Cybenko: approximation by superpositions of a sigmoidal function

What changed

Proved density of finite superpositions of continuous sigmoids in continuous functions on a compact cube.

Scientific scope

The theorem is a representational existence result under the paper's continuity, domain and activation assumptions. It does not guarantee efficient learning, finite-sample generalization, optimization success, minimal width or the performance of deeper architectures.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The theorem is a representational existence result under the paper's continuity, domain and activation assumptions. It does not guarantee efficient learning, finite-sample generalization, optimization success, minimal width or the performance of deeper architectures.

Contributors

• G. Cybenko · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Springer page for Cybenko universal-approximation paper
• MIT-hosted copy of Cybenko paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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