Grow or Prune? Constructive Neuroevolution of Kolmogorov–Arnold Networks

Kolmogorov–Arnold networks (KANs) are usually trained as fixed, over-parameterized graphs, then pruned and converted to equations. We study the constructive alternative: grow the graph from a minimal network. Constructive KAN (C-KAN) evolves typed, spline-edge graphs with short Lamarckian adaptation. Identity-oriented growth, fan-in normalization, amplitude-corrected Safe Mutation and behavioral speciation address mismatches between NEAT and function-valued edges; several species supply candidates for symbolic conversion. On 30 clean SRSD equations, C-KAN-GSR returns 12 high-accuracy equations, compared with none for two fixed-template PyKAN pipelines, and its delivered equations are more often valid and smaller. It also improves black-box SRBench predictive AUC over both templates. Yet neither KAN pipeline recovers an exact skeleton: PySR and KAN-SR recover 43.3% and 15.8%, respectively. A post-hoc constant refit raises PyKAN-1 above C-KAN in high-accuracy rate, but C-KAN's expressions remain smaller and structurally closer to the targets. Stage records locate C-KAN's main bottleneck in graph search: 17 of 30 equations lack an accurate prepared network; conversion and export cause further losses. Small ablations associate the KAN-specific mechanisms with higher validity and lower measured cost, without establishing a recovery gain. Constructive growth makes sparse KANs easier to export, but graph discovery alone does not solve equation recovery.