SciMLStyle VS Flux.jl

No, you do get type errors during runtime. The most common one is a MethodNotFound error, which corresponds to a dispatch not being found. This is the one that people then complain about for long stacktraces and as being hard to read (and that's a valid criticism). The reason for it is because if you do xy with a type combination that does not have a corresponding dispatch, i.e. (x::T1,y::T2) not defined anywhere, then it looks through the method table of the function, does not find one, and throws this MethodNotFound error. You will only get no error if a method is found. Now what can happen is that you can have a method to an abstract type, *(x::T1,y::AbstractArray), but `y` does not "actually" act like an AbstractArray in some way. If the way that it's "not an AbstractArray" is that it's missing some method overloads of the AbstractArray interface (https://docs.julialang.org/en/v1/manual/interfaces/#man-inte...), you will get a MethodNotFound error thrown on that interface function. Thus you will only not get an error if someone has declared `typeof(y) <: AbstractArray` and implemented the AbstractArray interface.

However, what Yuri pointed out is that there are some packages (specifically in the statistics area) which implemented functions like `f(A::AbstractArray)` but used `for i in 1:length(A)` to iterate through x's values. Notice that the AbstractArray interface has interface functions for "non-traditional indices", including `axes(A)` which is a function to call to get "the a tuple of AbstractUnitRange{<:Integer} of valid indices". Thus these codes are incorrect, because by the definition of the interface you should be doing `for i in axes(A)` if you want to support an AbstractArray because there is no guarantee that its indices go from `1:length(A)`. Note that this was added to the `AbstractArray` interface in the v1.0 change, which is notably after the codes he referenced were written, and thus it's more that they were not updated to handle this expanded interface when the v1.0 transition occurred.

This is important to understand because the criticisms and proposed "solutions" don't actually match the case... at all. This is not a case of Julia just letting anything through: someone had to purposefully define these functions for them to exist. And interfaces are not a solution here because there is an interface here, its rules were just not followed. I don't know of an interface system which would actually throw an error if someone does a loop `for i in 1:length(A)` in a code where `A` is then indexed by the element. That analysis is rather difficult at the compiler level because it's non-local: `length(A)` is valid since querying for the length is part of the AbstractArray interface (for good reasons), so then `1:length(A)` is valid since that's just range construction on integers, so the for loop construction itself is valid, and it's only invalid because of some other knowledge about how `A[i]` should work (this look structure could be correct if it's not used to `A[i]` but rather do something like `sum(i)` without indexing). If you want this to throw an error, the only real thing you could do is remove indexing from the AbstractArray interface and solely rely on iteration, which I'm not opposed to (given the relationship to GPUs of course), but etc. you can see the question to solving this is "what is the right interface?" not "are there even interfaces?" (of which the answer is, yes but the errors are thrown at runtime MethodNotFound instead of compile time MethodNotImplemented for undefined things, the latter would be cool for better debugging and stacktraces but isn't a solution).

This is why the real discussions are not about interfaces as a solution, they don't solve this issue, and even further languages with interfaces also have this issue. It's about tools for helping code style. You probably should just never do `for i in 1:length(A)`, probably you should always do `for i in eachindex(A)` or `for i in axes(A)` because those iteration styles work for `Array` but also work for any `AbstractArray` and thus it's just a safer way to code. That is why there are specific mentions to not do this in style guides (for example, https://github.com/SciML/SciMLStyle#generic-code-is-preferre...), and things like JuliaFormatter automatically flag it as a style break (which would cause CI failures in organizations like SciML which enforce SciML Style formatting as a CI run with Github Actions https://github.com/SciML/ModelingToolkit.jl/blob/v8.14.1/.gi...). There's a call to add linting support for this as well, flagging it any time someone writes this code. If everyone is told to not assume 1-based indexing, formatting CI fails if it is assumed, and the linter underlines every piece of code that does it as red, (along with many other measures, which includes extensive downstream testing, fuzzing against other array types, etc.) then we're at least pretty well guarded against it. And many Julia organizations, like SciML, have these practices in place to guard against it. Yuri's specific discussion is more that JuliaStats does not.

