A real trained 3-layer ReLU classifier's composed linear-region partition is directly visualized on 2D data, and the per-layer regions are neither convex nor connected

A real 3-layer fully-connected classifier (2 -> 45 -> 3 -> 4, softmax output, biases and batch normalization) is trained with Adam on 20,000 synthetic 2D points (5,000 per class, 4 classes) to 98% training accuracy [balestriero-baraniuk-2018-mad-max-affine-spline-insights] The network's induced polyhedral partition of the full 2D input domain is sampled and directly plotted, both per-layer and as the full composed arrangement [balestriero-baraniuk-2018-mad-max-affine-spline-insights] Even in this simple network, the composed partition regions are neither convex nor connected once composed across layers -- a direct empirical counterexample to assuming the arrangement inherits simple convex shape from its individual linear layers [balestriero-baraniuk-2018-mad-max-affine-spline-insights]