Name
Abstract | ||
|---|---|---|
We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. Under these conditions, it is also possible to construct networks that provide a geometric order of approximation for analytic target functions. The permissible activation functions include the squashing function (1 − e−x)−1 as well as a variety of radial basis functions. Our proofs are constructive. The weights and thresholds of our networks are chosen independently of the target function; we give explicit formulas for the coefficients as simple, continuous, linear functionals of the target function. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1162/neco.1996.8.1.164 | Neural Computation |
Keywords | Field | DocType |
certain technical condition,neural network,explicit formula,analytic function,radial basis function,analytic target function,permissible activation function,squashing function,optimal approximation,target function,activation function,optimal order,geometric order,satisfiability | Universal approximation theorem,Radial basis function network,Mathematical optimization,Radial basis function,Mathematical analysis,Activation function,Analytic function,Non-analytic smooth function,Complex-valued function,Smoothness,Mathematics | Journal |
Volume | Issue | ISSN |
8 | 1 | 0899-7667 |
Citations | PageRank | References |
61 | 4.82 | 10 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hrushikesh Narhar Mhaskar | 1 | 257 | 61.07 |