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recurrent.py
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recurrent.py
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# -*- coding: utf-8 -*-
from __future__ import absolute_import
import numpy as np
np.set_printoptions(threshold=np.inf)
from .. import backend as K
from .. import activations, initializations, regularizers
from ..engine import Layer, InputSpec
def time_distributed_dense(x, w, b=None, dropout=None,
input_dim=None, output_dim=None, timesteps=None):
'''Apply y.w + b for every temporal slice y of x.
'''
if not input_dim:
input_dim = K.shape(x)[2]
if not timesteps:
timesteps = K.shape(x)[1]
if not output_dim:
output_dim = K.shape(w)[1]
if dropout is not None and 0. < dropout < 1.:
# apply the same dropout pattern at every timestep
ones = K.ones_like(K.reshape(x[:, 0, :], (-1, input_dim)))
dropout_matrix = K.dropout(ones, dropout)
expanded_dropout_matrix = K.repeat(dropout_matrix, timesteps)
x = K.in_train_phase(x * expanded_dropout_matrix, x)
# collapse time dimension and batch dimension together
x = K.reshape(x, (-1, input_dim))
x = K.dot(x, w)
if b:
x = x + b
# reshape to 3D tensor
if K.backend() == 'tensorflow':
x = K.reshape(x, K.stack([-1, timesteps, output_dim]))
x.set_shape([None, None, output_dim])
else:
x = K.reshape(x, (-1, timesteps, output_dim))
return x
class Recurrent(Layer):
'''Abstract base class for recurrent layers.
Do not use in a model -- it's not a valid layer!
Use its children classes `LSTM`, `GRU` and `SimpleRNN` instead.
All recurrent layers (`LSTM`, `GRU`, `SimpleRNN`) also
follow the specifications of this class and accept
the keyword arguments listed below.
# Example
```python
# as the first layer in a Sequential model
model = Sequential()
model.add(LSTM(32, input_shape=(10, 64)))
# now model.output_shape == (None, 32)
# note: `None` is the batch dimension.
# the following is identical:
model = Sequential()
model.add(LSTM(32, input_dim=64, input_length=10))
# for subsequent layers, not need to specify the input size:
model.add(LSTM(16))
```
# Arguments
weights: list of Numpy arrays to set as initial weights.
The list should have 3 elements, of shapes:
`[(input_dim, output_dim), (output_dim, output_dim), (output_dim,)]`.
return_sequences: Boolean. Whether to return the last output
in the output sequence, or the full sequence.
go_backwards: Boolean (default False).
If True, process the input sequence backwards.
stateful: Boolean (default False). If True, the last state
for each sample at index i in a batch will be used as initial
state for the sample of index i in the following batch.
unroll: Boolean (default False). If True, the network will be unrolled,
else a symbolic loop will be used. When using TensorFlow, the network
is always unrolled, so this argument does not do anything.
Unrolling can speed-up a RNN, although it tends to be more memory-intensive.
Unrolling is only suitable for short sequences.
consume_less: one of "cpu", "mem", or "gpu" (LSTM/GRU only).
If set to "cpu", the RNN will use
an implementation that uses fewer, larger matrix products,
thus running faster on CPU but consuming more memory.
If set to "mem", the RNN will use more matrix products,
but smaller ones, thus running slower (may actually be faster on GPU)
while consuming less memory.
If set to "gpu" (LSTM/GRU only), the RNN will combine the input gate,
the forget gate and the output gate into a single matrix,
enabling more time-efficient parallelization on the GPU. Note: RNN
dropout must be shared for all gates, resulting in a slightly
reduced regularization.
input_dim: dimensionality of the input (integer).
This argument (or alternatively, the keyword argument `input_shape`)
is required when using this layer as the first layer in a model.
input_length: Length of input sequences, to be specified
when it is constant.
This argument is required if you are going to connect
`Flatten` then `Dense` layers upstream
(without it, the shape of the dense outputs cannot be computed).
Note that if the recurrent layer is not the first layer
in your model, you would need to specify the input length
at the level of the first layer
(e.g. via the `input_shape` argument)
# Input shape
3D tensor with shape `(nb_samples, timesteps, input_dim)`.
# Output shape
- if `return_sequences`: 3D tensor with shape
`(nb_samples, timesteps, output_dim)`.
- else, 2D tensor with shape `(nb_samples, output_dim)`.
# Masking
This layer supports masking for input data with a variable number
of timesteps. To introduce masks to your data,
use an [Embedding](embeddings.md) layer with the `mask_zero` parameter
set to `True`.
