Model Calibration

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Overview

For classifiers and language models, calibration asks whether confidence matches empirical correctness and develops post-hoc methods such as temperature scaling, isotonic regression, and local corrections, alongside training-time objectives. Online and multicalibration methods extend reliability to changing data, subgroups, and selective prediction, while conformal methods provide coverage guarantees for prediction sets or intervals. A related line calibrates mechanistic models and simulators to measurements using Bayesian inference, evolutionary optimization, differentiable surrogates, and data assimilation in areas such as climate, traffic, medicine, and engineering. Across settings from CIFAR and ImageNet to language-model question answering and clinical data, a central challenge is that aggregate calibration may fail for particular groups or under distribution shift, while flexible corrections require representative validation data and may affect accuracy or decisions.

Latest papers

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218 papers39 papers in the last four weeks, up 39% on the four weeks before. 0.2% of all new papers.

Apr 13, 2026

PACO: Proxy-Task Alignment and Online Calibration for On-the-Fly Category Discovery

On-the-Fly Category Discovery (OCD) requires a model, trained on an offline support set, to recognize known classes while discovering new ones from an online streaming sequence. Existing methods focus heavily on offline training. They aim to learn discriminative representations on the support set so that novel classes can be separated at test time. However, their discovery mechanism at inference is typically reduced to a single threshold. We argue that this paradigm is fundamentally flawed as OCD is not a static classification problem, but a dynamic process. The model must continuously decide 1) whether a sample belongs to a known class, 2) matches an existing novel category, or 3) should initiate a new one. Moreover, prior methods treat the support set as fixed knowledge. They do not update their decision boundaries as new evidence arrives during inference. This leads to unstable and inconsistent category formation. Our experiments confirm these issues. With properly calibrated and adaptive thresholds, substantial improvements can be achieved, even without changing the representation. Motivated by this, we propose PACO, a support-set-calibrated, tree-structured online decision framework. The framework models inference as a sequence of hierarchical decisions, including known-class routing, birth-aware novel assignment, and attach-versus-create operations over a dynamic prototype memory. Furthermore, we simulate the proxy discovery process to initialize the thresholds during offline training to align with inference. Thresholds are continuously updated during inference using mature novel prototypes. Importantly, PACO requires no heavy training and no dataset-specific tuning. It can be directly integrated into existing OCD pipelines as an inference-time module. Extensive experiments show significant improvements over SOTA baselines across seven benchmarks.

Weidong Tang, Bohan Zhang, Zhixiang Chi +3

China Agricultural University, College of Information and Electrical Engineering, Beijing, China · Concordia University, Department of Computer Science and Software Engineering, Montreal, Canada

Generalized Category DiscoveryModel CalibrationPrototype-Based Classification
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Apr 10, 2026

Confident in a Confidence Score: Investigating the Sensitivity of Confidence Scores to Supervised Fine-Tuning

Uncertainty quantification techniques measure confidence in language model outputs to support critical applications like hallucination detection and selective prediction. While prior work has developed various confidence metrics and demonstrated their calibration for classification tasks or using verbalized confidence, the robustness of probability-based and self-consistency-based UQ metrics for natural language generation remains underexplored particularly under model adaptation. Since practitioners routinely apply supervised fine-tuning to adapt models to new tasks, a key question arises: do confidence metrics maintain their calibration when models are fine-tuned? We investigate this question across NLG tasks including translation, question answering, and mathematical reasoning. We find that calibration shifts substantially after SFT: across 216 configurations, it degrades in 112 cases and improves in 104, with confidence scores shifting due to factors beyond output quality, such as proximity to the training distribution. Degradation is therefore neither universal nor rare, and its direction cannot be anticipated from the pre-SFT model. Through a downstream task evaluation, we show that this miscalibration substantially reduces the practical utility of confidence scores for identifying correct answers. Our findings reveal that existing confidence metrics for NLG cannot be reliably deployed off-the-shelf after fine-tuning, highlighting the need for calibration-robust UQ methods under model adaptation.

Lorenzo Jaime Yu Flores, Cesare Spinoso di-Piano, Jackie Chi Kit Cheung

Mila - Quebec AI Institute · McGill University · Canada CIFAR AI Chair, Mila

Confidence Estimation in Language ModelsLanguage Model CalibrationModel CalibrationLLM Fine-Tuning
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Apr 9, 2026

Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)

Recent progress in AI-enabled constitutive modeling has concentrated on moving from a purely data-driven paradigm to the enforcement of physical constraints and mechanistic principles, a concept referred to as physics augmentation. Classical phenomenological approaches rely on selecting a pre-defined model and calibrating its parameters, while machine learning methods often focus on discovery of the model itself. Sparse regression approaches lie in between, where large libraries of pre-defined models are probed during calibration. Sparsification in the aforementioned paradigm, but also in the context of neural network architecture, has been shown to enable interpretability, uncertainty quantification, but also heterogeneous software integration due to the low-dimensional nature of the resulting models. Most works in AI-enabled constitutive modeling have also focused on data from a single source, but in reality, materials modeling workflows can contain data from many different sources (multi-modal data), and also from testing other materials within the same materials class (multi-fidelity data). In this work, we introduce physics augmented finite element model updating (paFEMU), as a transfer learning approach that combines AI-enabled constitutive modeling, sparsification for interpretable model discovery, and finite element-based adjoint optimization utilizing multi-modal data. This is achieved by combining simple mechanical testing data, potentially from a distinct material, with digital image correlation-type full-field data acquisition to ultimately enable rapid constitutive modeling discovery. The simplicity of the sparse representation enables easy integration of neural constitutive models in existing finite element workflows, and also enables low-dimensional updating during transfer learning.

