We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a smooth time-dependent variable, the associated response will be a set of neural spike timings (roughly the instants of successive action potential peaks) that have no amplitude information. A recurrent neural network model can be fitted to such a stimulus-response data pair by using the maximum likelihood estimation method where the likelihood function is derived from Poisson statistics of neural spiking. The universal approximation feature of the recurrent dynamical neuron network models allows us to describe excitatory-inhibitory characteristics of an actual sensory neural network with any desired number of neurons. The stimulus data are generated by a phased cosine Fourier series having a fixed amplitude and frequency but a randomly shot phase. Various values of amplitude, stimulus component size, and sample size are applied in order to examine the effect of the stimulus to the identification process. Results are presented in tabular and graphical forms at the end of this text. In addition, to demonstrate the success of this research, a study involving the same model, nominal parameters and stimulus structure, and another study that works on different models are compared to that of this research.

中文翻译：

---

动态循环神经网络模型与感觉刺激-反应数据的拟合

我们提出了一项针对感觉神经元模型拟合的理论研究。由于缺乏连续数据，传统的神经网络训练方法不适用于该问题。尽管刺激可以被视为平滑的时间相关变量，但相关的响应将是一组没有幅度信息的神经尖峰计时（大致是连续动作电位峰值的时刻）。可以通过使用最大似然估计方法将循环神经网络模型拟合到这样的刺激-响应数据对，其中似然函数是从神经尖峰的泊松统计中导出的。循环动态神经元网络模型的通用逼近特征使我们能够描述具有任何所需数量的神经元的实际感觉神经网络的兴奋-抑制特征。刺激数据由具有固定幅度和频率但随机发射相位的相控余弦傅里叶级数生成。应用振幅、刺激成分大小和样本大小的各种值，以便检查刺激对识别过程的影响。结果以表格和图形形式呈现在本文末尾。此外，为了证明这项研究的成功，一项涉及相同模型、标称参数和刺激结构的研究以及另一项针对不同模型的研究与本研究进行了比较。