Centre for Theoretical Neuroscience, University of Waterloo, Ontario, Canada.
Neural Comput. 2010 Mar;22(3):621-59. doi: 10.1162/neco.2009.02-09-970.
Temporal derivatives are computed by a wide variety of neural circuits, but the problem of performing this computation accurately has received little theoretical study. Here we systematically compare the performance of diverse networks that calculate derivatives using cell-intrinsic adaptation and synaptic depression dynamics, feedforward network dynamics, and recurrent network dynamics. Examples of each type of network are compared by quantifying the errors they introduce into the calculation and their rejection of high-frequency input noise. This comparison is based on both analytical methods and numerical simulations with spiking leaky-integrate-and-fire (LIF) neurons. Both adapting and feedforward-network circuits provide good performance for signals with frequency bands that are well matched to the time constants of postsynaptic current decay and adaptation, respectively. The synaptic depression circuit performs similarly to the adaptation circuit, although strictly speaking, precisely linear differentiation based on synaptic depression is not possible, because depression scales synaptic weights multiplicatively. Feedback circuits introduce greater errors than functionally equivalent feedforward circuits, but they have the useful property that their dynamics are determined by feedback strength. For this reason, these circuits are better suited for calculating the derivatives of signals that evolve on timescales outside the range of membrane dynamics and, possibly, for providing the wide range of timescales needed for precise fractional-order differentiation.
时变导数是由各种各样的神经回路计算得出的，但对于如何准确地进行这种计算的问题，理论研究却很少。在这里，我们系统地比较了使用细胞内自适应和突触抑制动力学、前馈网络动力学以及递归网络动力学来计算导数的各种网络的性能。通过量化它们在计算中引入的误差以及对高频输入噪声的拒绝能力，对每种类型的网络进行了比较。这种比较是基于尖峰泄漏积分和放电（LIF）神经元的分析方法和数值模拟。对于与突触后电流衰减和适应的时间常数分别匹配良好的频段的信号，自适应和前馈网络电路都能提供良好的性能。虽然严格来说，基于突触抑制的精确线性微分是不可能的，因为抑制会按比例缩放突触权重，但突触抑制电路的性能与适应电路相似。反馈电路比功能等效的前馈电路引入更大的误差，但它们具有有用的特性，即其动力学由反馈强度决定。因此，这些电路更适合于计算膜动力学范围以外的时间尺度上的信号导数，并且可能适合于提供用于精确分数阶微分的广泛时间尺度。
