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# 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.

# ==============================================================================

"""Operations often used for initializing tensors.

All variable initializers returned by functions in this file should have the

following signature:

def _initializer(shape, dtype=dtypes.float32, partition_info=None):

Args:

shape: List of `int` representing the shape of the output `Tensor`. Some

initializers may also be able to accept a `Tensor`.

dtype: (Optional) Type of the output `Tensor`.

partition_info: (Optional) variable_scope._PartitionInfo object holding

additional information about how the variable is partitioned. May be

`None` if the variable is not partitioned.

Returns:

A `Tensor` of type `dtype` and `shape`.

"""

from __future__ import absolute_import

from __future__ import division

from __future__ import print_function

import math

import numpy as np

from tensorflow.python.framework import constant_op

from tensorflow.python.framework import dtypes

from tensorflow.python.ops import array_ops

from tensorflow.python.ops import linalg_ops_impl

from tensorflow.python.ops import gen_linalg_ops

from tensorflow.python.ops import math_ops

from tensorflow.python.ops import random_ops

from tensorflow.python.util.deprecation import deprecated

from tensorflow.python.util.tf_export import tf_export

@tf_export("keras.initializers.Initializer")

class Initializer(object):

"""Initializer base class: all initializers inherit from this class.

"""

def __call__(self, shape, dtype=None, partition_info=None):

raise NotImplementedError

def get_config(self):

"""Returns the configuration of the initializer as a JSON-serializable dict.

Returns:

A JSON-serializable Python dict.

"""

return {}

@classmethod

def from_config(cls, config):

"""Instantiates an initializer from a configuration dictionary.

Example:

```python

initializer = RandomUniform(-1, 1)

config = initializer.get_config()

initializer = RandomUniform.from_config(config)

```

Args:

config: A Python dictionary.

It will typically be the output of `get_config`.

Returns:

An Initializer instance.

"""

return cls(**config)

@tf_export("keras.initializers.Zeros", "initializers.zeros",

"zeros_initializer", "keras.initializers.zeros")

class Zeros(Initializer):

"""Initializer that generates tensors initialized to 0."""

def __init__(self, dtype=dtypes.float32):

self.dtype = dtypes.as_dtype(dtype)

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

return array_ops.zeros(shape, dtype)

def get_config(self):

return {"dtype": self.dtype.name}

@tf_export("keras.initializers.Ones", "initializers.ones", "ones_initializer",

"keras.initializers.ones")

class Ones(Initializer):

"""Initializer that generates tensors initialized to 1."""

def __init__(self, dtype=dtypes.float32):

self.dtype = dtypes.as_dtype(dtype)

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

return array_ops.ones(shape, dtype)

def get_config(self):

return {"dtype": self.dtype.name}

@tf_export("keras.initializers.Constant", "initializers.constant",

"constant_initializer", "keras.initializers.constant")

class Constant(Initializer):

"""Initializer that generates tensors with constant values.

The resulting tensor is populated with values of type `dtype`, as

specified by arguments `value` following the desired `shape` of the

new tensor (see examples below).

The argument `value` can be a constant value, or a list of values of type

`dtype`. If `value` is a list, then the length of the list must be less

than or equal to the number of elements implied by the desired shape of the

tensor. In the case where the total number of elements in `value` is less

than the number of elements required by the tensor shape, the last element

in `value` will be used to fill the remaining entries. If the total number of

elements in `value` is greater than the number of elements required by the

tensor shape, the initializer will raise a `ValueError`.

Args:

value: A Python scalar, list or tuple of values, or a N-dimensional numpy

array. All elements of the initialized variable will be set to the

corresponding value in the `value` argument.

dtype: The data type.

verify_shape: Boolean that enables verification of the shape of `value`. If

`True`, the initializer will throw an error if the shape of `value` is not

compatible with the shape of the initialized tensor.

Raises:

TypeError: If the input `value` is not one of the expected types.

