import copy
import numpy
import six
from chainer import cuda
from chainer import function
from chainer import link
from chainer.utils import type_check
class TreeParser(object):
def __init__(self):
self.next_id = 0
def size(self):
return self.next_id
def get_paths(self):
return self.paths
def get_codes(self):
return self.codes
def parse(self, tree):
self.next_id = 0
self.path = []
self.code = []
self.paths = {}
self.codes = {}
self._parse(tree)
assert(len(self.path) == 0)
assert(len(self.code) == 0)
assert(len(self.paths) == len(self.codes))
def _parse(self, node):
if isinstance(node, tuple):
# internal node
if len(node) != 2:
raise ValueError(
'All internal nodes must have two child nodes')
left, right = node
self.path.append(self.next_id)
self.next_id += 1
self.code.append(1.0)
self._parse(left)
self.code[-1] = -1.0
self._parse(right)
self.path.pop()
self.code.pop()
else:
# leaf node
self.paths[node] = numpy.array(self.path, dtype=numpy.int32)
self.codes[node] = numpy.array(self.code, dtype=numpy.float32)
class BinaryHierarchicalSoftmaxFunction(function.Function):
"""Hierarchical softmax function based on a binary tree.
This function object should be allocated beforehand, and be copied on every
forward computation, since the initializer parses the given tree. See the
implementation of :class:`BinaryHierarchicalSoftmax` for details.
Args:
tree: A binary tree made with tuples like ``((1, 2), 3)``.
.. seealso::
See :class:`BinaryHierarchicalSoftmax` for details.
"""
def __init__(self, tree):
parser = TreeParser()
parser.parse(tree)
paths = parser.get_paths()
codes = parser.get_codes()
n_vocab = max(paths.keys()) + 1
self.paths = numpy.concatenate(
[paths[i] for i in range(n_vocab) if i in paths])
self.codes = numpy.concatenate(
[codes[i] for i in range(n_vocab) if i in codes])
begins = numpy.empty((n_vocab + 1,), dtype=numpy.int32)
begins[0] = 0
for i in range(0, n_vocab):
length = len(paths[i]) if i in paths else 0
begins[i + 1] = begins[i] + length
self.begins = begins
self.parser_size = parser.size()
def check_type_forward(self, in_types):
type_check.expect(in_types.size() == 3)
x_type, t_type, w_type = in_types
type_check.expect(
x_type.dtype == numpy.float32,
x_type.ndim == 2,
t_type.dtype == numpy.int32,
t_type.ndim == 1,
x_type.shape[0] == t_type.shape[0],
w_type.dtype == numpy.float32,
w_type.ndim == 2,
w_type.shape[0] == self.parser_size,
w_type.shape[1] == x_type.shape[1],
)
def to_gpu(self, device=None):
with cuda._get_device(device):
self.paths = cuda.to_gpu(self.paths)
self.codes = cuda.to_gpu(self.codes)
self.begins = cuda.to_gpu(self.begins)
def to_cpu(self):
self.paths = cuda.to_cpu(self.paths)
self.codes = cuda.to_cpu(self.codes)
self.begins = cuda.to_cpu(self.begins)
def forward_cpu(self, inputs):
x, t, W = inputs
loss = numpy.float32(0.0)
for ix, it in six.moves.zip(x, t):
loss += self._forward_cpu_one(ix, it, W)
return numpy.array(loss),
def _forward_cpu_one(self, x, t, W):
begin = self.begins[t]
end = self.begins[t + 1]
w = W[self.paths[begin:end]]
wxy = w.dot(x) * self.codes[begin:end]
loss = numpy.logaddexp(0.0, -wxy) # == log(1 + exp(-wxy))
return numpy.sum(loss)
def backward_cpu(self, inputs, grad_outputs):
x, t, W = inputs
gloss, = grad_outputs
gx = numpy.empty_like(x)
gW = numpy.zeros_like(W)
for i, (ix, it) in enumerate(six.moves.zip(x, t)):
gx[i] = self._backward_cpu_one(ix, it, W, gloss, gW)
return gx, None, gW
def _backward_cpu_one(self, x, t, W, gloss, gW):
begin = self.begins[t]
end = self.begins[t + 1]
path = self.paths[begin:end]
w = W[path]
wxy = w.dot(x) * self.codes[begin:end]
g = -gloss * self.codes[begin:end] / (1.0 + numpy.exp(wxy))
gx = g.dot(w)
gw = g.reshape((g.shape[0], 1)).dot(x.reshape(1, x.shape[0]))
gW[path] += gw
return gx
def forward_gpu(self, inputs):
x, t, W = inputs
max_length = cuda.reduce(
'T t, raw T begins', 'T out', 'begins[t + 1] - begins[t]',
'max(a, b)', 'out = a', '0',
'binary_hierarchical_softmax_max_length')(t, self.begins)
max_length = cuda.to_cpu(max_length)[()]
length = max_length * x.shape[0]
ls = cuda.cupy.empty((length,), dtype=numpy.float32)
n_in = x.shape[1]
wxy = cuda.cupy.empty_like(ls)
cuda.elementwise(
'''raw T x, raw T w, raw int32 ts, raw int32 paths,
raw T codes, raw int32 begins, int32 c, int32 max_length''',
'T ls, T wxy',
'''
int ind = i / max_length;
int offset = i - ind * max_length;
int t = ts[ind];
int begin = begins[t];
int length = begins[t + 1] - begins[t];
if (offset < length) {
int p = begin + offset;
int node = paths[p];
T wx = 0;
for (int j = 0; j < c; ++j) {
int w_ind[] = {node, j};
int x_ind[] = {ind, j};
