UNVaMP: Neural Knowledge Tracing with Variational Regularization of Latent Knowledge Dynamics
Authors: Carson J. Cook, Ahmed J. Zerouali, Anthony Schmidt, Reginald Ziedzor, Paul Lin, Luke G. Eglington
Organizations: Amplify Education, Inc.
Abstract
We introduce the Unified Neural Variational Measurement of Proficiency (UNVaMP) architecture, a knowledge tracing method that integrates observed student-item interactions with internal memory to produce evolving latent representations of student knowledge. These representations support accurate predictions of future responses while enabling explicit control over the smoothness of estimated learning trajectories. UNVaMP can be configured as either a purely neural model or a hybrid model that predicts responses through an interpretable measurement function over the latent space. We show that a pure neural configuration (UNVaMP-MLP) achieves the strongest predictive performance among compared models on three out of four datasets. Meanwhile, a hybrid configuration (UNVaMP-MIRT, using a 1PL MIRT measurement function) lags only slightly behind UNVaMP-MLP, indicating that the predictive cost of interpretability is modest. Beyond predictive accuracy, UNVaMP provides the following: a principled mechanism for controlling volatility when estimating student latent variables, quantification of uncertainty over student knowledge state estimates, and flexible input specification that supports heterogeneous student-item interaction features. In addition, the hybrid UNVaMP-MIRT configuration generates interpretable moment-in-time student knowledge state estimates. Using an experimental dataset, we show that auxiliary inputs induce structured changes in the predictive behavior of UNVaMP-MIRT, consistent with sensitivity to underlying structure beyond response correctness. Furthermore, through a simulation study, we show that UNVaMP yields well-behaved knowledge state estimates under controlled measurement conditions. In total, these results indicate that UNVaMP is both useful for real-world education systems and capable of recovering underlying structure from student-item interactions.
Knowledge Tracing (KT) models students' knowledge states based on learning interactions to predict performance. While deep learning-based KT models have boosted predictive accuracy, most models rely on deterministic vector embeddings and opaque latent state transitions, limiting interpretability regarding how specific past behaviors influence predictions. To address this limitation, we propose Probabilistic Logical Knowledge Tracing (PLKT), an interpretable KT framework that formulates prediction as a goal-conditioned evidence reasoning process over historical learning behaviors. Instead of representing knowledge states as deterministic vector embeddings, PLKT employs robust Beta-distributed probabilistic embeddings to represent student knowledge states. This probabilistic foundation allows us to model the uncertainty of historical behaviors and perform explicit logical operations (e.g., conjunction), constructing transparent reasoning paths that reveal how specific past interactions contribute to the prediction. Extensive experiments show that PLKT outperforms state-of-the-art KT methods while achieving superior interpretability. Our code is available at https://anonymous.4open.science/r/PLKT-D3CE/.
Knowledge tracing (KT) aims to predict students' future performance by modeling their evolving knowledge states from historical interactions. Existing KT methods usually treat the raw interaction sequence as a unified behavioral process, overlooking the phase-specific nature of learning behaviors. Our preliminary observations show that students are more likely to correctly answer previously failed knowledge concepts after sufficient practice, suggesting a transition from ability-building to proficiency-oriented learning. Motivated by this, we propose Phase-Aware Knowledge Tracing (PAKT), a KT framework that decomposes student interactions into ability and proficiency phases based on the tailored decomposition mechanism. To effectively exploit the decomposed sequences, we design a multi-branch Transformer with a type-aware readout module to jointly capture phase-specific and holistic knowledge states. We further provide a causal analysis to reveal the confounding bias caused by entangling complex learning behaviors in phase-agnostic KT models. Extensive experiments on six public benchmarks demonstrate that our method consistently outperforms representative baselines, with a maximum AUC gain of 1.33% and an average gain of 0.82%.
Predicting student performance and characterizing metacognitive calibration are essential for personalization in intelligent tutoring systems. Prior research treats performance prediction, calibration error calculation, and variance decomposition as separate pipelines, preventing unified interpretation. I propose the Unified Behavioral Prediction and Calibration Analysis Pipeline (UBP-CAP), an integrated framework processing student pre-execution behavioral telemetry through three linked modules: (1) a LightGBM classifier with SHAP for binary correctness prediction, (2) formal calibration metrics (ECE, MCE, and Brier score decomposition) to evaluate metacognitive alignment, and (3) a crossed Generalized Linear Mixed-Effects Model (GLMM) for decomposing calibration deviations. I introduce the Predictive-Explanatory Divergence Index (PEDI), which quantifies structural divergence between predictive and explanatory feature profiles. Evaluated on 1,195 interaction records (27 students, 45 tasks), Logistic Regression achieves AUC-ROC = 0.903, outperforming LightGBM (0.878). Student naive ECE (0.109) significantly exceeds model ECE (0.068), confirming systematic miscalibration. The crossed GLMM yields ICCStudent = 0.123, showing calibration is situational rather than dispositional. PEDIcos = 0.081 (p = 0.327) indicates structural alignment between prediction and explanation on shared behavioral features.