When Can We Trust LLM Graders? Calibrating Confidence for Automated Assessment

Large Language Models (LLMs) show promise for automated grading, but their outputs can be unreliable. Rather than improving grading accuracy directly, we address a complementary problem: \textit{predicting when an LLM grader is likely to be correct}. This enables selective automation where high-confidence predictions are processed automatically while uncertain cases are flagged for human review. We compare three confidence estimation methods (self-reported confidence, self-consistency voting, and token probability) across seven LLMs of varying scale (4B to 120B parameters) on three educational datasets: RiceChem (long-answer chemistry), SciEntsBank, and Beetle (short-answer science). Our experiments reveal that self-reported confidence consistently achieves the best calibration across all conditions (avg ECE 0.166 vs 0.229 for self-consistency). Surprisingly, self-consistency remains 38\% worse despite requiring 5$\times$ the inference cost. Larger models exhibit substantially better calibration though gains vary by dataset and method (e.g., a 28\% ECE reduction for self-reported), with GPT-OSS-120B achieving the best calibration (avg ECE 0.100) and strong discrimination (avg AUC 0.668). We also observe that confidence is strongly top-skewed across methods, creating a ``confidence floor'' that practitioners must account for when setting thresholds. These findings suggest that simply asking LLMs to report their confidence provides a practical approach for identifying reliable grading predictions. Code is available \href{https://github.com/sonkar-lab/llm_grading_calibration}{here}.

Reliable generation of isomorphic physics problems using ChatGPT with prompt-chaining and tool use

We present a method for generating large numbers of isomorphic physics problems using ChatGPT through prompt chaining and tool use. This approach enables precise control over structural variations-such as numeric values and spatial relations-while supporting diverse contextual variations in the problem body. By utilizing the Python code interpreter, the method supports automatic solution validation and simple diagram generation, addressing key limitations in existing LLM-based methods. We generated two example isomorphic problem banks and compared the outcome against simpler prompt-based approaches. Results show that prompt-chaining produces significantly higher quality and more consistent outputs than simpler, non-chaining prompts. This work demonstrates a promising method for efficient problem creation accessible to the average instructor, which opens new possibilities for personalized adaptive testing and automated content development.