Category Theory ∩ Machine Learning • Hacker News Board

Re: Category Theory ∩ Machine Learning

#71

Post by johnbernier » Wed, Mar 08, 2023, 8:24 PM UTC

epgui wrote: post #49

donnowhy wrote: post #16

category theory is 'native 2-dimensional' math. i.e. category theory explains everything in terms of graphs, where a graph is made from two different sorts of 'entities', nodes and vertices i.e. categories and morphisms this being math, I wonder to which extent can category theory be re-expressed in terms of sets. perhaps a better question is if category theory can be re-expressed (or founded on) functions? lastly, I…

Set theory is going the way of the dodo. There are modified versions of set theory, but afaik a lot of the more exciting work is happening around type theory and proof assistants these days.

Set theory is not going anywhere. It may be pushed to the sidelines by new developments in category theory but that is not the same as going extinct like the dodo.

Re: Category Theory ∩ Machine Learning

#72

Post by lgas » Fri, Mar 10, 2023, 2:53 AM UTC

AlexCoventry wrote: post #46

bawolff wrote: post #39

Earlier quoted context omitted.

Application in the sense they are using it is probably different than the sense you are using it. Although its still probably a fair question regardless.

Any application where Category Theory is making it substantially easier to express the software or reason about it is fair game, from my perspective.

How about https://arxiv.org/abs/1803.05316?

Re: Category Theory ∩ Machine Learning

#73

Post by hgsgm » Fri, Mar 17, 2023, 8:51 PM UTC

bgavran wrote: post #30

hgsgm wrote: post #9

Earlier quoted context omitted.

Why? How? The OP GitHub site doesn't promote any material that introduces the concepts at all. The "survey" paper at the top is nigh-impenetrable. I'm sure the category theorists are having fun modelling machine learning, but it doesn't show how machine learning benefits from the category theory.

There's a well-articulated essay from Christopher Olah that captures the undercurrent, and perhaps even the motivation of many of these papers https://colah.github.io/posts/2015-09-NN-Types-FP/ You're completely right that the repo doesn't promote any introductory material. CT is notoriously difficult to get into, and this repository wasn't meant to be a pedagogical one, but rather a list of all the relevant papers.…

Olah's blog entry is about types and algebra. We've had types and algebra for a long time distinct Category Theory, which is a further abstraction over algebraic structures.

A lot of computer programmers who never studied Abstract Algebra or Type Theory before think that all of that is Category Theory because Haskell is their first exposure to all that, and Category Theory is a big meme in Haskell, thanks to Monad.