Model Calibration

Extracting actionable knowledge from industrial visual data is fundamentally bottlenecked by extreme class imbalance and the prohibitive computational complexity of modern foundation models. In semi-conductor manufacturing, identifying multi-label wafer defects is a complex spatial data mining task where overlapping patterns obscure critical root-cause signals. While Vision Transformers (ViTs) excel at global dependency extraction, their quadratic scaling renders them inefficient for high-throughput, real-time anomaly detection. To overcome these computational barriers, this paper introduces Hybrid Quantum-MambaVision, a highly efficient architecture tailored for spatial knowledge discovery. We integrate a linear-complexity State-Space Model (SSM) backbone with a Parameterized Quantum Context Adapter (QCA) and Low-Rank Adaptation (LoRA). The Mamba backbone efficiently captures long-range spatial dependencies, while the quantum adapter maps compressed latent features into a high-dimensional Hilbert space to disentangle complex, overlapping signatures. On the highly imbalanced MixedWM38 dataset, Hybrid Quantum-MambaVision achieves exceptional multi-label classification performance, significantly reducing the error rate on complex multi-defect topologies compared to classical baselines. The quantum regularizer acts as a profound uncertainty calibrator, substantially reducing Maximum Calibration Error (MCE) and minimizing expected false-positive costs. This work establishes a scalable Quantum-Classical hybrid paradigm for efficient representation learning in industrial data mining.

Model merging combines task experts into one model and avoids joint training, retraining, or deploying many expert models, but the merged model often still underperforms task experts. We study this performance gap through feature drift, the difference between features produced by the merged model and by the expert on the same input. Our theory decomposes this drift into upstream propagation and local mismatch, tracks how it propagates and combines through later layers in forward order, and links final feature drift to output drift. This view motivates FeatCal, which uses a small calibration set to calibrate the merged model weights layer by layer in forward order, reducing feature drift while staying close to merged weights and preserving the benefits of model merging. FeatCal uses an efficient closed-form solution to update model weights, with no gradient descent, iterative optimization, or extra modules. On the main CLIP and GLUE benchmarks, FeatCal beats Surgery and ProbSurgery, the closest post-merging calibration baselines: 85.5% vs. 77.0%/78.8% on CLIP-ViT-B/32 Task Arithmetic (TA) and 85.2% vs. 83.7%/82.2% on FLAN-T5-base GLUE. On CLIP-ViT-B/32, 8 examples per task reach 82.9%, and 256 examples per task take 53 seconds, about 4x faster than both baselines, showing better sample efficiency and lower calibration cost.

We introduce Observation-aware Conformal Uncertainty Local-Calibration (OCULAR), a conformal prediction-based algorithm that uses perception information to provide uncertainty quantification guarantees for unseen test-time environments. While previous conformal approaches lack the ability to discriminate between state-action space regions leading to higher or lower model mismatch, and require environment-specific data, our method uses data collected from visually similar environments to provably calibrate a linear Gaussian dynamics model of arbitrary fidelity. The prediction regions generated from OCULAR are guaranteed to contain the future system states with, at least, a user-set likelihood, despite both aleatoric and epistemic uncertainty -- i.e., uncertainty arising from both stochastic disturbances and lack of data. Our guarantees are non-asymptotic and distribution-free, not requiring strong assumptions about the unknown real system dynamics. Our calibration procedure enables distinguishing between observation-velocity-action inputs leading to higher and lower next-state-uncertainty, which is helpful for probabilistically-safe planning. We numerically validate our algorithm on a double-integrator system subject to random perturbations and significant model mismatch, using both a simplified sensor and a more realistic simulated camera. Our approach calibrates approximate uncertainty estimates both when in-distribution and out-of-distribution, producing volume-efficient prediction regions without requiring environment-specific data.

