An Information-Theoretic Evaluation Framework for Benchmark and Model Diagnosis in Knowledge Tracing

2026-10-04

AI Summary

This study addresses the limitations of global evaluation metrics, which obscure error sources and complicate the assessment of benchmark saturation, by proposing an information-theoretic fine-grained evaluation framework. It introduces the Context Tree Weighting (CTW) algorithm as an operational coordinate to quantify local predictability at the entropy-band level, effectively distinguishing causal from irreducible uncertainty. Experiments demonstrate that modern models achieve significant yet non-uniform gains in high-entropy regions. Furthermore, the proposed method precisely identifies residual predictive structures and noise-sensitive areas, revealing inherent benchmark limitations. Ultimately, this framework provides a reliable analytical tool for diagnosing the performance of large language models.

Abstract

Knowledge tracing (KT) models are predominantly evaluated using aggregate metrics such as area under the curve (AUC) and accuracy. However, these global scores obscure where the remaining errors originate and fail to indicate whether a benchmark is approaching saturation. While estimating a global theoretical performance limit is challenging in realistic KT settings, it is possible to quantify local predictability. To address this, we propose an information-theoretic evaluation framework for KT benchmark diagnosis. We use Context Tree Weighting (CTW) on item-response histories and current-item queries as an operational causal uncertainty coordinate, while distinguishing it from the unobserved Local Irreducible Uncertainty (LIU) under the full KT information set. By projecting predictions onto this shared uncertainty coordinate, we evaluate model performance gains across distinct entropy bands rather than only at the global level. Comprehensive evaluations on NIPS Task 3/4 and Algebra 2005 reveal that model improvements are highly non-uniform. Modern KT models show substantial gains in high-entropy regions, and additional item-aware references, log-loss, and equal-frequency analyses support this localization. The framework also flags regions where apparent gains require checks for noise-sensitive behavior. By surfacing these local modeling failures alongside genuine gains, this approach provides a diagnostic tool for studying both residual predictive structure and the limitations of current KT benchmarks and models.

Problem

• Knowledge Tracing
• Model Evaluation
• Benchmark Diagnosis
• Information Theory
• Local Predictability

Innovation

• Knowledge Tracing
• Information-Theoretic Framework
• Context Tree Weighting
• Local Predictability
• Benchmark Diagnosis