Evidence-Guided Unknown Rejection for High-Confidence Near-Known Unknowns

Open-set recognition (OSR) requires a classifier to reject inputs from unseen classes which is essential in safety-critical settings such as medical imaging. Simplex based methods, which fix class prototypes at the vertices of a regular simplex and then reject via a distance-ratio score, perform well empirically but lack theoretical justification, and existing analysis applies only when the embedding dimension d is at least C-1, which is the regime in which a regular simplex exists. We give a theoretical account of simplex-ratio OSR that holds in every embedding dimension, including d < C-1. Our analysis centers on balanced equal-norm codes: prototype configurations with equal lengths and zero sum, which exist for all d >= 2 and include the regular simplex as a special case. For these codes we show that an auxiliary squared ratio score has sublevel sets that are exact unions of Euclidean balls, which in turn bracket the acceptance region of the operational score; and we prove a sharp dichotomy: the prototypes attain one-distance symmetry, behaving like a regular simplex, if and only if d >= C-1, with controlled degradation governed by an explicit defect parameter below that threshold. We further show the false-acceptance rate decays exponentially in d under natural isotropy assumptions, and that the operational score is globally Lipschitz with compact acceptance regions. Empirically, we study balanced prototype geometry as both an analytic tool and a representation-learning prior, rather than as a stand-alone state-of-the-art detector. Across CIFAR and MedMNIST open-set splits, the geometry provides useful structure, but OSR performance remains strongly dependent on the scoring rule: raw ratio scores typically underperform nearest-neighbor and logit-based alternatives.

In high-stakes automated decision-making, access to predictive uncertainty is essential for enabling users -- human or downstream systems -- to accept or reject predictions based on application-specific cost trade-offs. Such uncertainty-augmented (UA) systems -- i.e., systems that output both predictions and uncertainty scores -- are currently being assessed in the literature in a variety of ways, using separate metrics to evaluate the predictions and the uncertainty scores, setting a cost function with a fixed rejection cost or integrating over a coverage-risk curve. We argue that these evaluation approaches are inadequate for assessing overall performance of the UA system for decision making under uncertainty and propose a novel family of metrics, ECUAS$_n$, formulated as proper scoring rules for the task of interest. The parameter $n$ controls the trade-off between the cost of incorrect predictions and imperfect uncertainties depending on the needs of the use-case. We demonstrate the advantages of the ECUAS$_n$ metrics both theoretically and empirically, through experiments on diverse classification and generation datasets, including a manually annotated subset of TriviaQA.

Open-world object detection (OWOD) requires detectors to localize known classes while identifying unknown objects for future incremental learning. We find that the unknown prediction streams of strong OWOD detectors are heavily polluted: on M-OWODB, across PROB, OW-DETR, and HypOW, future-task positive unknowns make up less than 10% of unknown predictions, whereas background false positives account for 46-71%. We show that this is not a missing-information problem, but an information bottleneck at the objectness head. On PROB Task 1, a linear probe on the 256-D decoder query achieves an AUROC of 0.908 for positive-versus-negative unknown discrimination, but the final one-dimensional objectness scalar drops to 0.642. A frozen SigLIP feature, without access to the detector, independently recovers much of this proposal-level separability at the filtering stage (AUROC = 0.871). Motivated by this finding, we propose DualMem, a calibrated post-hoc filter that assumes a small image-disjoint annotated calibration split of held-out future-task objects and performs a non-parametric likelihood ratio test in frozen SigLIP feature space. DualMem uses a k-nearest-neighbor positive memory to protect future-task objects and a negative memory to suppress background-like proposals. Its decision threshold is chosen by Neyman-Pearson calibration, giving users an explicit trade-off between false-unknown suppression and novel recall. Across PROB, OW-DETR, and HypOW on M-OWODB Task 1, DualMem reduces background-type false unknown proposals per image by 44.9%-66.3%, with a mean reduction of 56.6%. On PROB Task 1, it more than doubles the reduction achieved by a natural K-means prototype baseline, while leaving known-class mAP unchanged because known detections bypass the filter.