Multimodal Large Language Models (MLLMs) have shown strong performance in multi-image cross-modal retrieval, yet suffer from severe position bias, where predictions are dominated by input order rather than semantic relevance. Through empirical analysis, we identify a phenomenon termed Logit-Attention Divergence, in which output logits are heavily biased while internal attention maps remain well-aligned with relevant visual evidence. This observation reveals a fundamental limitation of existing logit-level calibration methods such as PriDe. Based on this insight, we propose a training-free, attention-guided debiasing framework that leverages intrinsic attention signals for instance-level correction at inference time, requiring only a minimal calibration set with negligible computational overhead. Experiments on MS-COCO-based benchmarks show that our method substantially improves permutation invariance and achieves state-of-the-art performance, enhancing accuracy by over 40% compared to baselines. Code is available at https://github.com/brightXian/LAD.

Detecting out-of-distribution (OOD) samples is critical for safe deployment of neural networks in safety-critical applications. While maximum softmax probability (MSP) provides a simple baseline, it lacks theoretical grounding and suffers from miscalibration. We propose VNDUQE (VIB-based Novelty Detection and Uncertainty Quantification for Nondestructive Evaluation), which investigates novelty detection through the Deep Variational Information Bottleneck (VIB), which explicitly constrains information flow through learned representations. We train VIB models on MNIST with held-out digit classes and evaluate OOD detection using information-theoretic metrics: KL divergence and prediction entropy. Our results reveal complementary detection signals: KL divergence achieves perfect detection (100% AUROC on noise) on far-OOD samples (noise, domain shift), while prediction entropy excels at near-OOD detection (94.7% AUROC on novel digit classes). A parallel detection strategy combining both metrics achieves 95.3% average AUROC and 92% true positive rate at 5% false positive rate, which is a 32 percentage point improvement over baseline MSP (85.0% AUROC, 60.1% TPR). Compression via the information bottleneck principle ($β=10^{-3}$) reduces Expected Calibration Error by 38%, demonstrating that information-theoretic constraints produce fundamentally more reliable uncertainty estimates. These findings directly support active learning with expensive computational oracles, where well-calibrated novelty detection enables principled threshold selection for oracle queries.

Making calibrated online predictions is a central challenge in modern AI systems. Much of the existing literature focuses on fully adversarial environments where outcomes may be arbitrary, leading to conservative algorithms that can perform suboptimally in more benign settings, such as when outcomes are nearly stationary. This gap raises a natural question: can we design online prediction algorithms whose calibration error automatically adapts to the degree of non-stationarity in the environment, smoothly interpolating between i.i.d. and adversarial regimes? We answer this question in the affirmative and develop a suite of algorithms that achieve adaptive calibration guarantees under multiple calibration measures. Specifically, with $T$ being the number of rounds, $K$ being the unknown number of i.i.d. segments of the environment, and $C\in[0,T]$ being another unknown non-stationary measure defined as the minimal $\ell_1$ deviation of the mean outcomes, our algorithms attain $\widetilde{O}(\min\{\sqrt{T}+(TC)^{\frac{1}{3}}, \sqrt{KT}\})$ for $\ell_1$ calibration error and $\widetilde{O}(\min\{(1+C)^{\frac{1}{3}}, K\})$ for both $\ell_2$ and pseudo KL calibration error. These bounds match the optimal rates in the stationary case ($C=0$ and $K=1$) and recover known guarantees in the fully adversarial regime ($C, K=Ω(T)$). Our approach builds on and extends prior work [Hu et al., 2026, Luo et al., 2025], introducing an epoch-based scheduling together with a novel non-uniform partition of the prediction space that allocates finer resolution near the underlying ground truth.

Multicalibration requires predicted scores to agree with label probabilities across rich families of subgroups and score-dependent tests, but existing methods require clean input-label pairs for evaluation and post-processing. This assumption fails in weakly supervised learning (WSL) regimes -- including positive-unlabeled, unlabeled-unlabeled, and positive-confidence learning -- where clean labels are costly or unavailable even though reliable uncertainty estimates may be crucial. We address this gap by developing estimators of multicalibration error and post-hoc correction methods for WSL settings in which clean input-label pairs are unavailable. We propose a unified framework for estimating and correcting multicalibration under weak supervision by combining contamination-matrix risk rewrites with witness-based calibration constraints, yielding corrected multicalibration moments with finite-sample guarantees. We further propose weak-label multicalibration boost (WLMC), a generic post-hoc recalibration algorithm under weak supervision. Finally, we conduct experiments across multiple weak-supervision settings to evaluate multicalibration behavior and offer empirical insight into uncertainty estimation under weak supervision.

