Categories for AI 1: Why Category Theory? By Bruno Gavranović
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- čas přidán 9. 10. 2022
- Motivated by the recent emergence of category theory in machine learning, we teach a course on its philosophy, applications and outlook from the perspective of machine learning!
Sign up for the course at: cats.for.ai/
In this first seminar, you will:
- Get a sense of the philosophy and motivation behind Category Theory
- Learn about the recent wave of its applications emerging throughout the sciences
- Understand how this formal mathematical language rigorously adheres to the concept of modularity
- Dispel with the fallacy that CT is not relevant to practical disciplines such as programming or engineering
- Get a sense of how CT can help us design and scale our deep learning systems - Věda a technologie
The question at 51:09 is really good, asking if compositionality is the nature of things, or simply about the limit of our ability to understand. I think it's analogous to types in programming.
Are static types the true nature of computations, or just about our ability to understand them? While sound type systems are necessarily incomplete (i.e. they fail to accommodate some perfectly valid programs), the idea of static typing has proven valuable for reliably constructing and reasoning about programs. Historically, untypable but perfectly working programs have been an important source of inspiration for improving the expressiveness of static types (e.g. various forms of polymorphism, path-sensitive reasoning, delimited continuations, etc.). If one day we come across a perfectly clear and correct program that's untypable, that needs massaging just to appease the type-checker, such program will not be a sign that we should abandon the idea of static typing, nor should we dismiss such program as invalid just because a particular static discipline fails to explain it. Each instance of incompleteness can serve as an opportunity to improve the type system.
Similarly, if one day we come across an effective machine learning model that cannot be explained by the current building blocks, that won't mean that the idea of searching for compositional building blocks is worthless, and we obviously shouldn't dismiss that model's existence. That will simply mean we should revise the building blocks. After all, mathematics can't derive all truths, but it's the best tool we have for understanding truths.
I have just found recently that the way I think and model problems always matched the way category theory does. It's a very exciting area to explore :)
Thanks for publishing these lectures!
Thank you for publishing these!
Absolutely amazing playlist!
We need more content from you bring more theory
There I go, starting another amazing lecture series and leaving it when it gets hard 😩
please man do not give up!!
We've all been there, but this time, tell yourself you are taking a mental break, so that you can return harder. I have a strong sense that this is indeed worth your time. Do 20 minutes a day, take notes. You don't need to fully understand all the mathematical terms swung around. Cheers.
Whitesnake
Here’s another amazing series that you might be interested. Search group theory and deep learning. I also left it mid way when they started talking about steerable convolutions over spherical symmetries xd. But i like meeting fellow youtubers with same mindset. Thanks for sharing your story
Great introduction tutorial!
Great analysis
Good video. At time 10:35 suddenly a new word "Model of the system" added to explain compositionality. Now to understand compositionality, you need to understand what is "Model of system". Could you please first explain what is meant by "Model of the system" ?
What is the Zulip server URL?
👀👀
Structuralism, a 100 year old linguistic theory, finally mating with Math and Computer Science, making cute babies.
Maybe we can name the first two babies Ferdinand and Claude.
Is there any Google Colabs for these videos
Yes that’s what i need
Are guys ready for a corny ass joke: functors are funtors :D