The Ridge Function Representation of Polynomials and an Application to Neural Networks
The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained b...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2011-11, Vol.27 (11), p.2169-2176 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Xie, Ting Fan Cao, Fei Long |
| description | The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial. |
| doi_str_mv | 10.1007/s10114-011-9407-1 |
| format | Article |
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| ispartof | Acta mathematica Sinica. English series, 2011-11, Vol.27 (11), p.2169-2176 |
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| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Algebra Approximation Mathematical analysis Mathematics Mathematics and Statistics Multivariate analysis Neural networks Polynomials Representations Ridges Studies 代数多项式 多元多项式 多项式函数 应用 神经网络 表示法 连续函数 逼近问题 |
| title | The Ridge Function Representation of Polynomials and an Application to Neural Networks |
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