def _SubGrad(op, grad):
x = op.inputs[0]
y = op.inputs[1]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
return (array_ops.reshape(math_ops.reduce_sum(grad, rx), sx), array_ops.reshape(-math_ops.reduce_sum(grad, ry), sy))
def _BetaincGrad(op, grad):
"""Returns gradient of betainc(a, b, x) with respect to x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a, b
a, b, x = op.inputs
# two cases: x is a scalar and a/b are same-shaped tensors, or vice
# versa; so its sufficient to check against shape(a).
sa = array_ops.shape(a)
sx = array_ops.shape(x)
# pylint: disable=protected-access
_, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# pylint: enable=protected-access
# Perform operations in log space before summing, because terms
# can grow large.
log_beta = (
gen_math_ops.lgamma(a) + gen_math_ops.lgamma(b) -
gen_math_ops.lgamma(a + b))
partial_x = math_ops.exp((b - 1) * math_ops.log(1 - x) +
(a - 1) * math_ops.log(x) - log_beta)
# TODO(b/36815900): Mark None return values as NotImplemented
return (
None, # da
None, # db
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _reduce_and_reshape_grad(g, t): """Returns the gradient, sum-reduced and reshaped to `t`'s shape.""" shape = array_ops.shape(t) g_shape = array_ops.shape(g) # pylint: disable=protected-access bcast_dims, _ = gen_array_ops._broadcast_gradient_args(shape, g_shape) # pylint: enable=protected-access return array_ops.reshape(math_ops.reduce_sum(g, bcast_dims), shape)
def _DivGrad(op, grad):
x = op.inputs[0]
y = op.inputs[1]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy) # pylint: disable=protected-access
return (array_ops.reshape(math_ops.reduce_sum(grad / y, rx), sx),
array_ops.reshape(math_ops.reduce_sum(grad *
(-x / math_ops.square(y)), ry), sy))
def _ComplexGrad(op, grad):
"""Returns the real and imaginary components of 'grad', respectively."""
x = op.inputs[0]
y = op.inputs[1]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
return (array_ops.reshape(math_ops.reduce_sum(math_ops.real(grad), rx), sx),
array_ops.reshape(math_ops.reduce_sum(math_ops.imag(grad), ry), sy))
def _PowGrad(op, grad):
"""Returns grad * (y*x^(y-1), z*log(x))."""
x = op.inputs[0]
y = op.inputs[1]
z = op.outputs[0]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
gx = array_ops.reshape(math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
gy = array_ops.reshape(math_ops.reduce_sum(grad * z * math_ops.log(x), ry), sy)
return gx, gy
def _MulGrad(op, grad):
"""The gradient of scalar multiplication."""
x = op.inputs[0]
y = op.inputs[1]
assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
x = math_ops.conj(x)
y = math_ops.conj(y)
return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))
def _MulGrad(op, grad):
x = op.inputs[0]
y = op.inputs[1]
assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
if x.dtype.base_dtype == dtypes.complex64:
return (array_ops.reshape(math_ops.reduce_sum(grad * math_ops.conj(y), rx), sx),
array_ops.reshape(math_ops.reduce_sum(math_ops.conj(x) * grad, ry), sy))
else:
return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))
def _PowGrad(op, grad):
"""Returns grad * (y*x^(y-1), z*log(x))."""
x = op.inputs[0]
y = op.inputs[1]
z = op.outputs[0]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
gx = array_ops.reshape(math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
# Avoid false singularity at x = 0
log_x = math_ops.select(x > 0, math_ops.log(x), array_ops.zeros_like(x))
gy = array_ops.reshape(math_ops.reduce_sum(grad * z * log_x, ry), sy)
return gx, gy
def _PolygammaGrad(op, grad):
"""Returns gradient of psi(n, x) with respect to n and x."""
# TODO(tillahoffmann): Add derivative with respect to n
n = op.inputs[0]
x = op.inputs[1]
# Broadcast gradients
sn = array_ops.shape(n)
sx = array_ops.shape(x)
unused_rn, rx = gen_array_ops._broadcast_gradient_args(sn, sx)
# Evaluate gradient
with ops.control_dependencies([grad.op]):
partial_x = math_ops.polygamma(n + 1, x)
return (None, array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _ZetaGrad(op, grad):
"""Returns gradient of zeta(x, q) with respect to x and q."""
