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Issues with differentiating with respect to polynomial coefficients

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Assessment

Difficulty
3/5
Estimated time
1-2 days
Newbie friendliness
38/100
Issue type
Bug
Clarity
Mostly clear
Activity status
Stale
Tech stack
julia
Domain
tooling

Research direction

Start by running the provided Polynomials and ForwardDiff example and inspect how Polynomial(x) and ForwardDiff.gradient interact when trailing coefficients are zero. Compare the reported gradients with true_∇f(x); done means the zero-coefficient cases produce the expected coefficient derivatives without breaking the existing examples.

Written by the indexing model from the issue text.

Description

I am interested in taking the derivative of a polynomial with respect to its coefficients. When the coefficients are such that all terms of order $n \ge k$ for some $k$ are 0, automatic differentiation packages return 0 as the derivative with respect to those coefficients. Of course, the true derivative of $\beta_0 + \beta_1 x + \cdots + \beta_K x^K$ with respect to $\beta_n$ should be $x^n$.

Here is an example:

using Polynomials
using ForwardDiff

f(x) = Polynomial(x)(0.5)
∇f(x) = ForwardDiff.gradient(f, x)
true_∇f(x) = 0.5.^(0:length(x)-1)

all_params = [[1.0, 2.0, 3.0], [1.0, 0.0, 3.0], [1.0, 0.0, 0.0]]
for param in all_params
    println("Params are $(param).") 
    println("Gradient from ForwardDiff: $(∇f(param))") 
    println("True gradient: $(true_∇f(param))")
    println("")
end

The output from this example is below. Note the issue in the final example.

Params are [1.0, 2.0, 3.0].
Gradient from ForwardDiff: [1.0, 0.5, 0.25]
True gradient: [1.0, 0.5, 0.25]

Params are [1.0, 0.0, 3.0].
Gradient from ForwardDiff: [1.0, 0.5, 0.25]
True gradient: [1.0, 0.5, 0.25]

Params are [1.0, 0.0, 0.0].
Gradient from ForwardDiff: [1.0, 0.0, 0.0]
True gradient: [1.0, 0.5, 0.25]

Is there a way to avoid this issue?

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Avg merge
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Merged PRs (30d)
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