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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# =============================================================================
"""Implementation of Neural Net (NN) functions."""
import math
from tensorflow.python.distribute import distribute_lib
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import array_ops_stack
from tensorflow.python.ops import candidate_sampling_ops
from tensorflow.python.ops import check_ops
from tensorflow.python.ops import cond as tf_cond
from tensorflow.python.ops import custom_gradient
from tensorflow.python.ops import embedding_ops
from tensorflow.python.ops import gen_array_ops # pylint: disable=unused-import
from tensorflow.python.ops import gen_nn_ops
from tensorflow.python.ops import gen_sparse_ops
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops import variables
from tensorflow.python.ops.losses import util as losses_util
from tensorflow.python.platform import device_context
from tensorflow.python.util import dispatch
from tensorflow.python.util.deprecation import deprecated_args
from tensorflow.python.util.deprecation import deprecated_argument_lookup
from tensorflow.python.util.tf_export import tf_export
@tf_export("nn.log_poisson_loss")
@dispatch.add_dispatch_support
def log_poisson_loss(targets, log_input, compute_full_loss=False, name=None):
"""Computes log Poisson loss given `log_input`.
Gives the log-likelihood loss between the prediction and the target under the
assumption that the target has a Poisson distribution.
Caveat: By default, this is not the exact loss, but the loss minus a
constant term [log(z!)]. That has no effect for optimization, but
does not play well with relative loss comparisons. To compute an
approximation of the log factorial term, specify
compute_full_loss=True to enable Stirling's Approximation.
For brevity, let `c = log(x) = log_input`, `z = targets`. The log Poisson
loss is
-log(exp(-x) * (x^z) / z!)
= -log(exp(-x) * (x^z)) + log(z!)
~ -log(exp(-x)) - log(x^z) [+ z * log(z) - z + 0.5 * log(2 * pi * z)]
[ Note the second term is the Stirling's Approximation for log(z!).
It is invariant to x and does not affect optimization, though
important for correct relative loss comparisons. It is only
computed when compute_full_loss == True. ]
= x - z * log(x) [+ z * log(z) - z + 0.5 * log(2 * pi * z)]
= exp(c) - z * c [+ z * log(z) - z + 0.5 * log(2 * pi * z)]
Args:
targets: A `Tensor` of the same type and shape as `log_input`.
log_input: A `Tensor` of type `float32` or `float64`.
compute_full_loss: whether to compute the full loss. If false, a constant
term is dropped in favor of more efficient optimization.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `log_input` with the componentwise
logistic losses.
Raises:
ValueError: If `log_input` and `targets` do not have the same shape.
"""
with ops.name_scope(name, "log_poisson_loss", [log_input, targets]) as name:
log_input = ops.convert_to_tensor(log_input, name="log_input")
targets = ops.convert_to_tensor(targets, name="targets")
try:
targets.get_shape().assert_is_compatible_with(log_input.get_shape())
except ValueError:
raise ValueError(
"`log_input` and `targets` must have the same shape, received "
f"({log_input.get_shape()} vs {targets.get_shape()}).")
result = math_ops.exp(log_input) - log_input * targets
if compute_full_loss:
# need to create constant tensors here so that their dtypes can be matched
# to that of the targets.
point_five = constant_op.constant(0.5, dtype=targets.dtype)
two_pi = constant_op.constant(2 * math.pi, dtype=targets.dtype)
stirling_approx = (targets * math_ops.log(targets)) - targets + (
point_five * math_ops.log(two_pi * targets))
zeros = array_ops.zeros_like(targets, dtype=targets.dtype)
ones = array_ops.ones_like(targets, dtype=targets.dtype)
cond = math_ops.logical_and(targets >= zeros, targets <= ones)
result += array_ops.where(cond, zeros, stirling_approx)
return result
@tf_export(v1=["nn.sigmoid_cross_entropy_with_logits"])
@dispatch.add_dispatch_support
def sigmoid_cross_entropy_with_logits(
labels=None,
logits=None,
name=None):
"""See sigmoid_cross_entropy_with_logits_v2."""
# pylint: disable=protected-access
nn_ops._ensure_xent_args("sigmoid_cross_entropy_with_logits", labels, logits)
# pylint: enable=protected-access
with ops.name_scope(name, "logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().assert_is_compatible_with(logits.get_shape())
except ValueError:
raise ValueError("`logits` and `labels` must have the same shape, "
f"received ({logits.get_shape()} vs "
f"{labels.get_shape()}).")
# The logistic loss formula from above is
# x - x * z + log(1 + exp(-x))
# For x < 0, a more numerically stable formula is
# -x * z + log(1 + exp(x))
# Note that these two expressions can be combined into the following:
# max(x, 0) - x * z + log(1 + exp(-abs(x)))
# To allow computing gradients at zero, we define custom versions of max and
# abs functions.
zeros = array_ops.zeros_like(logits, dtype=logits.dtype)
cond = (logits >= zeros)
relu_logits = array_ops.where(cond, logits, zeros)
neg_abs_logits = array_ops.where(cond, -logits, logits) # pylint: disable=invalid-unary-operand-type
return math_ops.add(
relu_logits - logits * labels,
math_ops.log1p(math_ops.exp(neg_abs_logits)),
name=name)
# Note: intentionally calling this v2 to not allow existing code with indirect
# imports to ignore the sentinel behavior.
@tf_export("nn.sigmoid_cross_entropy_with_logits", v1=[])
@dispatch.register_binary_elementwise_api
@dispatch.add_dispatch_support
def sigmoid_cross_entropy_with_logits_v2( # pylint: disable=invalid-name
labels=None,
logits=None,
name=None):
r"""Computes sigmoid cross entropy given `logits`.
Measures the probability error in tasks with two outcomes in which each
outcome is independent and need not have a fully certain label. For instance,
one could perform a regression where the probability of an event happening is
known and used as a label. This loss may also be used for binary
classification, where labels are either zero or one.
For brevity, let `x = logits`, `z = labels`. The logistic loss is
z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + log(1 + exp(-x))
= x - x * z + log(1 + exp(-x))
For x < 0, to avoid overflow in exp(-x), we reformulate the above
x - x * z + log(1 + exp(-x))
= log(exp(x)) - x * z + log(1 + exp(-x))
= - x * z + log(1 + exp(x))
Hence, to ensure stability and avoid overflow, the implementation uses this
equivalent formulation
max(x, 0) - x * z + log(1 + exp(-abs(x)))
`logits` and `labels` must have the same type and shape.
>>> logits = tf.constant([1., -1., 0., 1., -1., 0., 0.])
>>> labels = tf.constant([0., 0., 0., 1., 1., 1., 0.5])
>>> tf.nn.sigmoid_cross_entropy_with_logits(
... labels=labels, logits=logits).numpy()
array([1.3132617, 0.3132617, 0.6931472, 0.3132617, 1.3132617, 0.6931472,
0.6931472], dtype=float32)
Compared to the losses which handle multiple outcomes,
`tf.nn.softmax_cross_entropy_with_logits` for general multi-class
classification and `tf.nn.sparse_softmax_cross_entropy_with_logits` for more
efficient multi-class classification with hard labels,
`sigmoid_cross_entropy_with_logits` is a slight simplification for binary
classification:
sigmoid(x) = softmax([x, 0])[0]
$$\frac{1}{1 + e^{-x}} = \frac{e^x}{e^x + e^0}$$
While `sigmoid_cross_entropy_with_logits` works for soft binary labels
(probabilities between 0 and 1), it can also be used for binary classification
where the labels are hard. There is an equivalence between all three symbols
in this case, with a probability 0 indicating the second class or 1 indicating
the first class:
>>> sigmoid_logits = tf.constant([1., -1., 0.])
>>> softmax_logits = tf.stack([sigmoid_logits, tf.zeros_like(sigmoid_logits)],
... axis=-1)
>>> soft_binary_labels = tf.constant([1., 1., 0.])
>>> soft_multiclass_labels = tf.stack(
... [soft_binary_labels, 1. - soft_binary_labels], axis=-1)
>>> hard_labels = tf.constant([0, 0, 1])
>>> tf.nn.sparse_softmax_cross_entropy_with_logits(
... labels=hard_labels, logits=softmax_logits).numpy()
array([0.31326166, 1.3132616 , 0.6931472 ], dtype=float32)
>>> tf.nn.softmax_cross_entropy_with_logits(
... labels=soft_multiclass_labels, logits=softmax_logits).numpy()
array([0.31326166, 1.3132616, 0.6931472], dtype=float32)
>>> tf.nn.sigmoid_cross_entropy_with_logits(
... labels=soft_binary_labels, logits=sigmoid_logits).numpy()
array([0.31326166, 1.3132616, 0.6931472], dtype=float32)
Args:
labels: A `Tensor` of the same type and shape as `logits`. Between 0 and 1,
inclusive.
logits: A `Tensor` of type `float32` or `float64`. Any real number.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
return sigmoid_cross_entropy_with_logits(
logits=logits, labels=labels, name=name)
sigmoid_cross_entropy_with_logits.__doc__ = (
sigmoid_cross_entropy_with_logits_v2.__doc__)
@tf_export("nn.weighted_cross_entropy_with_logits", v1=[])
@dispatch.add_dispatch_support
def weighted_cross_entropy_with_logits_v2(labels, logits, pos_weight,
name=None):
"""Computes a weighted cross entropy.
This is like `sigmoid_cross_entropy_with_logits()` except that `pos_weight`,
allows one to trade off recall and precision by up- or down-weighting the
cost of a positive error relative to a negative error.
The usual cross-entropy cost is defined as:
labels * -log(sigmoid(logits)) +
(1 - labels) * -log(1 - sigmoid(logits))
A value `pos_weight > 1` decreases the false negative count, hence increasing
the recall.
Conversely setting `pos_weight < 1` decreases the false positive count and
increases the precision.
This can be seen from the fact that `pos_weight` is introduced as a
multiplicative coefficient for the positive labels term
in the loss expression:
labels * -log(sigmoid(logits)) * pos_weight +
(1 - labels) * -log(1 - sigmoid(logits))
For brevity, let `x = logits`, `z = labels`, `q = pos_weight`.
The loss is:
qz * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= qz * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= qz * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= qz * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + (qz + 1 - z) * log(1 + exp(-x))
= (1 - z) * x + (1 + (q - 1) * z) * log(1 + exp(-x))
Setting `l = (1 + (q - 1) * z)`, to ensure stability and avoid overflow,
the implementation uses
(1 - z) * x + l * (log(1 + exp(-abs(x))) + max(-x, 0))
`logits` and `labels` must have the same type and shape.
>>> labels = tf.constant([1., 0.5, 0.])