wx += w[w_ind] * x[x_ind];
}
wxy = wx * codes[p];
ls = log(1 + exp(-wxy));
} else {
ls = 0;
}
''',
'binary_hierarchical_softmax_forward'
)(x, W, t, self.paths, self.codes, self.begins, n_in, max_length, ls,
wxy)
self.max_length = max_length
self.wxy = wxy
return ls.sum(),
def backward_gpu(self, inputs, grad_outputs):
x, t, W = inputs
gloss, = grad_outputs
n_in = x.shape[1]
gx = cuda.cupy.zeros_like(x)
gW = cuda.cupy.zeros_like(W)
cuda.elementwise(
'''T wxy, raw T x, raw T w, raw int32 ts, raw int32 paths,
raw T codes, raw int32 begins, raw T gloss,
int32 c, int32 max_length''',
'raw T gx, raw T gw',
'''
int ind = i / max_length;
int offset = i - ind * max_length;
int t = ts[ind];
int begin = begins[t];
int length = begins[t + 1] - begins[t];
if (offset < length) {
int p = begin + offset;
int node = paths[p];
T code = codes[p];
T g = -gloss[0] * code / (1.0 + exp(wxy));
for (int j = 0; j < c; ++j) {
int w_ind[] = {node, j};
int x_ind[] = {ind, j};
atomicAdd(&gx[x_ind], g * w[w_ind]);
atomicAdd(&gw[w_ind], g * x[x_ind]);
}
}
''',
'binary_hierarchical_softmax_bwd'
)(self.wxy, x, W, t, self.paths, self.codes, self.begins, gloss, n_in,
self.max_length, gx, gW)
return gx, None, gW
[docs]class BinaryHierarchicalSoftmax(link.Link):
"""Hierarchical softmax layer over binary tree.
In natural language applications, vocabulary size is too large to use
softmax loss.
Instead, the hierarchical softmax uses product of sigmoid functions.
It costs only :math:`O(\\log(n))` time where :math:`n` is the vocabulary
size in average.
At first a user need to prepare a binary tree whose each leaf is
corresponding to a word in a vocabulary.
When a word :math:`x` is given, exactly one path from the root of the tree
to the leaf of the word exists.
Let :math:`\\mbox{path}(x) = ((e_1, b_1), \\dots, (e_m, b_m))` be the path
of :math:`x`, where :math:`e_i` is an index of :math:`i`-th internal node,
and :math:`b_i \\in \\{-1, 1\\}` indicates direction to move at
:math:`i`-th internal node (-1 is left, and 1 is right).
Then, the probability of :math:`x` is given as below:
.. math::
P(x) &= \\prod_{(e_i, b_i) \\in \\mbox{path}(x)}P(b_i | e_i) \\\\
&= \\prod_{(e_i, b_i) \\in \\mbox{path}(x)}\\sigma(b_i x^\\top
w_{e_i}),
where :math:`\\sigma(\\cdot)` is a sigmoid function, and :math:`w` is a
weight matrix.
This function costs :math:`O(\\log(n))` time as an average length of paths
is :math:`O(\\log(n))`, and :math:`O(n)` memory as the number of internal
nodes equals :math:`n - 1`.
Args:
in_size (int): Dimension of input vectors.
tree: A binary tree made with tuples like `((1, 2), 3)`.
Attributes:
W (~chainer.Variable): Weight parameter matrix.
See: Hierarchical Probabilistic Neural Network Language Model [Morin+,
AISTAT2005].
"""
def __init__(self, in_size, tree):
# This function object is copied on every forward computation.
self._func = BinaryHierarchicalSoftmaxFunction(tree)
super(BinaryHierarchicalSoftmax, self).__init__(
W=(self._func.parser_size, in_size))
self.W.data[...] = numpy.random.uniform(-1, 1, self.W.shape)
def to_gpu(self, device=None):
with cuda._get_device(device):
super(BinaryHierarchicalSoftmax, self).to_gpu(device)
self._func.to_gpu(device)
def to_cpu(self):
super(BinaryHierarchicalSoftmax, self).to_cpu()
self._func.to_cpu()
@staticmethod
[docs] def create_huffman_tree(word_counts):
"""Makes a Huffman tree from a dictionary containing word counts.
This method creates a binary Huffman tree, that is required for
:class:`BinaryHierarchicalSoftmax`.
For example, ``{0: 8, 1: 5, 2: 6, 3: 4}`` is converted to
``((3, 1), (2, 0))``.
Args:
word_counts (dict of int key and int or float values):
Dictionary representing counts of words.
Returns:
Binary Huffman tree with tuples and keys of ``word_coutns``.
"""
if len(word_counts) == 0:
raise ValueError('Empty vocabulary')
q = six.moves.queue.PriorityQueue()
# Add unique id to each entry so that we can compare two entries with
# same counts.
# Note that itreitems randomly order the entries.
for uid, (w, c) in enumerate(six.iteritems(word_counts)):
q.put((c, uid, w))
while q.qsize() >= 2:
(count1, id1, word1) = q.get()
(count2, id2, word2) = q.get()
count = count1 + count2
tree = (word1, word2)
q.put((count, min(id1, id2), tree))
return q.get()[2]
[docs] def __call__(self, x, t):
"""Computes the loss value for given input and ground truth labels.
Args:
x (~chainer.Variable): Input to the classifier at each node.
t (~chainer.Variable): Batch of ground truth labels.
Returns:
~chainer.Variable: Loss value.
"""
f = copy.copy(self._func) # creates a copy of the function node
return f(x, t, self.W)