def backward_gpu(self, x, gy):
e1 = array.as_mat(x[0])
e2 = array.as_mat(x[1])
gy, = gy
kern_add = cuda.reduce('T in0, T in1, T in2', 'T out',
'in0 * in1 * in2', 'a + b', 'out += a', 0,
'bilinear_product_add')
kern = cuda.reduce('T in0, T in1, T in2', 'T out', 'in0 * in1 * in2',
'a + b', 'out = a', 0, 'bilinear_product')
e1_b = e1[:, :, numpy.newaxis, numpy.newaxis] # ij
e2_b = e2[:, numpy.newaxis, :, numpy.newaxis] # ik
gy_b = gy[:, numpy.newaxis, numpy.newaxis, :] # il
W_b = self.W[numpy.newaxis, :, :, :] # jkl
# 'ij,ik,il->jkl'
kern_add(e1_b, e2_b, gy_b, self.gW, axis=0)
if not self.nobias:
self.gV1 += e1.T.dot(gy)
self.gV2 += e2.T.dot(gy)
self.gb += gy.sum(axis=0)
# 'ik,jkl,il->ij'
ge1 = kern(e2_b, W_b, gy_b, axis=(2, 3))
# 'ij,jkl,il->ik'
ge2 = kern(e1_b, W_b, gy_b, axis=(1, 3))
if not self.nobias:
ge1 += gy.dot(self.V1.T)
ge2 += gy.dot(self.V2.T)
return (ge1.reshape(x[0].shape), ge2.reshape(x[1].shape))
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs[:2]
log_y = super(AdaptiveSoftmaxCrossEntropy, self).forward(inputs)[0]
self.y = cupy.exp(log_y)
if self.normalize:
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
if self.reduce == 'mean':
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff, '
'S ignore_label', 'T out',
't == ignore_label ? T(0) : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0',
'crossent_fwd')(t, log_y.reduced_view(), log_y.shape[-1],
self._coeff, self.ignore_label)
else:
ret = cuda.elementwise(
'S t, raw T log_y, int32 n_channel, T ignore', 'T out', '''
if (t == ignore) {
out = 0;
} else {
out = -log_y[i * n_channel + t];
}
''', 'softmax_crossent_no_reduce_fwd')(t, log_y.reduced_view(),
log_y.shape[-1],
self.ignore_label)
ret = ret.reshape(t.shape)
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
self._check_input_values(x, t)
log_y = softmax_log(x, self.use_cudnn)
if self.cache_score:
self.y = cupy.exp(log_y)
if getattr(self, "normalize", True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
"S t, raw T log_y, int32 n_channel, raw T coeff",
"T out",
"t == -1 ? T(0) : log_y[_j * n_channel + t]",
"a + b",
"out = a * -coeff[0]",
"0",
"crossent_fwd",
)(t, log_y.reduced_view(), log_y.shape[-1], self._coeff)
return (ret,)
def backward(self, inputs, grad_outputs):
e1 = array.as_mat(inputs[0])
e2 = array.as_mat(inputs[1])
W = inputs[2]
gy = grad_outputs[0]
xp = cuda.get_array_module(*inputs)
if xp is numpy:
gW = numpy.einsum('ij,ik,il->jkl', e1, e2, gy)
ge1 = numpy.einsum('ik,jkl,il->ij', e2, W, gy)
ge2 = numpy.einsum('ij,jkl,il->ik', e1, W, gy)
else:
kern = cuda.reduce('T in0, T in1, T in2', 'T out',
'in0 * in1 * in2', 'a + b', 'out = a', 0,
'bilinear_product')
e1_b = e1[:, :, None, None] # ij
e2_b = e2[:, None, :, None] # ik
gy_b = gy[:, None, None, :] # il
W_b = W[None, :, :, :] # jkl
gW = kern(e1_b, e2_b, gy_b, axis=0) # 'ij,ik,il->jkl'
ge1 = kern(e2_b, W_b, gy_b, axis=(2, 3)) # 'ik,jkl,il->ij'
ge2 = kern(e1_b, W_b, gy_b, axis=(1, 3)) # 'ij,jkl,il->ik'
ret = ge1.reshape(inputs[0].shape), ge2.reshape(inputs[1].shape), gW
if len(inputs) == 6:
V1, V2, b = inputs[3:]
gV1 = e1.T.dot(gy)
gV2 = e2.T.dot(gy)
gb = gy.sum(0)
ge1 += gy.dot(V1.T)
ge2 += gy.dot(V2.T)
ret += gV1, gV2, gb
return ret
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
self._check_input_values(x, t)
log_y = log_softmax._log_softmax(x, self.use_cudnn)
if self.cache_score:
self.y = cupy.exp(log_y)
if self.class_weight is not None:
shape = [1 if d != 1 else -1 for d in six.moves.range(x.ndim)]
log_y *= cupy.broadcast_to(
self.class_weight.reshape(shape), x.shape)
if self.normalize:
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff', 'T out',
't == -1 ? T(0) : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0', 'crossent_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1], self._coeff)
return ret,
def numerical_grad(f, inputs, grad_outputs, eps=1e-3):
"""Computes numerical gradient by finite differences.
This function is used to implement gradient check. For usage example, see
unit tests of :mod:`chainer.functions`.
Args:
f (function): Python function with no arguments that runs forward
computation and returns the result.
inputs (tuple of arrays): Tuple of arrays that should be treated as
inputs. Each element of them is slightly modified to realize
numerical gradient by finite differences.
grad_outputs (tuple of arrays): Tuple of arrays that are treated as
output gradients.
eps (float): Epsilon value of finite differences.
Returns:
tuple: Numerical gradient arrays corresponding to ``inputs``.
"""
assert eps > 0
inputs = tuple(inputs)
grad_outputs = tuple(grad_outputs)
gpu = any(isinstance(x, cuda.ndarray) for x in inputs + grad_outputs)
cpu = any(isinstance(x, numpy.ndarray) for x in inputs + grad_outputs)
if gpu and cpu:
raise RuntimeError('Do not mix GPU and CPU arrays in `numerical_grad`')
if gpu:
xp = cuda.cupy
numerical_grad_kernel = cuda.reduce(
'T y1, T y2, U gy, T eps', 'V gxi',
'(y1 - y2) * gy', 'a + b', 'gxi += a / (eps * 2)', '0',
'numerical_grad_kernel'
)
else:
xp = numpy
grads = [xp.zeros_like(x) for x in inputs]
with configuration.using_config('type_check', False):
for x, gx in six.moves.zip(inputs, grads):
for i in numpy.ndindex(x.shape):
orig = x[i].copy() # hold original value
x[i] = orig + eps
ys1 = _copy_arrays(f())
x[i] = orig - eps
ys2 = _copy_arrays(f())
x[i] = orig
for y1, y2, gy in six.moves.zip(ys1, ys2, grad_outputs):
if gy is not None:
if (gpu and isinstance(y1, cuda.ndarray) and
isinstance(y2, cuda.ndarray) and
isinstance(gy, cuda.ndarray)):
numerical_grad_kernel(y1, y2, gy, eps, gx[i])
else:
dot = ((y1 - y2) * gy).sum()
gx[i] += dot / (2 * eps)
return grads
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
self._check_input_values(x, t)
log_y = softmax_log(x, self.use_cudnn)
if self.cache_score:
self.y = cupy.exp(log_y)
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
tw = cupy.asnumpy(t.copy())
for i_class, weight in enumerate(self.class_weights):
tw[tw == i_class] = self.class_weights[i_class]
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
'S t, S tw, raw T log_y, int32 n_channel, raw T coeff', 'T out',
't == -1 ? 0 : log_y[_j * n_channel + t]*tw', 'a + b',
'out = a * -coeff[0]', '0', 'crossent_fwd')(t, cupy.array(tw),
log_y.reduced_view(),
log_y.shape[-1],
self._coeff)
return ret,
def numerical_grad(f, inputs, grad_outputs, eps=1e-3):
"""Computes numerical gradient by finite differences.
This function is used to implement gradient check. For usage example, see
unit tests of :mod:`chainer.functions`.
Args:
f (function): Python function with no arguments that runs forward
computation and returns the result.
inputs (tuple of arrays): Tuple of arrays that should be treated as
inputs. Each element of them is slightly modified to realize
numerical gradient by finite differences.
grad_outputs (tuple of arrays): Tuple of arrays that are treated as
output gradients.
eps (float): Epsilon value of finite differences.
Returns:
tuple: Numerical gradient arrays corresponding to ``inputs``.