We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known $\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\widetilde O(\sqrt T)$, and for piecewise-stationary means with $J$ segments its rate is $\widetilde O(\sqrt{JT})$. More generally, the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.

Macroscopic transport modelling aims to predict traffic flows after proposed public policy interventions, such as a new road or railway section or a temporary road closure. As such, it is a vital step in infrastructure planning and development. Traditionally, building a transport model has relied on complex understanding of socio-economic characteristics of the population requiring expensive data collection via surveys, which are prone to biases. Previous numerical frameworks to optimize transport models to fit observed traffic flows are not easily-interpretable and can lead to overfit. We present here an alternative: a data-driven modelling protocol with objective function based on traffic counts, which can be nowadays cheaply and reliably obtained; explainable model weights; and a controlled path to increase model complexity and accuracy. We demonstrate our approach on several toy and realistic examples, and suggest ways to generalize to multimodal systems including public transport.

Calibration measures whether a model's predicted confidence aligns with its empirical accuracy, and is central to the reliable deployment of large language models (LLMs) in high-stakes domains such as medicine and law. While much recent work focuses on improving LLM calibration, the equally important question of how to evaluate it in realistic settings remains underdeveloped. Open-ended question answering (QA), the most common deployment setting for modern LLMs, is where existing evaluation methods fall short: logit-based metrics need restricted output formats and internal probabilities; verbalized confidence is self-reported and often overconfident; and sampling-based methods rely on task-specific extraction rules without a clear finite-sample target. We introduce Sem-ECE (Semantic-Sampling Expected Calibration Error), a calibration evaluation framework for open-ended QA that samples answers from the model, groups them into semantic classes, and uses the resulting frequencies as confidence. We study two estimators within this framework: Sem$_1$-ECE, the same-sample self-consistency score, and Sem$_2$-ECE, a held-out variant that separates answer selection from confidence evaluation. We prove both are asymptotically unbiased, and further show that they agree on easy questions but diverge on hard ones with Sem$_2$ achieving strictly smaller calibration error, so their gap also serves as a diagnostic for question difficulty. Experiments on three open-ended QA benchmarks across five leading commercial LLMs match our theoretical predictions and show that Sem-ECE outperforms verbalized confidence and existing sampling-based methods, while complementing logit-based evaluation when internal probabilities are unavailable.

Second-order calibration error quantifies how closely a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label probability on its level sets. We characterize the minimax rate of estimating the second-order calibration error for binary classification in the regime where a small perturbation is applied to the classifier outputs. Our procedure is simple: add independent bandwidth-$h$ sech noise to the score coordinates, then regress $Y^{(1)}$ and $Y^{(1)}Y^{(2)}$ on the perturbed score using low-degree polynomials. Crucially, the sech perturbation makes the calibration functions analytic in a suitable strip. The resulting estimator has error $O_h(\log^{3/2}n/\sqrt n)$, with explicit constants. In the same setting, a matching $Ω(1/\sqrt{n})$ lower bound establishes minimax optimality up to logarithmic factors. As a corollary, we give a finite-sample guarantee for perturbed second-order Platt scaling, yielding a post-hoc procedure that recalibrates both the mean prediction and the epistemic-variance estimate of the perturbed higher-order predictor. Along the way, we give an explicit two-moment formulation of second-order calibration error and relate it quantitatively to the bucketed formulation of Ahdritz et al. [2025]. Our experiments confirm the predicted rate and the quality of the recalibrated uncertainties.

