Abstract
Modern deep neural networks are equipped with normalization layers such as batch normalization or layer normalization to enhance and stabilize training dynamics. If a network contains such normalization layers, the optimization objective is invariant to the scale of the neural network parameters. The scale-invariance induces the neural network’s output to be only affected by the weights’ direction and not the weights’ scale. We first find a common feature of good hyperparameter combinations on such a scale-invariant network, including learning rate, weight decay, number of data samples, and batch size. Then we observe that hyperparameter setups that lead to good performance show similar degrees of angular update during one epoch. Using a stochastic differential equation, we analyze the angular update and show how each hyperparameter affects it. With this relationship, we can derive a simple hyperparameter tuning method and apply it to the efficient hyperparameter search.
J. Yun—Work done during an internship at LG AI Research.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ba, J.L., Kiros, J.R., Hinton, G.E.: Layer normalization. arXiv preprint arXiv:1607.06450 (2016)
Gardiner, C.W., et al.: Handbook of stochastic methods, vol. 3. Springer, Berlin (1985)
Goyal, P., et al.: Accurate, large minibatch sgd: Training imagenet in 1 hour. arXiv preprint arXiv:1706.02677 (2017)
Han, D., Kim, J., Kim, J.: Deep pyramidal residual networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5927–5935 (2017)
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)
Hoffer, E., Banner, R., Golan, I., Soudry, D.: Norm matters: efficient and accurate normalization schemes in deep networks. In: Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems, vol. 31. Curran Associates, Inc. (2018). http://www.proceedings.neurips.cc/paper/2018/file/a0160709701140704575d499c997b6ca-Paper.pdf
Hoffer, E., Hubara, I., Soudry, D.: Train longer, generalize better: closing the generalization gap in large batch training of neural networks. arXiv preprint arXiv:1705.08741 (2017)
Hoffer, E., Hubara, I., Soudry, D.: Fix your classifier: the marginal value of training the last weight layer (2018)
Howard, A., et al.: Searching for mobilenetv3. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 1314–1324 (2019)
Hu, J., Shen, L., Sun, G.: Squeeze-and-excitation networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7132–7141 (2018)
Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 4700–4708 (2017)
Ioffe, S., Szegedy, C.: Batch normalization: Accelerating deep network training by reducing internal covariate shift. In: International Conference on Machine Learning, pp. 448–456. PMLR (2015)
Krizhevsky, A., Hinton, G., et al.: Learning multiple layers of features from tiny images (2009)
Le, Y., Yang, X.: Tiny imagenet visual recognition challenge. CS 231N 7(7), 3 (2015)
Lewkowycz, A., Gur-Ari, G.: On the training dynamics of deep networks with \( l_2 \) regularization. arXiv preprint arXiv:2006.08643 (2020)
Li, Q., Tai, C., Weinan, E.: Stochastic modified equations and adaptive stochastic gradient algorithms. In: International Conference on Machine Learning, pp. 2101–2110. PMLR (2017)
Li, Q., Tai, C., Weinan, E.: Stochastic modified equations and dynamics of stochastic gradient algorithms i: mathematical foundations. J. Mach. Learn. Res. 20(1), 1474–1520 (2019)
Li, Z., Arora, S.: An exponential learning rate schedule for deep learning. In: International Conference on Learning Representations (2020), http://www.openreview.net/forum?id=rJg8TeSFDH
Li, Z., Lyu, K., Arora, S.: Reconciling modern deep learning with traditional optimization analyses: the intrinsic learning rate. In: Advances in Neural Information Processing Systems 33 (2020)
Li, Z., Malladi, S., Arora, S.: On the validity of modeling sgd with stochastic differential equations (sdes). arXiv preprint arXiv:2102.12470 (2021)
Ramachandran, P., Zoph, B., Le, Q.V.: Searching for activation functions. arXiv preprint arXiv:1710.05941 (2017)
Russakovsky, O., et al.: ImageNet large scale visual recognition challenge. Int. J. Comput. Vision 115(3), 211–252 (2015). https://doi.org/10.1007/s11263-015-0816-y
Smith, S., Elsen, E., De, S.: On the generalization benefit of noise in stochastic gradient descent. In: International Conference on Machine Learning, pp. 9058–9067. PMLR (2020)
Smith, S.L., Kindermans, P.J., Ying, C., Le, Q.V.: Don’t decay the learning rate, increase the batch size. arXiv preprint arXiv:1711.00489 (2017)
Smith, S.L., Le, Q.V.: A bayesian perspective on generalization and stochastic gradient descent. arXiv preprint arXiv:1710.06451 (2017)
Tan, M., Le, Q.: Efficientnet: rethinking model scaling for convolutional neural networks. In: International Conference on Machine Learning, pp. 6105–6114. PMLR (2019)
Ulyanov, D., Vedaldi, A., Lempitsky, V.: Instance normalization: the missing ingredient for fast stylization. arXiv preprint arXiv:1607.08022 (2016)
Van Laarhoven, T.: L2 regularization versus batch and weight normalization. arXiv preprint arXiv:1706.05350 (2017)
Wan, R., Zhu, Z., Zhang, X., Sun, J.: Spherical motion dynamics: learning dynamics of normalized neural network using sgd and weight decay. In: Advances in Neural Information Processing Systems 34 (2021)
Welling, M., Teh, Y.W.: Bayesian learning via stochastic gradient langevin dynamics. In: Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 681–688. Citeseer (2011)
Wu, Y., He, K.: Group normalization. In: Ferrari, V., Hebert, M., Sminchisescu, C., Weiss, Y. (eds.) ECCV 2018. LNCS, vol. 11217, pp. 3–19. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01261-8_1
Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1492–1500 (2017)
Yun, J., Kim, B., Kim, J.: Weight decay scheduling and knowledge distillation for active learning. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) ECCV 2020. LNCS, vol. 12371, pp. 431–447. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58574-7_26
Zagoruyko, S., Komodakis, N.: Wide residual networks. In: British Machine Vision Conference 2016. British Machine Vision Association (2016)
Zhang, G., Wang, C., Xu, B., Grosse, R.: Three mechanisms of weight decay regularization. In: International Conference on Learning Representations (2019). http://www.openreview.net/forum?id=B1lz-3Rct7
Acknowledgment
This research was supported by the Engineering Research Center Program through the National Research Foundation of Korea (NRF) funded by the Korean Government MSIT (NRF-2018R1A5A1059921).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Yun, J., Lee, J., Shon, H., Yi, E., Kim, S.H., Kim, J. (2022). On the Angular Update and Hyperparameter Tuning of a Scale-Invariant Network. In: Avidan, S., Brostow, G., Cissé, M., Farinella, G.M., Hassner, T. (eds) Computer Vision – ECCV 2022. ECCV 2022. Lecture Notes in Computer Science, vol 13672. Springer, Cham. https://doi.org/10.1007/978-3-031-19775-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-031-19775-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-19774-1
Online ISBN: 978-3-031-19775-8
eBook Packages: Computer ScienceComputer Science (R0)