julia> using ComponentArrays, Zygote

julia> p = (; a = ones(2), b = zeros(2)) |> ComponentArray
ComponentVector{Float64}(a = [1.0, 1.0], b = [0.0, 0.0])

julia> Zygote.gradient(x -> sum(x.a), p)
((a = [1.0, 1.0], b = [0.0, 0.0]),)

julia> Zygote.hessian(x -> sum(x.a), p)
ERROR: type Array has no field a
Stacktrace:
  [1] adjoint
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/lib.jl:229 [inlined]
  [2] _pullback
    @ Zygote ~/.julia/packages/ZygoteRules/OgCVT/src/adjoint.jl:66 [inlined]
  [3] #19
    @ Zygote ./REPL[12]:1 [inlined]
  [4] _pullback(ctx::Zygote.Context{false}, f::var"#19#20", args::Vector{ForwardDiff.Dual{Nothing, Float64, 4}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface2.jl:0
  [5] pullback(f::Function, cx::Zygote.Context{false}, args::Vector{ForwardDiff.Dual{Nothing, Float64, 4}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface.jl:44
  [6] pullback(f::Any, cx::ZygoteRules.AContext, args::Vararg{Any})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface.jl:42 [inlined]
  [7] gradient(f::Function, args::Vector{ForwardDiff.Dual{Nothing, Float64, 4}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface.jl:96
  [8] (::Zygote.var"#125#126"{var"#19#20"})(x::Vector{ForwardDiff.Dual{Nothing, Float64, 4}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/grad.jl:64
  [9] forward_jacobian(f::Zygote.var"#125#126"{var"#19#20"}, x::ComponentVector{Float64, Vector{Float64}, Tuple{Axis{(a = 1:2, b = 3:4)}}}, ::Val{4})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:29
 [10] forward_jacobian(f::Function, x::ComponentVector{Float64, Vector{Float64}, Tuple{Axis{(a = 1:2, b = 3:4)}}}; chunk_threshold::Int64)
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:44
 [11] forward_jacobian
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:42 [inlined]
 [12] hessian_dual
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/grad.jl:64 [inlined]
 [13] hessian(f::Function, x::ComponentVector{Float64, Vector{Float64}, Tuple{Axis{(a = 1:2, b = 3:4)}}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/grad.jl:62
 [14] top-level scope
    @ REPL[12]:1
 [15] top-level scope
    @ ~/.julia/packages/CUDA/nbRJk/src/initialization.jl:205

julia> Zygote.hessian_reverse(x -> sum(x.a), p)                               
ERROR: Mutating arrays is not supported -- called setindex!(Vector{Float64}, ...)
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/latest/limitations                        
                                         
