text: import torch
  from torch.optim.optimizer import Optimizer, required
  from torch import optim, nn
  
  from nfnets.utils import unitwise_norm
  
  class SGD_AGC(Optimizer):
      r"""Implements stochastic gradient descent (optionally with momentum).
  
      Nesterov momentum is based on the formula from
      `On the importance of initialization and momentum in deep learning`__
      AGC from NFNets: https://arxiv.org/abs/2102.06171.pdf.
  
      Args:
          params (iterable): iterable of parameters to optimize or dicts defining
              parameter groups
          lr (float): learning rate
          momentum (float, optional): momentum factor (default: 0)
          weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
          dampening (float, optional): dampening for momentum (default: 0)
          nesterov (bool, optional): enables Nesterov momentum (default: False)
          dampening (float, optional): dampening for momentum (default: 0.01)
          clipping (float, optional): clipping value (default: 1e-3)
          eps (float, optional): eps (default: 1e-3)
  
      Example:
          >>> optimizer = torch.optim.SGD_AGC(model.parameters(), lr=0.1, momentum=0.9)
          >>> optimizer.zero_grad()
          >>> loss_fn(model(input), target).backward()
          >>> optimizer.step()
  
  
      .. note::
          The implementation has been adapted from the PyTorch framework and the official
          NF-Nets paper.
          The implementation of SGD with Momentum/Nesterov subtly differs from
          Sutskever et. al. and implementations in some other frameworks.
  
          Considering the specific case of Momentum, the update can be written as
  
          .. math::
              \begin{aligned}
                  v_{t+1} & = \mu * v_{t} + g_{t+1}, \\
                  p_{t+1} & = p_{t} - \text{lr} * v_{t+1},
              \end{aligned}
  
          where :math:`p`, :math:`g`, :math:`v` and :math:`\mu` denote the 
          parameters, gradient, velocity, and momentum respectively.
  
          This is in contrast to Sutskever et. al. and
          other frameworks which employ an update of the form
  
          .. math::
              \begin{aligned}
                  v_{t+1} & = \mu * v_{t} + \text{lr} * g_{t+1}, \\
                  p_{t+1} & = p_{t} - v_{t+1}.
              \end{aligned}
  
          The Nesterov version is analogously modified.
      """
  
      def __init__(self, params, lr=required, momentum=0, dampening=0,
                   weight_decay=0, nesterov=False, clipping=1e-2, eps=1e-3):
          if lr is not required and lr < 0.0:
              raise ValueError("Invalid learning rate: {}".format(lr))
          if momentum < 0.0:
              raise ValueError("Invalid momentum value: {}".format(momentum))
          if weight_decay < 0.0:
              raise ValueError(
                  "Invalid weight_decay value: {}".format(weight_decay))
          if clipping < 0.0:
              raise ValueError("Invalid clipping value: {}".format(clipping))
          if eps < 0.0:
              raise ValueError("Invalid eps value: {}".format(eps))
  
          defaults = dict(lr=lr, momentum=momentum, dampening=dampening,
                          weight_decay=weight_decay, nesterov=nesterov, clipping=clipping, eps=eps)
          if nesterov and (momentum <= 0 or dampening != 0):
              raise ValueError(
                  "Nesterov momentum requires a momentum and zero dampening")
          super(SGD_AGC, self).__init__(params, defaults)
  
      def __setstate__(self, state):
          super(SGD_AGC, self).__setstate__(state)
          for group in self.param_groups:
              group.setdefault('nesterov', False)
  
      @torch.no_grad()
      def step(self, closure=None):
          """Performs a single optimization step.
  
          Arguments:
              closure (callable, optional): A closure that reevaluates the model
                  and returns the loss.
          """
          loss = None
          if closure is not None:
              with torch.enable_grad():
                  loss = closure()
  
          for group in self.param_groups:
              for p in group['params']:
                  if p.grad is None:
                      continue
                  param_norm = torch.max(unitwise_norm(
                      p.detach()), torch.tensor(group['eps']).to(p.device))
                  grad_norm = unitwise_norm(p.grad.detach())
                  max_norm = param_norm * group['clipping']
  
                  trigger = grad_norm < max_norm
  
                  clipped_grad = p.grad * \
                      (max_norm / torch.max(grad_norm,
                                            torch.tensor(1e-6).to(grad_norm.device)))
                  p.grad.data.copy_(torch.where(trigger, clipped_grad, p.grad))
  
          for group in self.param_groups:
              weight_decay = group['weight_decay']
              momentum = group['momentum']
              dampening = group['dampening']
              nesterov = group['nesterov']
  
              for p in group['params']:
                  if p.grad is None:
                      continue
                  d_p = p.grad
                  if weight_decay != 0:
                      d_p = d_p.add(p, alpha=weight_decay)
                  if momentum != 0:
                      param_state = self.state[p]
                      if 'momentum_buffer' not in param_state:
                          buf = param_state['momentum_buffer'] = torch.clone(
                              d_p).detach()
                      else:
                          buf = param_state['momentum_buffer']
                          buf.mul_(momentum).add_(d_p, alpha=1 - dampening)
                      if nesterov:
                          d_p = d_p.add(buf, alpha=momentum)
                      else:
                          d_p = buf
  
                  p.add_(d_p, alpha=-group['lr'])
  
          return loss
  