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Learning spatiotemporal signals using a recurrent spiking network that discretizes time

Fig 7

Spectral analysis of reduced linear model.

(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 (2δϵ − 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 x1x2x3x1….

Fig 7