code: def dense_diff_pool(
      x: Tensor,
      adj: Tensor,
      s: Tensor,
      mask: Optional[Tensor] = None,
      normalize: bool = True,
  ) -> Tuple[Tensor, Tensor, Tensor, Tensor]:
      r"""The differentiable pooling operator from the `"Hierarchical Graph
      Representation Learning with Differentiable Pooling"
      <https://arxiv.org/abs/1806.08804>`_ paper.
  
      .. math::
          \mathbf{X}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot
          \mathbf{X}
  
          \mathbf{A}^{\prime} &= {\mathrm{softmax}(\mathbf{S})}^{\top} \cdot
          \mathbf{A} \cdot \mathrm{softmax}(\mathbf{S})
  
      based on dense learned assignments :math:`\mathbf{S} \in \mathbb{R}^{B
      \times N \times C}`.
      Returns the pooled node feature matrix, the coarsened adjacency matrix and
      two auxiliary objectives: (1) The link prediction loss
  
      .. math::
          \mathcal{L}_{LP} = {\| \mathbf{A} -
          \mathrm{softmax}(\mathbf{S}) {\mathrm{softmax}(\mathbf{S})}^{\top}
          \|}_F,
  
      and (2) the entropy regularization
  
      .. math::
          \mathcal{L}_E = \frac{1}{N} \sum_{n=1}^N H(\mathbf{S}_n).
  
      Args:
          x (torch.Tensor): Node feature tensor
              :math:`\mathbf{X} \in \mathbb{R}^{B \times N \times F}`, with
              batch-size :math:`B`, (maximum) number of nodes :math:`N` for
              each graph, and feature dimension :math:`F`.
          adj (torch.Tensor): Adjacency tensor
              :math:`\mathbf{A} \in \mathbb{R}^{B \times N \times N}`.
          s (torch.Tensor): Assignment tensor
              :math:`\mathbf{S} \in \mathbb{R}^{B \times N \times C}`
              with number of clusters :math:`C`.
              The softmax does not have to be applied before-hand, since it is
              executed within this method.
          mask (torch.Tensor, optional): Mask matrix
              :math:`\mathbf{M} \in {\{ 0, 1 \}}^{B \times N}` indicating
              the valid nodes for each graph. (default: :obj:`None`)
          normalize (bool, optional): If set to :obj:`False`, the link
              prediction loss is not divided by :obj:`adj.numel()`.
              (default: :obj:`True`)
  
      :rtype: (:class:`torch.Tensor`, :class:`torch.Tensor`,
          :class:`torch.Tensor`, :class:`torch.Tensor`)
      """
      x = x.unsqueeze(0) if x.dim() == 2 else x
      adj = adj.unsqueeze(0) if adj.dim() == 2 else adj
      s = s.unsqueeze(0) if s.dim() == 2 else s
  
      batch_size, num_nodes, _ = x.size()
  
      s = torch.softmax(s, dim=-1)
  
      if mask is not None:
          mask = mask.view(batch_size, num_nodes, 1).to(x.dtype)
          x, s = x * mask, s * mask
  
      out = torch.matmul(s.transpose(1, 2), x)
      out_adj = torch.matmul(torch.matmul(s.transpose(1, 2), adj), s)
  
      link_loss = adj - torch.matmul(s, s.transpose(1, 2))
      link_loss = torch.norm(link_loss, p=2)
      if normalize is True:
          link_loss = link_loss / adj.numel()
  
      ent_loss = (-s * torch.log(s + 1e-15)).sum(dim=-1).mean()
  
      return out, out_adj, link_loss, ent_loss
  
label_desc: Use image node_id 1 for calling a global function with example usage: dense_diff_pool(x, adj, s, mask, normalize) and returns: out,  out_adj,  link_loss,  ent_loss