Log in

End-to-end data-dependent routing in multi-path neural networks

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature extraction within a layer, which would reduce the need for mere parameter increment. The conventional widening of networks by having more filters in each layer introduces a quadratic increment of parameters. Having multiple parallel convolutional/dense operations in each layer solves this problem, but without any context-dependent allocation of input among these operations: The parallel computations tend to learn similar features making the widening process less effective. Therefore, we propose the use of multi-path neural networks with data-dependent resource allocation from parallel computations within layers, which also lets an input be routed end-to-end through these parallel paths. To do this, we first introduce a cross-prediction-based algorithm between parallel tensors of subsequent layers. Second, we further reduce the routing overhead by introducing feature-dependent cross-connections between parallel tensors of successive layers. Using image recognition tasks, we show that our multi-path networks show superior performance to existing widening and adaptive feature extraction, even ensembles and deeper networks at similar complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Canada)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

CIFAR10 and CIFAR100 datasets [58] are available at https://www.cs.toronto.edu/~kriz/cifar.html, and ILSVRC 2012 dataset [1, 21] is available at https://www.image-net.org/challenges/LSVRC/2012/

References

  1. Russakovsky O, Deng J, Su H, Krause J, Satheesh S, Ma S, Huang Z, Karpathy A, Khosla A, Bernstein M, Berg AC, Fei-Fei L (2015) ImageNet large scale visual recognition challenge. Int J Comput Vis (IJCV) 115(3):211–252. https://doi.org/10.1007/s11263-015-0816-y

    Article  MathSciNet  Google Scholar 

  2. He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR). pp 770–778

  3. He K, Zhang X, Ren S, Sun J (2016) Identity map**s in deep residual networks. European conference on computer vision (ECCV). Springer, London, pp 630–645

    Google Scholar 

  4. Romero A, Ballas N, Kahou SE, Chassang A, Gatta C, Bengio Y (2015) Fitnets: Hints for thin deep nets. In: proceedings of international conference on learning representations (ICLR)

  5. Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. ar**v preprint ar**v:1409.1556

  6. Szegedy C, Liu W, Jia Y, Sermanet P, Reed S, Anguelov D, Erhan D, Vanhoucke V, Rabinovich A (2015) Going deeper with convolutions. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pp. 1–9

  7. Zagoruyko S, Komodakis N (2016) Wide residual networks. In: proceedings of the british machine vision conference (BMVC). pp 87–18712

  8. **e S, Girshick R, Dollár P, Tu Z, He K (2017) Aggregated residual transformations for deep neural networks. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pp 1492–1500

  9. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. In: advances in neural information processing systems, pp. 1097–1105

  10. Ciregan D, Meier U, Schmidhuber J (2012) Multi-column deep neural networks for image classification. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pp. 3642–3649

  11. Wang M (2015) Multi-path convolutional neural networks for complex image classification. ar**v preprint ar**v:1506.04701

  12. Friedman JH (1991) Multivariate adaptive regression splines. Ann Statist 19(1):1–67

    MathSciNet  MATH  Google Scholar 

  13. Breiman L, Friedman JH, Olshen RA, Stone CJ (2017) Classification and regression trees. Routledge, Taylor, p 102

    Book  MATH  Google Scholar 

  14. Jacobs RA, Jordan MI, Nowlan SJ, Hinton GE (1991) Adaptive mixtures of local experts. Neural Computat 3(1):79–87

    Article  Google Scholar 

  15. Jordan MI, Jacobs RA (1994) Hierarchical mixtures of experts and the EM algorithm. Neural Computat 6(2):181–214

    Article  Google Scholar 

  16. Eigen D, Ranzato M, Sutskever I (2013) Learning factored representations in a deep mixture of experts. ar**v preprint ar**v:1312.4314

  17. Shazeer N, Mirhoseini A, Maziarz K, Davis A, Le Q, Hinton G, Dean J (2017) Outrageously large neural networks: the sparsely-gated mixture-of-experts layer. ar**v preprint ar**v:1701.06538

