code: """
  AdamP
  Copyright (c) 2020-present NAVER Corp.
  MIT license
  """
  
  import torch
  import torch.nn as nn
  from torch.optim.optimizer import Optimizer, required
  import math
  
  class SGDP(Optimizer):
      def __init__(self, params, lr=required, momentum=0, dampening=0,
                   weight_decay=0, nesterov=False, eps=1e-8, delta=0.1, wd_ratio=0.1):
          defaults = dict(lr=lr, momentum=momentum, dampening=dampening, weight_decay=weight_decay,
                          nesterov=nesterov, eps=eps, delta=delta, wd_ratio=wd_ratio)
          super(SGDP, self).__init__(params, defaults)
  
      def _channel_view(self, x):
          return x.view(x.size(0), -1)
  
      def _layer_view(self, x):
          return x.view(1, -1)
  
      def _cosine_similarity(self, x, y, eps, view_func):
          x = view_func(x)
          y = view_func(y)
  
          x_norm = x.norm(dim=1).add_(eps)
          y_norm = y.norm(dim=1).add_(eps)
          dot = (x * y).sum(dim=1)
  
          return dot.abs() / x_norm / y_norm
  
      def _projection(self, p, grad, perturb, delta, wd_ratio, eps):
          wd = 1
          expand_size = [-1] + [1] * (len(p.shape) - 1)
          for view_func in [self._channel_view, self._layer_view]:
  
              cosine_sim = self._cosine_similarity(grad, p.data, eps, view_func)
  
              if cosine_sim.max() < delta / math.sqrt(view_func(p.data).size(1)):
                  p_n = p.data / view_func(p.data).norm(dim=1).view(expand_size).add_(eps)
                  perturb -= p_n * view_func(p_n * perturb).sum(dim=1).view(expand_size)
                  wd = wd_ratio
  
                  return perturb, wd
  
          return perturb, wd
  
      def step(self, closure=None):
          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 p in group['params']:
                  if p.grad is None:
                      continue
                  grad = p.grad.data
                  state = self.state[p]
  
                  # State initialization
                  if len(state) == 0:
                      state['momentum'] = torch.zeros_like(p.data)
  
                  # SGD
                  buf = state['momentum']
                  buf.mul_(momentum).add_(1 - dampening, grad)
                  if nesterov:
                      d_p = grad + momentum * buf
                  else:
                      d_p = buf
  
                  # Projection
                  wd_ratio = 1
                  if len(p.shape) > 1:
                      d_p, wd_ratio = self._projection(p, grad, d_p, group['delta'], group['wd_ratio'], group['eps'])
  
                  # Weight decay
                  if weight_decay != 0:
                      p.data.mul_(1 - group['lr'] * group['weight_decay'] * wd_ratio / (1-momentum))
  
                  # Step
                  p.data.add_(-group['lr'], d_p)
  
          return loss
  
apis: torch.zeros_like