Help with Jacobian vector product to get natural gradient

Specific Domains Probabilistic programming
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12

The derivative of f(t * a + c) wrt t at 0 is the Jacobian vector product J(f, c) * a.

julia> using ForwardDiff

julia> foo(x) = [x[1], x[1]*x[3], x[2]^2]
foo (generic function with 1 method)

julia> ForwardDiff.derivative(t->foo([1,2,3] * t + [3, 4, 5]), 0)
3-element Vector{Int64}:
  1
 14
 16

julia> ForwardDiff.jacobian(foo, [3,4,5]) * [1,2,3]
3-element Vector{Int64}:
  1
 14
 16
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