# Note on performance
You are likely to see better performance with RNNs in Theano compared
to TensorFlow. Additionally, when using TensorFlow, it is often
preferable to set `unroll=True` for better performance.
# Note on using statefulness in RNNs
You can set RNN layers to be 'stateful', which means that the states
computed for the samples in one batch will be reused as initial states
for the samples in the next batch.
This assumes a one-to-one mapping between
samples in different successive batches.
To enable statefulness:
- specify `stateful=True` in the layer constructor.
- specify a fixed batch size for your model, by passing
if sequential model:
a `batch_input_shape=(...)` to the first layer in your model.
else for functional model with 1 or more Input layers:
a `batch_shape=(...)` to all the first layers in your model.
This is the expected shape of your inputs *including the batch size*.
It should be a tuple of integers, e.g. `(32, 10, 100)`.
To reset the states of your model, call `.reset_states()` on either
a specific layer, or on your entire model.
'''
def __init__(self, weights=None,
return_sequences=False, go_backwards=False, stateful=False,
unroll=False, consume_less='gpu',
input_dim=None, input_length=None, **kwargs):
self.return_sequences = return_sequences
self.initial_weights = weights
self.go_backwards = go_backwards
self.stateful = stateful
self.unroll = unroll
self.consume_less = consume_less
self.supports_masking = True
self.input_spec = [InputSpec(ndim=3)]
self.input_dim = input_dim
self.input_length = input_length
if self.input_dim:
kwargs['input_shape'] = (self.input_length, self.input_dim)
super(Recurrent, self).__init__(**kwargs)
def get_output_shape_for(self, input_shape):
if self.return_sequences:
return input_shape[0], input_shape[1], self.output_dim
else:
return input_shape[0], self.output_dim
def compute_mask(self, input, mask):
if self.return_sequences:
return mask
else:
return None
def step(self, x, states):
raise NotImplementedError
def get_constants(self, x):
return []
def get_initial_states(self, x):
# build an all-zero tensor of shape (samples, output_dim)
initial_state = K.zeros_like(x) # (samples, timesteps, input_dim)
initial_state = K.sum(initial_state, axis=(1, 2)) # (samples,)
initial_state = K.expand_dims(initial_state) # (samples, 1)
initial_state = K.tile(initial_state, [1, self.output_dim]) # (samples, output_dim)
initial_states = [initial_state for _ in range(len(self.states))]
return initial_states
def preprocess_input(self, x):
return x
def call(self, x, mask=None):
# input shape: (nb_samples, time (padded with zeros), input_dim)
# note that the .build() method of subclasses MUST define
# self.input_spec with a complete input shape.
input_shape = K.int_shape(x)
if self.unroll and input_shape[1] is None:
raise ValueError('Cannot unroll a RNN if the '
'time dimension is undefined. \n'
'- If using a Sequential model, '
'specify the time dimension by passing '
'an `input_shape` or `batch_input_shape` '
'argument to your first layer. If your '
'first layer is an Embedding, you can '
'also use the `input_length` argument.\n'
'- If using the functional API, specify '
'the time dimension by passing a `shape` '
'or `batch_shape` argument to your Input layer.')
if self.stateful:
initial_states = self.states
else:
initial_states = self.get_initial_states(x)
constants = self.get_constants(x)
preprocessed_input = self.preprocess_input(x)
last_output, outputs, states = K.rnn(self.step, preprocessed_input,
initial_states,
go_backwards=self.go_backwards,
mask=mask,
constants=constants,
unroll=self.unroll,
input_length=input_shape[1])
if self.stateful:
updates = []
for i in range(len(states)):
updates.append((self.states[i], states[i]))
self.add_update(updates, x)
if self.return_sequences:
return outputs
else:
return last_output
def get_config(self):
config = {'return_sequences': self.return_sequences,
'go_backwards': self.go_backwards,
'stateful': self.stateful,
'unroll': self.unroll,
'consume_less': self.consume_less}
if self.stateful and self.input_spec[0].shape:
config['batch_input_shape'] = self.input_spec[0].shape
else:
config['input_dim'] = self.input_dim
config['input_length'] = self.input_length
base_config = super(Recurrent, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
class SimpleRNN(Recurrent):
'''Fully-connected RNN where the output is to be fed back to input.
# Arguments
output_dim: dimension of the internal projections and the final output.
init: weight initialization function.
Can be the name of an existing function (str),
or a Theano function (see: [initializations](../initializations.md)).
inner_init: initialization function of the inner cells.
activation: activation function.
Can be the name of an existing function (str),
or a Theano function (see: [activations](../activations.md)).
