An Efficient Supervised Training Algorithm for Multilayer Spiking Neural Networks

The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical struc...

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Published in:	PloS one Vol. 11; no. 4; p. e0150329
Main Authors:	Xie, Xiurui, Qu, Hong, Liu, Guisong, Zhang, Malu, Kurths, Jürgen
Format:	Journal Article
Language:	English
Published:	United States Public Library of Science 04.04.2016 Public Library of Science (PLoS)
Subjects:	Algorithms Analysis Animals Artificial neural networks Back propagation Biology and Life Sciences Coding Cognition - physiology Cognitive ability Cognitive tasks Computation Computational neuroscience Computer and Information Sciences Data processing Efficiency Electric potential Feedforward Firing pattern Humans Information processing Machine Learning Medicine and Health Sciences Models, Neurological Nerve Net - physiology Neural networks Neurons Parameter sensitivity Parameters Pattern recognition Physical Sciences Physiological aspects Physiology Propagation Quadratic equations Research and Analysis Methods Sensitivity Spiking Structural hierarchy Teaching methods Training Vibration Voltage China Germany
ISSN:	1932-6203, 1932-6203
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Abstract	The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper.
AbstractList	The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper. The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper.The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper.
Audience	Academic
Author	Kurths, Jürgen Xie, Xiurui Qu, Hong Liu, Guisong Zhang, Malu
AuthorAffiliation	3 Potsdam Institute for Climate Impact Research(PIK), 14473 Potsdam, Germany Georgia State University, UNITED STATES 1 Department of Computer Science and Engineering, University of Electronic Science and Technology of China, 611731, Chengdu, Sichuan, China 2 Department of Physics, Humboldt University, 12489, Berlin, Berlin, Germany
AuthorAffiliation_xml	– name: 1 Department of Computer Science and Engineering, University of Electronic Science and Technology of China, 611731, Chengdu, Sichuan, China – name: Georgia State University, UNITED STATES – name: 3 Potsdam Institute for Climate Impact Research(PIK), 14473 Potsdam, Germany – name: 2 Department of Physics, Humboldt University, 12489, Berlin, Berlin, Germany
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Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 Conceived and designed the experiments: XX HQ. Performed the experiments: XX MZ. Analyzed the data: XX GL. Contributed reagents/materials/analysis tools: XX MZ. Wrote the paper: XX JK. Competing Interests: The authors have declared that no competing interests exist.
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Snippet	The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The...
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SubjectTerms	Algorithms Analysis Animals Artificial neural networks Back propagation Biology and Life Sciences Coding Cognition - physiology Cognitive ability Cognitive tasks Computation Computational neuroscience Computer and Information Sciences Data processing Efficiency Electric potential Feedforward Firing pattern Humans Information processing Machine Learning Medicine and Health Sciences Models, Neurological Nerve Net - physiology Neural networks Neurons Parameter sensitivity Parameters Pattern recognition Physical Sciences Physiological aspects Physiology Propagation Quadratic equations Research and Analysis Methods Sensitivity Spiking Structural hierarchy Teaching methods Training Vibration Voltage
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Title	An Efficient Supervised Training Algorithm for Multilayer Spiking Neural Networks
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