WTA-Noise

Preliminary Draft-please send comments to James Bonaiuto

Wta error

Blue x’s: The error rate of the WTA network for a given level of variance in the noise in the parallel planning layer. Green line: A logarithmic function fitted to the data.

A sensitivity analysis on the variance of the noise in the parallel planning layer, \sigma_{PP}^{2} was conducted using randomly generated inputs, again vectors with elements between 0.0 and 1.0. A random signal was added to each element, normally distributed with mean 0.0 and different levels of variance. For values of the variance between 0.0 and 2.0 in increments of 0.01, the network output error was averaged over 100 runs with random inputs. On each run, the network was simulated for 1s with dt=0.001 or until a winner was found, whichever came first. The criteria for a winner was that the maximum firing rate in the competitive choice layer must be greater than ε1 (set to 0.9), and all other firing rates must be less than ε2 (set to 0.1). An error was declared when the winning unit in the competitive choice layer did not correspond to the parallel planning layer unit that received the maximum input (before noise). A logarithmic function was fit to the data, with coefficients, a_{1}=0.1158a_{2}=0.6158. Given the variance of the noise in the parallel planning layer activity, the output error rate, err, is therefore approximated by err=0.1158log(\sigma_{PP}^{2})+0.6158.