Parametric Flatten-T Swish: An Adaptive Nonlinear Activation Function for Deep Learning
DOI:
https://doi.org/10.32890/jict2021.20.1.2Keywords:
Activation function, deep learning, Flatten-T Swish, non-linearity, ReLUAbstract
QActivation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community. However, ReLU contains several shortcomings that can result in inefficient training of the deep neural networks, these are: 1) the negative cancellation property of ReLU tends to treat negative inputs as unimportant information for the learning, resulting in performance degradation; 2) the inherent predefined nature of ReLU is unlikely to promote additional flexibility, expressivity, and robustness to the networks; 3) the mean activation of ReLU is highly positive and leads to bias shift effect in network layers; and 4) the multilinear structure of ReLU restricts the non-linear approximation power of the networks. To tackle these shortcomings, this paper introduced Parametric Flatten-T Swish (PFTS) as an alternative to ReLU. By taking ReLU as a baseline method, the experiments showed that PFTS improved classification accuracy on SVHN dataset by 0.31%, 0.98%, 2.16%, 17.72%, 1.35%, 0.97%, 39.99%, and 71.83% on DNN-3A, DNN-3B, DNN-4, DNN-5A, DNN-5B, DNN-5C, DNN-6, and DNN-7, respectively. Besides, PFTS also achieved the highest mean rank among the comparison methods. The proposed PFTS manifested higher non-linear approximation power during training and thereby improved the predictive performance of the networks.
References
Agostinelli, F., Hoffman, M., Sadowski, P., & Baldi, P. (2015). Learning activation functions to improve deep neural networks. Workshop Track Proceedings of the 3rd International Conference on Learning Representations (ICLR). CoRR. https://arxiv.org/abs/1412.6830
Alcantara, G. (2017). Empirical analysis of non-linear activation functions for Deep Neural Networks in classification tasks. CoRR. https://arxiv.org/ abs/1710.11272
Chen, J., Chen, J., Zhang, R., & Hu, X. (2019). Toward a Brain-Inspired System: Deep Recurrent Reinforcement Learning for a Simulated Self-Driving Agent. Frontiers in neurorobotics, 13(40) https://doi.org/10.3389/fnbot.2019.00040
Chieng, H. H., Wahid, N., Ong, P., & Perla, S. R. K. (2018). Flatten-T Swish: a thresholded ReLU-Swish-like activation function for deep learning. International Journal of Advances in Intelligent Informatics, 4(2), 76-86. https://doi.org/10.26555/ijain.v4i2.249
Ciuparu, A., Nagy-Dăbâcan, A., & Mureşan, R. C. (2019). Soft++, a multi-parametric non-saturating non-linearity that improves convergence in deep neural architectures. Neurocomputing, 384, 376-388. https://doi.org/10.1016/j.neucom.2019.12.014
Clevert, D. A., Unterthiner, T., & Hochreiter, S. (2016). Fast and accurate deep network learning by exponential linear units (ELUs). Proceedings of the International Conference on Learning Representations (ICLR), 1-15. https://arxiv.org/abs/1511.07289
Glorot, X., & Bengio, Y. (2010). Understanding the difficulty of training deep feedforward neural networks. Journal of Machine Learning Research, 9, 249-256. https://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf
Hassabis, D., Kumaran, D., Summerfield, C., & Botvinick, M. (2017). Neuroscience-inspired artificial intelligence. Neuron, 95(2), 245-258. https://doi.org/10.1016/j.neuron.2017.06.011
He, K., Zhang, X., Ren, S., & Sun, J. (2015). Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. Proceedings of the IEEE International Conference on Computer Vision, 1026-1034. https://doi:10.1109/ICCV.2015.123 Journal of ICT, 20, No. 1 (January) 2021, pp: 21-
Ioffe, S., & Szegedy, C. (2015). Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. In 32nd International Conference on Machine Learning (ICML), 37, 448-456. https://dl.acm.org/doi/10.5555/3045118.3045167
Jagtap, A. D., Kawaguchi, K., Karniadakis, G. E. (2019). Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Journal of Computational Physics, 404, 109136. https://doi: 10.1016/j.jcp.2019.109136
Jinsakul, N., Tsai, C. F., Tsai, C. E., & Wu, P. (2019). Enhancement of Deep Learning in Image Classification Performance Using Xception with the Swish Activation Function for Colorectal Polyp Preliminary Screening. Mathematics, 7(12), 1170. https://doi:10.3390/ MATH7121170
Klambauer, G., Unterthiner, T., Mayr, A., & Hochreiter, S. (2017). Self-normalizing neural networks. Advances in Neural Information Processing Systems, 972-981. https://dl.acm.org/doi/10.5555/3294771.3294864