"""
assert eps > 0
inputs = tuple(inputs)
grad_outputs = tuple(grad_outputs)
gpu = any(isinstance(x, cuda.ndarray) for x in inputs + grad_outputs)
cpu = any(isinstance(x, numpy.ndarray) for x in inputs + grad_outputs)
if gpu and cpu:
raise RuntimeError('Do not mix GPU and CPU arrays in `numerical_grad`')
if gpu:
xp = cuda.cupy
numerical_grad_kernel = cuda.reduce(
'T y1, T y2, U gy, T eps', 'V gxi',
'(y1 - y2) * gy', 'a + b', 'gxi += a / (eps * 2)', '0',
'numerical_grad_kernel'
)
else:
xp = numpy
grads = [xp.zeros_like(x) for x in inputs]
with configuration.using_config('type_check', False):
for x, gx in six.moves.zip(inputs, grads):
for i in numpy.ndindex(x.shape):
orig = x[i].copy() # hold original value
x[i] = orig + eps
ys1 = _copy_arrays(f())
x[i] = orig - eps
ys2 = _copy_arrays(f())
x[i] = orig
for y1, y2, gy in six.moves.zip(ys1, ys2, grad_outputs):
if gy is not None:
if (gpu and isinstance(y1, cuda.ndarray) and
isinstance(y2, cuda.ndarray) and
isinstance(gy, cuda.ndarray)):
numerical_grad_kernel(y1, y2, gy, eps, gx[i])
else:
dot = ((y1 - y2) * gy).sum()
gx[i] += dot / (2 * eps)
return grads
def backward(self, inputs, grad_outputs):
e1 = array.as_mat(inputs[0])
e2 = array.as_mat(inputs[1])
W = inputs[2]
gy = grad_outputs[0]
xp = cuda.get_array_module(*inputs)
if xp is numpy:
gW = numpy.einsum("ij,ik,il->jkl", e1, e2, gy)
ge1 = numpy.einsum("ik,jkl,il->ij", e2, W, gy)
ge2 = numpy.einsum("ij,jkl,il->ik", e1, W, gy)
else:
kern = cuda.reduce(
"T in0, T in1, T in2", "T out", "in0 * in1 * in2", "a + b", "out = a", 0, "bilinear_product"
)
e1_b = e1[:, :, None, None] # ij
e2_b = e2[:, None, :, None] # ik
gy_b = gy[:, None, None, :] # il
W_b = W[None, :, :, :] # jkl
gW = kern(e1_b, e2_b, gy_b, axis=0) # 'ij,ik,il->jkl'
ge1 = kern(e2_b, W_b, gy_b, axis=(2, 3)) # 'ik,jkl,il->ij'
ge2 = kern(e1_b, W_b, gy_b, axis=(1, 3)) # 'ij,jkl,il->ik'
ret = ge1.reshape(inputs[0].shape), ge2.reshape(inputs[1].shape), gW
if len(inputs) == 6:
V1, V2, b = inputs[3:]
gV1 = e1.T.dot(gy)
gV2 = e2.T.dot(gy)
gb = gy.sum(0)
ge1 += gy.dot(V1.T)
ge2 += gy.dot(V2.T)
ret += gV1, gV2, gb
return ret
def forward_gpu(self, inputs):
x0, x1 = inputs
ret = cuda.reduce('const float* x0, const float* x1',
'(x0[i] - x1[i]) * (x0[i] - x1[i])', 'a+b', '0',
'mse_fwd', numpy.float32)(x0, x1)
ret /= x0.size
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
self._check_input_values(x, t)
log_y = log_softmax._log_softmax(x, self.use_cudnn)
if self.cache_score:
self.y = cupy.exp(log_y)
if self.class_weight is not None:
shape = [1 if d != 1 else -1 for d in six.moves.range(x.ndim)]
log_y *= cupy.broadcast_to(self.class_weight.reshape(shape),
x.shape)
if self.normalize:
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce('S t, raw T log_y, int32 n_channel, raw T coeff',
'T out',
't == -1 ? T(0) : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0',
'crossent_fwd')(t, log_y.reduced_view(),
log_y.shape[-1], self._coeff)
return ret,
def forward_gpu(self, inputs):
x, t = inputs
self.y, = sigmoid.Sigmoid(self.use_cudnn).forward_gpu((x,))
loss = -cuda.reduce(
'int* t, float* x',
'x[i] * (t[i] - (x[i] >= 0)) - log1pf(expf(-fabsf(x[i])))',
'a+b', '0', 'sigmoid_crossent_fwd', numpy.float32)(t, x)
return loss / t.shape[0],
def _popcount():
return cuda.reduce(
"T x", "T y",
"2*__popc(x)-32",
"a+b",
"y = a",
"0",
"popcount")
def forward_gpu(self, inputs):
x0, x1 = inputs
ret = cuda.reduce(
'const float* x0, const float* x1',
'(x0[i] - x1[i]) * (x0[i] - x1[i])',
'a+b', '0', 'mse_fwd', numpy.float32)(x0, x1)
ret /= x0.size
return ret,
def forward_gpu(self, inputs):
x, t = inputs
self.y, = Softmax(self.use_cudnn).forward_gpu((x,))
ret = cuda.reduce(
'int* t, float* y, int n_channel', '-log(y[i * n_channel + t[i]])',
'a+b', '0', 'crossent_fwd', numpy.float32)(t, self.y, self.y.shape[1])
ret /= t.size
return ret,
def forward_gpu(self, inputs):
x, t = inputs
self.y, = sigmoid.Sigmoid(self.use_cudnn).forward_gpu((x, ))
loss = cuda.reduce('T x, S t, T inv_cnt', 'T out',
'x * (t - (x >= 0)) - log1p(exp(-fabs(x)))',
'a + b', 'out = a * inv_cnt', 0,
'sigmoid_crossent_fwd')(x, t, -1.0 / t.shape[0])
return loss,
def forward_gpu(self, inputs):
x, t = inputs
self.y, = sigmoid.Sigmoid(self.use_cudnn).forward_gpu((x, ))
loss = -cuda.reduce(
'int* t, float* x',
'x[i] * (t[i] - (x[i] >= 0)) - log1pf(expf(-fabsf(x[i])))', 'a+b',
'0', 'sigmoid_crossent_fwd', numpy.float32)(t, x)
return loss / t.shape[0],
def backward(self, inputs, grad_outputs):
#
# preprocess
#
x, gamma = inputs[:2]
gy, gl = grad_outputs
head_ndim = gamma.ndim + 1
expander = (None, Ellipsis) + (None, ) * (x.ndim - head_ndim)
m = gamma.dtype.type(x.size // gamma.size)
axis = (0, ) + tuple(range(head_ndim, x.ndim))
xp = cuda.get_array_module(x)
if len(inputs) == 6:
assert not chainer.config.train
# we do not have to consider Lipschitz constant
var = inputs[5] + self.eps
gs = gamma * self.std_inv
gbeta = gy.sum(axis=axis)
ggamma = (gy * self.x_hat).sum(axis=axis)
gmean = -gs * gbeta
gvar = -0.5 * gamma / var * ggamma
gx = gs[expander] * gy
return gx, ggamma, gbeta, None, gmean, gvar
assert chainer.config.train
gbeta = gy.sum(axis=axis)
ggamma = cuda.reduce('T gy, T x_hat', 'T out', 'gy * x_hat', 'a + b',
'out = a', '0', 'conv_bn_ggamma')(gy,
self.x_hat,
axis=axis,
keepdims=False)
if gl is not None:
assert getattr(chainer.config, 'lmt', False)
cuda.elementwise(
'T gl, T u, T u_mid, T std_inv', 'T ggamma', '''
ggamma += gl * u * u_mid * std_inv;
''', 'conv_bn_ggamma2')(gl, self.u.reshape(self.std_inv.shape),
self.u_mid.reshape(self.std_inv.shape),
self.std_inv, ggamma)
inv_m = numpy.float32(1) / m
if xp is numpy:
gx = (gamma * self.std_inv)[expander] * (
gy - (self.x_hat * ggamma[expander] + gbeta[expander]) / m)
else:
# in LMT, ggamma is changed and this automatically corrects gx
gx = cuda.elementwise(
'T gy, T x_hat, T gamma, T std_inv, T ggamma, T gbeta, \
T inv_m', 'T gx',
'gx = (gamma * std_inv) * (gy - (x_hat * ggamma + gbeta) * \
inv_m)',
'conv_bn_bwd')(gy, self.x_hat, gamma[expander],
self.std_inv[expander], ggamma[expander],
gbeta[expander], inv_m)
if gl is not None:
return gx, ggamma, gbeta, (gl * self.u_mid.T * self.v).reshape(
inputs[3].shape)
else:
return gx, ggamma, gbeta, None
def forward_gpu(self, inputs):
x, t = inputs
self.y, = sigmoid.Sigmoid(self.use_cudnn).forward_gpu((x,))
loss = cuda.reduce(
'T x, S t, T inv_cnt', 'T out',
'x * (t - (x >= 0)) - log1p(exp(-fabs(x)))',
'a + b', 'out = a * inv_cnt', 0,
'sigmoid_crossent_fwd')(x, t, -1.0 / t.shape[0])
return loss,
def forward_gpu(self, inputs):
x, t = inputs
self.y, = Softmax(self.use_cudnn).forward_gpu((x, ))
ret = cuda.reduce('int* t, float* y, int n_channel',
'-log(y[i * n_channel + t[i]])', 'a+b', '0',
'crossent_fwd', numpy.float32)(t, self.y,
self.y.shape[1])
ret /= t.size
return ret,
def forward_gpu(self, inputs):
x0, x1 = inputs
ret = cuda.reduce(
"const float* x0, const float* x1",
"(x0[i] - x1[i]) * (x0[i] - x1[i])",
"a+b",
"0",
"mse_fwd",
numpy.float32,
)(x0, x1)
ret /= x0.size
return (ret,)
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
_check_input_values(x, t, self.ignore_label)
if x.size == 0:
y = cupy.zeros(t.shape, dtype=x.dtype)
if self.cache_score:
self.y = y
if self.reduce == 'mean':
return y.sum(),
else:
return y,
log_y = log_softmax._log_softmax(x)
if self.cache_score:
self.y = cupy.exp(log_y)
if self.class_weight is not None:
shape = [1 if d != 1 else -1 for d in six.moves.range(x.ndim)]
log_y *= cupy.broadcast_to(
self.class_weight.reshape(shape), x.shape)
if self.normalize:
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
if self.reduce == 'mean':
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff, '
'S ignore_label',
'T out',
't == ignore_label ? T(0) : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0', 'crossent_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1],
self._coeff, self.ignore_label)
else:
ret = cuda.elementwise(
'S t, raw T log_y, int32 n_channel, T ignore', 'T out',
'''
if (t == ignore) {
out = 0;
} else {
out = -log_y[i * n_channel + t];
}
''',
'softmax_crossent_no_reduce_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1], self.ignore_label)
