On Relationship of Multilayer Perceptrons and Piecewise Polynomial Approximators

被引：8

作者：

Lin, Ruiyuan ^{[1
]}

You, Suya ^{[2
]}

Rao, Raghuveer ^{[2
]}

Kuo, C-C Jay ^{[1
]}

机构：

[1] Univ Southern Calif, Ming Hsieh Dept Elect & Comp Engn, Los Angeles, CA 90089 USA

[2] Army Res Lab, Adelphi, MD 20783 USA

来源：

IEEE SIGNAL PROCESSING LETTERS | 2021年 / 28卷

关键词：

Neurons; Multilayer perceptrons; Tools; Piecewise linear approximation; Biological neural networks; Transforms; Taylor series; Multilayer perceptron; feedforward neural network; approximation theory; piecewise polynomial approximation; FEEDFORWARD NETWORKS; NEURAL-NETWORKS; SUPERPOSITION; BOUNDS;

D O I：

10.1109/LSP.2021.3103130

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The relationship between a multilayer perceptron (MLP) regressor and a piecewise polynomial approximator is investigated in this work. We propose an MLP construction method, including the choice of activation, the specification of neuron numbers and filter weights. Through the construction, a one-to-one correspondence between an MLP and a piecewise polynomial is established. Especially, we point out that the form of nonlinear activation is related to the polynomial order. Since the approximation capability of piecewise polynomials is well understood, our study sheds new light on the universal approximation capability of an MLP.

引用

页码：1813 / 1817

页数：5

共 36 条

[1] [Anonymous], 2001, M.Sc. thesis
[2] [Anonymous], 1973, FUNCTIONAL ANAL
[3] UNIVERSAL APPROXIMATION BOUNDS FOR SUPERPOSITIONS OF A SIGMOIDAL FUNCTION
BARRON, AR
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1993, 39 (03) : 930 - 945
[4] APPROXIMATION-THEORY AND FEEDFORWARD NETWORKS
BLUM, EK
LI, LK
[J]. NEURAL NETWORKS, 1991, 4 (04) : 511 - 515
[5] Carroll S. M., 1989, IJCNN: International Joint Conference on Neural Networks (Cat. No.89CH2765-6), P607, DOI 10.1109/IJCNN.1989.118639
[6] Chen M.-S., 1990, IJCNN International Joint Conference on Neural Networks (Cat. No.90CH2879-5), P643, DOI 10.1109/IJCNN.1990.137643
[7] Chen M.-S., 1991, IJCNN-91-Seattle: International Joint Conference on Neural Networks (Cat. No.91CH3049-4), P295, DOI 10.1109/IJCNN.1991.155193
[8] CONVENTIONAL MODELING OF THE MULTILAYER PERCEPTRON USING POLYNOMIAL BASIS FUNCTIONS
CHEN, MS
MANRY, MT
[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS, 1993, 4 (01): : 164 - 166
[9] APPROXIMATIONS OF CONTINUOUS FUNCTIONALS BY NEURAL NETWORKS WITH APPLICATION TO DYNAMIC-SYSTEMS
CHEN, TP
CHEN, H
[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS, 1993, 4 (06): : 910 - 918
[10] CHEN TP, 1995, IEEE T NEURAL NETWOR, V6, P25

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