# Evaluating and Recalibrating Probabilistic Classifiers from One-Bit Threshold Queries

arXiv: https://arxiv.org/abs/2609.05125 · HTML: https://mlsanity.com/paper/2609.05125/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Stealing Part of a Production Language Model](https://mlsanity.com/paper/2403.06634/) (2024)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Fact-and-Reflection (FaR) Improves Confidence Calibration of Large Language Models](https://mlsanity.com/paper/2402.17124/) (2024)
- [Information-theoretic Generalization Analysis for Expected Calibration Error](https://mlsanity.com/paper/2405.15709/) (2024)

## Abstract (arXiv)

Standard calibration evaluation and recalibration methods assume access to predicted probabilities. We study one-bit threshold access, a setting in which probabilities are hidden and the evaluator observes only whether the predicted probability exceeds a single chosen threshold per sample. Under this restriction, we show that classifiers can nevertheless be evaluated and recalibrated without reconstructing their hidden scores. We derive a consistent estimator of True Calibration Error, unbiased estimators of strictly proper scoring rules, and a one-bit objective for Temperature Scaling whose expectation matches the standard log-loss objective. Across these settings, we quantify the statistical cost incurred by replacing standard probability-access procedures by our one-bit estimators. Finally, we instantiate the framework for black-box LLMs, where the logit_bias API parameter allows us to realize the required threshold queries in zero-shot binary question answering.