Alice's adventures in a differentiable wonderland

> Stripped of anything else, neural networks are compositions of differentiable primitives

I’m a sucker for statements like this. It almost feels philosophical, and makes the whole subject so much more comprehensible in only a single sentence.

I think François Chollet says something similar in his book on deep learning: one shouldn’t fall into the trap of anthropomorphising and mysticising models based on the ‘neural’ name; deep learning is simply the application of sequences of operations that are nonlinear (and hence capable of encoding arbitrary complexity) but nonetheless differentiable and so efficiently optimisable.

> > Stripped of anything else, neural networks are compositions of differentiable primitives

> I’m a sucker for statements like this. It almost feels philosophical, and makes the whole subject so much more comprehensible in only a single sentence.

And I hate inaccurate statements like this. It pretends to be rigorous mathematical, but really just propagates erroneous information, and makes the whole article so much more amateur in only a single sentence.

The simple relu is continuous but not differentiable at 0, and its derivative is discontinuous at 0.

It’s not ‘inaccurate’. The mark of true mastery is an ability to make terse statements that convey a huge amount without involving excessive formality or discussion of by-the-by technical details. If ever you’ve spoken to world-renowned experts in pure mathematics or other highly technical and pendantic fields, you’ll find they’ll say all sorts of ‘inaccurate’ things in conversation (or even in written documents). It doesn’t make them worthless; far from it.

If you want to have a war of petty pedantry, let’s go: the derivative of ReLU can’t be discontinuous at zero, as you say, because continuity (or indeed discontinuity) of a function at x requires the function to have a value at x (which is the negation of what your first statement correctly claims).

Invoking excessive formality and discussions of minute technical details leads to a cathedral of knowledge built on autistic pedantry. The chosen rabbit hole to get lost in needs to be the correct one. And human science is riddled with the paths that have naive or childish fundamentals.