I'm not experienced/well-read in either ML or CT, but awhile ago I remember hearing Tai-Danae Bradley equate "knowing a word by the company it keeps" to the Yoneda lemma, and I always thought that was kind of interesting (although I guess I'm not qualified enough to know whether that statement is useful or vacuous)
Category Theory ∩ Machine Learning
41–50 of 73 posts
Re: Category Theory ∩ Machine Learning
#42Earlier quoted context omitted.
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.
What about QC do I not understand? It's been a while since I have made any comments about QC so I'm glad that those comments made an impression.
Re: Category Theory ∩ Machine Learning
#43Earlier 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.
Go on what do I not understand about Hopf algebras?
Re: Category Theory ∩ Machine Learning
#44I have recently written a paper on understanding machine learning via the lens of Hopf algebra https://arxiv.org/abs/2302.01834 . Hopf algebras (which are really just tensors with recurrence relations built in) subsume convnets, transformers and diffusion model and also provide a theoretically better autodiff that operates within single layers as opposed to across entire graphs. Furthermore, there is a correspondence…
I just read your Coinductive guide to inductive transformer heads paper. My mind is blown. Is the Hopf Algebra based ML framework you are working on on your github? I took a glance, but you have 1500 repositories and it wasn't on the first few of them.
It's in very early stages and it's not there yet no. Join the discord https://discord.cofunctional.ai or my twitter https://twitter.com/adamnemecek1 if you want to follow progress. It might take some time.
Re: Category Theory ∩ Machine Learning
#45Earlier 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.
I'm saying there's a difference between equal sign that defines something and equal sign that declares a relation.
Re: Category Theory ∩ Machine Learning
#46> 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.
Any application where Category Theory is making it substantially easier to express the software or reason about it is fair game, from my perspective.
Re: Category Theory ∩ Machine Learning
#47Earlier quoted context omitted.
could you advertise your research a bit less often, please? i see your post like literally almost every other day here
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.
The discord channel is popping off. Come join, https://discord.cofunctional.ai I'll explain it
Re: Category Theory ∩ Machine Learning
#48It 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.
That's a supremely anti-intellectual take.
Re: Category Theory ∩ Machine Learning
#49category 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.
Re: Category Theory ∩ Machine Learning
#50Earlier quoted context omitted.
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 :)
and how does it work? Do they write drivers in some verifiable subset of C?