Examples:

The following example can be rewritten using a numpy.ndarray instead

of the `value` list, even reshaped, as shown in the two commented lines

below the `value` list initialization.

```python

>>> import numpy as np

>>> import tensorflow as tf

>>> value = [0, 1, 2, 3, 4, 5, 6, 7]

>>> # value = np.array(value)

>>> # value = value.reshape([2, 4])

>>> init = tf.constant_initializer(value)

>>> print('fitting shape:')

>>> with tf.Session():

>>> x = tf.get_variable('x', shape=[2, 4], initializer=init)

>>> x.initializer.run()

>>> print(x.eval())

fitting shape:

[[ 0. 1. 2. 3.]

[ 4. 5. 6. 7.]]

>>> print('larger shape:')

>>> with tf.Session():

>>> x = tf.get_variable('x', shape=[3, 4], initializer=init)

>>> x.initializer.run()

>>> print(x.eval())

larger shape:

[[ 0. 1. 2. 3.]

[ 4. 5. 6. 7.]

[ 7. 7. 7. 7.]]

>>> print('smaller shape:')

>>> with tf.Session():

>>> x = tf.get_variable('x', shape=[2, 3], initializer=init)

ValueError: Too many elements provided. Needed at most 6, but received 8

>>> print('shape verification:')

>>> init_verify = tf.constant_initializer(value, verify_shape=True)

>>> with tf.Session():

>>> x = tf.get_variable('x', shape=[3, 4], initializer=init_verify)

TypeError: Expected Tensor's shape: (3, 4), got (8,).

```

"""

def __init__(self, value=0, dtype=dtypes.float32, verify_shape=False):

if not (np.isscalar(value) or isinstance(value, (list, tuple, np.ndarray))):

raise TypeError(

"Invalid type for initial value: %s (expected Python scalar, list or "

"tuple of values, or numpy.ndarray)." % type(value))

self.value = value

self.dtype = dtypes.as_dtype(dtype)

self._verify_shape = verify_shape

def __call__(self, shape, dtype=None, partition_info=None, verify_shape=None):

if dtype is None:

dtype = self.dtype

if verify_shape is None:

verify_shape = self._verify_shape

return constant_op.constant(

self.value, dtype=dtype, shape=shape, verify_shape=verify_shape)

def get_config(self):

# We don't include `verify_shape` for compatibility with Keras.

# `verify_shape` should be passed as an argument to `__call__` rather

# than as a constructor argument: conceptually it isn't a property

# of the initializer.

return {"value": self.value, "dtype": self.dtype.name}

@tf_export("keras.initializers.RandomUniform", "initializers.random_uniform",

"random_uniform_initializer", "keras.initializers.uniform",

"keras.initializers.random_uniform")

class RandomUniform(Initializer):

"""Initializer that generates tensors with a uniform distribution.

Args:

minval: A python scalar or a scalar tensor. Lower bound of the range

of random values to generate.

maxval: A python scalar or a scalar tensor. Upper bound of the range

of random values to generate. Defaults to 1 for float types.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type.

"""

def __init__(self, minval=0, maxval=None, seed=None, dtype=dtypes.float32):

self.minval = minval

self.maxval = maxval

self.seed = seed

self.dtype = dtypes.as_dtype(dtype)

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

return random_ops.random_uniform(

shape, self.minval, self.maxval, dtype, seed=self.seed)

def get_config(self):

return {

"minval": self.minval,

"maxval": self.maxval,

"seed": self.seed,

"dtype": self.dtype.name

}

@tf_export("keras.initializers.RandomNormal", "initializers.random_normal",

"random_normal_initializer", "keras.initializers.normal",

"keras.initializers.random_normal")

class RandomNormal(Initializer):

"""Initializer that generates tensors with a normal distribution.

Args:

mean: a python scalar or a scalar tensor. Mean of the random values

to generate.

stddev: a python scalar or a scalar tensor. Standard deviation of the

random values to generate.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type. Only floating point types are supported.

