One Size Fits None: Exercise-Adaptive Cognitive Route Induction for Cognitive Diagnosis with LLM Supervision

Cognitive diagnosis aims to identify students' learning weaknesses, yet most existing models operate at the concept level, representing exercises as item IDs, Q-matrix entries, concept labels, or dense embeddings. Such representations obscure heterogeneous reasoning demands within the same concept: SQL exercises tagged with JOIN may require either simple recall or complex schema inspection, key-relation reasoning, constraint filtering, and query construction. To address this limitation, we propose Cognitive Route Induction (CRI), which parses exercise text into a Bloom-based cognitive route graph, where nodes denote activated cognitive processes and edges encode prerequisite dependencies. CRI defines the target representation for fine-grained diagnosis: the cognitive operations required by an exercise and their dependencies. Building on CRI, we introduce RouteCD, a route-aware cognitive diagnosis model that projects each exercise route into a shared concept-by-process space and predicts responses from the gap between student cognitive state and exercise demand. LLM-generated analyses provide node- and edge-level graph supervision during training, while inference requires no LLM calls. Experiments show improved response prediction and cognitive-structure modeling, and ablations confirm the diagnostic value of induced routes. Our code is available at: https://anonymous.4open.science/r/ROUTECD.