Why does FiniteDiff over FiniteDiff HVP fail?

[gdalle]

Does it have to do with the finite difference mode chosen by default?

[gdalle]

Non deterministic outputs:

julia> using DifferentiationInterface

julia> import FiniteDiff

julia> backend = AutoFiniteDiff()

julia> f(x) = sum(abs2, x)
f (generic function with 1 method)

julia> hessian(f, backend, rand(3))
3×3 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
 2.0         1.86265e-9  0.0
 1.86265e-9  2.0         0.0
 0.0         0.0         2.0

julia> hvp(f, backend, rand(3), ones(3))
3-element Vector{Float64}:
 2.5
 2.0
 2.0

julia> hvp(f, backend, rand(3), ones(3))
3-element Vector{Float64}:
 1.0
 1.0
 1.0

julia> hvp(f, backend, rand(3), ones(3))
3-element Vector{Float64}:
 1.5
 2.0
 1.5

[gdalle]

Apparently it's just a matter of correctly choosing the fdtype:

julia> import FiniteDiff

julia> backend = AutoFiniteDiff(fdtype=Val(:central))  
AutoFiniteDiff(fdtype=Val{:central}(), )

julia> f(x) = sum(abs2, x)
f (generic function with 1 method)

julia> hessian(f, backend, rand(3))
3×3 LinearAlgebra.Symmetric{Float64, Matrix{Float64}}:
  2.0         -3.72529e-9  0.0
 -3.72529e-9   2.0         0.0
  0.0          0.0         2.0

julia> hvp(f, backend, rand(3), Tangents(ones(3)))
Tangents{1, Vector{Float64}}(([2.0000000381273746, 2.0000000381273746, 2.0000000381273746],))

julia> hvp(f, backend, rand(3), Tangents(ones(3)))
Tangents{1, Vector{Float64}}(([1.9999996596714908, 1.9999996596531564, 2.000000416592426],))

julia> hvp(f, backend, rand(3), Tangents(ones(3)))
Tangents{1, Vector{Float64}}(([2.0000000381273746, 2.0000000381273746, 2.0000000381273746],))

julia> hvp(f, backend, rand(3), Tangents(ones(3)))
Tangents{1, Vector{Float64}}(([2.0000000381273746, 2.0000000381273746, 2.0000000381273746],))