W_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the input weights matrices.
U_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the recurrent weights matrices.
b_regularizer: instance of [WeightRegularizer](../regularizers.md),
applied to the bias.
dropout_W: float between 0 and 1. Fraction of the input units to drop for input gates.
dropout_U: float between 0 and 1. Fraction of the input units to drop for recurrent connections.
# References
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](http://arxiv.org/abs/1512.05287)
'''
def __init__(self, output_dim,
init='glorot_uniform', inner_init='orthogonal',
activation='tanh',
W_regularizer=None, U_regularizer=None, b_regularizer=None,
dropout_W=0., dropout_U=0., **kwargs):
self.output_dim = output_dim
self.init = initializations.get(init)
self.inner_init = initializations.get(inner_init)
self.activation = activations.get(activation)
self.W_regularizer = regularizers.get(W_regularizer)
self.U_regularizer = regularizers.get(U_regularizer)
self.b_regularizer = regularizers.get(b_regularizer)
self.dropout_W = dropout_W
self.dropout_U = dropout_U
if self.dropout_W or self.dropout_U:
self.uses_learning_phase = True
super(SimpleRNN, self).__init__(**kwargs)
def build(self, input_shape):
self.input_spec = [InputSpec(shape=input_shape)]
if self.stateful:
self.reset_states()
else:
# initial states: all-zero tensor of shape (output_dim)
self.states = [None]
input_dim = input_shape[2]
self.input_dim = input_dim
self.W = self.add_weight((input_dim, self.output_dim),
initializer=self.init,
name='{}_W'.format(self.name),
regularizer=self.W_regularizer)
self.U = self.add_weight((self.output_dim, self.output_dim),
initializer=self.inner_init,
name='{}_U'.format(self.name),
regularizer=self.U_regularizer)
self.b = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b'.format(self.name),
regularizer=self.b_regularizer)
if self.initial_weights is not None:
self.set_weights(self.initial_weights)
del self.initial_weights
self.built = True
def reset_states(self):
assert self.stateful, 'Layer must be stateful.'
input_shape = self.input_spec[0].shape
if not input_shape[0]:
raise ValueError('If a RNN is stateful, it needs to know '
'its batch size. Specify the batch size '
'of your input tensors: \n'
'- If using a Sequential model, '
'specify the batch size by passing '
'a `batch_input_shape` '
'argument to your first layer.\n'
'- If using the functional API, specify '
'the time dimension by passing a '
'`batch_shape` argument to your Input layer.')
if hasattr(self, 'states'):
K.set_value(self.states[0],
np.zeros((input_shape[0], self.output_dim)))
else:
self.states = [K.zeros((input_shape[0], self.output_dim))]
def preprocess_input(self, x):
if self.consume_less == 'cpu':
input_shape = K.int_shape(x)
input_dim = input_shape[2]
timesteps = input_shape[1]
return time_distributed_dense(x, self.W, self.b, self.dropout_W,
input_dim, self.output_dim,
timesteps)
else:
return x
def step(self, x, states):
prev_output = states[0]
B_U = states[1]
B_W = states[2]
if self.consume_less == 'cpu':
h = x
else:
h = K.dot(x * B_W, self.W) + self.b
output = self.activation(h + K.dot(prev_output * B_U, self.U))
return output, [output]
def get_constants(self, x):
constants = []
if 0 < self.dropout_U < 1:
ones = K.ones_like(K.reshape(x[:, 0, 0], (-1, 1)))
ones = K.tile(ones, (1, self.output_dim))
B_U = K.in_train_phase(K.dropout(ones, self.dropout_U), ones)
constants.append(B_U)
else:
constants.append(K.cast_to_floatx(1.))
if self.consume_less == 'cpu' and 0 < self.dropout_W < 1:
input_shape = K.int_shape(x)
input_dim = input_shape[-1]
ones = K.ones_like(K.reshape(x[:, 0, 0], (-1, 1)))
ones = K.tile(ones, (1, int(input_dim)))
B_W = K.in_train_phase(K.dropout(ones, self.dropout_W), ones)
constants.append(B_W)
else:
constants.append(K.cast_to_floatx(1.))
return constants
def get_config(self):
config = {'output_dim': self.output_dim,
'init': self.init.__name__,
'inner_init': self.inner_init.__name__,
'activation': self.activation.__name__,
'W_regularizer': self.W_regularizer.get_config() if self.W_regularizer else None,
'U_regularizer': self.U_regularizer.get_config() if self.U_regularizer else None,
'b_regularizer': self.b_regularizer.get_config() if self.b_regularizer else None,
'dropout_W': self.dropout_W,
'dropout_U': self.dropout_U}
base_config = super(SimpleRNN, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
class GRU(Recurrent):
'''Gated Recurrent Unit - Cho et al. 2014.
