It’s questionable how “immature” ML really is. Most methods that get used were initially designed 50+ years ago, with various improvements over time. E.g., neural networks were invented in the 1950s, backprop was introduced in the 80s, architectures like LSTM and CNN in the 90s, etc.
The only thing that’s really new is the amount of computational power at our hands. That has allowed us to shift from relatively simpler methods to more powerful but opaque methods like NNs. They just don’t lend themselves to easy analysis because it’s a lot harder to explain why inputs to these ML systems map to their respective outputs. Hence, attempts at drawing the connection between inputs and outputs become more speculative.
At the beginning the authors claim they're not just making a restatement of the Stone-Weierstrass theorem (any continuous function on a compact set can be approximated arbitrarily well by a polynomial), but reading through, I'm not sure what they're proving besides that. In fact, on pages 6-7 they simply appeal to that theorem before stating "NNs can loosely be viewed as a form of polynomial regression". Most of the rest of the paper is comparing polyreg and NNs on various datasets. Sec. 9 doesn't have anything doesn't have anything especially novel in it. For instance, in 9.3 they say they'll explore the causes of overfitting in the context of their "NN <-> PR" principle, but never actually do so...
Polynomial regression is nice because it's a little easier to interpret, and it's also a convex problem with a single, global minimum. OTOH you have to design features yourself, otherwise for high-dimensional problems polyreg quickly requires way too much memory and compute to solve in a reasonable amount of time.
This paper might have been more interesting if it had somehow connected neural nets to those facts, or if it had shown how insight on the way in which neural nets work can be used to improve polyreg. But (admittedly, from a brief reading) I don't anything like that here.
Nice! I like that the author wrote the code by hand rather than leaning on some framework. It makes it a lot easier to connect the math to the code. :)
As a meta-comment on these "Introduction to _____ neural network" articles (not just this one), I wish people would spend more time talking about when their neural net isn't the right tool for the job. SVMs, kNN, even basic regression techniques aren't any less effective than they were 20 years ago. They're easier to interpret and debug, require many fewer parameters, and potentially (you may need to apply some tricks here or there) faster at both training and evaluation time.
I used to play a lot, and hit 1900 (USCF) before I ran out of time to keep playing competitively. So I'm not a pro by any means, but I might know enough to help you get started.
The best way to increase your rating is to find a good chess coach. Otherwise, off the top of my head, my suggestions would be (in order of importance):
1. Learn an opening really well. Ideally, find one opening for white that doesn't generally have many weird transpositions, e.g. the London system. Also, find a couple of solid defenses for black in response to 1. e4 and 1. d4, e.g. the French and the Slav defenses.
2. Study the most basic endgames -- queen + king vs king, rook + king vs king, etc. I'd suggest [0] as a resource.
3. Practice a lot of tactics. You can do this through books (I'm partial to [1] for beginners and [2] when you reach 1600 or so) or through online services like lichess.org.
4. You can probably hit 1500-1600 fairly easily with 1-3. At this point I'd start learning the basics of strategy/positional play, e.g. static vs dynamic advantages. I think [3] is a pretty good resource for this.
5. Study some of the more advanced endgames in [0].
6. Start looking at some more complex openings and go a bit deeper into positional play. IMO the most important thing in the long run is just to find an opening and style of play that you really like.