Jingye Tan, Govinda Anantha Padmanabha, Steven J. Yang +1

University of Southern California · Cornell University · Ecole Polytechnique Federale de Lausanne (EPFL) +1

Physics-Informed MLModel Calibration
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Apr 8, 2026

Improving Semantic Uncertainty Quantification in Language Model Question-Answering via Token-Level Temperature Scaling

Calibration is central to reliable semantic uncertainty quantification, yet prior work has largely focused on discrimination, neglecting calibration. As calibration and discrimination capture distinct aspects of uncertainty, focusing on discrimination alone yields an incomplete picture. We address this gap by systematically evaluating both aspects across a broad set of confidence measures. We show that current approaches, particularly fixed-temperature heuristics, produce systematically miscalibrated and poorly discriminative semantic confidence distributions. We demonstrate that optimising a single scalar temperature, which, we argue, provides a suitable inductive bias, is a surprisingly simple yet effective solution. Our exhaustive evaluation confirms that temperature scaling consistently improves semantic calibration, discrimination, and downstream entropy, outperforming both heuristic baselines and more expressive token-level recalibration methods on question-answering tasks.

Tom A. Lamb, Desi R. Ivanova, Philip H. S. Torr +1

University of Oxford · University of Toronto & Vijil

Language Model CalibrationLLM Uncertainty EstimationSemantic Uncertainty EstimationModel CalibrationQuestion Answering
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Apr 7, 2026

Calibration of a neural network ocean closure for improved mean state and variability

Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we formulate parameter tuning as a calibration problem using Ensemble Kalman Inversion (EKI). We optimize parameters of a neural network parameterization of mesoscale eddies in two idealized ocean models at coarse resolution. The calibrated parameterization reduces errors by factors of 1.7-3.3 in the time-averaged fluid interfaces and their variability compared to the unparameterized model, depending on the metric and configuration. The EKI method is robust to noise in time-averaged statistics arising from chaotic ocean dynamics. Furthermore, we propose an efficient calibration protocol that bypasses integration to statistical equilibrium by carefully choosing an initial condition. These results demonstrate that systematic calibration can substantially improve coarse-resolution ocean simulations and provide a practical pathway for reducing biases in global ocean models.

Pavel Perezhogin, Alistair Adcroft, Laure Zanna

Courant Institute School of Mathematics, Computing, and Data Science, New York University, New York, NY, USA · Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA

Model CalibrationParameter EstimationComputational Fluid DynamicsClimate Modeling
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Mar 26, 2026

Ultra-fast Traffic Nowcasting and Control via Differentiable Agent-based Simulation

Traffic digital twins, which inform policymakers of effective interventions based on large-scale, high-fidelity computational models calibrated to real-world traffic, hold promise for addressing societal challenges in our rapidly urbanizing world. However, conventional fine-grained traffic simulations are non-differentiable and typically rely on inefficient gradient-free optimization, making calibration for real-world applications computationally infeasible. Here we present a differentiable agent-based traffic simulator that enables ultra-fast model calibration, traffic nowcasting, and control on large-scale networks. We develop several differentiable computing techniques for simulating individual vehicle movements, including stochastic decision-making and inter-agent interactions, while ensuring that entire simulation trajectories remain end-to-end differentiable for efficient gradient-based optimization. On the large-scale Chicago road network, with over 10,000 calibration parameters, our model simulates more than one million vehicles at 173 times real-time speed. This ultra-fast simulation, together with efficient gradient-based optimization, enables us to complete model calibration using the previous 30 minutes of traffic data in 455 s, provide a one-hour-ahead traffic nowcast in 21 s, and solve the resulting traffic control problem in 728 s. This yields a full calibration--nowcast--control loop in under 20 minutes, leaving about 40 minutes of lead time for implementing interventions. Our work thus provides a practical computational basis for realizing traffic digital twins.

Fumiyasu Makinoshima, Yuya Yamaguchi, Eigo Segawa +2

Fujitsu Limited, Kawasaki, Japan · Fujitsu Research of America, Pittsburgh, PA, USA · Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, USA +1

Intelligent Transportation SystemsAgent-Based ModelingDigital TwinsTraffic ForecastingModel CalibrationDifferentiable Physics
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Mar 21, 2026

SATTC: Structure-Aware Label-Free Test-Time Calibration for Cross-Subject EEG-to-Image Retrieval

Cross-subject EEG-to-image retrieval for visual decoding is challenged by subject shift and hubness in the embedding space, which distort similarity geometry and destabilize top-k rankings, making small-k shortlists unreliable. We introduce SATTC (Structure-Aware Test-Time Calibration), a label-free calibration head that operates directly on the similarity matrix of frozen EEG and image encoders. SATTC combines a geometric expert, subject-adaptive whitening of EEG embeddings with an adaptive variant of Cross-domain Similarity Local Scaling (CSLS), and a structural expert built from mutual nearest neighbors, bidirectional top-k ranks, and class popularity, fused via a simple Product-of-Experts rule. On THINGS-EEG2 under a strict leave-one-subject-out protocol, standardized inference with cosine similarities, L2-normalized embeddings, and candidate whitening already yields a strong cross-subject baseline over the original ATM retrieval setup. Building on this baseline, SATTC further improves Top-1 and Top-5 accuracy, reduces hubness and per-class imbalance, and produces more reliable small-k shortlists. These gains transfer across multiple EEG encoders, supporting SATTC as an encoder-agnostic, label-free test-time calibration layer for cross-subject neural decoding.

