From Misclassifications to Outliers: Joint Reliability Assessment in Classification

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 $α\in(0,1)$. 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.

We consider two approaches for assessing the reliability of the individual predictions of a classifier: Robustness Quantification (RQ) and Uncertainty Quantification (UQ). We explain the conceptual differences between the two approaches, compare both approaches on a number of benchmark datasets and show that RQ is capable of outperforming UQ, both in a standard setting and in the presence of distribution shift. Beside showing that RQ can be competitive with UQ, we also demonstrate the complementarity of RQ and UQ by showing that a combination of both approaches can lead to even better reliability assessments.

Out-of-distribution (OOD) detection is essential for deploying deep learning models reliably, yet no single method performs consistently across architectures and datasets -- a scorer that leads on one benchmark often falters on another. We attribute this inconsistency to a shared structural limitation: logit-based methods see only the classifier's confidence signal, while feature-based methods attempt to measure membership in the training distribution but do so in the full feature space where confidence and membership are entangled, inheriting architecture-sensitive failure modes. We observe that penultimate features naturally decompose into two orthogonal subspaces: a classifier-aligned component encoding confidence, and a residual the classifier discards. We discover that this residual carries a class-specific directional signature for in-distribution data -- a membership signal invisible to logit-based methods and entangled with noise in feature-based methods. We propose CORE (COnfidence + REsidual), which disentangles the two signals by scoring each subspace independently and combines them via normalized summation. Because the two signals are orthogonal by construction, their failure modes are approximately independent, producing robust detection where either view alone is unreliable. CORE achieves competitive or state-of-the-art performance across five architectures and five benchmark configurations, ranking first in three of five settings and achieving the highest grand average AUROC with negligible computational overhead.