Bag of Coins: A Statistical Probe into Neural Confidence Structures

• URL: http://arxiv.org/abs/2507.19774v1
• Date: Sat, 26 Jul 2025 03:54:32 GMT
• Title: Bag of Coins: A Statistical Probe into Neural Confidence Structures
• Authors: Agnideep Aich, Ashit Baran Aich, Md Monzur Murshed, Sameera Hewage, Bruce Wade,
• Abstract summary: Bag-of-Coins (BoC) test examines the internal consistency of a classifier's logits.<n>On Vision Transformers (ViTs), the BoC output serves as a state-of-the-art confidence score, achieving near-perfect calibration.<n>On Convolutional Neural Networks (CNNs) like ResNet, the probe reveals a deep inconsistency between the model's predictions and its internal logit structure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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