Kempter R, Gerstner W, van Hemmen J L
Keck Center for Integrative Neuroscience, University of California at San Francisco, San Francisco, CA 94143-0732, U.S.A.
Neural Comput. 2001 Dec;13(12):2709-41. doi: 10.1162/089976601317098501.
We study analytically a model of long-term synaptic plasticity where synaptic changes are triggered by presynaptic spikes, postsynaptic spikes, and the time differences between presynaptic and postsynaptic spikes. The changes due to correlated input and output spikes are quantified by means of a learning window. We show that plasticity can lead to an intrinsic stabilization of the mean firing rate of the postsynaptic neuron. Subtractive normalization of the synaptic weights (summed over all presynaptic inputs converging on a postsynaptic neuron) follows if, in addition, the mean input rates and the mean input correlations are identical at all synapses. If the integral over the learning window is positive, firing-rate stabilization requires a non-Hebbian component, whereas such a component is not needed if the integral of the learning window is negative. A negative integral corresponds to anti-Hebbian learning in a model with slowly varying firing rates. For spike-based learning, a strict distinction between Hebbian and anti-Hebbian rules is questionable since learning is driven by correlations on the timescale of the learning window. The correlations between presynaptic and postsynaptic firing are evaluated for a piecewise-linear Poisson model and for a noisy spiking neuron model with refractoriness. While a negative integral over the learning window leads to intrinsic rate stabilization, the positive part of the learning window picks up spatial and temporal correlations in the input.
我们通过分析研究了一种长期突触可塑性模型，其中突触变化由突触前尖峰、突触后尖峰以及突触前和突触后尖峰之间的时间差触发。由相关的输入和输出尖峰引起的变化通过一个学习窗口进行量化。我们表明，可塑性可导致突触后神经元平均放电率的内在稳定。此外，如果所有突触处的平均输入率和平均输入相关性相同，则突触权重（对汇聚在一个突触后神经元上的所有突触前输入求和）会进行减法归一化。如果学习窗口上的积分是正的，放电率稳定需要一个非赫布成分，而如果学习窗口的积分是负的，则不需要这样一个成分。在一个放电率缓慢变化的模型中，负积分对应于反赫布学习。对于基于尖峰的学习，由于学习是由学习窗口时间尺度上的相关性驱动的，因此严格区分赫布规则和反赫布规则是有问题的。我们针对分段线性泊松模型和具有不应期的噪声发放神经元模型评估了突触前和突触后发放之间的相关性。虽然学习窗口上的负积分会导致内在速率稳定，但学习窗口的正部分会捕捉输入中的空间和时间相关性。
