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conv_variational.py
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conv_variational.py
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# Copyright 2018 The TensorFlow Probability Authors.
#
# 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.
# ============================================================================
"""Convolutional variational layers."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import tensorflow.compat.v2 as tf
from tensorflow_probability.python import random as tfp_random
from tensorflow_probability.python.distributions import independent as independent_lib
from tensorflow_probability.python.distributions import kullback_leibler as kl_lib
from tensorflow_probability.python.distributions import normal as normal_lib
from tensorflow_probability.python.internal import docstring_util
from tensorflow_probability.python.layers import util as tfp_layers_util
from tensorflow_probability.python.util.seed_stream import SeedStream
from tensorflow.python.layers import utils as tf_layers_util # pylint: disable=g-direct-tensorflow-import
from tensorflow.python.ops import nn_ops # pylint: disable=g-direct-tensorflow-import
__all__ = [
'Convolution1DFlipout',
'Convolution1DReparameterization',
'Convolution2DFlipout',
'Convolution2DReparameterization',
'Convolution3DFlipout',
'Convolution3DReparameterization',
]
doc_args = """activation: Activation function. Set it to None to maintain a
linear activation.
activity_regularizer: Regularizer function for the output.
kernel_posterior_fn: Python `callable` which creates
`tfd.Distribution` instance representing the surrogate
posterior of the `kernel` parameter. Default value:
`default_mean_field_normal_fn()`.
kernel_posterior_tensor_fn: Python `callable` which takes a
`tfd.Distribution` instance and returns a representative
value. Default value: `lambda d: d.sample()`.
kernel_prior_fn: Python `callable` which creates `tfd`
instance. See `default_mean_field_normal_fn` docstring for required
parameter signature.
Default value: `tfd.Normal(loc=0., scale=1.)`.
kernel_divergence_fn: Python `callable` which takes the surrogate posterior
distribution, prior distribution and random variate sample(s) from the
surrogate posterior and computes or approximates the KL divergence. The
distributions are `tfd.Distribution`-like instances and the
sample is a `Tensor`.
bias_posterior_fn: Python `callable` which creates
`tfd.Distribution` instance representing the surrogate
posterior of the `bias` parameter. Default value:
`default_mean_field_normal_fn(is_singular=True)` (which creates an
instance of `tfd.Deterministic`).
bias_posterior_tensor_fn: Python `callable` which takes a
`tfd.Distribution` instance and returns a representative
value. Default value: `lambda d: d.sample()`.
bias_prior_fn: Python `callable` which creates `tfd` instance.
See `default_mean_field_normal_fn` docstring for required parameter
signature. Default value: `None` (no prior, no variational inference)
bias_divergence_fn: Python `callable` which takes the surrogate posterior
distribution, prior distribution and random variate sample(s) from the
surrogate posterior and computes or approximates the KL divergence. The
distributions are `tfd.Distribution`-like instances and the
sample is a `Tensor`."""
class _ConvVariational(tf.keras.layers.Layer):
"""Abstract nD convolution layer (private, used as implementation base).
This layer creates a convolution kernel that is convolved
(actually cross-correlated) with the layer input to produce a tensor of
outputs. It may also include a bias addition and activation function
on the outputs. It assumes the `kernel` and/or `bias` are drawn from
distributions.
By default, the layer implements a stochastic forward pass via
sampling from the kernel and bias posteriors,
```none
outputs = f(inputs; kernel, bias), kernel, bias ~ posterior
```
where f denotes the layer's calculation.
The arguments permit separate specification of the surrogate posterior
(`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias`
distributions.
"""
@docstring_util.expand_docstring(args=doc_args)
def __init__(
self,
rank,
filters,
kernel_size,
strides=1,
padding='valid',
data_format='channels_last',
dilation_rate=1,
activation=None,
activity_regularizer=None,
kernel_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(),
kernel_posterior_tensor_fn=lambda d: d.sample(),
kernel_prior_fn=tfp_layers_util.default_multivariate_normal_fn,
kernel_divergence_fn=(lambda q, p, ignore: kl_lib.kl_divergence(q, p)),
bias_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(
is_singular=True),
bias_posterior_tensor_fn=lambda d: d.sample(),
bias_prior_fn=None,
bias_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
**kwargs):
# pylint: disable=g-doc-args
"""Construct layer.
