Convolutional neural networks based on fractional-order momentum for parameter training
This paper proposes a parameter training method via the fractional-order momentum for convolutional neural networks (CNNs). To update the parameters of CNNs more smoothly, the parameter training method via the fractional-order momentum is proposed based on the Grünwald-Letnikov (G-L) difference oper...
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| Published in | Neurocomputing (Amsterdam) Vol. 449; pp. 85 - 99 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
18.08.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0925-2312 1872-8286 |
| DOI | 10.1016/j.neucom.2021.03.075 |
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| Abstract | This paper proposes a parameter training method via the fractional-order momentum for convolutional neural networks (CNNs). To update the parameters of CNNs more smoothly, the parameter training method via the fractional-order momentum is proposed based on the Grünwald-Letnikov (G-L) difference operation. The stochastic classical momentum (SCM) algorithm and adaptive moment (Adam) estimation algorithm are improved by replacing the integer-order difference with the fractional-order difference. Meanwhile, the linear and the nonlinear methods are discussed to adjust the fractional-order. Therefore, the proposed methods can improve the flexibility and the adaptive ability of CNN parameters. We analyze the validity of the methods by using MNIST dataset and CIFAR-10 dataset, and the experimental results show that the proposed methods can improve the recognition accuracy and the learning convergence speed of CNNs compared with the traditional SCM and Adam methods. |
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| AbstractList | This paper proposes a parameter training method via the fractional-order momentum for convolutional neural networks (CNNs). To update the parameters of CNNs more smoothly, the parameter training method via the fractional-order momentum is proposed based on the Grünwald-Letnikov (G-L) difference operation. The stochastic classical momentum (SCM) algorithm and adaptive moment (Adam) estimation algorithm are improved by replacing the integer-order difference with the fractional-order difference. Meanwhile, the linear and the nonlinear methods are discussed to adjust the fractional-order. Therefore, the proposed methods can improve the flexibility and the adaptive ability of CNN parameters. We analyze the validity of the methods by using MNIST dataset and CIFAR-10 dataset, and the experimental results show that the proposed methods can improve the recognition accuracy and the learning convergence speed of CNNs compared with the traditional SCM and Adam methods. |
| Author | Kan, Tao Gao, Zhe Yang, Chuang Jian, Jing |
| Author_xml | – sequence: 1 givenname: Tao surname: Kan fullname: Kan, Tao organization: School of Mathematics, Liaoning University, Shenyang 110036, PR China – sequence: 2 givenname: Zhe surname: Gao fullname: Gao, Zhe email: gaozhe@lnu.edu.cn organization: School of Mathematics, Liaoning University, Shenyang 110036, PR China – sequence: 3 givenname: Chuang surname: Yang fullname: Yang, Chuang organization: School of Mathematics, Liaoning University, Shenyang 110036, PR China – sequence: 4 givenname: Jing surname: Jian fullname: Jian, Jing organization: School of Mathematics, Liaoning University, Shenyang 110036, PR China |
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| Cites_doi | 10.14569/IJACSA.2020.0110719 10.1016/j.neucom.2019.04.087 10.2478/v10006-009-0022-6 10.1016/j.neucom.2019.07.016 10.1016/j.neucom.2019.10.017 10.1016/j.neucom.2019.04.057 10.3390/sym12050683 10.1162/neco.1989.1.4.541 10.1016/j.neucom.2019.10.048 10.1016/j.jvcir.2018.06.019 10.1109/5.726791 10.1016/j.amc.2018.10.037 10.1109/TNNLS.2013.2280458 10.1016/j.neucom.2020.07.036 10.1016/j.patrec.2019.12.013 10.1109/TITS.2019.2900385 10.1016/j.isprsjprs.2020.08.001 10.1016/j.neucom.2017.01.023 10.1016/j.neucom.2020.02.005 10.1109/TNNLS.2015.2506738 10.1016/S0893-6080(98)00116-6 |
