Figure 2.

Spike-Timing-Dependent Plasticity, Modulation, and Three-Factor Rule

The classical spike-timing dependent plasticity (STDP) rule modifies the synaptic strengths of connected pre- and post-synaptic neurons based on the spike history in the following way: if a post-synaptic neuron generates action potential within a time interval after the pre-synaptic neuron has fired multiple spikes, then the synaptic strength between these two neurons becomes stronger (causal updates, long-term potentiation [LTP]). On the other hand, if the post-synaptic neuron fires multiple spikes before the pre-synaptic neuron generates action potentials within that time interval, then the synaptic strength becomes weak (acausal updated, long-term depression [LTD]) (Bi and Poo, 1998, Sjöström et al., 2008). The learning window in this context refers to how weights change as a function of the spike time difference (insets in the panels). Generalizations of STDP often involve custom neural windows and state-dependent modulation of the updates.

The left plot shows an example of an online implementation of the classic STDP rule with nearest-neighbor interactions: $\Delta W\left(t\right)=s_{post}\left(t\right)X\left(t\right)+s_{pre}\left(t\right)Y\left(t\right)$, where X(t) and Y(t) are traces representing presynaptic and postsynaptic spike history, respectively. Nearest neighbor interactions refer to the fact that the weight update depends on the previous pre- or post-spike, respectively. The right plot is a modulated STDP rule corresponding to a type of three-factor rule: $\Delta W_M\left(t\right)=\Delta W\left(t\right)\cdot \text{Modulation}\left(t\right)$, where the three factors are pre-synaptic activity, post-synaptic activity, and modulation. For illustration purposes, here the modulation (green) is a random signal that multiplies the weight updates. In more practical examples, the modulation can represent reward (Florian, 2007) or classification error (Neftci et al., 2017).