Spike Timing Dependent Plasticity (STDP)

Spike Timing Dependent Plasticity is a variant on the Hebb rule for synapses between spiking neurons, where the relative timing of pre and post-synaptic spikes determines whether the synapse is strengthened or weakened. When a pre-synaptic neuron spikes before the post-synaptic neuron, the weight is strengthened (this is long term potentiation or "LTP"). When the pre-synaptic spike occurs after the post-synaptic spike, the weight is weakened (this is long term depression or "LTD").

$$ \Delta w_{ij} \;=\; \eta W_{+/-} exp \left(- \frac{|u|}{\tau_{+/-}} \right) $$ where: $$ u = t_{post} \;-\; t_{pre} $$ Such that LTP occurs when the post synaptic cell fires afte the pre-synaptic cell and vice versa for LTD. The sign of $\Delta w_{ij}$ in this case depends on the sign of $w_{ij}$ such that inhibitory synapses also increase in value absolute value under the same conditions as excitatory synapses. This window can be reversed if the anti-hebbian flag is set to true, i.e. anti-causal relationships will produce LTP and causal relationships will produce LTD.

Note that if post and/or pre-synaptic neuron is not spiking, then this behaves like a clamped synapse. However this is not recommended and can harm performance. STDP assumes that both the source and target neurons are spiking neurons.

Time constant ($\tau_{+/-}$)

Time course of plasticity for LTP and LTDP, determines how quickly LTP/LTD decays relative to the temporal distance between the pre and post synaptic spikes.

W +/-

Magnitude of change in synaptic efficacy for LTP and LTD. Also called A+/A-.

Learning rate ($\eta$)

Multiplied by delta-w in every time step to control how quickly the synapse changes.

Sources

Source: Jean-Philippe Thivierge and Paul Cisek (2008), Nonperiodic Synchronization in Heterogeneous Networks of Spiking Neurons. Journal of Neuroscience.

Also drew on this Scholarpedia article on STDP.