Advertisement

Training Very Deep Networks via Residual Learning with Stochastic Input Shortcut Connections

  • Oyebade K. OyedotunEmail author
  • Abd El Rahman Shabayek
  • Djamila Aouada
  • Björn Ottersten
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10635)

Abstract

Many works have posited the benefit of depth in deep networks. However, one of the problems encountered in the training of very deep networks is feature reuse; that is, features are ‘diluted’ as they are forward propagated through the model. Hence, later network layers receive less informative signals about the input data, consequently making training less effective. In this work, we address the problem of feature reuse by taking inspiration from an earlier work which employed residual learning for alleviating the problem of feature reuse. We propose a modification of residual learning for training very deep networks to realize improved generalization performance; for this, we allow stochastic shortcut connections of identity mappings from the input to hidden layers. We perform extensive experiments using the USPS and MNIST datasets. On the USPS dataset, we achieve an error rate of 2.69% without employing any form of data augmentation (or manipulation). On the MNIST dataset, we reach a comparable state-of-the-art error rate of 0.52%. Particularly, these results are achieved without employing any explicit regularization technique.

Keywords

Deep neural networks Residual learning Dropout Optimization 

Notes

Acknowledgments

This work was funded by the National Research Fund (FNR), Luxembourg, under the project reference R-AGR-0424-05-D/Björn Ottersten.