Args:
rank: An integer, the rank of the convolution, e.g. "2" for 2D
convolution.
filters: Integer, the dimensionality of the output space (i.e. the number
of filters in the convolution).
kernel_size: An integer or tuple/list of n integers, specifying the
length of the convolution window.
strides: An integer or tuple/list of n integers,
specifying the stride length of the convolution.
Specifying any stride value != 1 is incompatible with specifying
any `dilation_rate` value != 1.
padding: One of `"valid"` or `"same"` (case-insensitive).
data_format: A string, one of `channels_last` (default) or
`channels_first`. The ordering of the dimensions in the inputs.
`channels_last` corresponds to inputs with shape `(batch, ...,
channels)` while `channels_first` corresponds to inputs with shape
`(batch, channels, ...)`.
dilation_rate: An integer or tuple/list of n integers, specifying
the dilation rate to use for dilated convolution.
Currently, specifying any `dilation_rate` value != 1 is
incompatible with specifying any `strides` value != 1.
${args}
"""
# pylint: enable=g-doc-args
super(_ConvVariational, self).__init__(
activity_regularizer=activity_regularizer,
**kwargs)
self.rank = rank
self.filters = filters
self.kernel_size = tf_layers_util.normalize_tuple(
kernel_size, rank, 'kernel_size')
self.strides = tf_layers_util.normalize_tuple(strides, rank, 'strides')
self.padding = tf_layers_util.normalize_padding(padding)
self.data_format = tf_layers_util.normalize_data_format(data_format)
self.dilation_rate = tf_layers_util.normalize_tuple(
dilation_rate, rank, 'dilation_rate')
self.activation = tf.keras.activations.get(activation)
self.input_spec = tf.keras.layers.InputSpec(ndim=self.rank + 2)
self.kernel_posterior_fn = kernel_posterior_fn
self.kernel_posterior_tensor_fn = kernel_posterior_tensor_fn
self.kernel_prior_fn = kernel_prior_fn
self.kernel_divergence_fn = kernel_divergence_fn
self.bias_posterior_fn = bias_posterior_fn
self.bias_posterior_tensor_fn = bias_posterior_tensor_fn
self.bias_prior_fn = bias_prior_fn
self.bias_divergence_fn = bias_divergence_fn
def build(self, input_shape):
input_shape = tf.TensorShape(input_shape)
if self.data_format == 'channels_first':
channel_axis = 1
else:
channel_axis = -1
input_dim = tf.compat.dimension_value(input_shape[channel_axis])
if input_dim is None:
raise ValueError('The channel dimension of the inputs '
'should be defined. Found `None`.')
kernel_shape = self.kernel_size + (input_dim, self.filters)
# If self.dtype is None, build weights using the default dtype.
dtype = tf.as_dtype(self.dtype or tf.keras.backend.floatx())
# Must have a posterior kernel.
self.kernel_posterior = self.kernel_posterior_fn(
dtype, kernel_shape, 'kernel_posterior',
self.trainable, self.add_variable)
if self.kernel_prior_fn is None:
self.kernel_prior = None
else:
self.kernel_prior = self.kernel_prior_fn(
dtype, kernel_shape, 'kernel_prior',
self.trainable, self.add_variable)
if self.bias_posterior_fn is None:
self.bias_posterior = None
else:
self.bias_posterior = self.bias_posterior_fn(
dtype, (self.filters,), 'bias_posterior',
self.trainable, self.add_variable)
if self.bias_prior_fn is None:
self.bias_prior = None
else:
self.bias_prior = self.bias_prior_fn(
dtype, (self.filters,), 'bias_prior',
self.trainable, self.add_variable)
self.input_spec = tf.keras.layers.InputSpec(
ndim=self.rank + 2, axes={channel_axis: input_dim})
self._convolution_op = nn_ops.Convolution(
input_shape,
filter_shape=tf.TensorShape(kernel_shape),
dilation_rate=self.dilation_rate,
strides=self.strides,
padding=self.padding.upper(),
data_format=tf_layers_util.convert_data_format(
self.data_format, self.rank + 2))
self.built = True
def call(self, inputs):
inputs = tf.convert_to_tensor(value=inputs, dtype=self.dtype)
outputs = self._apply_variational_kernel(inputs)
outputs = self._apply_variational_bias(outputs)
if self.activation is not None:
outputs = self.activation(outputs)
self._apply_divergence(self.kernel_divergence_fn,
self.kernel_posterior,
self.kernel_prior,
self.kernel_posterior_tensor,
name='divergence_kernel')
self._apply_divergence(self.bias_divergence_fn,
self.bias_posterior,
self.bias_prior,
self.bias_posterior_tensor,
name='divergence_bias')
return outputs
def compute_output_shape(self, input_shape):
"""Computes the output shape of the layer.
