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
VerifiedThe 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% similarUnverifiedThe author proves the existence of a solution to the conjugate moment measure decomposition equation using Schauder's fixed-point theorem, with the proof requiring compactness assumptions (ρ absolutely continuous and supported on a compact convex set).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)