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| References | LeCun, Bottou, Bengio, Haffner (b0045) 1998; 86 He, Gong, Fan (b0075) 2019 Liu, Li, Wu, Cao, Hao, Xian (b0080) 2020; 378 Diederik, Jimmy (b0130) 2015 M.H. Zhou, Y. Feng, C. Xue, F.L. Han, Deep convolutional neural network based fractional-order terminal sliding-mode control for robotic manipulators, Neurocomputing, doi:10.1016/j.neucom.2019.04.087. Qian (b0145) 1999; 12 Sui, Z, Wei, Bi, Wu, Pan, Yin, Zhang (b0065) 2017; 237 Wei, Jiang, Li, Li, Jia, Li (b0030) 2020; 21 LeCun, Boser, Denker, Henderson (b0040) 1989; 1 Chanthorn, Rajchakit, Humphries, Kaewmesri, Sriraman, Lim (b0095) 2020; 12 Aqab, Tariq (b0005) 2020; 11 Zhang, Huang, Tian (b0010) 2020; 131 Bottou (b0140) 2010 Sierociuk, Dzielinski (b0150) 2006; 1 Johnson, Zhang (b0115) 2013 Wu, Weng, Chen, Lu (b0070) 2018; 55 Zhuang, Zhang, Pan, Ni, Xu, Yang, Zhang (b0015) 2019; 358 Simonyan, Zisserman (b0055) 2015 Xi, Hopkinson, Rood, Peddle (b0020) 2020; 168 Wang, Deng (b0035) 2020; 393 John, Elad, Yoram (b0125) 2011; 12 Sheng, Wei, Chen, Wang (b0105) 2020; 408 Zhao, Luo (b0135) 2019; 346 Rajchakit, Chanthorn, Niezabitowski, Raja, Baleanu, Pratap (b0085) 2020; 417 Buslowicz, Kaczorek (b0155) 2009; 19 Krizhevsky, Sutskever, Hinton (b0050) 2012 Szegedy, Liu, Jia, Sermant, Reed, Anguelov, Erhan, Vanhoucke, Rabinovich (b0060) 2015 Zhu, Sun, Cao, Wang, Wu, Yang, Ye (b0025) 2019; 365 Wu, Zeng (b0100) 2014; 25 Botev, Lever, Barber (b0120) 2017 Wu, Zeng (b0090) 2017; 28 Wu (10.1016/j.neucom.2021.03.075_b0090) 2017; 28 Chanthorn (10.1016/j.neucom.2021.03.075_b0095) 2020; 12 Johnson (10.1016/j.neucom.2021.03.075_b0115) 2013 Xi (10.1016/j.neucom.2021.03.075_b0020) 2020; 168 Sierociuk (10.1016/j.neucom.2021.03.075_b0150) 2006; 1 Zhuang (10.1016/j.neucom.2021.03.075_b0015) 2019; 358 He (10.1016/j.neucom.2021.03.075_b0075) 2019 Bottou (10.1016/j.neucom.2021.03.075_b0140) 2010 Wu (10.1016/j.neucom.2021.03.075_b0100) 2014; 25 Qian (10.1016/j.neucom.2021.03.075_b0145) 1999; 12 John (10.1016/j.neucom.2021.03.075_b0125) 2011; 12 Wu (10.1016/j.neucom.2021.03.075_b0070) 2018; 55 Zhang (10.1016/j.neucom.2021.03.075_b0010) 2020; 131 Aqab (10.1016/j.neucom.2021.03.075_b0005) 2020; 11 Liu (10.1016/j.neucom.2021.03.075_b0080) 2020; 378 Sui (10.1016/j.neucom.2021.03.075_b0065) 2017; 237 Wang (10.1016/j.neucom.2021.03.075_b0035) 2020; 393 Botev (10.1016/j.neucom.2021.03.075_b0120) 2017 LeCun (10.1016/j.neucom.2021.03.075_b0045) 1998; 86 10.1016/j.neucom.2021.03.075_b0110 Krizhevsky (10.1016/j.neucom.2021.03.075_b0050) 2012 LeCun (10.1016/j.neucom.2021.03.075_b0040) 1989; 1 Zhao (10.1016/j.neucom.2021.03.075_b0135) 2019; 346 Szegedy (10.1016/j.neucom.2021.03.075_b0060) 2015 Sheng (10.1016/j.neucom.2021.03.075_b0105) 2020; 408 Zhu (10.1016/j.neucom.2021.03.075_b0025) 2019; 365 Wei (10.1016/j.neucom.2021.03.075_b0030) 2020; 21 Rajchakit (10.1016/j.neucom.2021.03.075_b0085) 2020; 417 Diederik (10.1016/j.neucom.2021.03.075_b0130) 2015 Buslowicz (10.1016/j.neucom.2021.03.075_b0155) 2009; 19 Simonyan (10.1016/j.neucom.2021.03.075_b0055) 2015 |
| References_xml | – volume: 365 start-page: 191 year: 2019 end-page: 200 ident: b0025 article-title: TA-CNN: two-way attention models in deep convolutional neural network for plant recognition publication-title: Neurocomputing – volume: 28 start-page: 206 year: 2017 end-page: 217 ident: b0090 article-title: Global mittag-leffler stabilization of fractional-order memristive neural networks publication-title: IEEE Transactions on Neural Networks and Learning Systems – volume: 168 start-page: 1 year: 2020 end-page: 16 ident: b0020 article-title: See the forest and the trees: effective machine and deep learning algorithms for wood filtering and tree species classification from terrestrial laser scanning publication-title: Isprs Journal of Photogrammetry and Remote Sensing – start-page: 1 year: 2015 end-page: 15 ident: b0130 article-title: A method for stochastic optimization publication-title: Proceedings of International Conference on Learning Representations – start-page: 913 year: 2019 end-page: 921 ident: b0075 article-title: Optimize deep convolutional neural network with ternarized weights and high accuracy publication-title: Proceedings of 2019 IEEE Winter Conference on Applications of Computer Vision (Wacv) – volume: 378 start-page: 45 year: 2020 end-page: 53 ident: b0080 