Earlier quoted context omitted.
I disagree with you. > Essentially all we've done is pushed the basic model proposed by linear regression to it's absolutely limits No, we haven't pushed linear regression to its limits. If it was only linear regression, it wouldn't work. Neural networks need a non-linearity to model complex things. The beauty is that given an infinite series of nonlinearities, one can model any mathematical function. In practice we…
You don't need non-linearities, an infinite series of sine functions is enough to model any function. For extraordinary claims ('intelligence'), the burden of proof is on those making the claim, not on others to prove the negative.
y = b + x1 + x1^2 + x1^3 + ... + x1 * x2 + (x1 * x2)^2 + ... + x2 + x2^2 + ...
By that point you're making a Taylor approximation of the latent function through linear space, which is also a universal approximator.
So the commenter above is wrong -- neural networks are indeed just glorified linear regression from this point of view.
The main difference is that this kitchen sink regression is computationally inefficient which neural nets are extremely efficient computationally.*