Seems like a good collection of standard ML techniques, introduced with a fairly unified mathematical notation and quite a few proofs. Quite the Herculean effor

Seems like a good collection of standard ML techniques, introduced with a fairly unified mathematical notation and quite a few proofs. Quite the Herculean effort (600 pages!). It just seems to me like they're putting the emphasis on the stuff that is more straightforward to formalize rather than the stuff that would be interesting to understand. Look eg at the SGD chapter. I picked this because I think optimization is one of the areas where mathematicians actually can and do make impactful contributions to ML. But then look at the chapter in the book: most of the proofs are fairly elementary (like bias-variance decompositions or Jensen inequalities), some more interesting theorems (on convergence) are cited from the literature and do not build on the lemmata, and the sub-chapters on the actually interesting methods like ADAM,... are completely free of proofs or theory. It seems to me that after reading the chapter, a reader will have a good understanding of modern SGD methods and how we got there, but they won't necessarily be much wiser about why those methods work, other than having a good intuition confirmed by numerical experiments. If that's the outcome, then I wonder what the fuss proving all the basic stuff was all for. Wouldn't it be more useful to dedicate the space to convergence proofs for ADAM (which do exist) rather than showing lots of stuff like E(XY) = E(X)E(Y) for independent random variables? That's just one chapter, I may not be doing them full justice here, although I did read through a few others as well. I first got this impression from the ANN chapter, which is ripe with long proofs for rather basic and uninteresting stuff, and from the physics-informed neural networks paper (which I actually find really nice, although it suffers a bit from the same problem as the SGD chapter). I don't want to be too critical here, it is nice in general to move towards a more rigorous and unified exposition of ML methods, and their approach should extend to the more technical results as well, just questioning where they drew the line of what to include and what not.