Laurent, T., & Von Brecht, J. H. (2018). The multilinear structure of ReLU networks. In 35th International Conference on Machine Learning (ICML), 80, 2908-2916. http://proceedings.mlr.press/v80/laurent18b. html
Lin, G., & Shen, W. (2018). Research on convolutional neural network based on improved Relu piecewise activation function. Procedia Computer Science, 131, 977-984. http://doi.org/10.1016/j.procs.2018.04.239
Liu, Y., Zhang, J., Gao, C., Qu, J., & Ji, L. (2019). Natural-Logarithm-Rectified Activation Function in Convolutional Neural Networks. In 2019 IEEE 5th International Conference on Computer and Communications (ICCC), 2000-2008. https://doi.org/10.1109/ICCC47050.2019.9064398
Maas, A. L., Hannun, A. Y., & Ng, A. Y. (2013). Rectifier nonlinearities improve neural network acoustic models. Proceedings of the 30th International Conference on Machine Learning (ICML), Workshop on Deep Learning for Audio, Speech, and Language Processing, 30(1), 3. https://ai.stanford.edu/~amaas/papers/relu_hybrid_icml2013_final.pdf
Mohamed, A. R., Dahl, G. E., & Hinton, G. (2011). Acoustic modeling using deep belief networks. IEEE transactions on audio, speech, and language processing, 20(1), 14-22. https://doi.org/10.1109/TASL.2011.2109382
Nair, V., & Hinton G. E. (2010). Rectified linear units improve Restricted Boltzmann machines. Proceedings of the 27th International Conference on Machine Learning (ICML-10), 807-814. https://dl.acm.org/ doi/10.5555/3104322.3104425
Ohn, I., & Kim, Y. (2019). Smooth function approximation by deep neural networks with general activation functions. Entropy, 21(7), 627. https://doi:10.3390/e21070627 Journal of ICT, 20, No. 1 (January) 2021, pp: 21-
Pereyra, G., Tucker, G., Chorowski, J., Kaiser, Ł., & Hinton, G. (2017). Regularizing neural networks by penalizing confident output distributions. In Proceedings of the 5th International Conference on Learning Representations (ICLR). https://arxiv.org/abs/1701.06548
Qian, S., Liu, H., Liu, C., Wu, S., & Wong, H. S. (2018). Adaptive activation functions in convolutional neural networks. Neurocomputing, 272, 204-212. https://doi:10.1016/j.neucom.2017.06.070
Qiu, S., Xu, X., & Cai, B. (2018). FReLU: Flexible Rectified Linear Units for Improving Convolutional Neural Networks, In 24th International Conference on Pattern Recognition (ICPR), 1223-1228. https://doi:10.1109/ICPR.2018.8546022
Ramachandran, P., Zoph, B., & Le, Q. V. (2018). Searching for activation functions. Workshop Track Proceedings of the 6th International Conference on Learning Representations (ICLR).
Robbins, H., & Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics, 22(3), 400-407. https://doi:10.1214/ aoms/1177729586
Scardapane, S., Comminiello, D., Hussain, A., & Uncini, A. (2017). Group sparse regularization for deep neural networks. Neurocomputing, 241, 81-89. https://doi.org/10.1016/j.neucom.2017.02.
Sütfeld, L. R., Brieger, F., Finger, H., Füllhase, S., & Pipa, G. (2018). Adaptive blending units: Trainable activation functions for deep neural networks. https://arxiv.org/abs/1806.10064
Tripathi, G. C., Rawat, M., & Rawat, K. (2019). Swish Activation Based Deep Neural Network Predistorter for RF-PA. In IEEE Region 10 Annual International Conference (TENCON), 1239-1242. https://doi:10.1109/ TENCON.2019.8929500
Trottier, L., Gigu, P., Chaib-Draa, B. (2017). Parametric exponential linear unit for deep convolutional neural networks. Proceedings of 16th IEEE International Conference on Machine Learning and Applications (ICMLA), 207-214. https://doi:10.1109/ICMLA.2017.00038
Wang, L., Li, Q., & Guo, H. (2019). A Research on Deep Learning Model for Face Emotion Recognition Based on Swish Activation Function. Journal of Image and Signal Processing, 8(3), 110-120. https://doi:10.12677/JISP.2019.83016
Yarotsky, D. (2018). Optimal approximation of continuous functions by very deep relu networks. Proceedings of Machine Learning Research, Vol 75, 1-11. http://proceedings.mlr.press/v75/yarotsky18a
Zhou, Z. H., & Feng, J. (2017). Deep forest: towards an alternative to deep neural networks. In Proceedings of the 26th International Joint Conference on Artificial Intelligence, 3553-3559, AAAI Press. https://www.ijcai.org/Proceedings/2017/497
Published
Issue
Section
How to Cite
Research impact
Harvested 2026-09-06Counts differ between services because each indexes a different body of literature. None of them is the whole picture.
- OpenCitations 0 View →
- Crossref 0 View →
- Scopus 0 not indexed View →
- Google Scholar no free count Search →
- Dimensions no free count Search →
2002 - 2020






















