一类平衡神经网络的对称性约束动力学
Symmetries constrain dynamics in a family of balanced neural networks
摘要：
我们研究了一个随机发射率的神经网络家族，在这个网络中，我们执行了戴尔定律的神经生物学约束-每个神经元对其突触后靶点进行兴奋性或抑制性连接。我们发现，这个受约束的系统可以被描述为一个系统的扰动与非平凡的对称性。利用等变分歧理论对对称系统进行了分析，证明了在扰动系统中仍然存在明显的隐式结构。相比之下，网络耦合矩阵的谱特性相对没有关于约束系统的行为的信息。
英文摘要：
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 non-trivial 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.
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