Do Small Language Models Know When They're Wrong? Confidence-Based Cascade Scoring for Educational Assessment

Large language model (LLM) cascades reduce inference cost by routing easy queries to a small model and deferring hard queries to a larger one. Production cascades govern this deferral through a confidence threshold, but LLM confidence scores are miscalibrated, the threshold must be tuned per model pair and per domain, and no setting yields a formal bound on cascade accuracy. We introduce Conformal Cascade (CC), a multi-tier inference framework that uses conformal prediction set size as the deferral rule: accept when the calibrated set collapses to a single answer, defer otherwise. The procedure delivers a distribution-free, finite-sample accuracy guarantee. By a per-tier union bound, the prediction set at the accepting tier covers the correct answer with probability at least $1 - Kα$ for any user-specified $α$; under a selection-preservation condition (consistent with, but not strictly implied by, our marginal coverage results), the bound tightens to $1 - α$. We further characterise expected cascade cost as an explicit function of $α$ and the calibration-set acceptance rate. Across 18 multiple-choice benchmarks spanning science, medicine, commonsense, and standardized exams, evaluated on two-tier cascades drawn from four open-weight model families, CC strictly improves over the strongest calibration-tuned heuristic cascade on the majority of family--benchmark pairs, with the largest gains on reasoning-heavy benchmarks where majority vote is unreliable; on easier benchmarks the cascade commits the vast majority of queries to the small model at no accuracy cost. Extension to open-ended generation requires an answer-clustering step that we leave for future work. The method requires no model training and only black-box API access.

Strategic model selection and reasoning settings are more effective than ensembling for optimizing automated scoring with large language models (LLMs). We examined self-consistency (intra-model majority voting) and reasoning effort for scoring conversation-based assessment items in high school mathematics, evaluating 900 student conversations against human-scored ground truths using frontier and low-cost models from OpenAI and Google. Temperature sampling significantly improved accuracy over deterministic calls, but increasing ensemble size (j = 1 to 7) produced no significant gains. Higher reasoning effort showed a significant positive linear trend with scoring accuracy, though the benefit varied by model family. An efficiency frontier analysis identified Gemini 3.1 Pro Preview at low reasoning as the most accurate but costly configuration; GPT-5.4 Nano and Mini with no reasoning offered the best cost-performance balance.

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: 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 here.