article-title: Eye localization based on weight binarization cascade convolution neural network publication-title: Neurocomputing – volume: 86 start-page: 2278 year: 1998 end-page: 2324 ident: b0045 article-title: Gradient-based learning applied to document recognition publication-title: Proceedings of the IEEE – volume: 346 start-page: 531 year: 2019 end-page: 544 ident: b0135 article-title: Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds publication-title: Applied Mathematics and Computation – start-page: 1097 year: 2012 end-page: 1105 ident: b0050 article-title: classification with deep convolutional neural networks publication-title: 2012 Neural Information Processing Systems (NIPS), Lake Tahoe, USA – volume: 55 start-page: 424 year: 2018 end-page: 432 ident: b0070 article-title: Feedback weight convolutional neural network for gait recognition publication-title: Journal of Visual Communication and Image Representation – volume: 1 start-page: 129 year: 2006 end-page: 140 ident: b0150 article-title: Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation publication-title: International Journal of Applied Mathematics and Computer Science – start-page: 1 year: 2015 end-page: 9 ident: b0060 article-title: Going deeper with convolutions publication-title: 2015 IEEE Conference on Computer Vision and Pattern Recognization (CVPR), Boston, USA – volume: 25 start-page: 690 year: 2014 end-page: 703 ident: b0100 article-title: Lagrange stability of memristive neural networks with discrete and distributed delays publication-title: IEEE Transactions on Neural Networks and Learning Systems – start-page: 1899 year: 2017 end-page: 1903 ident: b0120 article-title: Nesterov’s accelerated gradient and momentum as approximations to regularised update descent publication-title: Proceeding of the 30th International Joint Conference on Neural Networks, Alaska, USA – volume: 21 start-page: 947 year: 2020 end-page: 958 ident: b0030 article-title: Defect detection of pantograph slide based on deep learning and image processing technology publication-title: IEEE Transactions on Intelligent Transportation Systems – volume: 12 year: 2020 ident: b0095 article-title: A delay-dividing approach to robust stability of uncertain stochastic complex-valued hopfield delayed neural networks publication-title: Symmetry – volume: 237 start-page: 332 year: 2017 end-page: 341 ident: b0065 article-title: Choroid segmentation from optical coherence tomography with graph-edge weights learned from deep convolutional neural networks publication-title: Neurocomputing – reference: M.H. Zhou, Y. Feng, C. Xue, F.L. Han, Deep convolutional neural network based fractional-order terminal sliding-mode control for robotic manipulators, Neurocomputing, doi:10.1016/j.neucom.2019.04.087. – start-page: 177 year: 2010 end-page: 186 ident: b0140 article-title: Large-scale machine learning with stochastic gradient descent publication-title: Proceeding of the 19th International Conference on Computational Statistics – start-page: 315 year: 2013 end-page: 323 ident: b0115 article-title: Accelerating stochastic gradient descent using predictive variance reduction publication-title: Proceeding of the 27th Neural Information Processing Systems – volume: 408 start-page: 42 year: 2020 end-page: 50 ident: b0105 article-title: Convolutional neural networks with fractional order gradient method publication-title: Neurocomputing – volume: 417 start-page: 290 year: 2020 end-page: 301 ident: b0085 article-title: Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks publication-title: Neurocomputing – volume: 11 start-page: 137 year: 2020 end-page: 146 ident: b0005 article-title: Handwriting recognition using artificial intelligence neural network and image processing publication-title: International Journal of Advanced Computer Science and Applications – volume: 19 start-page: 263 year: 2009 end-page: 269 ident: b0155 article-title: Simple conditions for practical stability of positive fractional discrete-time linear systems publication-title: International Journal of Applied Mathematics and Computer Science – volume: 12 start-page: 2121 year: 2011 end-page: 2159 ident: b0125 article-title: Adaptive subgradient methods for online