def _get_bn_correction(conv_type, kernel, bias, mu_bt, var_bt, mu_mv, var_mv,
gamma, epsilon):
"""Get batchnorm correction params.
Before freeze:
corr_scale = sigma_bt / sigma_mv
corr_recip = 1 / corr_scale
corr_offset = 0
After freeze:
corr_scale = sigma_bt / sigma_mv
corr_recip = 1
corr_offset = gamma * ( (mu_bt - bias)/sigma_bt - (mu_mv - bias)/sigma_mv)
"""
sigma_bt = math_ops.rsqrt(var_bt + epsilon)
sigma_bt_recip = math_ops.reciprocal(sigma_bt)
sigma_mv = math_ops.rsqrt(var_mv + epsilon)
sigma_mv_recip = math_ops.reciprocal(sigma_mv)
corr_scale = math_ops.divide(sigma_bt, sigma_mv, name='corr_scale')
corr_recip = math_ops.reciprocal(corr_scale)
corr_offset = array_ops.zeros(mu_bt.shape)
if conv_type == 'DepthwiseConv2D':
new_shape = [kernel.shape[2], kernel.shape[3]]
corr_scale = array_ops.reshape(corr_scale, new_shape)
return corr_scale, corr_recip, corr_offset
def _grad_and_hess_for_logloss(logits, labels):
# TODO(youngheek): add weights handling.
predictions = math_ops.reciprocal(math_ops.exp(-logits) + 1.0)
normalizer = math_ops.reciprocal(
math_ops.cast(array_ops.size(predictions), dtypes.float32))
gradients = (predictions - labels) * normalizer
hessians = predictions * (1.0 - predictions) * normalizer
return gradients, hessians
def _grad_and_hess_for_logloss(logits, labels):
# TODO(youngheek): add weights handling.
predictions = math_ops.reciprocal(math_ops.exp(-logits) + 1.0)
normalizer = math_ops.reciprocal(
math_ops.cast(array_ops.size(predictions), dtypes.float32))
gradients = (predictions - labels) * normalizer
hessians = predictions * (1.0 - predictions) * normalizer
return gradients, hessians
def _grad_and_hess_for_logloss(logits, labels):
"""A closed form gradient and hessian for logistic loss."""
# TODO(youngheek): add weights handling.
predictions = math_ops.reciprocal(math_ops.exp(-logits) + 1.0)
normalizer = math_ops.reciprocal(
math_ops.cast(array_ops.size(predictions), dtypes.float32))
labels = math_ops.cast(labels, dtypes.float32)
labels = head_lib._check_dense_labels_match_logits_and_reshape( # pylint: disable=protected-access
labels, logits, head.logits_dimension)
gradients = (predictions - labels) * normalizer
hessians = predictions * (1.0 - predictions) * normalizer
return gradients, hessians
def _grad_and_hess_for_logloss(logits, labels):
"""A closed form gradient and hessian for logistic loss."""
# TODO(youngheek): add weights handling.
predictions = math_ops.reciprocal(math_ops.exp(-logits) + 1.0)
normalizer = math_ops.reciprocal(
math_ops.cast(array_ops.size(predictions), dtypes.float32))
labels = math_ops.cast(labels, dtypes.float32)
labels = head_lib._check_dense_labels_match_logits_and_reshape( # pylint: disable=protected-access
labels, logits, head.logits_dimension)
gradients = (predictions - labels) * normalizer
hessians = predictions * (1.0 - predictions) * normalizer
return gradients, hessians
def _grad(op, grad):
"""A gradient function for IRFFT with the provided `rank` and `rfft_fn`."""
# Generate a simple mask like [1.0, 2.0, ..., 2.0, 1.0] for even-length FFTs
# and [1.0, 2.0, ..., 2.0] for odd-length FFTs. To reduce extra ops in the
# graph we special-case the situation where the FFT length and last
# dimension of the input are known at graph construction time.
fft_length = op.inputs[1]
fft_length_static = _tensor_util.constant_value(fft_length)
if fft_length_static is not None:
fft_length = fft_length_static
real_dtype = grad.dtype
if real_dtype == _dtypes.float32:
complex_dtype = _dtypes.complex64
elif real_dtype == _dtypes.float64:
complex_dtype = _dtypes.complex128
is_odd = _math_ops.mod(fft_length[-1], 2)
input_last_dimension = _array_ops.shape(op.inputs[0])[-1]
mask = _array_ops.concat(
[[1.0], 2.0 *
_array_ops.ones([input_last_dimension - 2 + is_odd], real_dtype),
_array_ops.ones([1 - is_odd], real_dtype)], 0)
rsize = _math_ops.reciprocal(
_math_ops.cast(_fft_size_for_grad(grad, rank), real_dtype))
# The gradient of IRFFT is the RFFT of the incoming gradient times a scaling
# factor and a mask. The mask scales the gradient for the Hermitian
# symmetric components of the RFFT by a factor of two, since these
# components are de-duplicated in the RFFT.
the_rfft = rfft_fn(grad, fft_length)
return the_rfft * _math_ops.cast(rsize * mask, complex_dtype), None
def normalize_moments(counts, mean_ss, variance_ss, shift, name=None):
"""Calculate the mean and variance of based on the sufficient statistics.
Args:
counts: A `Tensor` containing a the total count of the data (one value).
mean_ss: A `Tensor` containing the mean sufficient statistics: the (possibly
shifted) sum of the elements to average over.
variance_ss: A `Tensor` containing the variance sufficient statistics: the
(possibly shifted) squared sum of the data to compute the variance over.
shift: A `Tensor` containing the value by which the data is shifted for
numerical stability, or `None` if no shift was performed.
name: Name used to scope the operations that compute the moments.
Returns:
Two `Tensor` objects: `mean` and `variance`.
"""
with ops.name_scope(name, "normalize", [counts, mean_ss, variance_ss, shift]):
divisor = math_ops.reciprocal(counts, name="divisor")
if shift is not None:
shifted_mean = math_ops.multiply(mean_ss, divisor, name="shifted_mean")
mean = math_ops.add(shifted_mean, shift, name="mean")
else: # no shift.
shifted_mean = math_ops.multiply(mean_ss, divisor, name="mean")
mean = shifted_mean
variance = math_ops.subtract(math_ops.multiply(variance_ss, divisor),
math_ops.square(shifted_mean),
name="variance")
return (mean, variance)
def normalize_moments(counts, mean_ss, variance_ss, shift, name=None):
"""Calculate the mean and variance of based on the sufficient statistics.
Args:
counts: A `Tensor` containing a the total count of the data (one value).
mean_ss: A `Tensor` containing the mean sufficient statistics: the (possibly
shifted) sum of the elements to average over.
variance_ss: A `Tensor` containing the variance sufficient statistics: the
(possibly shifted) squared sum of the data to compute the variance over.
shift: A `Tensor` containing the value by which the data is shifted for
numerical stability, or `None` if no shift was performed.
name: Name used to scope the operations that compute the moments.
Returns:
Two `Tensor` objects: `mean` and `variance`.
"""
with ops.name_scope(name, "normalize", [counts, mean_ss, variance_ss, shift]):
divisor = math_ops.reciprocal(counts, name="divisor")
if shift is not None:
shifted_mean = math_ops.mul(mean_ss, divisor, name="shifted_mean")
mean = math_ops.add(shifted_mean, shift, name="mean")
else: # no shift.
shifted_mean = math_ops.mul(mean_ss, divisor, name="mean")
mean = shifted_mean
variance = math_ops.sub(math_ops.mul(variance_ss, divisor),
math_ops.square(shifted_mean),
name="variance")
return (mean, variance)
def _TanGrad(op, grad):
"""Returns grad * 1/sec^2(x)."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
secx = math_ops.reciprocal(math_ops.cos(x))
secx2 = math_ops.square(secx)
return grad * secx2
def _TanGrad(op, grad):
"""Returns grad * 1/sec^2(x)."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
secx = math_ops.reciprocal(math_ops.cos(x))
secx2 = math_ops.square(secx)
return grad * secx2
def _AtanGrad(op, grad):
"""Returns grad * 1/ (1 + x^2)."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
x2 = math_ops.square(x)
one = constant_op.constant(1, dtype=grad.dtype)
inv = math_ops.reciprocal(math_ops.add(one, x2))
return grad * inv
def _AtanGrad(op, grad):
"""Returns grad * 1/ (1 + x^2)."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
x2 = math_ops.square(x)
one = constant_op.constant(1, dtype=grad.dtype)
inv = math_ops.reciprocal(math_ops.add(one, x2))
return grad * inv
def qbatch_normalization(x,
mean,
variance,
offset,
scale,
variance_epsilon,
quantizer,
name=None):
r"""Batch normalization.
As described in http://arxiv.org/abs/1502.03167.
