StochasticAD.jl VS RecursiveFactorization.jl

This is disregarding the development of said ecosystems though. The point is that Python has been quite inhibitory to the development of this ecosystem. There are many corpses of automatic differentiation libraries (starting from autograd and tangent and then to things like theano to finally tensorflow and pytorch) and many corpses of JIT compilers and accelerators (Cython, Numba, pypy, and TensorFlow XLA, now PyTorch v2's JIT, etc.).

What has been found over the last decade is that a large part of that is due to the design of the languages. Jan Vitek for example has a great talk which describes how difficult it is to write a JIT compiler for R due to certain design choices in the language (https://www.youtube.com/watch?v=VdD0nHbcyk4, or the more detailed version https://www.youtube.com/watch?v=HStF1RJOyxI). There are certain language constructs that void lots of optimizations which have to then be worked around, which is why Python JITs choose subsets of the language to avoid specific parts that are not easy to optimize or not possible to optimize. This is why each take a domain-specific subset, a different subset of the language for numba vs jax vs etc., to choose something that is nice for ML vs for more generic codes.

With all of that, it's perfectly reasonable to point out that there have been languages which have been designed to not have the compilation difficulties, which have resulted having a single (JIT) compiler for the language. And by extension, it has made building machine learning and autodiff libraries not something that's a Google or Meta scale project (for example, PyTorch involves building GPU code bindings and a specialized JIT, not something very accessible). Julia is a language to point to here, but I think well-designed static languages like Rust also deserve a mention. How much further would we have gone if every new ML project didn't build a new compiler and a new automatic differentiation engine? What if the development was more modular and people could easy just work on the one thing they cared about?

As a nice example, for last NeurIPS we put out a paper on automatic differentiation of discrete stochastic models, i.e. extending AD to automatically handle cases like agent-based models. The code is open source (https://github.com/gaurav-arya/StochasticAD.jl), and you can see it's almost all written by a (talented) undergraduate over a span of about 6 months. It requires the JIT compilation because it works on a lot of things that are not solely in big matrix multiplication GPU kernels, but Julia provides that. And multiple dispatch gives GPU support. Done. The closest thing in PyTorch, storchastic, gets exponential scaling instead of StochasticAD's linear, and isn't quite compatible with a lot of what's required for ML, so it benchmarks as thousands of times slower than the simple Julia code. Of course, when Meta needs it they can and will put the minds of 5-10 top PhDs on it to build it out into a feature of PyTorch over 2 years and have a nice release. But at the end of the day we really need to ask, is that how it should be?

Found relevant code at https://github.com/gaurav-arya/StochasticAD.jl + all code implementations here

What about the other benchmarks on the same site? https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Bio/BCR/ BCR takes about a hundred seconds and is pretty indicative of systems biological models, coming from 1122 ODEs with 24388 terms that describe a stiff chemical reaction network modeling the BCR signaling network from Barua et al. Or the discrete diffusion models https://docs.sciml.ai/SciMLBenchmarksOutput/stable/Jumps/Dif... which are the justification behind the claims in https://www.biorxiv.org/content/10.1101/2022.07.30.502135v1 that the O(1) scaling methods scale better than O(log n) scaling for large enough models? I mean.

> If you use special routines (BLAS/LAPACK, ...), use them everywhere as the respective community does.

It tests with and with BLAS/LAPACK (which isn't always helpful, which of course you'd see from the benchmarks if you read them). One of the key differences of course though is that there are some pure Julia tools like https://github.com/JuliaLinearAlgebra/RecursiveFactorization... which outperform the respective OpenBLAS/MKL equivalent in many scenarios, and that's one noted factor for the performance boost (and is not trivial to wrap into the interface of the other solvers, so it's not done). There are other benchmarks showing that it's not apples to apples and is instead conservative in many cases, for example https://github.com/SciML/SciPyDiffEq.jl#measuring-overhead showing the SciPyDiffEq handling with the Julia JIT optimizations gives a lower overhead than direct SciPy+Numba, so we use the lower overhead numbers in https://docs.sciml.ai/SciMLBenchmarksOutput/stable/MultiLang....