Args:
input_shape: Shape tuple (tuple of integers) or list of shape tuples
(one per output tensor of the layer). Shape tuples can include None for
free dimensions, instead of an integer.
Returns:
output_shape: A tuple representing the output shape.
"""
input_shape = tf.TensorShape(input_shape).as_list()
if self.data_format == 'channels_last':
space = input_shape[1:-1]
new_space = []
for i in range(len(space)):
new_dim = tf_layers_util.conv_output_length(
space[i],
self.kernel_size[i],
padding=self.padding,
stride=self.strides[i],
dilation=self.dilation_rate[i])
new_space.append(new_dim)
return tf.TensorShape([input_shape[0]] + new_space + [self.filters])
else:
space = input_shape[2:]
new_space = []
for i in range(len(space)):
new_dim = tf_layers_util.conv_output_length(
space[i],
self.kernel_size[i],
padding=self.padding,
stride=self.strides[i],
dilation=self.dilation_rate[i])
new_space.append(new_dim)
return tf.TensorShape([input_shape[0], self.filters] + new_space)
def get_config(self):
"""Returns the config of the layer.
A layer config is a Python dictionary (serializable) containing the
configuration of a layer. The same layer can be reinstantiated later
(without its trained weights) from this configuration.
Returns:
config: A Python dictionary of class keyword arguments and their
serialized values.
"""
config = {
'filters': self.filters,
'kernel_size': self.kernel_size,
'strides': self.strides,
'padding': self.padding,
'data_format': self.data_format,
'dilation_rate': self.dilation_rate,
'activation': (tf.keras.activations.serialize(self.activation)
if self.activation else None),
'activity_regularizer':
tf.keras.initializers.serialize(self.activity_regularizer),
}
function_keys = [
'kernel_posterior_fn',
'kernel_posterior_tensor_fn',
'kernel_prior_fn',
'kernel_divergence_fn',
'bias_posterior_fn',
'bias_posterior_tensor_fn',
'bias_prior_fn',
'bias_divergence_fn',
]
for function_key in function_keys:
function = getattr(self, function_key)
if function is None:
function_name = None
function_type = None
else:
function_name, function_type = tfp_layers_util.serialize_function(
function)
config[function_key] = function_name
config[function_key + '_type'] = function_type
base_config = super(_ConvVariational, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
@classmethod
def from_config(cls, config):
"""Creates a layer from its config.
This method is the reverse of `get_config`, capable of instantiating the
same layer from the config dictionary.
Args:
config: A Python dictionary, typically the output of `get_config`.
Returns:
layer: A layer instance.
"""
config = config.copy()
function_keys = [
'kernel_posterior_fn',
'kernel_posterior_tensor_fn',
'kernel_prior_fn',
'kernel_divergence_fn',
'bias_posterior_fn',
'bias_posterior_tensor_fn',
'bias_prior_fn',
'bias_divergence_fn',
]
for function_key in function_keys:
serial = config[function_key]
function_type = config.pop(function_key + '_type')
if serial is not None:
config[function_key] = tfp_layers_util.deserialize_function(
serial,
function_type=function_type)
return cls(**config)
def _apply_variational_bias(self, inputs):
if self.bias_posterior is None:
self.bias_posterior_tensor = None
return inputs
self.bias_posterior_tensor = self.bias_posterior_tensor_fn(
self.bias_posterior)
outputs = inputs
if self.data_format == 'channels_first':
if self.rank == 1:
# tf.nn.bias_add does not accept a 1D input tensor.
bias = tf.reshape(self.bias_posterior_tensor,
[1, self.filters, 1])
outputs += bias
if self.rank == 2:
outputs = tf.nn.bias_add(outputs,
self.bias_posterior_tensor,
data_format='NCHW')
if self.rank == 3:
