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Comparison of FORCE trained spiking and rate neural networks shows spiking networks learn slowly with noisy, cross-trial firing rates

Fig 7

Variance dominates LIF-spiking networks while bias dominates LIF-matched rate networks in mean squared error decomposition.

A For the 5 Hz sinusoidal oscillator task, we trained networks over a grid of points in the (Q,G) hyperparameter space with 4 different learning rates for both LIF and LIF-matched rate networks. For each point in the (Q,G) space, we simulated the trained network for 100 (20s) repetitions of the sinusoidal output, then computed the cross trail bias and variance of the networks output. Columns of heatmaps within each sub-panel from left to right are: the time averaged bias squared, time averaged variance, and the proportion of the variance to bias squared. The left panel and right panels contain the plotted values for the spiking network simulations and rate networks, respectively. B–C For a selected point (indicated by star in A) in the (Q,G) grid, the corresponding trained network was simulated with both LIF and rate neuron models for slow and fast learning rates for 100 (20s) repetitions of the 5 Hz sinusoidal task. For 5 randomly chosen neurons, the spike times (B) for the spiking networks and filtered postsynaptic currents (C) for both networks were recorded. To counteract output time-drift, each repetition of the network output was time-aligned to the first peak of the supervisor. B Each spike time was represented by a dot, where the colour indicates the order of the spike time within each repetition of the task, indicating their high variability. C The postsynaptic filters for both the LIF and rate networks, where the shaded areas indicate the corrected sample standard deviation for both. Note that the deviation for the rate network is also displayed.

doi: https://doi.org/10.1371/journal.pcbi.1013224.g007