  18. Albawi S, Mohammed TA, Al-Zawi S (2017) Understanding of a convolutional neural network. In: 2017 international conference on engineering and technology (ICET), pp. 1–6

  19. Erhan D, Bengio Y, Courville A, Vincent P (2009) Visualizing higher-layer features of a deep network. Univ Montr 1341(3):1

    Google Scholar 

  20. Kahatapitiya K, Tissera D, Rodrigo R (2019) Context-aware automatic occlusion removal. In: 2019 IEEE international conference on image processing (ICIP), pp. 1895–1899

  21. Deng J, Dong W, Socher R, Li LJ, Li K, Fei-Fei L (2009) Imagenet: a large-scale hierarchical image database. In: 2009 IEEE conference on computer vision and pattern recognition, pp. 248–255

  22. Tissera D, Kahatapitiya K, Wijesinghe R, Fernando S, Rodrigo R (2019) Context-aware multipath networks. ar**v preprint ar**v:1907.11519

  23. Tissera D, Vithanae K, Wijesinghe R, Kahatapitiya K, Fernando S, Rodrigo R (2020) Feature-dependant cross-connections in multi-path neural networks. In: international conference on pattern recognition (ICPR), pp 4032–4039

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  26. Szegedy C, Ioffe S, Vanhoucke V, Alemi AA (2017) Inception-v4, inception-resnet and the impact of residual connections on learning. In: AAAI conference on artificial intelligence

  27. Szegedy C, Vanhoucke V, Ioffe S, Shlens J, Wojna Z (2016) Rethinking the inception architecture for computer vision. In: proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2818–2826

  28. Misra I, Shrivastava A, Gupta A, Hebert M (2016) Cross-stitch networks for multi-task learning. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pp 3994–4003

  29. Caruana R (1997) Multitask learning. Mach Learn 28(1):41–75

    Article  MathSciNet  Google Scholar 

  30. Thung K-H, Wee C-Y (2018) A brief review on multi-task learning. Multimed Tools Appl 77(22):29705–29725

    Article  Google Scholar 

  31. Crawshaw M (2020) Multi-task learning with deep neural networks: a survey. ar**v preprint ar**v:2009.09796

  32. Ruder S, Bingel J, Augenstein I, Søgaard A (2019) Latent multi-task architecture learning. In: proceedings of AAAI conference of artificial intelligence. pp 4822–4829

  33. Gao Y, Ma J, Zhao M, Liu W, Yuille AL (2019) Nddr-cnn: Layerwise feature fusing in multi-task cnns by neural discriminative dimensionality reduction. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR). pp 3205–3214

  34. Ha D, Dai A, Le QV (2017) Hypernetworks. In: proceedings of international conference on learning representations (ICLR)

  35. Cai S, Shu Y, Wang W (2021) Dynamic routing networks. In: proceedings of the IEEE/CVF winter conference on applications of computer vision. pp 3588–3597

  36. Hinton GE, Sabour S, Frosst N (2018) Matrix capsules with EM routing. In: proceedings of international conference on learning representations (iclr)

  37. Hu J, Shen L, Albanie S, Sun G, Vedaldi A (2018) Gather-excite: Exploiting feature context in convolutional neural networks. In: advances in neural information processing systems. pp 9401–9411

  38. Hu J, Shen L, Sun G (2018) Squeeze-and-excitation networks. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR). pp 7132–7141

  39. Sabour S, Frosst N, Hinton GE (2017) Dynamic routing between capsules. In: advances in neural information processing systems, pp. 3856–3866

  40. Wang Q, Wu B, Zhu P, Li P, Zuo W, Hu Q (2019) Eca-net: efficient channel attention for deep convolutional neural networks. ar**v preprint ar**v:1910.03151

  41. Veit A, Belongie S (2018) Convolutional networks with adaptive inference graphs. In: European conference on computer vision. pp 3–18

  42. Wu Z, Nagarajan T, Kumar A, Rennie S, Davis LS, Grauman K, Feris R (2018) Blockdrop: Dynamic inference paths in residual networks. In: proceedings of the IEEE conference on computer vision and pattern recognition (CVPR). pp 8817–8826

