def mst(scores, mask, multiroot=False):
"""
MST algorithm for decoding non-pojective trees.
This is a wrapper for ChuLiu/Edmonds algorithm.
The algorithm first runs ChuLiu/Edmonds to parse a tree and then have a check of multi-roots,
If ``multiroot=True`` and there indeed exist multi-roots, the algorithm seeks to find
best single-root trees by iterating all possible single-root trees parsed by ChuLiu/Edmonds.
Otherwise the resulting trees are directly taken as the final outputs.
Args:
scores (~torch.Tensor): ``[batch_size, seq_len, seq_len]``.
Scores of all dependent-head pairs.
mask (~torch.BoolTensor): ``[batch_size, seq_len]``.
Mask to avoid parsing over padding tokens.
The first column serving as pseudo words for roots should be ``False``.
muliroot (bool):
Ensures to parse a single-root tree If ``False``.
Returns:
~torch.Tensor:
A tensor with shape ``[batch_size, seq_len]`` for the resulting non-projective parse trees.
Examples:
>>> scores = torch.tensor([[[-11.9436, -13.1464, -6.4789, -13.8917],
[-60.6957, -60.2866, -48.6457, -63.8125],
[-38.1747, -49.9296, -45.2733, -49.5571],
[-19.7504, -23.9066, -9.9139, -16.2088]]])
>>> scores[:, 0, 1:] = float('-inf')
>>> scores.diagonal(0, 1, 2)[1:].fill_(float('-inf'))
>>> mask = torch.tensor([[False, True, True, True]])
>>> mst(scores, mask)
tensor([[0, 2, 0, 2]])
"""
batch_size, seq_len, _ = scores.shape
scores = scores.cpu().unbind()
preds = []
for i, length in enumerate(mask.sum(1).tolist()):
s = scores[i][:length+1, :length+1]
tree = chuliu_edmonds(s)
roots = torch.where(tree[1:].eq(0))[0] + 1
if not multiroot and len(roots) > 1:
s_root = s[:, 0]
s_best = float('-inf')
s = s.index_fill(1, torch.tensor(0), float('-inf'))
for root in roots:
s[:, 0] = float('-inf')
s[root, 0] = s_root[root]
t = chuliu_edmonds(s)
s_tree = s[1:].gather(1, t[1:].unsqueeze(-1)).sum()
if s_tree > s_best:
s_best, tree = s_tree, t
preds.append(tree)
return pad(preds, total_length=seq_len).to(mask.device)
def compose(self, sequences):
"""
Composes a batch of sequences into a padded tensor.
Args:
sequences (list[~torch.Tensor]):
A list of tensors.
Returns:
A padded tensor converted to proper device.
"""
return pad(sequences, self.pad_index).to(self.device)
def transform(self, sequences):
sequences = [[self.preprocess(token) for token in seq]
for seq in sequences]
if self.fix_len <= 0:
self.fix_len = max(
len(token) for seq in sequences for token in seq)
if self.use_vocab:
sequences = [[[self.vocab[i]
for i in token] if token else [self.unk]
for token in seq] for seq in sequences]
if self.bos:
sequences = [[[self.bos_index]] + seq for seq in sequences]
if self.eos:
sequences = [seq + [[self.eos_index]] for seq in sequences]
lens = [
min(self.fix_len, max(len(ids) for ids in seq))
for seq in sequences
]
sequences = [
pad([torch.tensor(ids[:i]) for ids in seq], self.pad_index, i)
for i, seq in zip(lens, sequences)
]
return sequences
def eisner2o(scores, mask):
"""
Second-order Eisner algorithm for projective decoding.
This is an extension of the first-order one that further incorporates sibling scores into tree scoring.
References:
- Ryan McDonald and Fernando Pereira. 2006.
`Online Learning of Approximate Dependency Parsing Algorithms`_.
Args:
scores (~torch.Tensor, ~torch.Tensor):
A tuple of two tensors representing the first-order and second-order scores repectively.
The first (``[batch_size, seq_len, seq_len]``) holds scores of all dependent-head pairs.
