Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning

TL;DR

ORCA introduces a test-time calibration framework for large language models that improves reasoning efficiency and generalization by dynamically calibrating sampling processes with conformal prediction and meta-learning.

Contribution

It presents a novel online calibration method that provides theoretical guarantees and enhances reasoning task performance across diverse settings.

Findings

Up to 47.5% efficiency savings on in-distribution tasks.

67.0% savings in out-of-domain zero-shot settings.

Maintains low empirical error rates across benchmarks.

Abstract

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level $\delta=0.1$, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.