Normalizes a tensor by `mean` and `variance`, and applies (optionally) a
`scale` \\(\gamma\\) to it, as well as an `offset` \\(\beta\\):
\\(\frac{\gamma(x-\mu)}{\sigma}+\beta\\)
`mean`, `variance`, `offset` and `scale` are all expected to be of one of two
shapes:
* In all generality, they can have the same number of dimensions as the
input `x`, with identical sizes as `x` for the dimensions that are not
normalized over (the 'depth' dimension(s)), and dimension 1 for the
others which are being normalized over.
`mean` and `variance` in this case would typically be the outputs of
`tf.nn.moments(..., keep_dims=True)` during training, or running averages
thereof during inference.
* In the common case where the 'depth' dimension is the last dimension in
the input tensor `x`, they may be one dimensional tensors of the same
size as the 'depth' dimension.
This is the case for example for the common `[batch, depth]` layout of
fully-connected layers, and `[batch, height, width, depth]` for
convolutions.
`mean` and `variance` in this case would typically be the outputs of
`tf.nn.moments(..., keep_dims=False)` during training, or running averages
thereof during inference.
Args:
x: Input `Tensor` of arbitrary dimensionality.
mean: A mean `Tensor`.
variance: A variance `Tensor`.
offset: An offset `Tensor`, often denoted \\(\beta\\) in equations, or
None. If present, will be added to the normalized tensor.
scale: A scale `Tensor`, often denoted \\(\gamma\\) in equations, or
`None`. If present, the scale is applied to the normalized tensor.
variance_epsilon: A small float number to avoid dividing by 0.
name: A name for this operation (optional).
Returns:
the normalized, scaled, offset tensor.
"""
with ops.name_scope(name, "batchnorm", [x, mean, variance, scale, offset]):
#internal calculation of sqrt is NOT quantized!
inv = quantizer.quantize(math_ops.sqrt(variance + variance_epsilon))
inv = quantizer.quantize(math_ops.reciprocal(inv))
if scale is not None:
inv = quantizer.quantize(inv * scale)
#return x * inv + (offset - mean * inv if offset is not None else -mean * inv)
if offset is not None:
rest = quantizer.quantize(offset - quantizer.quantize(mean * inv))
else:
rest = quantizer.quantize(-mean * inv)
result = quantizer.quantize(quantizer.quantize(x * inv) + rest)
return result
def _AcosGrad(op, grad):
"""Returns grad * -1/sqrt(1-x^2)."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
x2 = math_ops.square(x)
one = constant_op.constant(1, dtype=grad.dtype)
den = math_ops.sqrt(math_ops.subtract(one, x2))
inv = math_ops.reciprocal(den)
return -grad * inv
def _AcosGrad(op, grad):
"""Returns grad * -1/sqrt(1-x^2)."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
x2 = math_ops.square(x)
one = constant_op.constant(1, dtype=grad.dtype)
den = math_ops.sqrt(math_ops.subtract(one, x2))
inv = math_ops.reciprocal(den)
return -grad * inv
def _AngleGrad(op, grad):
"""Returns -grad / (Im(x) + iRe(x))"""
x = op.inputs[0]
with ops.control_dependencies([grad]):
re = math_ops.real(x)
im = math_ops.imag(x)
z = math_ops.reciprocal(math_ops.complex(im, re))
zero = constant_op.constant(0, dtype=grad.dtype)
complex_grad = math_ops.complex(grad, zero)
return -complex_grad * z
def _AngleGrad(op, grad):
"""Returns -grad / (Im(x) + iRe(x))"""
x = op.inputs[0]
with ops.control_dependencies([grad]):
re = math_ops.real(x)
im = math_ops.imag(x)
z = math_ops.reciprocal(math_ops.complex(im, re))
zero = constant_op.constant(0, dtype=grad.dtype)
complex_grad = math_ops.complex(grad, zero)
return -complex_grad * z
def _get_matches_hook(self, y_pred_click_ranks):
"""
Return reciprocal click ranks for MRR
Parameters
----------
y_pred_click_ranks: Tensor object
Tensor object containing the ranks of the clicked records for each query
Returns
-------
Tensor object
Reciprocal ranks tensor
"""
return math_ops.reciprocal(tf.cast(y_pred_click_ranks, tf.float32))
def _BesselI1eGrad(op, grad):
"""Compute gradient of bessel_i1e(x) with respect to its argument."""
x = op.inputs[0]
y = op.outputs[0]
with ops.control_dependencies([grad]):
# For x = 0, the correct gradient is 0.5.
# However, the main branch gives NaN because of the division by x, so
# we impute the gradient manually.
# An alternative solution is to express the gradient via bessel_i0e and
# bessel_i2e, but the latter is not yet implemented in Eigen.
eps = np.finfo(x.dtype.as_numpy_dtype).eps
zeros = array_ops.zeros_like(x)
x_is_not_tiny = math_ops.abs(x) > eps
safe_x = array_ops.where(x_is_not_tiny, x, eps + zeros)
dy_dx = math_ops.bessel_i0e(safe_x) - y * (
math_ops.sign(safe_x) + math_ops.reciprocal(safe_x))
return grad * array_ops.where(x_is_not_tiny, dy_dx, 0.5 + zeros)
def _BesselI1eGrad(op, grad):
"""Compute gradient of bessel_i1e(x) with respect to its argument."""
x = op.inputs[0]
y = op.outputs[0]
with ops.control_dependencies([grad]):
# For x = 0, the correct gradient is 0.5.
# However, the main branch gives NaN because of the division by x, so
# we impute the gradient manually.
# An alternative solution is to express the gradient via bessel_i0e and
# bessel_i2e, but the latter is not yet implemented in Eigen.
eps = np.finfo(x.dtype.as_numpy_dtype).eps
zeros = array_ops.zeros_like(x)
x_is_not_tiny = math_ops.abs(x) > eps
safe_x = array_ops.where(x_is_not_tiny, x, eps + zeros)
dy_dx = math_ops.bessel_i0e(safe_x) - y * (
math_ops.sign(safe_x) + math_ops.reciprocal(safe_x))
return grad * array_ops.where(x_is_not_tiny, dy_dx, 0.5 + zeros)
def _BatchNormGrad(grad_y, x, scale, epsilon, data_format):
"""Returns the gradients for the 3 inputs of BatchNorm.
Args:
grad_y: A `Tensor` of 4 dimensions for gradient for y.
x: A `Tensor` of 4 dimensions for x.
scale: A `Tensor` of 1 dimension for scaling.
epsilon: A small float number added to the variance of x.
data_format: The data format for input. Either b"NHWC" or b"NCHW".
Returns:
A tuple (grad_x, grad_scale, grad_offset), where grad_x is the gradient
for x, grad_scale the gradient for scale, and grad_offset the gradient
for offset.
"""
if data_format == b"NHWC":
keep_dims = False
reduce_axis = [0, 1, 2]
else:
keep_dims = True
reduce_axis = [0, 2, 3]
shape = [1, array_ops.size(scale), 1, 1]
scale = array_ops.reshape(scale, shape)
mean_grad_y = math_ops.reduce_mean(grad_y,
reduce_axis,
keep_dims=keep_dims)
mean_x = math_ops.reduce_mean(x, reduce_axis, keep_dims=keep_dims)
var_x = math_ops.reduce_mean(math_ops.squared_difference(
x, array_ops.stop_gradient(mean_x)),
reduce_axis,
keep_dims=keep_dims)
grad_y_offset = grad_y - mean_grad_y
x_offset = x - mean_x
mean = math_ops.reduce_mean(grad_y * x_offset,
axis=reduce_axis,
keep_dims=keep_dims)
grad_x = scale * math_ops.rsqrt(var_x + epsilon) * (
grad_y_offset - math_ops.reciprocal(var_x + epsilon) * mean * x_offset)
grad_scale = math_ops.rsqrt(var_x + epsilon) * math_ops.reduce_sum(
grad_y * x_offset, axis=reduce_axis, keep_dims=keep_dims)
if data_format == b"NCHW":
grad_scale = array_ops.squeeze(grad_scale)
grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
return grad_x, grad_scale, grad_offset
def _BatchNormGrad(grad_y, x, scale, epsilon, data_format):
"""Returns the gradients for the 3 inputs of BatchNorm.
Args:
grad_y: A `Tensor` of 4 dimensions for gradient for y.
x: A `Tensor` of 4 dimensions for x.
scale: A `Tensor` of 1 dimension for scaling.
epsilon: A small float number added to the variance of x.
data_format: The data format for input. Either b"NHWC" or b"NCHW".
Returns:
A tuple (grad_x, grad_scale, grad_offset), where grad_x is the gradient
for x, grad_scale the gradient for scale, and grad_offset the gradient
for offset.
