`jacobian` is not differentiable

[YichengDWu]

julia> function f(x, bias)
              jac = Zygote.jacobian(x->x.^3, x)[1]
              return jac * x .+ bias
              end
f (generic function with 1 method)

julia> x,bias = rand(3),rand(3)
([0.2279638899624825, 0.6476786632858718, 0.13745627655377346], [0.051516386842686224, 0.6842360463718182, 0.22031281411507742])

julia> Zygote.gradient(b -> sum(f(x,b)), rand(3))
ERROR: Mutating arrays is not supported -- called copyto!(SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}, ...)
This error occurs when you ask Zygote to differentiate operations that change
the elements of arrays in place (e.g. setting values with x .= ...)

Possible fixes:
- avoid mutating operations (preferred)
- or read the documentation and solutions for this error
  https://fluxml.ai/Zygote.jl/dev/limitations.html#Array-mutation-1

Stacktrace:
  [1] error(s::String)
    @ Base .\error.jl:33
  [2] _throw_mutation_error(f::Function, args::SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true})
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\array.jl:70
  [3] (::Zygote.var"#448#449"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}})(#unused#::Nothing)
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\array.jl:85
  [4] (::Zygote.var"#2506#back#450"{Zygote.var"#448#449"{SubArray{Float64, 1, Matrix{Float64}, Tuple{Int64, Base.Slice{Base.OneTo{Int64}}}, true}}})(Δ::Nothing)
    @ Zygote C:\Users\Luffy\.julia\packages\ZygoteRules\AIbCs\src\adjoint.jl:67
  [5] Pullback
    @ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\grad.jl:183 [inlined]
  [6] (::typeof(∂(_gradcopy!)))(Δ::Nothing)
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
  [7] Pullback
    @ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\grad.jl:165 [inlined]
  [8] (::typeof(∂(withjacobian)))(Δ::NamedTuple{(:val, :grad), Tuple{Nothing, Tuple{Matrix{Float64}}}})
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
  [9] (::Zygote.var"#216#217"{Tuple{Tuple{Nothing}, Tuple{Nothing}}, typeof(∂(withjacobian))})(Δ::NamedTuple{(:val, :grad), Tuple{Nothing, Tuple{Matrix{Float64}}}})
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\lib.jl:207
 [10] #1909#back
    @ C:\Users\Luffy\.julia\packages\ZygoteRules\AIbCs\src\adjoint.jl:67 [inlined]
 [11] Pullback
    @ C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\lib\grad.jl:140 [inlined]
 [12] (::typeof(∂(jacobian)))(Δ::Tuple{Matrix{Float64}})
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
 [13] Pullback
    @ .\REPL[20]:2 [inlined]
 [14] (::typeof(∂(f)))(Δ::FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{Int64}}})
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
 [15] Pullback
    @ .\REPL[22]:1 [inlined]
 [16] (::typeof(∂(#23)))(Δ::Float64)
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface2.jl:0
 [17] (::Zygote.var"#60#61"{typeof(∂(#23))})(Δ::Float64)
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface.jl:41
 [18] gradient(f::Function, args::Vector{Float64})
    @ Zygote C:\Users\Luffy\.julia\packages\Zygote\IoW2g\src\compiler\interface.jl:76
 [19] top-level scope
    @ REPL[22]:1
 [20] top-level scope
    @ C:\Users\Luffy\.julia\packages\CUDA\DfvRa\src\initialization.jl:52

[mcabbott]

Possible duplicate of #953

Notice that in this particular example, no derivatives with respect to inputs of jacobian are requested, so it could be ignored. But Zygote does not automatically know this.

First posted in https://github.com/FluxML/Zygote.jl/issues/1264, discussion there starts at https://github.com/FluxML/Zygote.jl/issues/1264#issuecomment-1189603440

[DhairyaLGandhi]

See #1254 also

[YichengDWu]

But it looks like graident is

julia> function f(x, bias)
           grad = Zygote.gradient(x->sum(x.^3), x)[1]
           return grad .* x .+ bias
       end
julia> Zygote.gradient(b -> sum(f(x,b)), rand(3))
(Fill(1.0, 3),)