class_docstr: 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`__.
  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)
      grad_threshold (float, optional): imposes a threshold on the magnitude of gradient values.
          Gradient values with magnitude above the threshold will be replaced with 0.
  Example:
      >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
      >>> optimizer.zero_grad()
      >>> loss_fn(model(input), target).backward()
      >>> optimizer.step()
  __ 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::
          \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.
code: def __init__(
      self,
      params,
      lr,
      momentum=0,
      dampening=0,
      weight_decay=0,
      nesterov=False,
      grad_threshold=None,
  ):
      if not isinstance(lr, (int, float)) or lr < 0.0:
          raise ValueError("Invalid learning rate: {}".format(lr))
      if not isinstance(momentum, (int, float)) or momentum < 0.0:
          raise ValueError(
              "Invalid momentum value: {}".format(momentum)
          )
      if not isinstance(dampening, (int, float)):
          raise ValueError(
              "Invalid dampening value {}".format(dampening)
          )
      if (
          not isinstance(weight_decay, (int, float))
          or weight_decay < 0.0
      ):
          raise ValueError(
              "Invalid weight_decay value: {}".format(weight_decay)
          )
  
      defaults = {
          "lr": lr,
          "momentum": momentum,
          "dampening": dampening,
          "weight_decay": weight_decay,
          "nesterov": nesterov,
      }
      if nesterov and (momentum <= 0 or dampening != 0):
          raise ValueError(
              "Nesterov momentum requires a momentum and zero dampening"
          )
  
      # Compute thresholding based on square value since abs is more expensive
      self.square_threshold = grad_threshold
      if self.square_threshold is not None:
          self.square_threshold *= self.square_threshold
  
      super(SGD, self).__init__(params, defaults)
  
imports: import crypten
  from .optimizer import Optimizer
label_desc: Use image node_id 1 to create a new SGD object from inherited base classes: Optimizer with example: obj = SGD(params, lr, momentum, dampening, weight_decay, nesterov, grad_threshold)