Unified Semantic Student Modeling with Learner-State Trajectories

Student modeling infers a learner's evolving knowledge and error patterns from interaction traces. Standard knowledge tracing and cognitive diagnosis mostly use identifiers, correctness bits, and skill tags, so they record whether a learner was wrong but not what the error means. Language models can read questions and written responses, yet they rarely maintain an explicit learner state that is reusable across tasks and causally used when generating predictions. We introduce the Unified Semantic Student Model (USSM), a task-conditioned generator that compresses semantic interaction histories into a layerwise learner-state trajectory at a dedicated state token. A late-fusion attention mask forces every history-dependent prediction to pass through this state, allowing one representation to support correctness prediction, written-response prediction, misconception diagnosis, future-response prediction, and error-persistence prediction. Counterfactual recombination encourages rule-level state learning, and state transplantation tests whether the state is used rather than merely readable. Across FoundationalASSIST, DBE-KT22, XES3G5M, Eedi, and MalRule, one USSM remains competitive with task-specific specialists. Unified training improves semantic accuracy on Eedi-Mining misconception diagnosis from 0.445 to 0.517. Under candidate support, transplanting a donor state raises donor-directed errors from 0.168 to 0.411. After no-candidate training, transplanted states reproduce trained error rules on new numerical instances. These results show that USSM learns an explicit semantic learner state that is reusable across heterogeneous student-modeling tasks and can causally steer generation toward persistent learner-specific error patterns.