Figure 2.

(A) A temporal relation function g(Δt), representing an excitatory post-synaptic potential (EPSP) or current (EPSC), when the pre-synaptic spike is elicited at s = 0 ms. The parameters were set to μ = 1.5 ms and σ = 1.0 ms and the conduction delay τ_i was set to τ = 10 ms. (B–D) The gradients of the lower bound $\mathcal{L}(\theta )$ of the model evidence 𝔼_x~X[log p(x; θ)] with respect to the parameters W_i and τ_i. The time step δ was 0.05 ms, the experimental time period T was 50 ms, and the remaining parameters were set to v = 10, and η = 0.001. The gradient shapes depend on the shape of the temporal relation function g(Δt). (B) Temporal window of the delay learning, showing the relationship between the temporal difference Δt and the change Δτ_i in conduction delay τ_i, where Δt = s + τ_i − t. (C) Temporal window of the synaptic plasticity, showing the relationship between the temporal difference Δt and the change ΔW_i in synaptic weight W_i. (D) The change ΔW_i in synaptic weight W_i versus the current synaptic weight W_i for Δt = 1.5 ms (orange) and Δt = -5.0 ms (blue).