"""
if data_format == b"NHWC":
keep_dims = False
reduce_axis = [0, 1, 2]
else:
keep_dims = True
reduce_axis = [0, 2, 3]
shape = [1, array_ops.size(scale), 1, 1]
scale = array_ops.reshape(scale, shape)
mean_grad_y = math_ops.reduce_mean(grad_y, reduce_axis, keep_dims=keep_dims)
mean_x = math_ops.reduce_mean(x, reduce_axis, keep_dims=keep_dims)
var_x = math_ops.reduce_mean(
math_ops.squared_difference(x, array_ops.stop_gradient(mean_x)),
reduce_axis,
keep_dims=keep_dims)
grad_y_offset = grad_y - mean_grad_y
x_offset = x - mean_x
mean = math_ops.reduce_mean(
grad_y * x_offset, axis=reduce_axis, keep_dims=keep_dims)
grad_x = scale * math_ops.rsqrt(var_x + epsilon) * (
grad_y_offset - math_ops.reciprocal(var_x + epsilon) * mean * x_offset)
grad_scale = math_ops.rsqrt(var_x + epsilon) * math_ops.reduce_sum(
grad_y * x_offset, axis=reduce_axis, keep_dims=keep_dims)
if data_format == b"NCHW":
grad_scale = array_ops.squeeze(grad_scale)
grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
return grad_x, grad_scale, grad_offset
def _Grad(op, grad):
"""A gradient function for IRFFT with the provided `rank` and `rfft_fn`."""
# Generate a simple mask like [1.0, 2.0, ..., 2.0, 1.0] for even-length FFTs
# and [1.0, 2.0, ..., 2.0] for odd-length FFTs. To reduce extra ops in the
# graph we special-case the situation where the FFT length and last
# dimension of the input are known at graph construction time.
fft_length = op.inputs[1]
is_odd = math_ops.mod(fft_length[-1], 2)
input_last_dimension = array_ops.shape(op.inputs[0])[-1]
mask = array_ops.concat(
[[1.0], 2.0 * array_ops.ones([input_last_dimension - 2 + is_odd]),
array_ops.ones([1 - is_odd])], 0)
rsize = math_ops.reciprocal(math_ops.to_float(_FFTSizeForGrad(grad, rank)))
# The gradient of IRFFT is the RFFT of the incoming gradient times a scaling
# factor and a mask. The mask scales the gradient for the Hermitian
# symmetric components of the RFFT by a factor of two, since these
# components are de-duplicated in the RFFT.
rfft = rfft_fn(grad, fft_length)
return rfft * math_ops.cast(rsize * mask, dtypes.complex64), None
def _SelfAdjointEigV2Grad(op, grad_e, grad_v):
"""Gradient for SelfAdjointEigV2."""
e = op.outputs[0]
compute_v = op.get_attr("compute_v")
# a = op.inputs[0], which satisfies
# a[...,:,:] * v[...,:,i] = e[...,i] * v[...,i]
with ops.control_dependencies([grad_e, grad_v]):
if compute_v:
v = op.outputs[1]
# Construct the matrix f(i,j) = (i != j ? 1 / (e_i - e_j) : 0).
# Notice that because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when eigenvalues are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate eigenvalues, the corresponding eigenvectors are only defined
# up to arbitrary rotation in a (k-dimensional) subspace.
f = array_ops.matrix_set_diag(
math_ops.reciprocal(
array_ops.expand_dims(e, -2) - array_ops.expand_dims(e, -1)),
array_ops.zeros_like(e))
grad_a = math_ops.matmul(
v,
math_ops.matmul(
array_ops.matrix_diag(grad_e) +
f * math_ops.matmul(v, grad_v, adjoint_a=True),
v,
adjoint_b=True))
else:
_, v = linalg_ops.self_adjoint_eig(op.inputs[0])
grad_a = math_ops.matmul(v,
math_ops.matmul(
array_ops.matrix_diag(grad_e),
v,
adjoint_b=True))
# The forward op only depends on the lower triangular part of a, so here we
# symmetrize and take the lower triangle
grad_a = array_ops.matrix_band_part(
grad_a + math_ops.conj(array_ops.matrix_transpose(grad_a)), -1, 0)
grad_a = array_ops.matrix_set_diag(grad_a,
0.5 * array_ops.matrix_diag_part(grad_a))
return grad_a
def _SelfAdjointEigV2Grad(op, grad_e, grad_v):
"""Gradient for SelfAdjointEigV2."""
e = op.outputs[0]
compute_v = op.get_attr("compute_v")
# a = op.inputs[0], which satisfies
# a[...,:,:] * v[...,:,i] = e[...,i] * v[...,i]
with ops.control_dependencies([grad_e, grad_v]):
if compute_v:
v = op.outputs[1]
# Construct the matrix f(i,j) = (i != j ? 1 / (e_i - e_j) : 0).
# Notice that because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when eigenvalues are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate eigenvalues, the corresponding eigenvectors are only defined
# up to arbitrary rotation in a (k-dimensional) subspace.
f = array_ops.matrix_set_diag(
math_ops.reciprocal(
array_ops.expand_dims(e, -2) -
array_ops.expand_dims(e, -1)), array_ops.zeros_like(e))
grad_a = math_ops.matmul(
v,
math_ops.matmul(array_ops.matrix_diag(grad_e) +
f * math_ops.matmul(v, grad_v, adjoint_a=True),
v,
adjoint_b=True))
else:
_, v = linalg_ops.self_adjoint_eig(op.inputs[0])
grad_a = math_ops.matmul(
v,
math_ops.matmul(array_ops.matrix_diag(grad_e),
v,
adjoint_b=True))
# The forward op only depends on the lower triangular part of a, so here we
# symmetrize and take the lower triangle
grad_a = array_ops.matrix_band_part(grad_a + _linalg.adjoint(grad_a),
-1, 0)
grad_a = array_ops.matrix_set_diag(
grad_a, 0.5 * array_ops.matrix_diag_part(grad_a))
return grad_a
def _Grad(op, grad):
"""A gradient function for IRFFT with the provided `rank` and `rfft_fn`."""
# Generate a simple mask like [1.0, 2.0, ..., 2.0, 1.0] for even-length FFTs
# and [1.0, 2.0, ..., 2.0] for odd-length FFTs. To reduce extra ops in the
# graph we special-case the situation where the FFT length and last
# dimension of the input are known at graph construction time.
fft_length = op.inputs[1]
is_odd = math_ops.mod(fft_length[-1], 2)
input_last_dimension = array_ops.shape(op.inputs[0])[-1]
mask = array_ops.concat(
[[1.0], 2.0 * array_ops.ones([input_last_dimension - 2 + is_odd]),
array_ops.ones([1 - is_odd])], 0)
rsize = math_ops.reciprocal(
math_ops.to_float(_FFTSizeForGrad(grad, rank)))
# The gradient of IRFFT is the RFFT of the incoming gradient times a scaling
# factor and a mask. The mask scales the gradient for the Hermitian
# symmetric components of the RFFT by a factor of two, since these
# components are de-duplicated in the RFFT.
rfft = rfft_fn(grad, fft_length)
return rfft * math_ops.cast(rsize * mask, dtypes.complex64), None
def QuantizedBatchNormalizationCore(inputs,
mean,
variance,
beta,
gamma,
variance_epsilon,
Q_info,
name=None):
""" Intrinsic quantization of BatchNormalization layer.
Parameters
----------
| inputs : Tensor.
| mean : tf.Variable
| variance : tf.Variable
| beta : tf.Variable
| gamma : tf.Variable
| variance_epsilon : Float
Returns
-------
output : Tensor
"""
with ops.name_scope(name, "batchnorm", [inputs, mean, variance, gamma, beta]):
coef = Q_info.quantize( math_ops.sqrt(variance + variance_epsilon))
coef = Q_info.quantize( math_ops.reciprocal(coef))
if gamma is not None:
coef = Q_info.quantize(coef*gamma)
if beta is not None:
const = Q_info.quantize( beta - Q_info.quantize(mean * coef))
else:
const = Q_info.quantize(-mean * coef)
output = Q_info.quantize( Q_info.quantize(inputs * coef) + const)
return output
def _SvdGrad(op, grad_s, grad_u, grad_v):
"""Gradient for the singular value decomposition."""
