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import torch.nn as nn
import torch
import torch.cuda
class MatrixTree(nn.Module):
"""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`.
"""
def __init__(self, eps=1e-5):
self.eps = eps
super(MatrixTree, self).__init__()
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
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