Least-Path Intelligence: Curvature-Guided Student Pruning and Dynamic Sparse Expert Routing

This exploratory study examines curvature-aware weight pruning and input-dependent sparse expert routing in small synthetic teacher–student models. An exact two-weight quadratic example illustrates a case where local compensation reduces removal loss from 0.0800 to 0.0152, and a correlation-reversal counterexample where compensated loss is 0.2744 versus 0.0800 without compensation. Five paired seeds compare pruning and routing methods on synthetic regression and classification using CPU and GTX 1650 runs. The draft reports that dynamic routing reduces estimated linear MACs from 90 to roughly 57–60 per input, while increasing batch-one latency relative to the dense student. Results vary by task and metric. This package includes the manuscript, derivations, prototype code, tests, and CPU/CUDA results. It reports no real-world or large-language-model evaluation; all scientific claims require author review.