# TODO(tillahoffmann): Add derivative with respect to x
x = op.inputs[0]
q = op.inputs[1]
# Broadcast gradients
sx = array_ops.shape(x)
sq = array_ops.shape(q)
unused_rx, rq = gen_array_ops._broadcast_gradient_args(sx, sq)
# Evaluate gradient
with ops.control_dependencies([grad.op]):
partial_q = -x * math_ops.zeta(x + 1, q)
return (None, array_ops.reshape(math_ops.reduce_sum(partial_q * grad, rq), sq))
def _IgammaGrad(op, grad):
"""Returns gradient of igamma(a, x) with respect to a and x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a
a = op.inputs[0]
x = op.inputs[1]
sa = array_ops.shape(a)
sx = array_ops.shape(x)
unused_ra, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# Perform operations in log space before summing, because Gamma(a)
# and Gamma'(a) can grow large.
partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x) - math_ops.lgamma(a))
return (None, array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _SubGrad(op, grad):
"""Gradient for Sub."""
x = op.inputs[0]
y = op.inputs[1]
if (isinstance(grad, ops.Tensor) and
_ShapesFullySpecifiedAndEqual(x, y, grad)):
return grad, -grad
sx = array_ops.shape(x)
sy = array_ops.shape(y)
# pylint: disable=protected-access
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
# pylint: enable=protected-access
return (array_ops.reshape(math_ops.reduce_sum(grad, rx), sx),
array_ops.reshape(-math_ops.reduce_sum(grad, ry), sy))
def _DivGrad(op, grad):
"""The gradient for the Div operator."""
x = op.inputs[0]
y = op.inputs[1]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
# pylint: disable=protected-access
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
# pylint: enable=protected-access
x = math_ops.conj(x)
y = math_ops.conj(y)
return (array_ops.reshape(math_ops.reduce_sum(math_ops.div(grad, y), rx), sx),
array_ops.reshape(math_ops.reduce_sum(
grad * math_ops.div(-x, math_ops.square(y)), ry), sy))
def _FloorModGrad(op, grad):
"""Returns grad * (1, -floor(x/y))."""
x = math_ops.conj(op.inputs[0])
y = math_ops.conj(op.inputs[1])
sx = array_ops.shape(x)
sy = array_ops.shape(y)
# pylint: disable=protected-access
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
# pylint: enable=protected-access
floor_xy = math_ops.floor_div(x, y)
gx = array_ops.reshape(math_ops.reduce_sum(grad, rx), sx)
gy = array_ops.reshape(
math_ops.reduce_sum(grad * math_ops.negative(floor_xy), ry), sy)
return gx, gy
def _SquaredDifferenceGrad(op, grad):
"""Returns the gradient for (x-y)^2."""
x = op.inputs[0]
y = op.inputs[1]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
# pylint: disable=protected-access
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
# pylint: enable=protected-access
with ops.control_dependencies([grad]):
# The parens ensure that if grad is IndexedSlices, it'll get multiplied by
# Tensor (not a number like 2.0) which causes it to convert to Tensor.
x_grad = math_ops.scalar_mul(2.0, grad) * (x - y)
return (array_ops.reshape(math_ops.reduce_sum(x_grad, rx), sx),
-array_ops.reshape(math_ops.reduce_sum(x_grad, ry), sy))
def _MaximumMinimumGrad(op, grad, selector_op): """Factor out the code for the gradient of Maximum or Minimum.""" x = op.inputs[0] y = op.inputs[1] gdtype = grad.dtype sx = array_ops.shape(x) sy = array_ops.shape(y) gradshape = array_ops.shape(grad) zeros = array_ops.zeros(gradshape, gdtype) xmask = selector_op(x, y) rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy) xgrad = array_ops.where(xmask, grad, zeros) ygrad = array_ops.where(xmask, zeros, grad) gx = array_ops.reshape(math_ops.reduce_sum(xgrad, rx), sx) gy = array_ops.reshape(math_ops.reduce_sum(ygrad, ry), sy) return (gx, gy)
def _IgammaGrad(op, grad):
"""Returns gradient of igamma(a, x) with respect to x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a
a = op.inputs[0]
x = op.inputs[1]
sa = array_ops.shape(a)
sx = array_ops.shape(x)
# pylint: disable=protected-access
unused_ra, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# pylint: enable=protected-access