ret = ret.reshape(t.shape)
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
_check_input_values(x, t, self.ignore_label)
if x.size == 0:
y = cupy.zeros(t.shape, dtype=x.dtype)
if self.cache_score:
self.y = y
if self.reduce == 'mean':
return y.sum(),
else:
return y,
log_y = log_softmax._log_softmax(x)
if self.cache_score:
self.y = cupy.exp(log_y)
if self.class_weight is not None:
shape = [1 if d != 1 else -1 for d in six.moves.range(x.ndim)]
log_y *= cupy.broadcast_to(
self.class_weight.reshape(shape), x.shape)
if self.normalize:
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
if self.reduce == 'mean':
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff, '
'S ignore_label',
'T out',
't == ignore_label ? T(0) : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0', 'crossent_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1],
self._coeff, self.ignore_label)
else:
ret = cuda.elementwise(
'S t, raw T log_y, int32 n_channel, T ignore', 'T out',
'''
if (t == ignore) {
out = 0;
} else {
out = -log_y[i * n_channel + t];
}
''',
'softmax_crossent_no_reduce_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1], self.ignore_label)
ret = ret.reshape(t.shape)
return ret,
def normalize(arr, eps):
"""normalize input array and return its norm
from https://github.com/pfnet-research/sngan_projection/blob/master/source/functions/max_sv.py#L5
:param arr: numpy ndarray or cupy ndarray
:param eps: epsilon for numerical stability
:return: norm of input array
"""
norm = cuda.reduce('T x', 'T out', 'x * x', 'a + b', 'out = sqrt(a)', 0,
'norm_sn')(arr)
cuda.elementwise('T norm, T eps', 'T x', 'x /= (norm + eps)',
'div_sn')(norm, eps, arr)
return norm
def backward_gpu(self, x, gy):
e1 = array.as_mat(x[0])
e2 = array.as_mat(x[1])
gy, = gy
kern_add = cuda.reduce(
'T in0, T in1, T in2', 'T out',
'in0 * in1 * in2', 'a + b', 'out += a', 0,
'bilinear_product_add')
kern = cuda.reduce(
'T in0, T in1, T in2', 'T out',
'in0 * in1 * in2', 'a + b', 'out = a', 0,
'bilinear_product')
e1_b = e1[:, :, numpy.newaxis, numpy.newaxis] # ij
e2_b = e2[:, numpy.newaxis, :, numpy.newaxis] # ik
gy_b = gy[:, numpy.newaxis, numpy.newaxis, :] # il
W_b = self.W[numpy.newaxis, :, :, :] # jkl
# 'ij,ik,il->jkl'
kern_add(e1_b, e2_b, gy_b, self.gW, axis=0)
if not self.nobias:
self.gV1 += e1.T.dot(gy)
self.gV2 += e2.T.dot(gy)
self.gb += gy.sum(axis=0)
# 'ik,jkl,il->ij'
ge1 = kern(e2_b, W_b, gy_b, axis=(2, 3))
# 'ij,jkl,il->ik'
ge2 = kern(e1_b, W_b, gy_b, axis=(1, 3))
if not self.nobias:
ge1 += gy.dot(self.V1.T)
ge2 += gy.dot(self.V2.T)
return (ge1.reshape(x[0].shape), ge2.reshape(x[1].shape))
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
self.y, = softmax.Softmax(self.use_cudnn).forward((x, ))
n_unit = int(numpy.prod(self.y.shape[2:]))
if getattr(self, 'normalize', True):
count = t.shape[0] * n_unit
else:
count = t.shape[0]
y = cupy.rollaxis(self.y, 1, len(self.y))
ret = cuda.reduce('S t, raw T y, int32 n_channel, T inv_count',
'T out', 'log(y[_j * n_channel + t])', 'a + b',
'out = a * inv_count', '0',
'crossent_fwd')(t, y, y.shape[-1], -1.0 / count)
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
self.y, = softmax.Softmax(self.use_cudnn).forward((x, ))
if getattr(self, 'normalize', True):
count = x.size // x.shape[1]
else:
count = x.shape[0]
y = cupy.rollaxis(self.y, 1, self.y.ndim)
ret = cuda.reduce('S t, raw T y, int32 n_channel, T inv_count',
'T out', 'log(y[_j * n_channel + t])', 'a + b',
'out = a * inv_count', '0',
'crossent_fwd')(t, y.reduced_view(), y.shape[-1],
-1.0 / count)
return ret,
def forward_gpu(self, inputs):
x, t = inputs
max_length = cuda.reduce(
'int* t, int* begins', 'begins[t[i] + 1] - begins[t[i]]',
'max(a,b)', '0', 'binary_hierarchical_softmax_max_length',
numpy.int32
)(t, self.begins)
max_length = cuda.to_cpu(max_length)[()]
length = max_length * x.shape[0]
ls = cuda.empty((length,), dtype=numpy.float32)
n_in = x.shape[1]
wxy = cuda.empty((length,), dtype=numpy.float32)
cuda.elementwise(
'''float* ls, float* wxy, const float* x, const float* w,
const int* ts, const int* paths, const float* codes,
const int* begins, int c, int max_length''',
'''
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];
x = &x[ind * c];
float wx = 0;
for (int j = 0; j < c; ++j) {
wx += w[node * c + j] * x[j];
}
wxy[i] = wx * codes[p];
ls[i] = log(1 + exp(-wxy[i]));
} else {
ls[i] = 0;
}
''',
'binary_hierarchical_softmax_forward'
)(ls, wxy, x, self.W, t, self.paths, self.codes, self.begins,
n_in, max_length)
self.max_length = max_length
self.wxy = wxy
return cuda.gpuarray.sum(ls),
def forward_gpu(self, inputs):
x, t = inputs
max_length = cuda.reduce(
'int* t, int* begins', 'begins[t[i] + 1] - begins[t[i]]',
'max(a,b)', '0', 'binary_hierarchical_softmax_max_length',
numpy.int32
)(t, self.begins)
max_length = cuda.to_cpu(max_length)[()]
length = max_length * x.shape[0]
ls = cuda.empty((length,), dtype=numpy.float32)
n_in = x.shape[1]
wxy = cuda.empty((length,), dtype=numpy.float32)
cuda.elementwise(
'''float* ls, float* wxy, const float* x, const float* w,
const int* ts, const int* paths, const float* codes,
const int* begins, int c, int max_length''',
'''
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];
x = &x[ind * c];
float wx = 0;
for (int j = 0; j < c; ++j) {
wx += w[node * c + j] * x[j];
}
wxy[i] = wx * codes[p];
ls[i] = log(1 + exp(-wxy[i]));
} else {
ls[i] = 0;
}
''',
'binary_hierarchical_softmax_forward'
)(ls, wxy, x, self.W, t, self.paths, self.codes, self.begins,
n_in, max_length)
self.max_length = max_length
self.wxy = wxy
return cuda.gpuarray.sum(ls),
def forward_gpu(self, inputs):
cupy = cuda.cupy
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 = cupy.empty((length,), dtype=numpy.float32)
n_in = x.shape[1]
wxy = 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 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 forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
log_y = softmax_log(x, self.use_cudnn)
self.y = cupy.exp(log_y)
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff', 'T out',
't == -1 ? 0 : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0', 'crossent_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1], self._coeff)
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
log_y = softmax_log(x, self.use_cudnn)
self.y = cupy.exp(log_y)
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce('S t, raw T log_y, int32 n_channel, raw T coeff',
'T out', 't == -1 ? 0 : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0',
'crossent_fwd')(t, log_y.reduced_view(),
log_y.shape[-1], self._coeff)
return ret,
def backward(self, inputs, grad_outputs):
x, gamma = inputs[:2]
gy, gl = grad_outputs
head_ndim = gamma.ndim + 1
expander = (None, Ellipsis) + (None, ) * (x.ndim - head_ndim)
m = gamma.dtype.type(x.size // gamma.size)
axis = (0, ) + tuple(range(head_ndim, x.ndim))
xp = cuda.get_array_module(x)
if len(inputs) == 5:
assert not chainer.config.train
# we do not have to consider Lipschitz constant
var = inputs[4] + self.eps
gs = gamma * self.std_inv
gbeta = gy.sum(axis=axis)
ggamma = (gy * self.x_hat).sum(axis=axis)
gmean = -gs * gbeta
gvar = -0.5 * gamma / var * ggamma
gx = gs[expander] * gy
return gx, ggamma, gbeta, gmean, gvar
assert configuration.config.train
gbeta = gy.sum(axis=axis)
ggamma = cuda.reduce('T gy, T x_hat', 'T out', 'gy * x_hat', 'a + b',
'out = a', '0', 'bn_ggamma')(gy,
self.x_hat,
axis=axis,
keepdims=False)
if gl is not None:
assert getattr(chainer.config, 'lmt', False)
ggamma[self.index] += gl.reshape(
tuple()) * self.std_inv[self.index]
inv_m = numpy.float32(1) / m
if xp is numpy:
gx = (gamma * self.std_inv)[expander] * (
gy - (self.x_hat * ggamma[expander] + gbeta[expander]) / m)
else:
gx = cuda.elementwise(
'T gy, T x_hat, T gamma, T std_inv, T ggamma, T gbeta, \
T inv_m', 'T gx',
'gx = (gamma * std_inv) * (gy - (x_hat * ggamma + gbeta) * \
inv_m)', 'bn_bwd')(gy, self.x_hat, gamma[expander],
self.std_inv[expander], ggamma[expander],
gbeta[expander], inv_m)
return gx, ggamma, gbeta
def __init__(self, epsilon=1e-5, stability=1e0):
"""
Args:
epsilon: How close to take point for perturbation calc
stability: Add this term to denominator to stabilize...
