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complexnn/init.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Contributors: Titouan Parcollet
# Authors: Chiheb Trabelsi
import numpy as np
from numpy.random import RandomState
from random import gauss
import keras.backend as K
from keras import initializers
from keras.initializers import Initializer
from keras.utils.generic_utils import (serialize_keras_object,
deserialize_keras_object)
#####################################################################
# Quaternion Implementations #
#####################################################################
class QuaternionIndependentFilters(Initializer):
# This initialization constructs quaternion-valued kernels
# that are independent as much as possible from each other
# while respecting either the He or the Glorot criterion.
def __init__(self, kernel_size, input_dim,
weight_dim, nb_filters=None,
criterion='glorot', seed=None):
# `weight_dim` is used as a parameter for sanity check
# as we should not pass an integer as kernel_size when
# the weight dimension is >= 2.
# nb_filters == 0 if weights are not convolutional (matrix instead of filters)
# then in such a case, weight_dim = 2.
# (in case of 2D input):
# nb_filters == None and len(kernel_size) == 2 and_weight_dim == 2
# conv1D: len(kernel_size) == 1 and weight_dim == 1
# conv2D: len(kernel_size) == 2 and weight_dim == 2
# conv3d: len(kernel_size) == 3 and weight_dim == 3
assert len(kernel_size) == weight_dim and weight_dim in {0, 1, 2, 3}
self.nb_filters = nb_filters
self.kernel_size = kernel_size
self.input_dim = input_dim
self.weight_dim = weight_dim
self.criterion = criterion
self.seed = 1337 if seed is None else seed
def __call__(self, shape, dtype=None):
if self.nb_filters is not None:
num_rows = self.nb_filters * self.input_dim
num_cols = np.prod(self.kernel_size)
else:
# in case it is the kernel is a matrix and not a filter
# which is the case of 2D input (No feature maps).
num_rows = self.input_dim
num_cols = self.kernel_size[-1]
flat_shape = (int(num_rows), int(num_cols))
rng = RandomState(self.seed)
r = rng.uniform(size=flat_shape)
i = rng.uniform(size=flat_shape)
z = r + 1j * i
u, _, v = np.linalg.svd(z)
unitary_z = np.dot(u, np.dot(np.eye(int(num_rows), int(num_cols)), np.conjugate(v).T))
real_unitary = unitary_z.real
imag_unitary = unitary_z.imag
if self.nb_filters is not None:
indep_real = np.reshape(real_unitary, (num_rows,) + tuple(self.kernel_size))
indep_imag = np.reshape(imag_unitary, (num_rows,) + tuple(self.kernel_size))
fan_in, fan_out = initializers._compute_fans(
tuple(self.kernel_size) + (int(self.input_dim), self.nb_filters)
)
else:
indep_real = real_unitary
indep_imag = imag_unitary
fan_in, fan_out = (int(self.input_dim), self.kernel_size[-1])
if self.criterion == 'glorot':
desired_var = 1. / (fan_in + fan_out)
elif self.criterion == 'he':
desired_var = 1. / (fan_in)
else:
raise ValueError('Invalid criterion: ' + self.criterion)
multip_real = np.sqrt(desired_var / np.var(indep_real))
multip_imag = np.sqrt(desired_var / np.var(indep_imag))
scaled_real = multip_real * indep_real
scaled_imag = multip_imag * indep_imag
if self.weight_dim == 2 and self.nb_filters is None:
weight_real = scaled_real
weight_imag = scaled_imag
else:
kernel_shape = tuple(self.kernel_size) + (int(self.input_dim), self.nb_filters)
if self.weight_dim == 1:
transpose_shape = (1, 0)
elif self.weight_dim == 2 and self.nb_filters is not None:
transpose_shape = (1, 2, 0)
elif self.weight_dim == 3 and self.nb_filters is not None:
transpose_shape = (1, 2, 3, 0)
weight_real = np.transpose(scaled_real, transpose_shape)
weight_imag = np.transpose(scaled_imag, transpose_shape)
weight_real = np.reshape(weight_real, kernel_shape)
weight_imag = np.reshape(weight_imag, kernel_shape)
weight = np.concatenate([weight_real, weight_imag], axis=-1)
return weight
def get_config(self):
return {'nb_filters': self.nb_filters,
'kernel_size': self.kernel_size,
'input_dim': self.input_dim,
'weight_dim': self.weight_dim,
'criterion': self.criterion,
'seed': self.seed}
class QuaternionInit(Initializer):
# The standard complex initialization using
# either the He or the Glorot criterion.
def __init__(self, kernel_size, input_dim,
weight_dim, nb_filters=None,
criterion='glorot', seed=None):
