class_docstr: This class implements the imperceptible, robust, and targeted attack to generate adversarial examples for automatic
  speech recognition models. This attack will be implemented specifically for DeepSpeech model and is framework
  dependent, specifically for PyTorch.
  
  | Paper link: https://arxiv.org/abs/1903.10346
docstr: The second stage of the attack.
  
  :param x: Samples of shape (nb_samples, seq_length). Note that, it is allowable that sequences in the batch
            could have different lengths. A possible example of `x` could be:
            `x = np.array([np.array([0.1, 0.2, 0.1, 0.4]), np.array([0.3, 0.1])])`.
  :param y: Target values of shape (nb_samples). Each sample in `y` is a string and it may possess different
            lengths. A possible example of `y` could be: `y = np.array(['SIXTY ONE', 'HELLO'])`. Note that, this
            class only supports targeted attack.
  :param theta_batch: Original thresholds.
  :param original_max_psd_batch: Original maximum psd.
  :return: An array holding the candidate adversarial examples.
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code: def _attack_2nd_stage(
      self,
      x: np.ndarray,
      y: np.ndarray,
      theta_batch: List[np.ndarray],
      original_max_psd_batch: List[np.ndarray],
  ) -> "torch.Tensor":
      """
      The second stage of the attack.
  
      :param x: Samples of shape (nb_samples, seq_length). Note that, it is allowable that sequences in the batch
                could have different lengths. A possible example of `x` could be:
                `x = np.array([np.array([0.1, 0.2, 0.1, 0.4]), np.array([0.3, 0.1])])`.
      :param y: Target values of shape (nb_samples). Each sample in `y` is a string and it may possess different
                lengths. A possible example of `y` could be: `y = np.array(['SIXTY ONE', 'HELLO'])`. Note that, this
                class only supports targeted attack.
      :param theta_batch: Original thresholds.
      :param original_max_psd_batch: Original maximum psd.
      :return: An array holding the candidate adversarial examples.
      """
      import torch
  
      # Compute local shape
      local_batch_size = len(x)
      real_lengths = np.array([x_.shape[0] for x_ in x])
      local_max_length = np.max(real_lengths)
  
      # Initialize alpha and rescale
      alpha = np.array(
          [self.alpha] * local_batch_size, dtype=np.float64
      )
      rescale = (
          np.ones(
              [local_batch_size, local_max_length], dtype=np.float64
          )
          * self.initial_rescale
      )
  
      # Reformat input
      input_mask = np.zeros(
          [local_batch_size, local_max_length], dtype=np.float64
      )
      original_input = np.zeros(
          [local_batch_size, local_max_length], dtype=np.float64
      )
  
      for local_batch_size_idx in range(local_batch_size):
          input_mask[
              local_batch_size_idx, : len(x[local_batch_size_idx])
          ] = 1
          original_input[
              local_batch_size_idx, : len(x[local_batch_size_idx])
          ] = x[local_batch_size_idx]
  
      # Optimization loop
      successful_adv_input: List[Optional["torch.Tensor"]] = [
          None
      ] * local_batch_size
      best_loss_2nd_stage = [np.inf] * local_batch_size
      trans = [None] * local_batch_size
  
      for iter_2nd_stage_idx in range(self.max_iter_2):
          # Zero the parameter gradients
          self.optimizer_2.zero_grad()
  
          # Call to forward pass of the first stage
          (
              loss_1st_stage,
              _,
              decoded_output,
              masked_adv_input,
              local_delta_rescale,
          ) = self._forward_1st_stage(
              original_input=original_input,
              original_output=y,
              local_batch_size=local_batch_size,
              local_max_length=local_max_length,
              rescale=rescale,
              input_mask=input_mask,
              real_lengths=real_lengths,
          )
  
          # Call to forward pass of the first stage
          loss_2nd_stage = self._forward_2nd_stage(
              local_delta_rescale=local_delta_rescale,
              theta_batch=theta_batch,
              original_max_psd_batch=original_max_psd_batch,
              real_lengths=real_lengths,
          )
  
          # Total loss
          loss = (
              loss_1st_stage.type(torch.float64)
              + torch.tensor(alpha).to(self.estimator.device)
              * loss_2nd_stage
          )
          loss = torch.mean(loss)
  
          # Actual training
          if self._use_amp:  # pragma: no cover
              from apex import amp  # pylint: disable=E0611
  
              with amp.scale_loss(
                  loss, self.optimizer_2
              ) as scaled_loss:
                  scaled_loss.backward()
  
          else:
              loss.backward()
  
          # Do optimization
          self.optimizer_2.step()
  
          # Save the best adversarial example and adjust the alpha coefficient
          for local_batch_size_idx in range(local_batch_size):
              if (
                  decoded_output[local_batch_size_idx]
                  == y[local_batch_size_idx]
              ):
                  if (
                      loss_2nd_stage[local_batch_size_idx]
                      < best_loss_2nd_stage[local_batch_size_idx]
                  ):
                      # Update best loss at 2nd stage
                      best_loss_2nd_stage[local_batch_size_idx] = (
                          loss_2nd_stage[local_batch_size_idx]
                          .detach()
                          .cpu()
                          .numpy()
                      )
  
                      # Save the best adversarial example
                      successful_adv_input[
                          local_batch_size_idx
                      ] = masked_adv_input[local_batch_size_idx]
                      trans[local_batch_size_idx] = decoded_output[
                          local_batch_size_idx
                      ]
  
                  # Adjust to increase the alpha coefficient
                  if (
                      iter_2nd_stage_idx % self.num_iter_increase_alpha
                      == 0
                  ):
                      alpha[
                          local_batch_size_idx
                      ] *= self.increase_factor_alpha
  
              # Adjust to decrease the alpha coefficient
              elif (
                  iter_2nd_stage_idx % self.num_iter_decrease_alpha == 0
              ):
                  alpha[
                      local_batch_size_idx
                  ] *= self.decrease_factor_alpha
                  alpha[local_batch_size_idx] = max(
                      alpha[local_batch_size_idx], 0.0005
                  )
  
          # If attack is unsuccessful
          if iter_2nd_stage_idx == self.max_iter_2 - 1:
              for local_batch_size_idx in range(local_batch_size):
                  if successful_adv_input[local_batch_size_idx] is None:
                      successful_adv_input[
                          local_batch_size_idx
                      ] = masked_adv_input[local_batch_size_idx]
                      trans[local_batch_size_idx] = decoded_output[
                          local_batch_size_idx
                      ]
  
      result = torch.stack(successful_adv_input)  # type: ignore
  
      return result
  
imports: from __future__ import absolute_import, division, print_function, unicode_literals
  import logging
  from typing import TYPE_CHECKING, Optional, Tuple, List
  import numpy
  import scipy
  from art.attacks.attack import EvasionAttack
  from art.estimators.pytorch import PyTorchEstimator
  from art.estimators.speech_recognition.pytorch_deep_speech import PyTorchDeepSpeech
  from art.estimators.speech_recognition.speech_recognizer import SpeechRecognizerMixin
  from art.estimators.speech_recognition.speech_recognizer import PytorchSpeechRecognizerMixin
label_desc: Use image node_id 6 for calling the ImperceptibleASRPyTorch obj's underlying member method code with example usage: obj._attack_2nd_stage(x, y, theta_batch, original_max_psd_batch) and returns: result