# Arguments
output_dim: dimension of the internal projections and the final output.
init: weight initialization function.
Can be the name of an existing function (str),
or a Theano function (see: [initializations](../initializations.md)).
inner_init: initialization function of the inner cells.
activation: activation function.
Can be the name of an existing function (str),
or a Theano function (see: [activations](../activations.md)).
inner_activation: activation function for the inner cells.
W_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the input weights matrices.
U_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the recurrent weights matrices.
b_regularizer: instance of [WeightRegularizer](../regularizers.md),
applied to the bias.
dropout_W: float between 0 and 1. Fraction of the input units to drop for input gates.
dropout_U: float between 0 and 1. Fraction of the input units to drop for recurrent connections.
# References
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](http://www.aclweb.org/anthology/W14-4012)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](http://arxiv.org/pdf/1412.3555v1.pdf)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](http://arxiv.org/abs/1512.05287)
'''
def __init__(self, output_dim,
init='glorot_uniform', inner_init='orthogonal',
activation='tanh', inner_activation='hard_sigmoid',
W_regularizer=None, U_regularizer=None, b_regularizer=None,
dropout_W=0., dropout_U=0., **kwargs):
self.output_dim = output_dim
self.init = initializations.get(init)
self.inner_init = initializations.get(inner_init)
self.activation = activations.get(activation)
self.inner_activation = activations.get(inner_activation)
self.W_regularizer = regularizers.get(W_regularizer)
self.U_regularizer = regularizers.get(U_regularizer)
self.b_regularizer = regularizers.get(b_regularizer)
self.dropout_W = dropout_W
self.dropout_U = dropout_U
if self.dropout_W or self.dropout_U:
self.uses_learning_phase = True
super(GRU, self).__init__(**kwargs)
def build(self, input_shape):
self.input_spec = [InputSpec(shape=input_shape)]
self.input_dim = input_shape[2]
if self.stateful:
self.reset_states()
else:
# initial states: all-zero tensor of shape (output_dim)
self.states = [None]
if self.consume_less == 'gpu':
self.W = self.add_weight((self.input_dim, 3 * self.output_dim),
initializer=self.init,
name='{}_W'.format(self.name),
regularizer=self.W_regularizer)
self.U = self.add_weight((self.output_dim, 3 * self.output_dim),
initializer=self.inner_init,
name='{}_U'.format(self.name),
regularizer=self.U_regularizer)
self.b = self.add_weight((self.output_dim * 3,),
initializer='zero',
name='{}_b'.format(self.name),
regularizer=self.b_regularizer)
else:
self.W_z = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init,
name='{}_W_z'.format(self.name),
regularizer=self.W_regularizer)
self.U_z = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init,
name='{}_U_z'.format(self.name),
regularizer=self.W_regularizer)
self.b_z = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b_z'.format(self.name),
regularizer=self.b_regularizer)
self.W_r = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init,
name='{}_W_r'.format(self.name),
regularizer=self.W_regularizer)
self.U_r = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init,
name='{}_U_r'.format(self.name),
regularizer=self.W_regularizer)
self.b_r = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b_r'.format(self.name),
regularizer=self.b_regularizer)
self.W_h = self.add_weight((self.input_dim, self.output_dim),
initializer=self.init,
name='{}_W_h'.format(self.name),
regularizer=self.W_regularizer)
self.U_h = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init,
name='{}_U_h'.format(self.name),
regularizer=self.W_regularizer)
self.b_h = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b_h'.format(self.name),
regularizer=self.b_regularizer)
self.W = K.concatenate([self.W_z, self.W_r, self.W_h])
self.U = K.concatenate([self.U_z, self.U_r, self.U_h])
self.b = K.concatenate([self.b_z, self.b_r, self.b_h])
if self.initial_weights is not None:
self.set_weights(self.initial_weights)
del self.initial_weights
self.built = True
def reset_states(self):
assert self.stateful, 'Layer must be stateful.'
input_shape = self.input_spec[0].shape
if not input_shape[0]:
raise ValueError('If a RNN is stateful, a complete ' +
'input_shape must be provided (including batch size).')
