2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62927In this note, we derive an improved upper bound for the VC-dimension of neural networks with polynomial activation functions. This improved bound is based on a result of Rojas on the number of connected components of a semi-algebraic set.9 pages, submitted for publication. Various typos fixed and the proof of the main result has been streamlinedOptimization and ControlAlgebraic Geometrytext