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Balanced Gradient Training of Feed Forward Networks

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Abstract

We show that there are infinitely many valid scaled gradients which can be used to train a neural network. A novel training method is proposed that finds the best scaled gradients in each training iteration. The method’s implementation uses first order derivatives which makes it scalable and suitable for deep learning and big data. In simulations, the proposed method has similar or less testing error than conjugate gradient and Levenberg Marquardt. The method reaches the final network utilizing fewer multiplies than the other two algorithms. It also works better than conjugate gradient in convolutional neural networks.

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References

  1. Akram M Usman, Usman Anam (2011) Computer aided system for brain tumor detection and segmentation. In: 2011 International Conference on Computer Networks and Information Technology (ICCNIT). pp 299–302 IEEE

  2. Atkinson PM, Tatnall ARL (1997) Introduction neural networks in remote sensing. Int J Remote Sens 18(4):699–709

    Article  Google Scholar 

  3. Auddy S S, Tyagi K, Nguyen S, Manry M (2016) Discriminant vector tranformations in neural network classifiers. In: 2016 International Joint Conference on Neural Networks (IJCNN)

  4. Baxt WG (1991) Use of an artificial neural network for the diagnosis of myocardial infarction. Ann Intern Med 115(11):843–848

    Article  Google Scholar 

  5. Beck C, Weinan E, Jentzen A (2019) Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. J Nonlinear Sci 29(4):1563–1619

    Article  MathSciNet  Google Scholar 

  6. Bhandarkar SM, Koh J, Suk M (1997) Multiscale image segmentation using a hierarchical self-organizing map. Neurocomputing 14(3):241–272

    Article  Google Scholar 

  7. Bishop CM (2006) Pattern recognition and machine learning. Springer, Berlin

    MATH  Google Scholar 

  8. Blackard JA, Dean DJ (1999) Comparative accuracies of artificial neural networks and discriminant analysis in predicting forest cover types from cartographic variables. Comput Electron Agric 24(3):131–151

    Article  Google Scholar 

  9. Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, England

    Book  Google Scholar 

  10. Brause Rüdiger W (2001) Medical analysis and diagnosis by neural networks. In: International Symposium on Medical Data Analysis. pp 1–13 Springer

  11. Dai T, Cai J, Zhang Y, Xia ST, Zhang L (2019) Second-order attention network for single image super-resolution. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 11065–11074

  12. Eapi GR (2015) Comprehensive neural network forecasting system for ground level ozone in multiple regions. Ph.D. dissertation, The University of Texas at Arlington

  13. Economou G-PK, Spiropoulos C, Economopoulos NM, Charokopos N, Lymberopoulos D, Spiliopoulou M, Haralambopulu E, Goutis CE (1994) Medical diagnosis and artificial neural networks: a medical expert system applied to pulmonary diseases. In: Neural Networks for Signal Processing [1994] IV. Proceedings of the 1994 IEEE Workshop. pp 482–489 IEEE

  14. Egmont-Petersen M, de Ridder D, Handels H (2002) Image processing with neural networks a review. Pattern Recogn 35(10):2279–2301

    Article  Google Scholar 

  15. Gill PE, Murray W (1979) Conjugate-Gradient methods for large-scale nonlinear optimization. Technical report, Standford Univ Calif Systems Optimization LAB

  16. Goodfellow I, Bengio Y, Courville A (2016) Deep Learn. MIT press, USA

    MATH  Google Scholar 

  17. Gore RG, Li J, Manry M, Liu L-M, Changhua Yu, Wei J (2005) Iterative design of neural network classifiers through regression. Int J Artif Intell Tools 14(01n02):281–301

    Article  Google Scholar 

  18. Hamidieh K (2018) A data-driven statistical model for predicting the critical temperature of a superconductor. Comput Mater Sci 154:346–354

    Article  Google Scholar 

  19. Ho Y-C, Kashyap RL (1965) An algorithm for linear inequalities and its applications. IEEE Transactions on Electronic Computers 5:683–688

    Article  Google Scholar 

  20. Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2(5):359–366

    Article  Google Scholar 

  21. Kavzoglu T, Mather PM (1999) Pruning artificial neural networks: an example using land cover classification of multi-sensor images. Int J Remote Sens 20(14):2787–2803

    Article  Google Scholar 

  22. Krizhevsky A, Hinton G (2009) Learning multiple layers of features from tiny images. Technical report, Citeseer

  23. Kulluk S, Ozbakir L, Baykasoglu A (2012) Training neural networks with harmony search algorithms for classification problems. Eng Appl Artif Intell 25(1):11–19

    Article  Google Scholar 

  24. Le QV, Ngiam J, Coates A, Lahiri A, Prochnow Bobby, Ng Andrew Y (2011) On optimization methods for deep learning. In: Proceedings of the 28th International Conference on International Conference on Machine Learning. pp 265–272 Omnipress

  25. LeCun Y, Bengio Y et al (1995) Convolutional networks for images, speech, and time series. Handb Brain Theor Neural Netw 3361(10):1995

    Google Scholar 

  26. LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324

    Article  Google Scholar 

  27. LeCun Y A, Bottou Léon, Orr Genevieve B, Müller Klaus-Robert (2012) Efficient backprop. In: Neural networks: Tricks of the trade. pp 9–48 Springer

  28. Lee KY, Cha YT, Park JH (1992) Short-term load forecasting using an artificial neural network. IEEE Trans Power Syst 7(1):124–132

    Article  Google Scholar 

  29. Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Q Appl Math 2(2):164–168

    Article  MathSciNet  Google Scholar 

  30. Lin JT, Inigo R (1991) Hand written zip code recognition by back propagation neural network. In: IEEE Proceedings of Southeastcon’91. pp 731–735 IEEE

