PreprintCC BY 4.0arXiv
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.
Related
- A bounded degree SDSOS hierarchy for solving SPLD polynomial programs
- The weak cylinder conjecture for polynomial graphs of bounded degree
- A Bounded Degree SOS Plus SONC Hierarchy for Polynomial Optimization
- Degree profiles of uniform polynomial consequences: Linear lower bounds for Nullstellensatz and Polynomial Calculus
- A Bounded Finite-One Degree Whose One-One Degrees Form Exactly a Dense Linear Order
BibTeX
@misc{chang2026linear,
title = {{Linear Independence of Polynomial Compositions with Bounded Input Degree}},
author = {Xiaotian Chang and Yacoub Hendi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20825},
eprint = {2610.20825},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20825},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear Independence of Polynomial Compositions with Bounded Input Degree
AU - Xiaotian Chang
AU - Yacoub Hendi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20825
UR - https://arxiv.org/abs/2610.20825
AB - 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.
ER -