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complexnn/conv.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Contributors : Titouan Parcollet
# Initial Authors: Chiheb Trabelsi
from keras import backend as K
from keras import activations, initializers, regularizers, constraints
from keras.layers import Lambda, Layer, InputSpec, Convolution1D, Convolution2D, add, multiply, Activation, Input, concatenate
from keras.layers.convolutional import _Conv
from keras.layers.merge import _Merge
from keras.layers.recurrent import Recurrent
from keras.utils import conv_utils
from keras.models import Model
import numpy as np
from theano.sandbox.rng_mrg import MRG_RandomStreams as RandomStreams
from .fft import fft, ifft, fft2, ifft2
from .init import *
import sys
#####################################################################
#Quaternion Implementations #
#####################################################################
class QuaternionConv(Layer):
"""Abstract nD quaternion convolution layer.
This layer creates a quaternion convolution kernel that is convolved
with the layer input to produce a tensor of outputs.
If `use_bias` is True, a bias vector is created and added to the outputs.
Finally, if `activation` is not `None`,
it is applied to the outputs as well.
# Arguments
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 quaternion feature maps. It is also the effective number
of feature maps for each of the real and imaginary parts.
(i.e. the number of quaternion filters in the convolution)
The total effective number of filters is 2 x filters.
kernel_size: An integer or tuple/list of n integers, specifying the
dimensions of the convolution window.
strides: An integer or tuple/list of n integers,
spfying the strides 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, ...)`.
It defaults to the `image_data_format` value found in your
Keras config file at `~/.keras/keras.json`.
If you never set it, then it will be "channels_last".
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.
activation: Activation function to use
(see keras.activations).
If you don't specify anything, no activation is applied
(ie. "linear" activation: `a(x) = x`).
use_bias: Boolean, whether the layer uses a bias vector.
normalize_weight: Boolean, whether the layer normalizes its quaternion
weights before convolving the quaternion input.
The quaternion normalization performed is similar to the one
for the batchnorm. Each of the quaternion kernels are centred and multiplied by
the inverse square root of covariance matrix.
Then, a quaternion multiplication is perfromed as the normalized weights are
multiplied by the quaternion scaling factor gamma.
kernel_initializer: Initializer for the quaternion `kernel` weights matrix.
By default it is 'quaternion'. The 'quaternion_independent'
and the usual initializers could also be used.
(see keras.initializers and init.py).
bias_initializer: Initializer for the bias vector
(see keras.initializers).
kernel_regularizer: Regularizer function applied to
the `kernel` weights matrix
(see keras.regularizers).
bias_regularizer: Regularizer function applied to the bias vector
(see keras.regularizers).
activity_regularizer: Regularizer function applied to
the output of the layer (its "activation").
(see keras.regularizers).
kernel_constraint: Constraint function applied to the kernel matrix
(see keras.constraints).
bias_constraint: Constraint function applied to the bias vector
(see keras.constraints).
spectral_parametrization: Whether or not to use a spectral
parametrization of the parameters.