if hasattr(self, 'states'):
K.set_value(self.states[0],
np.zeros((input_shape[0], self.output_dim)))
else:
self.states = [K.zeros((input_shape[0], self.output_dim))]
def preprocess_input(self, x):
if self.consume_less == 'cpu':
input_shape = K.int_shape(x)
input_dim = input_shape[2]
timesteps = input_shape[1]
x_z = time_distributed_dense(x, self.W_z, self.b_z, self.dropout_W,
input_dim, self.output_dim, timesteps)
x_r = time_distributed_dense(x, self.W_r, self.b_r, self.dropout_W,
input_dim, self.output_dim, timesteps)
x_h = time_distributed_dense(x, self.W_h, self.b_h, self.dropout_W,
input_dim, self.output_dim, timesteps)
return K.concatenate([x_z, x_r, x_h], axis=2)
else:
return x
def step(self, x, states):
h_tm1 = states[0] # previous memory
B_U = states[1] # dropout matrices for recurrent units
B_W = states[2]
if self.consume_less == 'gpu':
matrix_x = K.dot(x * B_W[0], self.W) + self.b
matrix_inner = K.dot(h_tm1 * B_U[0], self.U[:, :2 * self.output_dim])
x_z = matrix_x[:, :self.output_dim]
x_r = matrix_x[:, self.output_dim: 2 * self.output_dim]
inner_z = matrix_inner[:, :self.output_dim]
inner_r = matrix_inner[:, self.output_dim: 2 * self.output_dim]
z = self.inner_activation(x_z + inner_z)
r = self.inner_activation(x_r + inner_r)
x_h = matrix_x[:, 2 * self.output_dim:]
inner_h = K.dot(r * h_tm1 * B_U[0], self.U[:, 2 * self.output_dim:])
hh = self.activation(x_h + inner_h)
else:
if self.consume_less == 'cpu':
x_z = x[:, :self.output_dim]
x_r = x[:, self.output_dim: 2 * self.output_dim]
x_h = x[:, 2 * self.output_dim:]
elif self.consume_less == 'mem':
x_z = K.dot(x * B_W[0], self.W_z) + self.b_z
x_r = K.dot(x * B_W[1], self.W_r) + self.b_r
x_h = K.dot(x * B_W[2], self.W_h) + self.b_h
else:
raise ValueError('Unknown `consume_less` mode.')
z = self.inner_activation(x_z + K.dot(h_tm1 * B_U[0], self.U_z))
r = self.inner_activation(x_r + K.dot(h_tm1 * B_U[1], self.U_r))
hh = self.activation(x_h + K.dot(r * h_tm1 * B_U[2], self.U_h))
h = z * h_tm1 + (1 - z) * hh
return h, [h]
def get_constants(self, x):
constants = []
if 0 < self.dropout_U < 1:
ones = K.ones_like(K.reshape(x[:, 0, 0], (-1, 1)))
ones = K.tile(ones, (1, self.output_dim))
B_U = [K.in_train_phase(K.dropout(ones, self.dropout_U), ones) for _ in range(3)]
constants.append(B_U)
else:
constants.append([K.cast_to_floatx(1.) for _ in range(3)])
if 0 < self.dropout_W < 1:
input_shape = K.int_shape(x)
input_dim = input_shape[-1]
ones = K.ones_like(K.reshape(x[:, 0, 0], (-1, 1)))
ones = K.tile(ones, (1, int(input_dim)))
B_W = [K.in_train_phase(K.dropout(ones, self.dropout_W), ones) for _ in range(3)]
constants.append(B_W)
else:
constants.append([K.cast_to_floatx(1.) for _ in range(3)])
return constants
def get_config(self):
config = {'output_dim': self.output_dim,
'init': self.init.__name__,
'inner_init': self.inner_init.__name__,
'activation': self.activation.__name__,
'inner_activation': self.inner_activation.__name__,
'W_regularizer': self.W_regularizer.get_config() if self.W_regularizer else None,
'U_regularizer': self.U_regularizer.get_config() if self.U_regularizer else None,
'b_regularizer': self.b_regularizer.get_config() if self.b_regularizer else None,
'dropout_W': self.dropout_W,
'dropout_U': self.dropout_U}
base_config = super(GRU, self).get_config()
return dict(list(base_config.items()) + list(config.items()))
class GRUCond(Recurrent):
'''Gated Recurrent Unit - Cho et al. 2014. with the previously generated word fed to the current timestep.
You should give two inputs to this layer:
1. The shifted sequence of words (shape: (mini_batch_size, output_timesteps, embedding_size))
# Arguments
output_dim: dimension of the internal projections and the final output.
init: weight initialization function.
Can be the name of an existing function (str),
or a Theano function (see: [initializations](../initializations.md)).
inner_init: initialization function of the inner cells.
return_states: boolean indicating if we want the intermediate states (hidden_state and memory) as additional outputs
activation: activation function.