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploits the likelihood hypothesis: that machine-generated text should appear more probable to a detector language model than human-written text. However, we demonstrate that the token-level signal distinguishing human and machine text is non-uniform across the hidden space of the detector model, and naively averaging likelihood-based token scores across regions with fundamentally different statistical structure, as most detectors do, causes a form of Simpson's paradox: a strong local signal is destroyed by inappropriate aggregation. To correct for this, we introduce a learned local calibration step grounded in Bayesian decision theory. Rather than aggregating raw token scores, we first learn lightweight predictors of the score distributions conditioned on position in hidden space, and aggregate calibrated log-likelihood ratios instead. This single intervention dramatically and consistently improves detection performance across all baseline detectors and all datasets we consider. For example, our calibrated variant of Fast-DetectGPT improves AUROC from $0.63$ to $0.85$ on GPT-5.4 text, and a locally-calibrated DMAP detector we introduce achieves state-of-the-art performance across the board. That said, our central contribution is not a new detector, but a precise diagnosis of a significant cause of under-performance of existing detectors and a principled, modular remedy compatible with any token-averaging pipeline. This will serve as a foundation for the community to build upon, with natural avenues including richer distributional models, improved calibration strategies, and principled ensembling with hidden-space geometry signals via the full Bayes-optimal decision rule.

In routine care, individuals identified a priori as high-risk are usually tested for conditions more frequently. Protected attributes, such as sex or ethnicity may also determine testing frequency. Such heterogeneous detection rates across a population induce label error. This causes systematic model error for specific groups and biases performance metrics during validation. This paper proposes a method to correct for such bias in prediction models due to differential diagnostic delay. We use a causal inference framework to define our target estimand: an individual's diagnosis probability in a counterfactual scenario where their diagnosis rate matches that of a reference group. We model the longitudinal process as a hidden Markov model, in which confirmatory test results are emissions from a latent progressive disease stage. We validate our approach in simulated data and apply it to a case study of chronic kidney disease prediction using electronic health records. In simulations, our method reduces prediction bias and improves calibration-in-the-large, correcting the Observed:Expected ratio in the underdiagnosed group from 1.34 (standard deviation: 0.09) in a model developed without any correction for underdiagnosis bias to 1.02 (0.09). Violations of assumptions in the simulation affected the estimation of model parameters, but the proposed approach nonetheless remained better calibrated than the standard model. In the clinical case study, we identify diabetes as the main driver of observability, with an odds ratio of 10.36 (95% confidence interval, 9.80 - 11.02) in 6-month urine albumin-creatinine ratio testing rate. Using our approach to predict the counterfactual diagnostic rate in patients without diabetes, we improved the Observed:Expected ratio of a developed clinical prediction model from 1.55 (1.51 - 1.59) to 1.01 (0.98 - 1.04).

The Brier score conflates two distinct properties of probabilistic predictions: reliability (calibration error) and resolution (discriminatory power). We introduce the Manokhin Probability Matrix, a BCG-style two-dimensional diagnostic framework that separates them. Classifiers are placed on a 2x2 grid by Spiegelhalter Z-statistic and AUC-ROC expected rank, then assigned to one of four archetypes: Eagle (good on both axes), Bull (strong discrimination, poor calibration), Sloth (well-calibrated, weak discriminator), and Mole (poor on both). Each archetype carries a distinct prescription. We populate the matrix from a large-scale empirical study spanning 21 classifiers, 5 post-hoc calibrators, and 30 real-world binary classification tasks from the TabArena-v0.1 suite. The assignment is unambiguous. CatBoost, TabICL, EBM, TabPFN, GBC, and Random Forest are Eagles. XGBoost, LightGBM, and HGB are Bulls; Venn-Abers calibration cuts log-loss by 6.5 to 12.6% on Bulls but degrades Eagles by 2.1%. SVM, LR, LDA, and the empirical base-rate predictor are Sloths. MLP, KNN, Naive Bayes, and ExtraTrees are Moles. A theoretical asymmetry follows: no order-preserving post-hoc calibrator can add discriminatory power (Proposition 1), so calibration is the fixable part and discrimination is the hard part. The practical rule is direct: do not optimise aggregate Brier score without first decomposing it; optimise discrimination first, then fix calibration post-hoc. Code and raw experimental data are available at https://github.com/valeman/classifier_calibration.

