>>13247295No. Machine learning is a mathematical wasteland. My plan was to learn all this fancy match during undergrad (algebraic geometry and topology, category theory, measure theory, differential geometry, advanced graph theory and combinatorics etc etc), and then when grad school came around, I'd be the "advanced math ML guy", who applied tons of fancy math to prove cool shit about ML, and derive cool things to do or new algorthms with novel theoretical basis.
IT DOESNT WORK. NOONE DOES ANYTHING INTERESTING MATHEMATICALLY WITH ML. Seriously. If you know linear algebra (say to a hoffmann and kunze level), multivariate calc. You are 90% there to knowing all the math you'll ever need. Certainly enough to do research. If you wanna be a tryhard, you can learn measure theory, elementary functional analysis, and some computational algebraic topology. But it's not gonna illuminate anything, all its gonna do is make you able to formalize somethings brainlet ML people do occationally when they fiddle around with shit they don't understand.
Also, this is ignoring the biggest issue, which is that including any ""higher""" math in your ML paper is instantly gonna make that paper 100% worthless. Meaning, most ML people will read your paper just searching for some quick idea that could make their job easier. If they see the word "group" or "sobolev space" INSTANTLY they will drop your paper and not read it. So, no, your quest is doomed from the start. 1) Because its not gonna do shit, and 2) Even if it did do interesting and novel shit, noone is gonna care or bother to parse your paper.
I now realize I might've misinterpreted your question. If all youre interested in is software for working with abstract math, you can just google it. something like
https://www.gap-system.org/ might be what you're after