# `weight_dim` is used as a parameter for sanity check
# as we should not pass an integer as kernel_size when
# the weight dimension is >= 2.
# nb_filters == 0 if weights are not convolutional (matrix instead of filters)
# then in such a case, weight_dim = 2.
# (in case of 2D input):
# nb_filters == None and len(kernel_size) == 2 and_weight_dim == 2
# conv1D: len(kernel_size) == 1 and weight_dim == 1
# conv2D: len(kernel_size) == 2 and weight_dim == 2
# conv3d: len(kernel_size) == 3 and weight_dim == 3
assert len(kernel_size) == weight_dim and weight_dim in {0, 1, 2, 3}
self.nb_filters = nb_filters
self.kernel_size = kernel_size
self.input_dim = input_dim
self.weight_dim = weight_dim
self.criterion = criterion
self.seed = 1337 if seed is None else seed
def __call__(self, shape, dtype=None):
if self.nb_filters is not None:
kernel_shape = tuple(self.kernel_size) + (int(self.input_dim), self.nb_filters)
else:
kernel_shape = (int(self.input_dim), self.kernel_size[-1])
fan_in, fan_out = initializers._compute_fans(
tuple(self.kernel_size) + (self.input_dim, self.nb_filters)
)
# Quaternion operations start here
if self.criterion == 'glorot':
s = 1. / np.sqrt(2*(fan_in + fan_out))
elif self.criterion == 'he':
s = 1. / np.sqrt(2*fan_in)
else:
raise ValueError('Invalid criterion: ' + self.criterion)
#Generating randoms and purely imaginary quaternions :
number_of_weights = np.prod(kernel_shape)
v_i = np.random.uniform(0.0,1.0,number_of_weights)
v_j = np.random.uniform(0.0,1.0,number_of_weights)
v_k = np.random.uniform(0.0,1.0,number_of_weights)
#Make these purely imaginary quaternions unitary
for i in range(0, number_of_weights):
norm = np.sqrt(v_i[i]**2 + v_j[i]**2 + v_k[i]**2)
v_i[i]/= norm
v_j[i]/= norm
v_k[i]/= norm
v_i = v_i.reshape(kernel_shape)
v_j = v_j.reshape(kernel_shape)
v_k = v_k.reshape(kernel_shape)
rng = RandomState(self.seed)
modulus = rng.rayleigh(scale=s, size=kernel_shape)
phase = rng.uniform(low=-np.pi, high=np.pi, size=kernel_shape)
weight_r = modulus * np.cos(phase)
weight_i = modulus * v_i*np.sin(phase)
weight_j = modulus * v_j*np.sin(phase)
weight_k = modulus * v_k*np.sin(phase)
weight = np.concatenate([weight_r, weight_i, weight_j, weight_k], axis=-1)
return weight
#####################################################################
# Complex Implementations #
#####################################################################
class IndependentFilters(Initializer):
# This initialization constructs real-valued kernels
# that are independent as much as possible from each other
# while respecting either the He or the Glorot criterion.
def __init__(self, kernel_size, input_dim,
weight_dim, nb_filters=None,
criterion='glorot', seed=None):
# `weight_dim` is used as a parameter for sanity check
# as we should not pass an integer as kernel_size when
# the weight dimension is >= 2.
# nb_filters == 0 if weights are not convolutional (matrix instead of filters)
# then in such a case, weight_dim = 2.
# (in case of 2D input):
# nb_filters == None and len(kernel_size) == 2 and_weight_dim == 2
# conv1D: len(kernel_size) == 1 and weight_dim == 1
# conv2D: len(kernel_size) == 2 and weight_dim == 2
# conv3d: len(kernel_size) == 3 and weight_dim == 3
assert len(kernel_size) == weight_dim and weight_dim in {0, 1, 2, 3}
self.nb_filters = nb_filters
self.kernel_size = kernel_size
self.input_dim = input_dim
self.weight_dim = weight_dim
self.criterion = criterion
self.seed = 1337 if seed is None else seed
def __call__(self, shape, dtype=None):
if self.nb_filters is not None:
num_rows = self.nb_filters * self.input_dim
num_cols = np.prod(self.kernel_size)
else:
