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((len(x), 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 aa = tanh(a); \
T ai = sigmoid(i_); \
T af = sigmoid(f); \
T ao = sigmoid(o);
'''
class LSTM(function.Function):
"""Long short-term memory unit with forget gate.
It has two inputs (c, x) and two outputs (c, h), where c indicates the cell
state. x must have four times channels compared to the number of units.
"""
def check_type_forward(self, in_types):
type_check.expect(in_types.size() == 2)
c_type, x_type = in_types
type_check.expect(
c_type.dtype.kind == 'f',
x_type.dtype == c_type.dtype,
c_type.ndim >= 2,
x_type.ndim >= 2,
c_type.ndim == x_type.ndim,
x_type.shape[0] <= c_type.shape[0],
x_type.shape[1] == 4 * c_type.shape[1],
)
for i in six.moves.range(2, c_type.ndim.eval()):
type_check.expect(x_type.shape[i] == c_type.shape[i])
def forward(self, inputs):
c_prev, x = inputs
a, i, f, o = _extract_gates(x)
batch = len(x)
if isinstance(x, numpy.ndarray):
self.a = numpy.tanh(a)
self.i = _sigmoid(i)
self.f = _sigmoid(f)
self.o = _sigmoid(o)
c_next = numpy.empty_like(c_prev)
c_next[:batch] = self.a * self.i + self.f * c_prev[:batch]
h = self.o * numpy.tanh(c_next[:batch])
else:
c_next = cuda.cupy.empty_like(c_prev)
h = cuda.cupy.empty_like(c_next[:batch])
cuda.elementwise(
'T c_prev, T a, T i_, T f, T o', 'T c, T h',
'''
COMMON_ROUTINE;
c = aa * ai + af * c_prev;
h = ao * tanh(c);
''',
'lstm_fwd', preamble=_preamble)(
c_prev[:batch], a, i, f, o, c_next[:batch], h)
c_next[batch:] = c_prev[batch:]
self.c = c_next[:batch]
return c_next, h
def backward(self, inputs, grad_outputs):
xp = cuda.get_array_module(*inputs)
c_prev, x = inputs
batch = len(x)
gc, gh = grad_outputs
gx = xp.empty_like(x)
ga, gi, gf, go = _extract_gates(gx)
# Consider the case that either gradient is not given
if gc is None:
gc_update = 0
gc_rest = 0
else:
gc_update = gc[:batch]
gc_rest = gc[batch:]
if gh is None:
gh = 0
if xp is numpy:
co = numpy.tanh(self.c)
gc_prev = numpy.empty_like(c_prev)
# multiply f later
gc_prev[:batch] = gh * self.o * _grad_tanh(co) + gc_update
gc = gc_prev[:batch]
ga[:] = gc * self.i * _grad_tanh(self.a)
gi[:] = gc * self.a * _grad_sigmoid(self.i)
gf[:] = gc * c_prev[:batch] * _grad_sigmoid(self.f)
go[:] = gh * co * _grad_sigmoid(self.o)
gc_prev[:batch] *= self.f # multiply f here
gc_prev[batch:] = gc_rest
else:
a, i, f, o = _extract_gates(x)
gc_prev = xp.empty_like(c_prev)
cuda.elementwise(
'T c_prev, T c, T gc, T gh, T a, T i_, T f, T o',
'T gc_prev, T ga, T gi, T gf, T go',
'''
COMMON_ROUTINE;
T co = tanh(c);
T temp = gh * ao * grad_tanh(co) + gc;
ga = temp * ai * grad_tanh(aa);
gi = temp * aa * grad_sigmoid(ai);
gf = temp * c_prev * grad_sigmoid(af);
go = gh * co * grad_sigmoid(ao);
gc_prev = temp * af;
''',
'lstm_bwd', preamble=_preamble)(
c_prev[:batch], self.c, gc_update, gh, a, i, f, o,
gc_prev[:batch], ga, gi, gf, go)
gc_prev[batch:] = gc_rest
return gc_prev, gx
[docs]def lstm(c_prev, x):
"""Long Short-Term Memory units as an activation function.
This function implements LSTM units with forget gates. Let the previous
cell state ``c_prev`` and the input array ``x``.
First, the input array ``x`` is split into four arrays
:math:`a, i, f, o` of the same shapes along the second axis. It means that
``x`` 's second axis must have 4 times the ``c_prev`` 's second axis.
The split input arrays are corresponding to:
- :math:`a` : sources of cell input
- :math:`i` : sources of input gate
- :math:`f` : sources of forget gate
- :math:`o` : sources of output gate
Second, it computes the updated cell state ``c`` and the outgoing signal
``h`` as:
.. math::
c &= \\tanh(a) \\sigma(i)
+ c_{\\text{prev}} \\sigma(f), \\\\
h &= \\tanh(c) \\sigma(o),
where :math:`\\sigma` is the elementwise sigmoid function.
These are returned as a tuple of two variables.
This function supports variable length inputs. The mini-batch size of
the current input must be equal to or smaller than that of the previous
one. When mini-batch size of ``x`` is smaller than that of ``c``, this
function only updates ``c[0:len(x)]`` and doesn't change the rest of ``c``,
``c[len(x):]``.
So, please sort input sequences in descending order of lengths before
applying the function.
Args:
c_prev (:class:`~chainer.Variable` or :class:`numpy.ndarray` or \
:class:`cupy.ndarray`):
Variable that holds the previous cell state. The cell state
should be a zero array or the output of the previous call of LSTM.
x (: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. It must have the second dimension whose size
is four times of that of the cell state.
Returns:
tuple: Two :class:`~chainer.Variable` objects ``c`` and ``h``.
``c`` is the updated cell state. ``h`` indicates the outgoing signal.
See the original paper proposing LSTM with forget gates:
`Long Short-Term Memory in Recurrent Neural Networks \
<http://www.felixgers.de/papers/phd.pdf>`_.
.. seealso::
:class:`~chainer.links.LSTM`
.. admonition:: Example
Assuming ``y`` is the current incoming signal, ``c`` is the previous
cell state, and ``h`` is the previous outgoing signal from an ``lstm``
function. Each of ``y``, ``c`` and ``h`` has ``n_units`` channels.
Most typical preparation of ``x`` is:
>>> n_units = 100
>>> y = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> h = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> c = chainer.Variable(np.zeros((1, n_units), 'f'))
>>> model = chainer.Chain(w=L.Linear(n_units, 4 * n_units),
... v=L.Linear(n_units, 4 * n_units),)
>>> x = model.w(y) + model.v(h)
>>> c, h = F.lstm(c, x)
It corresponds to calculate the input array ``x``, or the input
sources :math:`a, i, f, o`, from the current incoming signal ``y`` and
the previous outgoing signal ``h``. Different parameters are used for
different kind of input sources.
.. note::
We use the naming rule below.
- incoming signal
The formal input of the formulation of LSTM (e.g. in NLP, word
vector or output of lower RNN layer). The input of
:class:`chainer.links.LSTM` is the *incoming signal*.
- input array
The array which is linear transformed from *incoming signal* and
the previous outgoing signal. The *input array* contains four
sources, the sources of cell input, input gate, forget gate and
output gate. The input of :class:`chainer.functions.LSTM` is the
*input array*.
"""
return LSTM()(c_prev, x)