How it works. The network starts with a bump approximation (initial \(\mathcal{N}_2\) construction). At each iteration, Theorem 3.4 identifies overshoot (\(U^+\), red) and undershoot (\(U^-\), blue) regions. Down-bumps of amplitude \(\alpha/2\) are placed on \(U^+\); up-bumps on \(U^-\). Neutral zones are left untouched, so \(\alpha\) halves cleanly each step. Hover over the function plot to see individual neuron activations light up in the network diagram.