"""
def __init__(self, rank,
filters,
kernel_size,
strides=1,
padding='valid',
data_format=None,
dilation_rate=1,
activation=None,
use_bias=True,
normalize_weight=False,
kernel_initializer='quaternion',
bias_initializer='zeros',
gamma_diag_initializer=sqrt_init,
gamma_off_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
gamma_diag_regularizer=None,
gamma_off_regularizer=None,
activity_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
gamma_diag_constraint=None,
gamma_off_constraint=None,
init_criterion='he',
seed=None,
spectral_parametrization=False,
epsilon=1e-7,
**kwargs):
super(QuaternionConv, self).__init__(**kwargs)
self.rank = rank
self.filters = filters
self.kernel_size = conv_utils.normalize_tuple(kernel_size, rank, 'kernel_size')
self.strides = conv_utils.normalize_tuple(strides, rank, 'strides')
self.padding = conv_utils.normalize_padding(padding)
self.data_format = 'channels_last' if rank == 1 else conv_utils.normalize_data_format(data_format)
self.dilation_rate = conv_utils.normalize_tuple(dilation_rate, rank, 'dilation_rate')
self.activation = activations.get(activation)
self.use_bias = use_bias
self.normalize_weight = normalize_weight
self.init_criterion = init_criterion
self.spectral_parametrization = spectral_parametrization
self.epsilon = epsilon
self.kernel_initializer = sanitizedInitGet(kernel_initializer)
self.bias_initializer = sanitizedInitGet(bias_initializer)
self.gamma_diag_initializer = sanitizedInitGet(gamma_diag_initializer)
self.gamma_off_initializer = sanitizedInitGet(gamma_off_initializer)
self.kernel_regularizer = regularizers.get(kernel_regularizer)
self.bias_regularizer = regularizers.get(bias_regularizer)
self.gamma_diag_regularizer = regularizers.get(gamma_diag_regularizer)
self.gamma_off_regularizer = regularizers.get(gamma_off_regularizer)
self.activity_regularizer = regularizers.get(activity_regularizer)
self.kernel_constraint = constraints.get(kernel_constraint)
self.bias_constraint = constraints.get(bias_constraint)
self.gamma_diag_constraint = constraints.get(gamma_diag_constraint)
self.gamma_off_constraint = constraints.get(gamma_off_constraint)
if seed is None:
self.seed = np.random.randint(1, 10e6)
else:
self.seed = seed
self.input_spec = InputSpec(ndim=self.rank + 2)
def build(self, input_shape):
if self.data_format == 'channels_first':
channel_axis = 1
else:
channel_axis = -1
if input_shape[channel_axis] is None:
raise ValueError('The channel dimension of the inputs '
'should be defined. Found `None`.')
input_dim = input_shape[channel_axis] // 4
self.kernel_shape = self.kernel_size + (input_dim , self.filters)
# The kernel shape here is a complex kernel shape:
# nb of complex feature maps = input_dim;
# nb of output complex feature maps = self.filters;
# imaginary kernel size = real kernel size
# = self.kernel_size
# = complex kernel size
if self.kernel_initializer in {'quaternion', 'quaternion_independent'}:
kls = {'quaternion': QuaternionInit,
'quaternion_independent': QuaternionIndependentFilters}[self.kernel_initializer]
kern_init = kls(
kernel_size=self.kernel_size,
input_dim=input_dim,
weight_dim=self.rank,
nb_filters=self.filters,
criterion=self.init_criterion
)
else:
kern_init = self.kernel_initializer
self.kernel = self.add_weight(
self.kernel_shape,
initializer=kern_init,
name='kernel',
regularizer=self.kernel_regularizer,
constraint=self.kernel_constraint
)
if self.normalize_weight:
gamma_shape = (input_dim * self.filters,)
self.gamma_rr = self.add_weight(
shape=gamma_shape,
name='gamma_rr',
initializer=self.gamma_diag_initializer,
regularizer=self.gamma_diag_regularizer,
