1. Measure theoretic results for approximation by neural networks with limited weights
- Author
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Ekrem Savaş, Vugar E. Ismailov, and Bölüm Yok
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Control and Optimization ,neural network ,Activation function ,Space (mathematics) ,Topology ,01 natural sciences ,Measure (mathematics) ,Machine Learning (cs.LG) ,orthogonal measure ,010104 statistics & probability ,FOS: Mathematics ,0101 mathematics ,lightning bolt ,Borel measure ,orbit ,Mathematics ,density ,Quantitative Biology::Neurons and Cognition ,Artificial neural network ,Weak convergence ,010102 general mathematics ,Computer Science Applications ,Functional Analysis (math.FA) ,41A30, 41A63, 92B20 ,Mathematics - Functional Analysis ,Signal Processing ,Orbit (dynamics) ,weak convergence ,Analysis ,Open interval - Abstract
In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons., 12 pages
- Published
- 2023