Learning and autoencoding framework for recurrent spiking networks.

Abstract

(a) We implement autoencoding in a recurrent network between the activity of the neurons across time, t. This can be visualised schematically where the activity of the network is unfolded in time, and the activity of the network at these timepoints become layers. Autoencoding between successive layers/timepoints is indicated by dotted red lines, with the same connections between each pair of layers/timepoints. Autoencoding also occurs in the traditional sense between the separate populations. (b) A schematic period of postsynaptic spiking activity A(t) enclosed in the red rectangle from time t to t + τA is used to compute the expected instantaneous firing rate of presynaptic neuron j (green) at time t. In this example, presynaptic neuron j spikes at t (but this does not always occur) so the Hebbian plasticity rule, ΔwH, is applied once to each synapse from presynaptic neuron j to the postsynaptic neurons that subsequently spike between t and t + τA, for each postsynaptic neuron’s first spike only (red dots). In applying the non-Hebbian plasticity rule, ΔwnH, in response to a spike in postsynaptic neuron i (blue) at ti, the integration in Eq (6) is over the time period from the most recent previous spike tk to the current spike at ti.</p