Calibrating the urban underlying surface parameters is crucial for urban flood simulation. We formulate the parameter calibration problem into an optimization problem within the Bayesian framework using the maximum likelihood principle. We adopt the urban flood dynamical system model as the surrogate model and innovatively introduce latent variables inspired by machine learning to represent more uncertainties, which can also be compatible with common physical parameter calibration. For more efficient optimization, we construct the adjoint equation of the surrogate model to obtain gradient information and propose the parameter sharing technique and the localization technique to reduce the computation complexity of the adjoint equation. A simple case verifies the proposed method can converge quickly and is insensitive to the observation time interval. In the case derived from Test 8A, we calibrate Manning's coefficient of urban roads, with a maximum relative error of 13.88% and a minimum of 1.16%.

Flavor-tagging calibrations are often provided either as scale factors measured at a finite set of working points or as binned corrections to a chosen one-dimensional discriminant. However, this approach falls short of providing continuous, event-level calibration across the full multicomponent outputs of modern taggers. This limitation leads to information loss in analyses that demand high-performance flavor tagging, restricting analyses to a limited set of predefined variables. In this work, we propose a geometry-aware framework that formulates flavor-tagger calibration as an optimal transport problem on the probability simplex. The transport maps are parameterized and trained in the isometric log-ratio coordinate system. Because the quadratic Euclidean cost of Brenier transport in this coordinate system is equivalent to the Aitchison distance on the simplex, the learned map induces a minimal deformation under the Aitchison geometry. Furthermore, we extract flavor-conditional target distributions directly from control-region data using an expectation-maximization (EM) technique that simultaneously fits multiple control regions, models each flavor component with a normalizing flow, and estimates the regional mixture fractions. The extracted targets are subsequently used to learn flavor-factorized transport maps. Because the joint estimation of mixture fractions and flexible component densities admits weakly constrained directions, we further introduce a linearized feedback-operator analysis that propagates the fitted composition covariance into the extracted component densities, separating data-constrained modes from those dominated by the composition prior. The simulation-based closure study demonstrates improved closure in dedicated control regions and in independent validation mixtures.

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time trajectory increments, state-space partitioning, or repeated simulation of candidate models, which become unreliable or computationally expensive for high-dimensional systems, coarse temporal sampling, or unevenly sampled data. We introduce a data-driven calibration method based on a novel relationship between the coefficients of a stochastic reduced model and the conditional score of the finite-time transition density, defined as the gradient of the logarithm of the transition density with respect to the initial state. The resulting identity expresses derivatives of lagged correlation functions as stationary expectations over observed lagged pairs involving this conditional score and the unknown model coefficients. This formulation allows the drift and diffusion structure to be constrained directly from finite-lag statistics, without differentiating trajectories, partitioning state space, or repeatedly integrating candidate reduced models during calibration, yielding a least-squares fitting problem over stationary lagged pairs. We validate the approach on three systems of increasing complexity: an analytically tractable Cox--Ingersoll--Ross diffusion, a two-dimensional nonequilibrium diffusion with affine multiplicative noise, and a periodic soft-spin stochastic Landau--Lifshitz chain. Across these tests, the inferred models preserve the invariant statistics while reproducing finite-lag dynamical correlations. The framework provides a scalable route for learning stochastic reduced-order models from data that reproduce prescribed statistical and dynamical properties.

Systematic biases in General Circulation Model (GCM) outputs limit their direct applicability in regional planning, making bias correction a technically demanding but necessary step for both short-term and long-term impact assessment. Correcting precipitation is particularly challenging due to its non-Gaussian distribution, intermittent nature, and heavy-tailed extremes. However, traditional statistical bias-correction methods have limited ability to learn systematic patterns from large datasets or generalize to new locations. While machine learning (ML) provides greater flexibility, it can produce unpredictable and difficult-to-interpret results, limiting generalization across GCMs and locations. In this study, we propose a differentiable bias-adjustment framework called dCLIMBA, that learns a spatiotemporally adaptive parametric bias-adjustment procedure, rather than corrected precipitation directly, between historical CMIP6 model outputs and a gridded observation-based dataset, Livneh. Results demonstrate that the proposed method corrects the magnitude and distribution of extreme precipitation with particularly strong performance in the upper tail. The quantile distribution of precipitation was well reproduced across diverse U.S. cities, and spatial patterns were comparable to those from the widely used LOCA2 statistical downscaling product. In addition, the framework showed partial future trend preservation and promising attenuation of marginal biases in unseen regions. This work presents a modular and efficient bias-correction approach. The differentiable approach provides an easy-to-use option for connecting atmospheric-model outputs to on-the-ground impacts.