# Perform operations in log space before summing, because Gamma(a)
# and Gamma'(a) can grow large.
partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x) - math_ops.lgamma(a))
# TODO(b/36815900): Mark None return values as NotImplemented
return (None, array_ops.reshape(
math_ops.reduce_sum(partial_x * grad, rx), sx))
def _PowGrad(op, grad):
"""Returns grad * (y*x^(y-1), z*log(x))."""
x = op.inputs[0]
y = op.inputs[1]
z = op.outputs[0]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
gx = array_ops.reshape(math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
# Avoid false singularity at x = 0
if x.dtype.is_complex:
# real(x) < 0 is fine for the complex case
log_x = math_ops.select(math_ops.not_equal(x, 0), math_ops.log(x), array_ops.zeros_like(x))
else:
# There's no sensible real value to return if x < 0, so return 0
log_x = math_ops.select(x > 0, math_ops.log(x), array_ops.zeros_like(x))
gy = array_ops.reshape(math_ops.reduce_sum(grad * z * log_x, ry), sy)
return gx, gy
def _MulGrad(op, grad):
"""The gradient of scalar multiplication."""
x = op.inputs[0]
y = op.inputs[1]
# pylint: disable=protected-access
if (isinstance(grad, ops.Tensor) and
_ShapesFullySpecifiedAndEqual(x, y, grad) and
grad.dtype in (dtypes.int32, dtypes.float32)):
return gen_math_ops._mul(grad, y), gen_math_ops._mul(grad, x)
assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
# pylint: enable=protected-access
x = math_ops.conj(x)
y = math_ops.conj(y)
return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))
def _ZetaGrad(op, grad):
"""Returns gradient of zeta(x, q) with respect to x and q."""
# TODO(tillahoffmann): Add derivative with respect to x
x = op.inputs[0]
q = op.inputs[1]
# Broadcast gradients
sx = array_ops.shape(x)
sq = array_ops.shape(q)
unused_rx, rq = gen_array_ops._broadcast_gradient_args(sx, sq)
# Evaluate gradient
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
q = math_ops.conj(q)
partial_q = -x * math_ops.zeta(x + 1, q)
# TODO(b/36815900): Mark None return values as NotImplemented
return (None,
array_ops.reshape(math_ops.reduce_sum(partial_q * grad, rq),
sq))
def _PolygammaGrad(op, grad):
"""Returns gradient of psi(n, x) with respect to n and x."""
# TODO(tillahoffmann): Add derivative with respect to n
n = op.inputs[0]
x = op.inputs[1]
# Broadcast gradients
sn = array_ops.shape(n)
sx = array_ops.shape(x)
unused_rn, rx = gen_array_ops._broadcast_gradient_args(sn, sx)
# Evaluate gradient
with ops.control_dependencies([grad]):
n = math_ops.conj(n)
x = math_ops.conj(x)
partial_x = math_ops.polygamma(n + 1, x)
# TODO(b/36815900): Mark None return values as NotImplemented
return (None,
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx),
sx))
def _IgammaGrad(op, grad):
"""Returns gradient of igamma(a, x) with respect to x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a
a = op.inputs[0]
x = op.inputs[1]
sa = array_ops.shape(a)
sx = array_ops.shape(x)
# pylint: disable=protected-access
unused_ra, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# pylint: enable=protected-access
# Perform operations in log space before summing, because Gamma(a)
# and Gamma'(a) can grow large.
partial_x = math_ops.exp(-x + (a - 1) * math_ops.log(x) -
math_ops.lgamma(a))
# TODO(b/36815900): Mark None return values as NotImplemented
return (None,
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _MulGrad(op, grad):
"""The gradient of scalar multiplication."""
x = op.inputs[0]
y = op.inputs[1]
# pylint: disable=protected-access
if (isinstance(grad, ops.Tensor) and
_ShapesFullySpecifiedAndEqual(x, y, grad) and
grad.dtype in (dtypes.int32, dtypes.float32)):
return gen_math_ops._mul(grad, y), gen_math_ops._mul(grad, x)
assert x.dtype.base_dtype == y.dtype.base_dtype, (x.dtype, " vs. ", y.dtype)
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
# pylint: enable=protected-access
x = math_ops.conj(x)
y = math_ops.conj(y)
return (array_ops.reshape(math_ops.reduce_sum(grad * y, rx), sx),
array_ops.reshape(math_ops.reduce_sum(x * grad, ry), sy))
def _PolygammaGrad(op, grad):
"""Returns gradient of psi(n, x) with respect to n and x."""
