A General Constructive Upper Bound on Shallow Neural Nets Complexity

2025/10/07 by F. Hakl, Hakl, Frantisek, Vit Fojtik +1
Computer Science · #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2510.06372

openalex publication_date 2025/10/07 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem, is constructive and more general than previous bounds of this character, as it applies to any continuous function on any compact set.

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