content: # coding=utf-8
  # Copyright 2018 The Google AI Language Team Authors and The HuggingFace Inc. team.
  #
  # 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.
  """PyTorch optimization for BERT model."""
  
  import math
  import torch
  from torch.optim import Optimizer
  from torch.optim.optimizer import required
  from torch.nn.utils import clip_grad_norm_
  import logging
  import abc
  import sys
  
  logger = logging.getLogger(__name__)
  
  
  if sys.version_info >= (3, 4):
      ABC = abc.ABC
  else:
      ABC = abc.ABCMeta('ABC', (), {})
  
  
  class _LRSchedule(ABC):
      """ Parent of all LRSchedules here. """
      warn_t_total = False        # is set to True for schedules where progressing beyond t_total steps doesn't make sense
      def __init__(self, warmup=0.002, t_total=-1, **kw):
          """
          :param warmup:  what fraction of t_total steps will be used for linear warmup
          :param t_total: how many training steps (updates) are planned
          :param kw:
          """
          super(_LRSchedule, self).__init__(**kw)
          if t_total < 0:
              logger.warning("t_total value of {} results in schedule not being applied".format(t_total))
          if not 0.0 <= warmup < 1.0 and not warmup == -1:
              raise ValueError("Invalid warmup: {} - should be in [0.0, 1.0[ or -1".format(warmup))
          warmup = max(warmup, 0.)
          self.warmup, self.t_total = float(warmup), float(t_total)
          self.warned_for_t_total_at_progress = -1
  
      def get_lr(self, step, nowarn=False):
          """
          :param step:    which of t_total steps we're on
          :param nowarn:  set to True to suppress warning regarding training beyond specified 't_total' steps
          :return:        learning rate multiplier for current update
          """
          if self.t_total < 0:
              return 1.
          progress = float(step) / self.t_total
          ret = self.get_lr_(progress)
          # warning for exceeding t_total (only active with warmup_linear
          if not nowarn and self.warn_t_total and progress > 1. and progress > self.warned_for_t_total_at_progress:
              logger.warning(
                  "Training beyond specified 't_total'. Learning rate multiplier set to {}. Please set 't_total' of {} correctly."
                      .format(ret, self.__class__.__name__))
              self.warned_for_t_total_at_progress = progress
          # end warning
          return ret
  
      @abc.abstractmethod
      def get_lr_(self, progress):
          """
          :param progress:    value between 0 and 1 (unless going beyond t_total steps) specifying training progress
          :return:            learning rate multiplier for current update
          """
          return 1.
  
  
  class ConstantLR(_LRSchedule):
      def get_lr_(self, progress):
          return 1.
  
  
  class WarmupCosineSchedule(_LRSchedule):
      """
      Linearly increases learning rate from 0 to 1 over `warmup` fraction of training steps.
      Decreases learning rate from 1. to 0. over remaining `1 - warmup` steps following a cosine curve.
      If `cycles` (default=0.5) is different from default, learning rate follows cosine function after warmup.
      """
      warn_t_total = True
      def __init__(self, warmup=0.002, t_total=-1, cycles=.5, **kw):
          """
          :param warmup:      see LRSchedule
          :param t_total:     see LRSchedule
          :param cycles:      number of cycles. Default: 0.5, corresponding to cosine decay from 1. at progress==warmup and 0 at progress==1.
          :param kw:
          """
          super(WarmupCosineSchedule, self).__init__(warmup=warmup, t_total=t_total, **kw)
          self.cycles = cycles
  
      def get_lr_(self, progress):
          if progress < self.warmup:
              return progress / self.warmup
          else:
              progress = (progress - self.warmup) / (1 - self.warmup)   # progress after warmup
              return 0.5 * (1. + math.cos(math.pi * self.cycles * 2 * progress))
  
  
  class WarmupCosineWithHardRestartsSchedule(WarmupCosineSchedule):
      """
      Linearly increases learning rate from 0 to 1 over `warmup` fraction of training steps.
      If `cycles` (default=1.) is different from default, learning rate follows `cycles` times a cosine decaying
      learning rate (with hard restarts).
      """
      def __init__(self, warmup=0.002, t_total=-1, cycles=1., **kw):
          super(WarmupCosineWithHardRestartsSchedule, self).__init__(warmup=warmup, t_total=t_total, cycles=cycles, **kw)
          assert(cycles >= 1.)
  