constraint=self.gamma_diag_constraint
)
self.gamma_ri = self.add_weight(
shape=gamma_shape,
name='gamma_ri',
initializer=self.gamma_off_initializer,
regularizer=self.gamma_off_regularizer,
constraint=self.gamma_off_constraint
)
self.gamma_rj = self.add_weight(
shape=gamma_shape,
name='gamma_rj',
initializer=self.gamma_off_initializer,
regularizer=self.gamma_off_regularizer,
constraint=self.gamma_off_constraint
)
self.gamma_rk = self.add_weight(
shape=gamma_shape,
name='gamma_rk',
initializer=self.gamma_off_initializer,
regularizer=self.gamma_off_regularizer,
constraint=self.gamma_off_constraint
)
self.gamma_ii = self.add_weight(
shape=gamma_shape,
name='gamma_ii',
initializer=self.gamma_diag_initializer,
regularizer=self.gamma_diag_regularizer,
constraint=self.gamma_diag_constraint
)
self.gamma_ij = self.add_weight(
shape=gamma_shape,
name='gamma_ij',
initializer=self.gamma_off_initializer,
regularizer=self.gamma_off_regularizer,
constraint=self.gamma_off_constraint
)
self.gamma_ik = self.add_weight(
shape=gamma_shape,
name='gamma_ik',
initializer=self.gamma_off_initializer,
regularizer=self.gamma_off_regularizer,
constraint=self.gamma_off_constraint
)
self.gamma_jj = self.add_weight(
shape=gamma_shape,
name='gamma_jj',
initializer=self.gamma_diag_initializer,
regularizer=self.gamma_diag_regularizer,
constraint=self.gamma_diag_constraint
)
self.gamma_jk = self.add_weight(
shape=gamma_shape,
name='gamma_jk',
initializer=self.gamma_diag_initializer,
regularizer=self.gamma_diag_regularizer,
constraint=self.gamma_diag_constraint
)
self.gamma_kk = self.add_weight(
shape=gamma_shape,
name='gamma_kk',
initializer=self.gamma_off_initializer,
regularizer=self.gamma_off_regularizer,
constraint=self.gamma_off_constraint
)
else:
self.gamma_rr = None
self.gamma_ri = None
self.gamma_rj = None
self.gamma_rk = None
self.gamma_ii = None
self.gamma_ij = None
self.gamma_ik = None
self.gamma_jj = None
self.gamma_jk = None
self.gamma_kk = None
#End of non understanded block
if self.use_bias:
bias_shape = (4 * self.filters,)
self.bias = self.add_weight(
bias_shape,
initializer=self.bias_initializer,
name='bias',
regularizer=self.bias_regularizer,
constraint=self.bias_constraint
)
else:
self.bias = None
# Set input spec.
self.input_spec = InputSpec(ndim=self.rank + 2,
axes={channel_axis: input_dim * 4})
self.built = True
def call(self, inputs):
channel_axis = 1 if self.data_format == 'channels_first' else -1
input_dim = K.shape(inputs)[channel_axis] // 4
index2 = self.filters*2
index3 = self.filters*3
if self.rank == 1:
f_r = self.kernel[:, :, :self.filters]
f_i = self.kernel[:, :, self.filters:index2]
f_j = self.kernel[:, :, index2:index3]
f_k = self.kernel[:, :, index3:]
elif self.rank == 2:
f_r = self.kernel[:, :, :, :self.filters]
f_i = self.kernel[:, :, :, self.filters:index2]
f_j = self.kernel[:, :, :, index2:index3]
f_k = self.kernel[:, :, :, index3:]
elif self.rank == 3:
f_r = self.kernel[:, :, :, :, :self.filters]
f_i = self.kernel[:, :, :, :, self.filters:index2]
f_j = self.kernel[:, :, :, :, index2:index3]
f_k = self.kernel[:, :, :, :, index3:]
convArgs = {"strides": self.strides[0] if self.rank == 1 else self.strides,
"padding": self.padding,
"data_format": self.data_format,
"dilation_rate": self.dilation_rate[0] if self.rank == 1 else self.dilation_rate}
convFunc = {1: K.conv1d,
2: K.conv2d,
3: K.conv3d}[self.rank]
# processing if the weights are assumed to be represented in the spectral domain
# Do we conserve this for quaternions ? Currently no
if self.spectral_parametrization:
print("Quaternion spectral weights parametrization not implemented yet, aborting.")