"""
self.epsilon = epsilon
self.stability_term = stability
self.init = True
self.calc_inner_product_sum = cuda.reduce(
'T u, T v',
'T sum_uv',
'u * v',
'a + b',
'sum_uv = a',
'0',
'calc_inner_product_sum'
)
def forward_gpu(self, inputs):
x, t = inputs
self.y, = softmax.Softmax(self.use_cudnn).forward_gpu((x,))
n_unit = int(numpy.prod(self.y.shape[2:]))
# the map_expr is equivalent to the pseudo code -log(y[n, c, m]),
# where n = i / n_unit, c = t[i], and m = i % n_unit
ret = cuda.reduce(
'int* t, float* y, int n_channel, int n_unit',
'-log(y[n_unit * ((i / n_unit) * n_channel + t[i])'
' + (i % n_unit)])',
'a+b', '0', 'crossent_fwd', numpy.float32
)(t, self.y, self.y.shape[1], n_unit)
if getattr(self, 'normalize', True):
n_unit = int(numpy.prod(self.y.shape[2:]))
count = t.shape[0] * n_unit
else:
count = t.shape[0]
ret /= count
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
self.y, = softmax.Softmax(self.use_cudnn).forward((x,))
if getattr(self, "normalize", True):
count = x.size // x.shape[1]
else:
count = x.shape[0]
y = cupy.rollaxis(self.y, 1, self.y.ndim)
ret = cuda.reduce(
"S t, raw T y, int32 n_channel, T inv_count",
"T out",
"log(y[_j * n_channel + t])",
"a + b",
"out = a * inv_count",
"0",
"crossent_fwd",
)(t, y.reduced_view(), y.shape[-1], -1.0 / count)
return (ret,)
def forward_gpu(self, inputs):
x, t = inputs
self.y, = softmax.Softmax(self.use_cudnn).forward_gpu((x,))
n_unit = int(numpy.prod(self.y.shape[2:]))
# the map_expr is equivalent to the pseudo code -log(y[n, c, m]),
# where n = i / n_unit, c = t[i], and m = i % n_unit
ret = cuda.reduce(
'int* t, float* y, int n_channel, int n_unit',
'-log(y[n_unit * ((i / n_unit) * n_channel + t[i])'
' + (i % n_unit)])',
'a+b', '0', 'crossent_fwd', numpy.float32
)(t, self.y, self.y.shape[1], n_unit)
if getattr(self, 'normalize', True):
n_unit = int(numpy.prod(self.y.shape[2:]))
count = t.shape[0] * n_unit
else:
count = t.shape[0]
ret /= count
return ret,
def backward(self, inputs, grad_outputs):
e1 = array.as_mat(inputs[0])
e2 = array.as_mat(inputs[1])
W = inputs[2]
if not type_check.same_types(*inputs):
raise ValueError(
'numpy and cupy must not be used together\n'
'type(W): {0}, type(e1): {1}, type(e2): {2}'.format(
type(W), type(e1), type(e2)))
gy = grad_outputs[0]
xp = cuda.get_array_module(*inputs)
if xp is numpy:
gW = numpy.einsum('ij,ik,il->jkl', e1, e2, gy)
ge1 = numpy.einsum('ik,jkl,il->ij', e2, W, gy)
ge2 = numpy.einsum('ij,jkl,il->ik', e1, W, gy)
else:
kern = cuda.reduce('T in0, T in1, T in2', 'T out',
'in0 * in1 * in2', 'a + b', 'out = a', 0,
'bilinear_product')
e1_b = e1[:, :, None, None] # ij
e2_b = e2[:, None, :, None] # ik
gy_b = gy[:, None, None, :] # il
W_b = W[None, :, :, :] # jkl
gW = kern(e1_b, e2_b, gy_b, axis=0) # 'ij,ik,il->jkl'
ge1 = kern(e2_b, W_b, gy_b, axis=(2, 3)) # 'ik,jkl,il->ij'
ge2 = kern(e1_b, W_b, gy_b, axis=(1, 3)) # 'ij,jkl,il->ik'
ret = ge1.reshape(inputs[0].shape), ge2.reshape(inputs[1].shape), gW
if len(inputs) == 6:
V1, V2, b = inputs[3:]
gV1 = e1.T.dot(gy)
gV2 = e2.T.dot(gy)
gb = gy.sum(0)
ge1 += gy.dot(V1.T)
ge2 += gy.dot(V2.T)
ret += gV1, gV2, gb
return ret
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
self.y, = softmax.Softmax(self.use_cudnn).forward((x,))
if getattr(self, 'normalize', True):
count = float((t != self.ignore_label).sum())
else:
count = t.shape[0]
self.count = count
if count == 0:
return cupy.zeros((), dtype=x.dtype),
y = cupy.rollaxis(self.y, 1, self.y.ndim)
ret = cuda.reduce(
'S t, raw T y, int32 n_channel, T inv_count', 'T out',
't == -1 ? 0 : log(y[_j * n_channel + t])',
'a + b', 'out = a * inv_count', '0', 'crossent_fwd'
)(t, y.reduced_view(), y.shape[-1], -1.0 / count)
return ret,
def backward(self, inputs, grad_outputs):
e1 = array.as_mat(inputs[0])
e2 = array.as_mat(inputs[1])
W = inputs[2]
if not type_check.same_types(*inputs):
raise ValueError('numpy and cupy must not be used together\n'
'type(W): {0}, type(e1): {1}, type(e2): {2}'
.format(type(W), type(e1), type(e2)))
gy = grad_outputs[0]
xp = cuda.get_array_module(*inputs)
if xp is numpy:
gW = numpy.einsum('ij,ik,il->jkl', e1, e2, gy)
ge1 = numpy.einsum('ik,jkl,il->ij', e2, W, gy)
ge2 = numpy.einsum('ij,jkl,il->ik', e1, W, gy)
else:
kern = cuda.reduce('T in0, T in1, T in2', 'T out',
'in0 * in1 * in2', 'a + b', 'out = a', 0,
'bilinear_product')
e1_b = e1[:, :, None, None] # ij
e2_b = e2[:, None, :, None] # ik
gy_b = gy[:, None, None, :] # il
W_b = W[None, :, :, :] # jkl
gW = kern(e1_b, e2_b, gy_b, axis=0) # 'ij,ik,il->jkl'
ge1 = kern(e2_b, W_b, gy_b, axis=(2, 3)) # 'ik,jkl,il->ij'
ge2 = kern(e1_b, W_b, gy_b, axis=(1, 3)) # 'ij,jkl,il->ik'
ret = ge1.reshape(inputs[0].shape), ge2.reshape(inputs[1].shape), gW
if len(inputs) == 6:
V1, V2, b = inputs[3:]
gV1 = e1.T.dot(gy)
gV2 = e2.T.dot(gy)
gb = gy.sum(0)
ge1 += gy.dot(V1.T)
ge2 += gy.dot(V2.T)
ret += gV1, gV2, gb
return ret
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
self._check_input_values(x, t)
log_y = cupy.log(x)
if self.cache_score:
self.y = x
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff', 'T out',
't == -1 ? 0 : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0', 'crossent_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1], self._coeff)
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
log_y = cupy.log(x + 1e-5)
self.y = x
if(self.debug):
ipdb.set_trace()
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff, raw T weights', 'T out',
't == -1 ? 0 : log_y[_j * n_channel + t] * weights[t]',
'a + b', 'out = a * -coeff[0]', '0', 'crossent_fwd'
)(t, log_y.reduced_view(), log_y.shape[-1], self._coeff, self.weights.reduced_view())
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
if chainer.is_debug():
self._check_input_values(x, t)
log_y = cupy.log(x)
if self.cache_score:
self.y = x
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce('S t, raw T log_y, int32 n_channel, raw T coeff',
'T out', 't == -1 ? 0 : log_y[_j * n_channel + t]',
'a + b', 'out = a * -coeff[0]', '0',
'crossent_fwd')(t, log_y.reduced_view(),
log_y.shape[-1], self._coeff)
return ret,
def forward_gpu(self, inputs):
cupy = cuda.cupy
x, t = inputs
log_y = cupy.log(x + 1e-5)
self.y = x
if (self.debug):
ipdb.set_trace()
if getattr(self, 'normalize', True):
coeff = cupy.maximum(1, (t != self.ignore_label).sum())
else:
coeff = max(1, len(t))
self._coeff = cupy.divide(1.0, coeff, dtype=x.dtype)
log_y = cupy.rollaxis(log_y, 1, log_y.ndim)
ret = cuda.reduce(
'S t, raw T log_y, int32 n_channel, raw T coeff, raw T weights',
'T out', 't == -1 ? 0 : log_y[_j * n_channel + t] * weights[t]',
'a + b', 'out = a * -coeff[0]', '0',
'crossent_fwd')(t, log_y.reduced_view(), log_y.shape[-1],
self._coeff, self.weights.reduced_view())
return ret,
