Tensor-Accelerated Eager Multi-Resolution Grids for Evolving Large-Scale Substrates

ES-HyperNEAT (ES-HN) discovers neural network topology by querying a CPPN at candidate positions and placing nodes where the CPPN output shows high variation. However, ES-HN builds a different quadtree for each network in the population, forcing sequential execution. Each depth has 4× more positions, so computation grows exponentially, and deep substrates become infeasible. We present Eager Multi-Resolution HyperNEAT (EMR, EMRHyperNEAT), which matches or exceeds ES-HN results while scaling across parallel cores. Instead of building quadtrees adaptively, we precompute position grids for each depth level, evaluate all positions simultaneously, then filter using the same variance threshold. All networks share these grids, enabling evaluation of the entire population in parallel. Main result: EMR enables scalability to arbitrarily large substrates through parallelization. While ES-HN runs in 𝑂(4𝐷) time sequentially, EMR achieves 𝑂(4𝐷/𝑃) by dividing work across P cores, yielding linear speedup. Comparing ES-HN on CPU against EMR on GPU: on XOR (pop=1000), EMR overtakes at depth 4, 34× per-generation speedup at depth 7 (∼100× over 30 gens). Additional capabilities: EMR’s scalability enables: (1) recurrent networks through hidden-to-hidden connections; (2) evolution at extreme resolutions via memory streaming (validated on depth 13: 358M positions). To our knowledge, this is the first massively parallel implementation of adaptive substrate discovery.