def Orthonorm(x, name=None):
'''
Builds keras layer that handles orthogonalization of x
x: an n x d input matrix
name: name of the keras layer
returns: a keras layer instance. during evaluation, the instance returns an n x d orthogonal matrix
if x is full rank and not singular
'''
# get dimensionality of x
d = x.get_shape().as_list()[-1]
# compute orthogonalizing matrix
ortho_weights = orthonorm_op(x)
# create variable that holds this matrix
ortho_weights_store = K.variable(np.zeros((d, d)))
# create op that saves matrix into variable
ortho_weights_update = tf.assign(ortho_weights_store,
ortho_weights,
name='ortho_weights_update')
# switch between stored and calculated weights based on training or validation
l = Lambda(lambda x: K.in_train_phase(K.dot(x, ortho_weights),
K.dot(x, ortho_weights_store)),
name=name)
l.add_update(ortho_weights_update)
return l
def call(self, inputs, mask=None, **kwargs):
"""Core implemention of soft attention
Args:
inputs (object): input tensor.
Returns:
object: weighted sum of input tensors.
"""
attention = K.tanh(K.dot(inputs, self.W) + self.b)
attention = K.dot(attention, self.q)
attention = K.squeeze(attention, axis=2)
if mask is None:
attention = K.exp(attention)
else:
attention = K.exp(attention) * K.cast(mask, dtype="float32")
attention_weight = attention / (
K.sum(attention, axis=-1, keepdims=True) + K.epsilon())
attention_weight = K.expand_dims(attention_weight)
weighted_input = inputs * attention_weight
return K.sum(weighted_input, axis=1)
def call(self, QKVs):
"""Core logic of multi-head self attention.
Args:
QKVs (list): inputs of multi-head self attention i.e. query, key and value.
Returns:
object: ouput tensors.
"""
if len(QKVs) == 3:
Q_seq, K_seq, V_seq = QKVs
Q_len, V_len = None, None
elif len(QKVs) == 5:
Q_seq, K_seq, V_seq, Q_len, V_len = QKVs
Q_seq = K.dot(Q_seq, self.WQ)
Q_seq = K.reshape(Q_seq,
shape=(-1, K.shape(Q_seq)[1], self.multiheads,
self.head_dim))
Q_seq = K.permute_dimensions(Q_seq, pattern=(0, 2, 1, 3))
K_seq = K.dot(K_seq, self.WK)
K_seq = K.reshape(K_seq,
shape=(-1, K.shape(K_seq)[1], self.multiheads,
self.head_dim))
K_seq = K.permute_dimensions(K_seq, pattern=(0, 2, 1, 3))
V_seq = K.dot(V_seq, self.WV)
V_seq = K.reshape(V_seq,
shape=(-1, K.shape(V_seq)[1], self.multiheads,
self.head_dim))
V_seq = K.permute_dimensions(V_seq, pattern=(0, 2, 1, 3))
A = einsum("abij, abkj -> abik", Q_seq, K_seq) / K.sqrt(
K.cast(self.head_dim, dtype="float32"))
A = K.permute_dimensions(
A, pattern=(0, 3, 2, 1)
) # A.shape=[batch_size,K_sequence_length,Q_sequence_length,self.multiheads]
A = self.Mask(A, V_len, "add")
A = K.permute_dimensions(A, pattern=(0, 3, 2, 1))
if self.mask_right:
ones = K.ones_like(A[:1, :1])
lower_triangular = K.tf.matrix_band_part(ones,
num_lower=-1,
num_upper=0)
mask = (ones - lower_triangular) * 1e12
A = A - mask
A = K.softmax(A)
O_seq = einsum("abij, abjk -> abik", A, V_seq)
O_seq = K.permute_dimensions(O_seq, pattern=(0, 2, 1, 3))
O_seq = K.reshape(O_seq,
shape=(-1, K.shape(O_seq)[1], self.output_dim))
O_seq = self.Mask(O_seq, Q_len, "mul")
return O_seq
def call(self, x):
WQ = K.dot(x, self.kernel[0])
WK = K.dot(x, self.kernel[1])
WV = K.dot(x, self.kernel[2])
# print("WQ.shape",WQ.shape)
# print("K.permute_dimensions(WK, [0, 2, 1]).shape",K.permute_dimensions(WK, [0, 2, 1]).shape)
QK = K.batch_dot(WQ, K.permute_dimensions(WK, [0, 2, 1]))
QK = QK / (64**0.5)
QK = K.softmax(QK)
# print("QK.shape",QK.shape)
V = K.batch_dot(QK, WV)
return V
def gru_with_z_gate(x, weight):
h_tm1, inputs, r, hh = x[0], x[1], x[2], x[3]
weight = K.variable(weight)
units = h_tm1.shape[-1]
kernel_z = weight[:units, :units]
recurrent_kernel_z = weight[units:units * 2, :units]
input_bias_z = weight[units * 2, :units] # Change to 1 dim.
x_z = K.bias_add(K.dot(inputs, kernel_z), input_bias_z)
recurrent_z = K.dot(h_tm1, recurrent_kernel_z)
z_without_activate = x_z + recurrent_z
z = hard_sigmoid(z_without_activate)
h = z * h_tm1 + (1 - z) * hh
#return h
return z
def gru_with_r_gate(x, weight):
h_tm1, inputs, z, x_h, split_recurrent_h = x[0], x[1], x[2], x[3], x[4]
weight = K.variable(weight)
units = h_tm1.shape[-1]
kernel_r = weight[:units, units:units * 2]
recurrent_kernel_r = weight[units:units * 2, units:units * 2]
input_bias_r = weight[units * 2, units:units * 2] # Change to 1 dim.