# As of Mar 2017, direct addition is significantly slower than
# bias_add when computing gradients. To use bias_add, we collapse Z
# and Y into a single dimension to obtain a 4D input tensor.
outputs_shape = tf.shape(outputs)
outputs_4d = tf.reshape(outputs,
[outputs_shape[0], outputs_shape[1],
outputs_shape[2] * outputs_shape[3],
outputs_shape[4]])
outputs_4d = tf.nn.bias_add(outputs_4d,
self.bias_posterior_tensor,
data_format='NCHW')
outputs = tf.reshape(outputs_4d, outputs_shape)
else:
outputs = tf.nn.bias_add(outputs,
self.bias_posterior_tensor,
data_format='NHWC')
return outputs
def _apply_divergence(self, divergence_fn, posterior, prior,
posterior_tensor, name):
if (divergence_fn is None or
posterior is None or
prior is None):
divergence = None
return
divergence = tf.identity(
divergence_fn(posterior, prior, posterior_tensor),
name=name)
self.add_loss(divergence)
class _ConvReparameterization(_ConvVariational):
"""Abstract nD convolution layer (private, used as implementation base).
This layer creates a convolution kernel that is convolved
(actually cross-correlated) with the layer input to produce a tensor of
outputs. It may also include a bias addition and activation function
on the outputs. It assumes the `kernel` and/or `bias` are drawn from
distributions.
By default, the layer implements a stochastic forward pass via
sampling from the kernel and bias posteriors,
```none
outputs = f(inputs; kernel, bias), kernel, bias ~ posterior
```
where f denotes the layer's calculation. It uses the reparameterization
estimator [(Kingma and Welling, 2014)][1], which performs a Monte Carlo
approximation of the distribution integrating over the `kernel` and `bias`.
The arguments permit separate specification of the surrogate posterior
(`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias`
distributions.
#### References
[1]: Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In
_International Conference on Learning Representations_, 2014.
https://arxiv.org/abs/1312.6114
"""
@docstring_util.expand_docstring(args=doc_args)
def __init__(
self,
rank,
filters,
kernel_size,
strides=1,
padding='valid',
data_format='channels_last',
dilation_rate=1,
activation=None,
activity_regularizer=None,
kernel_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(),
kernel_posterior_tensor_fn=lambda d: d.sample(),
kernel_prior_fn=tfp_layers_util.default_multivariate_normal_fn,
kernel_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
bias_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(
is_singular=True),
bias_posterior_tensor_fn=lambda d: d.sample(),
bias_prior_fn=None,
bias_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
**kwargs):
# pylint: disable=g-doc-args
"""Construct layer.
Args:
rank: An integer, the rank of the convolution, e.g. "2" for 2D
convolution.
filters: Integer, the dimensionality of the output space (i.e. the number
of filters in the convolution).
kernel_size: An integer or tuple/list of n integers, specifying the
length of the convolution window.
strides: An integer or tuple/list of n integers,
specifying the stride length of the convolution.
Specifying any stride value != 1 is incompatible with specifying
any `dilation_rate` value != 1.
padding: One of `"valid"` or `"same"` (case-insensitive).
data_format: A string, one of `channels_last` (default) or
`channels_first`. The ordering of the dimensions in the inputs.
`channels_last` corresponds to inputs with shape `(batch, ...,
channels)` while `channels_first` corresponds to inputs with shape
`(batch, channels, ...)`.
dilation_rate: An integer or tuple/list of n integers, specifying
the dilation rate to use for dilated convolution.
Currently, specifying any `dilation_rate` value != 1 is
incompatible with specifying any `strides` value != 1.
${args}
"""
# pylint: enable=g-doc-args
super(_ConvReparameterization, self).__init__(
rank=rank,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format=data_format,
dilation_rate=dilation_rate,
activation=tf.keras.activations.get(activation),
activity_regularizer=activity_regularizer,
kernel_posterior_fn=kernel_posterior_fn,
kernel_posterior_tensor_fn=kernel_posterior_tensor_fn,
kernel_prior_fn=kernel_prior_fn,
kernel_divergence_fn=kernel_divergence_fn,
bias_posterior_fn=bias_posterior_fn,
bias_posterior_tensor_fn=bias_posterior_tensor_fn,
bias_prior_fn=bias_prior_fn,
bias_divergence_fn=bias_divergence_fn,
**kwargs)
def _apply_variational_kernel(self, inputs):
self.kernel_posterior_tensor = self.kernel_posterior_tensor_fn(
self.kernel_posterior)
self.kernel_posterior_affine = None
self.kernel_posterior_affine_tensor = None
outputs = self._convolution_op(inputs, self.kernel_posterior_tensor)
return outputs
class Conv1DReparameterization(_ConvReparameterization):
"""1D convolution layer (e.g. temporal convolution).