>>> logits = tf.constant([1.5, -0.1, -10.])
>>> tf.nn.weighted_cross_entropy_with_logits(
... labels=labels, logits=logits, pos_weight=tf.constant(1.5)).numpy()
array([3.0211994e-01, 8.8049585e-01, 4.5776367e-05], dtype=float32)
>>> tf.nn.weighted_cross_entropy_with_logits(
... labels=labels, logits=logits, pos_weight=tf.constant(0.5)).numpy()
array([1.00706644e-01, 5.08297503e-01, 4.57763672e-05], dtype=float32)
Args:
labels: A `Tensor` of the same type and shape as `logits`, with values
between 0 and 1 inclusive.
logits: A `Tensor` of type `float32` or `float64`, any real numbers.
pos_weight: A coefficient to use on the positive examples, typically a
scalar but otherwise broadcastable to the shape of `logits`. Its value
should be non-negative.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
weighted logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
with ops.name_scope(name, "logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().assert_is_compatible_with(logits.get_shape())
except ValueError:
raise ValueError("`logits` and `labels` must have the same shape, "
f"received ({logits.get_shape()} vs "
f"{labels.get_shape()}).")
# The logistic loss formula from above is
# (1 - z) * x + (1 + (q - 1) * z) * log(1 + exp(-x))
# For x < 0, a more numerically stable formula is
# (1 - z) * x + (1 + (q - 1) * z) * log(1 + exp(x)) - l * x
# To avoid branching, we use the combined version
# (1 - z) * x + l * (log(1 + exp(-abs(x))) + max(-x, 0))
log_weight = 1 + (pos_weight - 1) * labels
return math_ops.add(
(1 - labels) * logits,
log_weight * (math_ops.log1p(math_ops.exp(-math_ops.abs(logits))) +
nn_ops.relu(-logits)), # pylint: disable=invalid-unary-operand-type
name=name)
@tf_export(v1=["nn.weighted_cross_entropy_with_logits"])
@dispatch.add_dispatch_support
@deprecated_args(None, "targets is deprecated, use labels instead", "targets")
def weighted_cross_entropy_with_logits(labels=None,
logits=None,
pos_weight=None,
name=None,
targets=None):
"""Computes a weighted cross entropy.
This is like `sigmoid_cross_entropy_with_logits()` except that `pos_weight`,
allows one to trade off recall and precision by up- or down-weighting the
cost of a positive error relative to a negative error.
The usual cross-entropy cost is defined as:
labels * -log(sigmoid(logits)) +
(1 - labels) * -log(1 - sigmoid(logits))
A value `pos_weight > 1` decreases the false negative count, hence increasing
the recall.
Conversely setting `pos_weight < 1` decreases the false positive count and
increases the precision.
This can be seen from the fact that `pos_weight` is introduced as a
multiplicative coefficient for the positive labels term
in the loss expression:
labels * -log(sigmoid(logits)) * pos_weight +
(1 - labels) * -log(1 - sigmoid(logits))
For brevity, let `x = logits`, `z = labels`, `q = pos_weight`.
The loss is:
qz * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= qz * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= qz * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= qz * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + (qz + 1 - z) * log(1 + exp(-x))
= (1 - z) * x + (1 + (q - 1) * z) * log(1 + exp(-x))
Setting `l = (1 + (q - 1) * z)`, to ensure stability and avoid overflow,
the implementation uses
(1 - z) * x + l * (log(1 + exp(-abs(x))) + max(-x, 0))
`logits` and `labels` must have the same type and shape.
Args:
labels: A `Tensor` of the same type and shape as `logits`.
logits: A `Tensor` of type `float32` or `float64`.
pos_weight: A coefficient to use on the positive examples.
name: A name for the operation (optional).
targets: Deprecated alias for labels.
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
weighted logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
labels = deprecated_argument_lookup("labels", labels, "targets", targets)
return weighted_cross_entropy_with_logits_v2(labels, logits, pos_weight, name)
@tf_export("nn.compute_average_loss")
@dispatch.add_dispatch_support
def compute_average_loss(per_example_loss,
sample_weight=None,
global_batch_size=None):
"""Scales per-example losses with sample_weights and computes their average.
Usage with distribution strategy and custom training loop:
```python
with strategy.scope():
def compute_loss(labels, predictions, sample_weight=None):
# If you are using a `Loss` class instead, set reduction to `NONE` so that
# we can do the reduction afterwards and divide by global batch size.
per_example_loss = tf.keras.losses.sparse_categorical_crossentropy(
labels, predictions)
# Compute loss that is scaled by sample_weight and by global batch size.
return tf.nn.compute_average_loss(
per_example_loss,
sample_weight=sample_weight,
global_batch_size=GLOBAL_BATCH_SIZE)
```
Args:
per_example_loss: Per-example loss.
sample_weight: Optional weighting for each example.
global_batch_size: Optional global batch size value. Defaults to (size of
first dimension of `losses`) * (number of replicas).
Returns:
Scalar loss value, obtained by summing the `per_example_loss` and dividing
by `global_batch_size`. If `global_batch_size` is zero, the result is zero.
""" # pylint: disable=g-doc-exception
per_example_loss = ops.convert_to_tensor(per_example_loss)
input_dtype = per_example_loss.dtype
with losses_util.check_per_example_loss_rank(per_example_loss):
if sample_weight is not None:
sample_weight = ops.convert_to_tensor(sample_weight)
per_example_loss = losses_util.scale_losses_by_sample_weight(
per_example_loss, sample_weight)
per_example_loss = math_ops.cast(per_example_loss, input_dtype)
if global_batch_size is None:
if (distribute_lib.has_strategy()
and distribute_lib.in_cross_replica_context()):
raise RuntimeError(
"You are calling `compute_average_loss` in cross replica context, "
"while it was expected to be called in replica context.")
num_replicas = distribute_lib.get_strategy().num_replicas_in_sync
per_replica_batch_size = array_ops.shape_v2(per_example_loss)[0]
global_batch_size = per_replica_batch_size * num_replicas
check_ops.assert_scalar_v2(
global_batch_size, message="global_batch_size must be scalar.")
check_ops.assert_integer_v2(
global_batch_size,
message="global_batch_size must be an integer.")
check_ops.assert_non_negative_v2(
global_batch_size, message="global_batch_size must be non-negative.")
loss = math_ops.reduce_sum(per_example_loss)
global_batch_size = math_ops.cast(global_batch_size, input_dtype)
return math_ops.div_no_nan(loss, global_batch_size)
@tf_export("nn.scale_regularization_loss")
@dispatch.add_dispatch_support
def scale_regularization_loss(regularization_loss):
"""Scales the sum of the given regularization losses by number of replicas.
Usage with distribution strategy and custom training loop:
```python
with strategy.scope():
def compute_loss(self, label, predictions):
per_example_loss = tf.keras.losses.sparse_categorical_crossentropy(
labels, predictions)
# Compute loss that is scaled by sample_weight and by global batch size.
loss = tf.nn.compute_average_loss(
per_example_loss,
sample_weight=sample_weight,
global_batch_size=GLOBAL_BATCH_SIZE)
# Add scaled regularization losses.
loss += tf.nn.scale_regularization_loss(tf.nn.l2_loss(weights))
return loss
```
Args:
regularization_loss: Regularization loss.
Returns:
Scalar loss value.
""" # pylint: disable=g-doc-exception
if (distribute_lib.has_strategy()
and distribute_lib.in_cross_replica_context()):
raise RuntimeError(
"You are calling `scale_regularization_loss` in cross replica context, "
"while it was expected to be called in replica context.")
num_replicas = distribute_lib.get_strategy().num_replicas_in_sync
return math_ops.reduce_sum(regularization_loss) / num_replicas
@tf_export(v1=["nn.relu_layer"])
@dispatch.add_dispatch_support
def relu_layer(x, weights, biases, name=None):
"""Computes Relu(x * weight + biases).
Args:
x: a 2D tensor. Dimensions typically: batch, in_units
weights: a 2D tensor. Dimensions typically: in_units, out_units
biases: a 1D tensor. Dimensions: out_units
name: A name for the operation (optional). If not specified
"nn_relu_layer" is used.
Returns:
A 2-D Tensor computing relu(matmul(x, weights) + biases).
Dimensions typically: batch, out_units.
"""
with ops.name_scope(name, "relu_layer", [x, weights, biases]) as name:
x = ops.convert_to_tensor(x, name="x")
weights = ops.convert_to_tensor(weights, name="weights")
biases = ops.convert_to_tensor(biases, name="biases")
xw_plus_b = nn_ops.bias_add(math_ops.matmul(x, weights), biases)
return nn_ops.relu(xw_plus_b, name=name)
@tf_export("nn.silu", "nn.swish")
@dispatch.register_unary_elementwise_api
@dispatch.add_dispatch_support
def swish(features, beta=1.0):
# pylint: disable=g-doc-args
"""Computes the SiLU or Swish activation function: `x * sigmoid(beta * x)`.
beta : Hyperparameter for Swish activation function. Default value 1.0.
The SiLU activation function was introduced in "Gaussian Error Linear Units
(GELUs)" [Hendrycks et al. 2016](https://arxiv.org/abs/1606.08415) and
"Sigmoid-Weighted Linear Units for Neural Network Function Approximation in
Reinforcement Learning"
[Elfwing et al. 2017](https://arxiv.org/abs/1702.03118) and was independently
discovered (and called swish) in "Searching for Activation Functions"
[Ramachandran et al. 2017](https://arxiv.org/abs/1710.05941)
Args:
features: A `Tensor` representing preactivation values.
beta: A 'Tensor' representing value of beta hyperparameter.
Returns:
The activation value.
"""
# pylint: enable=g-doc-args
features = ops.convert_to_tensor(features, name="features")
beta = ops.convert_to_tensor(beta, name="beta")
beta = math_ops.cast(beta, features.dtype)
@custom_gradient.custom_gradient
def swish_impl(features, beta):
def grad(dy):
"""Gradient for the Swish activation function."""
# Naively, x * tf.nn.sigmoid(x) requires keeping both x and sigmoid(x)
# around for backprop, effectively doubling the tensor's memory
# consumption. We use a control dependency here so that sigmoid(features)
# is re-computed during backprop (the control dep prevents it being
# de-duped with the forward pass) and we can free the sigmoid(features)
# expression immediately after use during the forward pass.
with ops.control_dependencies([dy]):
sigmoid_features = math_ops.sigmoid(beta * features)
activation_grad = (
sigmoid_features * (1.0 + (beta * features) *
(1.0 - sigmoid_features)))
beta_grad = math_ops.reduce_sum(
dy * math_ops.square(features) * sigmoid_features *
(1.0 - sigmoid_features))
return (dy * activation_grad, beta_grad)
return features * math_ops.sigmoid(beta * features), grad
return swish_impl(features, beta)
# pylint: disable=redefined-builtin
@tf_export("linalg.normalize")
@dispatch.add_dispatch_support
def normalize(tensor, ord="euclidean", axis=None, name=None):
"""Normalizes `tensor` along dimension `axis` using specified norm.
