Information-Geometric Trajectory Routing

This preprint introduces Information-Geometric Trajectory Routing (IGTR), a framework for anticipatory compute and memory allocation in large language models and Mixture-of-Experts architectures. Within Information Geometry (IG), successive user interactions are not treated as independent prompts, but as observable projections of recurrent information-geometric states. These states generate characteristic sequences of expert and layer activations in the processing model. IGTR uses these observed activation trajectories as measurable projections of the underlying information geometry and combines them with vector representations, RAG, and graph-based memory to construct an Information-Geometric Activation Graph. The resulting structure is organized around an Information-Geometric Attractor, which identifies the geometrically consistent continuation of an interaction trajectory. From this attractor, the system derives the expected MoE and layer activation path before the corresponding computational demand becomes critical. Required modules can therefore remain resident in GPU memory, likely continuation modules can be staged in host RAM, and unrelated components can remain in colder storage. The approach does not interpret apparent branching as intrinsic randomness. Within IG, unresolved branches reflect insufficient geometric resolution of the underlying informational state. Increasing trajectory resolution should therefore improve activation-path determination and reduce apparent ambiguity. IGTR provides both a practical architecture for sparse execution of very large models and a directly testable consequence of Information Geometry: recurrent informational trajectories must generate reproducible and anticipatable model-activation structures across longitudinal interaction.