The code of implementation is available in https://github.com/UHIF/PID_AGD.

During model optimization, the expected calibration error tends to overfit earlier than classification accuracy, indicating distinct optimization objectives for classification error and calibration error. To ensure consistent optimization of both model accuracy and model calibration, we propose a novel method incorporating a probability-dependent gradient decay coefficient into loss function. This coefficient exhibits a strong correlation with the overall confidence level.

In machine learning, model calibration and predictive inference are essential for producing reliable predictions and quantifying uncertainty to support decision-making. Recognizing the complementary roles of point and interval predictions, we introduce Self-Calibrating Conformal Prediction, a method that combines Venn-Abers calibration and conformal prediction to deliver calibrated point predictions alongside prediction intervals with finite-sample validity conditional on these predictions. To achieve this, we extend the original Venn-Abers procedure from binary classification to regression. Our theoretical framework supports analyzing conformal prediction methods that involve calibrating model predictions and subsequently constructing conditionally valid prediction intervals on the same data, where the conditioning set or conformity scores may depend on the calibrated predictions. Real-data experiments show that our method improves interval efficiency through model calibration and offers a practical alternative to feature-conditional validity.

Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. Uncertainty calibration is a challenging problem as there is no ground truth available for uncertainty estimates. We propose an optimization method that leverages the relationship between accuracy and uncertainty as an anchor for uncertainty calibration. We introduce a differentiable accuracy versus uncertainty calibration (AvUC) loss function that allows a model to learn to provide well-calibrated uncertainties, in addition to improved accuracy. We also demonstrate the same methodology can be extended to post-hoc uncertainty calibration on pretrained models. We illustrate our approach with mean-field stochastic variational inference and compare with state-of-the-art methods. Extensive experiments demonstrate our approach yields better model calibration than existing methods on large-scale image classification tasks under distributional shift.

Accurate estimation of predictive uncertainty (model calibration) is essential for the safe application of neural networks. Many instances of miscalibration in modern neural networks have been reported, suggesting a trend that newer, more accurate models produce poorly calibrated predictions. Here, we revisit this question for recent state-of-the-art image classification models. We systematically relate model calibration and accuracy, and find that the most recent models, notably those not using convolutions, are among the best calibrated. Trends observed in prior model generations, such as decay of calibration with distribution shift or model size, are less pronounced in recent architectures. We also show that model size and amount of pretraining do not fully explain these differences, suggesting that architecture is a major determinant of calibration properties.

Vanilla models for object detection and instance segmentation suffer from the heavy bias toward detecting frequent objects in the long-tailed setting. Existing methods address this issue mostly during training, e.g., by re-sampling or re-weighting. In this paper, we investigate a largely overlooked approach --- post-processing calibration of confidence scores. We propose NorCal, Normalized Calibration for long-tailed object detection and instance segmentation, a simple and straightforward recipe that reweighs the predicted scores of each class by its training sample size. We show that separately handling the background class and normalizing the scores over classes for each proposal are keys to achieving superior performance. On the LVIS dataset, NorCal can effectively improve nearly all the baseline models not only on rare classes but also on common and frequent classes. Finally, we conduct extensive analysis and ablation studies to offer insights into various modeling choices and mechanisms of our approach. Our code is publicly available at https://github.com/tydpan/NorCal.

Large Language Models (LLMs) have demonstrated inherent calibration capabilities, where predicted probabilities align well with correctness, despite prior findings that deep neural networks are often overconfident. Recent studies have linked this behavior to specific components in the final layer, such as entropy neurons and the unembedding matrix null space. In this work, we provide a complementary perspective by investigating how calibration evolves throughout the network depth. Analyzing multiple open-weight models on the MMLU benchmark, we uncover a distinct confidence correction phase in the upper/later layers, where model confidence is actively recalibrated after decision certainty has been reached. Furthermore, we identify a low-dimensional calibration direction in the residual stream whose perturbation significantly improves calibration metrics (ECE and MCE) without harming accuracy. Our findings suggest that calibration is a distributed phenomenon, shaped throughout the network forward pass, not just in its final projection, providing new insights into how confidence-regulating mechanisms operate within LLMs.

The Heston stochastic volatility model is a widely used tool in financial mathematics for pricing European options. However, its calibration remains computationally intensive and sensitive to local minima due to the model's nonlinear structure and high-dimensional parameter space. This paper introduces a hybrid deep learning-based framework that enhances both the computational efficiency and the accuracy of the calibration procedure. The proposed approach integrates two supervised feedforward neural networks: the Price Approximator Network (PAN), which approximates the option price surface based on strike and moneyness inputs, and the Calibration Correction Network (CCN), which refines the Heston model's output by correcting systematic pricing errors. Experimental results on real S\&P 500 option data demonstrate that the deep learning approach outperforms traditional calibration techniques across multiple error metrics, achieving faster convergence and superior generalization in both in-sample and out-of-sample settings. This framework offers a practical and robust solution for real-time financial model calibration.