Qunjie Huang, Weina Zhu

Yunnan University, China

Cross-Subject EEG DecodingEEG-Based Visual DecodingModel Calibration
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Mar 18, 2026

Variational Kernel Design for Internal Noise: Gaussian Chaos Noise, Representation Compatibility, and Reliable Deep Learning

Internal noise in deep networks is usually inherited from heuristics such as dropout, hard masking, or additive perturbation. We ask two questions: what correlation geometry should internal noise have, and is the implemented perturbation compatible with the representations it acts on? We answer these questions through Variational Kernel Design (VKD), a framework in which a noise mechanism is specified by a law family, a correlation kernel, and an injection operator, and is derived from learning desiderata. In a solved spatial subfamily, a quadratic maximum-entropy principle over latent log-fields yields a Gaussian optimizer with precision given by the Dirichlet Laplacian, so the induced geometry is the Dirichlet Green kernel. Wick normalization then gives a canonical positive mean-one gate, Gaussian Chaos Noise (GCh). For the sample-wise gate used in practice, we prove exact Gaussian control of pairwise log-ratio deformation, margin-sensitive ranking stability, and an exact expected intrinsic roughness budget; hard binary masks instead induce singular or coherence-amplified distortions on positive coherent representations. On ImageNet and ImageNet-C, GCh consistently improves calibration and under shift also improves NLL at competitive accuracy.

Ziran Liu

Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS), Shanghai 200433, China · Research Institute of Intelligent Complex Systems, Fudan University, Shanghai 200433, China

Kernel MethodsModel CalibrationDistribution Shift Robustness
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Mar 16, 2026

The Importance of Being Smoothly Calibrated

Recent work has highlighted the centrality of smooth calibration [Kakade and Foster, 2008] as a robust measure of calibration error. We generalize, unify, and extend previous results on smooth calibration, both as a robust calibration measure, and as a step towards omniprediction, which enables predictions with low regret for downstream decision makers seeking to optimize some proper loss unknown to the predictor. We present a new omniprediction guarantee for smoothly calibrated predictors, for the class of all bounded proper losses. We smooth the predictor by adding some noise to it, and compete against smoothed versions of any benchmark predictor on the space, where we add some noise to the predictor and then post-process it arbitrarily. The omniprediction error is bounded by the smooth calibration error of the predictor and the earth mover's distance from the benchmark. We exhibit instances showing that this dependence cannot, in general, be improved. We show how this unifies and extends prior results [Foster and Vohra, 1998; Hartline, Wu, and Yang, 2025] on omniprediction from smooth calibration. We present a crisp new characterization of smooth calibration in terms of the earth mover's distance to the closest perfectly calibrated joint distribution of predictions and labels. This also yields a simpler proof of the relation to the lower distance to calibration from [Blasiok, Gopalan, Hu, and Nakkiran, 2023]. We use this to show that the upper distance to calibration cannot be estimated within a quadratic factor with sample complexity independent of the support size of the predictions. This is in contrast to the distance to calibration, where the corresponding problem was known to be information-theoretically impossible: no finite number of samples suffice [Blasiok, Gopalan, Hu, and Nakkiran, 2023].

Parikshit Gopalan, Konstantinos Stavropoulos, Kunal Talwar +1

Apple · UT Austin · Harvard

Model CalibrationProbability Calibration
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Mar 14, 2026

Soft Mean Expected Calibration Error (SMECE): A Calibration Metric for Probabilistic Labels

The Expected Calibration Error (ece), the dominant calibration metric in machine learning, compares predicted probabilities against empirical frequencies of binary outcomes. This is appropriate when labels are binary events. However, many modern settings produce labels that are themselves probabilities rather than binary outcomes: a radiologist's stated confidence, a teacher model's soft output in knowledge distillation, a class posterior derived from a generative model, or an annotator agreement fraction. In these settings, ece commits a category error - it discards the probabilistic information in the label by forcing it into a binary comparison. The result is not a noisy approximation that more data will correct. It is a structural misalignment that persists and converges to the wrong answer with increasing precision as sample size grows. We introduce the Soft Mean Expected Calibration Error (smece), a calibration metric for settings where labels are of probabilistic nature. The modification to the ece formula is one line: replace the empirical hard-label fraction in each prediction bin with the mean probability label of the samples in that bin. smece reduces exactly to ece when labels are binary, making it a strict generalisation.

Michael Leznik

Probability CalibrationModel Calibration
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Mar 13, 2026

Analytical Logit Scaling for High-Resolution Sea Ice Topology Retrieval from Weakly Labeled SAR Imagery

High-resolution sea ice mapping using Synthetic Aperture Radar (SAR) is crucial for Arctic navigation and climate monitoring. However, operational ice charts provide only coarse, region-level polygons (weak labels), forcing automated segmentation models to struggle with pixel-level accuracy and often yielding under-confident, blurred concentration maps. In this paper, we propose a weakly supervised deep learning pipeline that fuses Sentinel-1 SAR and AMSR-2 radiometry data using a U-Net architecture trained with a region-based loss. To overcome the severe under-confidence caused by weak labels, we introduce an Analytical Logit Scaling method applied post-inference. By dynamically calculating the temperature and bias based on the latent space percentiles (2% and 98%) of each scene, we force a physical binarization of the predictions. This adaptive scaling acts as a topological extractor, successfully revealing fine-grained sea ice fractures (leads) at a 40-meter resolution without requiring any manual pixel-level annotations. Our approach not only resolves local topology but also perfectly preserves regional macroscopic concentrations, achieving a 78% accuracy on highly fragmented summer scenes, thereby bridging the gap between weakly supervised learning and high-resolution physical segmentation.