References

  1. 1.
    Oyedotun, O.K., Khashman, A.: Deep learning in vision-based static hand gesture recognition. Neural Comput. Appl. 27(3), 1–11 (2016)Google Scholar
  2. 2.
    Oyedotun, O.K., Khashman, A.: Banknote recognition: investigating processing and cognition framework using competitive neural network. Cogn. Neurodyn. 11(1), 67–79 (2017)CrossRefGoogle Scholar
  3. 3.
    Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Netw. 4(2), 251–257 (1991)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Funahashi, K.I.: On the approximate realization of continuous mappings by neural networks. Neural Netw. 2(3), 183–192 (1989)CrossRefGoogle Scholar
  5. 5.
    Delalleau, O., Bengio, Y.: Shallow vs. deep sum-product networks. In: Advances in Neural Information Processing Systems, pp. 666–674 (2011)Google Scholar
  6. 6.
    Mhaskar, H., Liao, Q., Poggio, T.: Learning functions: When is deep better than shallow. arXiv preprint (2016). arXiv:1603.00988
  7. 7.
    Bianchini, M., Scarselli, F.: On the complexity of neural network classifiers: a comparison between shallow and deep architectures. IEEE Trans. Neural Netw. Learn. Syst. 25(8), 1553–1565 (2014)CrossRefGoogle Scholar
  8. 8.
    Wan, L., Zeiler, M., Zhang, S., Cun, Y.L., Fergus, R.: Regularization of neural networks using dropconnect. In: Proceedings of the 30th International Conference on Machine Learning (ICML-2013), pp. 1058–1066 (2013)Google Scholar
  9. 9.
    Graham, B.: Fractional max-pooling. arXiv preprint (2014). arXiv:1412.6071
  10. 10.
    Clevert, D.A., Unterthiner, T., Hochreiter, S.: Fast and accurate deep network learning by exponential linear units (ELUs), arXiv preprint, arXiv:1511.07289 (2015)
  11. 11.
    Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition, arXiv preprint, arXiv:1409.1556 (2014)
  12. 12.
    Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., et al.: Going deeper with convolutions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–9 (2015)Google Scholar
  13. 13.
    Srivastava, R.K., Greff, K., Schmidhuber, J.: Training very deep networks. In: Advances in Neural Information Processing Systems, pp. 2377–2385 (2015)Google Scholar
  14. 14.
    He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016)Google Scholar
  15. 15.
    He, K., Zhang, X., Ren, S., Sun, J.: Delving deep into rectifiers: surpassing human-level performance on imagenet classification. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1026–1034 (2015)Google Scholar
  16. 16.
    Glorot, X., Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks. AISTATS 9, 249–256 (2010)Google Scholar
  17. 17.
    Ioffe, S., Szegedy, C.: Batch normalization: accelerating deep network training by reducing internal covariate shift, arXiv preprint, arXiv:1502.03167 (2015)
  18. 18.
    He, K., Zhang, X., Ren, S., Sun, J.: Identity mappings in deep residual networks. In: European Conference on Computer Vision, pp. 630–645 (2016)Google Scholar
  19. 19.
    Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(1), 1929–1958 (2014)zbMATHMathSciNetGoogle Scholar
  20. 20.
    Schlkopf, B., Simard, P., Smola, A., Vapnik, V.: Prior knowledge in support vector Kernels. In: Proceedings of the 10th International Conference on Neural Information Processing Systems, pp. 640–646 (1997)Google Scholar
  21. 21.
    Simard, P.Y., LeCun, Y.A., Denker, J.S., Victorri, B.: Transformation invariance in pattern recognition – tangent distance and tangent propagation. In: Montavon, G., Orr, G.B., Müller, K.-R. (eds.) Neural Networks: Tricks of the Trade. LNCS, vol. 7700, pp. 235–269. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-35289-8_17 CrossRefGoogle Scholar
  22. 22.
    Wu, M., Schlkopf, B., Bakir, G.: Building sparse large margin classifiers. In: Proceedings of the 22nd International Conference on Machine Learning, pp. 996–1003 (2005)Google Scholar
  23. 23.
    Trottier, L., Chaib-draa, B., Giguère, P.: Incrementally built dictionary learning for sparse representation. In: Arik, S., Huang, T., Lai, W.K., Liu, Q. (eds.) ICONIP 2015. LNCS, vol. 9489, pp. 117–126. Springer, Cham (2015). doi: 10.1007/978-3-319-26532-2_14 CrossRefGoogle Scholar
  24. 24.
    Simard, P., LeCun, Y., Denker, J.S.: Efficient pattern recognition using a new transformation distance. In: Advances in Neural Information Processing Systems, pp. 50–58 (1993)Google Scholar
  25. 25.
    Keysers, D., Dahmen, J., Theiner, T., Ney, H.: Experiments with an extended tangent distance. In: 15th International Conference on Pattern Recognition, Proceedings, vol. 2, pp. 38–42 (2000)Google Scholar
  26. 26.
    Yang, J., Yu, K., Huang, T.: Supervised translation-invariant sparse coding. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3517–3524 (2010)Google Scholar
  27. 27.
    Yang, Z., Moczulski, M., Denil, M., de Freitas, N., Smola, A., Song, L., Wang, Z.: Deep fried convnets. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1476–1483 (2015)Google Scholar
  28. 28.
    Chan, T.H., Jia, K., Gao, S., Lu, J., Zeng, Z., Ma, Y.: Pcanet: a simple deep learning baseline for image classification? IEEE Trans. Image Process. 24(12), 5017–5032 (2015)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Lin, M., Chen, Q., Yan, S.: Network in network. In: International Conference on Learning Representations, abs/1312.4400 (2014)Google Scholar
  30. 30.
    Lee, C.Y., Xie, S., Gallagher, P., Zhang, Z., Tu, Z.: Deeply-supervised nets. In: Artificial Intelligence and Statistics, pp. 562–570 (2015)Google Scholar
  31. 31.
    Ngiam, J., Coates, A., Lahiri, A., Prochnow, B., Le, Q.V., Ng, A.Y.: On optimization methods for deep learning. In: Proceedings of the 28th International Conference on Machine Learning (ICML-2011), pp. 265–272 (2011)Google Scholar
  32. 32.
    Goodfellow, I.J., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples. In: International Conference on Learning Representations, arXiv preprint, arXiv:1412.6572 (2015)
  33. 33.
    Huang, G., Sun, Y., Liu, Z., Sedra, D., Weinberger, K.Q.: Deep networks with stochastic depth. In: European Conference on Computer Vision, pp. 646–661 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Oyebade K. Oyedotun
    • 1
    Email author
  • Abd El Rahman Shabayek
    • 1
  • Djamila Aouada
    • 1
  • Björn Ottersten
    • 1
  1. 1.Interdisciplinary Centre for Security, Reliability and Trust (SnT)University of LuxembourgLuxembourg CityLuxembourg

Personalised recommendations