sys.exit(1)
if self.rank == 1:
f_r = K.permute_dimensions(f_r, (2,1,0))
f_i = K.permute_dimensions(f_i, (2,1,0))
f = K.concatenate([f_r, f_i], axis=0)
fshape = K.shape(f)
f = K.reshape(f, (fshape[0] * fshape[1], fshape[2]))
f = ifft(f)
f = K.reshape(f, fshape)
f_r = f[:fshape[0]//2]
f_i = f[fshape[0]//2:]
f_r = K.permute_dimensions(f_r, (2,1,0))
f_i = K.permute_dimensions(f_i, (2,1,0))
elif self.rank == 2:
f_r = K.permute_dimensions(f_r, (3,2,0,1))
f_i = K.permute_dimensions(f_i, (3,2,0,1))
f = K.concatenate([f_r, f_i], axis=0)
fshape = K.shape(f)
f = K.reshape(f, (fshape[0] * fshape[1], fshape[2], fshape[3]))
f = ifft2(f)
f = K.reshape(f, fshape)
f_r = f[:fshape[0]//2]
f_i = f[fshape[0]//2:]
f_r = K.permute_dimensions(f_r, (2,3,1,0))
f_i = K.permute_dimensions(f_i, (2,3,1,0))
# In case of weight normalization, real and imaginary weights are normalized
if self.normalize_weight:
print("Quaternion weights normalization not implemented yet, aborting.")
sys.exit(1)
ker_shape = self.kernel_shape
nb_kernels = ker_shape[-2] * ker_shape[-1]
kernel_shape_4_norm = (np.prod(self.kernel_size), nb_kernels)
reshaped_f_r = K.reshape(f_r, kernel_shape_4_norm)
reshaped_f_i = K.reshape(f_i, kernel_shape_4_norm)
reduction_axes = list(range(2))
del reduction_axes[-1]
mu_real = K.mean(reshaped_f_r, axis=reduction_axes)
mu_imag = K.mean(reshaped_f_i, axis=reduction_axes)
broadcast_mu_shape = [1] * 2
broadcast_mu_shape[-1] = nb_kernels
broadcast_mu_real = K.reshape(mu_real, broadcast_mu_shape)
broadcast_mu_imag = K.reshape(mu_imag, broadcast_mu_shape)
reshaped_f_r_centred = reshaped_f_r - broadcast_mu_real
reshaped_f_i_centred = reshaped_f_i - broadcast_mu_imag
Vrr = K.mean(reshaped_f_r_centred ** 2, axis=reduction_axes) + self.epsilon
Vii = K.mean(reshaped_f_i_centred ** 2, axis=reduction_axes) + self.epsilon
Vri = K.mean(reshaped_f_r_centred * reshaped_f_i_centred,
axis=reduction_axes) + self.epsilon
normalized_weight = complex_normalization(
K.concatenate([reshaped_f_r, reshaped_f_i], axis=-1),
Vrr, Vii, Vri,
beta = None,
gamma_rr = self.gamma_rr,
gamma_ri = self.gamma_ri,
gamma_ii = self.gamma_ii,
scale=True,
center=False,
axis=-1
)
normalized_real = normalized_weight[:, :nb_kernels]
normalized_imag = normalized_weight[:, nb_kernels:]
f_r = K.reshape(normalized_real, self.kernel_shape)
f_i = K.reshape(normalized_imag, self.kernel_shape)
#
# Performing quaternion convolution
#
f_r._keras_shape = self.kernel_shape
f_i._keras_shape = self.kernel_shape
f_j._keras_shape = self.kernel_shape
f_k._keras_shape = self.kernel_shape
cat_kernels_4_r = K.concatenate([f_r, -f_i, -f_j, -f_k], axis=-2)
cat_kernels_4_i = K.concatenate([f_i, f_r, -f_k, f_j], axis=-2)
cat_kernels_4_j = K.concatenate([f_j, f_k, f_r, -f_i], axis=-2)
cat_kernels_4_k = K.concatenate([f_k, -f_j, f_i, f_r], axis=-2)
cat_kernels_4_quaternion = K.concatenate([cat_kernels_4_r, cat_kernels_4_i, cat_kernels_4_j, cat_kernels_4_k], axis=-1)
cat_kernels_4_quaternion._keras_shape = self.kernel_size + (4 * input_dim, 4 * self.filters)
output = convFunc(inputs, cat_kernels_4_quaternion, **convArgs)
if self.use_bias:
output = K.bias_add(
output,
self.bias,
data_format=self.data_format
)
if self.activation is not None:
output = self.activation(output)
return output
def compute_output_shape(self, input_shape):
if self.data_format == 'channels_last':
space = input_shape[1:-1]
new_space = []
for i in range(len(space)):
new_dim = conv_utils.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 (input_shape[0],) + tuple(new_space) + (4 * self.filters,)
if self.data_format == 'channels_first':
space = input_shape[2:]
