Fig. 1.

The task is to efficiently encode analog input signals x by the response of a population of spiking neurons z. (A) To that end, neurons couple to the input via feedforward weights F (dominated by excitation) and to each other via recurrent weights W (dominated by inhibition). From the encoding an external observer can decode an approximation $\widehat{\mathbf{x}}$ of the original input signal x via a linear transformation D. (B) The membrane potential u_j of neuron j is a linear sum of continuous inputs x_i and spike traces z_k. Spikes cause an immediate self-inhibition, which can be seen as an approximate reset of u_j. Spikes of other neurons are transmitted with a delay δ. When recurrent weights are learned such that recurrent input z_k cancels feedforward input x_i, u_j is balanced and reflects the global encoding error $\mathbf{x}-\widehat{\mathbf{x}}$. In that case, spikes are fired only when the encoding error is high, so that the spike encoding is efficiently distributed over the population.