Learning spatiotemporal signals using a recurrent spiking network that discretizes time
(A) Cartoon of a simplified linearised rate model with three nodes x1, x2, x3 corresponding to three clusters of excitatory neurons with recurrent strength δ connected to a central cluster of inhibitory neurons x4. The cyclic connections are stronger clockwise than anticlockwise since ϵ > 1. (B) The spectrum shows a conjugate complex eigenvalue pair with large real part (2δ − ϵ − 1)/2 and an imaginary part which grows linearly with the asymmetry of the clockwise/anticlockwise strength (ϵ − 1). This pair of eigenvalues dominates the dynamics as their real parts are close to 1 and leads to the periodic behaviour corresponding to propagation around the cycle x1 → x2 → x3 → x1….