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ntm.py
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ntm.py
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# credit: this code is derived from https://github.com/snowkylin/ntm
# the major changes made are to make this compatible with the abstract class tf.contrib.rnn.RNNCell
# an LSTM controller is used instead of a RNN controller
# 3 memory inititialization schemes are offered instead of 1
# the outputs of the controller heads are clipped to an absolute value
# we find that our modification result in more reliable training (we never observe gradients going to NaN) and faster convergence
import numpy as np
import tensorflow as tf
from tensorflow.python.util import nest
import collections
from utils import expand, learned_init, create_linear_initializer
NTMControllerState = collections.namedtuple('NTMControllerState', ('controller_state', 'read_vector_list', 'w_list', 'M'))
class NTMCell(tf.contrib.rnn.RNNCell):
def __init__(self, controller_layers, controller_units, memory_size, memory_vector_dim, read_head_num, write_head_num,
addressing_mode='content_and_location', shift_range=1, reuse=False, output_dim=None, clip_value=20,
init_mode='constant'):
self.controller_layers = controller_layers
self.controller_units = controller_units
self.memory_size = memory_size
self.memory_vector_dim = memory_vector_dim
self.read_head_num = read_head_num
self.write_head_num = write_head_num
self.addressing_mode = addressing_mode
self.reuse = reuse
self.clip_value = clip_value
def single_cell(num_units):
return tf.contrib.rnn.BasicLSTMCell(num_units, forget_bias=1.0)
self.controller = tf.contrib.rnn.MultiRNNCell([single_cell(self.controller_units) for _ in range(self.controller_layers)])
self.init_mode = init_mode
self.step = 0
self.output_dim = output_dim
self.shift_range = shift_range
self.o2p_initializer = create_linear_initializer(self.controller_units)
self.o2o_initializer = create_linear_initializer(self.controller_units + self.memory_vector_dim * self.read_head_num)
def __call__(self, x, prev_state):
prev_read_vector_list = prev_state.read_vector_list
controller_input = tf.concat([x] + prev_read_vector_list, axis=1)
with tf.variable_scope('controller', reuse=self.reuse):
controller_output, controller_state = self.controller(controller_input, prev_state.controller_state)
num_parameters_per_head = self.memory_vector_dim + 1 + 1 + (self.shift_range * 2 + 1) + 1
num_heads = self.read_head_num + self.write_head_num
total_parameter_num = num_parameters_per_head * num_heads + self.memory_vector_dim * 2 * self.write_head_num
with tf.variable_scope("o2p", reuse=(self.step > 0) or self.reuse):
parameters = tf.contrib.layers.fully_connected(
controller_output, total_parameter_num, activation_fn=None,
weights_initializer=self.o2p_initializer)
parameters = tf.clip_by_value(parameters, -self.clip_value, self.clip_value)
head_parameter_list = tf.split(parameters[:, :num_parameters_per_head * num_heads], num_heads, axis=1)
erase_add_list = tf.split(parameters[:, num_parameters_per_head * num_heads:], 2 * self.write_head_num, axis=1)
prev_w_list = prev_state.w_list
prev_M = prev_state.M
w_list = []
for i, head_parameter in enumerate(head_parameter_list):
k = tf.tanh(head_parameter[:, 0:self.memory_vector_dim])
beta = tf.nn.softplus(head_parameter[:, self.memory_vector_dim])
g = tf.sigmoid(head_parameter[:, self.memory_vector_dim + 1])
s = tf.nn.softmax(
head_parameter[:, self.memory_vector_dim + 2:self.memory_vector_dim + 2 + (self.shift_range * 2 + 1)]
)
gamma = tf.nn.softplus(head_parameter[:, -1]) + 1
with tf.variable_scope('addressing_head_%d' % i):
w = self.addressing(k, beta, g, s, gamma, prev_M, prev_w_list[i])
w_list.append(w)
# Reading (Sec 3.1)
read_w_list = w_list[:self.read_head_num]
read_vector_list = []
for i in range(self.read_head_num):
