Continuous-Time Latent Belief-State Dynamics with Query-Conditioned Uncertainty for Knowledge Tracing

Knowledge tracing is commonly formulated as next-response prediction over or-dered student interaction logs. Existing time-aware models often use elapsedtime as an additional feature, gate, attention bias, or forgetting signal. This paperstudies a complementary question: what changes if elapsed time acts directlyon the learner state before the next response is predicted? We propose BRIDGE-FLowKT, a continuous-time knowledge tracing model that represents each learnerby latent mean and uncertainty coordinates. Between observed attempts, bothcoordinates are transported by an exact exponential dynamics; at an observedresponse, a bounded event bridge updates the state; before prediction, the targetquestion reads the pre-event state through query-conditioned mean and uncertaintyinteractions. This design keeps the roles of time, response evidence, and question-specific uncertainty explicit while still allowing a closed-form event scan. Weanalyze the resulting system through semigroup transport, stability under eventperturbations, separation of histories with identical event order but different timegaps, uncertainty-channel separability, and nested mechanism ablations. Exper-iments on five benchmark datasets show that BRIDGEFLOwKT is competitiveunder matched per-dataset comparisons, improves consistently over the matcheduncertainty-aware baseline, obtains its clearest aggregate temporal gain on AS-SIST2012 with dataset-dependent evidence elsewhere, and benefits reliably fromquery-conditioned uncertainty interactions in matched ablations.