code: def negative_sampling(
      x, t, W, sampler, sample_size, reduce="sum", **kwargs
  ):
      """negative_sampling(x, t, W, sampler, sample_size, reduce='sum', *, \
  return_samples=False)
  
      Negative sampling loss function.
  
      In natural language processing, especially language modeling, the number of
      words in a vocabulary can be very large.
      Therefore, you need to spend a lot of time calculating the gradient of the
      embedding matrix.
  
      By using the negative sampling trick you only need to calculate the
      gradient for a few sampled negative examples.
  
      The loss is defined as follows.
  
      .. math::
  
         f(x, p) = - \\log \\sigma(x^\\top w_p) - \\
         k E_{i \\sim P(i)}[\\log \\sigma(- x^\\top w_i)]
  
      where :math:`\\sigma(\\cdot)` is a sigmoid function, :math:`w_i` is the
      weight vector for the word :math:`i`, and :math:`p` is a positive example.
      It is approximated with :math:`k` examples :math:`N` sampled from
      probability :math:`P(i)`.
  
      .. math::
  
         f(x, p) \\approx - \\log \\sigma(x^\\top w_p) - \\
         \\sum_{n \\in N} \\log \\sigma(-x^\\top w_n)
  
      Each sample of :math:`N` is drawn from the word distribution
      :math:`P(w) = \\frac{1}{Z} c(w)^\\alpha`, where :math:`c(w)` is the
      unigram count of the word :math:`w`, :math:`\\alpha` is a hyper-parameter,
      and :math:`Z` is the normalization constant.
  
      Args:
          x (:class:`~chainer.Variable` or :ref:`ndarray`):
              Batch of input vectors.
          t (:class:`~chainer.Variable` or :ref:`ndarray`):
              Vector of ground truth labels.
          W (:class:`~chainer.Variable` or :ref:`ndarray`):
              Weight matrix.
          sampler (~types.FunctionType): Sampling function. It takes a shape and
              returns an integer array of the shape. Each element of this array
              is a sample from the word distribution.
              A :class:`~chainer.utils.WalkerAlias` object built with the power
              distribution of word frequency is recommended.
          sample_size (int): Number of samples.
          reduce (str): Reduction option. Its value must be either
              ``'sum'`` or ``'no'``. Otherwise, :class:`ValueError` is raised.
          return_samples (bool):
              If ``True``, the sample array is also returned.
              The sample array is a
              :math:`(\\text{batch_size}, \\text{sample_size} + 1)`-array of
              integers whose first column is fixed to the ground truth labels
              and the other columns are drawn from the ``sampler``.
  
      Returns:
          ~chainer.Variable or tuple:
              If ``return_samples`` is ``False`` (default), the output
              variable holding the loss value(s) calculated by the
              above equation is returned. Otherwise, a tuple of the output
              variable and the sample array is returned.
  
              If ``reduce`` is ``'no'``, the output variable holds array
              whose shape is same as one of (hence both of) input variables.
              If it is ``'sum'``, the output variable holds a scalar value.
  
      See: `Distributed Representations of Words and Phrases and their
      Compositionality <https://arxiv.org/abs/1310.4546>`_
  
      .. seealso::
  
          :class:`~chainer.links.NegativeSampling` to manage the model parameter
          ``W``.
  
      """
      return_samples = False
      if kwargs:
          (return_samples,) = argument.parse_kwargs(
              kwargs, ("return_samples", return_samples)
          )
  
      func = NegativeSamplingFunction(sampler, sample_size, reduce)
      out = func.apply((x, t, W))[0]
  
      if return_samples:
          return out, func.samples
      return out
  
imports: import numpy
  import six
  import chainer
  from chainer import backend
  from chainer.backends import cuda
  from chainer import function_node
  from chainer import utils
  from chainer.utils import argument
  from chainer.utils import precision
  from chainer.utils import type_check
label_desc: Use image node_id 2 for calling a global function with example usage: negative_sampling(x, t, W, sampler, sample_size, reduce) and returns: out, out,  func