# TODO(tillahoffmann): Add derivative with respect to n
n = op.inputs[0]
x = op.inputs[1]
# Broadcast gradients
sn = array_ops.shape(n)
sx = array_ops.shape(x)
# pylint: disable=protected-access
unused_rn, rx = gen_array_ops._broadcast_gradient_args(sn, sx)
# pylint: enable=protected-access
# Evaluate gradient
with ops.control_dependencies([grad]):
n = math_ops.conj(n)
x = math_ops.conj(x)
partial_x = math_ops.polygamma(n + 1, x)
# TODO(b/36815900): Mark None return values as NotImplemented
return (None,
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _ZetaGrad(op, grad):
"""Returns gradient of zeta(x, q) with respect to x and q."""
# TODO(tillahoffmann): Add derivative with respect to x
x = op.inputs[0]
q = op.inputs[1]
# Broadcast gradients
sx = array_ops.shape(x)
sq = array_ops.shape(q)
# pylint: disable=protected-access
unused_rx, rq = gen_array_ops._broadcast_gradient_args(sx, sq)
# pylint: enable=protected-access
# Evaluate gradient
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
q = math_ops.conj(q)
partial_q = -x * math_ops.zeta(x + 1, q)
# TODO(b/36815900): Mark None return values as NotImplemented
return (None,
array_ops.reshape(math_ops.reduce_sum(partial_q * grad, rq), sq))
def _PowGrad(op, grad):
"""Returns grad * (y*x^(y-1), z*log(x))."""
x = op.inputs[0]
y = op.inputs[1]
z = op.outputs[0]
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops._broadcast_gradient_args(sx, sy)
gx = array_ops.reshape(
math_ops.reduce_sum(grad * y * math_ops.pow(x, y - 1), rx), sx)
# Avoid false singularity at x = 0
if x.dtype.is_complex:
# real(x) < 0 is fine for the complex case
log_x = math_ops.select(math_ops.not_equal(x, 0), math_ops.log(x),
array_ops.zeros_like(x))
else:
# There's no sensible real value to return if x < 0, so return 0
log_x = math_ops.select(x > 0, math_ops.log(x),
array_ops.zeros_like(x))
gy = array_ops.reshape(math_ops.reduce_sum(grad * z * log_x, ry), sy)
return gx, gy
def _BetaincGrad(op, grad):
"""Returns gradient of betainc(a, b, x) with respect to x."""
# TODO(ebrevdo): Perhaps add the derivative w.r.t. a, b
a, b, x = op.inputs
# two cases: x is a scalar and a/b are same-shaped tensors, or vice
# versa; so its sufficient to check against shape(a).
sa = array_ops.shape(a)
sx = array_ops.shape(x)
# pylint: disable=protected-access
_, rx = gen_array_ops._broadcast_gradient_args(sa, sx)
# pylint: enable=protected-access
# Perform operations in log space before summing, because terms
# can grow large.
log_beta = (gen_math_ops.lgamma(a) + gen_math_ops.lgamma(b)
- gen_math_ops.lgamma(a + b))
partial_x = math_ops.exp(
(b - 1) * math_ops.log(1 - x) + (a - 1) * math_ops.log(x) - log_beta)
# TODO(b/36815900): Mark None return values as NotImplemented
return (None, # da
None, # db
array_ops.reshape(math_ops.reduce_sum(partial_x * grad, rx), sx))
def _GetGradientArgs(self, xs, ys):
with self.test_session() as sess:
return sess.run(_broadcast_gradient_args(xs, ys))
def _GetGradientArgs(self, xs, ys):
with self.test_session() as sess:
return sess.run(_broadcast_gradient_args(xs, ys))
