Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi-Peliti-Janssen formalism, are particularly useful in this regard.

中文翻译：

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超越平均场理论：神经网络的统计场论

平均场理论一直是研究耦合神经元网络动力学的坚定支持者。它们很方便，因为它们相对简单并且可以分析。然而，经典平均场理论忽略了单神经元效应引起的波动和相关性的影响。在这里，我们考虑超越平均场理论并纳入相关效应的各种可能方法。统计场论方法，特别是 Doi-Peliti-Janssen 形式主义，在这方面特别有用。