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

Traditional knowledge tracing models often force a trade-off between predictive accuracy and interpretability. Deep learning models excel at prediction but often lack transparency and can exhibit volatile, unrealistic learning trajectories. This paper introduces the Unified Neural Variational Measurement of Proficiency (UNVaMP) to bridge this gap, aiming to provide a model that is both highly predictive and capable of producing stable, interpretable estimates of student knowledge.

UNVaMP integrates a memory model (an RNN) with an inference model (an encoder) to produce latent knowledge state distributions. The architecture is modular, allowing for two primary configurations:

1. UNVaMP-MLP: A purely neural configuration designed for maximum predictive power.
2. UNVaMP-MIRT: A hybrid configuration that uses a 1PL Multidimensional Item Response Theory (MIRT) measurement function as a decoder, ensuring the latent space corresponds to interpretable skill proficiencies.

Crucially, UNVaMP uses a variational regularization mechanism—a Kullback-Leibler divergence penalty—to enforce smoothness in the evolution of latent knowledge states over time. This prevents the model from producing erratic, high-volatility estimates of student proficiency.

• Predictive Performance: UNVaMP-MLP achieved the strongest predictive performance on three out of four benchmark datasets compared to existing models.
• Interpretability: The hybrid UNVaMP-MIRT configuration performed nearly as well as the neural version, suggesting that the cost of gaining interpretability is minimal.
• Stability and Uncertainty: The model provides a principled way to quantify uncertainty in student knowledge estimates and ensures that learning trajectories remain stable and well-behaved, even when incorporating heterogeneous auxiliary inputs.