new_space = []
for i in range(len(space)):
new_dim = conv_utils.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 (input_shape[0],) + (4 * self.filters,) + tuple(new_space)
def get_config(self):
config = {
'rank': self.rank,
'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': activations.serialize(self.activation),
'use_bias': self.use_bias,
'normalize_weight': self.normalize_weight,
'kernel_initializer': sanitizedInitSer(self.kernel_initializer),
'bias_initializer': sanitizedInitSer(self.bias_initializer),
'gamma_diag_initializer': sanitizedInitSer(self.gamma_diag_initializer),
'gamma_off_initializer': sanitizedInitSer(self.gamma_off_initializer),
'kernel_regularizer': regularizers.serialize(self.kernel_regularizer),
'bias_regularizer': regularizers.serialize(self.bias_regularizer),
'gamma_diag_regularizer': regularizers.serialize(self.gamma_diag_regularizer),
'gamma_off_regularizer': regularizers.serialize(self.gamma_off_regularizer),
'activity_regularizer': regularizers.serialize(self.activity_regularizer),
'kernel_constraint': constraints.serialize(self.kernel_constraint),
'bias_constraint': constraints.serialize(self.bias_constraint),
'gamma_diag_constraint': constraints.serialize(self.gamma_diag_constraint),
'gamma_off_constraint': constraints.serialize(self.gamma_off_constraint),
'init_criterion': self.init_criterion,
'spectral_parametrization': self.spectral_parametrization,
}
base_config = super(QuaternionConv, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
class QuaternionConv1D(QuaternionConv):
"""1D quaternion convolution layer.
This layer creates a quaternion convolution kernel that is convolved
with a quaternion input layer over a single quaternion spatial (or temporal) dimension
to produce a quaternion output tensor.
If `use_bias` is True, a bias vector is created and added to the quaternion output.
Finally, if `activation` is not `None`,
it is applied each of the real and imaginary parts of the output.
When using this layer as the first layer in a model,
provide an `input_shape` argument
(tuple of integers or `None`, e.g.
`(10, 128)` for sequences of 10 vectors of 128-dimensional vectors,
or `(None, 128)` for variable-length sequences of 128-dimensional vectors.
# Arguments
filters: Integer, the dimensionality of the output space, i.e,
the number of quaternion feature maps. It is also the effective number
of feature maps for each of the real and imaginary parts.
(i.e. the number of quaternion filters in the convolution)
The total effective number of filters is 2 x filters.
kernel_size: An integer or tuple/list of n integers, specifying the
dimensions of the 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"`, `"causal"` or `"same"` (case-insensitive).
`"causal"` results in causal (dilated) convolutions, e.g. output[t]
does not depend on input[t+1:]. Useful when modeling temporal data
where the model should not violate the temporal order.
See [WaveNet: A Generative Model for Raw Audio, section 2.1](https://arxiv.org/abs/1609.03499).
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.
activation: Activation function to use
(see keras.activations).
If you don't specify anything, no activation is applied
(ie. "linear" activation: `a(x) = x`).
use_bias: Boolean, whether the layer uses a bias vector.
normalize_weight: Boolean, whether the layer normalizes its quaternion
weights before convolving the quaternion input.
The quaternion normalization performed is similar to the one
for the batchnorm. Each of the quaternion kernels are centred and multiplied by
the inverse square root of covariance matrix.
