(Adaptive) SAM Optimizer

Sharpness-Aware Minimization for Efficiently Improving Generalization

~ in Pytorch ~

SAM simultaneously minimizes loss value and loss sharpness. In particular, it seeks parameters that lie in neighborhoods having uniformly low loss. SAM improves model generalization and yields SoTA performance for several datasets. Additionally, it provides robustness to label noise on par with that provided by SoTA procedures that specifically target learning with noisy labels.

This is an unofficial repository for Sharpness-Aware Minimization for Efficiently Improving Generalization and ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks. Implementation-wise, SAM class is a light wrapper that computes the regularized "sharpness-aware" gradient, which is used by the underlying optimizer (such as SGD with momentum). This repository also includes a simple WRN for Cifar10; as a proof-of-concept, it beats the performance of SGD with momentum on this dataset.

_{ResNet loss landscape at the end of training with and without SAM. Sharpness-aware updates lead to a significantly wider minimum, which then leads to better generalization properties.}

Usage

It should be straightforward to use SAM in your training pipeline. Just keep in mind that the training will run twice as slow, because SAM needs two forward-backward passes to estime the "sharpness-aware" gradient. If you're using gradient clipping, make sure to change only the magnitude of gradients, not their direction.

from sam import SAM
...

model = YourModel()
base_optimizer = torch.optim.SGD  # define an optimizer for the "sharpness-aware" update
optimizer = SAM(model.parameters(), base_optimizer, lr=0.1, momentum=0.9)
...

for input, output in data:

  # first forward-backward pass
  loss = loss_function(output, model(input))  # use this loss for any training statistics
  loss.backward()
  optimizer.first_step(zero_grad=True)

  # second forward-backward pass
  loss_function(output, model(input)).backward()  # make sure to do a full forward pass
  optimizer.second_step(zero_grad=True)
...

Alternative usage with a single closure-based step function. This alternative offers similar API to native PyTorch optimizers like LBFGS (kindly suggested by @rmcavoy):

from sam import SAM
...

model = YourModel()
base_optimizer = torch.optim.SGD  # define an optimizer for the "sharpness-aware" update
optimizer = SAM(model.parameters(), base_optimizer, lr=0.1, momentum=0.9)
...

for input, output in data:
  def closure():
    loss = loss_function(output, model(input))
    loss.backward()
    return loss

  loss = loss_function(output, model(input))
  loss.backward()
  optimizer.step(closure)
  optimizer.zero_grad()
...

Training tips

• @hjq133: The suggested usage can potentially cause problems if you use batch normalization. The running statistics are computed in both forward passes, but they should be computed only for the first one. A possible solution is to set BN momentum to zero (kindly suggested by @ahmdtaha) to bypass the running statistics during the second pass. An example usage is on lines 51 and 58 in example/train.py:

  for batch in dataset.train:
  inputs, targets = (b.to(device) for b in batch)
  
  # first forward-backward step
  enable_running_stats(model)  # <- this is the important line
  predictions = model(inputs)
  loss = smooth_crossentropy(predictions, targets)
  loss.mean().backward()
  optimizer.first_step(zero_grad=True)
  
  # second forward-backward step
  disable_running_stats(model)  # <- this is the important line
  smooth_crossentropy(model(inputs), targets).mean().backward()
  optimizer.second_step(zero_grad=True)

• @evanatyourservice: If you plan to train on multiple GPUs, the paper states that "To compute the SAM update when parallelizing across multiple accelerators, we divide each data batch evenly among the accelerators, independently compute the SAM gradient on each accelerator, and average the resulting sub-batch SAM gradients to obtain the final SAM update." This can be achieved by the following code:

  for input, output in data:
  # first forward-backward pass
  loss = loss_function(output, model(input))
  with model.no_sync():  # <- this is the important line
  loss.backward()
  optimizer.first_step(zero_grad=True)
  
  # second forward-backward pass
  loss_function(output, model(input)).backward()
  optimizer.second_step(zero_grad=True)

• @evanatyourservice: Adaptive SAM reportedly performs better than the original SAM. The ASAM paper suggests to use higher rho for the adaptive updates (~10x larger)

• @mlaves: LR scheduling should be either applied to the base optimizer or you should use SAM with a single step call (with a closure):

  scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer.base_optimizer, T_max=200)

• @AlbertoSabater: Integration with Pytorch Lightning — you can write the training_step function as:

  def training_step(self, batch, batch_idx):
  optimizer = self.optimizers()
  
  # first forward-backward pass
  loss_1 = self.compute_loss(batch)
  self.manual_backward(loss_1, optimizer)
  optimizer.first_step(zero_grad=True)
  
  # second forward-backward pass
  loss_2 = self.compute_loss(batch)
  self.manual_backward(loss_2, optimizer)
  optimizer.second_step(zero_grad=True)
  
  return loss_1

  
  

Documentation

SAM.__init__

SAM.first_step

Performs the first optimization step that finds the weights with the highest loss in the local rho-neighborhood.

SAM.second_step

Performs the second optimization step that updates the original weights with the gradient from the (locally) highest point in the loss landscape.

SAM.step

Performs both optimization steps in a single call. This function is an alternative to explicitly calling SAM.first_step and SAM.second_step.

Experiments

I've verified that SAM works on a simple WRN 16-8 model run on CIFAR10; you can replicate the experiment by running train.py. The Wide-ResNet is enhanced only by label smoothing and the most basic image augmentations with cutout, so the errors are higher than those in the SAM paper. Theoretically, you can get even lower errors by running for longer (1800 epochs instead of 200), because SAM shouldn't be as prone to overfitting. SAM uses rho=0.05, while ASAM is set to rho=2.0, as suggested by its authors.

Cite

Please cite the original authors if you use this optimizer in your work:

@inproceedings{foret2021sharpnessaware,
  title={Sharpness-aware Minimization for Efficiently Improving Generalization},
  author={Pierre Foret and Ariel Kleiner and Hossein Mobahi and Behnam Neyshabur},
  booktitle={International Conference on Learning Representations},
  year={2021},
  url={https://openreview.net/forum?id=6Tm1mposlrM}
}

@inproceesings{pmlr-v139-kwon21b,
  title={ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks},
  author={Kwon, Jungmin and Kim, Jeongseop and Park, Hyunseo and Choi, In Kwon},
  booktitle ={Proceedings of the 38th International Conference on Machine Learning},
  pages={5905--5914},
  year={2021},
  editor={Meila, Marina and Zhang, Tong},
  volume={139},
  series={Proceedings of Machine Learning Research},
  month={18--24 Jul},
  publisher ={PMLR},
  pdf={http://proceedings.mlr.press/v139/kwon21b/kwon21b.pdf},
  url={https://proceedings.mlr.press/v139/kwon21b.html},
  abstract={Recently, learning algorithms motivated from sharpness of loss surface as an effective measure of generalization gap have shown state-of-the-art performances. Nevertheless, sharpness defined in a rigid region with a fixed radius, has a drawback in sensitivity to parameter re-scaling which leaves the loss unaffected, leading to weakening of the connection between sharpness and generalization gap. In this paper, we introduce the concept of adaptive sharpness which is scale-invariant and propose the corresponding generalization bound. We suggest a novel learning method, adaptive sharpness-aware minimization (ASAM), utilizing the proposed generalization bound. Experimental results in various benchmark datasets show that ASAM contributes to significant improvement of model generalization performance.}
}