This uses `tf.linalg.norm` to compute the norm along `axis`.
This function can compute several different vector norms (the 1-norm, the
Euclidean or 2-norm, the inf-norm, and in general the p-norm for p > 0) and
matrix norms (Frobenius, 1-norm, 2-norm and inf-norm).
Args:
tensor: `Tensor` of types `float32`, `float64`, `complex64`, `complex128`
ord: Order of the norm. Supported values are `'fro'`, `'euclidean'`, `1`,
`2`, `np.inf` and any positive real number yielding the corresponding
p-norm. Default is `'euclidean'` which is equivalent to Frobenius norm if
`tensor` is a matrix and equivalent to 2-norm for vectors.
Some restrictions apply: a) The Frobenius norm `'fro'` is not defined for
vectors, b) If axis is a 2-tuple (matrix norm), only `'euclidean'`,
'`fro'`, `1`, `2`, `np.inf` are supported. See the description of `axis`
on how to compute norms for a batch of vectors or matrices stored in a
tensor.
axis: If `axis` is `None` (the default), the input is considered a vector
and a single vector norm is computed over the entire set of values in the
tensor, i.e. `norm(tensor, ord=ord)` is equivalent to
`norm(reshape(tensor, [-1]), ord=ord)`. If `axis` is a Python integer, the
input is considered a batch of vectors, and `axis` determines the axis in
`tensor` over which to compute vector norms. If `axis` is a 2-tuple of
Python integers it is considered a batch of matrices and `axis` determines
the axes in `tensor` over which to compute a matrix norm.
Negative indices are supported. Example: If you are passing a tensor that
can be either a matrix or a batch of matrices at runtime, pass
`axis=[-2,-1]` instead of `axis=None` to make sure that matrix norms are
computed.
name: The name of the op.
Returns:
normalized: A normalized `Tensor` with the same shape as `tensor`.
norm: The computed norms with the same shape and dtype `tensor` but the
final axis is 1 instead. Same as running
`tf.cast(tf.linalg.norm(tensor, ord, axis keepdims=True), tensor.dtype)`.
Raises:
ValueError: If `ord` or `axis` is invalid.
"""
with ops.name_scope(name, "normalize", [tensor]) as name:
tensor = ops.convert_to_tensor(tensor)
norm = linalg_ops.norm(tensor, ord, axis, keepdims=True)
norm = math_ops.cast(norm, tensor.dtype)
normalized = tensor / norm
return normalized, norm
@tf_export("math.l2_normalize", "linalg.l2_normalize", "nn.l2_normalize",
v1=["math.l2_normalize", "linalg.l2_normalize", "nn.l2_normalize"])
@dispatch.add_dispatch_support
@deprecated_args(None, "dim is deprecated, use axis instead", "dim")
def l2_normalize(x, axis=None, epsilon=1e-12, name=None, dim=None):
"""Normalizes along dimension `axis` using an L2 norm.
For a 1-D tensor with `axis = 0`, computes
output = x / sqrt(max(sum(x**2), epsilon))
For `x` with more dimensions, independently normalizes each 1-D slice along
dimension `axis`.
1-D tensor example:
>>> x = tf.constant([3.0, 4.0])
>>> tf.math.l2_normalize(x).numpy()
array([0.6, 0.8], dtype=float32)
2-D tensor example:
>>> x = tf.constant([[3.0], [4.0]])
>>> tf.math.l2_normalize(x, 0).numpy()
array([[0.6],
[0.8]], dtype=float32)
>>> x = tf.constant([[3.0], [4.0]])
>>> tf.math.l2_normalize(x, 1).numpy()
array([[1.],
[1.]], dtype=float32)
Args:
x: A `Tensor`.
axis: Dimension along which to normalize. A scalar or a vector of
integers.
epsilon: A lower bound value for the norm. Will use `sqrt(epsilon)` as the
divisor if `norm < sqrt(epsilon)`.
name: A name for this operation (optional).
dim: Deprecated, do not use.
Returns:
A `Tensor` with the same shape as `x`.
"""
axis = deprecated_argument_lookup("axis", axis, "dim", dim)
with ops.name_scope(name, "l2_normalize", [x]) as name:
x = ops.convert_to_tensor(x, name="x")
if x.dtype.is_complex:
square_real = math_ops.square(math_ops.real(x))
square_imag = math_ops.square(math_ops.imag(x))
square_sum = math_ops.real(
math_ops.reduce_sum(square_real + square_imag, axis, keepdims=True))
x_inv_norm = math_ops.rsqrt(math_ops.maximum(square_sum, epsilon))
norm_real = math_ops.multiply(math_ops.real(x), x_inv_norm)
norm_imag = math_ops.multiply(math_ops.imag(x), x_inv_norm)
return math_ops.complex(norm_real, norm_imag, name=name)
square_sum = math_ops.reduce_sum(math_ops.square(x), axis, keepdims=True)
x_inv_norm = math_ops.rsqrt(math_ops.maximum(square_sum, epsilon))
return math_ops.multiply(x, x_inv_norm, name=name)
def _count_nonzero(input_tensor, dtype=dtypes.int64):
"""Same as math_ops.count_nonzero.
The reduction is done in dtype, which can be faster for 32-bit dtypes.
Args:
input_tensor: numeric tensor
dtype: reduction dtype
Returns:
number of nonzero values with type dtype
"""
with ops.name_scope("count_nonzero", values=[input_tensor]):
zero = array_ops.zeros([], dtype=input_tensor.dtype)
nonzero_count = math_ops.reduce_sum(
math_ops.cast(
math_ops.not_equal(input_tensor, zero),
dtype=dtype), name="nonzero_count")
return nonzero_count
@tf_export("math.zero_fraction", "nn.zero_fraction")
@dispatch.add_dispatch_support
def zero_fraction(value, name=None):
"""Returns the fraction of zeros in `value`.
If `value` is empty, the result is `nan`.
This is useful in summaries to measure and report sparsity. For example,
```python
z = tf.nn.relu(...)
summ = tf.compat.v1.summary.scalar('sparsity', tf.nn.zero_fraction(z))
```
Args:
value: A tensor of numeric type.
name: A name for the operation (optional).
Returns:
The fraction of zeros in `value`, with type `float32`.
"""
with ops.name_scope(name, "zero_fraction", [value]):
value = ops.convert_to_tensor(value, name="value")
size = array_ops.size(value, out_type=dtypes.int64)
# If the count is small, we can save memory/CPU with an int32 reduction.
num_nonzero = tf_cond.cond(
size <= dtypes.int32.max,
# pylint: disable=g-long-lambda
true_fn=lambda: math_ops.cast(
_count_nonzero(value, dtype=dtypes.int32),
dtype=dtypes.int64),
false_fn=lambda: _count_nonzero(value, dtype=dtypes.int64))
with ops.name_scope("counts_to_fraction"):
num_zero = size - num_nonzero
num_zero_float32 = math_ops.cast(num_zero, dtype=dtypes.float32)
size_float32 = math_ops.cast(size, dtype=dtypes.float32)
zero_fraction_float32 = num_zero_float32 / size_float32
return array_ops.identity(zero_fraction_float32, "fraction")
# pylint: disable=redefined-builtin
@tf_export(v1=["nn.depthwise_conv2d"])
@dispatch.add_dispatch_support
def depthwise_conv2d(input,
filter,
strides,
padding,
rate=None,
name=None,
data_format=None,
dilations=None):
"""Depthwise 2-D convolution.
Given a 4D input tensor ('NHWC' or 'NCHW' data formats)
and a filter tensor of shape
`[filter_height, filter_width, in_channels, channel_multiplier]`
containing `in_channels` convolutional filters of depth 1, `depthwise_conv2d`
applies a different filter to each input channel (expanding from 1 channel
to `channel_multiplier` channels for each), then concatenates the results
together. The output has `in_channels * channel_multiplier` channels.
In detail, with the default NHWC format,
output[b, i, j, k * channel_multiplier + q] = sum_{di, dj}
filter[di, dj, k, q] * input[b, strides[1] * i + rate[0] * di,
strides[2] * j + rate[1] * dj, k]
Must have `strides[0] = strides[3] = 1`. For the most common case of the
same horizontal and vertical strides, `strides = [1, stride, stride, 1]`.
If any value in `rate` is greater than 1, we perform atrous depthwise
convolution, in which case all values in the `strides` tensor must be equal
to 1.
Usage Example:
>>> x = np.array([
... [1., 2.],
... [3., 4.],
... [5., 6.]
... ], dtype=np.float32).reshape((1, 3, 2, 1))
>>> kernel = np.array([
... [1., 2.],
... [3., 4]
... ], dtype=np.float32).reshape((2, 1, 1, 2))
>>> tf.compat.v1.nn.depthwise_conv2d(x, kernel, strides=[1, 1, 1, 1],
... padding='VALID').numpy()
array([[[[10., 14.],
[14., 20.]],
[[18., 26.],
[22., 32.]]]], dtype=float32)
>>> tf.compat.v1.nn.depthwise_conv2d(x, kernel, strides=[1, 1, 1, 1],
... padding=[[0, 0], [1, 0], [1, 0], [0, 0]]
... ).numpy()
array([[[[ 0., 0.],
[ 3., 4.],
[ 6., 8.]],
[[ 0., 0.],
[10., 14.],
[14., 20.]],
[[ 0., 0.],
[18., 26.],
[22., 32.]]]], dtype=float32)
Args:
input: 4-D with shape according to `data_format`.
filter: 4-D with shape
`[filter_height, filter_width, in_channels, channel_multiplier]`.
strides: 1-D of size 4. The stride of the sliding window for each
dimension of `input`.
padding: Controls how to pad the image before applying the convolution. Can
be the string `"SAME"` or `"VALID"` indicating the type of padding
algorithm to use, or a list indicating the explicit paddings at the start
and end of each dimension. When explicit padding is used and data_format
is `"NHWC"`, this should be in the form `[[0, 0], [pad_top, pad_bottom],
[pad_left, pad_right], [0, 0]]`. When explicit padding used and
data_format is `"NCHW"`, this should be in the form `[[0, 0], [0, 0],
[pad_top, pad_bottom], [pad_left, pad_right]]`.
rate: 1-D of size 2. The dilation rate in which we sample input values
across the `height` and `width` dimensions in atrous convolution. If it is
greater than 1, then all values of strides must be 1.
name: A name for this operation (optional).
data_format: The data format for input. Either "NHWC" (default) or "NCHW".
dilations: Alias of rate.
