class_docstr: Implements Novograd algorithm.
  It has been proposed  in "Stochastic Gradient Methods with Layer-wise
  Adaptive Moments for Training of Deep Networks"
  (https://arxiv.org/abs/1905.11286)
  Arguments:
      params (iterable): iterable of parameters to optimize or dicts defining
          parameter groups
      lr (float, optional): learning rate (default: 1e-3)
      betas (Tuple[float, float], optional): coefficients used for computing
          running averages of gradient and its square (default: (0.9, 0.999))
      eps (float, optional): term added to the denominator to improve
          numerical stability (default: 1e-8)
      weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
      amsgrad (boolean, optional): whether to use the AMSGrad variant of this
          algorithm from the paper "On the Convergence of Adam and Beyond"
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:
          for p in group["params"]:
              if p.grad is None:
                  continue
              grad = p.grad.data
              if grad.is_sparse:
                  raise RuntimeError(
                      "Sparse gradients are not supported."
                  )
              amsgrad = group["amsgrad"]
              state = self.state[p]
  
              # State initialization
              if not state:
                  state["step"] = 0
                  # Exponential moving average of gradient values
                  state["exp_avg"] = torch.zeros_like(p.data)
                  # Exponential moving average of squared gradient values
                  state["exp_avg_sq"] = torch.zeros([]).to(
                      state["exp_avg"].device
                  )
                  if amsgrad:
                      # Maintains max of all exp moving avg of squared grad
                      state["max_exp_avg_sq"] = torch.zeros([]).to(
                          state["exp_avg"].device
                      )
  
              exp_avg, exp_avg_sq = (
                  state["exp_avg"],
                  state["exp_avg_sq"],
              )
              if amsgrad:
                  max_exp_avg_sq = state["max_exp_avg_sq"]
              beta1, beta2 = group["betas"]
  
              state["step"] += 1
  
              norm = grad.norm().pow(2)
  
              if exp_avg_sq == 0:
                  exp_avg_sq.copy_(norm)
              else:
                  exp_avg_sq.mul_(beta2).add_(norm, alpha=1.0 - beta2)
  
              if amsgrad:
                  # Maintains max of all 2nd moment running avg till now
                  torch.max(
                      max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq
                  )
                  # Use the max for normalizing running avg. of gradient
                  denom = max_exp_avg_sq.sqrt().add_(group["eps"])
              else:
                  denom = exp_avg_sq.sqrt().add_(group["eps"])
  
              grad.div_(denom)
              if group["weight_decay"] != 0:
                  grad.add_(p.data, alpha=group["weight_decay"])
              if group["grad_averaging"]:
                  grad.mul_(1 - beta1)
              exp_avg.mul_(beta1).add_(grad)
  
              if self.luc:
                  # Clip update so that updates are less than eta*weights
                  data_norm = torch.norm(p.data)
                  grad_norm = torch.norm(exp_avg.data)
                  luc_factor = (
                      self.luc_trust
                      * data_norm
                      / (grad_norm + self.luc_eps)
                  )
                  luc_factor = min(luc_factor, group["lr"])
                  p.data.add_(exp_avg, alpha=-luc_factor)
              else:
                  p.data.add_(exp_avg, alpha=-group["lr"])
  
      return loss
  
file_path: NeMo/nemo/core/optim/novograd.py
imports: import torch
  from torch.optim.optimizer import Optimizer
label_desc: Use image node_id 3 for calling the Novograd obj's underlying member method code with example usage: obj.step(closure) and returns: loss