slstm.py

import numpy
import six

from chainer import backend
from chainer.backends import cuda
from chainer.backends import intel64
from chainer import function
from chainer import function_node
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, xp=numpy):
    half = x.dtype.type(0.5)
    return xp.tanh(x * half) * half + half


def _grad_sigmoid(x):
    return x * (1 - x)


def _grad_grad_sigmoid(x):
    return x * (1 - x) * (1 - 2 * x)


def _grad_tanh(x):
    return 1 - x * x


def _grad_grad_tanh(x, gx):
    return -2 * x * gx


_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_node.FunctionNode):

    """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._argname(in_types, ('c_prev1', 'c_prev2', 'x1', 'x2'))
        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, type_check.eval(c1_type.ndim)):
            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):
        self.retain_inputs((0, 1, 2, 3))
        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):
            a1 = numpy.tanh(a1)
            i1 = _sigmoid(i1)
            f1 = _sigmoid(f1)

            a2 = numpy.tanh(a2)
            i2 = _sigmoid(i2)
            f2 = _sigmoid(f2)

            o = _sigmoid(o1 + o2)
            c = a1 * i1 + a2 * i2 + \
                f1 * c_prev1 + f2 * c_prev2

            h = o * numpy.tanh(c)
        else:
            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)
        self.retain_outputs((0,))
        return c, h

    def backward(self, indexes, grads):
        grad_inputs = (
            self.get_retained_inputs() + self.get_retained_outputs() + grads)
        return SLSTMGrad()(*grad_inputs)


class SLSTMGrad(function.Function):

    def forward(self, inputs):
        xp = backend.get_array_module(*inputs)
        c_prev1, c_prev2, x1, x2, c_next, gc, gh = inputs

        gx1 = xp.empty_like(x1)
        gx2 = xp.empty_like(x2)
        ga1, gi1, gf1, go1 = _extract_gates(gx1)
        ga2, gi2, gf2, go2 = _extract_gates(gx2)

        if gc is None:
            gc = 0
        if gh is None:
            gh = 0

        a1, i1, f1, o1 = _extract_gates(x1)
        a2, i2, f2, o2 = _extract_gates(x2)
        if xp is numpy:
            if intel64.should_use_ideep('>=auto'):
                xp = intel64.ideep.get_array_module(x1)
            tanh_a1 = xp.tanh(a1)
            sig_i1 = _sigmoid(i1, xp)
            sig_f1 = _sigmoid(f1, xp)
            tanh_a2 = xp.tanh(a2)
            sig_i2 = _sigmoid(i2, xp)
            sig_f2 = _sigmoid(f2, xp)
            sig_o = _sigmoid(o1 + o2, xp)

            co = xp.tanh(c_next)
            # multiply f later
            gc_prev = gh * sig_o * _grad_tanh(co) + gc
            ga1[:] = gc_prev * sig_i1 * _grad_tanh(tanh_a1)
            gi1[:] = gc_prev * tanh_a1 * _grad_sigmoid(sig_i1)
            gf1[:] = gc_prev * c_prev1 * _grad_sigmoid(sig_f1)
            go1[:] = gh * co * _grad_sigmoid(sig_o)
            ga2[:] = gc_prev * sig_i2 * _grad_tanh(tanh_a2)
            gi2[:] = gc_prev * tanh_a2 * _grad_sigmoid(sig_i2)
            gf2[:] = gc_prev * c_prev2 * _grad_sigmoid(sig_f2)
            go2[:] = gh * co * _grad_sigmoid(sig_o)
            # multiply f here
            gc_prev1 = gc_prev * sig_f1
            gc_prev2 = gc_prev * sig_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,
                    c_next, gc, gh,
                    gc_prev1, ga1, gi1, gf1, go1,
                    gc_prev2, ga2, gi2, gf2, go2)

        return gc_prev1, gc_prev2, gx1, gx2

    def backward(self, inputs, grads):

        xp = backend.get_array_module(*inputs)

        c_prev1, c_prev2, x1, x2, c, gc, gh = inputs
        ggc_prev1, ggc_prev2, ggx1, ggx2 = grads

        if gc is None:
            gc = xp.zeros_like(c)
        if gh is None:
            gh = xp.zeros_like(c)
        if ggc_prev1 is None:
            ggc_prev1 = xp.zeros_like(c_prev1)
        if ggc_prev2 is None:
            ggc_prev2 = xp.zeros_like(c_prev2)

        gc_prev1 = xp.empty_like(c_prev1)
        gc_prev2 = xp.empty_like(c_prev2)
        gx1 = xp.empty_like(x1)
        gx2 = xp.empty_like(x2)
        gc_next = xp.empty_like(c)
        ggc = xp.empty_like(ggc_prev1)
        ggh = xp.empty_like(gh)

        a1, i1, f1, o1 = _extract_gates(x1)
        a2, i2, f2, o2 = _extract_gates(x2)
        gga1, ggi1, ggf1, ggo1 = _extract_gates(ggx1)
        gga2, ggi2, ggf2, ggo2 = _extract_gates(ggx2)
        ga1, gi1, gf1, go1 = _extract_gates(gx1)
        ga2, gi2, gf2, go2 = _extract_gates(gx2)

        o = o1 + o2

        gc_prev1[:], ga1[:], gi1[:], gf1[:], go1[:], \
            gc_prev2[:], ga2[:], gi2[:], gf2[:], go2[:], \
            gc_next[:], ggc[:], ggh[:] \
            = slstm_grad_grad(c_prev1, a1, i1, f1,
                              c_prev2, a2, i2, f2, o, c, gc, gh,
                              ggc_prev1, gga1, ggi1, ggf1, ggo1,
                              ggc_prev2, gga2, ggi2, ggf2, ggo2)
        return gc_prev1, gc_prev2, gx1, gx2, gc_next, ggc, ggh


