Incidence-based random walks on simplicial complexes

What the math gives to ML

The paper offers a transferable higher-order transport mechanism: an edge-state random walk mixes transitions mediated by shared vertices with transitions mediated by shared triangles. Randomly retained triangles create heterogeneous higher-order connectivity and produce a non-monotonic transport bottleneck at intermediate face density. A neural-network analogue is a simplicial diffusion layer that keeps these two propagation channels separate and mixes them with a controllable parameter q. The main falsifiable prediction is that spectral relaxation time, stationary localization, and long-range feature transport will peak at an intermediate triangle density rather than change monotonically.