# STDP, wikipedia
#research #SNN #STDP
Spiking-timing-dependent plasticity(STDP) is biological process that adjusts the strength of connections between neurons in the brain. This process adjusts the connection strengths based on the relative timing of a particular neuron’s output and input spikes. If the input spike from Neuron A occur immediately before that neuron B’s output spike, then that particular input is made somewhat stronger the synapse between Neuron A and Neuron B. If the input spike occur after an output spike, then that particular input is made somewhat weaker. (Wikipedia)
With STDP, repeated presynaptic spike arrival a few milliseconds before postsynaptic spike leads in many synapse types to Long-Term Potentiation (LTP) of the synapses, whereas repeated spike arrival after postsynaptic spikes leads to Long-Term Depression (LTD) of the same synapse. The change of the synapse plotted as a function of the relative timing of pre- and postsynaptic action potentials is called the STDP function or learning window and varies between synapse types.
[image:6F56A2F7-212C-46AE-8AB7-4BB944050328-13930-000260942B8E46BB/STDP_learning_window.JPEG]
Figure 1: Spike-Timing Dependent Plasticity (schematic): The STDP function shows the change of synaptic connections as a function of the relative timing of pre- and postsynaptic spikes after 60 spike parings. Schematically redrawn after Bi and Poo (1998)
When weight increases, the amount of increase is related to the current weight.
<Experimental STDP Protocol>
The paring is repeated for 50-100 times at a fixed frequency (for example 10 Hz). (이것은 Neuron의 firing frequency가 0.5~1kHz쯤 된다는 것인가?) The weight of the synapse is measured as the amplitude (or initial slope) of the postsynaptic potential.
<Basic STDP Model>
The weight change delta w_j of a synapse from a presynaptic neuron j depends on the relative timing between presynaptic spike arrivals and postsynaptic spikes. Let us name the presynaptic spike arrival times at synapse j by t_j^f where 1, 2, 3, … counts the presynaptic spikes. Similarly, t_i^n with n = 1, 2, 3, … labels the firing times of the postsynaptic neuron. The total weight change delta w_j induced by a stimulation protocol with pairs of pre-and postsynaptic spikes is then (Gerstner and al. 1996, Kempter et al. 1999)
[image:66CCECA4-C660-475A-A1D1-D9C463F5F5AB-13930-000261A3D76D62FE/FC770EDA-98FA-4DD0-B957-A02CFA95AFBC.png]
의문점) 그럼 만약에 postsynaptic spiking 전에 presynaptic spiking이 2번 있었으면 나중의 것으로 생각해서 계산하는 것인가? -> 다양한 버전이 존재한다. 전체를 모두 고려하는 all-to-all 혹은 제일 가까운 애만 고려하는 nearest 같은 것도 존재하고.
where W(x) denotes one of the STDP functions (also called learning window)
A popular choice for the STDP function W(x)
[image:8B313596-6CAB-463B-90BC-635900C43535-13930-000261BA7801BC5F/419F7E0C-D679-4451-9EE3-3D1EAC4D5D64.png]
Which has been used in fits to experimental data (Zhang et al. 1998) and models (e.g, Song et al. .2000). The parameters A_+ and A_- may depend on the current value of the synaptic weight w_j. The time constants are on the order of taw_+ = 10ms and tow_- = 10ms