read_vector = tf.reduce_sum(tf.expand_dims(read_w_list[i], dim=2) * prev_M, axis=1)
read_vector_list.append(read_vector)
# Writing (Sec 3.2)
write_w_list = w_list[self.read_head_num:]
M = prev_M
for i in range(self.write_head_num):
w = tf.expand_dims(write_w_list[i], axis=2)
erase_vector = tf.expand_dims(tf.sigmoid(erase_add_list[i * 2]), axis=1)
add_vector = tf.expand_dims(tf.tanh(erase_add_list[i * 2 + 1]), axis=1)
M = M * (tf.ones(M.get_shape()) - tf.matmul(w, erase_vector)) + tf.matmul(w, add_vector)
if not self.output_dim:
output_dim = x.get_shape()[1]
else:
output_dim = self.output_dim
with tf.variable_scope("o2o", reuse=(self.step > 0) or self.reuse):
NTM_output = tf.contrib.layers.fully_connected(
tf.concat([controller_output] + read_vector_list, axis=1), output_dim, activation_fn=None,
weights_initializer=self.o2o_initializer)
NTM_output = tf.clip_by_value(NTM_output, -self.clip_value, self.clip_value)
self.step += 1
return NTM_output, NTMControllerState(
controller_state=controller_state, read_vector_list=read_vector_list, w_list=w_list, M=M)
def addressing(self, k, beta, g, s, gamma, prev_M, prev_w):
# Sec 3.3.1 Focusing by Content
# Cosine Similarity
k = tf.expand_dims(k, axis=2)
inner_product = tf.matmul(prev_M, k)
k_norm = tf.sqrt(tf.reduce_sum(tf.square(k), axis=1, keep_dims=True))
M_norm = tf.sqrt(tf.reduce_sum(tf.square(prev_M), axis=2, keep_dims=True))
norm_product = M_norm * k_norm
K = tf.squeeze(inner_product / (norm_product + 1e-8)) # eq (6)
# Calculating w^c
K_amplified = tf.exp(tf.expand_dims(beta, axis=1) * K)
w_c = K_amplified / tf.reduce_sum(K_amplified, axis=1, keep_dims=True) # eq (5)
if self.addressing_mode == 'content': # Only focus on content
return w_c
# Sec 3.3.2 Focusing by Location
g = tf.expand_dims(g, axis=1)
w_g = g * w_c + (1 - g) * prev_w # eq (7)
s = tf.concat([s[:, :self.shift_range + 1],
tf.zeros([s.get_shape()[0], self.memory_size - (self.shift_range * 2 + 1)]),
s[:, -self.shift_range:]], axis=1)
t = tf.concat([tf.reverse(s, axis=[1]), tf.reverse(s, axis=[1])], axis=1)
s_matrix = tf.stack(
[t[:, self.memory_size - i - 1:self.memory_size * 2 - i - 1] for i in range(self.memory_size)],
axis=1
)
w_ = tf.reduce_sum(tf.expand_dims(w_g, axis=1) * s_matrix, axis=2) # eq (8)
w_sharpen = tf.pow(w_, tf.expand_dims(gamma, axis=1))
w = w_sharpen / tf.reduce_sum(w_sharpen, axis=1, keep_dims=True) # eq (9)
return w
def zero_state(self, batch_size, dtype):
with tf.variable_scope('init', reuse=self.reuse):
read_vector_list = [expand(tf.tanh(learned_init(self.memory_vector_dim)), dim=0, N=batch_size)
for i in range(self.read_head_num)]
w_list = [expand(tf.nn.softmax(learned_init(self.memory_size)), dim=0, N=batch_size)
for i in range(self.read_head_num + self.write_head_num)]
controller_init_state = self.controller.zero_state(batch_size, dtype)
if self.init_mode == 'learned':
M = expand(tf.tanh(
tf.reshape(
learned_init(self.memory_size * self.memory_vector_dim),
[self.memory_size, self.memory_vector_dim])
), dim=0, N=batch_size)
elif self.init_mode == 'random':
M = expand(
tf.tanh(tf.get_variable('init_M', [self.memory_size, self.memory_vector_dim],
initializer=tf.random_normal_initializer(mean=0.0, stddev=0.5))),
dim=0, N=batch_size)
elif self.init_mode == 'constant':
M = expand(
tf.get_variable('init_M', [self.memory_size, self.memory_vector_dim],
initializer=tf.constant_initializer(1e-6)),
dim=0, N=batch_size)
return NTMControllerState(
controller_state=controller_init_state,
read_vector_list=read_vector_list,
w_list=w_list,
M=M)
@property
def state_size(self):
return NTMControllerState(
controller_state=self.controller.state_size,
read_vector_list=[self.memory_vector_dim for _ in range(self.read_head_num)],
w_list=[self.memory_size for _ in range(self.read_head_num + self.write_head_num)],
M=tf.TensorShape([self.memory_size * self.memory_vector_dim]))
@property
def output_size(self):
return self.output_dim