      def get_lr_(self, progress):
          if progress < self.warmup:
              return progress / self.warmup
          else:
              progress = (progress - self.warmup) / (1 - self.warmup)     # progress after warmup
              ret = 0.5 * (1. + math.cos(math.pi * ((self.cycles * progress) % 1)))
              return ret
  
  
  class WarmupCosineWithWarmupRestartsSchedule(WarmupCosineWithHardRestartsSchedule):
      """
      All training progress is divided in `cycles` (default=1.) parts of equal length.
      Every part follows a schedule with the first `warmup` fraction of the training steps linearly increasing from 0. to 1.,
      followed by a learning rate decreasing from 1. to 0. following a cosine curve.
      """
      def __init__(self, warmup=0.002, t_total=-1, cycles=1., **kw):
          assert(warmup * cycles < 1.)
          warmup = warmup * cycles if warmup >= 0 else warmup
          super(WarmupCosineWithWarmupRestartsSchedule, self).__init__(warmup=warmup, t_total=t_total, cycles=cycles, **kw)
  
      def get_lr_(self, progress):
          progress = progress * self.cycles % 1.
          if progress < self.warmup:
              return progress / self.warmup
          else:
              progress = (progress - self.warmup) / (1 - self.warmup)     # progress after warmup
              ret = 0.5 * (1. + math.cos(math.pi * progress))
              return ret
  
  
  class WarmupConstantSchedule(_LRSchedule):
      """
      Linearly increases learning rate from 0 to 1 over `warmup` fraction of training steps.
      Keeps learning rate equal to 1. after warmup.
      """
      def get_lr_(self, progress):
          if progress < self.warmup:
              return progress / self.warmup
          return 1.
  
  
  class WarmupLinearSchedule(_LRSchedule):
      """
      Linearly increases learning rate from 0 to 1 over `warmup` fraction of training steps.
      Linearly decreases learning rate from 1. to 0. over remaining `1 - warmup` steps.
      """
      warn_t_total = True
      def get_lr_(self, progress):
          if progress < self.warmup:
              return progress / self.warmup
          return max((progress - 1.) / (self.warmup - 1.), 0.)
  
  
  SCHEDULES = {
      None:       ConstantLR,
      "none":     ConstantLR,
      "warmup_cosine": WarmupCosineSchedule,
      "warmup_constant": WarmupConstantSchedule,
      "warmup_linear": WarmupLinearSchedule
  }
  
