Categories for AI 3: Categorical Dataflow: Optics and Lenses as data structures for backpropagation

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Speaker: Bruno Gavranović
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 third seminar, you will:
Understand the difference between a monoidal and a cartesian category
Get comfortable using their formal graphical language: string diagrams
Learn about lenses and optics, abstract interfaces for modelling bidirectional data flow
See examples of lenses and optics modelling backpropagation, gradient descent, value iteration and more
Understand how the chain rule is a special case of lens composition
These lectures will help explain key parts of Categorical Foundations of Gradient-Based Learning (ESOP 2022) arxiv.org/abs/...

Опубликовано:

4 окт 2024

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Комментарии : 8

@johnhart1790 Год назад

@ 26:42 that should be F(g): F(B) -> F(C) for covariant functor F

@muttdev 8 месяцев назад

In the notation X ⊗ Y, Are X, Y objects or morphisms? So far small letters f,g,h were used to represent morphisms and capital letter A,B,X,Y were used to represent objects in a category. That is why I am having confusion about X and Y

@dirrelito Год назад

Nice understandable lens explanation. Thanks!

@franzschlicht1307 7 месяцев назад

How did Grav. do the animated gifs in his presentation? Did he draw them frame by frame?

@muttdev 8 месяцев назад

In monoidal category, what are the objects, morphisms and composition?

@mateuszbaginski5075 6 месяцев назад

~anything; these are not included in the definition of a monoidal category e.g., there are monoidal categories where objects are sets, functors, lenses, etc

@Jacob011 8 дней назад

About the diagrams @ 37:30: This is pedagogical suicide! How can you just drop on us diagrams in a graphical language we've never seen before and expect us to reason about them? We don't even know what the boxes represent, what the lines connecting the boxes represent, etc. We don't know how to read these diagrams!! It was immediately clear to me what the students were asking about: apparently reshuffling parts of the diagram produces a different diagram (hence why they were asking about the "box position encoding information") For someone who understands category theory, it sure as hell shouldn't be a problem to understand that people can't know what you haven't told them yet!!!

@ryderbrooks1783 Год назад

The ipad drawing thing is a crutch for the presenter. It introduces unnecessary points of confusion for the viewer while giving a false sense of clear communication to the presenter. Watching you scribble the chain rule for a trivial example is a waste of my time even at 2x.