Returns:
A 4-D `Tensor` with shape according to `data_format`. E.g., for
"NHWC" format, shape is
`[batch, out_height, out_width, in_channels * channel_multiplier].`
"""
rate = deprecated_argument_lookup("dilations", dilations, "rate", rate)
with ops.name_scope(name, "depthwise", [input, filter]) as name:
input = ops.convert_to_tensor(input, name="tensor_in")
filter = ops.convert_to_tensor(filter, name="filter_in")
if rate is None:
rate = [1, 1]
# Use depthwise_conv2d_native if executing on TPU.
if device_context.enclosing_tpu_context() is not None:
if data_format == "NCHW":
dilations = [1, 1, rate[0], rate[1]]
else:
dilations = [1, rate[0], rate[1], 1]
return nn_ops.depthwise_conv2d_native(
input=input,
filter=filter,
strides=strides,
padding=padding,
data_format=data_format,
dilations=dilations,
name=name)
def op(input_converted, _, padding):
return nn_ops.depthwise_conv2d_native(
input=input_converted,
filter=filter,
strides=strides,
padding=padding,
data_format=data_format,
name=name)
return nn_ops.with_space_to_batch(
input=input,
filter_shape=array_ops.shape(filter),
dilation_rate=rate,
padding=padding,
data_format=data_format,
op=op)
@tf_export("nn.depthwise_conv2d", v1=[])
@dispatch.add_dispatch_support
def depthwise_conv2d_v2(input,
filter,
strides,
padding,
data_format=None,
dilations=None,
name=None):
"""Depthwise 2-D convolution.
Given a 4D input tensor ('NHWC' or 'NCHW' data formats)
and a filter tensor of shape
`[filter_height, filter_width, in_channels, channel_multiplier]`
containing `in_channels` convolutional filters of depth 1, `depthwise_conv2d`
applies a different filter to each input channel (expanding from 1 channel
to `channel_multiplier` channels for each), then concatenates the results
together. The output has `in_channels * channel_multiplier` channels.
In detail, with the default NHWC format,
output[b, i, j, k * channel_multiplier + q] =
sum_{di, dj} filter[di, dj, k, q] *
input[b, strides[1] * i + dilations[0] * di,
strides[2] * j + dilations[1] * dj, k]
Must have `strides[0] = strides[3] = 1`. For the most common case of the
same horizontal and vertical strides, `strides = [1, stride, stride, 1]`.
If any value in `dilations` is greater than 1, we perform atrous depthwise
convolution, in which case all values in the `strides` tensor must be equal
to 1.
Usage Example:
>>> x = np.array([
... [1., 2.],
... [3., 4.],
... [5., 6.]
... ], dtype=np.float32).reshape((1, 3, 2, 1))
>>> kernel = np.array([
... [1., 2.],
... [3., 4]
... ], dtype=np.float32).reshape((2, 1, 1, 2))
>>> tf.nn.depthwise_conv2d(x, kernel, strides=[1, 1, 1, 1],
... padding='VALID').numpy()
array([[[[10., 14.],
[14., 20.]],
[[18., 26.],
[22., 32.]]]], dtype=float32)
>>> tf.nn.depthwise_conv2d(x, kernel, strides=[1, 1, 1, 1],
... padding=[[0, 0], [1, 0], [1, 0], [0, 0]]).numpy()
array([[[[ 0., 0.],
[ 3., 4.],
[ 6., 8.]],
[[ 0., 0.],
[10., 14.],
[14., 20.]],
[[ 0., 0.],
[18., 26.],
[22., 32.]]]], dtype=float32)
Args:
input: 4-D with shape according to `data_format`.
filter: 4-D with shape
`[filter_height, filter_width, in_channels, channel_multiplier]`.
strides: 1-D of size 4. The stride of the sliding window for each
dimension of `input`.
padding: Controls how to pad the image before applying the convolution. Can
be the string `"SAME"` or `"VALID"` indicating the type of padding
algorithm to use, or a list indicating the explicit paddings at the start
and end of each dimension. See
[here](https://www.tensorflow.org/api_docs/python/tf/nn#notes_on_padding_2)
for more information. When explicit padding is used and data_format
is `"NHWC"`, this should be in the form `[[0, 0], [pad_top, pad_bottom],
[pad_left, pad_right], [0, 0]]`. When explicit padding used and
data_format is `"NCHW"`, this should be in the form `[[0, 0], [0, 0],
[pad_top, pad_bottom], [pad_left, pad_right]]`.
data_format: The data format for input. Either "NHWC" (default) or "NCHW".
dilations: 1-D of size 2. The dilation rate in which we sample input values
across the `height` and `width` dimensions in atrous convolution. If it is
greater than 1, then all values of strides must be 1.
name: A name for this operation (optional).
Returns:
A 4-D `Tensor` with shape according to `data_format`. E.g., for
"NHWC" format, shape is
`[batch, out_height, out_width, in_channels * channel_multiplier].`
"""
return depthwise_conv2d(input=input,
filter=filter,
strides=strides,
padding=padding,
rate=dilations,
name=name,
data_format=data_format)
# pylint: enable=redefined-builtin
# pylint: disable=redefined-builtin,line-too-long
@tf_export(v1=["nn.separable_conv2d"])
@dispatch.add_dispatch_support
def separable_conv2d(input,
depthwise_filter,
pointwise_filter,
strides,
padding,
rate=None,
name=None,
data_format=None,
dilations=None):
"""2-D convolution with separable filters.
Performs a depthwise convolution that acts separately on channels followed by
a pointwise convolution that mixes channels. Note that this is separability
between dimensions `[1, 2]` and `3`, not spatial separability between
dimensions `1` and `2`.
In detail, with the default NHWC format,
output[b, i, j, k] = sum_{di, dj, q, r}
input[b, strides[1] * i + di, strides[2] * j + dj, q] *
depthwise_filter[di, dj, q, r] *
pointwise_filter[0, 0, q * channel_multiplier + r, k]
`strides` controls the strides for the depthwise convolution only, since
the pointwise convolution has implicit strides of `[1, 1, 1, 1]`. Must have
`strides[0] = strides[3] = 1`. For the most common case of the same
horizontal and vertical strides, `strides = [1, stride, stride, 1]`.
If any value in `rate` is greater than 1, we perform atrous depthwise
convolution, in which case all values in the `strides` tensor must be equal
to 1.
Args:
input: 4-D `Tensor` with shape according to `data_format`.
depthwise_filter: 4-D `Tensor` with shape
`[filter_height, filter_width, in_channels, channel_multiplier]`.
Contains `in_channels` convolutional filters of depth 1.
pointwise_filter: 4-D `Tensor` with shape
`[1, 1, channel_multiplier * in_channels, out_channels]`. Pointwise
filter to mix channels after `depthwise_filter` has convolved spatially.
strides: 1-D of size 4. The strides for the depthwise convolution for
each dimension of `input`.
padding: Controls how to pad the image before applying the depthwise
convolution. Can be the string `"SAME"` or `"VALID"` indicating the type
of padding algorithm to use, or a Python list indicating the explicit
paddings at the start and end of each dimension. When explicit padding is
used and data_format is `"NHWC"`, this should be in the form `[[0, 0],
[pad_top, pad_bottom], [pad_left, pad_right], [0, 0]]`. When explicit
padding used and data_format is `"NCHW"`, this should be in the form
`[[0, 0], [0, 0], [pad_top, pad_bottom], [pad_left, pad_right]]`.
rate: 1-D of size 2. The dilation rate in which we sample input values
across the `height` and `width` dimensions in atrous convolution. If it is
greater than 1, then all values of strides must be 1.
name: A name for this operation (optional).
data_format: The data format for input. Either "NHWC" (default) or "NCHW".
dilations: Alias of rate.
Returns:
A 4-D `Tensor` with shape according to 'data_format'. For
example, with data_format="NHWC", shape is [batch, out_height,
out_width, out_channels].
"""
rate = deprecated_argument_lookup("dilations", dilations, "rate", rate)
with ops.name_scope(name, "separable_conv2d",
[input, depthwise_filter, pointwise_filter]) as name:
input = ops.convert_to_tensor(input, name="tensor_in")
depthwise_filter = ops.convert_to_tensor(
depthwise_filter, name="depthwise_filter")
pointwise_filter = ops.convert_to_tensor(
pointwise_filter, name="pointwise_filter")
pointwise_filter_shape = pointwise_filter.get_shape().with_rank(4)
pointwise_filter_shape.dims[0].assert_is_compatible_with(1)
pointwise_filter_shape.dims[1].assert_is_compatible_with(1)
if rate is None:
rate = [1, 1]
# The layout of the ops in the graph are expected to be as follows:
# depthwise_conv2d // Conv2D op corresponding to native depthwise conv.
# separable_conv2d // Conv2D op corresponding to the pointwise conv.
def op(input_converted, _, padding):
return nn_ops.depthwise_conv2d_native(
input=input_converted,
filter=depthwise_filter,
strides=strides,
padding=padding,
data_format=data_format,
name="depthwise")
depthwise = nn_ops.with_space_to_batch(
input=input,
filter_shape=array_ops.shape(depthwise_filter),
dilation_rate=rate,
padding=padding,
data_format=data_format,
op=op)
return nn_ops.conv2d(
depthwise,
pointwise_filter, [1, 1, 1, 1],
padding="VALID",
data_format=data_format,
name=name)
@tf_export("nn.separable_conv2d", v1=[])
@dispatch.add_dispatch_support
def separable_conv2d_v2(
input,
depthwise_filter,
pointwise_filter,
strides,
padding,
data_format=None,
dilations=None,
name=None,
):
"""2-D convolution with separable filters.
Performs a depthwise convolution that acts separately on channels followed by
a pointwise convolution that mixes channels. Note that this is separability
between dimensions `[1, 2]` and `3`, not spatial separability between
dimensions `1` and `2`.
In detail, with the default NHWC format,
output[b, i, j, k] = sum_{di, dj, q, r}
input[b, strides[1] * i + di, strides[2] * j + dj, q] *
depthwise_filter[di, dj, q, r] *
pointwise_filter[0, 0, q * channel_multiplier + r, k]
`strides` controls the strides for the depthwise convolution only, since
the pointwise convolution has implicit strides of `[1, 1, 1, 1]`. Must have
`strides[0] = strides[3] = 1`. For the most common case of the same
horizontal and vertical strides, `strides = [1, stride, stride, 1]`.
