cybenko-universal-approximation-theorem-1989

IN premise — entries/2026/06/21/wiki-Neural_network_28machine_learning29-chunk-9.md

Created 2026-06-21T09:55:51+00:00

Cybenko's Universal Approximation Theorem (1989) proves that a single hidden layer with sigmoidal activation functions can approximate any continuous function on compact subsets of R^n.

Dependents

These beliefs depend on this one:

• IN universal-approximation-vs-practical-depth — Universal approximation theory (Cybenko, 1989) establishes that shallow networks with sigmoidal activations can approximate any continuous function on compact subsets of R^n, but this existence guarantee has practical caveats: deep networks leverage hierarchical feature learning across multiple layers, and ReLU networks require width strictly greater than input dimension to maintain universal approximation — suggesting that theoretical approximation capacity alone does not determine architectural effectiveness.