This layer creates a convolution kernel that is convolved
(actually cross-correlated) with the layer input to produce a tensor of
outputs. It may also include a bias addition and activation function
on the outputs. It assumes the `kernel` and/or `bias` are drawn from
distributions.
By default, the layer implements a stochastic forward pass via
sampling from the kernel and bias posteriors,
```none
outputs = f(inputs; kernel, bias), kernel, bias ~ posterior
```
where f denotes the layer's calculation. It uses the reparameterization
estimator [(Kingma and Welling, 2014)][1], which performs a Monte Carlo
approximation of the distribution integrating over the `kernel` and `bias`.
The arguments permit separate specification of the surrogate posterior
(`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias`
distributions.
Upon being built, this layer adds losses (accessible via the `losses`
property) representing the divergences of `kernel` and/or `bias` surrogate
posteriors and their respective priors. When doing minibatch stochastic
optimization, make sure to scale this loss such that it is applied just once
per epoch (e.g. if `kl` is the sum of `losses` for each element of the batch,
you should pass `kl / num_examples_per_epoch` to your optimizer).
You can access the `kernel` and/or `bias` posterior and prior distributions
after the layer is built via the `kernel_posterior`, `kernel_prior`,
`bias_posterior` and `bias_prior` properties.
#### Examples
We illustrate a Bayesian neural network with [variational inference](
https://en.wikipedia.org/wiki/Variational_Bayesian_methods),
assuming a dataset of `features` and `labels`.
```python
import tensorflow as tf
import tensorflow_probability as tfp
model = tf.keras.Sequential([
tf.keras.layers.Reshape([128, 1]),
tfp.layers.Convolution1DReparameterization(
64, kernel_size=5, padding='SAME', activation=tf.nn.relu),
tf.keras.layers.Flatten(),
tfp.layers.DenseReparameterization(10),
])
logits = model(features)
neg_log_likelihood = tf.nn.softmax_cross_entropy_with_logits(
labels=labels, logits=logits)
kl = sum(model.losses)
loss = neg_log_likelihood + kl
train_op = tf.train.AdamOptimizer().minimize(loss)
```
It uses reparameterization gradients to minimize the
Kullback-Leibler divergence up to a constant, also known as the
negative Evidence Lower Bound. It consists of the sum of two terms:
the expected negative log-likelihood, which we approximate via
Monte Carlo; and the KL divergence, which is added via regularizer
terms which are arguments to the layer.
#### References
[1]: Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In
_International Conference on Learning Representations_, 2014.
https://arxiv.org/abs/1312.6114
"""
@docstring_util.expand_docstring(args=doc_args)
def __init__(
self,
filters,
kernel_size,
strides=1,
padding='valid',
data_format='channels_last',
dilation_rate=1,
activation=None,
activity_regularizer=None,
kernel_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(),
kernel_posterior_tensor_fn=lambda d: d.sample(),
kernel_prior_fn=tfp_layers_util.default_multivariate_normal_fn,
kernel_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
bias_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(
is_singular=True),
bias_posterior_tensor_fn=lambda d: d.sample(),
bias_prior_fn=None,
bias_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
**kwargs):
# pylint: disable=g-doc-args
"""Construct layer.
Args:
filters: Integer, the dimensionality of the output space (i.e. the number
of filters in the convolution).
kernel_size: An integer or tuple/list of a single integer, specifying the
length of the 1D convolution window.
strides: An integer or tuple/list of a single integer,
specifying the stride length of the convolution.
Specifying any stride value != 1 is incompatible with specifying
any `dilation_rate` value != 1.
padding: One of `"valid"` or `"same"` (case-insensitive).
data_format: A string, one of `channels_last` (default) or
`channels_first`. The ordering of the dimensions in the inputs.
`channels_last` corresponds to inputs with shape `(batch, length,
channels)` while `channels_first` corresponds to inputs with shape
`(batch, channels, length)`.
dilation_rate: An integer or tuple/list of a single integer, specifying
the dilation rate to use for dilated convolution.
Currently, specifying any `dilation_rate` value != 1 is
incompatible with specifying any `strides` value != 1.