Then, a quaternion multiplication is perfromed as the normalized weights are
multiplied by the quaternion scaling factor gamma.
kernel_initializer: Initializer for the quaternion `kernel` weights matrix.
By default it is 'quaternion'. The 'quaternion_independent'
and the usual initializers could also be used.
(see keras.initializers and init.py).
bias_initializer: Initializer for the bias vector
(see keras.initializers).
kernel_regularizer: Regularizer function applied to
the `kernel` weights matrix
(see keras.regularizers).
bias_regularizer: Regularizer function applied to the bias vector
(see keras.regularizers).
activity_regularizer: Regularizer function applied to
the output of the layer (its "activation").
(see keras.regularizers).
kernel_constraint: Constraint function applied to the kernel matrix
(see keras.constraints).
bias_constraint: Constraint function applied to the bias vector
(see keras.constraints).
spectral_parametrization: Whether or not to use a spectral
parametrization of the parameters.
# Input shape
3D tensor with shape: `(batch_size, steps, input_dim)`
# Output shape
3D tensor with shape: `(batch_size, new_steps, 2 x filters)`
`steps` value might have changed due to padding or strides.
"""
def __init__(self, filters,
kernel_size,
strides=1,
padding='valid',
dilation_rate=1,
activation=None,
use_bias=True,
kernel_initializer='quaternion',
bias_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
activity_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
seed=None,
init_criterion='he',
spectral_parametrization=False,
**kwargs):
super(QuaternionConv1D, self).__init__(
rank=1,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format='channels_last',
dilation_rate=dilation_rate,
activation=activation,
use_bias=use_bias,
kernel_initializer=kernel_initializer,
bias_initializer=bias_initializer,
kernel_regularizer=kernel_regularizer,
bias_regularizer=bias_regularizer,
activity_regularizer=activity_regularizer,
kernel_constraint=kernel_constraint,
bias_constraint=bias_constraint,
init_criterion=init_criterion,
spectral_parametrization=spectral_parametrization,
**kwargs)
def get_config(self):
config = super(QuaternionConv1D, self).get_config()
config.pop('rank')
config.pop('data_format')
return config
class QuaternionConv2D(QuaternionConv):
"""2D Quaternion convolution layer (e.g. spatial convolution over images).
This layer creates a quaternion convolution kernel that is convolved
with a quaternion input layer to produce a quaternion output tensor. If `use_bias`
is True, a quaternion bias vector is created and added to the outputs.
Finally, if `activation` is not `None`, it is applied to both the
real and imaginary parts of the output.
When using this layer as the first layer in a model,
provide the keyword argument `input_shape`
(tuple of integers, does not include the sample axis),
e.g. `input_shape=(128, 128, 3)` for 128x128 RGB pictures
in `data_format="channels_last"`.
# Arguments
filters: Integer, the dimensionality of the quaternion output space
(i.e, the number quaternion feature maps in the convolution).
The total effective number of filters or feature maps is 2 x filters.
kernel_size: An integer or tuple/list of 2 integers, specifying the
width and height 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 width and height.
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)`.
It defaults to the `image_data_format` value found in your
Keras config file at `~/.keras/keras.json`.
If you never set it, then it will be "channels_last".
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.
activation: Activation function to use
(see keras.activations).
If you don't specify anything, no activation is applied
(ie. "linear" activation: `a(x) = x`).
use_bias: Boolean, whether the layer uses a bias vector.
normalize_weight: Boolean, whether the layer normalizes its quaternion
weights before convolving the quaternion input.
The quaternion normalization performed is similar to the one
for the batchnorm. Each of the quaternion kernels are centred and multiplied by
the inverse square root of covariance matrix.
Then, a quaternion multiplication is perfromed as the normalized weights are
multiplied by the quaternion scaling factor gamma.
kernel_initializer: Initializer for the quaternion `kernel` weights matrix.