The second (``[batch_size, seq_len, seq_len, seq_len]``) holds scores of all dependent-head-sibling triples.
mask (~torch.BoolTensor): ``[batch_size, seq_len]``.
Mask to avoid parsing over padding tokens.
The first column serving as pseudo words for roots should be ``False``.
Returns:
~torch.Tensor:
A tensor with shape ``[batch_size, seq_len]`` for the resulting projective parse trees.
Examples:
>>> s_arc = torch.tensor([[[ -2.8092, -7.9104, -0.9414, -5.4360],
[-10.3494, -7.9298, -3.6929, -7.3985],
[ 1.1815, -3.8291, 2.3166, -2.7183],
[ -3.9776, -3.9063, -1.6762, -3.1861]]])
>>> s_sib = torch.tensor([[[[ 0.4719, 0.4154, 1.1333, 0.6946],
[ 1.1252, 1.3043, 2.1128, 1.4621],
[ 0.5974, 0.5635, 1.0115, 0.7550],
[ 1.1174, 1.3794, 2.2567, 1.4043]],
[[-2.1480, -4.1830, -2.5519, -1.8020],
[-1.2496, -1.7859, -0.0665, -0.4938],
[-2.6171, -4.0142, -2.9428, -2.2121],
[-0.5166, -1.0925, 0.5190, 0.1371]],
[[ 0.5827, -1.2499, -0.0648, -0.0497],
[ 1.4695, 0.3522, 1.5614, 1.0236],
[ 0.4647, -0.7996, -0.3801, 0.0046],
[ 1.5611, 0.3875, 1.8285, 1.0766]],
[[-1.3053, -2.9423, -1.5779, -1.2142],
[-0.1908, -0.9699, 0.3085, 0.1061],
[-1.6783, -2.8199, -1.8853, -1.5653],
[ 0.3629, -0.3488, 0.9011, 0.5674]]]])
>>> mask = torch.tensor([[False, True, True, True]])
>>> eisner2o((s_arc, s_sib), mask)
tensor([[0, 2, 0, 2]])
.. _Online Learning of Approximate Dependency Parsing Algorithms:
https://www.aclweb.org/anthology/E06-1011/
"""
# the end position of each sentence in a batch
lens = mask.sum(1)
s_arc, s_sib = scores
batch_size, seq_len, _ = s_arc.shape
# [seq_len, seq_len, batch_size]
s_arc = s_arc.permute(2, 1, 0)
# [seq_len, seq_len, seq_len, batch_size]
s_sib = s_sib.permute(2, 1, 3, 0)
s_i = torch.full_like(s_arc, float('-inf'))
s_s = torch.full_like(s_arc, float('-inf'))
s_c = torch.full_like(s_arc, float('-inf'))
p_i = s_arc.new_zeros(seq_len, seq_len, batch_size).long()
p_s = s_arc.new_zeros(seq_len, seq_len, batch_size).long()
p_c = s_arc.new_zeros(seq_len, seq_len, batch_size).long()
s_c.diagonal().fill_(0)
for w in range(1, seq_len):
# n denotes the number of spans to iterate,
# from span (0, w) to span (n, n+w) given width w
n = seq_len - w
starts = p_i.new_tensor(range(n)).unsqueeze(0)
# I(j->i) = max(I(j->r) + S(j->r, i)), i < r < j |
# C(j->j) + C(i->j-1))
# + s(j->i)
# [n, w, batch_size]
il = stripe(s_i, n, w, (w, 1)) + stripe(s_s, n, w, (1, 0), 0)
il += stripe(s_sib[range(w, n+w), range(n)], n, w, (0, 1))
# [n, 1, batch_size]
il0 = stripe(s_c, n, 1, (w, w)) + stripe(s_c, n, 1, (0, w - 1))
# il0[0] are set to zeros since the scores of the complete spans starting from 0 are always -inf
il[:, -1] = il0.index_fill_(0, lens.new_tensor(0), 0).squeeze(1)