Reda Elwaradi, Julien Gimenez, Stéphane Hordoir +3

Mastère Spécialisé IA Télécom Paris, Institut Polytechnique de Paris Palaiseau, France · DTIS ONERA, Université Paris-Saclay 91120, Palaiseau, France

Remote Sensing Image SegmentationWeakly Supervised Image SegmentationTopology-Preserving Image SegmentationModel Calibration
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Mar 12, 2026

Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.

Kaushik Bhattacharya, Lianghao Cao, Andrew Stuart

California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA.

Bayesian Experimental DesignModel CalibrationParameter IdentifiabilityMaterials Science
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Mar 10, 2026

First Estimation of Model Parameters for Neutrino-Induced Nucleon Knockout Using Simulation-Based Inference

To enable an accurate determination of oscillation parameters, accelerator-based neutrino experiments require detailed simulations of nuclear interaction physics in the GeV regime. While substantial effort from both theory and experiment is currently being invested to improve the fidelity of these simulations, their present deficiencies typically oblige experimental collaborations to resort to empirical tuning of simulation model parameters. As the precision requirements of the field continue to become more stringent, machine learning techniques may provide a powerful means of handling corresponding growth in the complexity of future neutrino interaction model tuning exercises. To study the suitability of simulation-based inference (SBI) for this physics application, in this paper we revisit a tuned configuration of the GENIE neutrino event generator that was originally developed by the MicroBooNE collaboration. Despite closely reproducing the adopted values of four physics parameters when confronted with the tuned cross-section predictions as input, we find that our trained SBI algorithm prefers modestly different values (within MicroBooNE's assigned uncertainties) and achieves slightly better goodness-of-fit when inference is run on the experimental data set originally used by MicroBooNE. We also find that our trained algorithm can create a fair approximation of an alternative neutrino scattering simulation, NuWro, that shares only a subset of its physics model parameters with GENIE.

Karla Tame-Narvaez, Steven Gardiner, Aleksandra Ćiprijanović +1

Fermi National Accelerator Laboratory, Batavia, Illinois 60510 USA · Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637 · NSF-Simons AI Institute for the Sky (SkAI), 172 E. Chestnut St., Chicago, IL 60611

Parameter EstimationModel CalibrationSimulation-Based InferenceHigh-Energy PhysicsPhysics-Based Simulation
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Mar 9, 2026

Airborne Magnetic Anomaly Navigation with Neural-Network-Augmented Online Calibration

Airborne Magnetic Anomaly Navigation (MagNav) provides a jamming-resistant and robust alternative to satellite navigation but requires the real-time compensation of the aircraft platform's large and dynamic magnetic interference. State-of-the-art solutions often rely on extensive offline calibration flights or pre-training, creating a logistical barrier to operational deployment. We present a fully adaptive MagNav architecture featuring a "cold-start" capability that identifies and compensates for the aircraft's magnetic signature entirely in-flight. The proposed method utilizes an extended Kalman filter with an augmented state vector that simultaneously estimates the aircraft's kinematic states as well as the coefficients of the physics-based Tolles-Lawson calibration model and the parameters of a Neural Network to model aircraft interferences. The Kalman filter update is mathematically equivalent to an online Natural Gradient descent, integrating superior convergence and data efficiency of state-of-the-art second-order optimization directly into the navigation filter. To enhance operational robustness, the neural network is constrained to a residual learning role, modeling only the nonlinearities uncorrected by the explainable physics-based calibration baseline. Validated on the MagNav Challenge dataset, our framework effectively bounds inertial drift using a magnetometer-only feature set. The results demonstrate navigation accuracy comparable to state-of-the-art models trained offline, without requiring prior calibration flights or dedicated maneuvers.

Antonia Hager, Sven Nebendahl, Alexej Klushyn +3

Airbus, 82024 Taufkirchen, Germany. · Norwegian University of Science and Technology, 7034 Trondheim, Norway.

Online CalibrationGNSS-Denied LocalizationModel CalibrationExtended Kalman Filtering
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Mar 9, 2026

Slumbering to Precision: Enhancing Artificial Neural Network Calibration Through Sleep-like Processes

Artificial neural networks are often overconfident, undermining trust because their predicted probabilities do not match actual accuracy. Inspired by biological sleep and the role of spontaneous replay in memory and learning, we introduce Sleep Replay Consolidation (SRC), a novel calibration approach. SRC is a post-training, sleep-like phase that selectively replays internal representations to update network weights and improve calibration without supervised retraining. Across multiple experiments, SRC is competitive with and complementary to standard approaches such as temperature scaling. Combining SRC with temperature scaling achieves the best Brier score and entropy trade-offs for AlexNet and VGG19. These results show that SRC provides a fundamentally novel approach to improving neural network calibration. SRC-based calibration offers a practical path toward more trustworthy confidence estimates and narrows the gap between human-like uncertainty handling and modern deep networks.