# The derivation for the compute_uv=False case, and most of
# the derivation for the full_matrices=True case, are in
# Giles' paper (see reference at top of file). A derivation for
# the full_matrices=False case is available at
# https://j-towns.github.io/papers/svd-derivative.pdf
a = op.inputs[0]
a_shape = a.get_shape().with_rank_at_least(2)
grad_s_mat = array_ops.matrix_diag(grad_s)
if not op.get_attr("compute_uv"):
s, u, v = linalg_ops.svd(a, compute_uv=True)
grad_a = math_ops.matmul(
u, math_ops.matmul(grad_s_mat, v, adjoint_b=True))
grad_a.set_shape(a_shape)
return grad_a
full_matrices = op.get_attr("full_matrices")
# TODO(rmlarsen): Make this work with complex types.
if a.dtype.is_complex:
raise NotImplementedError(
"SVD gradient is not implemented for complex types and "
"compute_uv=True.")
grad_u_shape = grad_u.get_shape().with_rank_at_least(2)
grad_v_shape = grad_v.get_shape().with_rank_at_least(2)
m = a_shape[-2].merge_with(grad_u_shape[-2])
n = a_shape[-1].merge_with(grad_v_shape[-2])
batch_shape = a_shape[:-2].merge_with(grad_u_shape[:-2]).merge_with(
grad_v_shape[:-2])
a_shape = batch_shape.concatenate([m, n])
m = a_shape[-2].value
n = a_shape[-1].value
# TODO(rmlarsen): Make this work with placeholders.
if m is None or n is None:
raise NotImplementedError(
"SVD gradient has not been implemented for input with unknown "
"inner matrix shape.")
s = op.outputs[0]
u = op.outputs[1]
v = op.outputs[2]
use_adjoint = False
if m > n:
# Compute the gradient for A^H = V * S^T * U^H, and (implicitly) take the
# Hermitian transpose of the gradient at the end.
use_adjoint = True
m, n = n, m
u, v = v, u
grad_u, grad_v = grad_v, grad_u
with ops.control_dependencies([grad_s, grad_u, grad_v]):
if full_matrices and abs(m - n) > 1:
raise NotImplementedError(
"svd gradient is not implemented for abs(m - n) > 1 "
"when full_matrices is True")
s_mat = array_ops.matrix_diag(s)
s2 = math_ops.square(s)
# NOTICE: Because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when singular values are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate singular values, the corresponding singular vectors are
# only defined up a (k-dimensional) subspace. In practice, this can
# lead to numerical instability when singular values are close but not
# exactly equal.
f = array_ops.matrix_set_diag(
math_ops.reciprocal(
array_ops.expand_dims(s2, -2) - array_ops.expand_dims(s2, -1)),
array_ops.zeros_like(s))
s_inv_mat = array_ops.matrix_diag(math_ops.reciprocal(s))
v1 = v[..., :, :m]
grad_v1 = grad_v[..., :, :m]
u_gu = math_ops.matmul(u, grad_u, adjoint_a=True)
v_gv = math_ops.matmul(v1, grad_v1, adjoint_a=True)
f_u = f * u_gu
f_v = f * v_gv
term1_nouv = (grad_s_mat +
math_ops.matmul(f_u + _linalg.adjoint(f_u), s_mat) +
math_ops.matmul(s_mat, f_v + _linalg.adjoint(f_v)))
term1 = math_ops.matmul(
u, math_ops.matmul(term1_nouv, v1, adjoint_b=True))
if m == n:
grad_a_before_transpose = term1
else:
gv1t = array_ops.matrix_transpose(grad_v1)
gv1t_v1 = math_ops.matmul(gv1t, v1)
term2_nous = gv1t - math_ops.matmul(gv1t_v1, v1, adjoint_b=True)
if full_matrices:
v2 = v[..., :, m:n]
grad_v2 = grad_v[..., :, m:n]
v1t_gv2 = math_ops.matmul(v1, grad_v2, adjoint_a=True)
term2_nous -= math_ops.matmul(v1t_gv2, v2, adjoint_b=True)
u_s_inv = math_ops.matmul(u, s_inv_mat)
term2 = math_ops.matmul(u_s_inv, term2_nous)
grad_a_before_transpose = term1 + term2
if use_adjoint:
grad_a = array_ops.matrix_transpose(grad_a_before_transpose)
else:
grad_a = grad_a_before_transpose
grad_a.set_shape(a_shape)
return grad_a
def _BatchNormGrad(grad_y,
x,
scale,
pop_mean,
pop_var,
epsilon,
data_format,
is_training=True):
"""Returns the gradients for the 3 inputs of BatchNorm.
Args:
grad_y: A `Tensor` of 4 dimensions for gradient for y.
x: A `Tensor` of 4 dimensions for x.
scale: A `Tensor` of 1 dimension for scaling.
pop_mean: A `Tensor` of 1 dimension for the population mean. Only used when
is_training=False.
pop_var: A `Tensor` of 1 dimension for the population variance. Only used
when is_training=False.
epsilon: A small float number added to the variance of x.
data_format: The data format for input. Either b"NHWC" or b"NCHW".
is_training: A bool value to indicate the operation is for training
(default) or inference.
Returns:
A tuple (grad_x, grad_scale, grad_offset), where grad_x is the gradient
for x, grad_scale the gradient for scale, and grad_offset the gradient
for offset.
"""
x_dtype = x.dtype.base_dtype
if x_dtype == dtypes.float16:
# float16 math is too imprecise, so we do the batch norm gradient
# computations in float32.
x = math_ops.cast(x, dtypes.float32)
grad_y = math_ops.cast(grad_y, dtypes.float32)
if is_training:
if data_format == b"NHWC":
keepdims = False
reduce_axis = [0, 1, 2]
else:
keepdims = True
reduce_axis = [0, 2, 3]
shape = [1, array_ops.size(scale), 1, 1]
scale = array_ops.reshape(scale, shape)
mean_grad_y = math_ops.reduce_mean(grad_y,
reduce_axis,
keepdims=keepdims)
mean_x = math_ops.reduce_mean(x, reduce_axis, keepdims=keepdims)
var_x = math_ops.reduce_mean(math_ops.squared_difference(
x, array_ops.stop_gradient(mean_x)),
reduce_axis,
keepdims=keepdims)
grad_y_offset = grad_y - mean_grad_y
x_offset = x - mean_x
mean = math_ops.reduce_mean(grad_y * x_offset,
axis=reduce_axis,
keepdims=keepdims)
grad_x = scale * math_ops.rsqrt(var_x + epsilon) * (
grad_y_offset -
math_ops.reciprocal(var_x + epsilon) * mean * x_offset)
grad_scale = math_ops.rsqrt(var_x + epsilon) * math_ops.reduce_sum(
grad_y * x_offset, axis=reduce_axis, keepdims=keepdims)
if data_format == b"NCHW":
grad_scale = array_ops.squeeze(grad_scale)
grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
return math_ops.cast(grad_x, x_dtype), grad_scale, grad_offset
else:
if data_format == b"NHWC":
reduce_axis = [0, 1, 2]
else:
reduce_axis = [0, 2, 3]
shape = [1, array_ops.size(pop_mean), 1, 1]
pop_mean = array_ops.reshape(pop_mean, shape)
pop_var = array_ops.reshape(pop_var, shape)
scale = array_ops.reshape(scale, shape)
grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
var_rsqrt = math_ops.rsqrt(pop_var + epsilon)
grad_scale = math_ops.reduce_sum(grad_y * (x - pop_mean) * var_rsqrt,
axis=reduce_axis)
grad_x = grad_y * scale * var_rsqrt
return math_ops.cast(grad_x, x_dtype), grad_scale, grad_offset
def _ComputeBatchNormCorrections(context, match, freeze_batch_norm_delay,
fused_batch_norm):
"""Computes batch norm correction params.
Before batch normalization is frozen:
We use batch statistics for batch norm.
correction_scale = sigma_b/sigma_mv
correction_recip = 1/correction_scale
correction_offset = 0
After batch normalization is frozen:
correction_scale = sigma_b/sigma_mv
correction_recip = 1
correction_offset = gamma*(mu_b/sigma_b-mu_mv/sigma_mv).
Batch norm is frozen if global_step > bn_freeze_delay.
The corrections ensure that:
a) The weights are quantized after scaling by gamma/sigma_mv. This enables
smoother training as the scaling on the weights changes slowly, rather than
jump across mini-batches
b) Changing the values of the corrections allows for one to switch between
using batch statistics to using moving mean and average, without requiring
changes to batch_norm
Args:
context: The scope under which we look for batch norm params
match: Object containing required batch norm tensors for correction
computation.
freeze_batch_norm_delay: Delay in steps at which computation switches
from regular batch norm to frozen mean and variance.
fused_batch_norm: Bool, true if fused batch norm is used.
