I eventually put together a fast type of neural network with an external associative memory system.
The AI code is fine I would say, the example problem code shows signs perhaps of reluctance.
Certainly the thing is even further abstracted from the biological brain than conventional artificial neural networks.
The associative memory is based on hash functions.
Hashing produces ‘random’ vectors in higher dimensional space that are approximately orthogonal. It is easy then for the weighted sum (dot product) to associate scalar values with a certain number of those ‘random’ vectors.
Using milder hashing (eg. Locality Sensitive Hashing) further mathematics apples allowing interpolation between the data points stored in higher dimension space that isn’t possible with conventional hashing.
The variance equation for linear combinations of random variables and the central limit theorem then play a role.
The fast neural network I used is a swap around between the variable weights and a fixed activation function used in conventional artificial neural networks.
Instead the weights are fixed by using a fast transform for them (fixed filter bank) and the activation functions are made individually adjustable (parameterized.)