def forward(self, inputs):
cs, ls, alpha_hat, beta_hat, kappa_hat, kappa_prev = inputs
# cs : one-hot-encoding vectors whose shape is (W, U)
# U: maximal length of character sequences in a batch
# W: number of characters used in a data
#
# ls : a vector containing lengths of character sequences in a batch
#
# alpha, beta, kappa: length K vectors. shape = (batchsize, K)
#
batchsize, W, U = cs.shape
K = alpha_hat.shape[1]
if isinstance(cs, numpy.ndarray):
self.alpha = numpy.exp(alpha_hat).reshape((batchsize, K, 1))
self.beta = numpy.exp(beta_hat).reshape((batchsize, K, 1))
self.kappa = (kappa_prev + numpy.exp(kappa_hat)).reshape(
(batchsize, K, 1))
us = numpy.arange(U).astype(numpy.float32).reshape((1, 1, U))
self.phai_mat = self.alpha * numpy.exp(
-self.beta * (self.kappa - us)**2) # --> (batchsize, K, U)
ws = numpy.matmul(
cs,
self.phai_mat.sum(axis=1).reshape(batchsize, U, 1)
) # (batchsize, W, U) x (batchsize, U, 1)--> (batchsize, W, 1)
if ls.sum() > 0: #ls is not None:
max_phai_idx = numpy.sum(self.phai_mat, axis=1).argmax(
axis=1
) # (batchsize, K, U) --> (batchsize, U) --> (batchsize, 1)
eow = numpy.where(max_phai_idx > ls, max_phai_idx,
-1) # (batchsize, 1)
else:
eow = numpy.zeros((batchsize, U)) #None
else:
self.alpha, self.beta, self.kappa = cuda.elementwise(
'T a_hat, T b_hat, T ka_hat, T ka_prev', 'T a, T b, T ka', '''
a = exp(a_hat);
b = exp(b_hat);
ka = ka_prev + exp(ka_hat);
''', 'softwindow_fwd1')(alpha_hat, beta_hat, kappa_hat, kappa_prev)
us = cuda.cupy.arange(U).astype(cuda.cupy.float32).reshape(
(1, 1, U))
self.phai_mat = cuda.elementwise(
'T a, T b, T k, T u', 'T ph', '''
ph = a * exp(- b *(k - u)*(k - u));
''', 'softwindow_fwd2'
)(
self.alpha.reshape(batchsize, K, 1),
self.beta.reshape(batchsize, K, 1),
self.kappa.reshape(batchsize, K, 1),
us #cuda.cupy.arange(U).astype(cuda.cupy.float32).reshape((1, 1, U))
)
#phais = self.phai_mat.sum(axis=1).reshape(batchsize, U, 1)
phais = cuda.reduce(
'T x',
'T y',
'x',
'a+b',
'y=a',
'0',
'softwindow_fwd3',
)(self.phai_mat, axis=1)
if ls.sum() > 0: # ls is not None:
max_phai_idx = cuda.cupy.argmax(phais, axis=1, keepdims=True)
phais = phais.reshape(batchsize, U, 1)
ws = cuda.cupy.empty((batchsize, W, 1)).astype(cuda.cupy.float32)
_batch_matmul_gpu(cs, phais, out=ws)
if ls.sum() > 0: # ls is not None:
eow = cuda.cupy.where(max_phai_idx > ls, max_phai_idx, -1)
else:
eow = cuda.cupy.zeros((batchsize, U)) #None
return ws.reshape(batchsize, W), self.kappa.reshape(
(batchsize, K)), eow
def forward(self, inputs):
xp = cuda.get_array_module(*inputs)
xnext, eow, e_hat, pi_hat, mux_hat, muy_hat, sgmx_hat, sgmy_hat, rho_hat = inputs
batchsize, M = pi_hat.shape
x1 = xnext[:, 0].reshape((batchsize, 1))
x2 = xnext[:, 1].reshape((batchsize, 1))
x3 = xnext[:, 2].reshape((batchsize, 1))
if isinstance(mux_hat, numpy.ndarray):
self.x = xnext
self.eos = 1. / (1. + numpy.exp(e_hat)) #_sigmoid(e_hat)
self.pi_ = numpy.exp(pi_hat) / numpy.exp(pi_hat).sum(
axis=1).reshape((batchsize, 1))
self.mux = mux_hat
self.muy = muy_hat
self.sgmx = numpy.exp(sgmx_hat)
self.sgmy = numpy.exp(sgmy_hat)
self.rho_ = numpy.tanh(rho_hat)
if x3.sum() >= 0.0: #xnext is not None: # training & validation
#x1 = xnext[:,0].reshape((batchsize, 1))
#x2 = xnext[:,1].reshape((batchsize, 1))
#x3 = xnext[:,2].reshape((batchsize, 1))
dx1 = (x1 - self.mux) / self.sgmx
dx2 = (x2 - self.muy) / self.sgmy
self.Zs = dx1 * dx1 + dx2 * dx2 - 2. * self.rho_ * dx1 * dx2
Ns = numpy.exp(-0.5 * self.Zs / (1. - self.rho_**2)) / (
2. * 3.1415927 * self.sgmx * self.sgmy *
numpy.sqrt(1. - self.rho_**2) + 1e-10)
gamma_hats = self.pi_ * Ns
sum_gamma_hats = gamma_hats.sum(axis=1).reshape(
(batchsize, 1)) + 1e-10
self.gammas = gamma_hats / sum_gamma_hats
loss_t = -numpy.log(sum_gamma_hats) - x3 * numpy.log(
self.eos) - (1. - x3) * numpy.log(1. - self.eos)
idx = numpy.where(x3 == 2)[0]
self.update_or_not = numpy.ones_like(x3)
self.update_or_not[idx, 0] = 0.0
loss_t = loss_t * self.update_or_not
self.xnext = xnext
# Prediction in training
xnext_h = numpy.copy(xnext)
with chainer.no_backprop_mode():
myux_min_h = mux_hat.min(axis=1).reshape((batchsize, 1))
myux_max_h = mux_hat.max(axis=1).reshape((batchsize, 1))
myuy_min_h = muy_hat.min(axis=1).reshape((batchsize, 1))
myuy_max_h = muy_hat.max(axis=1).reshape((batchsize, 1))
protect_mask = numpy.ones((batchsize, 1))
while protect_mask.sum() > 0:
z1_h = numpy.random.uniform(size=batchsize).reshape(
(batchsize, 1))
z2_ = numpy.random.uniform(size=batchsize).reshape(
(batchsize, 1))
x1_h = myux_min_h + (myux_max_h - myux_min_h) * z1_h
x2_h = myuy_min_h + (myuy_max_h - myuy_min_h) * z2_
dx1_h = (x1_h - self.mux) / self.sgmx
dx2_h = (x2_h - self.muy) / self.sgmy
self.Zs_h = dx1_h * dx1_h + dx2_h * dx2_h - 2. * self.rho_ * dx1_h * dx2_h
Ns = numpy.exp(
-0.5 * self.Zs_h / (1. - self.rho_**2)) / (
2. * 3.1415927 * self.sgmx * self.sgmy *
numpy.sqrt(1. - self.rho_**2) + 1e-10)
gamma_hats_h = self.pi_ * Ns
sum_gamma_hats = gamma_hats_h.sum(axis=1) # Pr(x|ys)
us_h = numpy.random.uniform(size=batchsize)
idx = numpy.where(sum_gamma_hats > us_h)[0]
xnext_h[idx, 0] += (x1_h * protect_mask)[idx, 0]
xnext_h[idx, 1] += (x2_h * protect_mask)[idx, 0]
protect_mask[idx, 0] = 0.0
#xnext[:, 2] = self.eos[:, 0]
#xnext[:, 2] = numpy.where(eow < 0, xnext[:, 2], 2.)
#xnext_h[:, 2] = self.eos[:, 0]
#mask = eow < 0
#if not mask.all():
# xnext_h[:, 2] = 2.0
#xnext[:, 2:] = xp.where(eow < 0, self.eos[:, 0:1], 2.)
xnext_h[:, 2] = xp.where(self.eos[:, 0] > 0.10, 1.0, 0.0)
self.xnext = xnext_h
else: # prediction
xnext = numpy.zeros((batchsize, 3))
myux_min = mux_hat.min(axis=1).reshape((batchsize, 1))
myux_max = mux_hat.max(axis=1).reshape((batchsize, 1))
myuy_min = muy_hat.min(axis=1).reshape((batchsize, 1))
myuy_max = muy_hat.max(axis=1).reshape((batchsize, 1))
protect_mask = numpy.ones((batchsize, 1))
while protect_mask.sum() > 0:
z1 = numpy.random.uniform(size=batchsize).reshape(
(batchsize, 1))
z2 = numpy.random.uniform(size=batchsize).reshape(
(batchsize, 1))
x1 = myux_min + (myux_max - myux_min) * z1
x2 = myuy_min + (myuy_max - myuy_min) * z2
dx1 = (x1 - self.mux) / self.sgmx
dx2 = (x2 - self.muy) / self.sgmy
self.Zs = dx1 * dx1 + dx2 * dx2 - 2. * self.rho_ * dx1 * dx2
Ns = numpy.exp(-0.5 * self.Zs / (1. - self.rho_**2)) / (
2. * 3.1415927 * self.sgmx * self.sgmy *
numpy.sqrt(1. - self.rho_**2) + 1e-10)
gamma_hats = self.pi_ * Ns
sum_gamma_hats = gamma_hats.sum(axis=1) # Pr(x|ys)
us = numpy.random.uniform(size=batchsize)
idx = numpy.where(sum_gamma_hats > us)[0]
xnext[idx, 0] += (x1 * protect_mask)[idx, 0]
xnext[idx, 1] += (x2 * protect_mask)[idx, 0]
protect_mask[idx, 0] = 0.0
#xnext[:, 2] = self.eos[:, 0]
#xnext[:, 2] = numpy.where(eow < 0, xnext[:, 2], 2.)
