Skip to main content
Springer Nature Link
Log in

P + FELU: Flexible and trainable fast exponential linear unit for deep learning architectures

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

Abstract

Activation functions have an important role in obtaining the most appropriate output by processing the information coming into the network in deep learning architectures. Deep learning architectures are widely used in areas such as image processing applications, time series, and disease classification, generally in line with the analysis of large and complex data. Choosing the appropriate architecture and activation function is an important factor in achieving successful learning and classification performance. There are many studies to improve the performance of deep learning architectures and to overcome the disappearing gradient and negative region problems in activation functions. A flexible and trainable fast exponential linear unit (P + FELU) activation function is proposed to overcome existing problems. With the proposed P + FELU activation function, a higher success rate and faster calculation time can be achieved by incorporating the advantages of fast exponentially linear unit (FELU), exponential linear unit (ELU), and rectified linear unit (RELU) activation functions. Performance evaluations of the proposed P + FELU activation function were made on MNIST, CIFAR-10, and CIFAR-100 benchmark datasets. Experimental evaluations have shown that the proposed activation function outperforms the ReLU, ELU, SELU, MPELU, TReLU, and FELU activation functions and effectively improves the noise robustness of the network. Experimental results show that this activation function with “flexible and trainable” properties can effectively prevent vanishing gradient and make multilayer perceptron neural networks deeper.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

1. References

  1. Adem K (2018) Exudate detection for diabetic retinopathy with circular Hough transformation and convolutional neural networks. Expert Syst Appl 114:289–295

    Article  Google Scholar 

  2. Adem K, Közkurt C (2019) Defect detection of seals in multilayer aseptic packages using deep learning. Turk J Electr Eng Comput Sci 27(6):4220–4230

    Article  Google Scholar 

  3. Bawa VS, Kumar V (2019) Linearized sigmoidal activation: A novel activation function with tractable non-linear characteristics to boost representation capability. Expert Syst Appl 120:346–356

    Article  Google Scholar 

  4. Clevert, D. A., Unterthiner, T., & Hochreiter, S. (2015). Fast and accurate deep network learning by exponential linear units (Elus). 

  5. Gao H, Xu K, Cao M, Xiao J, Xu Q, Yin Y (2021) The deep features and attention mechanism-based method to dish healthcare under social IoT systems: an empirical study with a hand-deep local-global net. IEEE Transact Comput Soc Syst 9(1):336–347

    Article  Google Scholar 

  6. Glorot, X., & Bengio, Y. (2010, March). Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth int conf on art intell stat JMLR Workshop and Conference Proceedings: 249–256)

  7. Godfrey LB (2019) An evaluation of parametric activation functions for deep learning. In IEEE Int Conf Syst, Man Cybern (SMC) IEEE, pp 3006–3011

    Google Scholar 

  8. Godin F, Degrave J, Dambre J, De Neve W (2018) Dual rectified linear units (DReLUs): A replacement for tanh activation functions in quasi-recurrent neural networks. Pattern Recogn Lett 116:8–14

    Article  Google Scholar 

  9. Gupta, S., & Dinesh, D. A. (2017). Resource usage prediction of cloud workloads using deep bidirectional long short term memory networks. In 2017 IEEE international conference on advanced networks and telecommunications systems (ANTS): 1–6 IEEE.

  10. He, K., Zhang, X., Ren, S., & Sun, J. (2015). Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision: 1026–1034

  11. Huizhen ZHAO, Fuxian L, Longyue L (2018) A novel softplus linear unit for deep CNN. J Harbin Inst Technol 50(4):117–123

    Google Scholar 

  12. Kiliçarslan S, Celik M (2021) RSigELU: A nonlinear activation function for deep neural networks. Expert Syst Appl 174:114805

    Article  Google Scholar 

  13. Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv preprint .

