They are not "equivalent". Polynomials can only produce polynomials, but these polynomials can be made to be as close as you want to any continuous function (se

They are not "equivalent". Polynomials can only produce polynomials, but these polynomials can be made to be as close as you want to any continuous function (see Stone-Weierstrass theorem). For example, a NN with a ReLU activation function produce a function that is not a polynomial. Now I understand that this not the main point; both polynomials and NN can approximate any function that is not artificially nasty. The only thing is that a NN is easier to optimize and generalizes better for high dimensional problems such as image classification. The issue is more complicated than simply expressiveness. The author claim that "one should use PR instead" seems dubious at best, but I'm now going to read the paper and figure it out.