> Category Theory has been finding increasing applications in machine learning
What's the most compelling application so far?
Category Theory ∩ Machine Learning
31–40 of 73 posts
Re: Category Theory ∩ Machine Learning
#32Earlier quoted context omitted.
Or at least explain it in more accessible way. Every time Adam posts about the paper, it gets confused comments and no engagement on the content, because it's pretty deep graduate level pure math, which is occasionally seen but rare on HN.
As a maths PhD student that has seen Hopf algebras before (though I'm no expert, and the context was different), I'm not convinced Adam understands things about Hopf algebras.
He doesn’t understand quantum computing either. I wish he would stop writing authoritatively about things he doesn’t understand.
Re: Category Theory ∩ Machine Learning
#33Earlier 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.
Category Theory (just as all mathematical models for programming or subsets thereof) are building blocks for reasoning on what we build. Past applications of such mathematical models include: - programming languages with semantics that are better adapted to specific problems (e.g. Rust's ownership); - better compilers (see e.g. Haskell's supercompiler, which puts to shame `constexpr`-style features); - better static…
Intuition from category theory has certainly been useful for some programming language features (eg. algebraic effects, modal types or lenses), but I don't think it has helped with the things you cite. Rusts ownership model was created with little formal, academic understanding - or do you mean more foundational stuff like linear logic? And I don't think that Haskell does supercompilation today? It does optimize a whole lot but that is more due to laziness and other optimizations. But neither these optimizations nor supercompilation have much to do with category theory as far as I am aware.
Re: Category Theory ∩ Machine Learning
#34Earlier quoted context omitted.
Category Theory (just as all mathematical models for programming or subsets thereof) are building blocks for reasoning on what we build. Past applications of such mathematical models include: - programming languages with semantics that are better adapted to specific problems (e.g. Rust's ownership); - better compilers (see e.g. Haskell's supercompiler, which puts to shame `constexpr`-style features); - better static…
Intuition from category theory has certainly been useful for some programming language features (eg. algebraic effects, modal types or lenses), but I don't think it has helped with the things you cite. Rusts ownership model was created with little formal, academic understanding - or do you mean more foundational stuff like linear logic? And I don't think that Haskell does supercompilation today? It does optimize a wh…
Yeah, my phrasing is probably unclear. I meant to give examples of applications of formal semantics (huddling everything together). I should probably sleep instead of commenting on HN :)
But it is my understanding that Rust's ownership traces its roots back to both linear logic (well, affine logic) and region-based resource management, both of which have formal semantics.
I haven't followed what got merged into GHC, but I remember seeing demos (and a paper) of a Haskell supercompiler during a conference many years ago, so it is something.
In my sleep-deprived brain, supercompilation is directly related to algebraic effects (although probably not in Haskell itself), which are themselves related to category theory. I could be wrong.
Re: Category Theory ∩ Machine Learning
#35Earlier quoted context omitted.
Category Theory (just as all mathematical models for programming or subsets thereof) are building blocks for reasoning on what we build. Past applications of such mathematical models include: - programming languages with semantics that are better adapted to specific problems (e.g. Rust's ownership); - better compilers (see e.g. Haskell's supercompiler, which puts to shame `constexpr`-style features); - better static…
why those approaches never picked up outside of some academia projects?..
These days, Microsoft requires model-checking proofs before accepting new device drivers. That's their secret weapon that finally got (mostly) rid of the BSOD.
I suspect that Apple is also using model-checking at various layers, but I have no proof :)
Re: Category Theory ∩ Machine Learning
#36It is tempting to believe that category theory will shed new light on and simplify machine learning, just like it did in algebraic geometry, algebraic topology and other mathematical things. This is wishful thinking. Folks who care about doing something useful should stay away from this content.
I'd suggest providing some justification for your declaration if you want anyone to listen to you.
Re: Category Theory ∩ Machine Learning
#37category 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…
> for some reason I don't think just sets are sufficient The reason you're looking for is that the category of sets is not a set.
While category of sets technically could not be expressed as a ZFC set, the idea behind the set theory is enough. Also you could add an axiom[0] in ZFC to make category of set a set.
Re: Category Theory ∩ Machine Learning
#38Earlier quoted context omitted.
The field needs better foundations. CT is pretty good.
No. It won't make a significant (if any at all) difference to effectiveness. Rewriting Pytorch in Haskell won't magically get you AGI.
You wouldn't expect improved foundations to increase effectiveness in the short term.
And AGI is totally irrelavent here.
Re: Category Theory ∩ Machine Learning
#39> Category Theory has been finding increasing applications in machine learning What's the most compelling application so far?
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.
Re: Category Theory ∩ Machine Learning
#40Earlier quoted context omitted.
adamnemecek has posted too many comments and is in cooldown phase, but he's asked me to post this comment: "It's the programmers equal sign. I think that the surrounding text provides a decent explanation what the deal is. You are right, there's a missing sentence fragment, "standard tensor product that satisfies the property...". Read the Diaconis paper. " --- This isn't a sock puppet and I hope this isn't against s…
> It's the programmers equal sign. That doesn’t seem to make any sense.
It seems fine to me, although maybe it's backwards. Add a prime to the RHS, perhaps.