If you are really committed to running on Apple hardware then take a look at Tensorflow for macOS. Another option is the Julia programming language which has very basic Metal support at a CUDA-like level. FluxML would be the ML framework in Julia. I’m not sure either option will be painless or let you do everything you could do with a Nvidia GPU.

Flux dominance!

I’m no compiler expert but check out flux and zygote https://fluxml.ai/ https://fluxml.ai/

I would suggest you to look into Julia ecosystem instead of C++. Julia is almost identical to Python in terms of how you use it but it's still very fast. You should look into flux.jl package for Julia.

Give Julia a try: https://fluxml.ai

2) Flux treats softmax a little different than most other activation functions (see here for more details) such as relu and sigmoid. When you pass an activation function into a layer like Dense(3, 32, relu), Flux expects that the function is broadcast over the layer's output. However, softmax cannot be broadcast as it operates over vectors rather than scalars. This means that if you want to use softmax as the final activation in your model, you need to pass it into Chain() like so:

Can you point to a concrete example of one that someone would run into when using the differential equation solvers with the default and recommended Enzyme AD for vector-Jacobian products? I'd be happy to look into it, but there do not currently seem to be any correctness issues in the Enzyme issue tracker that are current (3 issues are open but they all seem to be fixed, other than https://github.com/EnzymeAD/Enzyme.jl/issues/278 which is actually an activity analysis bug in LLVM). So please be more specific. The issue with Enzyme right now seems to moreso be about finding functional forms that compile, and it throws compile-time errors in the event that it cannot fully analyze the program and if it has too much dynamic behavior (example: https://github.com/EnzymeAD/Enzyme.jl/issues/368).

Additional note, we recently did a overhaul of SciMLSensitivity (https://sensitivity.sciml.ai/dev/) and setup a system which amounts to 15 hours of direct unit tests doing a combinatoric check of arguments with 4 hours of downstream testing (https://github.com/SciML/SciMLSensitivity.jl/actions/runs/25...). What that identified is that any remaining issues that can arise are due to the implicit parameters mechanism in Zygote (Zygote.params). To counteract this upstream issue, we (a) try to default to never default to Zygote VJPs whenever we can avoid it (hence defaulting to Enzyme and ReverseDiff first as previously mentioned), and (b) put in a mechanism for early error throwing if Zygote hits any not implemented derivative case with an explicit error message (https://github.com/SciML/SciMLSensitivity.jl/blob/v7.0.1/src...). We have alerted the devs of the machine learning libraries, and from this there has been a lot of movement. In particular, a globals-free machine learning library, Lux.jl, was created with fully explicit parameters https://lux.csail.mit.edu/dev/, and thus by design it cannot have this issue. In addition, the Flux.jl library itself is looking to do a redesign that eliminates implicit parameters (https://github.com/FluxML/Flux.jl/issues/1986). Which design will be the one in the end, that's uncertain right now, but it's clear that no matter what the future designs of the deep learning libraries will fully cut out that part of Zygote.jl. And additionally, the other AD libraries (Enzyme and Diffractor for example) do not have this "feature", so it's an issue that can only arise from a specific (not recommended) way of using Zygote (which now throws explicit error messages early and often if used anywhere near SciML because I don't tolerate it).

So from this, SciML should be rather safe and if not, please share some details and I'd be happy to dig in.

> In his item #1, he links to https://discourse.julialang.org/t/loaderror-when-using-inter... The issue is actually a Zygote bug, a Julia package for auto-differentiation, and is not directly related to Julia codebase (or Flux package) itself. Furthermore, the problematic code is working fine now, because DiffEqFlux has switched to Enzyme, which doesn't have that bug. He should first confirm whether the problem he is citing is actually a problem or not.

> Item #2, again another Zygote bug.

If flux chose a buggy package as a dependency, that's on them, and users are well justified in steering clear of Flux if it has buggy dependencies. As of today, the Project.toml for both Flux and DiffEqFlux still lists Zygote as a dependency. Neither list Enzyme.

https://github.com/FluxML/Flux.jl/blob/master/Project.toml