Silent failure differentiating ClassicalOrthogonalPolynomials.jl

[lxvm]

Hi,

I was trying to differentiate the hermiteh polynomial from ClassicalOrthogonalPolynomials.jl using Zygote.gradient and I saw that Zygote hung, started consuming a lot of memory, and then the Julia instance was terminated by the OS. Since there was no error message I am not sure what to investigate. I am attaching my environment information:

pkg> status Zygote ClassicalOrthogonalPolynomials
Status `/tmp/jl_aeo7Zi/Project.toml`
  [b30e2e7b] ClassicalOrthogonalPolynomials v0.10.1
  [e88e6eb3] Zygote v0.6.62

julia> versioninfo()
Julia Version 1.9.2
Commit e4ee485e909 (2023-07-05 09:39 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, skylake)
  Threads: 1 on 12 virtual cores
Environment:
  LD_PRELOAD = /usr/lib/x86_64-linux-gnu/libstdc++.so.6
  JULIA_IMAGE_THREADS = 1

This is the MWE

julia> using ClassicalOrthogonalPolynomials, Zygote
 
julia> gradient(x -> hermiteh(3, x), 0.5)

[ToucheSir]

I have no understanding of anything related to that package, but calling hermiteh(1, x) doesn't run out of memory and still takes forever to run. The proximal Zygote code failing is https://github.com/FluxML/Zygote.jl/blob/master/src/lib/array.jl#L36, which looks innocent enough. But from Ctrl+C interrupting and profiling, I see it gets stuck on https://github.com/JuliaApproximation/ClassicalOrthogonalPolynomials.jl/blob/02fbe50d44d43d9634acd1151585d187277090c9/src/classical/hermite.jl#L47. I suspect it's trying to sum an infinite array, hence the hang.

Evidently the internals of ClassicalOrthogonalPolynomials are not that AD-friendly. I would recommend either trying different AD libraries or writing AD rules using ChainRulesCore for it. Asking Zygote to handle infinite-length arrays is probably too much!

[lxvm]

I see! Thank you for finding the infinite-length array that can't be summed. I'll write a rrule using the recurrence relations described here