${args}
"""
# pylint: enable=g-doc-args
super(Conv1DReparameterization, self).__init__(
rank=1,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format=data_format,
dilation_rate=dilation_rate,
activation=tf.keras.activations.get(activation),
activity_regularizer=activity_regularizer,
kernel_posterior_fn=kernel_posterior_fn,
kernel_posterior_tensor_fn=kernel_posterior_tensor_fn,
kernel_prior_fn=kernel_prior_fn,
kernel_divergence_fn=kernel_divergence_fn,
bias_posterior_fn=bias_posterior_fn,
bias_posterior_tensor_fn=bias_posterior_tensor_fn,
bias_prior_fn=bias_prior_fn,
bias_divergence_fn=bias_divergence_fn,
**kwargs)
class Conv2DReparameterization(_ConvReparameterization):
"""2D convolution layer (e.g. spatial convolution over images).
This layer creates a convolution kernel that is convolved
(actually cross-correlated) with the layer input to produce a tensor of
outputs. It may also include a bias addition and activation function
on the outputs. It assumes the `kernel` and/or `bias` are drawn from
distributions.
By default, the layer implements a stochastic forward pass via
sampling from the kernel and bias posteriors,
```none
outputs = f(inputs; kernel, bias), kernel, bias ~ posterior
```
where f denotes the layer's calculation. It uses the reparameterization
estimator [(Kingma and Welling, 2014)][1], which performs a Monte Carlo
approximation of the distribution integrating over the `kernel` and `bias`.
The arguments permit separate specification of the surrogate posterior
(`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias`
distributions.
Upon being built, this layer adds losses (accessible via the `losses`
property) representing the divergences of `kernel` and/or `bias` surrogate
posteriors and their respective priors. When doing minibatch stochastic
optimization, make sure to scale this loss such that it is applied just once
per epoch (e.g. if `kl` is the sum of `losses` for each element of the batch,
you should pass `kl / num_examples_per_epoch` to your optimizer).
You can access the `kernel` and/or `bias` posterior and prior distributions
after the layer is built via the `kernel_posterior`, `kernel_prior`,
`bias_posterior` and `bias_prior` properties.
#### Examples
We illustrate a Bayesian neural network with [variational inference](
https://en.wikipedia.org/wiki/Variational_Bayesian_methods),
assuming a dataset of `features` and `labels`.
```python
import tensorflow as tf
import tensorflow_probability as tfp
model = tf.keras.Sequential([
tf.keras.layers.Reshape([32, 32, 3]),
tfp.layers.Convolution2DReparameterization(
64, kernel_size=5, padding='SAME', activation=tf.nn.relu),
tf.keras.layers.MaxPooling2D(pool_size=[2, 2],
strides=[2, 2],
padding='SAME'),
tf.keras.layers.Flatten(),
tfp.layers.DenseReparameterization(10),
])
logits = model(features)
neg_log_likelihood = tf.nn.softmax_cross_entropy_with_logits(
labels=labels, logits=logits)
kl = sum(model.losses)
loss = neg_log_likelihood + kl
train_op = tf.train.AdamOptimizer().minimize(loss)
```
It uses reparameterization gradients to minimize the
Kullback-Leibler divergence up to a constant, also known as the
negative Evidence Lower Bound. It consists of the sum of two terms:
the expected negative log-likelihood, which we approximate via
Monte Carlo; and the KL divergence, which is added via regularizer
terms which are arguments to the layer.
#### References
[1]: Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In
_International Conference on Learning Representations_, 2014.
https://arxiv.org/abs/1312.6114
"""
@docstring_util.expand_docstring(args=doc_args)
def __init__(
self,
filters,
kernel_size,
strides=(1, 1),
padding='valid',
data_format='channels_last',
dilation_rate=(1, 1),
activation=None,
activity_regularizer=None,
kernel_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(),
kernel_posterior_tensor_fn=lambda d: d.sample(),
kernel_prior_fn=tfp_layers_util.default_multivariate_normal_fn,
kernel_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
bias_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(
is_singular=True),
bias_posterior_tensor_fn=lambda d: d.sample(),
bias_prior_fn=None,
bias_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
**kwargs):
# pylint: disable=g-doc-args
"""Construct layer.
Args:
filters: Integer, the dimensionality of the output space (i.e. the number
of filters in the convolution).
kernel_size: An integer or tuple/list of 2 integers, specifying the
height and width of the 2D convolution window.
