From token probabilities to calibrated confidence: An empirical study of mathematical question answering

Confidence estimation for large language models (LLMs) aims to estimate the probability that a generated answer is correct, while calibration aligns these estimates with empirical accuracy. Prior work has shown that token probabilities are often overconfident, we investigate whether these readily available signals can nevertheless provide well-calibrated confidence estimation for mathematical question answering. We compare single-pass estimators, which reuse token probabilities from the original generation, with multi-pass estimators, which obtain additional confidence signals through verification or stochastic forward passes. While individual token probabilities can be highly saturated, we find that aggregating token probabilities over the full sequence captures small but consistent differences between correct and incorrect generations, yielding more informative confidence estimates. Multi-pass methods can yield calibrated confidence estimates. We study two such approaches: self-verification through re-prompting, including a lower-cost in-situ variant, and Monte Carlo Dropout, which derives confidence from variation across stochastic forward passes. We further evaluate two post-hoc calibration methods, Platt scaling and isotonic regression, both of which substantially reduce in-domain calibration error. However, their data efficiency varies with dataset difficulty, and the calibration mappings often transfer asymmetrically across datasets and models.

AutoGrid AI: Deep Reinforcement Learning Framework for Autonomous Microgrid Management

We present a deep reinforcement learning-based framework for autonomous microgrid management. tailored for remote communities. Using deep reinforcement learning and time-series forecasting models, we optimize microgrid energy dispatch strategies to minimize costs and maximize the utilization of renewable energy sources such as solar and wind. Our approach integrates the transformer architecture for forecasting of renewable generation and a proximal-policy optimization (PPO) agent to make decisions in a simulated environment. Our experimental results demonstrate significant improvements in both energy efficiency and operational resilience when compared to traditional rule-based methods. This work contributes to advancing smart-grid technologies in pursuit of zero-carbon energy systems. We finally provide an open-source framework for simulating several microgrid environments.