il_span, il_path = il.permute(2, 0, 1).max(-1)
s_i.diagonal(-w).copy_(il_span + s_arc.diagonal(-w))
p_i.diagonal(-w).copy_(il_path + starts + 1)
# I(i->j) = max(I(i->r) + S(i->r, j), i < r < j |
# C(i->i) + C(j->i+1))
# + s(i->j)
# [n, w, batch_size]
ir = stripe(s_i, n, w) + stripe(s_s, n, w, (0, w), 0)
ir += stripe(s_sib[range(n), range(w, n+w)], n, w)
ir[0] = float('-inf')
# [n, 1, batch_size]
ir0 = stripe(s_c, n, 1) + stripe(s_c, n, 1, (w, 1))
ir[:, 0] = ir0.squeeze(1)
ir_span, ir_path = ir.permute(2, 0, 1).max(-1)
s_i.diagonal(w).copy_(ir_span + s_arc.diagonal(w))
p_i.diagonal(w).copy_(ir_path + starts)
# [n, w, batch_size]
slr = stripe(s_c, n, w) + stripe(s_c, n, w, (w, 1))
slr_span, slr_path = slr.permute(2, 0, 1).max(-1)
# S(j, i) = max(C(i->r) + C(j->r+1)), i <= r < j
s_s.diagonal(-w).copy_(slr_span)
p_s.diagonal(-w).copy_(slr_path + starts)
# S(i, j) = max(C(i->r) + C(j->r+1)), i <= r < j
s_s.diagonal(w).copy_(slr_span)
p_s.diagonal(w).copy_(slr_path + starts)
# C(j->i) = max(C(r->i) + I(j->r)), i <= r < j
cl = stripe(s_c, n, w, (0, 0), 0) + stripe(s_i, n, w, (w, 0))
cl_span, cl_path = cl.permute(2, 0, 1).max(-1)
s_c.diagonal(-w).copy_(cl_span)
p_c.diagonal(-w).copy_(cl_path + starts)
# C(i->j) = max(I(i->r) + C(r->j)), i < r <= j
cr = stripe(s_i, n, w, (0, 1)) + stripe(s_c, n, w, (1, w), 0)
cr_span, cr_path = cr.permute(2, 0, 1).max(-1)
s_c.diagonal(w).copy_(cr_span)
# disable multi words to modify the root
s_c[0, w][lens.ne(w)] = float('-inf')
p_c.diagonal(w).copy_(cr_path + starts + 1)
def backtrack(p_i, p_s, p_c, heads, i, j, flag):
if i == j:
return
if flag == 'c':
r = p_c[i, j]
backtrack(p_i, p_s, p_c, heads, i, r, 'i')
backtrack(p_i, p_s, p_c, heads, r, j, 'c')
elif flag == 's':
r = p_s[i, j]
i, j = sorted((i, j))
backtrack(p_i, p_s, p_c, heads, i, r, 'c')
backtrack(p_i, p_s, p_c, heads, j, r + 1, 'c')
elif flag == 'i':
r, heads[j] = p_i[i, j], i
if r == i:
r = i + 1 if i < j else i - 1
backtrack(p_i, p_s, p_c, heads, j, r, 'c')
else:
backtrack(p_i, p_s, p_c, heads, i, r, 'i')
backtrack(p_i, p_s, p_c, heads, r, j, 's')
preds = []
p_i = p_i.permute(2, 0, 1).cpu()
p_s = p_s.permute(2, 0, 1).cpu()
p_c = p_c.permute(2, 0, 1).cpu()
for i, length in enumerate(lens.tolist()):
heads = p_c.new_zeros(length + 1, dtype=torch.long)
backtrack(p_i[i], p_s[i], p_c[i], heads, 0, length, 'c')
preds.append(heads.to(mask.device))
return pad(preds, total_length=seq_len).to(mask.device)
def eisner(scores, mask):
"""
First-order Eisner algorithm for projective decoding.
References:
- Ryan McDonald, Koby Crammer and Fernando Pereira. 2005.
`Online Large-Margin Training of Dependency Parsers`_.
Args:
scores (~torch.Tensor): ``[batch_size, seq_len, seq_len]``.
