Abstract
Investigated in this paper are the uniform approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by an SOPNN with its activation function in C(ℝ) is dense in \(C(\mathbb{K})\) for any compact \(\mathbb{K}\in \mathbb{R}^N\), if and only if the activation function is not a polynomial. It is also shown that if the activation function of an SPSNN is in C(ℝ), then the functions generated by the SPSNN are dense in \(C(\mathbb{K})\) if and only if the activation function is not a constant.
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Long, J., Wu, W., Nan, D. (2007). Uniform Approximation Capabilities of Sum-of-Product and Sigma-Pi-Sigma Neural Networks. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_130
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DOI: https://doi.org/10.1007/978-3-540-72383-7_130
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