Training dynamically balanced excitatory-inhibitory networks
Fig 5
A: Top: Balanced E/I spiking network of size N = 300 producing a sawtooth wave of frequency 1 Hz. Bottom: E/I rate network producing a frequency-modulated oscillation obtained by Fout(t) = sin (ω(t)t) with ω(t) linearly increasing from 2π to 6π Hz for the first half of the oscillation period, then reflected in time around the midpoint of the period. Parameters: N = 500, ϕ = halftanh, trained using feedback (Methods, ΔtL = 1 s). B: Top: Eigenvalue spectrum of Jtestϕ′|x0 for a dynamically balanced rate network with sigmoid activation function trained to produce a square wave (N = 200, output frequency f = 0.04, τ = 1), for gtest = 0.8. The two red dots indicate the two conjugate eigenvalues λ1,2 with largest real value. Bottom: Oscillation frequency as a function of gtest comparing simulation results (solid curve) with approximate prediction (dashed lines). C: Readout signal with gtest = 0.8 (top) and gtest = 1.0 (bottom).