Can be the name of an existing function (str),
or a Theano function (see: [activations](../activations.md)).
inner_activation: activation function for the inner cells.
W_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the input weights matrices.
U_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the recurrent weights matrices.
b_regularizer: instance of [WeightRegularizer](../regularizers.md),
applied to the bias.
dropout_W: float between 0 and 1. Fraction of the input units to drop for input gates.
dropout_U: float between 0 and 1. Fraction of the input units to drop for recurrent connections.
w_a_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the input weights matrices.
W_a_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the input weights matrices.
U_a_regularizer: instance of [WeightRegularizer](../regularizers.md)
(eg. L1 or L2 regularization), applied to the recurrent weights matrices.
b_a_regularizer: instance of [WeightRegularizer](../regularizers.md),
applied to the bias.
dropout_w_a: float between 0 and 1.
dropout_W_a: float between 0 and 1.
dropout_U_a: float between 0 and 1.
# Formulation
The resulting attention vector 'phi' at time 't' is formed by applying a weighted sum over
the set of inputs 'x_i' contained in 'X':
phi(X, t) = ∑_i alpha_i(t) * x_i,
where each 'alpha_i' at time 't' is a weighting vector over all the input dimension that
accomplishes the following condition:
∑_i alpha_i = 1
and is dynamically adapted at each timestep w.r.t. the following formula:
alpha_i(t) = exp{e_i(t)} / ∑_j exp{e_j(t)}
where each 'e_i' at time 't' is calculated as:
e_i(t) = wa' * tanh( Wa * x_i + Ua * h(t-1) + ba ),
where the following are learnable with the respectively named sizes:
wa Wa Ua ba
[input_dim] [input_dim, input_dim] [output_dim, input_dim] [input_dim]
The names of 'Ua' and 'Wa' are exchanged w.r.t. the provided reference as well as 'v' being renamed
to 'x' for matching Keras LSTM's nomenclature.
# References
- [On the Properties of Neural Machine Translation: Encoder–Decoder Approaches](http://www.aclweb.org/anthology/W14-4012)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling:(http://arxiv.org/pdf/1412.3555v1.pdf)
- [Long short-term memory](http://deeplearning.cs.cmu.edu/pdfs/Hochreiter97_lstm.pdf) (original 1997 paper)
- [Learning to forget: Continual prediction with LSTM](http://www.mitpressjournals.org/doi/pdf/10.1162/089976600300015015)
- [Supervised sequence labeling with recurrent neural networks](http://www.cs.toronto.edu/~graves/preprint.pdf)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](http://arxiv.org/abs/1512.05287)
'''
def __init__(self, output_dim,
init='glorot_uniform', inner_init='orthogonal',
return_states=False,
activation='tanh', inner_activation='hard_sigmoid',
W_regularizer=None, U_regularizer=None, V_regularizer=None, b_regularizer=None,
dropout_W=0., dropout_U=0., dropout_V=0., **kwargs):
self.output_dim = output_dim
self.init = initializations.get(init)
self.inner_init = initializations.get(inner_init)
self.return_states = return_states
self.activation = activations.get(activation)
self.inner_activation = activations.get(inner_activation)
self.W_regularizer = regularizers.get(W_regularizer)
self.U_regularizer = regularizers.get(U_regularizer)
self.V_regularizer = regularizers.get(V_regularizer)
self.b_regularizer = regularizers.get(b_regularizer)
self.dropout_W, self.dropout_U, self.dropout_V = dropout_W, dropout_U, dropout_V
if self.dropout_W or self.dropout_U or self.dropout_V:
self.uses_learning_phase = True
super(GRUCond, self).__init__(**kwargs)
def build(self, input_shape):
assert len(input_shape) == 2 or len(input_shape) == 3, 'You should pass two inputs to GRUCond ' \
'(previous_embedded_words and context) and ' \
'one optional input (init_memory)'
if len(input_shape) == 2:
self.input_spec = [InputSpec(shape=input_shape[0]), InputSpec(shape=input_shape[1])]
self.num_inputs = 2
elif len(input_shape) == 3:
self.input_spec = [InputSpec(shape=input_shape[0]),
InputSpec(shape=input_shape[1]),
InputSpec(shape=input_shape[2])]
self.num_inputs = 3
