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Fast Dynamic Routing Based on Weighted Kernel Density Estimation

  • Suofei ZhangEmail author
  • Quan Zhou
  • Xiaofu Wu
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 810)

Abstract

Capsules as well as dynamic routing between them are most recently proposed structures for deep neural networks. A capsule groups data into vectors or matrices as poses rather than conventional scalars to represent specific properties of target instance. Besides of pose, a capsule should be attached with a probability (often denoted as activation) for its presence. The dynamic routing helps capsules achieve more generalization capacity with many fewer model parameters. However, the bottleneck that prevents widespread applications of capsule is the expense of computation during routing. To address this problem, we generalize existing routing methods within the framework of weighted kernel density estimation, and propose a fast routing methods. Our method prompts the time efficiency of routing by nearly 40% with negligible performance degradation. By stacking a hybrid of convolutional layers and capsule layers, we construct a network architecture to handle inputs at a resolution of \(64\times {64}\) pixels. The proposed models achieve a parallel performance with other leading methods in multiple benchmarks.

Keywords

Capsule Dynamic-routing Clustering Deep-learning 

Notes

Acknowledgements

This work was supported by the Chinese National Natural Science Foundation (Grant No. 61701252, 61881240048), Natural Science Foundation in Universities on Jiangsu Province (16KJB510032) and HIRP Open 2018 Project of Huawei.

References

  1. 1.
    Alain, G., Bengio, Y.: Understanding Intermediate Layers using Linear Classifier Probes. arXiv:1610.01644 (2016)
  2. 2.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the em algorithm. J. R. Stat. Soc. Series B (methodological), 1–38 (1977)Google Scholar
  3. 3.
    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
  4. 4.
    Hinton, G.E., Krizhevsky, A., Wang, S.D.: Transforming auto-encoders. In: International Conference on Artificial Neural Networks, pp. 44–51. Springer (2011)Google Scholar
  5. 5.
    Hinton, G.E., Sabour, S., Frosst, N.: Matrix capsules with em routing. In: ICLR 2018 Conference. p. accepted (2018)Google Scholar
  6. 6.
    Krizhevsky, A., Hinton, G.: Learning Multiple Layers of Features from Tiny Images (2009)Google Scholar
  7. 7.
    LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521(7553), 436 (2015)CrossRefGoogle Scholar
  8. 8.
    LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRefGoogle Scholar
  9. 9.
    LeCun, Y., Huang, F.J., Bottou, L.: Learning methods for generic object recognition with invariance to pose and lighting. In: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004, vol. 2, pp. II–104. IEEE (2004)Google Scholar
  10. 10.
    Lu, H., Li, B., Zhu, J., Li, Y., Li, Y., Xu, X., He, L., Li, X., Li, J., Serikawa, S.: Wound intensity correction and segmentation with convolutional neural networks. Concurr. Comput. Pract. Exp. 29(6) (2016)Google Scholar
  11. 11.
    Lu, H., Li, Y., Chen, M., Kim, H., Serikawa, S.: Brain intelligence: go beyond artificial intelligence. Mob. Netw. Appl. 23(2), 368–375 (2018)CrossRefGoogle Scholar
  12. 12.
    Lu, H., Li, Y., Mu, S., Wang, D., Kim, H., Serikawa, S.: Motor anomaly detection for unmanned aerial vehicles using reinforcement learning. IEEE Internet Things J. PP(99), 1–1 (2017)Google Scholar
  13. 13.
    Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A.C., Fei-Fei, L.: Image net large scale visual recognition challenge. Int. J. Comput. Vis. (IJCV) 115(3), 211–252 (2015).  https://doi.org/10.1007/s11263-015-0816-yCrossRefGoogle Scholar
  14. 14.
    Sabour, S., Frosst, N., Hinton, G.E.: Dynamic routing between capsules. In: Advances in Neural Information Processing Systems, pp. 3859–3869 (2017)Google Scholar
  15. 15.
    Serikawa, S., Lu, H.: Underwater Image Dehazing using Joint Trilateral Filter. Pergamon Press Inc. (2014)Google Scholar
  16. 16.
    Xiao, H., Rasul, K., Vollgraf, R.: Fashion-mnist: A Novel Image Dataset for Benchmarking Machine Learning Algorithms (2017)Google Scholar
  17. 17.
    Xu, X., He, L., Lu, H., Gao, L., Ji, Y.: Deep adversarial metric learning for cross-modal retrieval. In: World Wide Web-Internet & Web Information Systems, pp. 1–16 (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Nanjing University of Posts and TelecommunicationsNanjingChina

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