You're right they don't cover functions. I don't understand what about binding or sharing they don't deal with though. Could you elaborate?

For starters, what if you want to differentiate through code that traverses a collection, for example:

    val x = ...
    ys.map(y => y + x)

Each loop iteration needs to contribute a gradient update to x, which is defined in an outer scope. And what if y => y + x is not given as an inline lambda, but defined elsewhere. It doesn't seem like your blog posts discusses any such cases.

Correct, it doesn't discuss that case, indeed it doesn't treat user-defined functions at all. I just don't understand in what sense it doesn't treat binding or sharing.