statusfailed
Joined 4 years ago
Joined 4 years ago
This is a little outside my area, but I think the relevant part of that abstract is "Gradient-based optimization follows horizontal lifts across low-dimensional subspaces in the Grassmannian Gr(r, p), where r p is the rank of the Hessian at the optimum"
I think this question is super interesting though: why can massively overparametrised models can still generalise?
- 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
Hellas.AI is building a compiler for categorical deep learning to power decentralised, serverless AI.
We're looking for an experienced Rust engineer. You must have demonstrated:
* Experience in designing and implementing BFT consensus protocols * Ability to engage with academic literature on distributed systems * Understanding of ZK proofs and proof aggregation (you don't need to design these, but you should know how to use them)
Nice-to-have: interest or experience in:
* Deep Learning / ML / AI, GPU programming * Compilers and array programming languages * Category Theory and string diagrams
If you have project(s) demonstrating your experience in one or more of these areas, get in touch!
Our process is simple: we read code you've written and research you've published, then interview you about it. We don't do tedious coding tests.
Email us at [email protected]
@the author - I assume you're aware that morphisms in symmetric monoidal categories can be represented using cospans of hypergraphs - do you know if there's a similar combinatorial representation for braided monoidal categories?
More philosophically, the motto is "write programs as morphisms directly". Rather than writing a term in some type theory which you then (maybe) give a categorical semantics, why not just work directly in a category?
Long term, the goal is to have a compiler which is a stack of categories with functors as compiler passes. The idea being that in contrast to typical compilers where you are "stuck" at a given abstraction level, this would allow you to view your code at various levels of abstractions. So for example, you could write a program, then write an x86-specific optimization for one function which you can then prove correct with respect to the more abstract program specification.
Hellas.AI is building a compiler for categorical deep learning to power decentralised, serverless AI. If you're interested in any of the following, get in touch:
* Category Theory and string diagrams
* Compilers and array programming languages
* Deep Learning/ML/AI and/or GPU programming (e.g. CUDA/ WGSL)
* Building and deploying distributed systems
* Peer-to-peer software and blockchain
If you have project(s) demonstrating your experience in one or more of these areas, get in touch!
Our process is simple: we read code you've written and research you've published, then interview you about it. We don't do tedious coding tests.
Some experience of Rust or a functional language (Haskell, OCaml, any Lisp) is preferred.
Email us at [email protected]