A real ReLU network's connectivity graph of polyhedral linear regions converges toward its 2d average-degree bound, with data-containing regions more connected

Exact BFS enumeration (capped at 4,000,000 polytopes) of the polyhedral complex recovers the region-adjacency graph of real trained networks on MNIST (fully-connected [784,5,8,8,8,10]), CIFAR-10 (CNN classifier sub-network after the relu3 feature split), and California Housing (regression MLP), plus synthetic data [gaines-bi-2026-characterizing-the-discrete-geometry-of-relu-networks] As real-network size increases, the connectivity graph's average node degree climbs toward the proven upper bound of 2d (d = input dimension), independent of network width or depth [gaines-bi-2026-characterizing-the-discrete-geometry-of-relu-networks] The per-region neighbor-count distribution is unimodal and right-skewed, peaking just below 2d, and regions containing training data points are on average more connected than regions that do not [gaines-bi-2026-characterizing-the-discrete-geometry-of-relu-networks]