Rethinking-SWATS-Optimizer

Rethinking SWATS (Switches from Adam to SGD) Optimizer. Performing the switch Locally than Globally.

Prerequisites

• PyTorch == 1.5.1

Overview

Elementwise scaling of learning rate adopted by Adaptive Optimizers such as Adam, RMSProp etc often generalise poorly due to unstable and non-uniform learning rates at the end of training, although they scale well during the initial part of training. Hence SGD is the go-to for SOTA results since it generalizes better than adaptive methods.

SWATS is a method from Keskar and Socher which switches from Adam to SGD when the difference between the bias corrected projected learning rate and the projected learning rate is less than a threshold ϵ.The projected learning rate is found by projecting the SGD's update onto Adam's update. The switch is global i.e. if one of the layers of the network switches to SGD, all the layers are switched to SGD.

Switching Locally than Globally

Switching all the layers to SGD just because a particular layer switched to SGD is something which has to be investigated. Why should a Dense or Batch Norm Layer impact Convolutional layer's training? So I went ahead and made the switch local i.e a layer's switch to SGD is independent of other layer switching to SGD i.e. at a given time some layers will be in SGD Phase while the rest of them are still using Adam.

Experiment

To perform the analysis I use ResNet-18 on Cifar-10 from this repository.
Since paper's default value of ϵ (threshold to switch) wasn't working for me, I've reduced ϵ value from 10^-9 to 10^-5. Since ϵ value is left as a hyperparameter in the paper, I guess this is okay to do :)

Setup

• batch-size = 128
• epochs = 200

ResNet - 18

1. SWATS (GLOBAL SWITCH)

   • initial step size (adam) 0.001
   • step size decay by a factor of 10 at 100 epochs.

2. New SWATS (LOCAL SWITCH)

   • step size decay by a factor of 10 at 75,150 epochs for layers which are in SGD Phase.
   • step size decay by a factor of 10 at 100 epochs for layers which are in Adam.

3. Adabound

   • step size decay by a factor of 10 at 100 epochs for AdaBound.

DenseNet - 121

1. SWATS (GLOBAL SWITCH)

   • initial step size (adam) 0.001
   • step size decay by a factor of 10 at 150 epochs.

2. New SWATS (LOCAL SWITCH)

   • step size decay by a factor of 10 at 75,150 epochs for layers which are in SGD Phase.
   • step size decay by a factor of 10 at 100 epochs for layers which are in Adam.

3. Adabound

   • step size decay by a factor of 10 at 150 epochs for AdaBound.

Comparision

Since AdaBound is the only paper which I know which changes smoothly or in other words continuously transforms from Adam to SGD, rather than a hard switch like SWATS, it is fair to compare SWATS with AdaBound.

Results

Model	Optimizer	Switch	Test Acc.
ResNet-18	SWATS	Global (Vanilla)	92.89
ResNet-18	SWATS	Local	94.13
ResNet-18	AdaBound	NA	93.0
DenseNet-121	SWATS	Global (Vanilla)	93.30
DenseNet-121	SWATS	Local	94.62
DenseNet-121	AdaBound	NA	93.36

Switch Over Points(Steps) for Local Switch

ResNet-18

Layer	Steps	Estimated Learning Rate For SGD
linear.weight	29	0.015315
layer1.0.conv1.weight	1011	0.149228
layer2.0.conv1.weight	2354	0.673763
layer1.1.bn1.bias	2597	0.204322
layer2.1.bn1.weight	3230	0.416590
layer2.0.shortcut.0.weight	3415	0.278827
layer1.0.bn1.bias	3690	0.156899
bn1.bias	4850	0.117717
layer1.1.bn2.bias	5574	0.320231
linear.bias	5645	0.015616
layer3.0.bn2.weight	5744	0.420847
layer2.1.bn1.bias	6897	0.378199
layer3.0.bn1.bias	6996	0.599258
layer2.0.shortcut.1.weight	7972	0.276019
conv1.weight	7994	0.042911
layer1.0.conv2.weight	8079	0.649479
layer1.1.bn2.weight	10320	0.157036
layer2.0.bn2.bias	11477	0.382424
layer2.0.shortcut.1.bias	11477	0.382424
layer3.0.shortcut.0.weight	11729	1.180122

DenseNet-121

Layer	Steps	Estimated Learning Rate For SGD
conv1.weight	180	0.012701
dense2.0.conv1.weight	776	0.802031
dense1.0.bn2.weight	938	0.499405
dense1.0.conv1.weight	1020	0.199502
dense1.0.bn1.weight	1411	0.195258
trans1.conv.weight	1499	0.269556
dense2.10.conv2.weight	1683	3.295926
dense4.6.conv2.weight	1826	4.965084
dense3.0.bn1.weight	2013	4.180832
dense2.3.bn2.weight	2252	2.053317
linear.bias	2805	0.028812
dense3.9.bn2.weight	3695	2.368862
trans1.bn.bias	3782	0.382468
dense1.2.conv1.weight	4286	0.857455
trans1.bn.weight	4525	0.329345
dense3.9.bn1.weight	4629	4.333698
dense3.4.conv2.weight	4802	2.658655
dense2.1.bn1.bias	4953	1.257946
dense3.8.conv1.weight	5268	6.371582
dense2.0.bn2.bias	5538	1.395342
dense3.7.bn2.weight	5664	1.882873
dense2.4.bn2.weight	7457	1.158317
dense1.4.conv2.weight	8148	2.967311
trans3.bn.weight	8449	1.047665
dense2.2.bn1.bias	9793	1.812838
dense3.9.conv1.weight	10624	8.560639
dense3.4.bn1.weight	12009	1.662682
dense2.6.conv2.weight	22923	28.562759

Conclusion

The idea of having some layers stay back in Adam phase and some of them moving forward to SGD(M) phase show that you need not switch all the layers to generalize better. Morever in Vanilla SWATS if the switch happens too early, Adaptive estimates cannot be utilised to the full extent. But if the switch is Local, some layers which are in Adam phase will help the initial part of training although the remaining layers have moved on to SGD.

As seen from the table above some layers(convolutional) in DenseNet have learning rates 4.96,6.37,8.56, 28.56. One may wonder how is the model converging at such high lr. I think this is due to Batch Normalization and it working well with exotic exponential learning rate schedulers Ref

Note

Since there is no official implementation of SWATS from the authors, the code for it is borrowed from here . (SwatsVanillaGlobal.py).

If you find any bug in my implementation of switching it locally or find the idea of switching it locally "obscure", kindly feel free to drop an issue or email me at [email protected].