Returns:
A tuple of correction_scale, correction_recip, correction_offset
"""
g = ops.get_default_graph()
prefix = '' if not context else context + '/'
with g.name_scope(prefix + 'batch_norm_correction'):
recip_sigma_mv = math_ops.rsqrt(
match.moving_variance_tensor + match.batch_epsilon)
recip_sigma = math_ops.rsqrt(match.variance_tensor + match.batch_epsilon)
correction_scale = math_ops.divide(
recip_sigma_mv, recip_sigma, name='scale_compute')
correction_scale = array_ops.identity(
correction_scale, name='correction_scale')
correction_recip = math_ops.reciprocal(
correction_scale, name='reciprocal_compute')
correction_offset = math_ops.multiply(
match.gamma_tensor,
match.mean_tensor * recip_sigma -
match.moving_mean_tensor * recip_sigma_mv,
name='offset_compute')
if freeze_batch_norm_delay is not None:
use_mv_avg = math_ops.greater_equal(
common.CreateOrGetQuantizationStep(),
freeze_batch_norm_delay,
name='use_moving_average')
else:
use_mv_avg = False
bn_decay_zero = 0.0
bn_decay_mean_consumers = list(match.bn_decay_mean_tensor.consumers())
bn_decay_var_consumers = list(match.bn_decay_mean_tensor.consumers())
bn_decay_mean_out = utils.smart_cond(
use_mv_avg,
lambda: bn_decay_zero,
lambda: match.bn_decay_mean_tensor,
name='freeze_moving_mean')
graph_editor.reroute_ts(
[bn_decay_mean_out], [match.bn_decay_mean_tensor],
can_modify=bn_decay_mean_consumers)
if fused_batch_norm is False:
bn_decay_var_consumers = list(match.bn_decay_var_tensor.consumers())
bn_decay_var_out = utils.smart_cond(
use_mv_avg,
lambda: bn_decay_zero,
lambda: match.bn_decay_var_tensor,
name='freeze_moving_var')
graph_editor.reroute_ts(
[bn_decay_var_out], [match.bn_decay_var_tensor],
can_modify=bn_decay_var_consumers)
correction_recip = utils.smart_cond(
use_mv_avg,
lambda: array_ops.ones(correction_scale.shape),
lambda: correction_recip,
name='correction_recip')
correction_offset = utils.smart_cond(
use_mv_avg,
lambda: correction_offset,
lambda: array_ops.zeros(correction_offset.shape),
name='correction_offset')
return correction_scale, correction_recip, correction_offset
def _BatchNormGrad(grad_y,
x,
scale,
pop_mean,
pop_var,
epsilon,
data_format,
is_training=True):
"""Returns the gradients for the 3 inputs of BatchNorm.
Args:
grad_y: A `Tensor` of 4 dimensions for gradient for y.
x: A `Tensor` of 4 dimensions for x.
scale: A `Tensor` of 1 dimension for scaling.
pop_mean: A `Tensor` of 1 dimension for the population mean. Only used when
is_training=False.
pop_var: A `Tensor` of 1 dimension for the population variance. Only used
when is_training=False.
epsilon: A small float number added to the variance of x.
data_format: The data format for input. Either b"NHWC" or b"NCHW".
is_training: A bool value to indicate the operation is for training
(default) or inference.
Returns:
A tuple (grad_x, grad_scale, grad_offset), where grad_x is the gradient
for x, grad_scale the gradient for scale, and grad_offset the gradient
for offset.
"""
x_dtype = x.dtype.base_dtype
if x_dtype == dtypes.float16:
# float16 math is too imprecise, so we do the batch norm gradient
# computations in float32.
x = math_ops.cast(x, dtypes.float32)
grad_y = math_ops.cast(grad_y, dtypes.float32)
if is_training:
if data_format == b"NHWC":
keepdims = False
reduce_axis = [0, 1, 2]
else:
keepdims = True
reduce_axis = [0, 2, 3]
shape = [1, array_ops.size(scale), 1, 1]
scale = array_ops.reshape(scale, shape)
mean_grad_y = math_ops.reduce_mean(grad_y, reduce_axis, keepdims=keepdims)
mean_x = math_ops.reduce_mean(x, reduce_axis, keepdims=keepdims)
var_x = math_ops.reduce_mean(
math_ops.squared_difference(x, array_ops.stop_gradient(mean_x)),
reduce_axis,
keepdims=keepdims)
grad_y_offset = grad_y - mean_grad_y
x_offset = x - mean_x
mean = math_ops.reduce_mean(
grad_y * x_offset, axis=reduce_axis, keepdims=keepdims)
grad_x = scale * math_ops.rsqrt(var_x + epsilon) * (
grad_y_offset - math_ops.reciprocal(var_x + epsilon) * mean * x_offset)
grad_scale = math_ops.rsqrt(var_x + epsilon) * math_ops.reduce_sum(
grad_y * x_offset, axis=reduce_axis, keepdims=keepdims)
if data_format == b"NCHW":
grad_scale = array_ops.squeeze(grad_scale)
grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
return math_ops.cast(grad_x, x_dtype), grad_scale, grad_offset
else:
if data_format == b"NHWC":
reduce_axis = [0, 1, 2]
else:
reduce_axis = [0, 2, 3]
shape = [1, array_ops.size(pop_mean), 1, 1]
pop_mean = array_ops.reshape(pop_mean, shape)
pop_var = array_ops.reshape(pop_var, shape)
scale = array_ops.reshape(scale, shape)
grad_offset = math_ops.reduce_sum(grad_y, axis=reduce_axis)
var_rsqrt = math_ops.rsqrt(pop_var + epsilon)
grad_scale = math_ops.reduce_sum(
grad_y * (x - pop_mean) * var_rsqrt, axis=reduce_axis)
grad_x = grad_y * scale * var_rsqrt
return math_ops.cast(grad_x, x_dtype), grad_scale, grad_offset
def _SvdGrad(op, grad_s, grad_u, grad_v):
"""Gradient for the singular value decomposition."""
# The derivation for the compute_uv=False case, and most of
# the derivation for the full_matrices=True case, are in
# Giles' paper (see reference at top of file). A derivation for
# the full_matrices=False case is available at
# https://j-towns.github.io/papers/svd-derivative.pdf
a = op.inputs[0]
a_shape = a.get_shape().with_rank_at_least(2)
grad_s_mat = array_ops.matrix_diag(grad_s)
if not op.get_attr("compute_uv"):
s, u, v = linalg_ops.svd(a, compute_uv=True)
grad_a = math_ops.matmul(u, math_ops.matmul(grad_s_mat, v, adjoint_b=True))
grad_a.set_shape(a_shape)
return grad_a
full_matrices = op.get_attr("full_matrices")
# TODO(rmlarsen): Make this work with complex types.
if a.dtype.is_complex:
raise NotImplementedError(
"SVD gradient is not implemented for complex types and "
"compute_uv=True.")
grad_u_shape = grad_u.get_shape().with_rank_at_least(2)
grad_v_shape = grad_v.get_shape().with_rank_at_least(2)
m = a_shape.dims[-2].merge_with(grad_u_shape[-2])
n = a_shape.dims[-1].merge_with(grad_v_shape[-2])
batch_shape = a_shape[:-2].merge_with(grad_u_shape[:-2]).merge_with(
grad_v_shape[:-2])
a_shape = batch_shape.concatenate([m, n])
m = a_shape.dims[-2].value
n = a_shape.dims[-1].value
# TODO(rmlarsen): Make this work with placeholders.
if m is None or n is None:
raise NotImplementedError(
"SVD gradient has not been implemented for input with unknown "
"inner matrix shape.")
s = op.outputs[0]
u = op.outputs[1]
v = op.outputs[2]
use_adjoint = False
if m > n:
# Compute the gradient for A^H = V * S^T * U^H, and (implicitly) take the
# Hermitian transpose of the gradient at the end.
use_adjoint = True
m, n = n, m
u, v = v, u
grad_u, grad_v = grad_v, grad_u
with ops.control_dependencies([grad_s, grad_u, grad_v]):
if full_matrices and abs(m - n) > 1:
raise NotImplementedError(
"svd gradient is not implemented for abs(m - n) > 1 "
"when full_matrices is True")
s_mat = array_ops.matrix_diag(s)
s2 = math_ops.square(s)
# NOTICE: Because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when singular values are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate singular values, the corresponding singular vectors are
# only defined up a (k-dimensional) subspace. In practice, this can
# lead to numerical instability when singular values are close but not
# exactly equal.
f = array_ops.matrix_set_diag(
math_ops.reciprocal(
array_ops.expand_dims(s2, -2) - array_ops.expand_dims(s2, -1)),
array_ops.zeros_like(s))
s_inv_mat = array_ops.matrix_diag(math_ops.reciprocal(s))
v1 = v[..., :, :m]
grad_v1 = grad_v[..., :, :m]
u_gu = math_ops.matmul(u, grad_u, adjoint_a=True)
v_gv = math_ops.matmul(v1, grad_v1, adjoint_a=True)
f_u = f * u_gu
f_v = f * v_gv
term1_nouv = (
grad_s_mat + math_ops.matmul(f_u + _linalg.adjoint(f_u), s_mat) +
math_ops.matmul(s_mat, f_v + _linalg.adjoint(f_v)))
term1 = math_ops.matmul(u, math_ops.matmul(term1_nouv, v1, adjoint_b=True))
if m == n:
grad_a_before_transpose = term1
else:
gv1t = array_ops.matrix_transpose(grad_v1)
gv1t_v1 = math_ops.matmul(gv1t, v1)
term2_nous = gv1t - math_ops.matmul(gv1t_v1, v1, adjoint_b=True)
if full_matrices:
v2 = v[..., :, m:n]
grad_v2 = grad_v[..., :, m:n]
v1t_gv2 = math_ops.matmul(v1, grad_v2, adjoint_a=True)
term2_nous -= math_ops.matmul(v1t_gv2, v2, adjoint_b=True)
u_s_inv = math_ops.matmul(u, s_inv_mat)
term2 = math_ops.matmul(u_s_inv, term2_nous)
grad_a_before_transpose = term1 + term2
if use_adjoint:
grad_a = array_ops.matrix_transpose(grad_a_before_transpose)
else:
grad_a = grad_a_before_transpose
grad_a.set_shape(a_shape)
return grad_a
def _get_matches_hook(self, y_pred_click_ranks):
"""Return reciprocal click ranks for MRR"""
return math_ops.reciprocal(tf.cast(y_pred_click_ranks, tf.float32))
def _ComputeBatchNormCorrections(context, match, freeze_batch_norm_delay):
"""Computes batch norm correction params.
