TrajLift: Encoding Verbal Memory Dynamics via Heat Diffusion on Semantic Hierarchies

Verbal memory retrieval carries rich diagnostic information for Alzheimer's disease (AD) through the order, hesitation, and categorical organization of recalled words, yet computational modeling of this retrieval process remains largely unexplored. A key challenge is that timing and hierarchical structure are diagnostically entangled: the diagnostic meaning of retrieval timing depends on its hierarchical context. We propose TrajLift, a spectral framework that models verbal recall as timed trajectories on a hierarchical graph. Our central mechanism is graph heat diffusion on the semantic hierarchy, which provides a unified operator for capturing both multi-scale hierarchical structure and continuous retrieval timing. Formal analysis shows that the resulting representation is provably separable into structural and temporal components with spectral selectivity across hierarchical levels. Experiments on synthetic benchmarks and a real-world clinical corpus demonstrate consistent improvements over baselines lacking joint structure-time modeling.