ReliableNet: A Chance-Constrained Approach to Trustworthy Classification in Deep Learning
Authors: Ange-Clément Akazan, Ineza Remy Mugenga, Abebe Geletu, Jean Medard Ngnotchouye, Issa Karambal
Organizations: School of Agriculture and Science, University of KwaZulu-Natal, Pietermaritzburg, KwaZulu-Natal, South Africa · 2AIMS Research and Innovation Centre, African Institute for Mathematical Sciences, Kigali, Rwanda · 3African Institute for Mathematical Sciences, Kigali, Rwanda
Abstract
A prediction that is both confident and wrong is a critical reliability failure because it can bypass abstention and human review precisely when the model is mistaken. Empirical risk minimization (ERM) controls average loss but not this failure directly, while calibration, uncertainty estimation, conformal risk control, and selective prediction methods target related reliability properties rather than bounding the joint failure event during training. We propose ReliableNet, which constrains the Joint Confident-Wrong (JCW) probability, the probability that a prediction is simultaneously confident and incorrect, below a user-specified risk budget α∈(0,1). We formulate this as a chance-constrained ERM problem, use a conservative smooth inner approximation whose population feasibility implies the original JCW constraint. Across four tabular and two image datasets, ReliableNet is the only method certified within the JCW budget for every dataset and seed in distribution, when compared against baselines spanning ERM, post-hoc calibration, conformal risk control, and selective prediction. Under demographic, ambiguity, spurious-correlation, novel-class, and covariate shifts, it achieves the lowest empirical JCW among the compared methods while remaining very competitive in accuracy, coverage, calibration, and selective prediction. Risk-coverage results further indicate that ReliableNet achieves better selective ranking than the benchmark methods on most datasets. Overall, ReliableNet provides a principled approach to trustworthy classification.
Although deep neural networks (DNNs) achieve high predictive accuracy, their confidence estimates are often unreliable, potentially compromising user trust in their decisions. This has motivated research on calibrated models, where calibration measures how well a model's predicted confidence aligns with the empirical probability of correctness. However, calibration metrics can often be improved through post-processing techniques that merely mimic training-time uncertainty without genuinely improving the model's understanding. For this reason, statisticians recommend that models be not only calibrated but also refined. Intuitively, a model is considered more refined if it assigns significantly different confidence scores to correct and incorrect predictions, a property also referred to as sharpness. We observe that many existing calibration methods improve calibration at the cost of reduced refinement. To address this limitation, we propose: (1) a novel loss function that explicitly promotes refinement and can be optimized through supervised contrastive learning; and (2) a unified training framework, RefCal, that jointly optimizes calibration, refinement, and accuracy to improve DNN reliability. On the CIFAR-100-LT dataset with 10 percent class imbalance, RefCal achieves (accuracy, refinement, ECE) of (58.81, 95.67, 0.08), substantially outperforming the widely used Correctness Ranking Loss, which achieves (46.27, 93.7, 0.22).
Safety-critical applications require classifiers that are both robust and reliable. Adversarial training is a widely adopted defense for improving robustness in deep neural networks; however, its effect on the reliability of predictive uncertainty remains underexplored. We investigate this gap through the lens of selective classification, which has rarely been systematically analyzed alongside adversarial robustness. We introduce a unified benchmark for the robustness-uncertainty trade-off. It standardizes architectures, augmentations, threat models, and evaluation metrics across clean, adversarial, and common-corruption settings. Across a wide range of state-of-the-art adversarial training methods, we uncover a recurring failure mode: several approaches improve robust accuracy while degrading uncertainty ranking, leading to poorer selective behavior. To address this, we propose Evidential Adversarial Training (EV-AT), which models uncertainty through a Dirichlet distribution and combines (i) an evidence-based loss promoting clean accuracy and reliable uncertainty with (ii) a robust evidence-alignment loss matching clean and adversarial predictions in log Dirichlet-parameter space. Extensive experiments show that EV-AT shifts the Pareto frontier of robustness-uncertainty trade-offs beyond prior state-of-the-art adversarial training methods. Our source code is publicly available at https://github.com/NicolasSournac/Robustness_Meets_Uncertainty.EV-AT.
Nicolas Sournac, Ahmed Baha Ben Jmaa, Bertrand Braeckeveldt
Uncertainty estimation is critical for deploying machine learning models in high-stakes settings. However, classical calibration only assesses the reliability of predicted probabilities and does not evaluate whether epistemic uncertainty estimates are themselves trustworthy. This limitation is particularly relevant for second-order classification models. We introduce epistemic calibration, a principled criterion that measures whether reported epistemic uncertainty faithfully reflects the dispersion of model predictions around the ground truth. We show that epistemic calibration is a strictly stronger notion than classical calibration and captures failure modes invisible to standard metrics. We relate this work to the existing literature through an impossibility theorem that holds under the epistemic calibration hypothesis. To operationalize this concept, we propose the Expected Epistemic Calibration Error (EECE), which we prove to be a consistent estimator of a True Epistemic Calibration Error (TECE). Experiments across a broad range of uncertainty quantification methods show that epistemic calibration is a coherent and meaningful criterion and reveal substantial differences across methods, despite similar predictive performance.