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Input correlations impede suppression of chaos and learning in balanced firing-rate networks

Fig 7

Common input impedes learning in balanced networks.

A) Schematic of the training setup. A ‘student network’ (S) is trained to autonomously generate the output , by matching its recurrent inputs to those of a driven ‘teacher network’, whose weights are not changed during training. B) λ₁ in the teacher network as a function of I₁. C) Test error in the student network as a function of I₁. Critical input amplitude is indicated by vertical dashed lines. Consistent with the difference in , the teacher networks driven with common input require a larger I₁ to achieve small test errors in the student network. Error bars indicate interquartile range around the median. D) Top: Target output (green) and actual output z (dashed orange) for two input amplitudes I₁ ∈ {5, 15}. Bottom: Firing rate ϕ(h_i) for two example neurons in teacher network with common input (green full line) and student network (orange dotted line) for two input amplitudes. E) Scatter plot of test error as a function of λ₁ for each network realization in A and B, with both common and independent input. When chaos in the teacher network is not suppressed (λ₁ > 0), test error is high. Training is successful (small test error) when targets are strong enough to suppress chaos in the teacher network. Training is terminated when error reaches below 10⁻². Model parameters: N = 500, g = 2, I₀ = J₀ = 1, ϕ(x) = max(x, 0) in both teacher and student networks; f = 0.2/τ in the teacher network inputs and target .

doi: https://doi.org/10.1371/journal.pcbi.1010590.g007