We considered a simple version of the Wisconsin Card Sorting Test, with two objects (left and right) and one input object to provide the features used for feature matching. The network structure is as follows:
Figure 1. Network Structure
In the network implementing the Wisconsin Card Sorting Test, one sWTA netwok is used to represent the mental states about rules, one sWTA network is used to represent the transition conditions among rules, and one sWTA network is used to represent the final decision. The first two sWTA networks can be abstracted as a Neural State Machine, as shown in Figure 1.
When the mental state comes into one rule, it will inhibit the feature populations (output of the convolution network for feature extractions) that are not helpful to the decision makinig according to this rule.
There is a excitatory connection between the feature populations of the test object to the corresponding feature populations of the left and right objects. The dynamics of these feature populations are as follows:
Figure 2. Supralinear responses
We exploit the supralinear response of the sWTA: When configured appropriately, the response to the sum of two inputs can be much larger than the sum of the responses to each input taken separately, as shown in Figure 2.
Due to this activity difference, the ouput choice with higher excitatory input will get a higher probability to win, and this probability can be tuned with biases to 1.
The advantage of this network is that the network scale doesn't increase with the number of features and their combinations, and it linearly increases with the number of rules and the number of objects.