The Feynman machine is a unique model expressing spiking-timing-dependent neural interactions through path integrals. It provides the capability to predict neural firing statistics very precisely. If time-ordered neural interactions are to be represented more properly, however, the classical form of the model needs to be improved. We here introduce how to describe neural interactions by adopting the second quantization formalism; this is requisite for expressing adequately the firing states deviating from a reference state and for calculating firing statistics through a perturbation method. The formulation is also helpful in picking out the neural firings with causal relationships and in predicting activations of a neural network in response to a given external input. This capability is essential for describing the function of a neural network based on the relationship between the input and the output firing patterns.

中文翻译：

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尖峰神经网络的响应理论

费曼机是一种独特的模型，通过路径积分来表达与脉冲时间相关的神经交互作用。它提供了非常精确地预测神经放电统计数据的能力。然而，如果要更恰当地表示时序神经交互，则需要改进模型的经典形式。我们在此介绍如何采用二次量化形式来描述神经交互；这是充分表达偏离参考状态的点火状态以及通过扰动方法计算点火统计数据所必需的。该公式还有助于找出具有因果关系的神经放电，并有助于预测神经网络响应给定外部输入的激活。