text: # Copyright 2019 Ross Wightman
  # Copyright 2021 Huawei Technologies Co., Ltd
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  # http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  """
  AdamP Optimizer Implementation copied from https://github.com/clovaai/AdamP/blob/master/adamp/adamp.py
  
  Paper: `Slowing Down the Weight Norm Increase in Momentum-based Optimizers` - https://arxiv.org/abs/2006.08217
  Code: https://github.com/clovaai/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 AdamP(Optimizer):
      def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                   weight_decay=0, delta=0.1, wd_ratio=0.1, nesterov=False):
          defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay,
                          delta=delta, wd_ratio=wd_ratio, nesterov=nesterov)
          super(AdamP, 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:
              for p in group['params']:
                  if p.grad is None:
                      continue
  
                  grad = p.grad.data
                  beta1, beta2 = group['betas']
                  nesterov = group['nesterov']
  
                  state = self.state[p]
  
                  # State initialization
                  if len(state) == 0:
                      state['step'] = 0
                      state['exp_avg'] = torch.zeros_like(p.data)
                      state['exp_avg_sq'] = torch.zeros_like(p.data)
  
                  # Adam
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
  
                  state['step'] += 1
                  bias_correction1 = 1 - beta1 ** state['step']
                  bias_correction2 = 1 - beta2 ** state['step']
  
                  exp_avg.mul_(beta1).add_(1 - beta1, grad)
                  exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
  
                  denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
                  step_size = group['lr'] / bias_correction1
  
                  if nesterov:
                      perturb = (beta1 * exp_avg + (1 - beta1) * grad) / denom
                  else:
                      perturb = exp_avg / denom
  
                  # Projection
                  wd_ratio = 1
                  if len(p.shape) > 1:
                      perturb, wd_ratio = self._projection(p, grad, perturb, group['delta'], group['wd_ratio'], group['eps'])
  
                  # Weight decay
                  if group['weight_decay'] > 0:
                      p.data.mul_(1 - group['lr'] * group['weight_decay'] * wd_ratio)
  
                  # Step
                  p.data.add_(-step_size, perturb)
  
          return loss
  