In this study, deep learning is used to estimate kinetic parameters for modeling itaconic acid production based on real batch experiments conducted at different agitation speeds and reactor scales. Two deep learning strategies, namely direct deep learning (DDL) and generative conditional flow matching (CFM) are compared and benchmarked against nonlinear regression as a reference method. Compared with DDL, CFM consistently yields more accurate results. The concentration profiles predicted by CFM closely match those obtained from nonlinear regression, whereas DDL results in larger deviations. Similar behavior is observed in the scale-up experiments, where the CFM model again generalizes better and is more robust than the direct approach. These findings demonstrate that CFM can reliably predict system behavior across different operating conditions and scales, offering a flexible and data-efficient framework for parameter estimation in dynamic bioprocess models.

Optical motion capture (mocap) systems are widely used for ground-truth capture in AR/VR, SLAM and robotics datasets. These datasets require extrinsic calibration to align mocap coordinates to external camera frames -- a step that is subject to multiple sources of error in practice, and failures often go undetected until they corrupt downstream data. These issues are compounded for fisheye cameras, where spatially non-uniform distortion makes both calibration and verification more challenging. We present a calibration and verification system designed for this setting. Concretely, we target robustness to board-to-marker attachment variation, optimization initialization ambiguity, and session-to-session calibration drift after deployment. The calibration jointly estimates camera extrinsics and the board-to-marker transform, and uses a staged solver to improve convergence reliability under ambiguous initialization. The verification component, \lollypop, provides fast, operator-independent assessment through a measurement chain entirely independent of the calibration data. In experiments on a Meta Quest 3 headset with fisheye cameras, our calibration outperforms existing benchwork, and lollypop reliably detects calibration degradation over time. The system has been deployed in production data collection pipelines.

We study the minimax sample complexity of multicalibration in the batch setting. A learner observes $n$ i.i.d. samples from an unknown distribution and must output a (possibly randomized) predictor whose population multicalibration error, measured by Expected Calibration Error (ECE), is at most $\varepsilon$ with respect to a given family of groups. For every fixed $κ> 0$, in the regime $|G|\le \varepsilon^{-κ}$, we prove that $\widetildeΘ(\varepsilon^{-3})$ samples are necessary and sufficient, up to polylogarithmic factors. The lower bound holds even for randomized predictors, and the upper bound is realized by a randomized predictor obtained via an online-to-batch reduction. This separates the sample complexity of multicalibration from that of marginal calibration, which scales as $\widetildeΘ(\varepsilon^{-2})$, and shows that mean-ECE multicalibration is as difficult in the batch setting as it is in the online setting, in contrast to marginal calibration which is strictly more difficult in the online setting. In contrast we observe that for $κ= 0$, the sample complexity of multicalibration remains $\widetildeΘ(\varepsilon^{-2})$ exhibiting a sharp threshold phenomenon. More generally, we establish matching upper and lower bounds, up to polylogarithmic factors, for a weighted $L_p$ multicalibration metric for all $1 \le p \le 2$, with optimal exponent $3/p$. We also extend the lower-bound template to a regular class of elicitable properties, and combine it with the online upper bounds of Hu et al. (2025) to obtain matching bounds for calibrating properties including expectiles and bounded-density quantiles.

Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches correct for known device error rates but assume these rates remain stable across populations. We show this assumption fails under covariate shift and that multicalibration, which enforces calibration conditional on the input features rather than just on average, is sufficient for unbiased prevalence estimation under such shift. Standard calibration and quantification methods fail to provide this guarantee. Our work connects recent theoretical work on fairness to a longstanding measurement problem spanning nearly all academic disciplines. A simulation confirms that standard methods exhibit bias growing with shift magnitude, while a multicalibrated estimator maintains near-zero bias. While we focus the discussion mostly on LLMs, our theoretical results apply to any classification model. Two empirical applications -- estimating employment prevalence across U.S. states using the American Community Survey, and classifying political texts across four countries using an LLM -- demonstrate that multicalibration substantially reduces bias in practice, while highlighting that calibration data should cover the key feature dimensions along which target populations may differ.

