Spectral representation of multi-valued functions
Spectral representation of multi-valued functions
- Author(s): Dezheng Zhang ; Nan Jiang ; A. Wulamu ; Jing Wang
- DOI: 10.1049/cp.2012.1364
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- Author(s): Dezheng Zhang ; Nan Jiang ; A. Wulamu ; Jing Wang Source: International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), 2012 p. 1902 – 1905
- Conference: International Conference on Automatic Control and Artificial Intelligence (ACAI 2012)
- DOI: 10.1049/cp.2012.1364
- ISBN: 978-1-84919-537-9
- Location: Xiamen, China
- Conference date: 3-5 March 2012
- Format: PDF
Multi-valued functions can be compute by multi-valued neural network. In order to use linear algebra method for analysis of multi-valued function, this paper gives the spectral representation of multi-valued functions. By define a checksum function of n variables, this paper gives an group of orthogonal bases. Any multi-valued function in GF(p)p* can p be uniquely represented as a linear combination of the bases. The coefficients are the correlations of the multi-valued function and the bases. All the coefficients combine the generalized spectrum of the multi-valued function. For a multi-valued function that can be realized by a multi-valued neuron, it is computable by depth-2 polynomial-size neural networks.
Inspec keywords: linear algebra; neural nets
Subjects: Algebra; Neural nets (theory)
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