Stacktrace:                                                                                                                                                          
  [1] error(s::String)                                                                                                                                               
    @ Base ./error.jl:35                                                          
  [2] _throw_mutation_error(f::Function, args::Vector{Float64})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/array.jl:88                   
  [3] (::Zygote.var"#555#556"{Vector{Float64}})(::Nothing)                 
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/array.jl:100        
  [4] (::Zygote.var"#2655#back#557"{Zygote.var"#555#556"{Vector{Float64}}})(Δ::Nothing)                                                                                  @ Zygote ~/.julia/packages/ZygoteRules/OgCVT/src/adjoint.jl:71                
  [5] (::Zygote.var"#291#292"{Tuple{Tuple{Nothing, Nothing}, Tuple{Nothing}}, Zygote.var"#2655#back#557"{Zygote.var"#555#556"{Vector{Float64}}}})(Δ::Nothing)        
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/lib.jl:206
  [6] (::Zygote.var"#2169#back#293"{Zygote.var"#291#292"{Tuple{Tuple{…}, Tuple{…}}, Zygote.var"#2655#back#557"{Zygote.var"#555#556"{…}}}})(Δ::Nothing)
    @ Zygote ~/.julia/packages/ZygoteRules/OgCVT/src/adjoint.jl:71                                                                                                   
  [7] macro expansion                                                             
    @ Zygote ~/.julia/dev/ComponentArrays/src/array_interface.jl:0 [inlined]                                                                                         
  [8] _setindex!                                                                  
    @ Zygote ~/.julia/dev/ComponentArrays/src/array_interface.jl:131 [inlined]
  [9] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Nothing)                         
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface2.jl:0                                                                                             
 [10] setproperty!                                                                
    @ ComponentArrays ~/.julia/dev/ComponentArrays/src/namedtuple_interface.jl:17 [inlined]                                                                          
 [11] (::ComponentArrays.var"#getproperty_adjoint#87"{ComponentVector{Float64, Vector{…}, Tuple{…}}, Symbol})(Δ::FillArrays.Fill{Float64, 1, Tuple{Base.OneTo{…}}})
    @ ComponentArrays ~/.julia/dev/ComponentArrays/src/compat/chainrulescore.jl:4 [inlined]
 [12] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Tuple{Nothing, Vector{…}, Nothing})                                                
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface2.jl:0                                                                                             
 [13] ZBack                                                                       
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/chainrules.jl:211 [inlined]
 [14] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Tuple{Nothing, Vector{…}, Nothing})                                                                       
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface2.jl:0
 [15] #37                                                                         
    @ Zygote ./REPL[22]:1 [inlined]                                               
 [16] (::Zygote.Pullback{Tuple{…}, Tuple{…}})(Δ::Tuple{Nothing, Vector{…}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface2.jl:0
 [17] #75
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface.jl:45 [inlined]
 [18] (::Zygote.Pullback{Tuple{Zygote.var"#75#76"{…}, Float64}, Tuple{Zygote.Pullback{…}, Zygote.var"#2180#back#303"{…}, Zygote.Pullback{…}}})(Δ::Tuple{Vector{Float6
4}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/compiler/interface2.jl:0

julia> using CUDA

julia> CUDA.allowscalar(false)

julia> Zygote.hessian(x -> sum(x.a), p |> cu)
ERROR: Scalar indexing is disallowed.
Invocation of getindex resulted in scalar indexing of a GPU array.
This is typically caused by calling an iterating implementation of a method.
Such implementations *do not* execute on the GPU, but very slowly on the CPU,
and therefore are only permitted from the REPL for prototyping purposes.
If you did intend to index this array, annotate the caller with @allowscalar.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] assertscalar(op::String)
    @ GPUArraysCore ~/.julia/packages/GPUArraysCore/uOYfN/src/GPUArraysCore.jl:103
  [3] getindex
    @ Zygote ~/.julia/packages/GPUArrays/EZkix/src/host/indexing.jl:9 [inlined]
  [4] getindex (repeats 2 times)
    @ Zygote ~/.julia/dev/ComponentArrays/src/array_interface.jl:94 [inlined]
  [5] extract(xs::ComponentVector{ForwardDiff.Dual{Nothing, Float32, 4}, ComponentVector{ForwardDiff.Dual{…}, CuArray{…}, Tuple{…}}, Tuple{Axis{…}}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:23
  [6] forward_jacobian(f::Zygote.var"#125#126"{var"#41#42"}, x::ComponentVector{Float32, CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{Axis{…}}}, ::Val{4})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:29
  [7] forward_jacobian(f::Function, x::ComponentVector{Float32, CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{Axis{(a = 1:2, b = 3:4)}}}; chunk_threshold::Int64)
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:44
  [8] forward_jacobian
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/forward.jl:42 [inlined]
  [9] hessian_dual
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/grad.jl:64 [inlined]
 [10] hessian(f::Function, x::ComponentVector{Float32, CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{Axis{(a = 1:2, b = 3:4)}}})
    @ Zygote ~/.julia/packages/Zygote/gsq4u/src/lib/grad.jl:62
 [11] top-level scope
    @ REPL[25]:1
 [12] top-level scope
    @ ~/.julia/packages/CUDA/nbRJk/src/initialization.jl:205
Some type information was truncated. Use `show(err)` to see complete types.