Memory that Imagines: Learner Mental World Models as Memory for Long-Horizon Tutoring Agents

Agent memory systems answer what happened. They store, retrieve and summarize interaction logs. A tutoring agent needs its memory to answer two other questions, what the learner knows now and what a candidate teaching action does. This paper casts the memory of a tutoring agent as a mental world model of the learner, a fixed-size belief state. The belief state supports three operations, WRITE (posterior update), READ (mastery with uncertainty) and IMAGINE (closed-loop rollout of candidate teaching sequences). Under a latent-state assumption, the belief retains all the evidence the history holds about future responses, whereas a log cut to any fixed budget can lose that evidence. The memory is a recurrent state-space model trained with closed-loop overshooting to roll forward on its own sampled responses. Two design choices adapt the model to learner data. Each exercise is bound to its response. Prediction and reconstruction use separate heads, because sharing one head costs 6.8 AUC points. On three knowledge-tracing benchmarks, this memory predicts the next 100 responses 8.5–16.2 AUC points better than a retrieval memory or a Bayesian Knowledge Tracing state, and better than two LLMs that read the full log. Over the same horizon, it matches knowledge-tracing models without a readable interface. In multi-session tutoring with simulated learners on ASSISTments 2017, planning with IMAGINE gains more on this memory than on a low-fidelity one in all ten protocol seeds. It lands above random sequencing on the former and below it on the latter. An LLM tutor reading the serialized READ interface also beats random sequencing, with both providers. Memory size is O(1) in history length, versus O(t) for logs.