#!/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 .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='channels_last', 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 = K.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) kls = {'quaternion': qconv_init}[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) 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 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] # # 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', data_format='channels_last', 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=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(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='channels_last', 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='channels_last', 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 == "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