> If you don't see it everywhere you either don't have an understanding or have discovered something those people would really like to know. From personal experience, it can be a quite useful tool to describe things because of this.
Get off your high horse. I've had my share of Mac Lane. If you can describe something in terms of CT, you can talk to mathematicians who care about CT. I don't see why this helps ML.
> The may be useful, but it has to be justified.
"May be useful" does not beget "justified." CT may be useful in all areas if you ask a CT theorist. I fail to see how CT helps me build a car.
>The latter is de facto the former.
No it's not. You can take you favorite analysis topic and find a suitable category to view your topic from a CT perspective, but this won't tell you how to prove anything. If you did the CT correct you can now make some analogies, but it won't tell you anything specific.
> And yes, math is just models. Or as Poincaré said, math is the study of relationship between numbers. One might also say "the map is not the territory" and you can find several math theorems making this point explicitly about math.
How do you square "math is the study of relationship between numbers" with CT? You can diagram chase without seeing a single number. I have no idea what mathematical theorem you are referring to, but if you're extrapolating philosophical points from a mathematical theorem, you're doing it wrong
> You may even find one by reading my username with a little care. More than one if you take more care.
Ok I'll bite. You seem to be into Normalizing Flows. How does CT explain it being useful?
Thanks for the reply. I'm glad my comment is no longer flagged.
What do you mean that "this point isn't particularly controversial?" If you just mean that "X may be useful", then of course. But the particular X matters, and "could be useful" is much different than "is useful".
People who like category theory want it everywhere. I don't know your mathematical background, but spend any time in a math department, or even classes, and you'll find people ready to explain any topic in the language of CT.
The may be useful, but it has to be justified. It's clear in some mathematical contexts, but definitely not in ML (yet alone analysis).
ML has a problem in that no one knows what certain methods work. Just look at something like batch normalization: I can think of at least 3 different "explanations" on why it works.
ML people want explanations, and mathematicians need work. Category theorists therefore have work. But I don't think you should mistake this as being an explanation. You just get a nice get a "cleaner way" to present concepts.
ML researchers saying they need "category theory" sounds like a way to try to convince mathematicians that their work is cool.
You absolutely do not need category theory.
Get off your high horse. I've had my share of Mac Lane. If you can describe something in terms of CT, you can talk to mathematicians who care about CT. I don't see why this helps ML.
> The may be useful, but it has to be justified. "May be useful" does not beget "justified." CT may be useful in all areas if you ask a CT theorist. I fail to see how CT helps me build a car.
>The latter is de facto the former.
No it's not. You can take you favorite analysis topic and find a suitable category to view your topic from a CT perspective, but this won't tell you how to prove anything. If you did the CT correct you can now make some analogies, but it won't tell you anything specific.
> And yes, math is just models. Or as Poincaré said, math is the study of relationship between numbers. One might also say "the map is not the territory" and you can find several math theorems making this point explicitly about math.
How do you square "math is the study of relationship between numbers" with CT? You can diagram chase without seeing a single number. I have no idea what mathematical theorem you are referring to, but if you're extrapolating philosophical points from a mathematical theorem, you're doing it wrong
> You may even find one by reading my username with a little care. More than one if you take more care.
Ok I'll bite. You seem to be into Normalizing Flows. How does CT explain it being useful?