"""

def __init__(self, mean=0.0, stddev=1.0, seed=None, dtype=dtypes.float32):

self.mean = mean

self.stddev = stddev

self.seed = seed

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

return random_ops.random_normal(

shape, self.mean, self.stddev, dtype, seed=self.seed)

def get_config(self):

return {

"mean": self.mean,

"stddev": self.stddev,

"seed": self.seed,

"dtype": self.dtype.name

}

@tf_export("keras.initializers.TruncatedNormal",

"initializers.truncated_normal", "truncated_normal_initializer",

"keras.initializers.truncated_normal")

class TruncatedNormal(Initializer):

"""Initializer that generates a truncated normal distribution.

These values are similar to values from a `random_normal_initializer`

except that values more than two standard deviations from the mean

are discarded and re-drawn. This is the recommended initializer for

neural network weights and filters.

Args:

mean: a python scalar or a scalar tensor. Mean of the random values

to generate.

stddev: a python scalar or a scalar tensor. Standard deviation of the

random values to generate.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type. Only floating point types are supported.

"""

def __init__(self, mean=0.0, stddev=1.0, seed=None, dtype=dtypes.float32):

self.mean = mean

self.stddev = stddev

self.seed = seed

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

return random_ops.truncated_normal(

shape, self.mean, self.stddev, dtype, seed=self.seed)

def get_config(self):

return {

"mean": self.mean,

"stddev": self.stddev,

"seed": self.seed,

"dtype": self.dtype.name

}

@tf_export("initializers.uniform_unit_scaling",

"uniform_unit_scaling_initializer")

class UniformUnitScaling(Initializer):

"""Initializer that generates tensors without scaling variance.

When initializing a deep network, it is in principle advantageous to keep

the scale of the input variance constant, so it does not explode or diminish

by reaching the final layer. If the input is `x` and the operation `x * W`,

and we want to initialize `W` uniformly at random, we need to pick `W` from

[-sqrt(3) / sqrt(dim), sqrt(3) / sqrt(dim)]

to keep the scale intact, where `dim = W.shape[0]` (the size of the input).

A similar calculation for convolutional networks gives an analogous result

with `dim` equal to the product of the first 3 dimensions. When

nonlinearities are present, we need to multiply this by a constant `factor`.

See [Sussillo et al., 2014](https://arxiv.org/abs/1412.6558)

([pdf](http://arxiv.org/pdf/1412.6558.pdf)) for deeper motivation, experiments

and the calculation of constants. In section 2.3 there, the constants were

numerically computed: for a linear layer it's 1.0, relu: ~1.43, tanh: ~1.15.

Args:

factor: Float. A multiplicative factor by which the values will be scaled.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type. Only floating point types are supported.

"""

@deprecated(None,

"Use tf.initializers.variance_scaling instead with distribution="

"uniform to get equivalent behavior.")

def __init__(self, factor=1.0, seed=None, dtype=dtypes.float32):

self.factor = factor

self.seed = seed

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

scale_shape = shape

if partition_info is not None:

scale_shape = partition_info.full_shape

input_size = 1.0

# Estimating input size is not possible to do perfectly, but we try.

# The estimate, obtained by multiplying all dimensions but the last one,

# is the right thing for matrix multiply and convolutions (see above).

for dim in scale_shape[:-1]:

input_size *= float(dim)

# Avoid errors when initializing zero-size tensors.

input_size = max(input_size, 1.0)

max_val = math.sqrt(3 / input_size) * self.factor

return random_ops.random_uniform(

shape, -max_val, max_val, dtype, seed=self.seed)

def get_config(self):

return {"factor": self.factor, "seed": self.seed, "dtype": self.dtype.name}

@tf_export("keras.initializers.VarianceScaling",

"initializers.variance_scaling", "variance_scaling_initializer")

class VarianceScaling(Initializer):

"""Initializer capable of adapting its scale to the shape of weights tensors.

