Figure 5.

Results of SNN based on the Multinoulli-Bernoulli mixture model, evaluated on the hand-written digits 0 and 8 in the MNIST dataset (LeCun et al., 1998). (A) Representative spatio-temporal spike patterns of digit 0 (top panel) and digit 8 (bottom panel), and the post-synaptic spikes z_t = 1 before learning. Thick colored lines indicate the pre-synaptic spikes x_is = 1, elicited within μ − 1 < Δt = s + τ_i − t < μ + 1 for z_t = 1; other pre-synaptic spikes x_is are depicted as thin gray lines (the left vertical axes). Gray shaded areas denote the probability of eliciting a post-synaptic spikes z_t = 1 per 1 ms (the right vertical axes). (B) Test distributions of the post-synaptic spike timings z_t = 1 before learning. (C) Post-synaptic spike timings z_t = 1 after learning, given the spatio-temporal spike patterns x in (A). (D) Test distributions of the post-synaptic spike timing z_t = 1 after learning. (E) Trajectories of the synaptic weights W_i and conduction delays τ_i during the learning procedure. The darkest lines denote the values of the parameters W₀ and τ₀, and the lighter lines denote W_i and τ_i for i = 1, 2, … . (F) Random samples of the post-synaptic spike timings z_t = 1. The black solid line marks the decision boundary between spike patterns the hand-written digits 0 and 8. (G) Classification accuracy in the training and test datasets, each averaged over 100 trials.