Calibrating LLM Confidence for Mathematical Question Answering

Large language models often exhibit overconfidence, making their raw token probabilities unreliable indicators of answer correctness. This research explores how to better estimate and calibrate LLM confidence, specifically in the domain of mathematical question answering. The study differentiates between single-pass methods, which aggregate existing token probabilities, and multi-pass methods, which generate additional signals through techniques like self-verification or Monte Carlo Dropout. Findings indicate that while individual token probabilities can be saturated, their aggregation across a sequence offers subtle but useful confidence signals. Multi-pass approaches, particularly self-verification and Monte Carlo Dropout, yield more calibrated confidence estimates. Furthermore, post-hoc calibration methods such as Platt scaling and isotonic regression are shown to substantially reduce calibration error, though their effectiveness can vary with dataset difficulty and transferability across models.