With `distribution="normal"`, samples are drawn from a truncated normal

distribution centered on zero, with `stddev = sqrt(scale / n)`

where n is:

- number of input units in the weight tensor, if mode = "fan_in"

- number of output units, if mode = "fan_out"

- average of the numbers of input and output units, if mode = "fan_avg"

With `distribution="uniform"`, samples are drawn from a uniform distribution

within [-limit, limit], with `limit = sqrt(3 * scale / n)`.

Args:

scale: Scaling factor (positive float).

mode: One of "fan_in", "fan_out", "fan_avg".

distribution: Random distribution to use. One of "normal", "uniform".

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type. Only floating point types are supported.

Raises:

ValueError: In case of an invalid value for the "scale", mode" or

"distribution" arguments.

"""

def __init__(self,

scale=1.0,

mode="fan_in",

distribution="normal",

seed=None,

dtype=dtypes.float32):

if scale <= 0.:

raise ValueError("`scale` must be positive float.")

if mode not in {"fan_in", "fan_out", "fan_avg"}:

raise ValueError("Invalid `mode` argument:", mode)

distribution = distribution.lower()

if distribution not in {"normal", "uniform"}:

raise ValueError("Invalid `distribution` argument:", distribution)

self.scale = scale

self.mode = mode

self.distribution = distribution

self.seed = seed

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

scale = self.scale

scale_shape = shape

if partition_info is not None:

scale_shape = partition_info.full_shape

fan_in, fan_out = _compute_fans(scale_shape)

if self.mode == "fan_in":

scale /= max(1., fan_in)

elif self.mode == "fan_out":

scale /= max(1., fan_out)

else:

scale /= max(1., (fan_in + fan_out) / 2.)

if self.distribution == "normal":

stddev = math.sqrt(scale)

return random_ops.truncated_normal(

shape, 0.0, stddev, dtype, seed=self.seed)

else:

limit = math.sqrt(3.0 * scale)

return random_ops.random_uniform(

shape, -limit, limit, dtype, seed=self.seed)

def get_config(self):

return {

"scale": self.scale,

"mode": self.mode,

"distribution": self.distribution,

"seed": self.seed,

"dtype": self.dtype.name

}

@tf_export("keras.initializers.Orthogonal", "initializers.orthogonal",

"orthogonal_initializer", "keras.initializers.orthogonal")

class Orthogonal(Initializer):

"""Initializer that generates an orthogonal matrix.

If the shape of the tensor to initialize is two-dimensional, it is initialized

with an orthogonal matrix obtained from the QR decomposition of a matrix of

random numbers drawn from a normal distribution.

If the matrix has fewer rows than columns then the output will have orthogonal

rows. Otherwise, the output will have orthogonal columns.

If the shape of the tensor to initialize is more than two-dimensional,

a matrix of shape `(shape[0] * ... * shape[n - 2], shape[n - 1])`

is initialized, where `n` is the length of the shape vector.

The matrix is subsequently reshaped to give a tensor of the desired shape.

Args:

gain: multiplicative factor to apply to the orthogonal matrix

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type.

"""

def __init__(self, gain=1.0, seed=None, dtype=dtypes.float32):

self.gain = gain

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

self.seed = seed

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

# Check the shape

if len(shape) < 2:

raise ValueError("The tensor to initialize must be "

"at least two-dimensional")

# Flatten the input shape with the last dimension remaining

# its original shape so it works for conv2d

num_rows = 1

for dim in shape[:-1]:

num_rows *= dim

num_cols = shape[-1]

flat_shape = (num_cols, num_rows) if num_rows < num_cols else (num_rows,

num_cols)

# Generate a random matrix

a = random_ops.random_normal(flat_shape, dtype=dtype, seed=self.seed)

# Compute the qr factorization

q, r = gen_linalg_ops.qr(a, full_matrices=False)

# Make Q uniform

d = array_ops.diag_part(r)

q *= math_ops.sign(d)

if num_rows < num_cols:

q = array_ops.matrix_transpose(q)

return self.gain * array_ops.reshape(q, shape)

def get_config(self):

return {"gain": self.gain, "seed": self.seed, "dtype": self.dtype.name}

class ConvolutionDeltaOrthogonal(Initializer):

"""Initializer that generates a delta orthogonal kernel for ConvNets.

