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Category Theory ∩ Machine Learning

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Re: Category Theory ∩ Machine Learning

#51

Post by moralestapia »

bgavran wrote: post #27
rmdamiao wrote: post #2

Is this simply a consequence of exponential growth in CS publications driven by machine learning or is there something really going on here?

OP here. The exponential growth in CS publication is much faster. This repository is simply a testament that CT is slowly ramping up. It's meant to show what kind of expressive power and breadth current CT models have, which to my knowledge isn't something that's well-known outside of our niche community.

>The exponential growth in CS publication is much faster.

So ... yes?

Re: Category Theory ∩ Machine Learning

#52

Post by bawolff »

gaze wrote: post #32
red_trumpet wrote: post #23

Earlier 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.

I was kind of curious what all the controversy is about, but looking back at that users comments, it doesn't seem like he has even commented once in the last six months about QC, unless i missed it (?)

Re: Category Theory ∩ Machine Learning

#53

Post by adamnemecek »

bawolff wrote: post #52
gaze wrote: post #32

Earlier quoted context omitted.

He doesn’t understand quantum computing either. I wish he would stop writing authoritatively about things he doesn’t understand.

I was kind of curious what all the controversy is about, but looking back at that users comments, it doesn't seem like he has even commented once in the last six months about QC, unless i missed it (?)

At some point I said that analog QC will be the future rather than what's considered QC today. I still stand by those comments.

Re: Category Theory ∩ Machine Learning

#54

Post by gaze »

adamnemecek wrote: post #42
gaze wrote: post #32

Earlier quoted context omitted.

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.

I don’t think they made the kind of impression you wanted

Re: Category Theory ∩ Machine Learning

#55

Post by adamnemecek »

gaze wrote: post #54
adamnemecek wrote: post #42

Earlier quoted context omitted.

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.

I don’t think they made the kind of impression you wanted

Ok go ahead what do I not understand? Can you at least tell me which comments you are talking about?

Re: Category Theory ∩ Machine Learning

#56

Post by nicwilson »

adamnemecek wrote: post #3

I 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…

Intersting papers.

https://arxiv.org/abs/2302.01834 appears to have a typo in section 4.5

S(hg) = S(g)S(g)

looks like it should be S(hg) = S(h)S(g) or S(hg) = S(g)S(h)

Re: Category Theory ∩ Machine Learning

#57

Post by adamnemecek »

nicwilson wrote: post #56
adamnemecek wrote: post #3

I 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…

Intersting papers. https://arxiv.org/abs/2302.01834 appears to have a typo in section 4.5 S(hg) = S(g)S(g) looks like it should be S(hg) = S(h)S(g) or S(hg) = S(g)S(h)

Right thanks.

Re: Category Theory ∩ Machine Learning

#58

Post by ginnungagap »

mydogcanpurr wrote: post #21
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…

> 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.

This is routinely dealt with through Grothendieck universes. Those are a fancy name for what is pretty much an inaccessible level of the cumulative hierarchy, indeed ZFC+"every set belongs to a Grothendieck universe" is equiconsistent with ZFC+"there is a proper class of inaccessible cardinals". This is not a strong assumption over pure ZFC compared to those set theorists interested in large cardinals work with

Re: Category Theory ∩ Machine Learning

#59

Post by ginnungagap »

justatdotin wrote: post #25
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…

> I wonder to which extent can category theory be re-expressed in terms of sets... yoneda

This also requires universes/inaccessible cardinals to even be stated for categories that are not locally small. But as I mentioned in another comment assuming enough universes exist is not a big deal for set theorists

Re: Category Theory ∩ Machine Learning

#60

Post by red_trumpet »

adamnemecek wrote: post #45
LudwigNagasena wrote: post #22

Earlier quoted context omitted.

> 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.

Sure. In mathematics this is why we often use ":=" for definitions, or we indicate in the surrounding text that the next equation is a definition. That would be helpful.

But even then, you cannot define "C" as "C \otimes C", because the right hand side only makes sense if "C" is already defined. And in math you cannot define something twice. As soon as you defined something, it stays the same in the given context.

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