Bridging Shannon Surprisal and Latent Geometry: A Unified Framework for VLM Storage, Attention Routing, and Data Pruning

As Vision-Language Models (VLMs) expand into unconstrained, in-the-wild continuous spatiotemporal domains, uniform vector processing creates severe KV-Cache and computational attention bottlenecks. We propose a sparsity-driven methodology that bridges these geometric latent constraints with Shannon's Information Theory. By modeling dense background representations as a von Mises-Fisher (vMF) distribution, we derive that local surprisal exhibits an affine relationship with a vector's cosine similarity with the inverse global mean ($-\bar{v}$). To overcome representation degeneration—where vectors are constrained within narrow anisotropic boundaries—we formulate an exponential weighting function equipped with a Dimensionality Compensator ($\alpha$) and a Structural Domain Shifter ($\beta$). This formulation drives a dual-phase optimization framework. First, in static environments, our Surprisal-Weighted Mixed-Precision (SWMP) strategy achieves a 57.50% memory reduction by quantizing low-surprisal representations. Second, for continuous video streams, we introduce Temporal SWMP, leveraging an Exponential Moving Average (EMA) to transition the framework into an Information-Theoretic Attention Router. We further observe strong metric coupling between adjacent-difference routing and a second-difference kinematic evaluation proxy. Under extreme Iso-KV Cache constraints ($\sim$3% of frames), Temporal SWMP exceeds uniform sampling in recall while exhibiting selection behavior distinct from adjacent-difference routing. Together, these results support an information-theoretic criterion for attention routing in resource-constrained continuous VLM deployments across unpredictable real-world environments.