Information-Geometric Trajectory Routing

Abstract

Large language model inference is usually optimized from the model inward: runtime systems predict future experts from hidden states, router scores, token statistics, or local activation correlations, while dynamic-depth methods decide which model layers can be skipped for the current input. This preprint proposes a different measurement level. A user who repeatedly interacts with a model generates a longitudinal sequence of prompts; those prompts, in turn, induce recurring expert and layer activation signatures. The activation sequence is treated not as the primary object to be explained, but as an observable projection of a recurrent user-specific information trajectory. If these projected trajectories contain stable transition structure, the next likely expert/layer demand can be forecast before the next prompt is fully processed, and in the strongest formulation before the next prompt is even submitted. The forecast can drive anticipatory memory placement: high-probability modules remain GPU-resident, alternative branches are staged in host RAM, and low-probability modules remain in colder storage. A wrong forecast need not change model semantics; it can degrade only latency if the native router or full execution path remains authoritative. The framework combines longitudinal activation graphs, contextual vector representations, probabilistic branching, and hierarchical memory scheduling. It is compatible with mixture-of-experts models, dynamic layer selection, and external graph/RAG memory, while requiring no semantic inspection of hidden representations. The paper formalizes the hypothesis, distinguishes it from current expert-prefetch and dynamic-depth work, proposes conservative and aggressive execution modes, and specifies an empirical validation protocol for user-specific routing graphs.