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wehub-resource-sync 1fad2ccf05 chore: import upstream snapshot with attribution
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# MIT License
#
# Copyright (c) 2020 Yu Zhang
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
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# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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# SOFTWARE.
import torch
from hanlp_common.conll import isprojective
def kmeans(x, k, max_it=32):
r"""
KMeans algorithm for clustering the sentences by length.
Args:
x (list[int]):
The list of sentence lengths.
k (int):
The number of clusters.
This is an approximate value. The final number of clusters can be less or equal to `k`.
max_it (int):
Maximum number of iterations.
If centroids does not converge after several iterations, the algorithm will be early stopped.
Returns:
list[float], list[list[int]]:
The first list contains average lengths of sentences in each cluster.
The second is the list of clusters holding indices of data points.
Examples:
>>> x = torch.randint(10,20,(10,)).tolist()
>>> x
[15, 10, 17, 11, 18, 13, 17, 19, 18, 14]
>>> centroids, clusters = kmeans(x, 3)
>>> centroids
[10.5, 14.0, 17.799999237060547]
>>> clusters
[[1, 3], [0, 5, 9], [2, 4, 6, 7, 8]]
"""
# the number of clusters must not be greater than the number of datapoints
x, k = torch.tensor(x, dtype=torch.float), min(len(x), k)
# collect unique datapoints
d = x.unique()
# initialize k centroids randomly
c = d[torch.randperm(len(d))[:k]]
# assign each datapoint to the cluster with the closest centroid
dists, y = torch.abs_(x.unsqueeze(-1) - c).min(-1)
for _ in range(max_it):
# if an empty cluster is encountered,
# choose the farthest datapoint from the biggest cluster and move that the empty one
mask = torch.arange(k).unsqueeze(-1).eq(y)
none = torch.where(~mask.any(-1))[0].tolist()
while len(none) > 0:
for i in none:
# the biggest cluster
b = torch.where(mask[mask.sum(-1).argmax()])[0]
# the datapoint farthest from the centroid of cluster b
f = dists[b].argmax()
# update the assigned cluster of f
y[b[f]] = i
# re-calculate the mask
mask = torch.arange(k).unsqueeze(-1).eq(y)
none = torch.where(~mask.any(-1))[0].tolist()
# update the centroids
c, old = (x * mask).sum(-1) / mask.sum(-1), c
# re-assign all datapoints to clusters
dists, y = torch.abs_(x.unsqueeze(-1) - c).min(-1)
# stop iteration early if the centroids converge
if c.equal(old):
break
# assign all datapoints to the new-generated clusters
# the empty ones are discarded
assigned = y.unique().tolist()
# get the centroids of the assigned clusters
centroids = c[assigned].tolist()
# map all values of datapoints to buckets
clusters = [torch.where(y.eq(i))[0].tolist() for i in assigned]
return centroids, clusters
def eisner(scores, mask):
r"""
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]``.
The 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 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)
def stripe(x, n, w, offset=(0, 0), dim=1):
"""r'''Returns a diagonal stripe of the tensor.
Args:
x: Tensor
n: int
w: int
offset: tuple (Default value = (0)
dim: int (Default value = 1)
Example:
0):
Returns:
>>> x = torch.arange(25).view(5, 5)
>>> x
tensor([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24]])
>>> stripe(x, 2, 3, (1, 1))
tensor([[ 6, 7, 8],
[12, 13, 14]])
>>> stripe(x, 2, 3, dim=0)
tensor([[ 0, 5, 10],
[ 6, 11, 16]])
"""
x, seq_len = x.contiguous(), x.size(1)
stride, numel = list(x.stride()), x[0, 0].numel()
stride[0] = (seq_len + 1) * numel
stride[1] = (1 if dim == 1 else seq_len) * numel
return x.as_strided(size=(n, w, *x.shape[2:]),
stride=stride,
storage_offset=(offset[0] * seq_len + offset[1]) * numel)
def cky(scores, mask):
r"""
The implementation of `Cocke-Kasami-Younger`_ (CKY) algorithm to parse constituency trees.
References:
- Yu Zhang, Houquan Zhou and Zhenghua Li. 2020.
`Fast and Accurate Neural CRF Constituency Parsing`_.
Args:
scores (~torch.Tensor): ``[batch_size, seq_len, seq_len]``.
Scores of all candidate constituents.
mask (~torch.BoolTensor): ``[batch_size, seq_len, seq_len]``.
The mask to avoid parsing over padding tokens.
For each square matrix in a batch, the positions except upper triangular part should be masked out.
Returns:
Sequences of factorized predicted bracketed trees that are traversed in pre-order.
