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Common Nature of Learning Between Back-Propagation and Hopfield-Type Neural Networks for Generalized Matrix Inversion With Simplified Models

Yunnong Zhang 1 Dongsheng Guo 1 Zhan Li 2
2 DEMAR - Artificial movement and gait restoration
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper, two simple-structure neural networks based on the error back-propagation (BP) algorithm (i.e., BP-type neural networks, BPNNs) are proposed, developed, and investigated for online generalized matrix inversion. Specifically, the BPNN-L and BPNN-R models are proposed and investigated for the left and right generalized matrix inversion, respectively. In addition, for the same problem-solving task, two discrete-time Hopfield-type neural networks (HNNs) are developed and investigated in this paper. Similar to the classification of the presented BPNN-L and BPNN-R models, the presented HNN-L and HNN-R models correspond to the left and right generalized matrix inversion, respectively. Comparing the BPNN weight-updating formula with the HNN state-transition equation for the specific (i.e., left or right) generalized matrix inversion, we show that such two derived learning-expressions turn out to be the same (in mathematics), although the BP and Hopfield-type neural networks are evidently different from each other a great deal, in terms of network architecture, physical meaning, and training patterns. Numerical results with different illustrative examples further demonstrate the efficacy of the presented BPNNs and HNNs for online generalized matrix inversion and, more importantly, their common natures of learning.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00799204
Contributor : Zhan Li <>
Submitted on : Monday, March 11, 2013 - 5:54:20 PM
Last modification on : Thursday, April 30, 2020 - 1:22:02 PM

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Yunnong Zhang, Dongsheng Guo, Zhan Li. Common Nature of Learning Between Back-Propagation and Hopfield-Type Neural Networks for Generalized Matrix Inversion With Simplified Models. IEEE Transactions on Neural Networks and Learning Systems, IEEE, 2013, 24 (4), pp.579-592. ⟨10.1109/TNNLS.2013.2238555⟩. ⟨lirmm-00799204⟩

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