The shape of the tensor must have length 3, 4 or 5. The number of input

filters must not exceed the number of output filters. The center pixels of the

tensor form an orthogonal matrix. Other pixels are set to be zero.

Args:

gain: Multiplicative factor to apply to the orthogonal matrix. Default is 1.

The 2-norm of an input is multiplied by a factor of 'sqrt(gain)' after

applying this convolution.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed} for behavior.

dtype: The data type.

"""

def __init__(self, gain=1.0, seed=None, dtype=dtypes.float32):

self.gain = gain

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

self.seed = seed

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

# Check the shape

if len(shape) < 3 or len(shape) > 5:

raise ValueError("The tensor to initialize must be at least "

"three-dimensional and at most five-dimensional")

if shape[-2] > shape[-1]:

raise ValueError("In_filters cannot be greater than out_filters.")

# Generate a random matrix

a = random_ops.random_normal([shape[-1], shape[-1]],

dtype=dtype, seed=self.seed)

# Compute the qr factorization

q, r = gen_linalg_ops.qr(a, full_matrices=False)

# Make Q uniform

d = array_ops.diag_part(r)

q *= math_ops.sign(d)

q = q[:shape[-2], :]

q *= math_ops.sqrt(math_ops.cast(self.gain, dtype=dtype))

if len(shape) == 3:

weight = array_ops.scatter_nd([[(shape[0]-1)//2]],

array_ops.expand_dims(q, 0), shape)

elif len(shape) == 4:

weight = array_ops.scatter_nd([[(shape[0]-1)//2, (shape[1]-1)//2]],

array_ops.expand_dims(q, 0), shape)

else:

weight = array_ops.scatter_nd([[(shape[0]-1)//2, (shape[1]-1)//2,

(shape[2]-1)//2]],

array_ops.expand_dims(q, 0), shape)

return weight

def get_config(self):

return {"gain": self.gain, "seed": self.seed, "dtype": self.dtype.name}

class ConvolutionOrthogonal(Initializer):

"""Initializer that generates orthogonal kernel for ConvNets.

Base class used to construct 1D, 2D and 3D orthogonal kernels for convolution.

Args:

gain: multiplicative factor to apply to the orthogonal matrix. Default is 1.

The 2-norm of an input is multiplied by a factor of 'sqrt(gain)' after

applying this convolution.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed} for behavior.

dtype: The data type.

"""

def __init__(self, gain=1.0, seed=None, dtype=dtypes.float32):

self.gain = gain

self.dtype = _assert_float_dtype(dtypes.as_dtype(dtype))

self.seed = seed

def __call__(self, shape, dtype=None, partition_info=None):

raise NotImplementedError

def get_config(self):

return {"gain": self.gain, "seed": self.seed, "dtype": self.dtype.name}

# Helper functions.

def _orthogonal_matrix(self, n):

"""Construct an n x n orthogonal matrix.

Args:

n: Dimension.

Returns:

A n x n orthogonal matrix.

"""

a = random_ops.random_normal([n, n], dtype=self.dtype, seed=self.seed)

if self.seed:

self.seed += 1

q, r = gen_linalg_ops.qr(a)

d = array_ops.diag_part(r)

# make q uniform

q *= math_ops.sign(d)

return q

def _symmetric_projection(self, n):

"""Compute a n x n symmetric projection matrix.

Args:

n: Dimension.