xnext[:, 2] = self.eos[:, 0]
mask = eow < 0
if not mask.all():
xnext[:, 2] = 2.0
#xnext[:, 2:] = xp.where(eow < 0, self.eos[:, 0:1], 2.)
self.xnext = xnext
#loss_t = None
loss_t = xp.zeros((batchsize, 1)).astype(xp.float32)
self.Zs = None
else:
self.mux = mux_hat
self.muy = muy_hat
self.pi_hat = pi_hat - pi_hat.max(axis=1).reshape(batchsize, 1)
sum_exp_pi = cuda.reduce(
'T x', # input params
'T y', # output params
'exp(x)', # map
'a+b', # reduce
'y=a', # post-reduction map
'1e-10', # identity value
'mdout_sumexp' # kernel name
)(self.pi_hat, axis=1)
self.eos = 1. / (1. + cuda.cupy.exp(e_hat))
if x3.sum() >= 0.0: #xnext is not None: # training & validation
gamma_hats, self.Zs, self.pi_, self.sgmx, self.sgmy, self.rho_ = cuda.elementwise(
'T x1, T x2, T pi_hat, T mux_, T muy_, T sgmx_hat, T sgmy_hat, T rho_hat, T sum_exp_pi', # input
'T gammas, T Zs, T pi_, T sgmx_, T sgmy_, T rho_', # output
'''
pi_ = exp(pi_hat)/sum_exp_pi;
sgmx_ = exp(sgmx_hat) + 1e-10;
sgmy_ = exp(sgmy_hat) + 1e-10;
rho_ = tanh(rho_hat);
T rho2 = 1. - rho_*rho_ + 1e-10;
T dx1 = (x1 - mux_)/sgmx_;
T dx2 = (x2 - muy_)/sgmy_;
Zs = dx1*dx1 + dx2*dx2- 2.*rho_*dx1*dx2;
T Ns = exp( -0.5*Zs /rho2)/(2. * 3.1415927 * sgmx_ * sgmy_ * sqrt(rho2));
gammas = pi_ * Ns;
''',
'mdout_fwd1',
)(x1, x2, self.pi_hat, mux_hat, muy_hat, sgmx_hat, sgmy_hat,
rho_hat, sum_exp_pi.reshape((batchsize, 1)))
sum_gamma_hats = gamma_hats.sum(axis=1).reshape(
(batchsize, 1)) + 1e-10
self.gammas = gamma_hats / sum_gamma_hats
loss_t = cuda.elementwise(
'T sum_, T x3, T eos',
'T loss',
'''
loss = -log(sum_) - x3 * log(eos) - (1. - x3) * log(1.-eos);
''',
'mdout_fwd2',
)(sum_gamma_hats, x3, self.eos)
self.update_or_not = xp.where(x3 == 2., 0.0,
1.0).astype(xp.float32)
loss_t = loss_t * self.update_or_not
self.xnext = xnext
# Prediction in training
with chainer.no_backprop_mode():
self.sgmx_h = xp.where(self.sgmx < 0.0015, 0.0015,
self.sgmx)
self.sgmy_h = xp.where(self.sgmy < 0.0015, 0.0015,
self.sgmy)
muxs = xp.empty((batchsize, M, M)).astype(xp.float32)
muys = xp.empty((batchsize, M, M)).astype(xp.float32)
_batch_matmul_gpu(mux_hat.reshape((batchsize, M, 1)),
xp.ones((batchsize, 1,
M)).astype(xp.float32),
out=muxs)
_batch_matmul_gpu(muy_hat.reshape((batchsize, M, 1)),
xp.ones((batchsize, 1,
M)).astype(xp.float32),
out=muys)
gamma_hats_at_components = cuda.elementwise(
'T x1, T x2, T pi_, T mux_, T muy_, T sgmx_, T sgmy_, T rho_', # input
'T gammas', # output
'''
T rho2 = 1. - rho_*rho_ + 1e-10;
T dx1 = (x1 - mux_)/sgmx_;
T dx2 = (x2 - muy_)/sgmy_;
T Zs = dx1*dx1 + dx2*dx2- 2.*rho_*dx1*dx2;
T Ns = exp( -0.5*Zs /rho2)/(2. * 3.1415927 * sgmx_ * sgmy_ * sqrt(rho2));
gammas = pi_ * Ns;
''',
'mdout_fwd5',
)(muxs, muys, self.pi_.reshape((batchsize, 1, M)),
mux_hat.reshape((batchsize, 1, M)),
muy_hat.reshape((batchsize, 1, M)),
self.sgmx_h.reshape((batchsize, 1, M)),
self.sgmy_h.reshape((batchsize, 1, M)),
self.rho_.reshape((batchsize, 1, M)))
sum_gamma_hats_at_components = gamma_hats_at_components.sum(
axis=2) # (batchsize, M)
p_maxs = sum_gamma_hats_at_components.max(axis=1).reshape(
(batchsize, 1)) # (batchsize, 1)
myux_min_h = mux_hat.min(axis=1).reshape(
(batchsize, 1, 1)) - 0.01
myux_max_h = mux_hat.max(axis=1).reshape(
(batchsize, 1, 1)) + 0.01
myuy_min_h = muy_hat.min(axis=1).reshape(
(batchsize, 1, 1)) - 0.01
myuy_max_h = muy_hat.max(axis=1).reshape(
(batchsize, 1, 1)) + 0.01
xnext_h = xp.zeros((batchsize, 3)).astype(xp.float32)
protect_mask = xp.ones((batchsize, 1)).astype(xp.float32)
n_samples = 32768 * 2 #16384 #8192 #4096 #2048 #1024 #512
x1_h = xp.copy(x1)
x2_h = xp.copy(x2)
while protect_mask.sum() > 0:
# sampling n (=n_samples) samples in parallel at a step
z1_h = xp.random.uniform(size=batchsize *
n_samples).reshape(
(batchsize, n_samples, 1))
z2_h = xp.random.uniform(size=batchsize *
n_samples).reshape(
(batchsize, n_samples, 1))
x1__h = (myux_min_h +
(myux_max_h - myux_min_h) * z1_h).astype(
xp.float32) # (batchsize, n_samples, 1)
x2__h = (myuy_min_h +
(myuy_max_h - myuy_min_h) * z2_h).astype(
xp.float32) # (batchsize, n_samples, 1)
gamma_hats_h = cuda.elementwise(
'T x1, T x2, T pi_, T mux_, T muy_, T sgmx_, T sgmy_, T rho_', # input
'T gammas', # output
'''
T rho2 = 1. - rho_*rho_ + 1e-10;
T dx1 = (x1 - mux_)/sgmx_;
T dx2 = (x2 - muy_)/sgmy_;
T Zs = dx1*dx1 + dx2*dx2- 2.*rho_*dx1*dx2;
T Ns = exp( -0.5*Zs /rho2)/(2. * 3.1415927 * sgmx_ * sgmy_ * sqrt(rho2));
gammas = pi_ * Ns;
''',
'mdout_fwd4',
)(x1__h, x2__h, self.pi_.reshape((batchsize, 1, M)),
mux_hat.reshape((batchsize, 1, M)),
muy_hat.reshape((batchsize, 1, M)),
self.sgmx_h.reshape((batchsize, 1, M)),
self.sgmy_h.reshape((batchsize, 1, M)),
self.rho_.reshape((batchsize, 1, M)))
sum_gamma_hats_h = gamma_hats_h.sum(axis=2)
us_h = xp.random.uniform(
size=batchsize * n_samples).reshape(
(batchsize, n_samples)) * p_maxs
update_mask__h = xp.where(
sum_gamma_hats_h > us_h, 1.0,
0.0).astype(xp.float32).reshape(
(batchsize, n_samples))
update_mask_h = update_mask__h.max(axis=1).reshape(
(batchsize, 1))
sample_idx_h = update_mask__h.argmax(axis=1).reshape(
(batchsize, 1))
for bb in xrange(batchsize):
this_midx = sample_idx_h[bb, 0]
x1_h[bb:bb + 1,
0] = x1__h[bb:bb + 1, this_midx:this_midx + 1,
0]
x2_h[bb:bb + 1,
0] = x2__h[bb:bb + 1, this_midx:this_midx + 1,
0]
xnext_h[:,
0] += (x1_h * protect_mask * update_mask_h)[:,
0]
xnext_h[:,
1] += (x2_h * protect_mask * update_mask_h)[:,
0]
protect_mask -= protect_mask * update_mask_h
xnext_h[:, 2:] = xp.where(self.eos[:, 0:1] > 0.10, 1.0,
0.0)
#xnext_h[:, 2:] = xp.where(eow < 0, self.eos[:, 0:1], 2.)
