Unverified50% confidenceFactExact time
The standard form of the universal approximation theorem states: for any continuous function f defined on a compact set and any ε>0, there exists a single-hidden-layer network such that for all inputs x, |f(x) - network output| < ε.
1
Sources
50%
Confidence
Long-term
Relevance
10/20/2026
First Seen
Sources
Related Entities
Related Claims
Unverified激活函数赋予深度网络拟合任意复杂非线性函数的理论能力，若无激活函数网络本质上仍是线性变换67% similarVerifiedThe output of each layer in a neural network can be expressed as f(Wx + b), where f is the activation function, W is the weight matrix, b is the bias vector, and x is the input vector.67% similarUnverifiedThe universal approximation theorem targets continuous functions; for discontinuous functions and cases where the domain is unbounded, the standard statement requires additional conditions.66% similarUnverifiedIn the one-dimensional case, the optimal transport map has a closed-form solution that can be expressed using the cumulative distribution function of the source distribution and the quantile function of the target distribution.66% similarUnverifiedThe paper proposes to directly study the topology β(Φ(X)) of network outputs rather than the topology of decision boundaries, because whether for classification or regression networks there will always be an output space.66% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/1077967API
curl https://kongchang.com/api/v1/knowledge/claims/1077967MCP
get_claim(id=1077967)