Examples:
>>> scores = torch.tensor([[[ 2.5659, 1.4253, -2.5272, 3.3011],
[ 1.3687, -0.5869, 1.0011, 3.3020],
[ 1.2297, 0.4862, 1.1975, 2.5387],
[-0.0511, -1.2541, -0.7577, 0.2659]]])
>>> mask = torch.tensor([[[False, True, True, True],
[False, False, True, True],
[False, False, False, True],
[False, False, False, False]]])
>>> cky(scores, mask)
[[(0, 3), (0, 1), (1, 3), (1, 2), (2, 3)]]
.. _Cocke-Kasami-Younger:
https://en.wikipedia.org/wiki/CYK_algorithm
.. _Fast and Accurate Neural CRF Constituency Parsing:
https://www.ijcai.org/Proceedings/2020/560/
"""
lens = mask[:, 0].sum(-1)
scores = scores.permute(1, 2, 0)
seq_len, seq_len, batch_size = scores.shape
s = scores.new_zeros(seq_len, seq_len, batch_size)
p = scores.new_zeros(seq_len, seq_len, batch_size).long()
for w in range(1, seq_len):
n = seq_len - w
starts = p.new_tensor(range(n)).unsqueeze(0)
if w == 1:
s.diagonal(w).copy_(scores.diagonal(w))
continue
# [n, w, batch_size]
s_span = stripe(s, n, w - 1, (0, 1)) + stripe(s, n, w - 1, (1, w), 0)
# [batch_size, n, w]
s_span = s_span.permute(2, 0, 1)
# [batch_size, n]
s_span, p_span = s_span.max(-1)
s.diagonal(w).copy_(s_span + scores.diagonal(w))
p.diagonal(w).copy_(p_span + starts + 1)
def backtrack(p, i, j):
if j == i + 1:
return [(i, j)]
split = p[i][j]
ltree = backtrack(p, i, split)
rtree = backtrack(p, split, j)
return [(i, j)] + ltree + rtree
p = p.permute(2, 0, 1).tolist()
trees = [backtrack(p[i], 0, length) if length else [] for i, length in enumerate(lens.tolist())]
return trees
def istree(sequence, proj=False, multiroot=False):
r"""
Checks if the arcs form an valid dependency tree.
Args:
sequence (list[int]):
A list of head indices.
proj (bool):
If ``True``, requires the tree to be projective. Default: ``False``.
multiroot (bool):
If ``False``, requires the tree to contain only a single root. Default: ``True``.
Returns:
``True`` if the arcs form an valid tree, ``False`` otherwise.
Examples:
>>> istree([3, 0, 0, 3], multiroot=True)
True
>>> istree([3, 0, 0, 3], proj=True)
False
"""
if proj and not isprojective(sequence):
return False
n_roots = sum(head == 0 for head in sequence)
if n_roots == 0:
return False
if not multiroot and n_roots > 1:
return False
if any(i == head for i, head in enumerate(sequence, 1)):
return False
return next(tarjan(sequence), None) is None
def tarjan(sequence):
r"""
Tarjan algorithm for finding Strongly Connected Components (SCCs) of a graph.
Args:
sequence (list):
List of head indices.
Yields:
A list of indices that make up a SCC. All self-loops are ignored.
Examples:
>>> next(tarjan([2, 5, 0, 3, 1])) # (1 -> 5 -> 2 -> 1) is a cycle
[2, 5, 1]
"""
sequence = [-1] + sequence
# record the search order, i.e., the timestep
dfn = [-1] * len(sequence)
# record the the smallest timestep in a SCC
low = [-1] * len(sequence)
# push the visited into the stack
stack, onstack = [], [False] * len(sequence)
def connect(i, timestep):
dfn[i] = low[i] = timestep[0]
timestep[0] += 1
stack.append(i)
onstack[i] = True
for j, head in enumerate(sequence):
if head != i:
continue
if dfn[j] == -1:
yield from connect(j, timestep)
low[i] = min(low[i], low[j])
elif onstack[j]:
low[i] = min(low[i], dfn[j])
# a SCC is completed
if low[i] == dfn[i]:
cycle = [stack.pop()]
while cycle[-1] != i:
onstack[cycle[-1]] = False
cycle.append(stack.pop())
onstack[i] = False
# ignore the self-loop
if len(cycle) > 1:
yield cycle
timestep = [0]
for i in range(len(sequence)):
if dfn[i] == -1:
yield from connect(i, timestep)
def chuliu_edmonds(s):
r"""
ChuLiu/Edmonds algorithm for non-projective decoding.
Some code is borrowed from `tdozat's implementation`_.
Descriptions of notations and formulas can be found in
`Non-projective Dependency Parsing using Spanning Tree Algorithms`_.
Notes:
The algorithm does not guarantee to parse a single-root tree.
References:
- Ryan McDonald, Fernando Pereira, Kiril Ribarov and Jan Hajic. 2005.
`Non-projective Dependency Parsing using Spanning Tree Algorithms`_.
Args:
s (~torch.Tensor): ``[seq_len, seq_len]``.