Jean Erik Delanois, Aditya Ahuja, Giri P. Krishnan +1

Department of Computer Science & Engineering, University of California, San Diego, La Jolla, California, USA · Department of Medicine, University of California, San Diego, La Jolla, California, USA · ARTISAN, Georgia Institute of Technology, Atlanta, Georgia, USA

Model CalibrationPost-Hoc Calibration
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Mar 6, 2026

Margin and Consistency Supervision for Calibrated and Robust Vision Models

Deep vision classifiers often achieve high accuracy while remaining poorly calibrated and fragile under small distribution shifts. We present Margin and Consistency Supervision (MaCS), a simple, architecture-agnostic regularization framework that jointly enforces logit-space separation and local prediction stability. MaCS augments cross-entropy with (i) a hinge-squared margin penalty that enforces a target logit gap between the correct class and the strongest competitor, and (ii) a consistency regularizer that minimizes the KL divergence between predictions on clean inputs and mildly perturbed views. We provide a unifying theoretical analysis showing that increasing classification margin while reducing local sensitivity formalized via a Lipschitz-type stability proxy yields improved generalization guarantees and a provable robustness radius bound scaling with the margin-to-sensitivity ratio. Across several image classification benchmarks and several backbones spanning CNNs and Vision Transformers, MaCS consistently improves calibration (lower ECE and NLL) and robustness to common corruptions while preserving or improving top-1 accuracy. Our approach requires no additional data, no architectural changes, and negligible inference overhead, making it an effective drop-in replacement for standard training objectives.

Salim Khazem

Talan Research Center, Paris, France.

Distribution Shift RobustnessModel CalibrationRobust Loss FunctionsImage ClassificationConsistency Regularization
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Mar 4, 2026

Algorithmic Compliance and Regulatory Loss in Digital Assets

We study the deployment performance of machine learning based enforcement systems used in cryptocurrency anti money laundering (AML). Using forward looking and rolling evaluations on Bitcoin transaction data, we show that strong static classification metrics substantially overstate real world regulatory effectiveness. Temporal nonstationarity induces pronounced instability in cost sensitive enforcement thresholds, generating large and persistent excess regulatory losses relative to dynamically optimal benchmarks. The core failure arises from miscalibration of decision rules rather than from declining predictive accuracy per se. These findings underscore the fragility of fixed AML enforcement policies in evolving digital asset markets and motivate loss-based evaluation frameworks for regulatory oversight.

Khem Raj Bhatt, Krishna Sharma

Anti-Money LaunderingAnti-Money Laundering DetectionModel CalibrationConcept DriftCost-Sensitive LearningFinancial Fraud Detection+1
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Mar 2, 2026

DOCFORGE-BENCH: A Comprehensive 0-shot Benchmark for Document Forgery Detection and Analysis

We present DOCFORGE-BENCH, the first unified zero-shot benchmark for document forgery detection, evaluating 14 methods across eight datasets spanning text tampering, receipt forgery, and identity document manipulation. Unlike fine-tuning-oriented evaluations such as ForensicHub [Du et al., 2025], DOCFORGE-BENCH applies all methods with their published pretrained weights and no domain adaptation -- a deliberate design choice that reflects the realistic deployment scenario where practitioners lack labeled document training data. Our central finding is a pervasive calibration failure invisible under single-threshold protocols: methods achieve moderate Pixel-AUC (>=0.76) yet near-zero Pixel-F1. This AUC-F1 gap is not a discrimination failure but a score-distribution shift: tampered regions occupy only 0.27-4.17% of pixels in document images -- an order of magnitude less than in natural image benchmarks -- making the standard tau=0.5 threshold catastrophically miscalibrated. Oracle-F1 is 2-10x higher than fixed-threshold Pixel-F1, confirming that calibration, not representation, is the bottleneck. A controlled calibration experiment validates this: adapting a single threshold on N=10 domain images recovers 39-55% of the Oracle-F1 gap, demonstrating that threshold adaptation -- not retraining -- is the key missing step for practical deployment. Overall, no evaluated method works reliably out-of-the-box on diverse document types, underscoring that document forgery detection remains an unsolved problem. We further note that all eight datasets predate the era of generative AI editing; benchmarks covering diffusion- and LLM-based document forgeries represent a critical open gap on the modern attack surface.

Zengqi Zhao, Weidi Xia, En Wei +7

University of North Carolina at Chapel Hill · University of California, Irvine · Washington University in St. Louis +4

Text Forgery DetectionDigital ForensicsDigital Image ForensicsModel Calibration
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Mar 1, 2026

Modeling and Controlling Deployment Reliability under Temporal Distribution Shift

Machine learning models deployed in non-stationary environments are exposed to temporal distribution shift, which can erode predictive reliability over time. While common mitigation strategies such as periodic retraining and recalibration aim to preserve performance, they typically focus on average metrics evaluated at isolated time points and do not explicitly model how reliability evolves during deployment. We propose a deployment-centric framework that treats reliability as a dynamic state composed of discrimination and calibration. The trajectory of this state across sequential evaluation windows induces a measurable notion of volatility, allowing deployment adaptation to be formulated as a multi-objective control problem that balances reliability stability against cumulative intervention cost. Within this framework, we define a family of state-dependent intervention policies and empirically characterize the resulting cost-volatility Pareto frontier. Experiments on a large-scale, temporally indexed credit-risk dataset (1.35M loans, 2007-2018) show that selective, drift-triggered interventions can achieve smoother reliability trajectories than continuous rolling retraining while substantially reducing operational cost. These findings position deployment reliability under temporal shift as a controllable multi-objective system and highlight the role of policy design in shaping stability-cost trade-offs in high-stakes tabular applications.

