gradient of maximum is not correct

[Roger-luo]

This is causing test broken in Zygote

fdm = central_fdm(5, 3)
Random.seed!(0);
M = rand(2, 3);
tmp = similar(M);

fdm(0.0) do ϵ
           tmp .= M
           tmp[1] += ϵ
           return maximum(tmp)
end
43.35451497451203

[willtebbutt]

Hmm. Well the gradient of maximum jumps around whenever you're near a point where the location of the maximum element changes (i.e. from 0 -> 1 and 1 -> 0 at the new max / old max locations respectively). So, for example,

julia> x = [1.0, 0.0];

julia> tmp = similar(x);

julia> fdm(0.0) do ϵ
           tmp .= x
           tmp[1] += ϵ
           return maximum(tmp)
       end
0.9999999999999811

julia> fdm(0.0) do ϵ
           tmp .= x
           tmp[2] += ϵ
           return maximum(tmp)
       end
6.5051510603102805e-15

This also gives well-behaved 3rd derivatives with central_fdm(5, 3). Conversely, if the values in x are too close together we get incorrect results:

julia> fdm = central_fdm(5, 1);
julia> x = [1e-6, 0.0];
julia> tmp = similar(x);

julia> fdm(0.0) do ϵ
           tmp .= x
           tmp[1] += ϵ
           return maximum(tmp)
       end
0.6175432605559212

julia> fdm(0.0) do ϵ
           tmp .= x
           tmp[2] += ϵ
           return maximum(tmp)
       end
0.3824567394426718

So I guess the question is whether you've happened to get some very close-together elements in M?

Also, are you intentionally taking the 3rd derivative? I wasn't aware that Zygote was doing anything nested at the minute.

[Roger-luo]

So I guess the question is whether you've happened to get some very close-together elements in M?

yes, but I can't workaround this, since it is just rand.

Also, are you intentionally taking the 3rd derivative? I wasn't aware that Zygote was doing anything nested at the minute.

no I'm just trying to fix the tests in Zygote (I've marked it broken for now)

[willtebbutt]

yes, but I can't workaround this, since it is just rand.

Okay. Could you provide the exact numbers that you have for M? I'm not able to reproduce the error (I correctly get zero), but that might be because we're generating different values for M.

no I'm just trying to fix the tests in Zygote (I've marked it broken for now)

Okay, you probably want central_fdm(5, 1) then. This constructs a 5th-order estimate of the 1st derivative.

[Roger-luo]

I have it in the example as M = rand(2, 3) (Random.seed!(0)) or you could just try to run the Zygote test: https://github.com/FluxML/Zygote.jl/pull/235/files#diff-d0759c4bbbe4bfe282ccf2f6fc082320R204

[willtebbutt]

Yup, I tried with your seed and wasn't able to reproduce locally. Possible I'm running a different Julia version to you or something, and consequently getting different numbers. For the sake of diagnosing the issue it would be helpful to know precisely which numbers are causing the issue, and I don't appear to be getting the correct ones.

[Roger-luo]

ok, this is the M I got

julia> M
2×3 Array{Float64,2}:
 0.823648  0.164566  0.27888 
 0.910357  0.177329  0.203477

[willtebbutt]

Okay, I am using the same numbers and am unable to reproduce. Am running the Zygote tests locally to see if I can reproduce.

[willtebbutt]

All of the maximum-related tests pass locally for me @Roger-luo . Not sure what's going on :S

[Roger-luo]

that's strange... this is my versioninfo:

julia> versioninfo()
Julia Version 1.2.0
Commit c6da87ff4b (2019-08-20 00:03 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin19.0.0)
  CPU: Intel(R) Core(TM) i7-7700HQ CPU @ 2.80GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-6.0.1 (ORCJIT, skylake)

what's yours?

[willtebbutt]

Hmmmm.

Julia Version 1.3.0-rc2.0
Commit a04936e3e0 (2019-09-12 19:49 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin18.6.0)
  CPU: Intel(R) Core(TM) i7-4870HQ CPU @ 2.50GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-6.0.1 (ORCJIT, haswell)
Environment:
  JULIA_NUM_THREADS = 1
  JULIA_EDITOR = subl

Would you mind trying out this version? Also, I'm running FiniteDifferences.jl on master.

[Roger-luo]

This is strange, I tried it on other versions e.g 1.3-rc4, or the master branch, this is 0.0, but on 1.2 it is not...

are you able to reproduce this behaviour on 1.2 as well? I'm running on FiniteDifferences master as well

[Roger-luo]

I guess there is some bug in 1.2, but since 1.3 is out now I think I'll just close this and move on somehow.