Scores of all dependent-head pairs.
Returns:
~torch.Tensor:
A tensor with shape ``[seq_len]`` for the resulting non-projective parse tree.
.. _tdozat's implementation:
https://github.com/tdozat/Parser-v3
.. _Non-projective Dependency Parsing using Spanning Tree Algorithms:
https://www.aclweb.org/anthology/H05-1066/
"""
s[0, 1:] = float('-inf')
# prevent self-loops
s.diagonal()[1:].fill_(float('-inf'))
# select heads with highest scores
tree = s.argmax(-1)
# return the cycle finded by tarjan algorithm lazily
cycle = next(tarjan(tree.tolist()[1:]), None)
# if the tree has no cycles, then it is a MST
if not cycle:
return tree
# indices of cycle in the original tree
cycle = torch.tensor(cycle)
# indices of noncycle in the original tree
noncycle = torch.ones(len(s)).index_fill_(0, cycle, 0)
noncycle = torch.where(noncycle.gt(0))[0]
def contract(s):
# heads of cycle in original tree
cycle_heads = tree[cycle]
# scores of cycle in original tree
s_cycle = s[cycle, cycle_heads]
# calculate the scores of cycle's potential dependents
# s(c->x) = max(s(x'->x)), x in noncycle and x' in cycle
s_dep = s[noncycle][:, cycle]
# find the best cycle head for each noncycle dependent
deps = s_dep.argmax(1)
# calculate the scores of cycle's potential heads
# s(x->c) = max(s(x'->x) - s(a(x')->x') + s(cycle)), x in noncycle and x' in cycle
# a(v) is the predecessor of v in cycle
# s(cycle) = sum(s(a(v)->v))
s_head = s[cycle][:, noncycle] - s_cycle.view(-1, 1) + s_cycle.sum()
# find the best noncycle head for each cycle dependent
heads = s_head.argmax(0)
contracted = torch.cat((noncycle, torch.tensor([-1])))
# calculate the scores of contracted graph
s = s[contracted][:, contracted]
# set the contracted graph scores of cycle's potential dependents
s[:-1, -1] = s_dep[range(len(deps)), deps]
# set the contracted graph scores of cycle's potential heads
s[-1, :-1] = s_head[heads, range(len(heads))]
return s, heads, deps
# keep track of the endpoints of the edges into and out of cycle for reconstruction later
s, heads, deps = contract(s)
# y is the contracted tree
y = chuliu_edmonds(s)
# exclude head of cycle from y
y, cycle_head = y[:-1], y[-1]
# fix the subtree with no heads coming from the cycle
# len(y) denotes heads coming from the cycle
subtree = y < len(y)
# add the nodes to the new tree
tree[noncycle[subtree]] = noncycle[y[subtree]]
# fix the subtree with heads coming from the cycle
subtree = ~subtree
# add the nodes to the tree
tree[noncycle[subtree]] = cycle[deps[subtree]]
# fix the root of the cycle
cycle_root = heads[cycle_head]
# break the cycle and add the root of the cycle to the tree
tree[cycle[cycle_root]] = noncycle[cycle_head]
return tree
def mst(scores, mask, multiroot=False):
r"""
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]``.
The 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.detach().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 eisner2o(scores, mask):
r"""
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]``.
The 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 pad(tensors, padding_value=0, total_length=None):
size = [len(tensors)] + [max(tensor.size(i) for tensor in tensors)
for i in range(len(tensors[0].size()))]
if total_length is not None:
assert total_length >= size[1]
size[1] = total_length
out_tensor = tensors[0].data.new(*size).fill_(padding_value)
for i, tensor in enumerate(tensors):
out_tensor[i][[slice(0, i) for i in tensor.size()]] = tensor
return out_tensor
def decode_dep(s_arc, mask, tree=False, proj=False):
r"""
Args:
s_arc (~torch.Tensor): ``[batch_size, seq_len, seq_len]``.
Scores of all possible arcs.
mask (~torch.BoolTensor): ``[batch_size, seq_len]``.
The mask for covering the unpadded tokens.
tree (bool):
If ``True``, ensures to output well-formed trees. Default: ``False``.
proj (bool):
If ``True``, ensures to output projective trees. Default: ``False``.
Returns:
~torch.Tensor, ~torch.Tensor:
Predicted arcs and labels of shape ``[batch_size, seq_len]``.
"""
lens = mask.sum(1)
arc_preds = s_arc.argmax(-1)
bad = [not istree(seq[1:i + 1], proj) for i, seq in zip(lens.tolist(), arc_preds.tolist())]
if tree and any(bad):
if proj:
alg = eisner
else:
alg = mst
s_arc.diagonal(0, 1, 2)[1:].fill_(float('-inf'))
arc_preds[bad] = alg(s_arc[bad], mask[bad])
return arc_preds
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