Naimur Rahman, Naazreen Tabassum

Temporal Distribution ShiftModel Calibration
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Feb 26, 2026

Communication-Guided Multi-Mutation Differential Evolution for Crop Model Calibration

In this paper, we propose a multi-mutation optimization algorithm, Differential Evolution with Multi-Mutation Operator-Guided Communication (DE-MMOGC), implemented to improve the performance and convergence abilities of standard differential evolution in uncertain environments. DE-MMOGC introduces a communication-guided scheme integrated with multiple mutation operators to encourage exploration and avoid premature convergence. Along with this, it includes a dynamic operator selection mechanism to use the best-performing operator over successive generations. To assimilate real-world uncertainties and missing observations into the predictive model, the proposed algorithm is combined with the Ensemble Kalman Filter. To evaluate the efficacy of the proposed DE-MMOGC in uncertain systems, the unified framework is applied to improve the predictive accuracy of crop simulation models. These simulation models are essential to precision agriculture, as they make it easier to estimate crop growth in a variety of unpredictable weather scenarios. Additionally, precisely calibrating these models raises a challenge due to missing observations. Hence, the simplified WOFOST crop simulation model is incorporated in this study for leaf area index (LAI)-based crop yield estimation. DE-MMOGC enhances the WOFOST performance by optimizing crucial weather parameters (temperature and rainfall), since these parameters are highly uncertain across different crop varieties, such as wheat, rice, and cotton. The experimental study shows that DE-MMOGC outperforms the traditional evolutionary optimizers and achieves better correlation with real LAI values. We found that DE-MMOGC is a resilient solution for crop monitoring.

Sakshi Aggarwal, Mudasir Ganaie, Mukesh Saini

Differential EvolutionModel CalibrationCrop Yield PredictionPrecision Agriculture
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Feb 26, 2026

Knob: A Physics-Inspired Gating Interface for Interpretable and Controllable Neural Dynamics

Existing neural network calibration methods often treat calibration as a static, post-hoc optimization task. However, this neglects the dynamic and temporal nature of real-world inference. Moreover, existing methods do not provide an intuitive interface enabling human operators to dynamically adjust model behavior under shifting conditions. In this work, we propose Knob, a framework that connects deep learning with classical control theory by mapping neural gating dynamics to a second-order mechanical system. By establishing correspondences between physical parameters -- damping ratio (ζζ) and natural frequency (ωnω_n) -- and neural gating, we create a tunable "safety valve". The core mechanism employs a logit-level convex fusion, functioning as an input-adaptive temperature scaling. It tends to reduce model confidence particularly when model branches produce conflicting predictions. Furthermore, by imposing second-order dynamics (Knob-ODE), we enable a dual-mode inference: standard i.i.d. processing for static tasks, and state-preserving processing for continuous streams. Our framework allows operators to tune "stability" and "sensitivity" through familiar physical analogues. This paper presents an exploratory architectural interface; we focus on demonstrating the concept and validating its control-theoretic properties rather than claiming state-of-the-art calibration performance. Experiments on CIFAR-10-C validate the calibration mechanism and demonstrate that, in Continuous Mode, the gate responses are consistent with standard second-order control signatures (step settling and low-pass attenuation), paving the way for predictable human-in-the-loop tuning.

Siyu Jiang, Sanshuai Cui, Hui Zeng

City University of Macau, Macau, China · Southwest University of Science and Technology, Mianyang, China

Model Calibration
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Feb 24, 2026

DA-Cal: Towards Cross-Domain Calibration in Semantic Segmentation

While existing unsupervised domain adaptation (UDA) methods greatly enhance target domain performance in semantic segmentation, they often neglect network calibration quality, resulting in misalignment between prediction confidence and actual accuracy---a significant risk in safety-critical applications. Our key insight emerges from observing that performance degrades substantially when soft pseudo-labels replace hard pseudo-labels in cross-domain scenarios due to poor calibration, despite the theoretical equivalence of perfectly calibrated soft pseudo-labels to hard pseudo-labels. Based on this finding, we propose DA-Cal, a dedicated cross-domain calibration framework that transforms target domain calibration into soft pseudo-label optimization. DA-Cal introduces a Meta Temperature Network to generate pixel-level calibration parameters and employs bi-level optimization to establish the relationship between soft pseudo-labels and UDA supervision, while utilizing complementary domain-mixing strategies to prevent overfitting and reduce domain discrepancies. Experiments demonstrate that DA-Cal seamlessly integrates with existing self-training frameworks across multiple UDA segmentation benchmarks, significantly improving target domain calibration while delivering performance gains without inference overhead.