Before batch normalization is frozen:
We use batch statistics for batch norm.
correction_scale = sigma_b/sigma_mv
correction_recip = 1/correction_scale
correction_offset = 0
After batch normalization is frozen:
correction_scale = sigma_b/sigma_mv
correction_recip = 1
correction_offset = gamma*(mu_b/sigma_b-mu_mv/sigma_mv).
Batch norm is frozen if global_step > bn_freeze_delay.
The corrections ensure that:
a) The weights are quantized after scaling by gamma/sigma_mv. This enables
smoother training as the scaling on the weights changes slowly, rather than
jump across mini-batches
b) Changing the values of the corrections allows for one to switch between
using batch statistics to using moving mean and average, without requiring
changes to batch_norm
Args:
context: The scope under which we look for batch norm params
match: Object containing required batch norm tensors for correction
computation.
freeze_batch_norm_delay: Delay in steps at which computation switches
from regular batch norm to frozen mean and variance.
Returns:
A tuple of correction_scale, correction_recip, correction_offset
"""
g = ops.get_default_graph()
prefix = '' if not context else context
with g.name_scope(prefix + 'batch_norm_correction'):
recip_sigma_mv = math_ops.rsqrt(match.moving_variance_tensor +
match.batch_epsilon)
recip_sigma = math_ops.rsqrt(match.variance_tensor +
match.batch_epsilon)
correction_scale = math_ops.divide(recip_sigma_mv,
recip_sigma,
name='scale_compute')
correction_scale = array_ops.identity(correction_scale,
name='correction_scale')
correction_recip = math_ops.reciprocal(correction_scale,
name='reciprocal_compute')
mv = match.moving_mean_tensor #if match.moving_mean_tensor is not None else 0
correction_offset = math_ops.multiply(match.gamma_tensor,
match.mean_tensor * recip_sigma -
mv,
name='offset_compute')
if freeze_batch_norm_delay is not None:
use_mv_avg = math_ops.greater_equal(
common.CreateOrGetQuantizationStep(),
freeze_batch_norm_delay,
name='use_moving_average')
else:
use_mv_avg = False
bn_decay_zero = 0.0
bn_decay_mean_consumers = list(match.bn_decay_mean_tensor.consumers())
bn_decay_var_consumers = list(match.bn_decay_mean_tensor.consumers())
bn_decay_mean_out = utils.smart_cond(
use_mv_avg,
lambda: bn_decay_zero,
lambda: match.bn_decay_mean_tensor,
name='freeze_moving_mean')
common.RerouteTensor(bn_decay_mean_out,
match.bn_decay_mean_tensor,
can_modify=bn_decay_mean_consumers)
bn_decay_var_consumers = list(match.bn_decay_var_tensor.consumers())
bn_decay_var_out = utils.smart_cond(use_mv_avg,
lambda: bn_decay_zero,
lambda: match.bn_decay_var_tensor,
name='freeze_moving_var')
common.RerouteTensor(bn_decay_var_out,
match.bn_decay_var_tensor,
can_modify=bn_decay_var_consumers)
correction_recip = utils.smart_cond(
use_mv_avg,
lambda: array_ops.ones(correction_scale.shape),
lambda: correction_recip,
name='correction_recip')
correction_offset = utils.smart_cond(
use_mv_avg,
lambda: correction_offset,
lambda: array_ops.zeros(correction_offset.shape),
name='correction_offset')
return correction_scale, correction_recip, correction_offset
def _Log1pGrad(op, grad):
"""Returns grad * (1/(1 + x))."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
return grad * math_ops.reciprocal(1 + x)
def _SvdGrad(op, grad_s, grad_u, grad_v):
"""Gradient for Svd based on Giles' algorithm. Reference at top of file."""
if op.get_attr("compute_uv") and not op.get_attr("full_matrices"):
raise NotImplementedError(
"SVD gradient is not implemented for compute_uv=True and "
"full_matrices=False.")
a = op.inputs[0]
a_shape = a.get_shape().with_rank_at_least(2)
if op.get_attr("compute_uv"):
# TODO(rmlarsen): Make this work with complex types.
if a.dtype.is_complex:
raise NotImplementedError(
"SVD gradient is not implemented for complex types and "
"compute_uv=True.")
grad_u_shape = grad_u.get_shape().with_rank_at_least(2)
grad_v_shape = grad_v.get_shape().with_rank_at_least(2)
m = a_shape[-2].merge_with(grad_u_shape[-2])
n = a_shape[-1].merge_with(grad_v_shape[-2])
batch_shape = a_shape[:-2].merge_with(grad_u_shape[:-2]).merge_with(
grad_v_shape[:-2])
a_shape = batch_shape.concatenate([m, n])
m = a_shape[-2].value
n = a_shape[-1].value
# TODO(rmlarsen): Make this work with placeholders.
if m is None or n is None:
raise NotImplementedError(
"SVD gradient has not been implemented for input with unknown "
"inner matrix shape.")
if not op.get_attr("full_matrices") or not op.get_attr("compute_uv"):
s, u, v = linalg_ops.svd(a, compute_uv=True, full_matrices=True)
else:
s = op.outputs[0]
u = op.outputs[1]
v = op.outputs[2]
use_adjoint = False
if m > n:
# Compute the gradient for A^H = V * S^T * U^H, and (implicitly) take the
# Hermitian transpose of the gradient at the end.
use_adjoint = True
m, n = n, m
u, v = v, u
grad_u, grad_v = grad_v, grad_u
with ops.control_dependencies([grad_s, grad_u, grad_v]):
grad_s_mat = array_ops.matrix_diag(grad_s)
if not op.get_attr("compute_uv"):
if use_adjoint:
grad_a = math_ops.matmul(
v[..., :, :m], math_ops.matmul(u, grad_s_mat), adjoint_b=True)
else:
grad_a = math_ops.matmul(u,
math_ops.matmul(
grad_s_mat, v[..., :, :m], adjoint_b=True))
grad_a.set_shape(a_shape)
return grad_a
# TODO(rmlarsen): Define a gradient that is numerically stable for
# abs(m-n) > 1. Currently this does not work because there are effectively
# multiple singular values with value zero. I am not sure if this is a true
# instability or if it simply throws off the finite difference gradient
# checker.
if abs(m - n) > 1:
raise NotImplementedError(
"svd gradient is not implemented for abs(m - n) > 1")
s_mat = array_ops.matrix_diag(s)
s2 = math_ops.square(s)
# NOTICE: Because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when singular values are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate singular values, the corresponding singular vectors are
# only defined up a (k-dimensional) subspace. In practice, this can
# lead to numerical instability when singular values are close but not
# exactly equal.
f = array_ops.matrix_set_diag(
math_ops.reciprocal(
array_ops.expand_dims(s2, -2) - array_ops.expand_dims(s2, -1)),
array_ops.zeros_like(s))
s_inv_mat = array_ops.matrix_diag(math_ops.reciprocal(s))
u_gu = math_ops.matmul(u, grad_u, adjoint_a=True)
v_gv = math_ops.matmul(v, grad_v, adjoint_a=True)
if m == n:
f_u = f * u_gu
f_v = f * v_gv
else:
dv2 = array_ops.matrix_transpose(v_gv[..., m:n, :m]) - v_gv[..., :m, m:n]
f_u = f * u_gu
f_v = f * v_gv[..., :m, :m]
grad_a_nouv = (
grad_s_mat + math_ops.matmul(f_u + _linalg.adjoint(f_u), s_mat) +
math_ops.matmul(s_mat, f_v + _linalg.adjoint(f_v)))
if m != n:
grad_a_nouv = array_ops.concat(
[grad_a_nouv, math_ops.matmul(s_inv_mat, dv2)], -1)
if use_adjoint:
# Use (U X V^H)^H = V (U X)^H.
grad_a = math_ops.matmul(
v, math_ops.matmul(u, grad_a_nouv), adjoint_b=True)
else:
grad_a = math_ops.matmul(u,
math_ops.matmul(grad_a_nouv, v, adjoint_b=True))
grad_a.set_shape(a_shape)
return grad_a
def weighted_moments(x,
axes,
frequency_weights,
tower_config,
name=None,
keep_dims=False):
"""Returns the frequency-weighted mean and variance of `x`.
