We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale’s Law—each neuron makes either excitatory or inhibitory connections onto its post-synaptic targets. We find that this constrained system may be described as a perturbation from a system with nontrivial symmetries. We analyze the symmetric system using the tools of equivariant bifurcation theory and demonstrate that the symmetry-implied structures remain evident in the perturbed system. In comparison, spectral characteristics of the network coupling matrix are relatively uninformative about the behavior of the constrained system.

中文翻译：

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对称性限制了平衡神经网络家族中的动力学。

我们研究了一个随机激发速率神经网络家族，在其中我们强制执行了戴尔定律的神经生物学约束，即每个神经元对其突触后靶点都具有兴奋性或抑制性联系。我们发现，这个受约束的系统可能被描述为来自具有非平凡对称性的系统的扰动。我们使用等变分叉理论的工具分析对称系统，并证明对称隐含结构在扰动系统中仍然很明显。相比之下，网络耦合矩阵的频谱特性对于受约束系统的行为而言相对而言没有信息。