Categorical Foundations for Cute Layouts
research.colfax-intl.com
research.colfax-intl.com
- Arrays are typed `S : D` with shape S and strides D
- Each of `S` and `D` is a nested tuple (instead of the flat tuples one typically sees in a tensor framework)
- Together `S` and `D` define the layout of a tensor
- Not every layout is "tractable", but the tractable ones form a nice category
A really good exposition, my only criticism is that it's quite front-heavy- it would be nice to see a detailed example like in 2.3.8 earlier in the document; there is a lot of detail presented early that doesn't seem necessary to understand the core ideas.
Last comment: I suspect there is a connection to strictification[0], would love to know more if the authors see this!
[0]: in the sense i mean here: https://arxiv.org/pdf/2201.11738v3
You could argue they didn't invent dot product attention nor transformers but they definitely formalized those so I'll leave that nitpicking to Schmidhuber lol. But the other stuff, they say just as much in the paper. It's easy to pass credit over to the ones who popularized a technique rather than the many people who developed it.