Low-cost air quality sensors (LCS) provide a practical alternative to expensive regulatory-grade instruments, making dense urban monitoring networks possible. Yet their adoption is limited by calibration challenges, including sensor drift, environmental cross-sensitivity, and variability in performance from device to device. This work presents a deep learning framework for calibrating LCS measurements of PM$_{2.5}$, PM$_{10}$, and NO$_2$ using a Long Short-Term Memory (LSTM) network, trained on co-located reference data from the OxAria network in Oxford, UK. Unlike the Random Forest (RF) baseline, which treats each observation independently, the proposed approach captures temporal dependencies and delayed environmental effects through sequence-based learning, achieving higher $R^2$ values across training, validation, and test sets for all three pollutants. A feature set is constructed combining time-lagged parameters, harmonic encodings, and interaction terms to improve generalization on unseen temporal windows. Validation of unseen calibrated values against the Equivalence Spreadsheet Tool 3.1 demonstrates regulatory compliance with expanded uncertainties of 22.11% for NO$_2$, 12.42% for PM$_{10}$, and 9.1% for PM$_{2.5}$.

Digital twins of natural systems must remain aligned with physical systems that evolve over time, are only partially observed, and are typically modeled by mechanistic simulators whose parameters cannot be measured directly. In such settings, model adaptation is naturally posed as a simulation-based inference problem. However, sparse and indirect observations often fail to identify a unique and optimal calibration, leaving several simulator parameterizations compatible with the available evidence. This article presents a GFlowNet-based approach to model adaptation for digital twins of natural systems. We formulate adaptation as a generative modeling problem over complete simulator configurations, so that plausible parameterizations can be sampled with probability proportional to a reward derived from agreement between simulated and observed behavior. Using a controlled environment agriculture case study based on a mechanistic tomato model, we show that the learned policy recovers dominant regions of the adaptation landscape, retrieves strong calibration hypotheses, and preserves multiple plausible configurations under uncertainty.

Modern neural networks can achieve high accuracy while remaining poorly calibrated, producing confidence estimates that do not match empirical correctness. Yet calibration is often treated as a post-hoc attribute. We take a different perspective: we study calibration as a training-time phenomenon on small vision tasks, and ask whether calibrated solutions can be obtained reliably by intervening on the training procedure. We identify a tight coupling between calibration, curvature, and margins during training of deep networks under multiple gradient-based methods. Empirically, Expected Calibration Error (ECE) closely tracks curvature-based sharpness throughout optimization. Mathematically, we show that both ECE and Gauss--Newton curvature are controlled, up to problem-specific constants, by the same margin-dependent exponential tail functional along the trajectory. Guided by this mechanism, we introduce a margin-aware training objective that explicitly targets robust-margin tails and local smoothness, yielding improved out-of-sample calibration across optimizers without sacrificing accuracy.

We give a Gordon-Greenwald-Marks (GGM) style black-box reduction from online learning to online multicalibration. Concretely, we show that to achieve high-dimensional multicalibration with respect to a class of functions H, it suffices to combine any no-regret learner over H with an expected variational inequality (EVI) solver. We also prove a converse statement showing that efficient multicalibration implies efficient EVI solving, highlighting how EVIs in multicalibration mirror the role of fixed points in the GGM result for $Φ$-regret. This first set of results resolves the main open question in Garg, Jung, Reingold, and Roth (SODA '24), showing that oracle-efficient online multicalibration with $\sqrt{T}$-type guarantees is possible in full generality. Furthermore, our GGM-style reduction unifies the analyses of existing online multicalibration algorithms, enables new algorithms for challenging environments with delayed observations or censored outcomes, and yields the first efficient black-box reduction between online learning and multiclass omniprediction. Our second main result is a fine-grained reduction from high-dimensional online multicalibration to (contextual) $Φ$-regret minimization. Together with our first result, this establishes a new route from external regret to Phi-regret that bypasses sophisticated fixed-point or semi-separation machinery, dramatically simplifies a result of Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25) while improving rates, and yields new algorithms that are robust to richer deviation classes, such as those belonging to any reproducing kernel Hilbert space.

