code: def _generate_noise(
      std: float,
      reference: torch.Tensor,
      generator=None,
      secure_mode: bool = False,
  ) -> torch.Tensor:
      """
      Generates noise according to a Gaussian distribution with mean 0
  
      Args:
          std: Standard deviation of the noise
          reference: The reference Tensor to get the appropriate shape and device
              for generating the noise
          generator: The PyTorch noise generator
          secure_mode: boolean showing if "secure" noise need to be generated
              (see the notes)
  
      Notes:
          If `secure_mode` is enabled, the generated noise is also secure
          against the floating point representation attacks, such as the ones
          in https://arxiv.org/abs/2107.10138 and https://arxiv.org/abs/2112.05307.
          The attack for Opacus first appeared in https://arxiv.org/abs/2112.05307.
          The implemented fix is based on https://arxiv.org/abs/2107.10138 and is
          achieved through calling the Gaussian noise function 2*n times, when n=2
          (see section 5.1 in https://arxiv.org/abs/2107.10138).
  
          Reason for choosing n=2: n can be any number > 1. The bigger, the more
          computation needs to be done (`2n` Gaussian samples will be generated).
          The reason we chose `n=2` is that, `n=1` could be easy to break and `n>2`
          is not really necessary. The complexity of the attack is `2^p(2n-1)`.
          In PyTorch, `p=53` and so complexity is `2^53(2n-1)`. With `n=1`, we get
          `2^53` (easy to break) but with `n=2`, we get `2^159`, which is hard
          enough for an attacker to break.
      """
      zeros = torch.zeros(reference.shape, device=reference.device)
      if std == 0:
          return zeros
      # TODO: handle device transfers: generator and reference tensor
      # could be on different devices
      if secure_mode:
          torch.normal(
              mean=0,
              std=std,
              size=(1, 1),
              device=reference.device,
              generator=generator,
          )  # generate, but throw away first generated Gaussian sample
          sum = zeros
          for _ in range(4):
              sum += torch.normal(
                  mean=0,
                  std=std,
                  size=reference.shape,
                  device=reference.device,
                  generator=generator,
              )
          return sum / 2
      else:
          return torch.normal(
              mean=0,
              std=std,
              size=reference.shape,
              device=reference.device,
              generator=generator,
          )
  
imports: from __future__ import annotations
  import logging
  from typing import Callable, List, Optional, Union
  import torch
  from opacus.optimizers.utils import params
  from opt_einsum.contract import contract
  from torch import nn
  from torch.optim import Optimizer
label_desc: Use image node_id 4 for calling a global function with example usage: _generate_noise(std, reference, generator, secure_mode) and returns: zeros, unknown, torch