UNVaMP: Neural Knowledge Tracing with Variational Regularization of Latent Knowledge Dynamics

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.

MOSAIC: Orchestrating Collaborative Knowledge Tracing with Hierarchical Semantic Alignment

Knowledge Tracing (KT) is important for personalized education but traditionally suffers from two key limitations: a reliance on shallow ID-based representations that neglect semantic depth and a restriction to single-granularity mastery estimation that overlooks hierarchical knowledge dependencies. To address these challenges, we propose MOSAIC (Multi-granularity Online Semantic AI for Collaborative Knowledge), a novel framework that orchestrates LLM-driven semantic alignment with sequential modeling. Unlike methods that use LLMs solely as predictors, MOSAIC leverages a frozen LLM to generate dynamic, context-aware embeddings and hierarchical prediction prompts, explicitly capturing collaborative signals and peer interactions. Furthermore, we introduce a cross-granularity consistency objective that jointly regularizes mastery estimation across concept, topic-cluster, and global proficiency levels. Extensive experiments on ASSISTments, EdNet, and a newly collected large-scale MOOC dataset demonstrate that MOSAIC establishes new state-of-the-art results. Specifically, our method achieves AUC improvements of up to 3.4\% and Accuracy gains of up to 2.5 \% across all benchmarks. Notably, MOSAIC exhibits superior robustness in collaboration-rich environments and long-sequence scenarios (AUC 0.862 on MOOC), offering both high predictive precision and semantically grounded interpretability.