Returns:

A n x n symmetric projection matrix, i.e. a matrix P s.t. P=P*P, P=P^T.

"""

q = self._orthogonal_matrix(n)

# randomly zeroing out some columns

mask = math_ops.cast(random_ops.random_normal([n], seed=self.seed) > 0,

self.dtype)

if self.seed:

self.seed += 1

c = math_ops.multiply(q, mask)

return math_ops.matmul(c, array_ops.matrix_transpose(c))

class ConvolutionOrthogonal2D(ConvolutionOrthogonal):

"""Initializer that generates a 2D orthogonal kernel for ConvNets.

The shape of the tensor must have length 4. The number of input

filters must not exceed the number of output filters.

The orthogonality(==isometry) is exact when the inputs are circular padded.

There are finite-width effects with non-circular padding (e.g. zero padding).

Args:

gain: Multiplicative factor to apply to the orthogonal matrix. Default is 1.

This has the effect of scaling the output 2-norm by a factor of

`sqrt(gain)`.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed} for behavior.

dtype: The data type.

"""

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

if len(shape) != 4:

raise ValueError("The tensor to initialize must be four-dimensional")

if shape[-2] > shape[-1]:

raise ValueError("In_filters cannot be greater than out_filters.")

if shape[0] != shape[1]:

raise ValueError("Kernel sizes must be equal.")

kernel = self._orthogonal_kernel(shape[0], shape[2], shape[3])

kernel *= math_ops.sqrt(math_ops.cast(self.gain, dtype=dtype))

return kernel

def _dict_to_tensor(self, x, k1, k2):

"""Convert a dictionary to a tensor.

Args:

x: A k1 * k2 dictionary.

k1: First dimension of x.

k2: Second dimension of x.

Returns:

A k1 * k2 tensor.

"""

return array_ops.stack([array_ops.stack([x[i, j] for j in range(k2)])

for i in range(k1)])

def _block_orth(self, p1, p2):

"""Construct a 2 x 2 kernel. Used to construct orthgonal kernel.

Args:

p1: A symmetric projection matrix.

p2: A symmetric projection matrix.

Returns:

A 2 x 2 kernel [[p1p2, p1(1-p2)],

[(1-p1)p2, (1-p1)(1-p2)]].

Raises:

ValueError: If the dimensions of p1 and p2 are different.

"""

if p1.shape.as_list() != p2.shape.as_list():

raise ValueError("The dimension of the matrices must be the same.")

n = p1.shape.as_list()[0]

kernel2x2 = {}

eye = linalg_ops_impl.eye(n, dtype=self.dtype)

kernel2x2[0, 0] = math_ops.matmul(p1, p2)

kernel2x2[0, 1] = math_ops.matmul(p1, (eye - p2))

kernel2x2[1, 0] = math_ops.matmul((eye - p1), p2)

kernel2x2[1, 1] = math_ops.matmul((eye - p1), (eye - p2))

return kernel2x2

def _matrix_conv(self, m1, m2):

"""Matrix convolution.

Args:

m1: A k x k dictionary, each element is a n x n matrix.

m2: A l x l dictionary, each element is a n x n matrix.

Returns:

(k + l - 1) * (k + l - 1) dictionary each element is a n x n matrix.

Raises:

ValueError: if the entries of m1 and m2 are of different dimensions.

"""

n = (m1[0, 0]).shape.as_list()[0]

if n != (m2[0, 0]).shape.as_list()[0]:

raise ValueError("The entries in matrices m1 and m2 "

"must have the same dimensions!")

k = int(np.sqrt(len(m1)))

l = int(np.sqrt(len(m2)))

result = {}

size = k + l - 1

# Compute matrix convolution between m1 and m2.

for i in range(size):

for j in range(size):

result[i, j] = array_ops.zeros([n, n], self.dtype)

for index1 in range(min(k, i + 1)):

for index2 in range(min(k, j + 1)):

if (i - index1) < l and (j - index2) < l:

result[i, j] += math_ops.matmul(m1[index1, index2],

m2[i - index1, j - index2])

return result

def _orthogonal_kernel(self, ksize, cin, cout):

"""Construct orthogonal kernel for convolution.