If any value in `rate` is greater than 1, we perform atrous depthwise
convolution, in which case all values in the `strides` tensor must be equal
to 1.
Args:
input: 4-D `Tensor` with shape according to `data_format`.
depthwise_filter: 4-D `Tensor` with shape `[filter_height, filter_width,
in_channels, channel_multiplier]`. Contains `in_channels` convolutional
filters of depth 1.
pointwise_filter: 4-D `Tensor` with shape `[1, 1, channel_multiplier *
in_channels, out_channels]`. Pointwise filter to mix channels after
`depthwise_filter` has convolved spatially.
strides: 1-D of size 4. The strides for the depthwise convolution for each
dimension of `input`.
padding: Controls how to pad the image before applying the depthwise
convolution. Can be the string `"SAME"` or `"VALID"` indicating the type
of padding algorithm to use, or a Python list indicating the explicit
paddings at the start and end of each dimension. When explicit padding is
used and data_format is `"NHWC"`, this should be in the form `[[0, 0],
[pad_top, pad_bottom], [pad_left, pad_right], [0, 0]]`. When explicit
padding used and data_format is `"NCHW"`, this should be in the form
`[[0, 0], [0, 0], [pad_top, pad_bottom], [pad_left, pad_right]]`.
data_format: The data format for input. Either "NHWC" (default) or "NCHW".
dilations: 1-D of size 2. The dilation rate in which we sample input values
across the `height` and `width` dimensions in atrous convolution. If it is
greater than 1, then all values of strides must be 1.
name: A name for this operation (optional).
Returns:
A 4-D `Tensor` with shape according to 'data_format'. For
example, with data_format="NHWC", shape is [batch, out_height,
out_width, out_channels].
"""
return separable_conv2d(
input,
depthwise_filter,
pointwise_filter,
strides,
padding,
rate=dilations,
name=name,
data_format=data_format)
# pylint: enable=redefined-builtin,line-too-long
@tf_export(v1=["nn.sufficient_statistics"])
@dispatch.add_dispatch_support
def sufficient_statistics(x, axes, shift=None, keep_dims=None, name=None,
keepdims=None):
"""Calculate the sufficient statistics for the mean and variance of `x`.
These sufficient statistics are computed using the one pass algorithm on
an input that's optionally shifted. See:
https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Computing_shifted_data
For example:
>>> t = [[1, 2, 3], [4, 5, 6]]
>>> sufficient_statistics(t, [1])
(<tf.Tensor: shape=(), dtype=int32, numpy=3>, <tf.Tensor: shape=(2,),
dtype=int32, numpy=array([ 6, 15], dtype=int32)>, <tf.Tensor: shape=(2,),
dtype=int32, numpy=array([14, 77], dtype=int32)>, None)
>>> sufficient_statistics(t, [-1])
(<tf.Tensor: shape=(), dtype=int32, numpy=3>, <tf.Tensor: shape=(2,),
dtype=int32, numpy=array([ 6, 15], dtype=int32)>, <tf.Tensor: shape=(2,),
dtype=int32, numpy=array([14, 77], dtype=int32)>, None)
Args:
x: A `Tensor`.
axes: Array of ints. Axes along which to compute mean and variance. As in
Python, the axes can also be negative numbers. A negative axis is
interpreted as counting from the end of the rank, i.e., axis +
rank(values)-th dimension.
shift: A `Tensor` containing the value by which to shift the data for
numerical stability, or `None` if no shift is to be performed. A shift
close to the true mean provides the most numerically stable results.
keep_dims: produce statistics with the same dimensionality as the input.
name: Name used to scope the operations that compute the sufficient stats.
keepdims: Alias for keep_dims.
Returns:
Four `Tensor` objects of the same type as `x`:
* the count (number of elements to average over).
* the (possibly shifted) sum of the elements in the array.
* the (possibly shifted) sum of squares of the elements in the array.
* the shift by which the mean must be corrected or None if `shift` is None.
"""
axes = list(set(axes))
keep_dims = deprecated_argument_lookup(
"keepdims", keepdims, "keep_dims", keep_dims)
if keep_dims is None:
keep_dims = False
with ops.name_scope(name, "sufficient_statistics", [x, shift]):
x = ops.convert_to_tensor(x, name="x")
x_shape = x.get_shape()
if x_shape.rank is not None and all(
x_shape.dims[d].value is not None for d in axes):
counts = 1
for d in axes:
counts *= x_shape.dims[d].value
counts = constant_op.constant(counts, dtype=x.dtype)
else: # shape needs to be inferred at runtime.
# Normalize axes to be positive. Required for gather.
rank = array_ops.rank(x)
positive_axes = [axis + rank if axis < 0 else axis for axis in axes]
x_dims = array_ops.gather(
math_ops.cast(array_ops.shape(x), x.dtype), positive_axes)
counts = math_ops.reduce_prod(x_dims, name="count")
if shift is not None:
shift = ops.convert_to_tensor(shift, name="shift")
m_ss = math_ops.subtract(x, shift)
v_ss = math_ops.squared_difference(x, shift)
else: # no shift.
m_ss = x
v_ss = math_ops.square(x)
m_ss = math_ops.reduce_sum(m_ss, axes, keepdims=keep_dims, name="mean_ss")
v_ss = math_ops.reduce_sum(v_ss, axes, keepdims=keep_dims, name="var_ss")
return counts, m_ss, v_ss, shift
@tf_export("nn.sufficient_statistics", v1=[])
@dispatch.add_dispatch_support
def sufficient_statistics_v2(x, axes, shift=None, keepdims=False, name=None):
"""Calculate the sufficient statistics for the mean and variance of `x`.
These sufficient statistics are computed using the one pass algorithm on
an input that's optionally shifted. See:
https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Computing_shifted_data
Args:
x: A `Tensor`.
axes: Array of ints. Axes along which to compute mean and variance.
shift: A `Tensor` containing the value by which to shift the data for
numerical stability, or `None` if no shift is to be performed. A shift
close to the true mean provides the most numerically stable results.
keepdims: produce statistics with the same dimensionality as the input.
name: Name used to scope the operations that compute the sufficient stats.
Returns:
Four `Tensor` objects of the same type as `x`:
* the count (number of elements to average over).
* the (possibly shifted) sum of the elements in the array.
* the (possibly shifted) sum of squares of the elements in the array.
* the shift by which the mean must be corrected or None if `shift` is None.
"""
return sufficient_statistics(
x=x, axes=axes, shift=shift, keep_dims=keepdims, name=name)
@tf_export("nn.normalize_moments")
@dispatch.add_dispatch_support
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 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)
@tf_export(v1=["nn.moments"])
@dispatch.add_dispatch_support
def moments(
x,
axes,
shift=None, # pylint: disable=unused-argument
name=None,
keep_dims=None,
keepdims=None):
"""Calculate the mean and variance of `x`.
The mean and variance are calculated by aggregating the contents of `x`
across `axes`. If `x` is 1-D and `axes = [0]` this is just the mean
and variance of a vector.
Note: shift is currently not used; the true mean is computed and used.
When using these moments for batch normalization (see
`tf.nn.batch_normalization`):
* for so-called "global normalization", used with convolutional filters with
shape `[batch, height, width, depth]`, pass `axes=[0, 1, 2]`.
* for simple batch normalization pass `axes=[0]` (batch only).
Args:
x: A `Tensor`.
axes: Array of ints. Axes along which to compute mean and
variance.
shift: Not used in the current implementation
name: Name used to scope the operations that compute the moments.
keep_dims: produce moments with the same dimensionality as the input.
keepdims: Alias to keep_dims.
Returns:
Two `Tensor` objects: `mean` and `variance`.
"""
keep_dims = deprecated_argument_lookup(
"keepdims", keepdims, "keep_dims", keep_dims)
if keep_dims is None:
keep_dims = False
with ops.name_scope(name, "moments", [x, axes]):
# The dynamic range of fp16 is too limited to support the collection of
# sufficient statistics. As a workaround we simply perform the operations
# on 32-bit floats before converting the mean and variance back to fp16
y = math_ops.cast(x, dtypes.float32) if x.dtype == dtypes.float16 else x
# Compute true mean while keeping the dims for proper broadcasting.
mean = math_ops.reduce_mean(y, axes, keepdims=True, name="mean")
# sample variance, not unbiased variance
# Note: stop_gradient does not change the gradient that gets
# backpropagated to the mean from the variance calculation,
# because that gradient is zero
variance = math_ops.reduce_mean(
math_ops.squared_difference(y, array_ops.stop_gradient(mean)),
axes,
keepdims=True,
name="variance")
if not keep_dims:
mean = array_ops.squeeze(mean, axes)
variance = array_ops.squeeze(variance, axes)
if x.dtype == dtypes.float16:
return (math_ops.cast(mean, dtypes.float16),
math_ops.cast(variance, dtypes.float16))
else:
return (mean, variance)
@tf_export("nn.moments", v1=[])
@dispatch.add_dispatch_support
def moments_v2(
x,
axes,
shift=None,
keepdims=False,
name=None):
"""Calculates the mean and variance of `x`.
The mean and variance are calculated by aggregating the contents of `x`
across `axes`. If `x` is 1-D and `axes = [0]` this is just the mean
and variance of a vector.
Note: shift is currently not used; the true mean is computed and used.
When using these moments for batch normalization (see
`tf.nn.batch_normalization`):
* for so-called "global normalization", used with convolutional filters with
shape `[batch, height, width, depth]`, pass `axes=[0, 1, 2]`.
* for simple batch normalization pass `axes=[0]` (batch only).
Args:
x: A `Tensor`.
axes: Array of ints. Axes along which to compute mean and
variance.
shift: Not used in the current implementation.
keepdims: produce moments with the same dimensionality as the input.
name: Name used to scope the operations that compute the moments.
Returns:
Two `Tensor` objects: `mean` and `variance`.
"""
return moments(x=x, axes=axes, shift=shift, name=name, keep_dims=keepdims)
@tf_export(v1=["nn.weighted_moments"])
@dispatch.add_dispatch_support
def weighted_moments(x, axes, frequency_weights, name=None, keep_dims=None,
keepdims=None):
"""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.
keepdims: Alias of keep_dims.
Returns:
Two tensors: `weighted_mean` and `weighted_variance`.
"""
keep_dims = deprecated_argument_lookup(
"keepdims", keepdims, "keep_dims", keep_dims)
if keep_dims is None:
keep_dims = False
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", keepdims=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 (frequency_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)
weighted_mean = math_ops.div_no_nan(weighted_input_sum, sum_of_weights)
# 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)
weighted_variance = math_ops.div_no_nan(weighted_distsq, sum_of_weights)
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
@tf_export("nn.weighted_moments", v1=[])
@dispatch.add_dispatch_support
def weighted_moments_v2(x, axes, frequency_weights, keepdims=False, name=None):
"""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.
keepdims: Produce moments with the same dimensionality as the input.
name: Name used to scope the operation.