learning and stochastic optimization publication-title: Journal of Machine Learning Research – volume: 1 start-page: 541 year: 1989 end-page: 551 ident: b0040 article-title: Backpropagation applied to handwritten zip code recognition publication-title: Neural Computation – volume: 12 start-page: 145 year: 1999 end-page: 151 ident: b0145 article-title: On the momentum term in gradient descent learning algorithms publication-title: Neural Networks – volume: 393 start-page: 1 year: 2020 end-page: 14 ident: b0035 article-title: Deep face recognition with clustering based domain adaptation publication-title: Neurocomputing – start-page: 1 year: 2015 end-page: 14 ident: b0055 article-title: deep convolutional networks for large scale image recognition publication-title: 2015 International Conference on Learning Representations (ICLR), San Diego, USA – volume: 131 start-page: 128 year: 2020 end-page: 134 ident: b0010 article-title: Facial expression recognition based on deep convolution long short-term memory networks of double-channel weighted mixture publication-title: Pattern Recognition Letters – volume: 358 start-page: 109 year: 2019 end-page: 118 ident: b0015 article-title: Recognition oriented facial image quality assessment via deep convolutional neural network publication-title: Neurocomputing – volume: 11 start-page: 137 issue: 7 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0005 article-title: Handwriting recognition using artificial intelligence neural network and image processing publication-title: International Journal of Advanced Computer Science and Applications doi: 10.14569/IJACSA.2020.0110719 – ident: 10.1016/j.neucom.2021.03.075_b0110 doi: 10.1016/j.neucom.2019.04.087 – volume: 19 start-page: 263 issue: 2 year: 2009 ident: 10.1016/j.neucom.2021.03.075_b0155 article-title: Simple conditions for practical stability of positive fractional discrete-time linear systems publication-title: International Journal of Applied Mathematics and Computer Science doi: 10.2478/v10006-009-0022-6 – volume: 12 start-page: 2121 year: 2011 ident: 10.1016/j.neucom.2021.03.075_b0125 article-title: Adaptive subgradient methods for online learning and stochastic optimization publication-title: Journal of Machine Learning Research – volume: 365 start-page: 191 year: 2019 ident: 10.1016/j.neucom.2021.03.075_b0025 article-title: TA-CNN: two-way attention models in deep convolutional neural network for plant recognition publication-title: Neurocomputing doi: 10.1016/j.neucom.2019.07.016 – start-page: 1899 year: 2017 ident: 10.1016/j.neucom.2021.03.075_b0120 article-title: Nesterov’s accelerated gradient and momentum as approximations to regularised update descent – volume: 408 start-page: 42 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0105 article-title: Convolutional neural networks with fractional order gradient method publication-title: Neurocomputing doi: 10.1016/j.neucom.2019.10.017 – start-page: 1097 year: 2012 ident: 10.1016/j.neucom.2021.03.075_b0050 article-title: classification with deep convolutional neural networks – start-page: 1 year: 2015 ident: 10.1016/j.neucom.2021.03.075_b0055 article-title: deep convolutional networks for large scale image recognition – volume: 1 start-page: 129 issue: 16 year: 2006 ident: 10.1016/j.neucom.2021.03.075_b0150 article-title: Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation publication-title: International Journal of Applied Mathematics and Computer Science – start-page: 1 year: 2015 ident: 10.1016/j.neucom.2021.03.075_b0060 article-title: Going deeper with convolutions – volume: 358 start-page: 109 year: 2019 ident: 10.1016/j.neucom.2021.03.075_b0015 article-title: Recognition oriented facial image quality assessment via deep convolutional neural network publication-title: Neurocomputing doi: 10.1016/j.neucom.2019.04.057 – volume: 12 issue: 5 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0095 article-title: A delay-dividing approach to robust stability of uncertain stochastic complex-valued hopfield delayed neural networks publication-title: Symmetry doi: 10.3390/sym12050683 – volume: 1 start-page: 541 issue: 4 year: 1989 ident: 10.1016/j.neucom.2021.03.075_b0040 article-title: Backpropagation applied