Department of Biomedical Engineering, Oregon Health & Science University, Portland, OR 97239, USA.
Neural Comput. 2012 May;24(5):1109-46. doi: 10.1162/NECO_a_00267. Epub 2012 Feb 1.
Online machine learning rules and many biological spike-timing-dependent plasticity (STDP) learning rules generate jump process Markov chains for the synaptic weights. We give a perturbation expansion for the dynamics that, unlike the usual approximation by a Fokker-Planck equation (FPE), is well justified. Our approach extends the related system size expansion by giving an expansion for the probability density as well as its moments. We apply the approach to two observed STDP learning rules and show that in regimes where the FPE breaks down, the new perturbation expansion agrees well with Monte Carlo simulations. The methods are also applicable to the dynamics of stochastic neural activity. Like previous ensemble analyses of STDP, we focus on equilibrium solutions, although the methods can in principle be applied to transients as well.
在线机器学习规则和许多生物尖峰时间依赖可塑性 (STDP) 学习规则为突触权重生成跳跃过程马尔可夫链。我们为动力学给出了一个微扰展开式，与通常通过福克-普朗克方程 (FPE) 进行的近似不同，这个展开式是有充分根据的。我们的方法通过为概率密度及其矩给出展开式，扩展了相关的系统大小展开式。我们将该方法应用于两种观察到的 STDP 学习规则，并表明在 FPE 失效的情况下，新的微扰展开式与蒙特卡罗模拟吻合得很好。这些方法也适用于随机神经活动的动力学。与之前的 STDP 集合分析一样，我们关注的是平衡解，尽管这些方法原则上也可以应用于瞬态。
