Linear Independence of Polynomial Compositions with Bounded Input Degree (arxiv.org)
arXiv:2610.20825v1 Announce Type: cross
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.
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.
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