BaseCal: Unsupervised Confidence Calibration via Base Model Signals

TL;DR

This work identifies a persistent miscalibration problem in post-trained LLMs (PoLLMs) and shows that base LLMs maintain superior confidence calibration in free-form QA. It introduces BaseCal, an unsupervised, plug-and-play framework with two instantiations: BaseCal-ReEval, which re-evaluates PoLLM outputs using the base LLM, and BaseCal-Proj, which learns a lightweight linear projection to map PoLLM hidden states into the base LLM space for confidence estimation. Across five datasets and three LLM families, BaseCal significantly reduces the Expected Calibration Error ($ECE$) compared to unsupervised baselines, with BaseCal-Proj offering a favorable trade-off between calibration quality and inference overhead. The findings demonstrate that calibration signals can be recovered from internal hidden states without labeled data or parameter updates, enabling practical deployment of more trustworthy PoLLMs and revealing a path for robust, real-world AI assistance with minimal modification to existing models.

Abstract

Reliable confidence is essential for trusting the outputs of LLMs, yet widely deployed post-trained LLMs (PoLLMs) typically compromise this trust with severe overconfidence. In contrast, we observe that their corresponding base LLMs often remain well-calibrated. This naturally motivates us to calibrate PoLLM confidence using the base LLM as a reference. This work proposes two ways to achieve this. A straightforward solution, BaseCal-ReEval, evaluates PoLLM's responses by feeding them into the base LLM to get average probabilities as confidence. While effective, this approach introduces additional inference overhead. To address this, we propose BaseCal-Proj, which trains a lightweight projection to map the final-layer hidden states of PoLLMs back to those of their base LLMs. These projected states are then processed by the base LLM's output layer to derive base-calibrated confidence for PoLLM's responses. Notably, BaseCal is an unsupervised, plug-and-play solution that operates without human labels or LLM modifications. Experiments across five datasets and three LLM families demonstrate the effectiveness of BaseCal, reducing Expected Calibration Error (ECE) by an average of 42.90\% compared to the best unsupervised baselines.

Figures (9)

• Figure 1: Calibration plots of PoLLM (right) and base LLM (left) on TriviaQA. The dashed line indicates perfect calibration; bars below it denote overconfidence.
• Figure 2: Calibration plots on TriviaQA across three model families. The top row presents Olmo2 checkpoints after different post-training stages. The dashed line is perfect calibration, while bars below denote overconfidence.
• Figure 3: Vanilla
• Figure 4: BaseCal-ReEval
• Figure 5: BaseCal-Proj