  31. Liu K, Subbarayan S, Shoults RR, Manry M, Kwan C, Lewis FI, Naccarino J (1996) Comparison of very short-term load forecasting techniques. IEEE Trans Power Syst 11(2):877–882

    Article  Google Scholar 

  32. Liu LM, Manry M, Amar F, Dawson MS, Fung AK (1994) Image classification in remote sensing using functional link neural networks. In: Proceedings of the IEEE southwest symposium on image analysis and interpretation. pp 54–58 IEEE

  33. Luxhøj JT (1998) An artificial neural network for nonlinear estimation of the turbine flow-meter coefficient. Eng Appl Artif Intell 11(6):723–734

    Article  Google Scholar 

  34. Manry M, Dawson MS, Fung AK, Apollo SJ, Allen LS, Lyle WD, Gong W (1994) Fast training of neural networks for remote sensing. Remote Sens Rev 9(1–2):77–96

    Article  Google Scholar 

  35. Morgan N, Bourlard HA (1995) Neural networks for statistical recognition of continuous speech. Proc IEEE 83(5):742–772

    Article  Google Scholar 

  36. Nazeer Shahrin Azuan, Omar Nazaruddin, Marzuki Khalid (2007) Face recognition system using artificial neural networks approach. In: 2007 International Conference on Signal Processing, Communications and Networking. pp 420–425 IEEE

  37. Netzer Y, Wang T, Coates A, Bissacco A, Wu B, Ng AY (2011) Reading digits in natural images with unsupervised feature learning. NIPS Workshop on Deep Learning and Unsupervised Feature Learning

  38. Nguyen S (2019) Affine invariance in multilayer perceptron training. Ph.D. dissertation, The University of Texas at Arlington

  39. Nguyen Son, Tyagi Kanishka, Kheirkhah Parastoo, Manry Michael (2016) Partially affine invariant back propagation. In: 2016 International Joint Conference on Neural Networks (IJCNN). pp 811–818 IEEE

  40. Yisok O, Sarabandi K, Ulaby FT (1992) An empirical model and an inversion technique for radar scattering from bare soil surfaces. IEEE Trans Geosci Remote Sens 30(2):370–381

    Article  Google Scholar 

  41. Osawa K, Tsuji Y, Ueno Y, Naruse A, Yokota R, Matsuoka S (2019) Large-scale distributed second-order optimization using kronecker-factored approximate curvature for deep convolutional neural networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition pp 12359–12367

  42. Oz C, Leu MC (2011) American sign language word recognition with a sensory glove using artificial neural networks. Eng Appl Artif Intell 24(7):1204–1213

    Article  Google Scholar 

  43. Parisini T, Zoppoli R (1994) Neural networks for nonlinear state estimation. Int J Robust Nonlinear Control 4(2):231–248

    Article  MathSciNet  Google Scholar 

  44. Patra JC, Panda G, Baliarsingh R (1994) Artificial neural network-based nonlinearity estimation of pressure sensors. IEEE Trans Instrum Meas 43(6):874–881

    Article  Google Scholar 

  45. Polak S, Skowron A, Brandys J, Mendyk A (2008) Artificial neural networks based modeling for pharmacoeconomics application. Appl Math Comput 203(2):482–492

    MathSciNet  MATH  Google Scholar 

  46. Raudys S (2012) Statistical and neural classifiers: an integrated approach to design. Springer, Berlin

    MATH  Google Scholar 

  47. Robinson MD, Manry M, Malalur SS, Changhua Yu (2017) Properties of a batch training algorithm for feedforward networks. Neural Process Lett 45(3):841–854

    Article  Google Scholar 

  48. Rosenbrock HH (1960) An automatic method for finding the greatest or least value of a function. Comput J 3(3):175–184

    Article  MathSciNet  Google Scholar 

  49. Rui Yong, El-Keib AA (1995) A review of ann-based short-term load forecasting models. In: Proceedings of the Twenty-Seventh Southeastern Symposium on System Theory, 1995. pp 78–82 IEEE

  50. Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323(6088):533–536

    Article  Google Scholar 

  51. Saifullah Y, Manry M (1993) Classification-based segmentation of zip codes. IEEE Trans Syst, Man, Cybern 23(5):1437–1443

    Article  Google Scholar 

  52. Shepherd AJ (1996) Second-order methods for neural networks fast and reliable training methods for multi-layer perceptrons, chapter 1. Multi-layer perceptron training, 1st edn. Springer, Berlin, pp 1–22

    Google Scholar 

  53. Tyagi K, Manry M (2018) Multi-step training of a generalized linear classifier. Neural Process Lett 50(2):1341–1360

    Article  Google Scholar 

  54. Tyagi K, Nguyen S, Rawat R, Manry M (2019) Second order training and sizing for the multilayer perceptron. Neural Process Lett 51(1):963–991

    Article  Google Scholar 

  55. Voultsidou M, Dodel S, Herrmann JM (2005) Neural networks approach to clustering of activity in fmri data. IEEE Trans Med Imaging 24(8):987–996

    Article  Google Scholar 

  56. Wang J, Huang J (2001) Neural network enhanced output regulation in nonlinear systems. Automatica 37(8):1189–1200

    Article  MathSciNet  Google Scholar 

  57. Werbos P (1974) Beyond regression: new tools for prediction and analysis in the behavioral sciences. Ph.D. dissertation, Harvard University

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Nguyen, S., Manry, M.T. Balanced Gradient Training of Feed Forward Networks. Neural Process Lett 53, 1823–1844 (2021). https://doi.org/10.1007/s11063-021-10474-1

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