Returns:
Two tensors: `weighted_mean` and `weighted_variance`.
"""
return weighted_moments(
x=x,
axes=axes,
frequency_weights=frequency_weights,
name=name,
keep_dims=keepdims)
@tf_export("nn.batch_normalization")
@dispatch.add_dispatch_support
def batch_normalization(x,
mean,
variance,
offset,
scale,
variance_epsilon,
name=None):
r"""Batch normalization.
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(..., keepdims=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(..., keepdims=False)` during training, or running averages
thereof during inference.
See equation 11 in Algorithm 2 of source:
[Batch Normalization: Accelerating Deep Network Training by
Reducing Internal Covariate Shift; S. Ioffe, C. Szegedy]
(http://arxiv.org/abs/1502.03167).
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.
References:
Batch Normalization - Accelerating Deep Network Training by Reducing
Internal Covariate Shift:
[Ioffe et al., 2015](http://arxiv.org/abs/1502.03167)
([pdf](http://proceedings.mlr.press/v37/ioffe15.pdf))
"""
with ops.name_scope(name, "batchnorm", [x, mean, variance, scale, offset]):
inv = math_ops.rsqrt(variance + variance_epsilon)
if scale is not None:
inv *= scale
# Note: tensorflow/contrib/quantize/python/fold_batch_norms.py depends on
# the precise order of ops that are generated by the expression below.
return x * math_ops.cast(inv, x.dtype) + math_ops.cast(
offset - mean * inv if offset is not None else -mean * inv, x.dtype)
@tf_export(v1=["nn.fused_batch_norm"])
@dispatch.add_dispatch_support
def fused_batch_norm(
x,
scale,
offset, # pylint: disable=invalid-name
mean=None,
variance=None,
epsilon=0.001,
data_format="NHWC",
is_training=True,
name=None,
exponential_avg_factor=1.0):
r"""Batch normalization.
See Source: [Batch Normalization: Accelerating Deep Network Training by
Reducing Internal Covariate Shift; S. Ioffe, C. Szegedy]
(http://arxiv.org/abs/1502.03167).
Args:
x: Input `Tensor` of 4 or 5 dimensions.
scale: A `Tensor` of 1 dimension for scaling.
offset: A `Tensor` of 1 dimension for bias.
mean: A `Tensor` of 1 dimension for population mean. The shape and meaning
of this argument depends on the value of is_training and
exponential_avg_factor as follows:
is_training==False (inference):
Mean must be a `Tensor` of the same shape as scale containing the
estimated population mean computed during training.
is_training==True and exponential_avg_factor == 1.0:
Mean must be None.
is_training==True and exponential_avg_factor != 1.0:
Mean must be a `Tensor` of the same shape as scale containing the
exponential running mean.
variance: A `Tensor` of 1 dimension for population variance. The shape and
meaning of this argument depends on the value of is_training and
exponential_avg_factor as follows:
is_training==False (inference):
Variance must be a `Tensor` of the same shape as scale containing
the estimated population variance computed during training.
is_training==True and exponential_avg_factor == 1.0:
Variance must be None.
is_training==True and exponential_avg_factor != 1.0:
Variance must be a `Tensor` of the same shape as scale containing
the exponential running variance.
epsilon: A small float number added to the variance of x.
data_format: The data format for x. Support "NHWC" (default) or "NCHW" for
4D tenors and "NDHWC" or "NCDHW" for 5D tensors.
is_training: A bool value to specify if the operation is used for
training or inference.
name: A name for this operation (optional).
exponential_avg_factor: A float number (usually between 0 and 1) used
for controlling the decay of the running
population average of mean and variance.
If set to 1.0, the current batch average is
returned.
Returns:
y: A 4D or 5D Tensor for the normalized, scaled, offsetted x.
running_mean: A 1D Tensor for the exponential running mean of x.
The output value is (1 - exponential_avg_factor) * mean +
exponential_avg_factor * batch_mean), where batch_mean
is the mean of the current batch in x.
running_var: A 1D Tensor for the exponential running variance
The output value is (1 - exponential_avg_factor) * variance +
exponential_avg_factor * batch_variance), where batch_variance
is the variance of the current batch in x.
References:
Batch Normalization - Accelerating Deep Network Training by Reducing
Internal Covariate Shift:
[Ioffe et al., 2015](http://proceedings.mlr.press/v37/ioffe15.html)
([pdf](http://proceedings.mlr.press/v37/ioffe15.pdf))
"""
if (not is_training or exponential_avg_factor != 1.0) and (
(mean is None) or (variance is None)):
raise ValueError("Both `mean` and `variance` must be a 1D tensor when "
"`is_training` is False or `exponential_avg_factor` != "
f"1.0. Received: `mean` {mean!r} and `variance` "
f"{variance!r}")
x = ops.convert_to_tensor(x, name="input")
scale = ops.convert_to_tensor(scale, name="scale")
offset = ops.convert_to_tensor(offset, name="offset")
if mean is None:
mean = constant_op.constant([])
if variance is None:
variance = constant_op.constant([])
y, running_mean, running_var, _, _, _ = gen_nn_ops.fused_batch_norm_v3(
x,
scale,
offset,
mean,
variance,
epsilon=epsilon,
exponential_avg_factor=exponential_avg_factor,
data_format=data_format,
is_training=is_training,
name=name)
return y, running_mean, running_var
@tf_export(v1=["nn.batch_norm_with_global_normalization"])
@dispatch.add_dispatch_support
def batch_norm_with_global_normalization(t=None,
m=None,
v=None,
beta=None,
gamma=None,
variance_epsilon=None,
scale_after_normalization=None,
name=None,
input=None, # pylint: disable=redefined-builtin
mean=None,
variance=None):
"""Batch normalization.
This op is deprecated. See `tf.nn.batch_normalization`.
Args:
t: A 4D input Tensor.
m: A 1D mean Tensor with size matching the last dimension of t.
This is the first output from tf.nn.moments,
or a saved moving average thereof.
v: A 1D variance Tensor with size matching the last dimension of t.
This is the second output from tf.nn.moments,
or a saved moving average thereof.
beta: A 1D beta Tensor with size matching the last dimension of t.
An offset to be added to the normalized tensor.
gamma: A 1D gamma Tensor with size matching the last dimension of t.
If "scale_after_normalization" is true, this tensor will be multiplied
with the normalized tensor.
variance_epsilon: A small float number to avoid dividing by 0.
scale_after_normalization: A bool indicating whether the resulted tensor
needs to be multiplied with gamma.
name: A name for this operation (optional).
input: Alias for t.
mean: Alias for m.
variance: Alias for v.
Returns:
A batch-normalized `t`.
References:
Batch Normalization - Accelerating Deep Network Training by Reducing
Internal Covariate Shift:
[Ioffe et al., 2015](http://proceedings.mlr.press/v37/ioffe15.html)
([pdf](http://proceedings.mlr.press/v37/ioffe15.pdf))
"""
t = deprecated_argument_lookup("input", input, "t", t)
m = deprecated_argument_lookup("mean", mean, "m", m)
v = deprecated_argument_lookup("variance", variance, "v", v)
return batch_normalization(t, m, v, beta, gamma if scale_after_normalization
else None, variance_epsilon, name)
# pylint: disable=redefined-builtin,line-too-long
@tf_export("nn.batch_norm_with_global_normalization", v1=[])
@dispatch.add_dispatch_support
def batch_norm_with_global_normalization_v2(input,
mean,
variance,
beta,
gamma,
variance_epsilon,
scale_after_normalization,
name=None):
"""Batch normalization.
This op is deprecated. See `tf.nn.batch_normalization`.
Args:
input: A 4D input Tensor.
mean: A 1D mean Tensor with size matching the last dimension of t.
This is the first output from tf.nn.moments,
or a saved moving average thereof.
variance: A 1D variance Tensor with size matching the last dimension of t.
This is the second output from tf.nn.moments,
or a saved moving average thereof.
beta: A 1D beta Tensor with size matching the last dimension of t.
An offset to be added to the normalized tensor.
gamma: A 1D gamma Tensor with size matching the last dimension of t.
If "scale_after_normalization" is true, this tensor will be multiplied
with the normalized tensor.
variance_epsilon: A small float number to avoid dividing by 0.
scale_after_normalization: A bool indicating whether the resulted tensor
needs to be multiplied with gamma.
name: A name for this operation (optional).
Returns:
A batch-normalized `t`.
References:
Batch Normalization - Accelerating Deep Network Training by Reducing Internal Covariate Shift:
[Ioffe et al., 2015](http://proceedings.mlr.press/v37/ioffe15.html)
([pdf](http://proceedings.mlr.press/v37/ioffe15.pdf))
"""
return batch_norm_with_global_normalization(t=input,
m=mean,
v=variance,
beta=beta,
gamma=gamma,
variance_epsilon=variance_epsilon,
scale_after_normalization=scale_after_normalization,
name=name)
# pylint: enable=redefined-builtin,line-too-long
def _sum_rows(x):
"""Returns a vector summing up each row of the matrix x."""
# _sum_rows(x) is equivalent to math_ops.reduce_sum(x, 1) when x is
# a matrix. The gradient of _sum_rows(x) is more efficient than
# reduce_sum(x, 1)'s gradient in today's implementation. Therefore,
# we use _sum_rows(x) in the nce_loss() computation since the loss
# is mostly used for training.
cols = array_ops.shape(x)[1]
ones_shape = array_ops_stack.stack([cols, 1])
ones = array_ops.ones(ones_shape, x.dtype)
return array_ops.reshape(math_ops.matmul(x, ones), [-1])
def _compute_sampled_logits(weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=1,
sampled_values=None,
subtract_log_q=True,
remove_accidental_hits=False,
partition_strategy="mod",
name=None,
seed=None):
"""Helper function for nce_loss and sampled_softmax_loss functions.
Computes sampled output training logits and labels suitable for implementing
e.g. noise-contrastive estimation (see nce_loss) or sampled softmax (see
sampled_softmax_loss).
Note: In the case where num_true > 1, we assign to each target class
the target probability 1 / num_true so that the target probabilities
sum to 1 per-example.
