import numpy
import six
from chainer import cuda
from chainer import function
from chainer.utils import type_check
def _extract_gates(x):
r = x.reshape((x.shape[0], x.shape[1] // 4, 4) + x.shape[2:])
return (r[:, :, i] for i in six.moves.range(4))
def _sigmoid(x):
half = x.dtype.type(0.5)
return numpy.tanh(x * half) * half + half
def _grad_sigmoid(x):
return x * (1 - x)
def _grad_tanh(x):
return 1 - x * x
_preamble = '''
template <typename T> __device__ T sigmoid(T x) {
const T half = 0.5;
return tanh(x * half) * half + half;
}
template <typename T> __device__ T grad_sigmoid(T y) { return y * (1 - y); }
template <typename T> __device__ T grad_tanh(T y) { return 1 - y * y; }
#define COMMON_ROUTINE \
T aa1 = tanh(a1); \
T ai1 = sigmoid(i1); \
T af1 = sigmoid(f1); \
T aa2 = tanh(a2); \
T ai2 = sigmoid(i2); \
T af2 = sigmoid(f2); \
T ao = sigmoid(o1 + o2);
'''
class SLSTM(function.Function):
"""S-LSTM unit.
It has four inputs (c1, c2, x1, x2) and two outputs (c, h), where c
indicates the cell state. x1 and x2 must have four times channels compared
to the number of units.
"""
def check_type_forward(self, in_types):
type_check.expect(in_types.size() == 4)
c1_type, c2_type, x1_type, x2_type = in_types
type_check.expect(
c1_type.dtype.kind == 'f',
c2_type.dtype == c1_type.dtype,
x1_type.dtype == c1_type.dtype,
x2_type.dtype == c1_type.dtype,
c1_type.ndim >= 2,
c2_type.ndim >= 2,
x1_type.ndim >= 2,
x2_type.ndim >= 2,
c1_type.ndim == x1_type.ndim,
c1_type.ndim == c2_type.ndim,
c1_type.ndim == x2_type.ndim,
c1_type.shape[0] == x1_type.shape[0],
c1_type.shape[0] == c2_type.shape[0],
c1_type.shape[0] == x2_type.shape[0],
x1_type.shape[1] == 4 * c1_type.shape[1],
x2_type.shape[1] == 4 * c2_type.shape[1],
)
for i in range(2, c1_type.ndim.eval()):
type_check.expect(x1_type.shape[i] == c1_type.shape[i])
type_check.expect(x2_type.shape[i] == c2_type.shape[i])
type_check.expect(x1_type.shape[i] == x2_type.shape[i])
def forward(self, inputs):
c_prev1, c_prev2, x1, x2 = inputs
a1, i1, f1, o1 = _extract_gates(x1)
a2, i2, f2, o2 = _extract_gates(x2)
if isinstance(x1, numpy.ndarray):
self.a1 = numpy.tanh(a1)
self.i1 = _sigmoid(i1)
self.f1 = _sigmoid(f1)
self.a2 = numpy.tanh(a2)
self.i2 = _sigmoid(i2)
self.f2 = _sigmoid(f2)
self.o = _sigmoid(o1 + o2)
self.c = self.a1 * self.i1 + self.a2 * self.i2 + \
self.f1 * c_prev1 + self.f2 * c_prev2
h = self.o * numpy.tanh(self.c)
else:
self.c, h = cuda.elementwise(
'''T c_prev1, T a1, T i1, T f1, T o1,
T c_prev2, T a2, T i2, T f2, T o2''',
'T c, T h',
'''
COMMON_ROUTINE;
c = aa1 * ai1 + af1 * c_prev1 + aa2 * ai2 + af2 * c_prev2;
h = ao * tanh(c);
''',
'slstm_fwd', preamble=_preamble)(
c_prev1, a1, i1, f1, o1, c_prev2, a2, i2, f2, o2)
return self.c, h
def backward(self, inputs, grad_outputs):
xp = cuda.get_array_module(*inputs)
c_prev1, c_prev2, x1, x2 = inputs
gc, gh = grad_outputs
gx1 = xp.empty_like(x1)
gx2 = xp.empty_like(x2)
ga1, gi1, gf1, go1 = _extract_gates(gx1)
ga2, gi2, gf2, go2 = _extract_gates(gx2)
# Consider the case that either gradient is not given
if gc is None:
gc = 0
if gh is None:
gh = 0
if xp is numpy:
co = numpy.tanh(self.c)
# multiply f later
gc_prev = gh * self.o * _grad_tanh(co) + gc
ga1[:] = gc_prev * self.i1 * _grad_tanh(self.a1)
gi1[:] = gc_prev * self.a1 * _grad_sigmoid(self.i1)
gf1[:] = gc_prev * c_prev1 * _grad_sigmoid(self.f1)
go1[:] = gh * co * _grad_sigmoid(self.o)
ga2[:] = gc_prev * self.i2 * _grad_tanh(self.a2)
gi2[:] = gc_prev * self.a2 * _grad_sigmoid(self.i2)
gf2[:] = gc_prev * c_prev2 * _grad_sigmoid(self.f2)
go2[:] = gh * co * _grad_sigmoid(self.o)
# multiply f here
gc_prev1 = gc_prev * self.f1
gc_prev2 = gc_prev * self.f2
else:
a1, i1, f1, o1 = _extract_gates(x1)
a2, i2, f2, o2 = _extract_gates(x2)
gc_prev1 = xp.empty_like(c_prev1)
gc_prev2 = xp.empty_like(c_prev2)
cuda.elementwise(
'''T c_prev1, T a1, T i1, T f1, T o1,
T c_prev2, T a2, T i2, T f2, T o2,
T c, T gc, T gh''',
'''T gc_prev1, T ga1, T gi1, T gf1, T go1,
T gc_prev2, T ga2, T gi2, T gf2, T go2''',