High-fidelity, scalable market simulation is a key instrument for mechanism evaluation, stress testing, and counterfactual policy analysis. Yet existing simulators rarely achieve mechanism fidelity beyond single-asset intraday settings, microstructure fidelity against historical limit order books (LOB), and computational tractability at market scale in a single system. This paper presents EvoMarket, a discrete-event, multi-agent financial market simulator designed for intervention-oriented experiments in multi-asset and cross-day environments. EvoMarket couples a high-throughput execution core (optimized LOB data structures, hierarchical scheduling under propagation delays, and asynchronous per-asset matching) with explicit institutional mechanisms (market calendars, opening call auctions, price limits, and T+1 settlement). To avoid expensive black-box calibration, EvoMarket introduces an Oracle-guided in-run self-calibration mechanism that interprets microstructure discrepancy as missing order flow and synthesizes corrective orders at recording checkpoints. Experiments on China A-share order-flow and LOB data show close replay alignment over five trading days, fidelity gains from budgeted in-run calibration across depth levels, broad agent order-space coverage, and scalable performance under increasing input order rates and market breadth. We further demonstrate cross-asset linkage and event-study style intervention evaluation that produces structured dependence and interpretable event-time responses.

Collisions between cyclists and pedestrians at urban intersections remain a persistent source of injuries, yet few systems attempt real-time warnings to unequipped road users using commodity hardware. We present a prototype collision warning system that runs on a single edge device with a wide-angle fisheye camera, producing audible and visual alerts at 30,fps. The system makes four contributions. First, we develop a calibration pipeline for ultra-wide fisheye lenses that overcomes corner-detection failure and optimizer divergence through perspective remapping and direct bundle adjustment. Second, we combine fisheye-aware object detection with a closed-form ground-plane projection via a precomputed lookup table. Third, we introduce a design-time conformance simulation with 24 scripted hazard scenarios, stochastic size-aware detection failures, and a latency sweep showing that a first-order kinematic predictor maintains the mean warning budget above the distracted-pedestrian reaction time across realistic camera latencies. Fourth, we formalize the decision layer as a separable, auditable testbench with explicit deployment gates, contestability mechanisms, and a residual risk register. Under conformance testing with fisheye localization error, the selected pipeline configuration achieves 93.3% sensitivity and 92.3% specificity, with a mean warning budget of 3.3,s. The system design was informed by community-aided design workshops. Code and replication scripts are available at https://github.com/mkturkcan/bikeped.

External validation is widely regarded as the gold standard for prognostic model evaluation. In this study, we challenge the assumption that successful external calibration guarantees model generalizability and propose two complementary strategies to improve transportability of prognostic models across cohorts. Using six real-world surgical cohorts from tertiary academic centers, we tested whether successful external calibration depends largely on similarity in covariates and outcomes between training and validation cohorts, quantified using Kullback-Leibler (KL) divergence, with calibration assessed by the Integrated Calibration Index (ICI). From the model-developer's perspective, we trained the "best-on-average" prognostic model by tuning toward a meta-analysis-derived covariate and outcome distribution as an approximation of the broader target population. From the end-user perspective, we proposed a simple measure for cohort outcome similarity to identify, among published models, the one most suitable for a given target cohort in terms of both calibration and clinical utility. External calibration worsened as distributional mismatch increased. Higher KL divergence was associated with higher ICI in both surgery-alone (Spearman $ρ=0.614$, $p=0.004$) and surgery + adjuvant chemotherapy cohorts (Spearman $ρ=0.738$, $p<0.001$). Meta-analysis-informed weighting improved calibration in most settings without materially affecting discrimination, with the clearest benefit when evaluated on the aggregated external population ($p=0.037$). Models developed in more similar cohorts achieved lower ICI in surgery-alone (Spearman $ρ=0.803$, $p<0.001$) and surgery + adjuvant chemotherapy cohorts (Spearman $ρ=0.737$, $p<0.001$), and provided greater clinical utility on DCA.