Fig. 5: Goal-directed networks trained to perform distinct computations have distinct single-neuron spiking dynamics arising from differences in connectivity patterns.

a Recurrent SNN architecture. A one-dimensional input is projected to the recurrently connected units within the SNN. The output is fed back to the network. We trained SNNs to perform integration, differentiation, or delayed replication of inputs. b Representative trials of three trained SNNs. Networks successfully performed the computations they were trained for. c Kolmogorov–Smirnov distance of node-based fractal dimensions or recurrent weights between pairs of trained SNNs. Distances of positive (top) and negative (bottom) recurrent weights are shown separately. Networks are ordered by their trained computations. d Same as (c) by for the outer product of output and feedback weights. e Distributions of generalized Hurst exponent at q = 2 of excitatory units in the SNNs performing different computations. f Average multifractal spectrum of the interspike interval of SNNs performing different computations. g Network connectivity patterns are closely correlated with single-unit spiking dynamics. The x-axis shows the averaged Kolmogorov–Smirnov distance of the node-based fractal dimensions of trained SNNs from the 10 SNNs performing delayed replication. The y-axis shows the difference in the Hurst exponent of SNNs from the representative SNN performing delayed replication. Note the positive correlation of network connectivity and single neurons' spiking dynamics, as well as clustering of SNNs in the scatter plot based on their trained computations.