Problems with grad after grad

[gforchini]

Hi
I am trying to implement a WGAN and I have problems to apply grad on a function to which grad has already been applied (although on a different variables). An example of the problem and error message is attached.
Giovanni

using Knet, StatsBase, Random, LinearAlgebra, AutoGrad

function D(w,x)
x =elu.( w[1]*x .+ w[2])
return sigm.(w[3]*x.+ w[4])[1]
end

w = Array{Float64}[ randn(12, 12), randn(12, 1),
randn(1, 12), randn(1, 1) ]

∇D = grad(D)
x=randn( 12, 1)

D(w,x)
typeof(D(w,x))

y=∇D(w,x)

typeof(∇D(w,x))

No problem up to now the function D is differentiable in both w and x
Now I construct a penalty as a function of the gradient of D with respect to x

function penalty(w,x)
g = grad(x -> D(w,x))
return (norm(g(x)) -1)^2
end

penalty(w,x)
typeof(penalty(w,x))

Taking the gradient of penalty with respect to w gives an error.

∇penalty=grad(penalty)

∇penalty(w,x)

MethodError: Cannot convert an object of type
AutoGrad.Result{Array{Float64,2}} to an object of type
Array{Float64,N} where N
Closest candidates are:
convert(::Type{T}, !Matched::AbstractArray) where T<:Array at array.jl:533
convert(::Type{T}, !Matched::T) where T<:AbstractArray at abstractarray.jl:14
convert(::Type{T}, !Matched::Factorization) where T<:AbstractArray at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.4/LinearAlgebra/src/factorization.jl:55
...
differentiate(::Function, ::Param{Array{Array{Float64,N} where N,1}}, ::Vararg{Any,N} where N; o::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at core.jl:148
differentiate(::Function, ::Param{Array{Array{Float64,N} where N,1}}, ::Vararg{Any,N} where N) at core.jl:135
(::AutoGrad.var"#gradfun#7"{AutoGrad.var"#gradfun#6#8"{typeof(penalty),Int64,Bool}})(::Array{Array{Float64,N} where N,1}, ::Vararg{Any,N} where N; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at core.jl:225
(::AutoGrad.var"#gradfun#7"{AutoGrad.var"#gradfun#6#8"{typeof(penalty),Int64,Bool}})(::Array{Array{Float64,N} where N,1}, ::Vararg{Any,N} where N) at core.jl:221
top-level scope at Problems.jl:38

Notice that w is a vector of arrays, which works in other situations and which I suspect is what is creating problems now. In other examples where w is a proper vector the second gradient works.

[denizyuret]

There is an implementation at https://github.com/KnetML/WGAN.jl that may help. Not all functions support higher order derivatives. Can say more when I have time to check the code in more detail.

…

On Thu, Jul 9, 2020, 3:40 PM gforchini ***@***.***> wrote: Hi I am trying to implement a WGAN and I have problems to apply grad on a function to which grad has already been applied (although on a different variables). An example of the problem and error message is attached. Giovanni using Knet, StatsBase, Random, LinearAlgebra, AutoGrad function D(w,x) x =elu.( w[1]*x .+ w[2]) return sigm.(w[3]*x.+ w[4])[1] end w = Array{Float64}[ randn(12, 12), randn(12, 1), randn(1, 12), randn(1, 1) ] ∇D = grad(D) x=randn( 12, 1) D(w,x) typeof(D(w,x)) y=∇D(w,x) typeof(∇D(w,x)) No problem up to now the function D is differentiable in both w and x Now I construct a penalty as a function of the gradient of D with respect to x function penalty(w,x) g = grad(x -> D(w,x)) return (norm(g(x)) -1)^2 end penalty(w,x) typeof(penalty(w,x)) Taking the gradient of penalty with respect to w gives an error. ∇penalty=grad(penalty) ∇penalty(w,x) MethodError: Cannot convert an object of type AutoGrad.Result{Array{Float64,2}} to an object of type Array{Float64,N} where N Closest candidates are: convert(::Type{T}, !Matched::AbstractArray) where T<:Array at array.jl:533 convert(::Type{T}, !Matched::T) where T<:AbstractArray at abstractarray.jl:14 convert(::Type{T}, !Matched::Factorization) where T<:AbstractArray at /Users/julia/buildbot/worker/package_macos64/build/usr/share/julia/stdlib/v1.4/LinearAlgebra/src/factorization.jl:55 ... differentiate(::Function, ::Param{Array{Array{Float64,N} where N,1}}, ::Vararg{Any,N} where N; o::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at core.jl:148 differentiate(::Function, ::Param{Array{Array{Float64,N} where N,1}}, ::Vararg{Any,N} where N) at core.jl:135 (::AutoGrad.var"#gradfun#7"{AutoGrad.var"#gradfun#6#8"{typeof(penalty),Int64,Bool}})(::Array{Array{Float64,N} where N,1}, ::Vararg{Any,N} where N; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at core.jl:225 (::AutoGrad.var"#gradfun#7"{AutoGrad.var"#gradfun#6#8"{typeof(penalty),Int64,Bool}})(::Array{Array{Float64,N} where N,1}, ::Vararg{Any,N} where N) at core.jl:221 top-level scope at Problems.jl:38 Notice that w is a vector of arrays, which works in other situations and which I suspect is what is creating problems now. In other examples where w is a proper vector the second gradient works. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#120>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAN43JWHFACB4AQCTBAFEKDR2W3DFANCNFSM4OVR6XVQ> .

[gforchini]

Thank you for getting back. Unfortunately the problem I am looking at is almost (but not quite) a WGAN and it doesn't quite fit into the implementation in the link.
Giovanni