Bag of Coins: A Statistical Probe into Neural Confidence Structures
This addresses reliability issues in high-stakes applications for AI practitioners by providing a diagnostic tool, though it is incremental as it builds on existing calibration methods.
The paper tackled the problem of poorly calibrated confidence scores in neural networks by introducing the Bag-of-Coins test, a statistical probe that reframes confidence estimation as a hypothesis test to examine internal consistency; it achieved near-perfect calibration on Vision Transformers with an ECE of 0.0212, an 88% improvement over baselines, and revealed inconsistencies in CNNs like ResNet.
Modern neural networks, despite their high accuracy, often produce poorly calibrated confidence scores, limiting their reliability in high-stakes applications. Existing calibration methods typically post-process model outputs without interrogating the internal consistency of the predictions themselves. In this work, we introduce a novel, non-parametric statistical probe, the Bag-of-Coins (BoC) test, that examines the internal consistency of a classifier's logits. The BoC test reframes confidence estimation as a frequentist hypothesis test: does the model's top-ranked class win 1-v-1 contests against random competitors at a rate consistent with its own stated softmax probability? When applied to modern deep learning architectures, this simple probe reveals a fundamental dichotomy. On Vision Transformers (ViTs), the BoC output serves as a state-of-the-art confidence score, achieving near-perfect calibration with an ECE of 0.0212, an 88% improvement over a temperature-scaled baseline. Conversely, on Convolutional Neural Networks (CNNs) like ResNet, the probe reveals a deep inconsistency between the model's predictions and its internal logit structure, a property missed by traditional metrics. We posit that BoC is not merely a calibration method, but a new diagnostic tool for understanding and exposing the differing ways that popular architectures represent uncertainty.