WTA-Contrast Dependent Latency

Preliminary Draft-please send comments to James Bonaiuto

Contrast Dependent Latency

Blue crosses: The latency of resolving a winner in the competitive choice layer given the contrast between the two most activated elements of the parallel planning layer. Green line: A logarithmic function fit to the data.

To test the effects of input contrast on latency in the winner-take-all process, the network was tested using 100 randomly generated vectors of elements between 0.0 and 1.0. For each vector, it was applied as input to the parallel planning layer of the ACQ network, and the network was run for 1s (with dt=0.001s) or until a winner was found. A winner was declared when the firing rate of any neuron in the competitive choice layer was greater than a threshold, ε1, and the firing rates of all other neurons in the layer were less than a second threshold, ε2. In this simulation, ε1 was set to 0.9, and ε2, was 0.1. The latency, l was defined as the time required for the network to run until a winner was declared. This value was compared to the contrast of the input vector, c, measured by 1-\frac{PP_{i}}{PP_{j}}, where i and j are such that PP_{i}(t) and PP_{j}(t) are the highest and second highest, respectively, firing rates in the competitive choice layer. A logarithmic function was fit to the data, with coefficients, a_{1}=-0.007a_{2}=0.0028. Given the contrast between the largest and second largest inputs, the latency is therefore approximated by l=-0.007log(c)+0.0028.

To further investigate the contrast-latency relationship we investigated input vectors with contrasts between 0.01 and 0.35 in increments of 0.01. For each contrast value c, 1000 random vectors were generated by setting a random element to a random value x above 0.5, setting another random element to x(1-c), and setting the other elements to random values less than x(1-c). A second order logarithmic function, \bar{l}=0.63923log(c)^2-2.6841og(c)+10.2532, was fitted to the mean latency, \bar{l} , for each contrast value (Figure 18). The standard deviation of the latency increased as a cubic function of the contrast c (\sigma_{l}=13.1039c^3-17.0382c^2+7.2617c+1.1985).

Mean contrast dependent latency

Blue crosses: The mean latency over 1000 trials of resolving a winner in the competitive choice layer given the contrast between the two most activated elements of the parallel planning layer. Green line: A second-order logarithmic function fit to the data.

Stddev contrast dependent latency

Blue crosses: The standard deviation of the latency over 1000 trials of resolving a winner in the competitive choice layer given the contrast between the two most active elements in the parallel planning layer. Green line: A cubic function fitted to the data.