Nếu H (τ) là dương tính với τ tích cực và tiêu cực đối với tiêu cực τ, nhiệm kỳ đầu tiên ở phía bên phải của phương trình này đại diện cho LTP và LTD thứ hai. Các đường cong rắn trong hình là một ví dụ của một chức năng như H. Thời gian không đối xứng của H có ảnh hưởng rất lớn về những thay đổi trọng lượng | Unsupervised Learning 13 pre- and postsynaptic rates as it is for a Hebbian rule the rate of change of the synaptic weights at time t is given by timing-based rule T - ỉ dT H T v t u t t H T v t T u t . dt J0 If H t is positive for positive T and negative for negative T the first term on the right side of this equation represents LTP and the second LTD. The solid curve in figure is an example of such an H function. The temporal asymmetry of H has a dramatic effect on synaptic weight changes because it causes them to depend on the temporal order of the activity during training. Among other things this allows synaptic weights to store information about temporal sequences. Rules in which synaptic plasticity is based on the relative timing of pre-and postsynaptic action potentials still require saturation constraints for stability but they can generate competition between synapses without further constraints or modifications at least in nonlinear spike-based models. This is because different synapses compete for control of the timing of postsynaptic spikes. Synapses that are able to evoke postsynaptic spikes rapidly get strengthened. These synapses then exert a more powerful influence on the timing of postsynaptic spikes and they tend to generate spikes at times that lead to the weakening of other synapses less capable of controlling spike timing. Unsupervised Learning We now consider the computational properties of the different synaptic modification rules we have introduced in the context of unsupervised learning. Unsupervised learning provides a model for the effects of activity on developing neural circuits and the effects of experience on mature networks. We separate the discussion of unsupervised learning into cases involving a single postsynaptic neuron and cases in which there are multiple postsynaptic neurons. Single Postsynaptic Neuron Equation which shows the consequence of averaging the basic Hebb rule over all the presynaptic training