Args:
x: A tensor.
axes: 1-d tensor of int32 values; these are the axes along which
to compute mean and variance.
frequency_weights: A tensor of positive weights which can be
broadcast with x.
name: Name used to scope the operation.
keep_dims: Produce moments with the same dimensionality as the input.
Returns:
Two tensors: `weighted_mean` and `weighted_variance`.
"""
with ops.name_scope(name, "weighted_moments",
[x, frequency_weights, axes]):
x = ops.convert_to_tensor(x, name="x")
frequency_weights = ops.convert_to_tensor(frequency_weights,
name="frequency_weights")
# Unlike moments(), this just uses a simpler two-pass method.
# See comment in moments() WRT precision; it applies here too.
needs_cast = x.dtype == dtypes.float16
if needs_cast:
x = math_ops.cast(x, dtypes.float32)
if frequency_weights.dtype != x.dtype:
frequency_weights = math_ops.cast(frequency_weights, x.dtype)
# Note that we use keep_dims=True for our reductions regardless of the arg;
# this is so that the results remain broadcast-compatible with the inputs.
# Original Code: weighted_input_sum = math_ops.reduce_sum(
# frequency_weights * x, axes, name="weighted_input_sum", keepdims=True)
nccl_name = "NCCL" if not tower_config.is_test else "NCCL_TEST"
shared_name = tf.get_variable_scope().name. \
replace(tower_config.name, tower_config.prefix.format(nccl_name))
device_weighted_input_sum = math_ops.reduce_sum(
frequency_weights * x,
axes,
name="weighted_input_sum",
keepdims=True)
weighted_input_sum = gen_nccl_ops.nccl_all_reduce(
input=device_weighted_input_sum,
reduction="sum",
num_devices=tower_config.num_devices,
shared_name=shared_name) / (1.0 * tower_config.num_devices)
# The shape of the weights isn't necessarily the same as x's
# shape, just broadcast-compatible with it -- so this expression
# performs broadcasting to give a per-item weight, with the same
# shape as (freqency_weights * x). This avoids having to reason
# through all the broadcast logic to compute a correct
# sum_of_weights.
broadcasted_weights = frequency_weights + array_ops.zeros_like(x)
sum_of_weights = math_ops.reduce_sum(broadcasted_weights,
axes,
name="sum_of_weights",
keepdims=True)
divisor = math_ops.reciprocal(sum_of_weights,
name="inv_weight_sum")
weighted_mean = math_ops.multiply(weighted_input_sum, divisor)
# Have the weighted mean; now on to variance:
# weighted_distsq = math_ops.reduce_sum(
# frequency_weights * math_ops.squared_difference(x, weighted_mean),
# axes,
# name="weighted_distsq",
# keepdims=True)
nccl_name = "NCCL" if not tower_config.is_test else "NCCL_TEST"
shared_name = tf.get_variable_scope().name. \
replace(tower_config.name, tower_config.prefix.format(nccl_name))
device_weighted_distsq = math_ops.reduce_sum(
frequency_weights *
math_ops.squared_difference(x, weighted_mean),
axes,
name="weighted_distsq",
keepdims=True)
weighted_distsq = gen_nccl_ops.nccl_all_reduce(
input=device_weighted_distsq,
reduction="sum",
num_devices=tower_config.num_devices,
shared_name=shared_name) / (1.0 * tower_config.num_devices)
weighted_variance = math_ops.multiply(weighted_distsq, divisor)
if not keep_dims:
weighted_mean = array_ops.squeeze(weighted_mean, axis=axes)
weighted_variance = array_ops.squeeze(weighted_variance,
axis=axes)
if needs_cast:
weighted_mean = math_ops.cast(weighted_mean, dtypes.float16)
weighted_variance = math_ops.cast(weighted_variance,
dtypes.float16)
return weighted_mean, weighted_variance
def _Log1pGrad(op, grad):
"""Returns grad * (1/(1 + x))."""
x = op.inputs[0]
with ops.control_dependencies([grad]):
x = math_ops.conj(x)
return grad * math_ops.reciprocal(1 + x)
def _SvdGrad(op, grad_s, grad_u, grad_v):
"""Gradient for Svd based on Giles' algorithm. Reference at top of file."""
if op.get_attr("compute_uv") and not op.get_attr("full_matrices"):
raise NotImplementedError(
"SVD gradient is not implemented for compute_uv=True and "
"full_matrices=False.")
a = op.inputs[0]
a_shape = a.get_shape().with_rank_at_least(2)
if op.get_attr("compute_uv"):
# TODO(rmlarsen): Make this work with complex types.
if a.dtype.is_complex:
raise NotImplementedError(
"SVD gradient is not implemented for complex types and "
"compute_uv=True.")
grad_u_shape = grad_u.get_shape().with_rank_at_least(2)
grad_v_shape = grad_v.get_shape().with_rank_at_least(2)
m = a_shape[-2].merge_with(grad_u_shape[-2])
n = a_shape[-1].merge_with(grad_v_shape[-2])
batch_shape = a_shape[:-2].merge_with(grad_u_shape[:-2]).merge_with(
grad_v_shape[:-2])
a_shape = batch_shape.concatenate([m, n])
m = a_shape[-2].value
n = a_shape[-1].value
# TODO(rmlarsen): Make this work with placeholders.
if m is None or n is None:
raise NotImplementedError(
"SVD gradient has not been implemented for input with unknown "
"inner matrix shape.")
if not op.get_attr("full_matrices") or not op.get_attr("compute_uv"):
s, u, v = linalg_ops.svd(a, compute_uv=True, full_matrices=True)
else:
s = op.outputs[0]
u = op.outputs[1]
v = op.outputs[2]
use_adjoint = False
if m > n:
# Compute the gradient for A^H = V * S^T * U^H, and (implicitly) take the
# Hermitian transpose of the gradient at the end.
use_adjoint = True
m, n = n, m
u, v = v, u
grad_u, grad_v = grad_v, grad_u
with ops.control_dependencies([grad_s, grad_u, grad_v]):
grad_s_mat = array_ops.matrix_diag(grad_s)
if not op.get_attr("compute_uv"):
if use_adjoint:
grad_a = math_ops.matmul(v[..., :, :m],
math_ops.matmul(u, grad_s_mat),
adjoint_b=True)
else:
grad_a = math_ops.matmul(
u,
math_ops.matmul(grad_s_mat, v[..., :, :m], adjoint_b=True))
grad_a.set_shape(a_shape)
return grad_a
# TODO(rmlarsen): Define a gradient that is numerically stable for
# abs(m-n) > 1. Currently this does not work because there are effectively
# multiple singular values with value zero. I am not sure if this is a true
# instability or if it simply throws off the finite difference gradient
# checker.
if abs(m - n) > 1:
raise NotImplementedError(
"svd gradient is not implemented for abs(m - n) > 1")
s_mat = array_ops.matrix_diag(s)
s2 = math_ops.square(s)
# NOTICE: Because of the term involving f, the gradient becomes
# infinite (or NaN in practice) when singular values are not unique.
# Mathematically this should not be surprising, since for (k-fold)
# degenerate singular values, the corresponding singular vectors are
# only defined up a (k-dimensional) subspace. In practice, this can
# lead to numerical instability when singular values are close but not
# exactly equal.
f = array_ops.matrix_set_diag(
math_ops.reciprocal(
array_ops.expand_dims(s2, -2) - array_ops.expand_dims(s2, -1)),
array_ops.zeros_like(s))
s_inv_mat = array_ops.matrix_diag(math_ops.reciprocal(s))
u_gu = math_ops.matmul(u, grad_u, adjoint_a=True)
v_gv = math_ops.matmul(v, grad_v, adjoint_a=True)
if m == n:
f_u = f * u_gu
f_v = f * v_gv
else:
dv2 = array_ops.matrix_transpose(
v_gv[..., m:n, :m]) - v_gv[..., :m, m:n]
f_u = f * u_gu
f_v = f * v_gv[..., :m, :m]
grad_a_nouv = (grad_s_mat +
math_ops.matmul(f_u + _linalg.adjoint(f_u), s_mat) +
math_ops.matmul(s_mat, f_v + _linalg.adjoint(f_v)))
if m != n:
grad_a_nouv = array_ops.concat(
[grad_a_nouv, math_ops.matmul(s_inv_mat, dv2)], -1)
if use_adjoint:
# Use (U X V^H)^H = V (U X)^H.
grad_a = math_ops.matmul(v,
math_ops.matmul(u, grad_a_nouv),
adjoint_b=True)
else:
grad_a = math_ops.matmul(
u, math_ops.matmul(grad_a_nouv, v, adjoint_b=True))
grad_a.set_shape(a_shape)
return grad_a
def weighted_moments(x, axes, frequency_weights, name=None, keep_dims=False):
"""Returns the frequency-weighted mean and variance of `x`.
