Linear Independence of Polynomial Compositions with Bounded Input Degree

Abstract:We prove the weak composition-independence conjectures of Kohn, Marchetti, Massarenti and Mella. The proof uses deformations of rational curves and a single kernel of the linearized equation. Riemann-Roch gives a contradiction from tangent fields with controlled poles. By settling these conjectures, we prove that a neural network with a general polynomial activation function of sufficiently large degree is identifiable.

Algebraic Geometry (math.AG); Machine Learning (cs.LG)

arXiv:2610.20825 [math.AG]

(or arXiv:2610.20825v1 [math.AG] for this version)

https://doi.org/10.48550/arXiv.2610.20825 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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