents not only achieve superior calibration but also exhibit robust generalization from local training environments to noisy web settings and to distinct domains such as mathematical reasoning. Our results highlight the necessity of domain-specific calibration strategies for tool-use agents. More broadly, this work establishes a foundation for building self-aware agents that can reliably communicate uncertainty in high-stakes, real-world deployments.

Neural NLP models are often miscalibrated, assigning high confidence to incorrect predictions, which undermines selective prediction and high-stakes deployment. Post-hoc calibration methods adjust output probabilities but leave internal computation unchanged, while ensemble and Bayesian approaches improve uncertainty at substantial training or storage cost. We propose UAT-LITE, an inference-time framework that makes self-attention uncertainty-aware using approximate Bayesian inference via Monte Carlo dropout in pretrained transformer classifiers. Token-level epistemic uncertainty is estimated from stochastic forward passes and used to modulate self-attention during contextualization, without modifying pretrained weights or training objectives. We additionally introduce a layerwise variance decomposition to diagnose how predictive uncertainty accumulates across transformer depth. Across the SQuAD 2.0 answerability, MNLI, and SST-2, UAT-LITE reduces Expected Calibration Error by approximately 20% on average relative to a fine-tuned BERT-base baseline while preserving task accuracy, and improves selective prediction and robustness under distribution shift.

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

Training terminal agents requires executable and verifiable tasks that are not merely solvable, but appropriately challenging for learning. Executable validation establishes feasibility, yet does not reveal how a task behaves relative to a given solver setting. In this paper, we present CalibForge, an autonomous terminal-task synthesis system that uses verified solver behavior to revise candidate tasks through adversarial solver calibration. Multi-solver calibration targets disagreement within a heterogeneous solver pool, whereas contrastive solver calibration targets a designated strong-pass/weak-fail relation; both operationalize a solver-relative learnable zone anchored in demonstrated solvability. Using CalibForge, we construct 5,431 calibrated terminal tasks. Our ablations show that both strategies yield more effective supervision than authoring and validation alone or ordinary single-solver feedback. Models trained on the full collection achieve 32.58% and 47.57% on Terminal-Bench 2.0. The largest improvements over the corresponding base model reach 24.71 percentage points on Terminal-Bench 2.0, 27.68 points on SWE-bench Pro, and 30.04 points on Doc2Repo. Together, these results support solver-relative learnability as a practical target for constructing effective and transferable agent training data.

Transformers, currently the state-of-the-art in natural language understanding (NLU) tasks, are prone to generate uncalibrated predictions or extreme probabilities, making the process of taking different decisions based on their output relatively difficult. In this paper we propose to build several inductive Venn--ABERS predictors (IVAP), which are guaranteed to be well calibrated under minimal assumptions, based on a selection of pre-trained transformers. We test their performance over a set of diverse NLU tasks and show that they are capable of producing well-calibrated probabilistic predictions that are uniformly spread over the [0,1] interval -- all while retaining the original model's predictive accuracy.