# in case it is the kernel is a matrix and not a filter
# which is the case of 2D input (No feature maps).
num_rows = self.input_dim
num_cols = self.kernel_size[-1]
flat_shape = (num_rows, num_cols)
rng = RandomState(self.seed)
x = rng.uniform(size=flat_shape)
u, _, v = np.linalg.svd(x)
orthogonal_x = np.dot(u, np.dot(np.eye(num_rows, num_cols), v.T))
if self.nb_filters is not None:
independent_filters = np.reshape(orthogonal_x, (num_rows,) + tuple(self.kernel_size))
fan_in, fan_out = initializers._compute_fans(
tuple(self.kernel_size) + (self.input_dim, self.nb_filters)
)
else:
independent_filters = orthogonal_x
fan_in, fan_out = (self.input_dim, self.kernel_size[-1])
if self.criterion == 'glorot':
desired_var = 2. / (fan_in + fan_out)
elif self.criterion == 'he':
desired_var = 2. / fan_in
else:
raise ValueError('Invalid criterion: ' + self.criterion)
multip_constant = np.sqrt (desired_var / np.var(independent_filters))
scaled_indep = multip_constant * independent_filters
if self.weight_dim == 2 and self.nb_filters is None:
weight_real = scaled_real
weight_imag = scaled_imag
else:
kernel_shape = tuple(self.kernel_size) + (self.input_dim, self.nb_filters)
if self.weight_dim == 1:
transpose_shape = (1, 0)
elif self.weight_dim == 2 and self.nb_filters is not None:
transpose_shape = (1, 2, 0)
elif self.weight_dim == 3 and self.nb_filters is not None:
transpose_shape = (1, 2, 3, 0)
weight = np.transpose(scaled_indep, transpose_shape)
weight = np.reshape(weight, kernel_shape)
return weight
def get_config(self):
return {'nb_filters': self.nb_filters,
'kernel_size': self.kernel_size,
'input_dim': self.input_dim,
'weight_dim': self.weight_dim,
'criterion': self.criterion,
'seed': self.seed}
class ComplexIndependentFilters(Initializer):
# This initialization constructs complex-valued kernels
# that are independent as much as possible from each other
# while respecting either the He or the Glorot criterion.
def __init__(self, kernel_size, input_dim,
weight_dim, nb_filters=None,
criterion='glorot', seed=None):
# `weight_dim` is used as a parameter for sanity check
# as we should not pass an integer as kernel_size when
# the weight dimension is >= 2.
# nb_filters == 0 if weights are not convolutional (matrix instead of filters)
# then in such a case, weight_dim = 2.
# (in case of 2D input):
# nb_filters == None and len(kernel_size) == 2 and_weight_dim == 2
# conv1D: len(kernel_size) == 1 and weight_dim == 1
# conv2D: len(kernel_size) == 2 and weight_dim == 2
# conv3d: len(kernel_size) == 3 and weight_dim == 3
assert len(kernel_size) == weight_dim and weight_dim in {0, 1, 2, 3}
self.nb_filters = nb_filters
self.kernel_size = kernel_size
self.input_dim = input_dim
self.weight_dim = weight_dim
self.criterion = criterion
self.seed = 1337 if seed is None else seed
def __call__(self, shape, dtype=None):
if self.nb_filters is not None:
num_rows = self.nb_filters * self.input_dim
num_cols = np.prod(self.kernel_size)
else:
