Related paper by the authors: https://dl.acm.org/doi/10.1145/3694906.3743326
We'll put that link in the top text too. Thanks!
This looks amazing, I've been shopping for an implementation of this I could play around with for a while now
They mention promising results on Apple Silicon GPUs and even cite the contributions from Vello, but I don't see a Metal implementation in there and the benchmark only shows results from an RTX 2080. Is it safe to assume that they're referring to the WGPU version when talking about M-series chips?
That and https://github.com/b0nes164/GPUSorting have been a tremendous help for me, since CUB does not nicely work with the Cuda Driver Api. The author is doing amazing work.
At what order of magnitude in the number of elements to be sorted (I'm thinking to the overhead of the GPU setup cost) is the break-even point reached, compared to a pure CPU sort?
this is missing the most important one (in today's world): extracting non-zero elements from a sparse vector/matrix
https://developer.nvidia.com/gpugems/gpugems3/part-vi-gpu-co...
Not even close. The most important application (in today's world) is radix sort.
What specific application do you have in mind that radix sort is more important than matrix multiplication?
Is that relevant for 4x4 multiplications? Because at least for me, radix sort is way more important than multiplying matrices beyond 4x4. E.g. for Gaussian Splatting.
I think they were trying to say “radix sort is a more important application of prefix sum than extraction of values from a sparse matrix/vector is.”
I understand what GP meant, but extraction of values from a sparse matrix is an essential operation of multiplying two sparse matrices. Sparse matmult in turn is an absolutely fundamental operation in everything from weather forecasting to logistics planning to electric grid control to training LLMs. Radix sort on the other hand is very nice but (as far as I know) not nearly used as widely. Matrix multiplication is just super fundamental to the modern world.
I would love to be enlightened about some real-world applications of radix sort I may have missed though, since it's a cool algorithm. Hence my question above.
> to training LLMs
LLMs are made from dense matrices, aren't they?
Not always, or rather not exclusively. For example, some types of distillation benefit from sparse-ifying the dense-ish matrices the original was made of [1]. There's also a lot of benefit to be had from sparsity in finetuning [2]. LLMs were merely one of the examples though, don't focus too much on them. The point was that sparse matmul makes up the bulk of scientific computations and a huge amount of industrial computations too. It's probably second only to the FFT in importance, so it would be wild if radix sort managed to eclipse it somehow.
[1] https://developer.nvidia.com/blog/mastering-llm-techniques-i...
Almost all performant kernels employ structured sparsity
Top K sampling comes to mind, although it's nowhere nearly as important as matmult.
ranking models benefit from gpu impls of sort but yup they're not nearly as common/important as spmm/spmv