class_docstr: Implementation of the matrix-tree theorem for computing marginals
  of non-projective dependency parsing. This attention layer is used
  in the paper "Learning Structured Text Representations"
  :cite:`DBLP:journals/corr/LiuL17d`.
code: def forward(self, input):
      laplacian = input.exp() + self.eps
      output = input.clone()
      for b in range(input.size(0)):
          lap = laplacian[b].masked_fill(
              torch.eye(input.size(1), device=input.device).ne(0), 0
          )
          lap = -lap + torch.diag(lap.sum(0))
          # store roots on diagonal
          lap[0] = input[b].diag().exp()
          inv_laplacian = lap.inverse()
  
          factor = (
              inv_laplacian.diag()
              .unsqueeze(1)
              .expand_as(input[b])
              .transpose(0, 1)
          )
          term1 = input[b].exp().mul(factor).clone()
          term2 = (
              input[b].exp().mul(inv_laplacian.transpose(0, 1)).clone()
          )
          term1[:, 0] = 0
          term2[0] = 0
          output[b] = term1 - term2
          roots_output = (
              input[b]
              .diag()
              .exp()
              .mul(inv_laplacian.transpose(0, 1)[0])
          )
          output[b] = output[b] + torch.diag(roots_output)
      return output
  
imports: import torch.nn
  import torch
  import torch.cuda
label_desc: Use image node_id 2 for calling the MatrixTree obj's underlying member method code with example usage: obj.forward(input) and returns: output