# in case it is the kernel is a matrix and not a filter
# which is the case of 2D input (No feature maps).
num_rows = self.input_dim
num_cols = self.kernel_size[-1]
flat_shape = (int(num_rows), int(num_cols))
rng = RandomState(self.seed)
r = rng.uniform(size=flat_shape)
i = rng.uniform(size=flat_shape)
z = r + 1j * i
u, _, v = np.linalg.svd(z)
unitary_z = np.dot(u, np.dot(np.eye(int(num_rows), int(num_cols)), np.conjugate(v).T))
real_unitary = unitary_z.real
imag_unitary = unitary_z.imag
if self.nb_filters is not None:
indep_real = np.reshape(real_unitary, (num_rows,) + tuple(self.kernel_size))
indep_imag = np.reshape(imag_unitary, (num_rows,) + tuple(self.kernel_size))
fan_in, fan_out = initializers._compute_fans(
tuple(self.kernel_size) + (int(self.input_dim), self.nb_filters)
)
else:
indep_real = real_unitary
indep_imag = imag_unitary
fan_in, fan_out = (int(self.input_dim), self.kernel_size[-1])
if self.criterion == 'glorot':
desired_var = 1. / (fan_in + fan_out)
elif self.criterion == 'he':
desired_var = 1. / (fan_in)
else:
raise ValueError('Invalid criterion: ' + self.criterion)
multip_real = np.sqrt(desired_var / np.var(indep_real))
multip_imag = np.sqrt(desired_var / np.var(indep_imag))
scaled_real = multip_real * indep_real
scaled_imag = multip_imag * indep_imag
if self.weight_dim == 2 and self.nb_filters is None:
weight_real = scaled_real
weight_imag = scaled_imag
else:
kernel_shape = tuple(self.kernel_size) + (int(self.input_dim), self.nb_filters)
if self.weight_dim == 1:
transpose_shape = (1, 0)
elif self.weight_dim == 2 and self.nb_filters is not None:
transpose_shape = (1, 2, 0)
elif self.weight_dim == 3 and self.nb_filters is not None:
transpose_shape = (1, 2, 3, 0)
weight_real = np.transpose(scaled_real, transpose_shape)
weight_imag = np.transpose(scaled_imag, transpose_shape)
weight_real = np.reshape(weight_real, kernel_shape)
weight_imag = np.reshape(weight_imag, kernel_shape)
weight = np.concatenate([weight_real, weight_imag], axis=-1)
return weight
def get_config(self):
return {'nb_filters': self.nb_filters,
'kernel_size': self.kernel_size,
'input_dim': self.input_dim,
'weight_dim': self.weight_dim,
'criterion': self.criterion,
'seed': self.seed}
class ComplexInit(Initializer):
# The standard complex initialization using
# either the He or the Glorot criterion.
def __init__(self, kernel_size, input_dim,
weight_dim, nb_filters=None,
criterion='glorot', seed=None):
# `weight_dim` is used as a parameter for sanity check
# as we should not pass an integer as kernel_size when
# the weight dimension is >= 2.
# nb_filters == 0 if weights are not convolutional (matrix instead of filters)
# then in such a case, weight_dim = 2.
# (in case of 2D input):
# nb_filters == None and len(kernel_size) == 2 and_weight_dim == 2
# conv1D: len(kernel_size) == 1 and weight_dim == 1
# conv2D: len(kernel_size) == 2 and weight_dim == 2
# conv3d: len(kernel_size) == 3 and weight_dim == 3
assert len(kernel_size) == weight_dim and weight_dim in {0, 1, 2, 3}
self.nb_filters = nb_filters
self.kernel_size = kernel_size
self.input_dim = input_dim
self.weight_dim = weight_dim
self.criterion = criterion
self.seed = 1337 if seed is None else seed
def __call__(self, shape, dtype=None):
if self.nb_filters is not None:
kernel_shape = tuple(self.kernel_size) + (int(self.input_dim), self.nb_filters)
else:
kernel_shape = (int(self.input_dim), self.kernel_size[-1])
fan_in, fan_out = initializers._compute_fans(
tuple(self.kernel_size) + (self.input_dim, self.nb_filters)
)
if self.criterion == 'glorot':
s = 1. / (fan_in + fan_out)
elif self.criterion == 'he':
s = 1. / fan_in
else:
raise ValueError('Invalid criterion: ' + self.criterion)
rng = RandomState(self.seed)
modulus = rng.rayleigh(scale=s, size=kernel_shape)
phase = rng.uniform(low=-np.pi, high=np.pi, size=kernel_shape)
weight_real = modulus * np.cos(phase)
weight_imag = modulus * np.sin(phase)
#print (weight_real.shape)
weight = np.concatenate([weight_real, weight_imag], axis=-1)
return weight
class SqrtInit(Initializer):
def __call__(self, shape, dtype=None):
return K.constant(1 / K.sqrt(2), shape=shape, dtype=dtype)
# Aliases:
sqrt_init = SqrtInit
independent_filters = IndependentFilters
quaternion_independent_filters = QuaternionIndependentFilters
complex_init = ComplexInit
quaternion_init = QuaternionInit
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