Model-Agnostic Neural Mean Field With The Refractory SoftPlus Transfer Function.
Model-Agnostic Neural Mean Field With The Refractory SoftPlus Transfer Function.
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具有 Refractory SoftPlus 传递函数的模型无关神经平均场。
DOI：
10.1101/2024.02.05.579047
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发表时间：
2024
期刊：
影响因子：
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通讯作者：
Teodorescu,Mircea
中科院分区：
文献类型：
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作者：
Spaeth,Alex;Haussler,David;Teodorescu,Mircea
由于神经元网络的复杂性和单个神经元的非线性动力学，开发一个足够准确、有用且易于应用的系统级模型具有挑战性。从单神经元描述推断到大规模模型的平均场模型可以从神经元的传递函数中推导出来，该函数给出了神经元的放电率作为其突触输入的函数。然而，分析导出的传递函数仅适用于它们最初导出的神经元和噪声模型。在最近的工作中，近似传递函数是通过拟合 S 形曲线凭经验得出的，它规定了最大发射率，并且仅适用于扩散极限，限制了应用。在本文中，我们提出了一种名为 Refractory SoftPlus 的近似传递函数，它很简单但适用于多种神经元类型。 Refractory SoftPlus 激活函数允许使用仿真结果推导简单的经验近似平均场模型，从而能够高精度预测随机连接的神经元网络对时变外部刺激的响应。这些模型还支持作为循环输入水平的函数的精确近似分岔分析。最后，该模型无需假设较大的突触前速率或较小的突触后电位大小即可工作，即使对于具有较大相互作用项的群体也可以开发平均场模型。
Due to the complexity of neuronal networks and the nonlinear dynamics of individual neurons, it is challenging to develop a systems-level model which is accurate enough to be useful yet tractable enough to apply. Mean-field models which extrapolate from single-neuron descriptions to large-scale models can be derived from the neuron’s transfer function, which gives its firing rate as a function of its synaptic input. However, analytically derived transfer functions are applicable only to the neurons and noise models from which they were originally derived. In recent work, approximate transfer functions have been empirically derived by fitting a sigmoidal curve, which imposes a maximum firing rate and applies only in the diffusion limit, restricting applications. In this paper, we propose an approximate transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. Refractory SoftPlus activation functions allow the derivation of simple empirically approximated mean-field models using simulation results, which enables prediction of the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. These models also support an accurate approximate bifurcation analysis as a function of the level of recurrent input. Finally, the model works without assuming large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.