Wangkai Li, Rui Sun, Zhaoyang Li +2

Deep Space Exploration Laboratory, School of Information Science and Technology, University of Science and Technology of China (USTC), Hefei 230026, China

Model CalibrationSemantic SegmentationUnsupervised Domain AdaptationPseudo-Labeling
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Feb 20, 2026

Multiclass Calibration Assessment and Recalibration of Probability Predictions via the Linear Log Odds Calibration Function

Machine-generated probability predictions are essential in modern classification tasks such as image classification. A model is well calibrated when its predicted probabilities correspond to observed event frequencies. Despite the need for multicategory recalibration methods, existing methods are limited to (i) comparing calibration between two or more models rather than directly assessing the calibration of a single model, (ii) requiring under-the-hood model access, e.g., accessing logit-scale predictions within the layers of a neural network, and (iii) providing output which is difficult for human analysts to understand. To overcome (i)-(iii), we propose Multicategory Linear Log Odds (MCLLO) recalibration, which (i) includes a likelihood ratio hypothesis test to assess calibration, (ii) does not require under-the-hood access to models and is thus applicable on a wide range of classification problems, and (iii) can be easily interpreted. We demonstrate the effectiveness of the MCLLO method through simulations and three real-world case studies involving image classification via convolutional neural network, obesity analysis via random forest, and ecology via regression modeling. We compare MCLLO to four comparator recalibration techniques utilizing both our hypothesis test and the existing calibration metric Expected Calibration Error to show that our method works well alone and in concert with other methods.

Amy Vennos, Xin Xing, Christopher T. Franck

Department of Statistics, Virginia Polytechnic Institute and State University

Probability CalibrationModel CalibrationPost-Hoc Calibration
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Feb 19, 2026

Neural Prior Estimation: Learning Class Priors from Latent Representations

Logit adjustment corrects class imbalance using the empirical class prior. We study whether a comparable class-frequency signal can instead be learned from the network representation, without explicitly supplying class counts to the correction rule. We introduce the Neural Prior Estimator (NPE), which attaches one or more lightweight Prior Estimation Modules (PEMs) to the latent representation. Each PEM is trained with a one-way logistic objective on the ground-truth coordinate. The resulting frequency-dependent outputs are combined into an NPE estimate and used as a learned logit correction, forming NPE-LA. In a simplified scalar model, the optimum of the PEM objective is monotone in the class count and grows asymptotically as log⁡Nc\log N_c, up to a slower log⁡log⁡Nc\log \log N_c term. Experiments on long-tailed CIFAR-10 and CIFAR-100 show that NPE-LA is competitive with standard logit adjustment and improves minority-class performance over CE and cRT in the reported settings. Experiments on STARE and ADE20K further show that the same idea can be used as a lightweight recalibration mechanism for dense prediction.

Masoud Yavari, Payman Moallem

Independent Researcher Isfahan, Iran · Department of Electrical Engineering Faculty of Engineering University of Isfahan, Iran

Logit AdjustmentClass-Imbalanced LearningParameter EstimationModel Calibration
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Feb 16, 2026

The Well-Tempered Classifier: Some Elementary Properties of Temperature Scaling

Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs). In both cases, temperature scaling is the most popular method for the job. Despite its popularity, a rigorous theoretical analysis of the properties of temperature scaling has remained elusive. We investigate here some of these properties. For classification, we show that increasing the temperature increases the uncertainty in the model in a very general sense (and in particular increases its entropy). However, for LLMs, we challenge the common claim that increasing temperature increases diversity. Furthermore, we introduce two new characterisations of temperature scaling. The first one is geometric: the tempered model is shown to be the information projection of the original model onto the set of models with a given entropy. The second characterisation clarifies the role of temperature scaling as a submodel of more general linear scalers such as matrix scaling and Dirichlet calibration: we show that temperature scaling is the only linear scaler that does not change the hard predictions of the model.

Pierre-Alexandre Mattei, Bruno Loureiro

Université Côte d’Azur, Inria, CNRS, LJAD, France · Département d’Informatique, École Normale Supérieure - PSL, CNRS, France

Model CalibrationLLM Uncertainty EstimationLanguage Model Calibration
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Jan 27, 2026

Online Regime-aware Calibration for Black-box Social Simulators via Posterior-assisted Evolutionary Dynamic Optimization

Evolutionary dynamic optimization (EDO) commonly assumes that environmental changes can be detected from fitness variations and handled through random re-initialization, historical solutions, or learned transition patterns. Online calibration of black-box simulators introduces a different setting, where the dynamic objective is induced by sequential observations and a changing calibration window, rather than being controlled by explicit variables. Fitness variations therefore cannot be directly attributed to regime changes, while the unknown relationship between successive regimes limits conventional adaptation. We formulate this setting as an observation-driven dynamic optimization problem and propose PosEDO, which augments fitness-based EDO with an observation-conditioned parameter-space signal. PosEDO learns this signal online as a posterior distribution over simulator parameters from parameter-trajectory pairs generated during evolutionary evaluation, using posterior shifts for change detection and posterior samples for population adaptation. The new evaluation records are further utilized for online posterior updating without additional simulator calls. Experiments on nonstationary economic and financial simulators show that PosEDO improves calibration accuracy, optimization performance, and change-detection quality over representative EDO baselines.

Peng Yang, Zhenhua Yang, Boquan Jiang +3

Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Southern University of Science and Technology, Shenzhen 518055, China · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China · Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen 518055, China +2

Evolutionary OptimizationBlack-Box OptimizationModel Calibration
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Jan 23, 2026

Is BatchEnsemble a Single Model? On Calibration and Diversity of Efficient Ensembles

In resource-constrained and low-latency settings, uncertainty estimates must be efficiently obtained. Deep Ensembles provide robust epistemic uncertainty (EU) but require training multiple full-size models. BatchEnsemble aims to deliver ensemble-like EU at far lower parameter and memory cost by applying learned rank-1 perturbations to a shared base network. We show that BatchEnsemble not only underperforms Deep Ensembles but closely tracks a single model baseline in terms of accuracy, calibration and out-of-distribution (OOD) detection on CIFAR10/10C/SVHN. A controlled study on MNIST finds members are near-identical in function and parameter space, indicating limited capacity to realize distinct predictive modes. Thus, BatchEnsemble behaves more like a single model than a true ensemble.