By default it is 'quaternion'. The 'quaternion_independent'
and the usual initializers could also be used.
(see keras.initializers and init.py).
bias_initializer: Initializer for the bias vector
(see keras.initializers).
kernel_regularizer: Regularizer function applied to
the `kernel` weights matrix
(see keras.regularizers).
bias_regularizer: Regularizer function applied to the bias vector
(see keras.regularizers).
activity_regularizer: Regularizer function applied to
the output of the layer (its "activation").
(see keras.regularizers).
kernel_constraint: Constraint function applied to the kernel matrix
(see keras.constraints).
bias_constraint: Constraint function applied to the bias vector
(see keras.constraints).
spectral_parametrization: Whether or not to use a spectral
parametrization of the parameters.
# Input shape
4D tensor with shape:
`(samples, channels, rows, cols)` if data_format='channels_first'
or 4D tensor with shape:
`(samples, rows, cols, channels)` if data_format='channels_last'.
# Output shape
4D tensor with shape:
`(samples, 2 x filters, new_rows, new_cols)` if data_format='channels_first'
or 4D tensor with shape:
`(samples, new_rows, new_cols, 2 x filters)` if data_format='channels_last'.
`rows` and `cols` values might have changed due to padding.
"""
def __init__(self, filters,
kernel_size,
strides=(1, 1),
padding='valid',
data_format=None,
dilation_rate=(1, 1),
activation=None,
use_bias=True,
kernel_initializer='quaternion',
bias_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
activity_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
seed=None,
init_criterion='he',
spectral_parametrization=False,
**kwargs):
super(QuaternionConv2D, self).__init__(
rank=2,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format=data_format,
dilation_rate=dilation_rate,
activation=activation,
use_bias=use_bias,
kernel_initializer=kernel_initializer,
bias_initializer=bias_initializer,
kernel_regularizer=kernel_regularizer,
bias_regularizer=bias_regularizer,
activity_regularizer=activity_regularizer,
kernel_constraint=kernel_constraint,
bias_constraint=bias_constraint,
init_criterion=init_criterion,
spectral_parametrization=spectral_parametrization,
**kwargs)
def get_config(self):
config = super(QuaternionConv2D, self).get_config()
config.pop('rank')
return config
class QuaternionConv3D(QuaternionConv):
"""3D convolution layer (e.g. spatial convolution over volumes).
This layer creates a quaternion convolution kernel that is convolved
with a quaternion layer input to produce a quaternion output tensor.
If `use_bias` is True,
a quaternion bias vector is created and added to the outputs. Finally, if
`activation` is not `None`, it is applied to each of the real and imaginary
parts of the output.
When using this layer as the first layer in a model,
provide the keyword argument `input_shape`
(tuple of integers, does not include the sample axis),
e.g. `input_shape=(2, 128, 128, 128, 3)` for 128x128x128 volumes
with 3 channels,
in `data_format="channels_last"`.
# Arguments
filters: Integer, the dimensionality of the quaternion output space
(i.e, the number quaternion feature maps in the convolution).
The total effective number of filters or feature maps is 2 x filters.
kernel_size: An integer or tuple/list of 3 integers, specifying the
width and height 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 each spatial dimension.
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, spatial_dim1, spatial_dim2, spatial_dim3, channels)`
while `channels_first` corresponds to inputs with shape
`(batch, channels, spatial_dim1, spatial_dim2, spatial_dim3)`.
It defaults to the `image_data_format` value found in your
Keras config file at `~/.keras/keras.json`.
If you never set it, then it will be "channels_last".
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.
activation: Activation function to use
(see keras.activations).
If you don't specify anything, no activation is applied
(ie. "linear" activation: `a(x) = x`).
use_bias: Boolean, whether the layer uses a bias vector.
normalize_weight: Boolean, whether the layer normalizes its quaternion
weights before convolving the quaternion input.
The quaternion normalization performed is similar to the one
for the batchnorm. Each of the quaternion kernels are centred and multiplied by
the inverse square root of covariance matrix.
