CT-LFSSM: Multiscale Continuous-Time State-Space Learning and Forgetting in Knowledge Tracing

Knowledge Tracing (KT) aims to model students' evolving knowledge from historical interactions and predict their future performance. However, existing methods often encode irregular temporal gaps as auxiliary inputs rather than explicitly evolving latent knowledge over elapsed time. They also tend to absorb forgetting, response evidence, and learning into a single state transition, making these effects difficult to distinguish. Independently parameterized items further limit statistical sharing across items associated with the same knowledge component. To address these limitations, we propose CT-LFSSM, a Continuous-Time Learning–Forgetting State-Space Model. CT-LFSSM represents each knowledge component with fast-, medium-, and slow-timescale latent states. It propagates these states over real elapsed time through personalized exponential decay, with half-lives constrained to increase from the fast to the slow timescale. Before each response, an event-conditioned convex gate aggregates the three states into a current mastery estimate. After observing the response, CT-LFSSM uses the prediction residual to revise the inferred pre-interaction state, while separately consolidating practice-induced learning gains across multiple timescales. This separation assigns distinct update paths to forgetting, response-driven belief revision, and learning. For response prediction, CT-LFSSM further decomposes item effects into shared knowledge-component-level parameters and regularized item-specific residuals. Experiments on four real-world datasets show that CT-LFSSM achieves state-of-the-art performance across all datasets, while remaining robust across varying temporal gaps and student interaction sequence lengths.