Args:
x: A tensor.
axes: 1-d tensor of int32 values; these are the axes along which
to compute mean and variance.
frequency_weights: A tensor of positive weights which can be
broadcast with x.
name: Name used to scope the operation.
keep_dims: Produce moments with the same dimensionality as the input.
Returns:
Two tensors: `weighted_mean` and `weighted_variance`.
"""
with ops.name_scope(name, "weighted_moments", [x, frequency_weights, axes]):
x = ops.convert_to_tensor(x, name="x")
frequency_weights = ops.convert_to_tensor(
frequency_weights, name="frequency_weights")
# Unlike moments(), this just uses a simpler two-pass method.
# See comment in moments() WRT precision; it applies here too.
needs_cast = x.dtype == dtypes.float16
if needs_cast:
x = math_ops.cast(x, dtypes.float32)
if frequency_weights.dtype != x.dtype:
frequency_weights = math_ops.cast(frequency_weights, x.dtype)
# Note that we use keep_dims=True for our reductions regardless of the arg;
# this is so that the results remain broadcast-compatible with the inputs.
weighted_input_sum = math_ops.reduce_sum(
frequency_weights * x, axes, name="weighted_input_sum", keep_dims=True)
# The shape of the weights isn't necessarily the same as x's
# shape, just broadcast-compatible with it -- so this expression
# performs broadcasting to give a per-item weight, with the same
# shape as (freqency_weights * x). This avoids having to reason
# through all the broadcast logic to compute a correct
# sum_of_weights.
broadcasted_weights = frequency_weights + array_ops.zeros_like(x)
sum_of_weights = math_ops.reduce_sum(
broadcasted_weights, axes, name="sum_of_weights", keep_dims=True)
divisor = math_ops.reciprocal(sum_of_weights, name="inv_weight_sum")
weighted_mean = math_ops.mul(weighted_input_sum, divisor)
# Have the weighted mean; now on to variance:
weighted_distsq = math_ops.reduce_sum(
frequency_weights * math_ops.squared_difference(x, weighted_mean),
axes,
name="weighted_distsq",
keep_dims=True)
weighted_variance = math_ops.mul(weighted_distsq, divisor)
if not keep_dims:
weighted_mean = array_ops.squeeze(weighted_mean, squeeze_dims=axes)
weighted_variance = array_ops.squeeze(
weighted_variance, squeeze_dims=axes)
if needs_cast:
weighted_mean = math_ops.cast(weighted_mean, dtypes.float16)
weighted_variance = math_ops.cast(weighted_variance, dtypes.float16)
return weighted_mean, weighted_variance
def _SafeReciprocal(x, epsilon=1E-20):
return x * math_ops.reciprocal(x * x + epsilon)
def _mini_batch_training_op(self, inputs, cluster_idx_list, cluster_centers,
cluster_centers_var, total_counts):
"""Creates an op for training for mini batch case.
Args:
inputs: list of input Tensors.
cluster_idx_list: A vector (or list of vectors). Each element in the
vector corresponds to an input row in 'inp' and specifies the cluster id
corresponding to the input.
cluster_centers: Tensor of cluster centers, possibly normalized.
cluster_centers_var: Tensor Ref of cluster centers.
total_counts: Tensor Ref of cluster counts.
Returns:
An op for doing an update of mini-batch k-means.
"""
update_ops = []
for inp, cluster_idx in zip(inputs, cluster_idx_list):
with ops.colocate_with(inp):
assert total_counts is not None
cluster_idx = array_ops.reshape(cluster_idx, [-1])
# Dedupe the unique ids of cluster_centers being updated so that updates
# can be locally aggregated.
unique_ids, unique_idx = array_ops.unique(cluster_idx)
num_unique_cluster_idx = array_ops.size(unique_ids)
# Fetch the old values of counts and cluster_centers.
with ops.colocate_with(total_counts):
old_counts = array_ops.gather(total_counts, unique_ids)
with ops.colocate_with(cluster_centers):
old_cluster_centers = array_ops.gather(cluster_centers, unique_ids)
# Locally aggregate the increment to counts.
count_updates = math_ops.unsorted_segment_sum(
array_ops.ones_like(
unique_idx, dtype=total_counts.dtype),
unique_idx,
num_unique_cluster_idx)
# Locally compute the sum of inputs mapped to each id.
# For a cluster with old cluster value x, old count n, and with data
# d_1,...d_k newly assigned to it, we recompute the new value as
# x += (sum_i(d_i) - k * x) / (n + k).
# Compute sum_i(d_i), see comment above.
cluster_center_updates = math_ops.unsorted_segment_sum(
inp, unique_idx, num_unique_cluster_idx)
# Shape to enable broadcasting count_updates and learning_rate to inp.
# It extends the shape with 1's to match the rank of inp.
broadcast_shape = array_ops.concat(
[
array_ops.reshape(num_unique_cluster_idx, [1]), array_ops.ones(
array_ops.reshape(array_ops.rank(inp) - 1, [1]),
dtype=dtypes.int32)
],
0)
# Subtract k * x, see comment above.
cluster_center_updates -= math_ops.cast(
array_ops.reshape(count_updates, broadcast_shape),
inp.dtype) * old_cluster_centers
learning_rate = math_ops.reciprocal(
math_ops.cast(old_counts + count_updates, inp.dtype))
learning_rate = array_ops.reshape(learning_rate, broadcast_shape)
# scale by 1 / (n + k), see comment above.
cluster_center_updates *= learning_rate
# Apply the updates.
update_counts = state_ops.scatter_add(total_counts, unique_ids,
count_updates)
update_cluster_centers = state_ops.scatter_add(cluster_centers_var,
unique_ids,
cluster_center_updates)
update_ops.extend([update_counts, update_cluster_centers])
return control_flow_ops.group(*update_ops)
def _mini_batch_training_op(self, inputs, cluster_idx_list,
cluster_centers, total_counts):
"""Creates an op for training for mini batch case.
Args:
inputs: list of input Tensors.
cluster_idx_list: A vector (or list of vectors). Each element in the
vector corresponds to an input row in 'inp' and specifies the cluster id
corresponding to the input.
cluster_centers: Tensor Ref of cluster centers.
total_counts: Tensor Ref of cluster counts.
Returns:
An op for doing an update of mini-batch k-means.
"""
update_ops = []
for inp, cluster_idx in zip(inputs, cluster_idx_list):
with ops.colocate_with(inp):
assert total_counts is not None
cluster_idx = array_ops.reshape(cluster_idx, [-1])
# Dedupe the unique ids of cluster_centers being updated so that updates
# can be locally aggregated.
unique_ids, unique_idx = array_ops.unique(cluster_idx)
num_unique_cluster_idx = array_ops.size(unique_ids)
# Fetch the old values of counts and cluster_centers.
with ops.colocate_with(total_counts, ignore_existing=True):
old_counts = array_ops.gather(total_counts, unique_ids)
# TODO(agarwal): This colocation seems to run into problems. Fix it.
with ops.colocate_with(cluster_centers, ignore_existing=True):
old_cluster_centers = array_ops.gather(
cluster_centers, unique_ids)
# Locally aggregate the increment to counts.
count_updates = math_ops.unsorted_segment_sum(
array_ops.ones_like(unique_idx, dtype=total_counts.dtype),
unique_idx, num_unique_cluster_idx)
# Locally compute the sum of inputs mapped to each id.
# For a cluster with old cluster value x, old count n, and with data
# d_1,...d_k newly assigned to it, we recompute the new value as
# x += (sum_i(d_i) - k * x) / (n + k).
# Compute sum_i(d_i), see comment above.
cluster_center_updates = math_ops.unsorted_segment_sum(
inp, unique_idx, num_unique_cluster_idx)
# Shape to enable broadcasting count_updates and learning_rate to inp.
# It extends the shape with 1's to match the rank of inp.
broadcast_shape = array_ops.concat([
array_ops.reshape(num_unique_cluster_idx, [1]),
array_ops.ones(array_ops.reshape(
array_ops.rank(inp) - 1, [1]),
dtype=dtypes.int32)
], 0)
# Subtract k * x, see comment above.
cluster_center_updates -= math_ops.cast(
array_ops.reshape(count_updates, broadcast_shape),
inp.dtype) * old_cluster_centers
learning_rate = math_ops.reciprocal(
math_ops.cast(old_counts + count_updates, inp.dtype))
learning_rate = array_ops.reshape(learning_rate,
broadcast_shape)
# scale by 1 / (n + k), see comment above.
cluster_center_updates *= learning_rate
# Apply the updates.
update_counts = state_ops.scatter_add(total_counts, unique_ids,
count_updates)
update_cluster_centers = state_ops.scatter_add(
cluster_centers, unique_ids, cluster_center_updates)
update_ops.extend([update_counts, update_cluster_centers])
return control_flow_ops.group(*update_ops)
