Will AI combined with the mathematics of category theory enable AI systems to have powerful and accurate reasoning capabilities and ability to explain their reasoning?
While I'm kind of doubtful, I'm not well-versed in category theory to be able to have an opinion. I tried to read the research paper, but I didn't understand it. I think one needs to be well-versed on category theory before reading the paper. I have the YouTube video of a discussion with one of the researchers (Paul Lessard) below, which I actually stumbled upon first. And I also have an introductory video to category theory.
Apparently they have gotten millions of dollars in investment for a startup to bring category-theory-based AI to market, which surprises me because it seems so abstract, I would not expect VCs to understand it and become strong enough believers in it to make millions in investments. Then again, maybe VCs see their job as taking huge risks for potentially huge returns, in which case, if this technology is successful and successfully takes over the AI industry, they win big.
As best I understand, set theory, which most of us learned (a little bit of) in school, and group theory (which we didn't learn in school, most of us) are foundations of category theory, which uses them as building blocks and extends the degree of abstraction out further. Set theory has to do with "objects" being members of "sets", from which you build concepts like subsets, unions, intersections, and so on. Group theory is all about symmetry, and I have this book called "The Symmetry of Things", which is absolutely gorgeous, with pictures of symmetrical tiling on planes and spheres using translation, reflection, rotation, and so on. The first have introduces a notation you can use to represent all the symmetries, and that part I understood, but the second half abstracts all that and goes deep into group theory, and it got so abstract that I got lost and could not understand it. From what I understand, group theory is incredibly powerful, though, such that, for example, all the computer algebra systems that perform integrals of complex functions symbolically do it with group theory, not with trial-and-error or exhaustive brute-force-search or any of the ways you as a human would probably try to do it with pencil and paper and tables of integrals from the back of your calculus book. Category theory I have not even tried to study, and it is supposed to be even more abstract than that.
Anyway, I thought I would pass this along on the possibility that some of you understand it and on the possibility that it might revolutionize AI as its proponents claim. If it does you heard it from me first, eh?
Categorical deep learning: An algebraic theory of architectures