Args:
weights: A `Tensor` of shape `[num_classes, dim]`, or a list of `Tensor`
objects whose concatenation along dimension 0 has shape
`[num_classes, dim]`. The (possibly-partitioned) class embeddings.
biases: A `Tensor` of shape `[num_classes]`. The (possibly-partitioned)
class biases.
labels: A `Tensor` of type `int64` and shape `[batch_size,
num_true]`. The target classes. Note that this format differs from
the `labels` argument of `nn.softmax_cross_entropy_with_logits`.
inputs: A `Tensor` of shape `[batch_size, dim]`. The forward
activations of the input network.
num_sampled: An `int`. The number of classes to randomly sample per batch.
num_classes: An `int`. The number of possible classes.
num_true: An `int`. The number of target classes per training example.
sampled_values: a tuple of (`sampled_candidates`, `true_expected_count`,
`sampled_expected_count`) returned by a `*_candidate_sampler` function.
(if None, we default to `log_uniform_candidate_sampler`)
subtract_log_q: A `bool`. whether to subtract the log expected count of
the labels in the sample to get the logits of the true labels.
Default is True. Turn off for Negative Sampling.
remove_accidental_hits: A `bool`. whether to remove "accidental hits"
where a sampled class equals one of the target classes. Default is
False.
partition_strategy: A string specifying the partitioning strategy, relevant
if `len(weights) > 1`. Currently `"div"` and `"mod"` are supported.
Default is `"mod"`. See `tf.nn.embedding_lookup` for more details.
name: A name for the operation (optional).
seed: random seed for candidate sampling. Default to None, which doesn't set
the op-level random seed for candidate sampling.
Returns:
out_logits: `Tensor` object with shape
`[batch_size, num_true + num_sampled]`, for passing to either
`nn.sigmoid_cross_entropy_with_logits` (NCE) or
`nn.softmax_cross_entropy_with_logits` (sampled softmax).
out_labels: A Tensor object with the same shape as `out_logits`.
"""
if isinstance(weights, variables.PartitionedVariable):
weights = list(weights)
if not isinstance(weights, list):
weights = [weights]
with ops.name_scope(name, "compute_sampled_logits",
weights + [biases, inputs, labels]):
if labels.dtype != dtypes.int64:
labels = math_ops.cast(labels, dtypes.int64)
labels_flat = array_ops.reshape(labels, [-1])
# Sample the negative labels.
# sampled shape: [num_sampled] tensor
# true_expected_count shape = [batch_size, 1] tensor
# sampled_expected_count shape = [num_sampled] tensor
if sampled_values is None:
sampled_values = candidate_sampling_ops.log_uniform_candidate_sampler(
true_classes=labels,
num_true=num_true,
num_sampled=num_sampled,
unique=True,
range_max=num_classes,
seed=seed)
# NOTE: pylint cannot tell that 'sampled_values' is a sequence
# pylint: disable=unpacking-non-sequence
sampled, true_expected_count, sampled_expected_count = (
array_ops.stop_gradient(s) for s in sampled_values)
# pylint: enable=unpacking-non-sequence
sampled = math_ops.cast(sampled, dtypes.int64)
# labels_flat is a [batch_size * num_true] tensor
# sampled is a [num_sampled] int tensor
all_ids = array_ops.concat([labels_flat, sampled], 0)
# Retrieve the true weights and the logits of the sampled weights.
# weights shape is [num_classes, dim]
all_w = embedding_ops.embedding_lookup(
weights, all_ids, partition_strategy=partition_strategy)
if all_w.dtype != inputs.dtype:
all_w = math_ops.cast(all_w, inputs.dtype)
# true_w shape is [batch_size * num_true, dim]
true_w = array_ops.slice(all_w, [0, 0],
array_ops_stack.stack(
[array_ops.shape(labels_flat)[0], -1]))
sampled_w = array_ops.slice(
all_w,
array_ops_stack.stack([array_ops.shape(labels_flat)[0], 0]), [-1, -1])
# inputs has shape [batch_size, dim]
# sampled_w has shape [num_sampled, dim]
# Apply X*W', which yields [batch_size, num_sampled]
sampled_logits = math_ops.matmul(inputs, sampled_w, transpose_b=True)
# Retrieve the true and sampled biases, compute the true logits, and
# add the biases to the true and sampled logits.
all_b = embedding_ops.embedding_lookup(
biases, all_ids, partition_strategy=partition_strategy)
if all_b.dtype != inputs.dtype:
all_b = math_ops.cast(all_b, inputs.dtype)
# true_b is a [batch_size * num_true] tensor
# sampled_b is a [num_sampled] float tensor
true_b = array_ops.slice(all_b, [0], array_ops.shape(labels_flat))
sampled_b = array_ops.slice(all_b, array_ops.shape(labels_flat), [-1])
# inputs shape is [batch_size, dim]
# true_w shape is [batch_size * num_true, dim]
# row_wise_dots is [batch_size, num_true, dim]
dim = array_ops.shape(true_w)[1:2]
new_true_w_shape = array_ops.concat([[-1, num_true], dim], 0)
row_wise_dots = math_ops.multiply(
array_ops.expand_dims(inputs, 1),
array_ops.reshape(true_w, new_true_w_shape))
# We want the row-wise dot plus biases which yields a
# [batch_size, num_true] tensor of true_logits.
dots_as_matrix = array_ops.reshape(row_wise_dots,
array_ops.concat([[-1], dim], 0))
true_logits = array_ops.reshape(_sum_rows(dots_as_matrix), [-1, num_true])
true_b = array_ops.reshape(true_b, [-1, num_true])
true_logits += true_b
sampled_logits += sampled_b
if remove_accidental_hits:
acc_hits = candidate_sampling_ops.compute_accidental_hits(
labels, sampled, num_true=num_true)
acc_indices, acc_ids, acc_weights = acc_hits
# This is how SparseToDense expects the indices.
acc_indices_2d = array_ops.reshape(acc_indices, [-1, 1])
acc_ids_2d_int32 = array_ops.reshape(
math_ops.cast(acc_ids, dtypes.int32), [-1, 1])
sparse_indices = array_ops.concat([acc_indices_2d, acc_ids_2d_int32], 1,
"sparse_indices")
# Create sampled_logits_shape = [batch_size, num_sampled]
sampled_logits_shape = array_ops.concat(
[array_ops.shape(labels)[:1],
array_ops.expand_dims(num_sampled, 0)], 0)
if sampled_logits.dtype != acc_weights.dtype:
acc_weights = math_ops.cast(acc_weights, sampled_logits.dtype)
sampled_logits += gen_sparse_ops.sparse_to_dense(
sparse_indices,
sampled_logits_shape,
acc_weights,
default_value=0.0,
validate_indices=False)
if subtract_log_q:
# Subtract log of Q(l), prior probability that l appears in sampled.
true_logits -= math_ops.log(true_expected_count)
sampled_logits -= math_ops.log(sampled_expected_count)
# Construct output logits and labels. The true labels/logits start at col 0.
out_logits = array_ops.concat([true_logits, sampled_logits], 1)
# true_logits is a float tensor, ones_like(true_logits) is a float
# tensor of ones. We then divide by num_true to ensure the per-example
# labels sum to 1.0, i.e. form a proper probability distribution.
out_labels = array_ops.concat([
array_ops.ones_like(true_logits) / num_true,
array_ops.zeros_like(sampled_logits)
], 1)
return out_logits, out_labels
@tf_export("nn.nce_loss", v1=[])
@dispatch.add_dispatch_support
def nce_loss_v2(weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=1,
sampled_values=None,
remove_accidental_hits=False,
name="nce_loss"):
"""Computes and returns the noise-contrastive estimation training loss.
See [Noise-contrastive estimation: A new estimation principle for
unnormalized statistical
models](https://arxiv.org/abs/1806.03664).
Also see our [Candidate Sampling Algorithms
Reference](https://www.tensorflow.org/extras/candidate_sampling.pdf)
A common use case is to use this method for training, and calculate the full
sigmoid loss for evaluation or inference as in the following example:
```python
if mode == "train":
loss = tf.nn.nce_loss(
weights=weights,
biases=biases,
labels=labels,
inputs=inputs,
...)
elif mode == "eval":
logits = tf.matmul(inputs, tf.transpose(weights))
logits = tf.nn.bias_add(logits, biases)
labels_one_hot = tf.one_hot(labels, n_classes)
loss = tf.nn.sigmoid_cross_entropy_with_logits(
labels=labels_one_hot,
logits=logits)
loss = tf.reduce_sum(loss, axis=1)
```
Note: when doing embedding lookup on `weights` and `bias`, "div" partition
strategy will be used. Support for other partition strategy will be added
later.
Note: By default this uses a log-uniform (Zipfian) distribution for sampling,
so your labels must be sorted in order of decreasing frequency to achieve
good results. For more details, see
`tf.random.log_uniform_candidate_sampler`.
Note: In the case where `num_true` > 1, we assign to each target class
the target probability 1 / `num_true` so that the target probabilities
sum to 1 per-example.
Note: It would be useful to allow a variable number of target classes per
example. We hope to provide this functionality in a future release.
For now, if you have a variable number of target classes, you can pad them
out to a constant number by either repeating them or by padding
with an otherwise unused class.
Args:
weights: A `Tensor` of shape `[num_classes, dim]`, or a list of `Tensor`
objects whose concatenation along dimension 0 has shape [num_classes,
dim]. The (possibly-partitioned) class embeddings.
biases: A `Tensor` of shape `[num_classes]`. The class biases.
labels: A `Tensor` of type `int64` and shape `[batch_size, num_true]`. The
target classes.
inputs: A `Tensor` of shape `[batch_size, dim]`. The forward activations of
the input network.
num_sampled: An `int`. The number of negative classes to randomly sample
per batch. This single sample of negative classes is evaluated for each
element in the batch.
num_classes: An `int`. The number of possible classes.
num_true: An `int`. The number of target classes per training example.
sampled_values: a tuple of (`sampled_candidates`, `true_expected_count`,
`sampled_expected_count`) returned by a `*_candidate_sampler` function.
(if None, we default to `log_uniform_candidate_sampler`)
remove_accidental_hits: A `bool`. Whether to remove "accidental hits"
where a sampled class equals one of the target classes. If set to `True`,
this is a "Sampled Logistic" loss instead of NCE, and we are learning to
generate log-odds instead of log probabilities. See our [Candidate
Sampling Algorithms Reference]
(https://www.tensorflow.org/extras/candidate_sampling.pdf). Default is
False.
name: A name for the operation (optional).
Returns:
A `batch_size` 1-D tensor of per-example NCE losses.
"""
# TODO(yuefengz): get partition_strategy from either variables or distribution
# strategies.
return nce_loss(
weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=num_true,
sampled_values=sampled_values,
remove_accidental_hits=remove_accidental_hits,
partition_strategy="div",
name=name)
@tf_export(v1=["nn.nce_loss"])
@dispatch.add_dispatch_support
def nce_loss(weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=1,
sampled_values=None,
remove_accidental_hits=False,
partition_strategy="mod",
name="nce_loss"):
"""Computes and returns the noise-contrastive estimation training loss.
