Paul William Berg

I like Gas Nets. They show great promise. However, there are a couple things I don't like about them, and I think I have devised a solution to these issues.

The traditional Gas Net goes like this:

You have an n-dimensional space, 2 dimensions being the standard, so that's what this example will use. A neuron has a specific X,Y coordinate in this space. The neuron's inputs are defined by 3 numbers. 2 numbers defining the arc extent and another defining the radius, this gives the neuron a semicircle inside which any neurons existing will supply inputs to the neuron. The gas is diffused from a neuron (or from a seperate coordinate) and effects other neurons in the gas's radius. The diffusion is generally modeled loosely, as to not become a fluid dynamics simulation at the expense of processing the neural network itself.

Now the problem I have with this is that I don't see an easy algorithm for either determining whether a neuron is within an input arc, or the level of gas a neuron is subjected to without going to an n-squared algorithm. There may be a vector-field calculation to determine the gas level at any point that isn't n-squared, but I'm just not up on my topological math enough to know it, and it seems that such an algorithm is not easily attainable from google.

However, I have been thinking (which is always dangerous) on why we need a spacial model in the first place. The behaviour we are trying to achieve is purely functional after all. So, here is my idea.

Neurons in the network are given "locality" connections between them. Locality connections do not convey any data themselves, but rather establish a non spacial topology. A Neuron, in emitting (or uptaking) gas, will simply iterate through it's locality connections, adding an amount of gas to that neuron, reduced by the distance. These first-order neurons would have a distance of 1 unit. Those neurons, in turn, would iterate their locality connections not already traversed, and increase the gas quantity of each of those by the gas emmitance amount reduced by a distance of 2. The amount would fall off linearly, or by the square of the distance, or however else you wanted to do it. This would continue to a cutoff distance. At each iteration, each neuron would lose an amount of gas to dispersion.

This seems to retain all of the functional benefits of gas nets without introducing any of the spacial topology problems.