@cuda.fuse()
def slstm_grad_grad(c_prev1, a1, i1, f1,
                    c_prev2, a2, i2, f2,
                    o, c, gc, gh,
                    ggc_prev1, gga1, ggi1, ggf1, ggo1,
                    ggc_prev2, gga2, ggi2, ggf2, ggo2):
    xp = backend.get_array_module(a1)
    sig_o = _sigmoid(o, xp)
    gsig_o = _grad_sigmoid(sig_o)
    ggsig_o = _grad_grad_sigmoid(sig_o)
    sig_i1 = _sigmoid(i1, xp)
    gsig_i1 = _grad_sigmoid(sig_i1)
    ggsig_i1 = _grad_grad_sigmoid(sig_i1)
    sig_i2 = _sigmoid(i2, xp)
    gsig_i2 = _grad_sigmoid(sig_i2)
    ggsig_i2 = _grad_grad_sigmoid(sig_i2)
    sig_f1 = _sigmoid(f1, xp)
    gsig_f1 = _grad_sigmoid(sig_f1)
    ggsig_f1 = _grad_grad_sigmoid(sig_f1)
    sig_f2 = _sigmoid(f2, xp)
    gsig_f2 = _grad_sigmoid(sig_f2)
    ggsig_f2 = _grad_grad_sigmoid(sig_f2)
    tanh_a1 = xp.tanh(a1)
    gtanh_a1 = _grad_tanh(tanh_a1)
    ggtanh_a1 = _grad_grad_tanh(tanh_a1, gtanh_a1)
    tanh_a2 = xp.tanh(a2)
    gtanh_a2 = _grad_tanh(tanh_a2)
    ggtanh_a2 = _grad_grad_tanh(tanh_a2, gtanh_a2)
    tanh_c = xp.tanh(c)
    gtanh_c = _grad_tanh(tanh_c)
    ggtanh_c = _grad_grad_tanh(tanh_c, gtanh_c)

    gc_bar = gh * sig_o * gtanh_c + gc

    gc_prev1 = ggf1 * gc_bar * gsig_f1
    gc_prev2 = ggf2 * gc_bar * gsig_f2
    ga1 = (gga1 * sig_i1 * ggtanh_a1 +
           ggi1 * gtanh_a1 * gsig_i1) * gc_bar
    ga2 = (gga2 * sig_i2 * ggtanh_a2 +
           ggi2 * gtanh_a2 * gsig_i2) * gc_bar
    gi1 = (gga1 * gtanh_a1 * gsig_i1 +
           ggi1 * tanh_a1 * ggsig_i1) * gc_bar
    gi2 = (gga2 * gtanh_a2 * gsig_i2 +
           ggi2 * tanh_a2 * ggsig_i2) * gc_bar
    gf1 = (ggc_prev1 * (gh * sig_o * gtanh_c + gc) * gsig_f1 +
           ggf1 * gc_bar * c_prev1 * ggsig_f1)
    gf2 = (ggc_prev2 * (gh * sig_o * gtanh_c + gc) * gsig_f2 +
           ggf2 * gc_bar * c_prev2 * ggsig_f2)

    ggc = (
        ggc_prev1 * sig_f1 +
        gga1 * sig_i1 * gtanh_a1 +
        ggi1 * tanh_a1 * gsig_i1 +
        ggf1 * c_prev1 * gsig_f1 +
        ggc_prev2 * sig_f2 +
        gga2 * sig_i2 * gtanh_a2 +
        ggi2 * tanh_a2 * gsig_i2 +
        ggf2 * c_prev2 * gsig_f2)

    dgc_do = gh * gsig_o * gtanh_c
    go1 = go2 = ggc * dgc_do + (ggo1 + ggo2) * gh * tanh_c * ggsig_o
    dgc_dc = gh * sig_o * ggtanh_c
    gc_next = ggc * dgc_dc + (ggo1 + ggo2) * gh * gtanh_c * gsig_o
    ggh = ggc * sig_o * gtanh_c + (ggo1 + ggo2) * tanh_c * gsig_o
    return gc_prev1, ga1, gi1, gf1, go1, gc_prev2, ga2, gi2, gf2, go2, \
        gc_next, ggc, ggh


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 :ref:`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 :ref:`ndarray`):
            Variable that holds the previous cell state of the second child
            node.
        x1 (:class:`~chainer.Variable` or :ref:`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 :ref:`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), np.float32))
        >>> h2 = chainer.Variable(np.zeros((1, n_units), np.float32))
        >>> c1 = chainer.Variable(np.zeros((1, n_units), np.float32))
        >>> c2 = chainer.Variable(np.zeros((1, n_units), np.float32))
        >>> model1 = chainer.Chain()
        >>> with model1.init_scope():
        ...   model1.w = L.Linear(n_units, 4 * n_units)
        ...   model1.v = L.Linear(n_units, 4 * n_units)
        >>> model2 = chainer.Chain()
        >>> with model2.init_scope():
        ...   model2.w = L.Linear(n_units, 4 * n_units)
        ...   model2.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().apply((c_prev1, c_prev2, x1, x2))