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. Author manuscript; available in PMC: 2022 Oct 21.
Published in final edited form as: Neural Comput. 2021 Apr 13;33(5):1199–1233. doi: 10.1162/neco_a_01379

Figure 5:

Figure 5:

Learning complex activity patterns under the ROWSUM constraint on multiple subpopulations. Target patterns consist of trajectories generated from the Ornstein-Ulenbeck process. (A) Schematic of constraining multiple subpopulations; black dot indicates one neuron; transparency indicates the within-group firing rate. (B) Excitatory (red), inhibitory (blue), and total (orange) synaptic inputs to trained neurons. (C) Spike trains of the same neurons in panel A across multiple trials. (D) Fano factor of trained neurons; dashed line indicates the mean. (E–G) Excitatory and inhibitory neurons are ordered by firing rates and assigned to five subpopulations (i.e., 100 neurons in each group); low- to high-rate groups are shown from left to right; neurons in the αth excitatory and inhibitory subpopulations are shown in the same panel, group α. (E) Distribution of firing rates of neurons in group α; the within-group average firing rates shown. (F) Mean strength of synaptic connections that each neuron in the αth excitatory (orange) and inhibitory (green) subpopulations receive from other neurons in the same subpopulation; black dots show the mean strength of initial connections. (G) Synaptic weight distribution of outgoing connections from neurons in the αth excitatory (red) and inhibitory (blue) subpopulations. The percentage of synapses (with respect to the total number of synapses in the network) that violates Dale’s law by the neurons in each group are shown. (H) Fraction of excitatory (red) and inhibitory (blue) synapses that violates Dale’s law after each training iteration; each line represents outgoing synapses from neurons in the αth subpopulation; light to dark color shows subpopulation 1 to 5. (I) Distribution of trained synaptic weights (black); outgoing synapses from top (green) and bottom (purple) 40% of neurons ordered by firing rates; dashed lines indicate initial synaptic weights. (J) Performance of trained networks after removing synapses that violate Dale’s law; constraints on multiple (black) and excitatory-inhibitory (orange) populations.