  43. Srivastava RK, Greff K, Schmidhuber J (2015) Highway networks. ar**v preprint ar**v:1505.00387

  44. Rao Y, Lu J, Lin J, Zhou J (2018) Runtime network routing for efficient image classification. IEEE Trans Patt Anal Mach Intell 41(10):2291–2304

    Article  Google Scholar 

  45. Wang X, Yu F, Dou ZY, Darrell T, Gonzalez JE (2018) Skipnet: Learning dynamic routing in convolutional networks. In: proceedings of the European conference on computer vision (ECCV), pp. 409–424

  46. Chen B, Zhao T, Liu J, Lin L (2021) Multipath feature recalibration densenet for image classification. Int J Mach Learn Cybernet 12(3):651–660

    Article  Google Scholar 

  47. Zhang H, Wu C, Zhang Z, Zhu Y, Lin H, Zhang Z, Sun Y, He T, Mueller J, Manmatha R, et al. (2022) Resnest: split-attention networks. In: proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 2736–2746

  48. Yu K, Wang X, Dong C, Tang X, Loy CC (2021) Path-restore: learning network path selection for image restoration. IEEE Trans Patt Anal Mach Intell 44(10):7078–7092

    Article  Google Scholar 

  49. Huang G, Liu Z, Van Der Maaten L, Weinberger KQ (2017) Densely connected convolutional networks. In: proceedings of the IEEE conference on computer vision and pattern recognition. pp 4700–4708

  50. Srivastava RK, Greff K, Schmidhuber J (2015) Training very deep networks. Adv Neural Inf Process Syst 28:2377–2385

    Google Scholar 

  51. Fedus W, Dean J, Zoph B (2022) A review of sparse expert models in deep learning. ar**v preprint ar**v:2209.01667

  52. Chen Z, Deng Y, Wu Y, Gu Q, Li Y (2022) Towards understanding mixture of experts in deep learning. ar**v preprint ar**v:2208.02813

  53. Lepikhin D, Lee H, Xu Y, Chen D, Firat O, Huang Y, Krikun M, Shazeer N, Chen Z (2020) Gshard: Scaling giant models with conditional computation and automatic sharding. ar**v preprint ar**v:2006.16668

  54. Fedus W, Zoph B, Shazeer N (2021) Switch transformers: scaling to trillion parameter models with simple and efficient sparsity. J Mach Learn Res 23:1–40

    MathSciNet  Google Scholar 

  55. Riquelme C, Puigcerver J, Mustafa B, Neumann M, Jenatton R, Susano Pinto A, Keysers D, Houlsby N (2021) Scaling vision with sparse mixture of experts. Adv Neural Inf Process Syst 34:8583–8595

    Google Scholar 

  56. Wu L, Liu M, Chen Y, Chen D, Dai X, Yuan L (2022) Residual mixture of experts. ar**v preprint ar**v:2204.09636

  57. Glorot X, Bordes A, Bengio Y (2011) Deep sparse rectifier neural networks. In: proceedings of the fourteenth international conference on artificial intelligence and statistics. pp 315–323

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

    Google Scholar 

  59. Ha D, Dai A, Le QV (2016) Hypernetworks. ar**v preprint ar**v:1609.09106

  60. Facebook: fb.resnet.torch. Github. https://github.com/facebookarchive/fb.resnet.torch

  61. Simonyan K, Vedaldi A, Zisserman A (2013) Deep inside convolutional networks: visualising image classification models and saliency maps. ar**v preprint ar**v:1312.6034

Download references

Funding

This research is funded by CODEGEN International (Pvt) Ltd, Sri Lanka.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dumindu Tissera.

Ethics declarations

Competing Interests

The authors have no competing interests to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tissera, D., Wijesinghe, R., Vithanage, K. et al. End-to-end data-dependent routing in multi-path neural networks. Neural Comput & Applic 35, 12655–12674 (2023). https://doi.org/10.1007/s00521-023-08381-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-023-08381-8

Keywords

Navigation