text: #copied from https://github.com/davda54/sam/blob/main/sam.py for simplicity
  import torch
  
  class SAM(torch.optim.Optimizer):
      def __init__(self, params, base_optimizer, rho=0.05, **kwargs):
          assert rho >= 0.0, f"Invalid rho, should be non-negative: {rho}"
  
          defaults = dict(rho=rho, **kwargs)
          super(SAM, self).__init__(params, defaults)
  
          self.base_optimizer = base_optimizer(self.param_groups, **kwargs)
          self.param_groups = self.base_optimizer.param_groups
  
      @torch.no_grad()
      def first_step(self, zero_grad=False):
          grad_norm = self._grad_norm()
          for group in self.param_groups:
              scale = group["rho"] / (grad_norm + 1e-12)
  
              for p in group["params"]:
                  if p.grad is None: continue
                  e_w = p.grad * scale.to(p)
                  p.add_(e_w)  # climb to the local maximum "w + e(w)"
                  self.state[p]["e_w"] = e_w
  
          if zero_grad: self.zero_grad()
  
      @torch.no_grad()
      def second_step(self, zero_grad=False):
          for group in self.param_groups:
              for p in group["params"]:
                  if p.grad is None: continue
                  p.sub_(self.state[p]["e_w"])  # get back to "w" from "w + e(w)"
  
          self.base_optimizer.step()  # do the actual "sharpness-aware" update
  
          if zero_grad: self.zero_grad()
  
      @torch.no_grad()
      def step(self, closure=None):
          assert closure is not None, "Sharpness Aware Minimization requires closure, but it was not provided"
          closure = torch.enable_grad()(closure)  # the closure should do a full forward-backward pass
  
          self.first_step(zero_grad=True)
          closure()
          self.second_step()
  
      def _grad_norm(self):
          shared_device = self.param_groups[0]["params"][0].device  # put everything on the same device, in case of model parallelism
          norm = torch.norm(
                      torch.stack([
                          p.grad.norm(p=2).to(shared_device)
                          for group in self.param_groups for p in group["params"]
                          if p.grad is not None
                      ]),
                      p=2
                 )
          return norm
  