Winner-Take-All Circuit

This entry is about a cortical processing motif, the Winner-Take-All circuit.

We implement a small system rate-based system with a uniform connectivity matrix between excitatory and inhibitory inputs. There are 9 excitatory cells and 3 inhibitory cells. Excitatory cells increase the rate of their target neurons and inhibitory neurons decrease it. This is a highly unrealistic model, but its simplicity has its appeal. You can see approximately how the system evolves.

The circuit connectivity is the following: recurrent excitatory connectivity (all excitatory cells are connected to all excitatory cells), excitatory to inhibitory connections and inhibitory to excitatory connections. This is reflected in the weight matrix. You can also easily alter the code to include inhibitory-inhibitory

connections.

The cells receive various levels of input. The Winner-Take-All circuit selects a cell with the highest input rate.

We use the DANA simulator in Python to simulate the circuit. The code can be found here: https://github.com/mariakesa/NeuralSimulations/blob/master/wta.py

This is the solution without inhibitory-inhibitory connections. The Purple are inhibitory rates, the Blue is the cell with the highest input and Green

are the all the other excitatory cells:

And this is the solution with inhibitory-inhibitory connections (oscillatory dynamics emerge):

It is interesting to reason why these dynamics emerge and I leave that for future entries.