Abstract
Optimization in Deep Learning is mainly guided by vague intuitions and strong assumptions, with a limited understanding how and why these work in practice. To shed more light on this, our work provides some deeper understandings of how SGD behaves by empirically analyzing the trajectory taken by SGD from a line search perspective. Specifically, a costly quantitative analysis of the full-batch loss along SGD trajectories from common used models trained on a subset of CIFAR-10 is performed. Our core results include that the full-batch loss along lines in update step direction is highly parabolically. Further on, we show that there exists a learning rate with which SGD always performs almost exact line searches on the full-batch loss. Finally, we provide a different perspective why increasing the batch size has almost the same effect as decreasing the learning rate by the same factor.
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Notes
- 1.
Better performance does not imply that the assumptions used are correct.
- 2.
Image classification on MNIST, SVHN, CIFAR-10, CIFAR-100 and ImageNet.
- 3.
See the GitHub link in Sect. 7 for further analyses and code. We are aware that our analysis of a small set of problems provides low evidence. Nevertheless, we consider it to be guiding. With the code published with this paper, it is simple to run our experiments on further problems.
- 4.
Cropping, horizontal flipping and normalization with mean and standard deviation.
- 5.
Best performing \(\lambda \) chosen of a grid search over \(\{10^{-i}| i \in \{0,1,1.3,2,3,4\}\}\).
- 6.
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8 Appendix
8 Appendix
SGD training process with momentum 0.9. See Fig. 6 for explanations. The core differences are, that for the proportionality, the noise is higher than in the SGD case. In addition, SGD with momentum overshoots the locally optimal step size less and does not perform an as exact line search.
SGD with a locally optimal learning rate of 0.05 performs worse than SGD with a globally optimal learning rate of 0.01. Trainings are performed on a ResNet-20 and 8% of CIFAR-10 with SGD without momentum.
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Mutschler, M., Zell, A. (2021). Empirically Explaining SGD from a Line Search Perspective. In: Farkaš, I., Masulli, P., Otte, S., Wermter, S. (eds) Artificial Neural Networks and Machine Learning – ICANN 2021. ICANN 2021. Lecture Notes in Computer Science(), vol 12892. Springer, Cham. https://doi.org/10.1007/978-3-030-86340-1_37
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