Reproduce “An elementary proof of a universal approximation theorem” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Chris Monico
Chris Monico from Texas Tech University developed an elementary proof demonstrating that three-hidden-layer neural networks, employing increasing, continuous, and bounded activation functions, can uniformly approximate any continuous function on a compact set. This proof exclusively utilizes concepts from undergraduate real analysis, aiming for greater accessibility.
Key insights
- The universal approximation capability of neural networks can be understood by demonstrating their ability to sequentially separate points and closed sets in the input space.
- Stacking multiple layers with a simple non-linear activation function allows for the construction of increasingly complex separating functions.
- The fundamental expressive power of neural networks can be rigorously proven using only elementary analytical techniques, without advanced mathematical machinery.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.