Can be a single integer to specify the same value for
all spatial dimensions.
strides: An integer or tuple/list of 2 integers,
specifying the strides of the convolution along the height and width.
Can be a single integer to specify the same value for
all spatial dimensions.
Specifying any stride value != 1 is incompatible with specifying
any `dilation_rate` value != 1.
padding: One of `"valid"` or `"same"` (case-insensitive).
data_format: A string, one of `channels_last` (default) or
`channels_first`. The ordering of the dimensions in the inputs.
`channels_last` corresponds to inputs with shape `(batch, height,
width, channels)` while `channels_first` corresponds to inputs with
shape `(batch, channels, height, width)`.
dilation_rate: An integer or tuple/list of 2 integers, specifying
the dilation rate to use for dilated convolution.
Can be a single integer to specify the same value for
all spatial dimensions.
Currently, specifying any `dilation_rate` value != 1 is
incompatible with specifying any stride value != 1.
${args}
"""
# pylint: enable=g-doc-args
super(Conv2DReparameterization, self).__init__(
rank=2,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format=data_format,
dilation_rate=dilation_rate,
activation=tf.keras.activations.get(activation),
activity_regularizer=activity_regularizer,
kernel_posterior_fn=kernel_posterior_fn,
kernel_posterior_tensor_fn=kernel_posterior_tensor_fn,
kernel_prior_fn=kernel_prior_fn,
kernel_divergence_fn=kernel_divergence_fn,
bias_posterior_fn=bias_posterior_fn,
bias_posterior_tensor_fn=bias_posterior_tensor_fn,
bias_prior_fn=bias_prior_fn,
bias_divergence_fn=bias_divergence_fn,
**kwargs)
class Conv3DReparameterization(_ConvReparameterization):
"""3D convolution layer (e.g. spatial convolution over volumes).
This layer creates a convolution kernel that is convolved
(actually cross-correlated) with the layer input to produce a tensor of
outputs. It may also include a bias addition and activation function
on the outputs. It assumes the `kernel` and/or `bias` are drawn from
distributions.
By default, the layer implements a stochastic forward pass via
sampling from the kernel and bias posteriors,
```none
outputs = f(inputs; kernel, bias), kernel, bias ~ posterior
```
where f denotes the layer's calculation. It uses the reparameterization
estimator [(Kingma and Welling, 2014)][1], which performs a Monte Carlo
approximation of the distribution integrating over the `kernel` and `bias`.
The arguments permit separate specification of the surrogate posterior
(`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias`
distributions.
Upon being built, this layer adds losses (accessible via the `losses`
property) representing the divergences of `kernel` and/or `bias` surrogate
posteriors and their respective priors. When doing minibatch stochastic
optimization, make sure to scale this loss such that it is applied just once
per epoch (e.g. if `kl` is the sum of `losses` for each element of the batch,
you should pass `kl / num_examples_per_epoch` to your optimizer).
#### Examples
We illustrate a Bayesian neural network with [variational inference](
https://en.wikipedia.org/wiki/Variational_Bayesian_methods),
assuming a dataset of `features` and `labels`.
```python
import tensorflow as tf
import tensorflow_probability as tfp
model = tf.keras.Sequential([
tf.keras.layers.Reshape([256, 32, 32, 3]),
tfp.layers.Convolution3DReparameterization(
64, kernel_size=5, padding='SAME', activation=tf.nn.relu),
tf.keras.layers.MaxPooling3D(pool_size=[2, 2, 2],
strides=[2, 2, 2],
padding='SAME'),
tf.keras.layers.Flatten(),
tfp.layers.DenseReparameterization(10),
])
logits = model(features)
neg_log_likelihood = tf.nn.softmax_cross_entropy_with_logits(
labels=labels, logits=logits)
kl = sum(model.losses)
loss = neg_log_likelihood + kl
train_op = tf.train.AdamOptimizer().minimize(loss)
```
It uses reparameterization gradients to minimize the
Kullback-Leibler divergence up to a constant, also known as the
negative Evidence Lower Bound. It consists of the sum of two terms:
the expected negative log-likelihood, which we approximate via
Monte Carlo; and the KL divergence, which is added via regularizer
terms which are arguments to the layer.