  14. Kiseľák J, Lu Y, Švihra J, Szépe P, Stehlík M (2021) “SPOCU”: scaled polynomial constant unit activation function. Neural Comput Appl 33(8):3385–3401

    Article  Google Scholar 

  15. LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  16. LeCun, Y., Boser, B., Denker, J., Henderson, D., Howard, R., Hubbard, W., & Jackel, L. (1989). Handwritten digit recognition with a back-propagation network. Advances in neural information processing systems 2

  17. Lee, J., Shridhar, K., Hayashi, H., Iwana, B. K., Kang, S., & Uchida, S. (2019). Probact: A probabilistic activation function for deep neural networks. arXiv preprint  5, 13

  18. Li Y, Fan C, Li Y, Wu Q, Ming Y (2018) Improving deep neural network with multiple parametric exponential linear units. Neurocomputing 301:11–24

    Article  Google Scholar 

  19. Livieris IE, Pintelas E, Pintelas P (2020) A CNN–LSTM model for gold price time-series forecasting. Neural Comput Appl 32(23):17351–17360

    Article  Google Scholar 

  20. Maas, A. L., Hannun, A. Y., & Ng, A. Y. (2013, June). Rectifier nonlinearities improve neural network acoustic models. In Proc Icml 30(1): 3

  21. Nair, V., & Hinton, G. E. (2010, January). Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th international conference on machine learning (Icml): 807–814

  22. Ozguven MM, Adem K (2019) Automatic detection and classification of leaf spot disease in sugar beet using deep learning algorithms. Physica A 535:122537

    Article  Google Scholar 

  23. Pacal I, Karaboga D (2021) A Robust Real-Time Deep Learning Based Automatic Polyp Detection System. Comput Biol Med 134:104519

    Article  Google Scholar 

  24. Qiumei Z, Dan T, Fenghua W (2019) Improved convolutional neural network based on fast exponentially linear unit activation function. Ieee Access 7:151359–151367

    Article  Google Scholar 

  25. Ramachandran, P., Zoph, B., & Le, Q. V. (2017). Searching for activation functions. arXiv preprint .

  26. Simonyan, K., & Zisserman, A. (2014). Very deep convolutional networks for large-scale image recognition. arXiv preprint .

  27. Trottier, L., Giguere, P., & Chaib-Draa, B. (2017, December). Parametric exponential linear unit for deep convolutional neural networks. In 2017 16th IEEE International Conference on Machine Learning and Applications (ICMLA): 207–214 IEEE

  28. Wang X, Qin Y, Wang Y, Xiang S, Chen H (2019) ReLTanh: An activation function with vanishing gradient resistance for SAE-based DNNs and its application to rotating machinery fault diagnosis. Neurocomputing 363:88–98

    Article  Google Scholar 

  29. Wang Y, Li Y, Song Y, Rong X (2020) The influence of the activation function in a convolution neural network model of facial expression recognition. Appl Sci 10(5):1897

    Article  Google Scholar 

  30. Xiao J, Xu H, Gao H, Bian M, Li Y (2021) A weakly supervised semantic segmentation network by aggregating seed cues: the multi-object proposal generation perspective. ACM Transact Multimidia Comput Communicat Appl 17(1s):1–19

    Article  Google Scholar 

  31. Zhang T, Yang J, Song WA, Song CF (2019) Research on improved activation function TReLU. J Chinese Comput Syst 40(1):58–63

    MathSciNet  Google Scholar 

  32. Zhou Y, Li D, Huo S, Kung SY (2021) Shape autotuning activation function. Expert Syst Appl 171:114534

    Article  Google Scholar 

  33. Zhu H, Zeng H, Liu J, Zhang X (2021) Logish: A new nonlinear nonmonotonic activation function for convolutional neural network. Neurocomputing 458:490–499

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sivas University of Science and Technology, Department of Computer Engineering, Sivas, Turkey

    Kemal Adem

Authors
  1. Kemal Adem
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Kemal Adem.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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 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

Adem, K. P + FELU: Flexible and trainable fast exponential linear unit for deep learning architectures. Neural Comput & Applic 34, 21729–21740 (2022). https://doi.org/10.1007/s00521-022-07625-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-022-07625-3

Keywords