self.xnext = xnext_h
#loss_t = xp.zeros((batchsize, 1)).astype(xp.float32)
#self.Zs = None
else: # prediction (sampling from probability distribution)
# pi, sgmx, sgmy, rho <-- pi_hat, sgmx_hat, sgmy_hat, rho_hat
self.pi_, self.sgmx, self.sgmy, self.rho_ = cuda.elementwise(
'T pi_hat, T sgmx_hat, T sgmy_hat, T rho_hat, T sum_exp_pi', # input
'T pi_, T sgmx_, T sgmy_, T rho_', # output
'''
pi_ = exp(pi_hat)/sum_exp_pi;
sgmx_ = exp(sgmx_hat) + 1e-10;
sgmy_ = exp(sgmy_hat) + 1e-10;
rho_ = tanh(rho_hat);
''',
'mdout_fwd3',
)(self.pi_hat, sgmx_hat, sgmy_hat, rho_hat,
sum_exp_pi.reshape((batchsize, 1)))
# because variances of gaussians are very small, sampling is virtually impossible, we set lower boundary for variances!
self.sgmx = xp.where(self.sgmx < 0.0015, 0.0015, self.sgmx)
self.sgmy = xp.where(self.sgmy < 0.0015, 0.0015, self.sgmy)
#print(self.sgmx.min(), self.sgmy.min())
# get the (aproximated) maximum p value of M-mixture gaussian distributions.
# Here I assume that the maximum p value is taken at a center of a gaussian component in the mixture.
# First, calculate p-values at each center of gaussian components,
# and the maximum of these p-values is considered as the upper boundary of the M-mixture gaussian distributions
# prepare x1 and x2 matrices like
# [ [mux0, mux0, ...., mux0],
# [mux1, mux1, ...., mux1],
# ...
# [muxn, muxn, ...., muxn]] where n = batchsize
muxs = xp.empty((batchsize, M, M)).astype(xp.float32)
muys = xp.empty((batchsize, M, M)).astype(xp.float32)
_batch_matmul_gpu(mux_hat.reshape((batchsize, M, 1)),
xp.ones(
(batchsize, 1, M)).astype(xp.float32),
out=muxs)
_batch_matmul_gpu(muy_hat.reshape((batchsize, M, 1)),
xp.ones(
(batchsize, 1, M)).astype(xp.float32),
out=muys)
# N_i((mux[j], muy[j])) for i = 0, 1, ..., M and j = 0, 1, ..., M
gamma_hats_at_components = cuda.elementwise(
'T x1, T x2, T pi_, T mux_, T muy_, T sgmx_, T sgmy_, T rho_', # input
'T gammas', # output
'''
T rho2 = 1. - rho_*rho_ + 1e-10;
T dx1 = (x1 - mux_)/sgmx_;
T dx2 = (x2 - muy_)/sgmy_;
T Zs = dx1*dx1 + dx2*dx2- 2.*rho_*dx1*dx2;
T Ns = exp( -0.5*Zs /rho2)/(2. * 3.1415927 * sgmx_ * sgmy_ * sqrt(rho2));
gammas = pi_ * Ns;
''',
'mdout_fwd5',
)(muxs, muys, self.pi_.reshape((batchsize, 1, M)),
mux_hat.reshape((batchsize, 1, M)),
muy_hat.reshape((batchsize, 1, M)),
self.sgmx.reshape((batchsize, 1, M)),
self.sgmy.reshape((batchsize, 1, M)),
self.rho_.reshape((batchsize, 1, M)))
# p[j] = sum(N_i((mux[j], muy[j])) for i = 0, 1, ..., M
sum_gamma_hats_at_components = gamma_hats_at_components.sum(
axis=2) # (batchsize, M)
# max(p[0], p[1], ..., p[M]) for each batch
p_maxs = sum_gamma_hats_at_components.max(axis=1).reshape(
(batchsize, 1)) # (batchsize, 1)
#print(p_maxs.reshape((1, batchsize)))
myux_min = mux_hat.min(axis=1).reshape(
(batchsize, 1, 1)) - 0.01
myux_max = mux_hat.max(axis=1).reshape(
(batchsize, 1, 1)) + 0.01
myuy_min = muy_hat.min(axis=1).reshape(
(batchsize, 1, 1)) - 0.01
myuy_max = muy_hat.max(axis=1).reshape(
(batchsize, 1, 1)) + 0.01
xnext = xp.zeros((batchsize, 3)).astype(xp.float32)
protect_mask = xp.ones((batchsize, 1)).astype(xp.float32)
n_samples = 32768 * 2 #16384 #8192 #4096 #2048 #1024 #512
while protect_mask.sum() > 0:
# sampling n (=n_samples) samples in parallel at a step
z1 = xp.random.uniform(size=batchsize * n_samples).reshape(
(batchsize, n_samples, 1))
z2 = xp.random.uniform(size=batchsize * n_samples).reshape(
(batchsize, n_samples, 1))
x1_ = (myux_min + (myux_max - myux_min) * z1).astype(
xp.float32) # (batchsize, n_samples, 1)
x2_ = (myuy_min + (myuy_max - myuy_min) * z2).astype(
xp.float32) # (batchsize, n_samples, 1)
gamma_hats = cuda.elementwise(
'T x1, T x2, T pi_, T mux_, T muy_, T sgmx_, T sgmy_, T rho_', # input
'T gammas', # output
'''
T rho2 = 1. - rho_*rho_ + 1e-10;
T dx1 = (x1 - mux_)/sgmx_;
T dx2 = (x2 - muy_)/sgmy_;
T Zs = dx1*dx1 + dx2*dx2- 2.*rho_*dx1*dx2;
T Ns = exp( -0.5*Zs /rho2)/(2. * 3.1415927 * sgmx_ * sgmy_ * sqrt(rho2));
gammas = pi_ * Ns;
''',
'mdout_fwd4',
)(x1_, x2_, self.pi_.reshape((batchsize, 1, M)),
mux_hat.reshape((batchsize, 1, M)),
muy_hat.reshape((batchsize, 1, M)),
self.sgmx.reshape((batchsize, 1, M)),
self.sgmy.reshape((batchsize, 1, M)),
self.rho_.reshape((batchsize, 1, M)))
sum_gamma_hats_ = gamma_hats.sum(axis=2)
"""
sum_gamma_hats = sum_gamma_hats_.max(axis=1).reshape((batchsize, 1))
sample_idx = sum_gamma_hats_.argmax(axis=1).reshape((batchsize, 1))
for bb in xrange(batchsize):
this_midx = sample_idx[bb, 0]
x1[bb:bb+1, 0] = x1_[bb:bb+1, this_midx:this_midx+1, 0]
x2[bb:bb+1, 0] = x2_[bb:bb+1, this_midx:this_midx+1, 0]
us = xp.random.uniform(size=batchsize).reshape((batchsize, 1)) * p_maxs
update_mask = xp.where(sum_gamma_hats > us, 1.0, 0.0).astype(xp.float32).reshape((batchsize, 1))
xnext[:, 0] += (x1*protect_mask*update_mask)[:, 0]
xnext[:, 1] += (x2*protect_mask*update_mask)[:, 0]
protect_mask -= protect_mask * update_mask
"""
"""
us_ = xp.random.uniform(size=batchsize* n_samples).reshape((batchsize, n_samples)) * p_maxs
update_mask_ = xp.where(sum_gamma_hats_ > us_, 1.0, 0.0).astype(xp.float32).reshape((batchsize, n_samples))
x1 = x1_.reshape((batchsize, n_samples)) * update_mask_
x2 = x2_.reshape((batchsize, n_samples)) * update_mask_
for i in xrange(n_samples):
xnext[:, 0] += (x1_[:,i, :]*protect_mask)[:, 0]
xnext[:, 1] += (x2_[:,i, :]*protect_mask)[:, 0]
#print(protect_mask.shape, update_mask_[:, i:(i+1)].shape)
protect_mask -= protect_mask * update_mask_[:, i:(i+1)]
"""
us_ = xp.random.uniform(
size=batchsize * n_samples).reshape(
(batchsize, n_samples)) * p_maxs
update_mask_ = xp.where(sum_gamma_hats_ > us_, 1.0,
0.0).astype(xp.float32).reshape(
(batchsize, n_samples))
update_mask = update_mask_.max(axis=1).reshape(
(batchsize, 1))
sample_idx = update_mask_.argmax(axis=1).reshape(
(batchsize, 1))
for bb in xrange(batchsize):
this_midx = sample_idx[bb, 0]
x1[bb:bb + 1, 0] = x1_[bb:bb + 1,
this_midx:this_midx + 1, 0]
x2[bb:bb + 1, 0] = x2_[bb:bb + 1,
this_midx:this_midx + 1, 0]
xnext[:, 0] += (x1 * protect_mask * update_mask)[:, 0]
xnext[:, 1] += (x2 * protect_mask * update_mask)[:, 0]
protect_mask -= protect_mask * update_mask
xnext[:, 2:] = self.eos[:, 0:1]
xnext[:, 2:] = xp.where(eow < 0, self.eos[:, 0:1], 2.)
