Verified70% confidenceFactExact time
The universal approximation theorem was rigorously proven by mathematician Cybenko in 1989 for the Sigmoid activation function.
4
Sources
70%
Confidence
Long-term
Relevance
7/23/2026
First Seen
Sources
Related Claims
UnverifiedThe classic proofs of the universal approximation theorem (such as Cybenko 1989, Hornik 1991) rely on the activation function satisfying conditions such as being non-polynomial and bounded, and both Sigmoid and ReLU satisfy them.79% similarVerifiedThe Universal Approximation Theorem was proved by George Cybenko in 1989, stating that given sufficient layers and neurons, a neural network can approximate any continuous function to arbitrary precision.77% similarUnverifiedCybenko的原始证明利用了Hahn-Banach定理来证明神经网络所张成的函数子空间在连续函数空间C(K)中稠密63% similarUnverifiedAI帮助发现Kazhdan-Lusztig多项式的组合结构规律,该发现后来被Geordie Williamson等人严格证明62% similarUnverifiedIn the two-dimensional case, the global existence and smoothness of solutions to the Navier–Stokes equations were proved in the 1960s by Soviet mathematician Ladyzhenskaya and others.61% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/601147API
curl https://kongchang.com/api/v1/knowledge/claims/601147MCP
get_claim(id=601147)