self.input_dim = input_shape[0][2]
self.context_dim = input_shape[1][1]
if self.stateful:
self.reset_states()
else:
# initial states: all-zero tensor of shape (output_dim)
self.states = [None]
if self.consume_less == 'gpu':
self.V = self.add_weight((self.input_dim, 3 * self.output_dim),
initializer=self.inner_init,
name='{}_V'.format(self.name),
regularizer=self.V_regularizer)
self.W = self.add_weight((self.context_dim, 3 * self.output_dim),
initializer=self.init,
name='{}_W'.format(self.name),
regularizer=self.W_regularizer)
self.U = self.add_weight((self.output_dim, 3 * self.output_dim),
initializer=self.inner_init,
name='{}_U'.format(self.name),
regularizer=self.U_regularizer)
self.b = self.add_weight((self.output_dim * 3,),
initializer='zero',
name='{}_b'.format(self.name),
regularizer=self.b_regularizer)
self.trainable_weights = [self.V, # Cond weights
self.W, self.U, self.b]
else:
self.V_z = self.add_weight((self.input_dim, self.output_dim),
initializer=self.inner_init,
name='{}_V_z'.format(self.name),
regularizer=self.W_regularizer)
self.W_z = self.add_weight((self.context_dim, self.output_dim),
initializer=self.init,
name='{}_W_z'.format(self.name),
regularizer=self.W_regularizer)
self.U_z = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init,
name='{}_U_z'.format(self.name),
regularizer=self.W_regularizer)
self.b_z = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b_z'.format(self.name),
regularizer=self.b_regularizer)
self.V_r = self.add_weight((self.input_dim, self.output_dim),
initializer=self.inner_init,
name='{}_V_r'.format(self.name),
regularizer=self.W_regularizer)
self.W_r = self.add_weight((self.context_dim, self.output_dim),
initializer=self.init,
name='{}_W_r'.format(self.name),
regularizer=self.W_regularizer)
self.U_r = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init,
name='{}_U_r'.format(self.name),
regularizer=self.W_regularizer)
self.b_r = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b_r'.format(self.name),
regularizer=self.b_regularizer)
self.V_h = self.add_weight((self.input_dim, self.output_dim),
initializer=self.inner_init,
name='{}_V_h'.format(self.name),
regularizer=self.W_regularizer)
self.W_h = self.add_weight((self.context_dim, self.output_dim),
initializer=self.init,
name='{}_W_h'.format(self.name),
regularizer=self.W_regularizer)
self.U_h = self.add_weight((self.output_dim, self.output_dim),
initializer=self.init,
name='{}_U_h'.format(self.name),
regularizer=self.W_regularizer)
self.b_h = self.add_weight((self.output_dim,),
initializer='zero',
name='{}_b_h'.format(self.name),
regularizer=self.b_regularizer)
self.trainable_weights = [self.V_z, self.W_r, self.U_h, self.b_z,
self.V_r, self.W_r, self.U_r, self.b_r,
self.V_h, self.W_h, self.U_h, self.b_h
]
self.W = K.concatenate([self.W_z, self.W_r, self.W_h])
self.U = K.concatenate([self.U_z, self.U_r, self.U_h])
self.b = K.concatenate([self.b_z, self.b_r, self.b_h])
if self.initial_weights is not None:
self.set_weights(self.initial_weights)
del self.initial_weights
self.built = True
def reset_states(self):
assert self.stateful, 'Layer must be stateful.'
input_shape = self.input_spec[0].shape
if not input_shape[0]:
raise ValueError('If a RNN is stateful, a complete ' +
'input_shape must be provided (including batch size).')
if hasattr(self, 'states'):
K.set_value(self.states[0],
np.zeros((input_shape[0], self.output_dim)))
K.set_value(self.states[1],
np.zeros((input_shape[0], self.output_dim)))
K.set_value(self.states[2],
np.zeros((input_shape[0], input_shape[3])))
else:
self.states = [K.zeros((input_shape[0], self.output_dim)),
K.zeros((input_shape[0], self.output_dim)),
K.zeros((input_shape[0], input_shape[3]))]
def preprocess_input(self, x, B_V):
return K.dot(x * B_V[0], self.V) + self.b
def get_output_shape_for(self, input_shape):
if self.return_sequences:
main_out = (input_shape[0][0], input_shape[0][1], self.output_dim)
else:
main_out = (input_shape[0][0], self.output_dim)
if self.return_states:
states_dim = (input_shape[0][0], input_shape[0][1], self.output_dim)
main_out = [main_out, states_dim]
return main_out
def call(self, x, mask=None):