#### References
[1]: Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In
_International Conference on Learning Representations_, 2014.
https://arxiv.org/abs/1312.6114
"""
@docstring_util.expand_docstring(args=doc_args)
def __init__(
self,
filters,
kernel_size,
strides=(1, 1, 1),
padding='valid',
data_format='channels_last',
dilation_rate=(1, 1, 1),
activation=None,
activity_regularizer=None,
kernel_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(),
kernel_posterior_tensor_fn=lambda d: d.sample(),
kernel_prior_fn=tfp_layers_util.default_multivariate_normal_fn,
kernel_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
bias_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(
is_singular=True),
bias_posterior_tensor_fn=lambda d: d.sample(),
bias_prior_fn=None,
bias_divergence_fn=lambda q, p, ignore: kl_lib.kl_divergence(q, p),
**kwargs):
# pylint: disable=g-doc-args
"""Construct layer.
Args:
filters: Integer, the dimensionality of the output space (i.e. the number
of filters in the convolution).
kernel_size: An integer or tuple/list of 3 integers, specifying the
depth, height and width of the 3D convolution window.
Can be a single integer to specify the same value for
all spatial dimensions.
strides: An integer or tuple/list of 3 integers,
specifying the strides of the convolution along the depth,
height and width.
Can be a single integer to specify the same value for
all spatial dimensions.
Specifying any stride value != 1 is incompatible with specifying
any `dilation_rate` value != 1.
padding: One of `"valid"` or `"same"` (case-insensitive).
data_format: A string, one of `channels_last` (default) or
`channels_first`. The ordering of the dimensions in the inputs.
`channels_last` corresponds to inputs with shape `(batch, depth,
height, width, channels)` while `channels_first` corresponds to inputs
with shape `(batch, channels, depth, height, width)`.
dilation_rate: An integer or tuple/list of 3 integers, specifying
the dilation rate to use for dilated convolution.
Can be a single integer to specify the same value for
all spatial dimensions.
Currently, specifying any `dilation_rate` value != 1 is
incompatible with specifying any stride value != 1.
${args}
"""
# pylint: enable=g-doc-args
super(Conv3DReparameterization, self).__init__(
rank=3,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format=data_format,
dilation_rate=dilation_rate,
activation=tf.keras.activations.get(activation),
activity_regularizer=activity_regularizer,
kernel_posterior_fn=kernel_posterior_fn,
kernel_posterior_tensor_fn=kernel_posterior_tensor_fn,
kernel_prior_fn=kernel_prior_fn,
kernel_divergence_fn=kernel_divergence_fn,
bias_posterior_fn=bias_posterior_fn,
bias_posterior_tensor_fn=bias_posterior_tensor_fn,
bias_prior_fn=bias_prior_fn,
bias_divergence_fn=bias_divergence_fn,
**kwargs)
class _ConvFlipout(_ConvVariational):
"""Abstract nD convolution layer (private, used as implementation base).
This layer creates a convolution kernel that is convolved
(actually cross-correlated) with the layer input to produce a tensor of
outputs. It may also include a bias addition and activation function
on the outputs. It assumes the `kernel` and/or `bias` are drawn from
distributions.
By default, the layer implements a stochastic forward pass via
sampling from the kernel and bias posteriors,
```none
outputs = f(inputs; kernel, bias), kernel, bias ~ posterior
```
where f denotes the layer's calculation. It uses the Flipout
estimator [(Wen et al., 2018)][1], which performs a Monte Carlo approximation
of the distribution integrating over the `kernel` and `bias`. Flipout uses
roughly twice as many floating point operations as the reparameterization
estimator but has the advantage of significantly lower variance.
The arguments permit separate specification of the surrogate posterior
(`q(W|x)`), prior (`p(W)`), and divergence for both the `kernel` and `bias`
distributions.
#### References
[1]: Yeming Wen, Paul Vicol, Jimmy Ba, Dustin Tran, and Roger Grosse. Flipout:
Efficient Pseudo-Independent Weight Perturbations on Mini-Batches. In
_International Conference on Learning Representations_, 2018.
https://arxiv.org/abs/1803.04386
"""
@docstring_util.expand_docstring(args=doc_args)
def __init__(
self,
rank,
filters,
kernel_size,
strides=1,
padding='valid',
data_format='channels_last',
dilation_rate=1,
activation=None,
activity_regularizer=None,
kernel_posterior_fn=tfp_layers_util.default_mean_field_normal_fn(),
kernel_posterior_tensor_fn=lambda d: d.sample(),
kernel_prior_fn=tfp_layers_util.default_multivariate_normal_fn,