发表机构
University of Neuchâtel; University College Dublin（纳沙泰尔大学; 都柏林大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对ES-HyperNEAT缺乏完整种群级GPU并行化实现的问题，提出基于JAX的JAX-ESHN，通过实验揭示其结构性瓶颈，配套的EMR-HyperNEAT解决了该瓶颈，实现了基于坐标的神经演化的规模化。
AI 中文摘要
ES-HyperNEAT通过自适应四叉树细分来演化基质拓扑结构；据我们所知，目前还不存在具备完整种群级GPU并行化的实现方案。我们提出了JAX-ESHN，这是一种基于JAX的实现方案，旨在通过批量CPPN查询实现GPU并行化，并在五个任务上与基于CPU的PUREPLES基准进行了基准测试：异或（XOR）、三奇偶校验（Parity-3）、圆分类、正弦回归和CartPole。核心限制是结构性的：每个CPPN会发现一组独特的基质位置，无法通过vmap实现种群级向量化。在XOR任务上，CPU基准的运行时间随深度呈指数级增长，而JAX-ESHN在GPU上的构建成本（编译加第一代评估）在深度基质时趋于平稳，因此JAX-ESHN能在基准极少成功的情况下可靠求解，且运行时间方差更低。CPU与CPU之间的多基准对照在布尔、连续和控制任务类型上重现了相同的缩放差异，证实这是基质发现实现的属性，而非GPU硬件的属性。一种替代数据结构（分层空间哈希网格）的失败并非因为它预先计算了位置，而是因为它对每个位置独立应用方差测试，丢弃了四叉树的父门控过滤机制以及ES-HyperNEAT所必需的自适应稀疏性。这些发现明确了任何基质发现方法要实现基于坐标的神经演化规模化必须满足的结构性约束；配套的EMR-HyperNEAT重新表述方案用静态多分辨率网格的 eager 评估取代自适应细分，满足了这些约束并解决了本文所表征的瓶颈。
英文摘要
ES-HyperNEAT evolves substrate topology through adaptive quadtree subdivision; to our knowledge, no implementation with full population-level GPU parallelization exists. We present JAX-ESHN, a JAX-based implementation targeting GPU parallelization with batched CPPN queries, and benchmark it against the CPU-based PUREPLES Baseline across five tasks: XOR, Parity-3, circle classification, sine regression, and CartPole. The core limitation is structural: each CPPN discovers a unique set of substrate positions, preventing population-level vectorization via vmap. On XOR, the CPU Baseline's runtime scales exponentially with depth while JAX-ESHN's construction cost on GPU (compilation plus first-generation evaluation) plateaus at deep substrates, so JAX-ESHN solves reliably where the Baseline rarely succeeds, with lower runtime variance. A CPU-vs-CPU multi-benchmark control reproduces the same scaling divergence across Boolean, continuous, and control task types, confirming it is a property of the substrate-discovery implementation, not of GPU hardware. An alternative data structure (Hierarchical Spatial Hash Grid) fails not because it precomputes positions but because it applies the variance test independently per position, discarding the quadtree's parent-gated filtering and with it the adaptive sparsity essential to ES-HyperNEAT. These findings define the structural constraints any substrate-discovery method must satisfy to scale coordinate-based neuroevolution; the companion EMR-HyperNEAT reformulation, which replaces adaptive subdivision with eager evaluation of a static multi-resolution grid, satisfies them and resolves the bottleneck this paper characterizes.
