`pushforward_function` and `pullback_function` are confused by tuples vs single input

[gdalle]

The setup:

Details

julia> import AbstractDifferentiation as AD

julia> using ForwardDiff: ForwardDiff

julia> using Zygote: Zygote

julia> b1 = AD.ZygoteBackend();

julia> b2 = AD.ForwardDiffBackend();

julia> f(x) = x .^ 2;

julia> x = rand(3)
3-element Vector{Float64}:
 0.4953469957333393
 0.16373195021545772
 0.9601871509472656

julia> y = f(x)
3-element Vector{Float64}:
 0.24536864618204485
 0.026808151521357126
 0.921959364844227

julia> dx = rand(size(x)...)
3-element Vector{Float64}:
 0.5968881542176618
 0.05494767011762569
 0.18061398390944328

julia> dy = rand(size(y)...)
3-element Vector{Float64}:
 0.9491707280920829
 0.2878716471988746
 0.15674572721525504

A pushforward with Zygote backend doesn't accept a single array as input.

Details

julia> pf1 = AD.pushforward_function(b1, f, x);

julia> pf2 = AD.pushforward_function(b2, f, x);

julia> pf1((dx,))  # works
([0.5913335079610738, 0.017993378376308967, 0.3468464532624872],)

julia> pf1(dx)  # fails but shouldn't
ERROR: ArgumentError: Tuple contains 3 elements, must contain exactly 1 element
Stacktrace:
 [1] only(x::Tuple{Float64, Float64, Float64})
   @ Base.Iterators ./iterators.jl:1531
 [2] (::AbstractDifferentiation.var"#14#16"{Vector{Float64}, typeof(f), Tuple{Vector{Float64}}})(::Float64, ::Vararg{Float64})
   @ AbstractDifferentiation ~/Work/GitHub/Julia/AbstractDifferentiation.jl/src/AbstractDifferentiation.jl:172
 [3] (::AbstractDifferentiation.var"#25#27"{AbstractDifferentiation.ReverseRuleConfigBackend{Zygote.ZygoteRuleConfig{Zygote.Context{false}}}, AbstractDifferentiation.var"#14#16"{Vector{Float64}, typeof(f), Tuple{Vector{Float64}}}, Tuple{Float64, Float64, Float64}})(ws::Nothing)
   @ AbstractDifferentiation ~/Work/GitHub/Julia/AbstractDifferentiation.jl/src/AbstractDifferentiation.jl:249
 [4] jacobian(::AbstractDifferentiation.ReverseRuleConfigBackend{Zygote.ZygoteRuleConfig{Zygote.Context{false}}}, ::Function, ::Float64, ::Float64, ::Vararg{Float64})
   @ AbstractDifferentiationChainRulesCoreExt ~/Work/GitHub/Julia/AbstractDifferentiation.jl/src/AbstractDifferentiation.jl:551
 [5] (::AbstractDifferentiation.var"#13#15"{AbstractDifferentiation.ReverseRuleConfigBackend{Zygote.ZygoteRuleConfig{Zygote.Context{false}}}, typeof(f), Tuple{Vector{Float64}}})(ds::Vector{Float64})
   @ AbstractDifferentiation ~/Work/GitHub/Julia/AbstractDifferentiation.jl/src/AbstractDifferentiation.jl:166
 [6] top-level scope
   @ ~/Work/GitHub/Julia/ImplicitDifferentiation.jl/test/playground.jl:54

julia> pf2((dx,))  # works
([0.5913335079610738, 0.017993378376308967, 0.3468464532624872],)

julia> pf2(dx)  # works
([0.5913335079610738, 0.017993378376308967, 0.3468464532624872],)

A pullback with ForwardDiff backend doesn't accept a tuple as input:

Details

julia> pb1 = AD.pullback_function(b1, f, x);

julia> pb2 = AD.pullback_function(b2, f, x);

julia> pb1(dy)  # works
([0.9403377371968791, 0.09426757241521588, 0.301010466475946],)

julia> pb1((dy,))  # works
([0.9403377371968791, 0.09426757241521588, 0.301010466475946],)

julia> pb2(dy)  # works
([0.9403377371968791, 0.09426757241521588, 0.301010466475946],)

julia> pb2((dy,))  # fails but shouldn't
ERROR: AssertionError: length(vs) == length(ws)
Stacktrace:
 [1] (::AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)})(xs::Vector{ForwardDiff.Dual{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3}})
   @ AbstractDifferentiation ~/Work/GitHub/Julia/AbstractDifferentiation.jl/src/AbstractDifferentiation.jl:231
 [2] vector_mode_dual_eval!
   @ ~/.julia/packages/ForwardDiff/vXysl/src/apiutils.jl:24 [inlined]
 [3] vector_mode_gradient(f::AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3, Vector{ForwardDiff.Dual{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3}}})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/vXysl/src/gradient.jl:89
 [4] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3, Vector{ForwardDiff.Dual{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3}}}, ::Val{true})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/vXysl/src/gradient.jl:19
 [5] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3, Vector{ForwardDiff.Dual{ForwardDiff.Tag{AbstractDifferentiation.var"#88#90"{Tuple{Vector{Float64}}, AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f)}, Float64}, Float64, 3}}})
   @ ForwardDiff ~/.julia/packages/ForwardDiff/vXysl/src/gradient.jl:17
 [6] gradient(ba::AbstractDifferentiation.ForwardDiffBackend{Nothing}, f::Function, x::Vector{Float64})
   @ AbstractDifferentiationForwardDiffExt ~/Work/GitHub/Julia/AbstractDifferentiation.jl/ext/AbstractDifferentiationForwardDiffExt.jl:46
 [7] (::AbstractDifferentiation.var"#87#89"{AbstractDifferentiation.ForwardDiffBackend{Nothing}, typeof(f), Tuple{Vector{Float64}}})(ws::Tuple{Vector{Float64}})
   @ AbstractDifferentiation ~/Work/GitHub/Julia/AbstractDifferentiation.jl/src/AbstractDifferentiation.jl:224
 [8] top-level scope
   @ ~/Work/GitHub/Julia/ImplicitDifferentiation.jl/test/playground.jl:63

Both of these uses are documented in the README