  
  class BertAdam(Optimizer):
      """Implements BERT version of Adam algorithm with weight decay fix.
      Params:
          lr: learning rate
          warmup: portion of t_total for the warmup, -1  means no warmup. Default: -1
          t_total: total number of training steps for the learning
              rate schedule, -1  means constant learning rate of 1. (no warmup regardless of warmup setting). Default: -1
          schedule: schedule to use for the warmup (see above).
              Can be `'warmup_linear'`, `'warmup_constant'`, `'warmup_cosine'`, `'none'`, `None` or a `_LRSchedule` object (see below).
              If `None` or `'none'`, learning rate is always kept constant.
              Default : `'warmup_linear'`
          b1: Adams b1. Default: 0.9
          b2: Adams b2. Default: 0.999
          e: Adams epsilon. Default: 1e-6
          weight_decay: Weight decay. Default: 0.01
          max_grad_norm: Maximum norm for the gradients (-1 means no clipping). Default: 1.0
      """
      def __init__(self, params, lr=required, warmup=-1, t_total=-1, schedule='warmup_linear',
                   b1=0.9, b2=0.999, e=1e-6, weight_decay=0.01, max_grad_norm=1.0, **kwargs):
          if lr is not required and lr < 0.0:
              raise ValueError("Invalid learning rate: {} - should be >= 0.0".format(lr))
          if not isinstance(schedule, _LRSchedule) and schedule not in SCHEDULES:
              raise ValueError("Invalid schedule parameter: {}".format(schedule))
          if not 0.0 <= b1 < 1.0:
              raise ValueError("Invalid b1 parameter: {} - should be in [0.0, 1.0[".format(b1))
          if not 0.0 <= b2 < 1.0:
              raise ValueError("Invalid b2 parameter: {} - should be in [0.0, 1.0[".format(b2))
          if not e >= 0.0:
              raise ValueError("Invalid epsilon value: {} - should be >= 0.0".format(e))
          # initialize schedule object
          if not isinstance(schedule, _LRSchedule):
              schedule_type = SCHEDULES[schedule]
              schedule = schedule_type(warmup=warmup, t_total=t_total)
          else:
              if warmup != -1 or t_total != -1:
                  logger.warning("warmup and t_total on the optimizer are ineffective when _LRSchedule object is provided as schedule. "
                                 "Please specify custom warmup and t_total in _LRSchedule object.")
          defaults = dict(lr=lr, schedule=schedule,
                          b1=b1, b2=b2, e=e, weight_decay=weight_decay,
                          max_grad_norm=max_grad_norm)
          super(BertAdam, self).__init__(params, defaults)
  
      def get_lr(self):
          lr = []
          for group in self.param_groups:
              for p in group['params']:
                  state = self.state[p]
                  if len(state) == 0:
                      return [0]
                  lr_scheduled = group['lr']
                  lr_scheduled *= group['schedule'].get_lr(state['step'])
                  lr.append(lr_scheduled)
          return lr
  
      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('Adam does not support sparse gradients, please consider SparseAdam instead')
  
                  state = self.state[p]
  
                  # State initialization
                  if len(state) == 0:
                      state['step'] = 0
                      # Exponential moving average of gradient values
                      state['next_m'] = torch.zeros_like(p.data)
                      # Exponential moving average of squared gradient values
                      state['next_v'] = torch.zeros_like(p.data)
  
                  next_m, next_v = state['next_m'], state['next_v']
                  beta1, beta2 = group['b1'], group['b2']
  
                  # Add grad clipping
                  if group['max_grad_norm'] > 0:
                      clip_grad_norm_(p, group['max_grad_norm'])
  
                  # Decay the first and second moment running average coefficient
                  # In-place operations to update the averages at the same time
                  next_m.mul_(beta1).add_(1 - beta1, grad)
                  next_v.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                  update = next_m / (next_v.sqrt() + group['e'])
  
                  # Just adding the square of the weights to the loss function is *not*
                  # the correct way of using L2 regularization/weight decay with Adam,
                  # since that will interact with the m and v parameters in strange ways.
                  #
                  # Instead we want to decay the weights in a manner that doesn't interact
                  # with the m/v parameters. This is equivalent to adding the square
                  # of the weights to the loss with plain (non-momentum) SGD.
                  if group['weight_decay'] > 0.0:
                      update += group['weight_decay'] * p.data
  
                  lr_scheduled = group['lr']
                  lr_scheduled *= group['schedule'].get_lr(state['step'])
  
                  update_with_lr = lr_scheduled * update
                  p.data.add_(-update_with_lr)
  
                  state['step'] += 1
  
                  # step_size = lr_scheduled * math.sqrt(bias_correction2) / bias_correction1
                  # No bias correction
                  # bias_correction1 = 1 - beta1 ** state['step']
                  # bias_correction2 = 1 - beta2 ** state['step']
  
          return loss
  