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2D neural representation video

These are 100 leaky integrate-and-fire (LIF) neurons. The neuron tuning properties have been randomly selected to encode a 2D space (i.e. each neuron has a "preferred direction vector" randomly selected from around the unit circle).

Transcript
Here we again have a simulation of 100 neurons in Nengo. The difference between this simulation and the previous one is that these neurons are now representing a 2-dimensional vector space, rather than a one-dimensional scalar. For this reason, we now have 2 inputs one controlling the x direction and the other controlling the y direction. So, as I change the input in the x direction, we can see that the point being encoded by this population of cells changes. Here we're plotting the point in the 2-D space that is being represented by the cells. And in this upper graph with the blue and the black lines, we are showing that same information plotted over time, where the black line indicates the x value the blue line indicates the y value. The plot of the cortical sheet is the same as before, where yellow is indicating that that particular neuron is spiking.

In the bottom right corner we have a new kind of plot. This is one that was made famous by Georgopoulos with his experiments on monkey arm movements. In the plot there we are showing the preferred direction vector of the neuron multiplied by the activity of that neuron. The "preferred direction vector" of a neuron is the direction which, when we move the stimulus in that direction, causes the neuron's response to increase most rapidly. Georgopoulos found that in the motor cortex neurons tend to have a even distribution of preferred direction vectors around the circle. So we have that same kind of distribution here in this representation. For this reason, we can see that as we move the input, for instance far over to the left, that neurons whose preferred direction vector is leftwards are the most active cells and those whose preferred direction vectors are rightward are the least active cells. As we move that same stimulus back towards the right, a different set of neurons turns on and those with preferred direction vectors rightward are most active. As we move throughout the space can see that the decoded value of the spiking activity does a good job of representing the input. We can choose some arbitrary points to see if they are approximately correct. You will notice that the output is in fact quite correct all the way up to the extremes of the unit circle.