Scores of all dependent-head pairs.
mask (~torch.BoolTensor): ``[batch_size, seq_len]``.
Mask to avoid parsing over padding tokens.
The first column serving as pseudo words for roots should be ``False``.
Returns:
~torch.Tensor:
A tensor with shape ``[batch_size, seq_len]`` for the resulting projective parse trees.
Examples:
>>> scores = torch.tensor([[[-13.5026, -18.3700, -13.0033, -16.6809],
[-36.5235, -28.6344, -28.4696, -31.6750],
[ -2.9084, -7.4825, -1.4861, -6.8709],
[-29.4880, -27.6905, -26.1498, -27.0233]]])
>>> mask = torch.tensor([[False, True, True, True]])
>>> eisner(scores, mask)
tensor([[0, 2, 0, 2]])
.. _Online Large-Margin Training of Dependency Parsers:
https://www.aclweb.org/anthology/P05-1012/
"""
lens = mask.sum(1)
batch_size, seq_len, _ = scores.shape
scores = scores.permute(2, 1, 0)
s_i = torch.full_like(scores, float('-inf'))
s_c = torch.full_like(scores, float('-inf'))
p_i = scores.new_zeros(seq_len, seq_len, batch_size).long()
p_c = scores.new_zeros(seq_len, seq_len, batch_size).long()
s_c.diagonal().fill_(0)
for w in range(1, seq_len):
n = seq_len - w
starts = p_i.new_tensor(range(n)).unsqueeze(0)
# ilr = C(i->r) + C(j->r+1)
ilr = stripe(s_c, n, w) + stripe(s_c, n, w, (w, 1))
# [batch_size, n, w]
il = ir = ilr.permute(2, 0, 1)
# I(j->i) = max(C(i->r) + C(j->r+1) + s(j->i)), i <= r < j
il_span, il_path = il.max(-1)
s_i.diagonal(-w).copy_(il_span + scores.diagonal(-w))
p_i.diagonal(-w).copy_(il_path + starts)
# I(i->j) = max(C(i->r) + C(j->r+1) + s(i->j)), i <= r < j
ir_span, ir_path = ir.max(-1)
s_i.diagonal(w).copy_(ir_span + scores.diagonal(w))
p_i.diagonal(w).copy_(ir_path + starts)
# C(j->i) = max(C(r->i) + I(j->r)), i <= r < j
cl = stripe(s_c, n, w, (0, 0), 0) + stripe(s_i, n, w, (w, 0))
cl_span, cl_path = cl.permute(2, 0, 1).max(-1)
s_c.diagonal(-w).copy_(cl_span)
p_c.diagonal(-w).copy_(cl_path + starts)
# C(i->j) = max(I(i->r) + C(r->j)), i < r <= j
cr = stripe(s_i, n, w, (0, 1)) + stripe(s_c, n, w, (1, w), 0)
cr_span, cr_path = cr.permute(2, 0, 1).max(-1)
s_c.diagonal(w).copy_(cr_span)
s_c[0, w][lens.ne(w)] = float('-inf')
p_c.diagonal(w).copy_(cr_path + starts + 1)
def backtrack(p_i, p_c, heads, i, j, complete):
if i == j:
return
if complete:
r = p_c[i, j]
backtrack(p_i, p_c, heads, i, r, False)
backtrack(p_i, p_c, heads, r, j, True)
else:
r, heads[j] = p_i[i, j], i
i, j = sorted((i, j))
backtrack(p_i, p_c, heads, i, r, True)
backtrack(p_i, p_c, heads, j, r + 1, True)
preds = []
p_c = p_c.permute(2, 0, 1).cpu()
p_i = p_i.permute(2, 0, 1).cpu()
for i, length in enumerate(lens.tolist()):
heads = p_c.new_zeros(length + 1, dtype=torch.long)
backtrack(p_i[i], p_c[i], heads, 0, length, True)
preds.append(heads.to(mask.device))
return pad(preds, total_length=seq_len).to(mask.device)
def compose(self, sequences):
return [pad(i).to(self.device) for i in zip(*sequences)]