Then, a quaternion multiplication is perfromed as the normalized weights are
multiplied by the quaternion scaling factor gamma.
kernel_initializer: Initializer for the quaternion `kernel` weights matrix.
By default it is 'quaternion'. The 'quaternion_independent'
and the usual initializers could also be used.
(see keras.initializers and init.py).
bias_initializer: Initializer for the bias vector
(see keras.initializers).
kernel_regularizer: Regularizer function applied to
the `kernel` weights matrix
(see keras.regularizers).
bias_regularizer: Regularizer function applied to the bias vector
(see keras.regularizers).
activity_regularizer: Regularizer function applied to
the output of the layer (its "activation").
(see keras.regularizers).
kernel_constraint: Constraint function applied to the kernel matrix
(see keras.constraints).
bias_constraint: Constraint function applied to the bias vector
(see keras.constraints).
spectral_parametrization: Whether or not to use a spectral
parametrization of the parameters.
# Input shape
5D tensor with shape:
`(samples, channels, conv_dim1, conv_dim2, conv_dim3)` if data_format='channels_first'
or 5D tensor with shape:
`(samples, conv_dim1, conv_dim2, conv_dim3, channels)` if data_format='channels_last'.
# Output shape
5D tensor with shape:
`(samples, 2 x filters, new_conv_dim1, new_conv_dim2, new_conv_dim3)` if data_format='channels_first'
or 5D tensor with shape:
`(samples, new_conv_dim1, new_conv_dim2, new_conv_dim3, 2 x filters)` if data_format='channels_last'.
`new_conv_dim1`, `new_conv_dim2` and `new_conv_dim3` values might have changed due to padding.
"""
def __init__(self, filters,
kernel_size,
strides=(1, 1, 1),
padding='valid',
data_format=None,
dilation_rate=(1, 1, 1),
activation=None,
use_bias=True,
kernel_initializer='quaternion',
bias_initializer='zeros',
kernel_regularizer=None,
bias_regularizer=None,
activity_regularizer=None,
kernel_constraint=None,
bias_constraint=None,
seed=None,
init_criterion='he',
spectral_parametrization=False,
**kwargs):
super(QuaternionConv3D, self).__init__(
rank=3,
filters=filters,
kernel_size=kernel_size,
strides=strides,
padding=padding,
data_format=data_format,
dilation_rate=dilation_rate,
activation=activation,
use_bias=use_bias,
kernel_initializer=kernel_initializer,
bias_initializer=bias_initializer,
kernel_regularizer=kernel_regularizer,
bias_regularizer=bias_regularizer,
activity_regularizer=activity_regularizer,
kernel_constraint=kernel_constraint,
bias_constraint=bias_constraint,
init_criterion=init_criterion,
spectral_parametrization=spectral_parametrization,
**kwargs)
def get_config(self):
config = super(QuaternionConv3D, self).get_config()
config.pop('rank')
return config
def sanitizedInitGet(init):
if init in ["sqrt_init"]:
return sqrt_init
elif init in ["complex", "complex_independent",
"glorot_complex", "he_complex",
"quaternion", "quaternion_independent"]:
return init
else:
return initializers.get(init)
def sanitizedInitSer(init):
if init in [sqrt_init]:
return "sqrt_init"
elif init == "complex" or isinstance(init, ComplexInit):
return "complex"
elif init == "complex_independent" or isinstance(init, ComplexIndependentFilters):
return "complex_independent"
elif init == "quaternion" or isinstance(init, QuaternionInit):
return "quaternion"
elif init == "quaternion_independent" or isinstance(init, QuaternionIndependentFilters):
return "quaternion_independent"
else:
return initializers.serialize(init)
# Aliases
QuaternionConvolution1D = QuaternionConv1D
QuaternionConvolution2D = QuaternionConv2D
QuaternionConvolution3D = QuaternionConv3D
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