A common use case is to use this method for training, and calculate the full
sigmoid loss for evaluation or inference. In this case, you must set
`partition_strategy="div"` for the two losses to be consistent, as in the
following example:
```python
if mode == "train":
loss = tf.nn.nce_loss(
weights=weights,
biases=biases,
labels=labels,
inputs=inputs,
...,
partition_strategy="div")
elif mode == "eval":
logits = tf.matmul(inputs, tf.transpose(weights))
logits = tf.nn.bias_add(logits, biases)
labels_one_hot = tf.one_hot(labels, n_classes)
loss = tf.nn.sigmoid_cross_entropy_with_logits(
labels=labels_one_hot,
logits=logits)
loss = tf.reduce_sum(loss, axis=1)
```
Note: By default this uses a log-uniform (Zipfian) distribution for sampling,
so your labels must be sorted in order of decreasing frequency to achieve
good results. For more details, see
`tf.random.log_uniform_candidate_sampler`.
Note: In the case where `num_true` > 1, we assign to each target class
the target probability 1 / `num_true` so that the target probabilities
sum to 1 per-example.
Note: It would be useful to allow a variable number of target classes per
example. We hope to provide this functionality in a future release.
For now, if you have a variable number of target classes, you can pad them
out to a constant number by either repeating them or by padding
with an otherwise unused class.
Args:
weights: A `Tensor` of shape `[num_classes, dim]`, or a list of `Tensor`
objects whose concatenation along dimension 0 has shape
[num_classes, dim]. The (possibly-partitioned) class embeddings.
biases: A `Tensor` of shape `[num_classes]`. The class biases.
labels: A `Tensor` of type `int64` and shape `[batch_size,
num_true]`. The target classes.
inputs: A `Tensor` of shape `[batch_size, dim]`. The forward
activations of the input network.
num_sampled: An `int`. The number of negative classes to randomly sample
per batch. This single sample of negative classes is evaluated for each
element in the batch.
num_classes: An `int`. The number of possible classes.
num_true: An `int`. The number of target classes per training example.
sampled_values: a tuple of (`sampled_candidates`, `true_expected_count`,
`sampled_expected_count`) returned by a `*_candidate_sampler` function.
(if None, we default to `log_uniform_candidate_sampler`)
remove_accidental_hits: A `bool`. Whether to remove "accidental hits"
where a sampled class equals one of the target classes. If set to
`True`, this is a "Sampled Logistic" loss instead of NCE, and we are
learning to generate log-odds instead of log probabilities. See
our Candidate Sampling Algorithms Reference
([pdf](https://www.tensorflow.org/extras/candidate_sampling.pdf)).
Default is False.
partition_strategy: A string specifying the partitioning strategy, relevant
if `len(weights) > 1`. Currently `"div"` and `"mod"` are supported.
Default is `"mod"`. See `tf.nn.embedding_lookup` for more details.
name: A name for the operation (optional).
Returns:
A `batch_size` 1-D tensor of per-example NCE losses.
References:
Noise-contrastive estimation - A new estimation principle for unnormalized
statistical models:
[Gutmann et al., 2010](http://proceedings.mlr.press/v9/gutmann10a)
([pdf](http://proceedings.mlr.press/v9/gutmann10a/gutmann10a.pdf))
"""
logits, labels = _compute_sampled_logits(
weights=weights,
biases=biases,
labels=labels,
inputs=inputs,
num_sampled=num_sampled,
num_classes=num_classes,
num_true=num_true,
sampled_values=sampled_values,
subtract_log_q=True,
remove_accidental_hits=remove_accidental_hits,
partition_strategy=partition_strategy,
name=name)
sampled_losses = sigmoid_cross_entropy_with_logits(
labels=labels, logits=logits, name="sampled_losses")
# sampled_losses is batch_size x {true_loss, sampled_losses...}
# We sum out true and sampled losses.
return _sum_rows(sampled_losses)
@tf_export("nn.sampled_softmax_loss", v1=[])
@dispatch.add_dispatch_support
def sampled_softmax_loss_v2(weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=1,
sampled_values=None,
remove_accidental_hits=True,
seed=None,
name="sampled_softmax_loss"):
"""Computes and returns the sampled softmax training loss.
This is a faster way to train a softmax classifier over a huge number of
classes.
This operation is for training only. It is generally an underestimate of
the full softmax loss.
A common use case is to use this method for training, and calculate the full
softmax loss for evaluation or inference as in the following example:
```python
if mode == "train":
loss = tf.nn.sampled_softmax_loss(
weights=weights,
biases=biases,
labels=labels,
inputs=inputs,
...)
elif mode == "eval":
logits = tf.matmul(inputs, tf.transpose(weights))
logits = tf.nn.bias_add(logits, biases)
labels_one_hot = tf.one_hot(labels, n_classes)
loss = tf.nn.softmax_cross_entropy_with_logits(
labels=labels_one_hot,
logits=logits)
```
See our [Candidate Sampling Algorithms Reference]
(https://www.tensorflow.org/extras/candidate_sampling.pdf)
Also see Section 3 of [Jean et al., 2014](http://arxiv.org/abs/1412.2007)
([pdf](http://arxiv.org/pdf/1412.2007.pdf)) for the math.
Note: when doing embedding lookup on `weights` and `bias`, "div" partition
strategy will be used. Support for other partition strategy will be added
later.
Args:
weights: A `Tensor` of shape `[num_classes, dim]`, or a list of `Tensor`
objects whose concatenation along dimension 0 has shape [num_classes,
dim]. The (possibly-sharded) class embeddings.
biases: A `Tensor` of shape `[num_classes]`. The class biases.
labels: A `Tensor` of type `int64` and shape `[batch_size, num_true]`. The
target classes. Note that this format differs from the `labels` argument
of `nn.softmax_cross_entropy_with_logits`.
inputs: A `Tensor` of shape `[batch_size, dim]`. The forward activations of
the input network.
num_sampled: An `int`. The number of classes to randomly sample per batch.
num_classes: An `int`. The number of possible classes.
num_true: An `int`. The number of target classes per training example.
sampled_values: a tuple of (`sampled_candidates`, `true_expected_count`,
`sampled_expected_count`) returned by a `*_candidate_sampler` function.
(if None, we default to `log_uniform_candidate_sampler`)
remove_accidental_hits: A `bool`. whether to remove "accidental hits"
where a sampled class equals one of the target classes. Default is True.
seed: random seed for candidate sampling. Default to None, which doesn't set
the op-level random seed for candidate sampling.
name: A name for the operation (optional).
Returns:
A `batch_size` 1-D tensor of per-example sampled softmax losses.
"""
return sampled_softmax_loss(
weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=num_true,
sampled_values=sampled_values,
remove_accidental_hits=remove_accidental_hits,
partition_strategy="div",
name=name,
seed=seed)
@tf_export(v1=["nn.sampled_softmax_loss"])
@dispatch.add_dispatch_support
def sampled_softmax_loss(weights,
biases,
labels,
inputs,
num_sampled,
num_classes,
num_true=1,
sampled_values=None,
remove_accidental_hits=True,
partition_strategy="mod",
name="sampled_softmax_loss",
seed=None):
"""Computes and returns the sampled softmax training loss.
This is a faster way to train a softmax classifier over a huge number of
classes.
This operation is for training only. It is generally an underestimate of
the full softmax loss.
A common use case is to use this method for training, and calculate the full
softmax loss for evaluation or inference. In this case, you must set
`partition_strategy="div"` for the two losses to be consistent, as in the
following example:
```python
if mode == "train":
loss = tf.nn.sampled_softmax_loss(
weights=weights,
biases=biases,
labels=labels,
inputs=inputs,
...,
partition_strategy="div")
elif mode == "eval":
logits = tf.matmul(inputs, tf.transpose(weights))
logits = tf.nn.bias_add(logits, biases)
labels_one_hot = tf.one_hot(labels, n_classes)
loss = tf.nn.softmax_cross_entropy_with_logits(
labels=labels_one_hot,
logits=logits)
```
See our Candidate Sampling Algorithms Reference
([pdf](https://www.tensorflow.org/extras/candidate_sampling.pdf)).
Also see Section 3 of (Jean et al., 2014) for the math.
Args:
weights: A `Tensor` of shape `[num_classes, dim]`, or a list of `Tensor`
objects whose concatenation along dimension 0 has shape
[num_classes, dim]. The (possibly-sharded) class embeddings.
biases: A `Tensor` of shape `[num_classes]`. The class biases.
labels: A `Tensor` of type `int64` and shape `[batch_size,
num_true]`. The target classes. Note that this format differs from
the `labels` argument of `nn.softmax_cross_entropy_with_logits`.
inputs: A `Tensor` of shape `[batch_size, dim]`. The forward
activations of the input network.
num_sampled: An `int`. The number of classes to randomly sample per batch.
num_classes: An `int`. The number of possible classes.
num_true: An `int`. The number of target classes per training example.
sampled_values: a tuple of (`sampled_candidates`, `true_expected_count`,
`sampled_expected_count`) returned by a `*_candidate_sampler` function.
(if None, we default to `log_uniform_candidate_sampler`)
remove_accidental_hits: A `bool`. whether to remove "accidental hits"
where a sampled class equals one of the target classes. Default is
True.
partition_strategy: A string specifying the partitioning strategy, relevant
if `len(weights) > 1`. Currently `"div"` and `"mod"` are supported.
Default is `"mod"`. See `tf.nn.embedding_lookup` for more details.
name: A name for the operation (optional).
seed: random seed for candidate sampling. Default to None, which doesn't set
the op-level random seed for candidate sampling.
Returns:
A `batch_size` 1-D tensor of per-example sampled softmax losses.
References:
On Using Very Large Target Vocabulary for Neural Machine Translation:
[Jean et al., 2014]
(https://aclanthology.coli.uni-saarland.de/papers/P15-1001/p15-1001)
([pdf](http://aclweb.org/anthology/P15-1001))
"""
logits, labels = _compute_sampled_logits(
weights=weights,
biases=biases,
labels=labels,
inputs=inputs,
num_sampled=num_sampled,
num_classes=num_classes,
num_true=num_true,
sampled_values=sampled_values,
subtract_log_q=True,
remove_accidental_hits=remove_accidental_hits,
partition_strategy=partition_strategy,
name=name,
seed=seed)
labels = array_ops.stop_gradient(labels, name="labels_stop_gradient")
sampled_losses = nn_ops.softmax_cross_entropy_with_logits_v2(
labels=labels, logits=logits)
# sampled_losses is a [batch_size] tensor.
return sampled_losses