# input shape: (nb_samples, time (padded with zeros), input_dim)
# note that the .build() method of subclasses MUST define
# self.input_spec with a complete input shape.
input_shape = self.input_spec[0].shape
state_below = x[0]
self.context = x[1]
if self.num_inputs == 2: # input: [state_below, context]
self.init_state = None
self.init_memory = None
elif self.num_inputs == 3: # input: [state_below, context, init_hidden_state]
self.init_state = x[2]
self.init_memory = None
if K._BACKEND == 'tensorflow':
if not input_shape[1]:
raise Exception('When using TensorFlow, you should define '
'explicitly the number of timesteps of '
'your sequences.\n'
'If your first layer is an Embedding, '
'make sure to pass it an "input_length" '
'argument. Otherwise, make sure '
'the first layer has '
'an "input_shape" or "batch_input_shape" '
'argument, including the time axis. '
'Found input shape at layer ' + self.name +
': ' + str(input_shape))
if self.stateful:
initial_states = self.states
else:
initial_states = self.get_initial_states(state_below)
constants, B_V = self.get_constants(state_below)
preprocessed_input = self.preprocess_input(state_below, B_V)
last_output, outputs, states = K.rnn(self.step, preprocessed_input,
initial_states,
go_backwards=self.go_backwards,
mask=mask[0],
constants=constants,
unroll=self.unroll,
input_length=state_below.shape[1])
if self.stateful:
self.updates = []
for i in range(len(states)):
self.updates.append((self.states[i], states[i]))
if self.return_sequences:
ret = outputs
else:
ret = last_output
# intermediate states as additional outputs
if self.return_states:
ret = [ret, states[0]]
return ret
def compute_mask(self, input, mask):
if self.return_sequences:
ret = mask[0]
else:
ret = None
if self.return_states:
ret = [ret, None]
return ret
def step(self, x, states):
h_tm1 = states[0] # previous hidden state
# dropout matrices for recurrent units
B_U = states[1] # Dropout U
B_W = states[2] # Dropout W
# Context (input sequence)
context = states[3] # Context
if self.consume_less == 'gpu':
matrix_x = x + K.dot(context * B_W[0], self.W)
matrix_inner = K.dot(h_tm1 * B_U[0], self.U[:, :2 * self.output_dim])
x_z = matrix_x[:, :self.output_dim]
x_r = matrix_x[:, self.output_dim: 2 * self.output_dim]
inner_z = matrix_inner[:, :self.output_dim]
inner_r = matrix_inner[:, self.output_dim: 2 * self.output_dim]
z = self.inner_activation(x_z + inner_z)
r = self.inner_activation(x_r + inner_r)
x_h = matrix_x[:, 2 * self.output_dim:]
inner_h = K.dot(r * h_tm1 * B_U[0], self.U[:, 2 * self.output_dim:])
hh = self.activation(x_h + inner_h)
h = z * h_tm1 + (1 - z) * hh
return h, [h]
def get_constants(self, x):
constants = []
# States[1]
if 0 < self.dropout_U < 1:
ones = K.ones_like(K.reshape(x[:, 0, 0], (-1, 1)))
ones = K.concatenate([ones] * self.output_dim, 1)
B_U = [K.in_train_phase(K.dropout(ones, self.dropout_U), ones) for _ in range(3)]
constants.append(B_U)
else:
constants.append([K.cast_to_floatx(1.) for _ in range(3)])
# States[2]
if 0 < self.dropout_W < 1:
input_shape = self.input_spec[0][0].shape
input_dim = input_shape[-1]
ones = K.ones_like(K.reshape(x[:, 0, 0], (-1, 1)))
ones = K.concatenate([ones] * input_dim, 1)
B_W = [K.in_train_phase(K.dropout(ones, self.dropout_W), ones) for _ in range(3)]
constants.append(B_W)
else:
constants.append([K.cast_to_floatx(1.) for _ in range(3)])
if 0 < self.dropout_V < 1:
input_dim = self.input_dim
ones = K.ones_like(K.reshape(x[:, :, 0], (-1, x.shape[1], 1))) # (bs, timesteps, 1)
ones = K.concatenate([ones] * input_dim, axis=2)
B_V = [K.in_train_phase(K.dropout(ones, self.dropout_V), ones) for _ in range(3)]
else:
B_V = [K.cast_to_floatx(1.) for _ in range(3)]
# States[3]
constants.append(self.context)
return constants, B_V
def get_initial_states(self, x):
# build an all-zero tensor of shape (samples, output_dim)
if self.init_state is None:
# build an all-zero tensor of shape (samples, output_dim)
initial_state = K.zeros_like(x) # (samples, timesteps, input_dim)
initial_state = K.sum(initial_state, axis=(1, 2)) # (samples,)
initial_state = K.expand_dims(initial_state) # (samples, 1)