Args:

ksize: Kernel size.

cin: Number of input channels.

cout: Number of output channels.

Returns:

An [ksize, ksize, cin, cout] orthogonal kernel.

Raises:

ValueError: If cin > cout.

"""

if cin > cout:

raise ValueError("The number of input channels cannot exceed "

"the number of output channels.")

orth = self._orthogonal_matrix(cout)[0:cin, :]

if ksize == 1:

return array_ops.expand_dims(array_ops.expand_dims(orth, 0), 0)

p = self._block_orth(self._symmetric_projection(cout),

self._symmetric_projection(cout))

for _ in range(ksize - 2):

temp = self._block_orth(self._symmetric_projection(cout),

self._symmetric_projection(cout))

p = self._matrix_conv(p, temp)

for i in range(ksize):

for j in range(ksize):

p[i, j] = math_ops.matmul(orth, p[i, j])

return self._dict_to_tensor(p, ksize, ksize)

class ConvolutionOrthogonal1D(ConvolutionOrthogonal):

"""Initializer that generates a 1D orthogonal kernel for ConvNets.

The shape of the tensor must have length 3. The number of input

filters must not exceed the number of output filters.

The orthogonality(==isometry) is exact when the inputs are circular padded.

There are finite-width effects with non-circular padding (e.g. zero padding).

Args:

gain: Multiplicative factor to apply to the orthogonal matrix. Default is 1.

The 2-norm of an input is multiplied by a factor of 'sqrt(gain)' after

applying this convolution.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed}

for behavior.

dtype: The data type.

"""

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

if len(shape) != 3:

raise ValueError("The tensor to initialize must be three-dimensional")

if shape[-2] > shape[-1]:

raise ValueError("In_filters cannot be greater than out_filters.")

kernel = self._orthogonal_kernel(shape[0], shape[-2], shape[-1])

kernel *= math_ops.sqrt(math_ops.cast(self.gain, dtype=dtype))

return kernel

def _dict_to_tensor(self, x, k):

"""Convert a dictionary to a tensor.

Args:

x: A dictionary of length k.

k: Dimension of x.

Returns:

A tensor with the same dimension.

"""

return array_ops.stack([x[i] for i in range(k)])

def _block_orth(self, projection_matrix):

"""Construct a kernel. Used to construct orthgonal kernel.

Args:

projection_matrix: A symmetric projection matrix of size n x n.

Returns:

[projection_matrix, (1 - projection_matrix)].

"""

n = projection_matrix.shape.as_list()[0]

kernel = {}

eye = linalg_ops_impl.eye(n, dtype=self.dtype)

kernel[0] = projection_matrix

kernel[1] = eye - projection_matrix

return kernel

def _matrix_conv(self, m1, m2):

"""Matrix convolution.

Args:

m1: A dictionary of length k, each element is a n x n matrix.

m2: A dictionary of length l, each element is a n x n matrix.

Returns:

(k + l - 1) dictionary each element is a n x n matrix.

Raises:

ValueError: Ff the entries of m1 and m2 are of different dimensions.

"""

n = (m1[0]).shape.as_list()[0]

if n != (m2[0]).shape.as_list()[0]:

raise ValueError("The entries in matrices m1 and m2 "

"must have the same dimensions!")

k = len(m1)

l = len(m2)

result = {}

size = k + l - 1

# Compute matrix convolution between m1 and m2.

for i in range(size):

result[i] = array_ops.zeros([n, n], self.dtype)

for index in range(min(k, i + 1)):

if (i - index) < l:

result[i] += math_ops.matmul(m1[index], m2[i - index])

return result

def _orthogonal_kernel(self, ksize, cin, cout):

"""Construct orthogonal kernel for convolution.