'''
COMMON_ROUTINE;
T co = tanh(c);
T temp = gh * ao * grad_tanh(co) + gc;
ga1 = temp * ai1 * grad_tanh(aa1);
gi1 = temp * aa1 * grad_sigmoid(ai1);
gf1 = temp * c_prev1 * grad_sigmoid(af1);
go1 = gh * co * grad_sigmoid(ao);
gc_prev1 = temp * af1;
ga2 = temp * ai2 * grad_tanh(aa2);
gi2 = temp * aa2 * grad_sigmoid(ai2);
gf2 = temp * c_prev2 * grad_sigmoid(af2);
go2 = gh * co * grad_sigmoid(ao);
gc_prev2 = temp * af2;
''',
'lstm_bwd', preamble=_preamble)(
c_prev1, a1, i1, f1, o1,
c_prev2, a2, i2, f2, o2,
self.c, gc, gh,
gc_prev1, ga1, gi1, gf1, go1,
gc_prev2, ga2, gi2, gf2, go2)
return gc_prev1, gc_prev2, gx1, gx2
[docs]def slstm(c_prev1, c_prev2, x1, x2):
"""S-LSTM units as an activation function.
This function implements S-LSTM unit. It is an extension of LSTM unit
applied to tree structures.
The function is applied to binary trees. Each node has two child nodes.
It gets four arguments, previous cell states ``c_prev1`` and ``c_prev2``,
and input arrays ``x1`` and ``x2``.
First both input arrays ``x1`` and ``x2`` are split into eight arrays
:math:`a_1, i_1, f_1, o_1`, and :math:`a_2, i_2, f_2, o_2`. They have the
same shape along the second axis.
It means that ``x1`` and ``x2`` 's second axis must have 4 times
the length of ``c_prev1`` and ``c_prev2``.
The split input arrays are corresponding to:
- :math:`a_i` : sources of cell input
- :math:`i_i` : sources of input gate
- :math:`f_i` : sources of forget gate
- :math:`o_i` : sources of output gate
It computes the updated cell state ``c`` and the outgoing signal
``h`` as:
.. math::
c &= \\tanh(a_1 + a_2) \\sigma(i_1 + i_2)
+ c_{\\text{prev}1} \\sigma(f_1)
+ c_{\\text{prev}2} \\sigma(f_2), \\\\
h &= \\tanh(c) \\sigma(o_1 + o_2),
where :math:`\\sigma` is the elementwise sigmoid function.
The function returns ``c`` and ``h`` as a tuple.
Args:
c_prev1 (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Variable that holds the previous cell state of the first child
node. The cell state should be a zero array or the output of
the previous call of LSTM.
c_prev2 (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Variable that holds the previous cell state of the second child
node.
x1 (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Variable that holds the sources of cell input, input gate, forget
gate and output gate from the first child node. It must have the
second dimension whose size is four times of that of the cell
state.
x2 (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Variable that holds the input sources from the second child node.
Returns:
tuple: Two :class:`~chainer.Variable` objects ``c`` and ``h``. ``c`` is
the cell state. ``h`` indicates the outgoing signal.
See detail in paper: `Long Short-Term Memory Over Tree Structures \
<https://arxiv.org/abs/1503.04881>`_.
.. admonition:: Example
Assuming ``c1``, ``c2`` is the previous cell state of children,
and ``h1``, ``h2`` is the previous outgoing signal from children.
Each of ``c1``, ``c2``, ``h1`` and ``h2`` has ``n_units`` channels.
Most typical preparation of ``x1``, ``x2`` is:
>>> n_units = 100
>>> h1 = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> h2 = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> c1 = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> c2 = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> model1 = chainer.Chain(w=L.Linear(n_units, 4 * n_units),
... v=L.Linear(n_units, 4 * n_units))
>>> model2 = chainer.Chain(w=L.Linear(n_units, 4 * n_units),
... v=L.Linear(n_units, 4 * n_units))
>>> x1 = model1.w(c1) + model1.v(h1)
>>> x2 = model2.w(c2) + model2.v(h2)
>>> c, h = F.slstm(c1, c2, x1, x2)
It corresponds to calculate the input array ``x1``, or the input
sources :math:`a_1, i_1, f_1, o_1` from the previous cell state of
first child node ``c1``, and the previous outgoing signal from first
child node ``h1``. Different parameters are used for different kind of
input sources.
"""
return SLSTM()(c_prev1, c_prev2, x1, x2)