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
本研究首次在间接编码中演化逐节点激活函数，证明激活函数选择决定进化搜索的可解性，并发现振荡函数可解决奇偶校验，单调函数则失败，且涌现出异质分配。
AI 中文摘要
生物神经元通过特化类型实现计算多样性：强直、爆发、适应和快速放电细胞在同一回路中共存。相比之下，人工神经网络对所有节点统一应用单一激活函数，这限制了其表达能力。我们表明，这种统一性为进化搜索造成了硬性极限：在稀疏的演化基质中，单调函数无法解决超过其最小实例（XOR）的奇偶校验问题，而单个振荡单元在所有测试规模下均足以解决。这一差距源于搜索和稀疏性，而非表示能力：单调网络可以用少量隐藏单元表示奇偶校验，且梯度下降可以恢复该解。据我们所知，我们首次在间接编码中，从18个函数的调色板中演化逐节点激活函数分配，跨越超过4,500次实验运行，涵盖布尔逻辑、回归和空间分类。在Parity-4上单独测试18个函数中的每一个，揭示了三级可解性结构：振荡函数达到100%，中间函数达到6.7-80%，而全部9个单调函数为0%。这种分化并非普遍存在。递归性使其崩溃，而梯度下降则完全逆转，表明该障碍特定于稀疏基质中的进化搜索。网络能使用哪些激活函数，超越其拓扑和权重，决定了进化搜索能解决什么问题。间接编码发现了不太可能由人工选择的异质逐节点激活分配。
英文摘要
Biological neurons achieve computational diversity through specialized types: tonic, bursting, adapting, and fast-spiking cells coexist within the same circuit. Artificial neural networks, by contrast, apply a single activation function uniformly to all nodes, which limits what they can represent. We show that this uniformity creates hard limits for evolutionary search: across sparse evolved substrates, monotonic functions fail to solve parity beyond its smallest instance, XOR, while a single oscillatory unit suffices at all tested scales. The gap is one of search and sparsity, not representation: monotonic networks can represent parity with a modest number of hidden units, and gradient descent recovers that solution. We evolve, to our knowledge for the first time in indirect encoding, per-node activation function assignments from an 18-function palette across more than 4,500 experimental runs spanning Boolean logic, regression, and spatial classification. Testing each of the 18 functions individually on Parity-4 reveals a three-tier solvability structure: oscillatory functions achieve 100%, intermediate functions 6.7-80%, and all 9 monotonic functions 0%. This divide is not universal. Recurrence collapses it, and gradient descent inverts it entirely, showing that the barrier is specific to evolutionary search in sparse substrates. What activation functions a network can use, beyond its topology and weights, determines what evolutionary search can solve. Indirect encoding discovers heterogeneous per-node activation assignments unlikely to be chosen by hand.
Comments9 pages, 2 figures, 10 tables. Published in ALIFE 2026 (MIT Press). This is the version of record, posted under CC BY 4.0
Journal refALIFE 2026: Proceedings of the 2026 Artificial Life Conference, MIT Press, 2026, p. 80