Args:

ksize: Kernel size.

cin: Number of input channels.

cout: Number of output channels.

Returns:

An [ksize, ksize, cin, cout] orthogonal kernel.

Raises:

ValueError: If cin > cout.

"""

if cin > cout:

raise ValueError("The number of input channels cannot exceed "

"the number of output channels.")

orth = self._orthogonal_matrix(cout)[0:cin, :]

if ksize == 1:

return array_ops.expand_dims(orth, 0)

p = self._block_orth(self._symmetric_projection(cout))

for _ in range(ksize - 2):

temp = self._block_orth(self._symmetric_projection(cout))

p = self._matrix_conv(p, temp)

for i in range(ksize):

p[i] = math_ops.matmul(orth, p[i])

return self._dict_to_tensor(p, ksize)

class ConvolutionOrthogonal3D(ConvolutionOrthogonal):

"""Initializer that generates a 3D orthogonal kernel for ConvNets.

The shape of the tensor must have length 5. The number of input

filters must not exceed the number of output filters.

The orthogonality(==isometry) is exact when the inputs are circular padded.

There are finite-width effects with non-circular padding (e.g. zero padding).

Args:

gain: Multiplicative factor to apply to the orthogonal matrix. Default is 1.

The 2-norm of an input is multiplied by a factor of 'sqrt(gain)' after

applying this convolution.

seed: A Python integer. Used to create random seeds. See

@{tf.set_random_seed} for behavior.

dtype: The data type.

"""

def __call__(self, shape, dtype=None, partition_info=None):

if dtype is None:

dtype = self.dtype

if len(shape) != 5:

raise ValueError("The tensor to initialize must be five-dimensional")

if shape[-2] > shape[-1]:

raise ValueError("In_filters cannot be greater than out_filters.")

if shape[0] != shape[1] or shape[0] != shape[2]:

raise ValueError("Kernel sizes must be equal.")

kernel = self._orthogonal_kernel(shape[0], shape[-2], shape[-1])

kernel *= math_ops.sqrt(math_ops.cast(self.gain, dtype=dtype))

return kernel

def _dict_to_tensor(self, x, k1, k2, k3):

"""Convert a dictionary to a tensor.

Args:

x: A k1 * k2 dictionary.

k1: First dimension of x.

k2: Second dimension of x.

k3: Third dimension of x.

Returns:

A k1 * k2 * k3 tensor.

"""

return array_ops.stack([array_ops.stack(

[array_ops.stack([x[i, j, k] for k in range(k3)])

for j in range(k2)]) for i in range(k1)])

def _block_orth(self, p1, p2, p3):

"""Construct a 3 x 3 kernel. Used to construct orthgonal kernel.

Args:

p1: A symmetric projection matrix.

p2: A symmetric projection matrix.

p3: A symmetric projection matrix.

Returns:

A 2 x 2 x 2 kernel.

Raises:

ValueError: If the dimensions of p1, p2 and p3 are different.

"""

p1_shape = p1.shape.as_list()

if p1_shape != p2.shape.as_list() or p1_shape != p3.shape.as_list():

raise ValueError("The dimension of the matrices must be the same.")

n = p1_shape[0]

eye = linalg_ops_impl.eye(n, dtype=self.dtype)

kernel2x2x2 = {}

def matmul(p1, p2, p3):

return math_ops.matmul(math_ops.matmul(p1, p2), p3)

def cast(i, p):

"""Return p or (1-p)."""

return i * p + (1-i) * (eye - p)

for i in [0, 1]:

for j in [0, 1]:

for k in [0, 1]:

kernel2x2x2[i, j, k] = matmul(cast(i, p1), cast(j, p2), cast(k, p3))

return kernel2x2x2

def _matrix_conv(self, m1, m2):

"""Matrix convolution.

Args:

m1: is a k x k x k dictionary, each element is a n x n matrix.

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