Tensor-Accelerated Eager Multi-Resolution Grids for Evolving Large-Scale Substrates
TL;DR
This work presents Eager Multi-Resolution HyperNEAT (EMR-HyperNEAT), which reformulates adaptive substrate discovery as a batch tensor operation: shared position grids are precomputed for all depths, every position is evaluated in one vectorized CPPN call, then the same variance criterion filters the output.
Abstract
Evolvable-Substrate HyperNEAT (ES-HyperNEAT) discovers neural network topology by querying a Compositional Pattern-Producing Network (CPPN) at spatial positions and placing nodes where output variance is high. Its sequential quadtree cannot be tensorized directly: each network produces a different tree with dynamic shapes. We present Eager Multi-Resolution HyperNEAT (EMR-HyperNEAT), which reformulates adaptive substrate discovery as a batch tensor operation: shared position grids are precomputed for all depths, every position is evaluated in one vectorized CPPN call, then the same variance criterion filters the output. This tensor formulation supports population-level batching, one-time JIT compilation, chunked memory streaming, and six substrate configurations (feedforward through full recurrent) that sequential traversal could not support at scale. On the CRSP/Compustat financial dataset (94K samples), EMR-HyperNEAT achieves 5.5× speedup at depth 6; on XOR (pop 1000), 12–34× per-generation GPU speedup at depths 5–7 (~100× over 30 generations). The reformulation also discovers a superset of ES-HyperNEAT's positions, yielding higher empirical solve rates. We validate substrate evolution up to depth 13 (358M positions, streamed from disk).
