Peirce's conjunction detector with different first-stage contrast-response functions. Stimulus components
S1 and
S2 each stimulate a first-stage neuron selectively tuned to that component. The contrast-response functions of these neurons are illustrated in the leftmost column of circles. Peirce's (
2007) original conjunction detector just summed the responses of the two first-stage neurons. Peirce's (
2011) extended conjunction detector included a threshold function on the output. Like Peirce (
2011), we set the threshold at 5% above the maximum expected response of a single first-stage neuron (i.e., 1.05 ×
rmax) to avoid a response to a single component presented in isolation. The Cartesian axes on the right represent all possible combinations of component contrasts. The purple-shaded regions represent those pairs of component contrasts for which the sum of responses of the first-stage neurons is above threshold, thereby allowing the conjunction to be detected. Each of A to E shows a different contrast-response function for the first-stage neurons. In A, the contrast-response function is linear: 45% of the possible conjunction stimuli are detected. In B, the contrast-response function is zero for zero contrast and
rmax for all other contrasts. This is the optimal contrast-response function shape for this model: All possible conjunction stimuli are detected. In C, the contrast-response function saturates at a contrast of 0.386. Although suboptimal, this function allows detection of the majority of possible conjunction stimuli (79%), and is much better than a linear function. In D and E, the portion of the contrast-response function to the left of the peak is identical to that in C, but the function supersaturates to the right. As the amount of supersaturation increases, the proportion of detected conjunctions falls (74% and 42% for D and E, respectively). The contrast-response function in D is described by Peirce's (
2007) modified Naka-Rushton function (May & Zhaoping,
2011, equation 11) with
c50 = 0.235,
q = 3.81, and supersaturation parameter,
s = 1.12. These parameters were fitted to the data for a supersaturating neuron shown in Peirce's Figure 2e (see May & Zhaoping,
2011, table 1, neuron e). In E, the portion of the contrast-response function to the right of the peak was constructed by taking the corresponding portion from D and linearly stretching it so that it reached all the way down to zero. The baseline firing rate was set to zero in all the contrast-response functions used here.