in support. They are doing focused work on reinforcement

learning. Baidu, Google, Facebook, etc. are all deeply in the

game.

Specifying Neural Networks to solve problems is easy. See

https://www.youtube.com/watch?v=sEciSlAClL8 which explains

the steps and the code to get 99+% accuracy on the MNIST

dataset (handwritten digits).

Tensorflow includes primitives, such as 2d convolution,

matrix multiplication, symbolic derivatives, RELU (rectified

linear unit which is just zero for negative values and linear

otherwise), sigmoid functions, atan functions, etc. The actual

computation is just linear matrix computations, XW+B where

X are the data, W are the weights, and B are the biases.

Latest "best practices" shows that deep neural networks are

best implemented by repeating layers of XW+B followed by

a non-linear (e.g. RELU, Sigmoid, Atan) step.

Axiom has the ability to do all of these tasks, making it a good

platform for further research. In particular, there seems to be

little "algorithmic analysis". The DNN area and NN research

in general seems to be a collection of "tricks" (e.g. dropout).

This is troubling since there is no easy way to predict the

actual result, and rather frightening when the DNN is driving

your car.

In theory what a DNN computes can be computed using a

single layer NN. Can Axiom be used to "collapse" the layers

by combining and spreading derivatives? A single layer NN

with complicated derivatives seems easier to analyze than a

multilayer iterated structure. The complicated derivatives could

be "grouped" into similar classes and the shape of the higher

order curves explored using symbolic expressions. This would

give a clearer view of what the NN will do, where the high

dimensional "valleys" lie, and where the system is sensitive.

Such an ability to do analysis could reshape the industry.

Tim