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 first 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.
  :return: A tuple of two tensors:
              - A tensor holding the candidate adversarial examples.
              - An array holding the original inputs.
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code: def _attack_1st_stage(
      self, x: np.ndarray, y: np.ndarray
  ) -> Tuple["torch.Tensor", np.ndarray]:
      """
      The first 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.
      :return: A tuple of two tensors:
                  - A tensor holding the candidate adversarial examples.
                  - An array holding the original inputs.
      """
      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 rescale
      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
      trans = [None] * local_batch_size
  
      for iter_1st_stage_idx in range(self.max_iter_1):
          # Zero the parameter gradients
          self.optimizer_1.zero_grad()
  
          # Call to forward pass
          (
              loss,
              local_delta,
              decoded_output,
              masked_adv_input,
              _,
          ) = 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,
          )
  
          # Actual training
          if self._use_amp:  # pragma: no cover
              from apex import amp  # pylint: disable=E0611
  
              with amp.scale_loss(
                  loss, self.optimizer_1
              ) as scaled_loss:
                  scaled_loss.backward()
  
          else:
              loss.backward()
  
          # Get sign of the gradients
          if self.global_optimal_delta.grad is not None:
              self.global_optimal_delta.grad = torch.sign(
                  self.global_optimal_delta.grad
              )
          else:
              raise ValueError(
                  "Received None instead of gradient tensor."
              )
  
          # Do optimization
          self.optimizer_1.step()
  
          # Save the best adversarial example and adjust the rescale coefficient if successful
          if iter_1st_stage_idx % self.num_iter_decrease_eps == 0:
              for local_batch_size_idx in range(local_batch_size):
                  if (
                      decoded_output[local_batch_size_idx]
                      == y[local_batch_size_idx]
                  ):
                      # Adjust the rescale coefficient
                      max_local_delta = np.max(
                          np.abs(
                              local_delta[local_batch_size_idx]
                              .detach()
                              .cpu()
                              .numpy()
                          )
                      )
  
                      if (
                          rescale[local_batch_size_idx][0] * self.eps
                          > max_local_delta
                      ):
                          rescale[local_batch_size_idx] = (
                              max_local_delta / self.eps
                          )
                      rescale[
                          local_batch_size_idx
                      ] *= self.decrease_factor_eps
  
                      # 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
                      ]
  
          # If attack is unsuccessful
          if iter_1st_stage_idx == self.max_iter_1 - 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, original_input
  
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 4 for calling the ImperceptibleASRPyTorch obj's underlying member method code with example usage: obj._attack_1st_stage(x, y) and returns: result,  original_input