class_docstr: Implements stochastic gradient descent (optionally with momentum).
  
  `FusedSGD` requires CUDA extensions which can be built during installation or runtime.
  
  This version of fused SGD implements 2 fusions.
  
    * Fusion of the SGD update's elementwise operations
    * A multi-tensor apply launch that batches the elementwise updates applied to all the model's parameters into one or a few kernel launches.
  
  :class:`colossalai.nn.optimizer.FusedSGD` may be used as a drop-in replacement for ``torch.optim.SGD``
  
  :class:`colossalai.nn.optimizer.FusedSGD` may be used with or without Amp.
  
  Nesterov momentum is based on the formula from
  `On the importance of initialization and momentum in deep learning`__.
  
  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)
  
  __ http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf
  
  .. note::
      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::
                v = \rho * v + g \\
                p = p - lr * v
  
      where p, g, v and :math:`\rho` 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::
           v = \rho * v + lr * g \\
           p = p - v
  
      The Nesterov version is analogously modified.
docstr: Performs a single optimization step.
  
  Arguments:
      closure (callable, optional): A closure that reevaluates the model
          and returns the loss.
docstr_tok: ["Performs","a","single","optimization","step",".","Arguments",":","closure","(","callable",",","optional",")",":","A","closure","that","reevaluates","the","model","and","returns","the","loss","."]
code: 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:
          loss = closure()
  
      for group in self.param_groups:
          weight_decay = group["weight_decay"]
          momentum = group["momentum"]
          dampening = group["dampening"]
          nesterov = group["nesterov"]
  
          # For each group, there are 3 possible combinations we need to consider:
          # grad_type, param_to_update_type, momentum_type
          # 1. fp16, fp16, fp16
          # 2. fp32, fp32, fp32
          # 3. fp16, fp32, fp32
          g_l, p_l = [], []
          for p in group["params"]:
              if p.grad is None:
                  continue
              if p.grad.data.is_sparse:
                  raise RuntimeError(
                      "FusedSGD does not support sparse gradients"
                  )
              g_l.append(p.grad)
              p_l.append(p)
          m_l, first_run = self.get_momentums(p_l)
          multi_tensor_applier(
              self.multi_tensor_sgd,
              self._dummy_overflow_buf,
              [g_l, p_l, m_l],
              weight_decay,
              momentum,
              dampening,
              group["lr"],
              nesterov,
              first_run,
              self.wd_after_momentum,
              1.0,
          )
  
      return loss
  
file_path: ColossalAI/colossalai/nn/optimizer/fused_sgd.py
imports: import torch
  from torch.optim.optimizer import Optimizer, required
  from colossalai.utils import multi_tensor_applier
label_desc: Use image node_id 4 for calling the FusedSGD obj's underlying member method code with example usage: obj.step(closure) and returns: loss