> you must compile/write whole programs in each of the respective languages to enable full compiler/interpreter optimizations

You do realize that a .so has lower overhead to call from a JIT compiled language than from a static compiled language like C because you can optimize away some of the bindings at the runtime right? https://github.com/dyu/ffi-overhead is a measurement of that, and you see LuaJIT and Julia as faster than C and Fortran here. This shouldn't be surprising because it's pretty clear how that works?

I mean yes, someone can always ask for more benchmarks, but now we have a site that's auto updating tons and tons of ODE benchmarks with ODE systems ranging from size 2 to the thousands, with as many things as we can wrap in as many scenarios as we can wrap. And we don't even "win" all of our benchmarks because unlike for you, these benchmarks aren't for winning but for tracking development (somehow for Hacker News folks they ignore the utility part and go straight to language wars...).

If you have a concrete change you think can improve the benchmarks, then please share it at https://github.com/SciML/SciMLBenchmarks.jl. We'll be happy to make and maintain another.

Ask them to download Julia and try it, and file an issue if it is not fast enough. We try to have the latest available.

See for example: https://github.com/JuliaLinearAlgebra/RecursiveFactorization...

Julia defaults to OpenBLAS but libblastrampoline makes it so that `using MKL` flips it to MKL on the fly. See the JuliaCon video for more details on that (https://www.youtube.com/watch?v=t6hptekOR7s). The recursive comparison is against OpenBLAS/LAPACK and MKL, see this PR for some (older) details: https://github.com/YingboMa/RecursiveFactorization.jl/pull/2... . What it really comes down to in the end is that OpenBLAS is rather bad, and MKL is optimized for Intel CPUs but not for AMD CPUs, so when the best CPUs are now all AMD CPUs, having a new set of BLAS tools and mixing that with recursive LAPACK tools is either as good or better on most modern systems. Then we see this in practice even when we build BLAS into Sundials for 1,000 ODE chemical reaction networks (https://benchmarks.sciml.ai/html/Bio/BCR.html).

>I hope those benchmarks are coming in hot

M1 is extremely good for PDEs because of its large cache lines.

https://github.com/SciML/DiffEqOperators.jl/issues/407#issue...

The JuliaSIMD tools which are internally used for BLAS instead of OpenBLAS and MKL (because they tend to outperform standard BLAS's for the operations we use https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...) also generate good code for M1, so that was giving us some powerful use cases right off the bat even before the heroics allowed C/Fortran compilers to fully work on M1.

Not necessarily true with Julia. Many libraries like DifferentialEquations.jl are Julia all of the way down because the pure Julia BLAS tools outperform OpenBLAS and MKL in certain areas. For example see:

https://github.com/YingboMa/RecursiveFactorization.jl/pull/2...

So a stiff ODE solve is pure Julia, LU-factorizations and all.

Also, the major point is that BLAS has little to no role played here. Algorithms which just hit BLAS are very suboptimal already. There's a tearing step which reduces the problem to many subproblems which is then more optimally handled by pure Julia numerical linear algebra libraries which greatly outperform OpenBLAS in the regime they are in:

https://github.com/YingboMa/RecursiveFactorization.jl#perfor...

And there are hooks in the differential equation solvers to not use OpenBLAS in many cases for this reason:

https://github.com/SciML/DiffEqBase.jl/blob/master/src/linea...

Instead what this comes out to is more of a deconstructed KLU, except instead of parsing to a single sparse linear solve you can do semi-independent nonlinear solves which are then spawning parallel jobs of small semi-dense linear solves which are handled by these pure Julia linear algebra libraries.

And that's only a small fraction of the details. But at the end of the day, if someone is thinking "BLAS", they are already about an order of magnitude behind on speed. The algorithms to do this effectively are much more complex than that.