Anton Zamyatin, Patrick Indri, Sagar Malhotra +1

TU Wien

Ensemble LearningEnsemble DiversityDeep EnsemblesModel Calibration
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Jan 12, 2026

When Models Know When They Do Not Know: Calibration, Cascading, and Cleaning

When a model knows when it does not know, many possibilities emerge. The first question is how to enable a model to recognize that it does not know. A promising approach is to use confidence, computed from the model's internal signals, to reflect its ignorance. Prior work in specific domains has shown that calibration can provide reliable confidence estimates. In this work, we propose a simple, effective, and universal training-free method that applies to both vision and language models, performing model calibration, cascading, and data cleaning to better exploit a model's ability to recognize when it does not know. We first highlight two key empirical observations: higher confidence corresponds to higher accuracy within a single model, and models calibrated on the validation set remain calibrated on a held-out test set. These findings empirically establish the reliability and comparability of calibrated confidence. Building on this, we introduce two applications: (1) model cascading with calibrated advantage routing and (2) data cleaning based on model ensemble. Using the routing signal derived from the comparability of calibrated confidences, we cascade large and small models to improve efficiency with almost no compromise in accuracy, and we further cascade two models of comparable scale to achieve performance beyond either model alone. Leveraging multiple experts and their calibrated confidences, we design a simple yet effective data-cleaning method that balances precision and detection rate to identify mislabeled samples in ImageNet and Massive Multitask Language Understanding (MMLU) datasets. Our results demonstrate that enabling models to recognize when they do not know is a practical step toward more efficient, reliable, and trustworthy AI.

Chenjie Hao, Weyl Lu, Yuko Ishiwaka +3

University of California, Davis · SoftBank Corp. · Aizip

Adaptive InferenceConfidence Estimation in Language ModelsTraining Data CurationModel CalibrationUncertainty Calibration
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Dec 19, 2025

Calibratable Disambiguation Loss for Multi-Instance Partial-Label Learning

Multi-instance partial-label learning (MIPL) is a weakly supervised framework that extends the principles of multi-instance learning (MIL) and partial-label learning (PLL) to address the challenges of inexact supervision in both instance and label spaces. However, existing MIPL approaches often suffer from poor calibration, undermining classifier reliability. In this work, we propose a plug-and-play calibratable disambiguation loss (CDL) for classification and calibration, which modulates a disambiguation objective by a top-vs-competitor prediction margin. The competitor is instantiated either as the second strongest candidate label or as the strongest non-candidate label, yielding two variants that respectively emphasize candidate-level separation and candidate-vs-non-candidate suppression. Theoretically, we analyze CDL as a margin-modulated momentum-based disambiguation loss (MDL) objective, derive a lower-bound and a pseudo-label confidence-alignment bound for calibration, and show through gradient and momentum analyses how margin shaping affects weight updates. Experimental results on benchmark and real-world MIPL datasets, together with representative PLL adaptation, confirm that our CDL significantly improves both classification accuracy and expected calibration error.

Wei Tang, Yin-Fang Yang, Weijia Zhang +1

School of Computer Science and Engineering, Southeast University, Nanjing 210096, China, and the Key Laboratory of Computer Network and Information Integration (Southeast University), MoE, China · School of Computer and Information Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia

Model CalibrationWeakly Supervised LearningMultiple Instance Learning
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Nov 9, 2025

Deep Reinforcement Learning for Dynamic Origin-Destination Matrix Estimation in Microscopic Traffic Simulations Considering Credit Assignment

This paper focuses on dynamic origin-destination matrix estimation (DODE), a crucial calibration process necessary for the effective application of microscopic traffic simulations. The fundamental challenge of the DODE problem in microscopic simulations stems from the complex temporal dynamics and inherent uncertainty of individual vehicle dynamics. This makes it highly challenging to precisely determine which vehicle traverses which link at any given moment, resulting in intricate and often ambiguous relationships between origin-destination (OD) matrices and their contributions to resultant link flows. This phenomenon constitutes the credit assignment problem, a central challenge addressed in this study. We formulate the DODE problem as a Markov Decision Process (MDP) and propose a novel framework that applies model-free deep reinforcement learning (DRL). Within our proposed framework, the agent learns an optimal policy to sequentially generate OD matrices, refining its strategy through direct interaction with the simulation environment. This approach was evaluated through a toy experiment on the Nguyen-Dupuis network and a case study utilizing an actual highway subnetwork spanning Santa Clara and San Jose. Experimental results show that the proposed method consistently improves calibration performance relative to the strongest conventional baseline, reducing link-flow MSE by 23.7% in the toy experiment and by 59.2-88.3% in the real-world case study. By reframing DODE as a sequential decision-making problem, our approach addresses the credit assignment challenge through a learned policy and provides a novel framework for calibration of microscopic traffic simulations.

Donggyu Min, Seongjin Choi, Dong-Kyu Kim

Seoul National University · Seoul, 08826 · University of Minnesota +1

Traffic Flow EstimationModel Calibration
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