to handwritten zip code recognition publication-title: Neural Computation doi: 10.1162/neco.1989.1.4.541 – start-page: 913 year: 2019 ident: 10.1016/j.neucom.2021.03.075_b0075 article-title: Optimize deep convolutional neural network with ternarized weights and high accuracy – start-page: 1 year: 2015 ident: 10.1016/j.neucom.2021.03.075_b0130 article-title: A method for stochastic optimization – volume: 378 start-page: 45 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0080 article-title: Eye localization based on weight binarization cascade convolution neural network publication-title: Neurocomputing doi: 10.1016/j.neucom.2019.10.048 – start-page: 177 year: 2010 ident: 10.1016/j.neucom.2021.03.075_b0140 article-title: Large-scale machine learning with stochastic gradient descent – volume: 55 start-page: 424 year: 2018 ident: 10.1016/j.neucom.2021.03.075_b0070 article-title: Feedback weight convolutional neural network for gait recognition publication-title: Journal of Visual Communication and Image Representation doi: 10.1016/j.jvcir.2018.06.019 – volume: 86 start-page: 2278 issue: 11 year: 1998 ident: 10.1016/j.neucom.2021.03.075_b0045 article-title: Gradient-based learning applied to document recognition publication-title: Proceedings of the IEEE doi: 10.1109/5.726791 – volume: 346 start-page: 531 year: 2019 ident: 10.1016/j.neucom.2021.03.075_b0135 article-title: Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2018.10.037 – volume: 25 start-page: 690 issue: 4 year: 2014 ident: 10.1016/j.neucom.2021.03.075_b0100 article-title: Lagrange stability of memristive neural networks with discrete and distributed delays publication-title: IEEE Transactions on Neural Networks and Learning Systems doi: 10.1109/TNNLS.2013.2280458 – volume: 417 start-page: 290 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0085 article-title: Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks publication-title: Neurocomputing doi: 10.1016/j.neucom.2020.07.036 – volume: 131 start-page: 128 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0010 article-title: Facial expression recognition based on deep convolution long short-term memory networks of double-channel weighted mixture publication-title: Pattern Recognition Letters doi: 10.1016/j.patrec.2019.12.013 – volume: 21 start-page: 947 issue: 3 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0030 article-title: Defect detection of pantograph slide based on deep learning and image processing technology publication-title: IEEE Transactions on Intelligent Transportation Systems doi: 10.1109/TITS.2019.2900385 – volume: 168 start-page: 1 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0020 article-title: See the forest and the trees: effective machine and deep learning algorithms for wood filtering and tree species classification from terrestrial laser scanning publication-title: Isprs Journal of Photogrammetry and Remote Sensing doi: 10.1016/j.isprsjprs.2020.08.001 – volume: 237 start-page: 332 year: 2017 ident: 10.1016/j.neucom.2021.03.075_b0065 article-title: Choroid segmentation from optical coherence tomography with graph-edge weights learned from deep convolutional neural networks publication-title: Neurocomputing doi: 10.1016/j.neucom.2017.01.023 – start-page: 315 year: 2013 ident: 10.1016/j.neucom.2021.03.075_b0115 article-title: Accelerating stochastic gradient descent using predictive variance reduction – volume: 393 start-page: 1 year: 2020 ident: 10.1016/j.neucom.2021.03.075_b0035 article-title: Deep face recognition with clustering based domain adaptation publication-title: Neurocomputing doi: 10.1016/j.neucom.2020.02.005 – volume: 28 start-page: 206 issue: 1 year: 2017 ident: 10.1016/j.neucom.2021.03.075_b0090 article-title: Global mittag-leffler stabilization of fractional-order memristive neural networks publication-title: IEEE Transactions on Neural Networks and Learning Systems doi: 10.1109/TNNLS.2015.2506738 – volume: 12 start-page: 145 issue: 1 year: 1999 ident: 10.1016/j.neucom.2021.03.075_b0145 article-title: On the momentum term in gradient descent learning algorithms publication-title: Neural Networks doi: 10.1016/S0893-6080(98)00116-6 |
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