self.xnext = xnext
loss_t = xp.zeros((batchsize, 1)).astype(xp.float32)
self.Zs = None
return loss_t, self.xnext, self.eos, self.pi_, self.mux, self.muy, self.sgmx, self.sgmy, self.rho_,
def _l2normalize(v, eps=1e-12):
norm = cuda.reduce('T x', 'T out', 'x * x', 'a + b', 'out = sqrt(a)', 0,
'norm_sn')
div = cuda.elementwise('T x, T norm, T eps', 'T out',
'out = x / (norm + eps)', 'div_sn')
return div(v, norm(v), eps)
def backward(self, inputs, grad_outputs):
xp = cuda.get_array_module(*inputs)
cs, ls, alpha_hat, beta_hat, kappa_hat, kappa_prev = inputs
batchsize, W, U = cs.shape
K = alpha_hat.shape[1]
gw, gk = grad_outputs[0:2] # (batchsize, W)
ga_hat = xp.empty_like(alpha_hat)
gb_hat = xp.empty_like(beta_hat)
gk_hat = xp.empty_like(kappa_hat)
gk_prev = xp.empty_like(kappa_prev) #gk)
gc = xp.empty_like(cs)
# Consider the case that either gradient is not given
if gw is None:
gw = 0
if gk is None:
gk = 0
if xp is numpy:
gwc = numpy.matmul(gw.reshape(batchsize, 1, W),
cs) # (batchsize, 1, U)
emat = self.phai_mat * gwc # (batchsize, K, U)
ga_hat[:] = emat.sum(axis=2)
us = numpy.arange(U).astype(numpy.float32).reshape((1, 1, U))
diff = us - self.kappa
b = self.beta.reshape((batchsize, K))
gb_hat[:] = -b * (emat * diff**2).sum(axis=2)
gk_prev[:] = gk + 2. * b * (emat * diff).sum(axis=2)
gk_hat[:] = numpy.exp(kappa_hat) * gk_prev
else:
gwc = cuda.cupy.empty((batchsize, 1, U)).astype(cuda.cupy.float32)
#for i in xrange(batchsize):
# gwc[i] = (gw.reshape(batchsize, 1, W))[i].dot(cs[i]) # (1, W).(W, U) --> (1, U)
_batch_matmul_gpu(gw.reshape(batchsize, 1, W), cs, out=gwc)
#emat = self.phai_mat * gwc
emat = cuda.elementwise(
'T phai, T gwc',
'T emat',
'''
emat = phai * gwc;
''',
'softwindow_bw1',
)(self.phai_mat, gwc)
#ga_hat[:] = emat.sum(axis=2)
ga_hat[:] = cuda.reduce(
'T x',
'T y',
'x',
'a+b',
'y=a',
'0',
'softwindow_bw2',
)(emat, axis=2)
us = cuda.cupy.arange(U).astype(cuda.cupy.float32).reshape(
(1, 1, U))
diff = us - self.kappa.reshape(batchsize, K, 1)
b = self.beta.reshape(batchsize, K)
tmp2, tmp1 = cuda.elementwise(
'T emat, T diff', 'T ed2, T ed1', '''
ed1 = emat * diff;
ed2 = ed1 * diff;
''', 'softwindow_bw3')(emat, diff)
sum1 = cuda.reduce(
'T x',
'T y',
'x',
'a+b',
'y=a',
'0',
'softwindow_bw4',
)(tmp1, axis=2)
sum2 = cuda.reduce(
'T x',
'T y',
'x',
'a+b',
'y=a',
'0',
'softwindow_bw5',
)(tmp2, axis=2)
gb_hat[:] = -b * sum2
gk_prev[:] = gk + 2. * b * sum1
#gb_hat[:] = - b * (emat * diff**2).sum(axis=2)
#gk_prev[:]= gk + 2. * b * (emat * diff).sum(axis=2)
#gk_hat[:] = cuda.cupy.exp(kappa_hat)*gk_prev
gk_hat = cuda.elementwise(
'T k_hat, T gk_prev', 'T gk_hat', '''
gk_hat = exp(k_hat)*gk_prev;
''', 'softwindow_bw6')(kappa_hat, gk_prev)
return None, None, ga_hat, gb_hat, gk_hat, gk_prev,
def forward_gpu(self, inputs):
from chainer.cuda import cupy
mean_x, cov_x, t = inputs
dim = len(mean_x[0])
self._make_samples(t)
self._pos_indexes = self.samples[:,0]
self._neg_indexes = self.samples[:,1]
self._m_pos = self.M.take(self._pos_indexes, axis=0)
self._c_pos = self.C.take(self._pos_indexes, axis=0)
self._m_neg = self.M.take(self._neg_indexes, axis=0)
self._c_neg = self.C.take(self._neg_indexes, axis=0)
if self._covariance_type == CovarianceType.diagonal:
kern_trace = cuda.reduce(
'T Ci, T Cj', 'T tr',
'Cj / Ci', 'a + b', 'tr = a', 0,
'trace')
tr_p = kern_trace(cov_x, self._c_pos, axis=1)
tr_n = kern_trace(cov_x, self._c_neg, axis=1)
kern_det = cuda.reduce(
'T Ci, T Cj', 'T det',
'__logf(Cj) - __logf(Ci)', 'a + b', 'det = a', 0,
'determinant')
det_p = kern_det(cov_x, self._c_pos, axis=1)
det_n = kern_det(cov_x, self._c_neg, axis=1)
kern_fac = cuda.reduce(
'T Mi, T Mj, T Ci', 'T out',
'__powf(abs(Mi - Mj), 2.0) / Ci', 'a + b', 'out = a', 0,
'factor')
fac_p = kern_fac(mean_x, self._m_pos, cov_x, axis=1)
fac_n = kern_fac(mean_x, self._m_neg, cov_x, axis=1)
self._kl_pos, self._kl_neg, loss = cuda.elementwise(
'T f_p, T f_n, T tr_p, T tr_n, T det_p, T det_n, S ip, S in, \
float32 m, int32 dim',
'T kl_p, T kl_n, T L',
'''
if (ip == in) {
kl_p = 0.0;
kl_n = 0.0;
L = m;
} else {
kl_p = -0.5 * (tr_p + f_p - dim - det_p);
kl_n = -0.5 * (tr_n + f_n - dim - det_n);
L = max(0.0, m - kl_p + kl_n);
}
''',
'loss_function_diagonal'
)(fac_p, fac_n, tr_p, tr_n, det_p, det_n, self._pos_indexes,
self._neg_indexes, self._margin, dim)
elif self._covariance_type == CovarianceType.spherical:
kern_sq_err_sum = cuda.reduce(
'T in0, T in1', 'T out',
'__powf(abs(in0 - in1), 2.0)', 'a + b', 'out = a', 0,
'residual_sum_of_squares')
sq_p = kern_sq_err_sum(mean_x, self._m_pos, axis=1)[cupy.newaxis, :].T
sq_n = kern_sq_err_sum(mean_x, self._m_neg, axis=1)[cupy.newaxis, :].T
self._kl_pos, self._kl_neg, loss = cuda.elementwise(
'T sq_p, T sq_n, T cx, T cp, T cn, S ip, S in, float32 m, int32 dim',
'T kl_p, T kl_n, T L',
'''
if (ip == in) {
kl_p = 0.0;
kl_n = 0.0;
L = m;
} else {
T tr_p = dim * cp / cx;
T tr_n = dim * cn / cx;
T det_p = dim * __logf(cp / cx);
T det_n = dim * __logf(cn / cx);
kl_p = -0.5 * (tr_p + sq_p / cx - dim - det_p);
kl_n = -0.5 * (tr_n + sq_n / cx - dim - det_n);
L = max(0.0, m - kl_p + kl_n);
}
''',
'loss_function_spherical'
)(sq_p, sq_n, cov_x, self._c_pos, self._c_neg,
self._pos_indexes[cupy.newaxis, :].T,
self._neg_indexes[cupy.newaxis, :].T,
self._margin, dim)
sum_loss = cuda.cupy.sum(loss)
return sum_loss,
def forward(self, inputs):
#
# preprocessing
#
xp = cuda.get_array_module(*inputs)
x, gamma, beta = inputs[:3]
if configuration.config.train:
if self.running_mean is None:
self.running_mean = xp.zeros_like(beta, dtype=xp.float32)
self.running_var = xp.zeros_like(gamma, dtype=xp.float32)
else:
self.running_mean = xp.array(self.running_mean)
self.running_var = xp.array(self.running_var)
elif len(inputs) == 6:
self.fixed_mean = inputs[4]
self.fixed_var = inputs[5]
head_ndim = beta.ndim + 1
expander = (None, Ellipsis) + (None, ) * (x.ndim - head_ndim)
#
# start of forward path
#
if configuration.config.train:
axis = (0, ) + tuple(range(head_ndim, x.ndim))
mean = x.mean(axis=axis)
var = cuda.reduce('S x, T mean, T alpha', 'T out',
'(x - mean) * (x - mean)', 'a + b',
'out = alpha * a', '0',
'conv_bn_var')(x,
mean[expander],
x.shape[1] / x.size,
axis=axis,
keepdims=False)
else:
mean = self.fixed_mean
var = self.fixed_var
if xp is numpy:
raise NotImplementedError()
else:
self.std_inv = cuda.elementwise(
'T var, T eps', 'T std_inv', '''
std_inv = 1 / sqrt(var + eps);
''', 'conv_bn_std_inv')(var, self.eps)
self.x_hat, y = cuda.elementwise(
'T x, T mean, T std_inv, T gamma, T beta', 'T x_hat, T y', '''
x_hat = (x - mean) * std_inv;
y = gamma * x_hat + beta;
''', 'conv_bn_fwd')(x, mean[expander], self.std_inv[expander],
gamma[expander], beta[expander])
#
# end of forward path
#
#
# calculation of lipschitz constant
#
if chainer.config.train and getattr(chainer.config, 'lmt', False):
#
# power iteration for a matrix Diag(\gamma_i/\sigma_i)W
#
# u <= Diag(\gamma_i/\sigma_i) u
# v <= W u
# u_mid <= W^T v
# u <= Diag(\gamma_i/\sigma_i)^T v
#
W = inputs[3].reshape((inputs[3].shape[0], -1))
tmp_l = gamma * self.std_inv
self.u *= tmp_l
self.v = self.u.dot(W)
# normalize for back propagation
normalize(self.v, eps=1e-20)
# do not normalize u_mid
self.u_mid = self.v.dot(W.T)
self.u[:] = self.u_mid * tmp_l
# normalize for back propagation
nu = normalize(self.u, eps=1e-20)
# spectral norm is approximated by the norm of a vector u
l = nu.reshape((1, ))
else:
# not used
l = xp.ones((1, ), dtype=xp.float32)
#
# calculate running average of statistics
#
if configuration.config.train:
self.running_mean *= self.decay
self.running_mean += mean * (1 - self.decay)
self.running_var *= self.decay
self.running_var += var * (1 - self.decay)
return y, l