Fig. 4. Trial-to-trial variability of the network in response to step stimuli. A step stimulus causing 100 Hz firing was repeatedly applied to the network, and the trial-to-trial variance was measured. a, The mean and variance of the total spike count per layer are plotted parametrically as a function of the count duration. In rate mode, the count obeys sub-Poisson statistics. The*straight line* indicates Poisson statistics, and the*bottom dashed line* is the lower limit of the variance for 20 periodically spiking neurons with independent phases. b, As in a, but for the synfire mode with a small amount of noise (20 pA). The fluctuations in the total count are larger (note difference in vertical scale). *Straight line*, Poisson statistics; *dashed curve*, the variance of 20 periodically spiking neurons with the same phase. Same *symbols* as in a. c, The accuracy of estimating firing rates in the network as a function of the integration time. The error in the firing rate estimate decreases as the square root of the integration time.*Solid line*, Error in layer 5 in a network with 20 neurons per layer firing at 100 Hz; *dashed line*, same network firing at 25 Hz; *dotted line*, synfire mode. d, The estimation error as a function of the number of neurons per layer. In the rate mode, the estimation error decreases approximately as the square root of the number of neurons per layer (*top solid curves*, 5 msec integration time; *bottom solid curve*, 50 msec integration time; 5 layer network). *Dashed lines* are fits with a square root function. In the synfire, the error remains approximately constant (*dotted line*, 5 msec integration time). e, The dependence of the error on the number of layers. In the rate mode, the estimate does not deteriorate much when the stimulus propagates through many layers; instead, the error remains fairly constant after the first couple of layers (*top* to*bottom curve*, 5, 10, and 50 msec integration time). In the synfire mode the estimate deteriorates with layer number (dashed curve, 50 msec integration time). f, The dependence of the estimate on the synaptic time constant. The integration time at the output layer was 5, 20, and 100 msec (*top* to *bottom curve*; 5 layer network). When the synaptic time constant is too short, the network starts to synchronize and the error increases. A longer synaptic time constant slows down propagation but does not yield much better performance.