x_r = K.bias_add(K.dot(inputs, kernel_r), input_bias_r)
recurrent_r = K.dot(h_tm1, recurrent_kernel_r)
r_without_activate = x_r + recurrent_r
r = hard_sigmoid(r_without_activate)
#r = hard_sigmoid(x_r + recurrent_r)
# Recompute recurrent_h by two parts.
r_unsqueeze = K.expand_dims(r, axis=-1)
recompute_recurrent_h = K.sum(r_unsqueeze * split_recurrent_h, axis=1)
hh = tanh(x_h + recompute_recurrent_h)
h = z * h_tm1 + (1 - z) * hh
#return h
return r
def orthonorm_op(x, epsilon=1e-7):
'''
Computes a matrix that orthogonalizes the input matrix x
x: an n x d input matrix
eps: epsilon to prevent nonzero values in the diagonal entries of x
returns: a d x d matrix, ortho_weights, which orthogonalizes x by
right multiplication
'''
x_2 = K.dot(K.transpose(x), x)
x_2 += K.eye(K.int_shape(x)[1]) * epsilon
L = tf.cholesky(x_2)
ortho_weights = tf.transpose(tf.matrix_inverse(L)) * tf.sqrt(
tf.cast(tf.shape(x)[0], dtype=K.floatx()))
return ortho_weights
def get_GRU_components(inputs, states, weight):
units = weight[0].shape[0]
kernel = K.variable(weight[0]) # shape = (input_dim, self.units * 3)
recurrent_kernel = K.variable(
weight[1]) # shape = (self.units, self.units * 3)
bias = K.variable(weight[2]) # bias_shape = (3 * self.units,)
inputs = K.variable(inputs) # Not sure.
h_tm1 = K.variable(states) # Previous memory state.
# Update gate.
kernel_z = kernel[:, :units]
recurrent_kernel_z = recurrent_kernel[:, :units]
input_bias_z = bias[:units]
# Reset gate.
kernel_r = kernel[:, units:units * 2]
recurrent_kernel_r = recurrent_kernel[:, units:units * 2]
input_bias_r = bias[units:units * 2]
# New gate.
kernel_h = kernel[:, units * 2:]
recurrent_kernel_h = recurrent_kernel[:, units * 2:]
input_bias_h = bias[units * 2:]
x_z = K.bias_add(K.dot(inputs, kernel_z), input_bias_z)
x_r = K.bias_add(K.dot(inputs, kernel_r), input_bias_r)
x_h = K.bias_add(K.dot(inputs, kernel_h), input_bias_h)
recurrent_z = K.dot(h_tm1, recurrent_kernel_z)
recurrent_r = K.dot(h_tm1, recurrent_kernel_r)
z = hard_sigmoid(x_z +
recurrent_z) # Recurrent activation = 'hard_sigmoid'.
r = hard_sigmoid(x_r + recurrent_r)
recurrent_h = K.dot(r * h_tm1, recurrent_kernel_h)
# Get split part of recurrent_h.
split_recurrent_h = K.expand_dims(h_tm1, axis=-1) * recurrent_kernel_h
r_unsqueeze = K.expand_dims(r, axis=-1)
recompute_recurrent_h = K.sum(r_unsqueeze * split_recurrent_h, axis=1)
#print(recurrent_h.shape, h_tm1.shape, recurrent_kernel_h.shape, split_recurrent_h.shape)
#print(K.get_value(recompute_recurrent_h)[0, :3], np.mean(K.get_value(recompute_recurrent_h)))
#print(K.get_value(recurrent_h)[0, :3], np.mean(K.get_value(recurrent_h)))
delta = np.mean(
np.abs(K.get_value(recompute_recurrent_h) - K.get_value(recurrent_h)))
print("delta =", delta, np.mean(K.get_value(recompute_recurrent_h)),
np.mean(K.get_value(recurrent_h)))
assert delta < 1e-6, "r gate is wrong."
hh = tanh(x_h + recurrent_h) # Activation = 'tanh'.
# Previous and candidate state mixed by update gate.
h = z * h_tm1 + (1 - z) * hh
return K.get_value(h_tm1), K.get_value(h), K.get_value(z), K.get_value(
r), K.get_value(hh), K.get_value(x_h), K.get_value(split_recurrent_h)
def call(self, input):
f = list()
fn = list()
c_dict = keypoint_connections()
for i in range(21):
f.append(self.conv2(input))
for i in range(21):
c = list()
c.append(f[i])
for j in c_dict[i]:
c.append(f[j])
c = K.concatenate(tuple(c), axis=-1)
h = self.conv2a[i](c)
g = self.conv2b[i](h)
l = K.dot(g, self.W[i])
print(l.shape)
fn.append(
K.sum(K.concatenate((f[i], l), axis=-1),
axis=-1,
keepdims=True))
return K.concatenate(tuple(fn), axis=-1)
def call(self, x, mask=None):
features_dim = self.features_dim
step_dim = self.step_dim
e = K.reshape(
K.dot(K.reshape(x, (-1, features_dim)),
K.reshape(self.W, (features_dim, 1))),
(-1, step_dim)) # e = K.dot(x, self.W)
if self.bias:
e += self.b
e = K.tanh(e)
a = K.exp(e)
# apply mask after the exp. will be re-normalized next
if mask is not None:
# cast the mask to floatX to avoid float64 upcasting in theano
a *= K.cast(mask, K.floatx())
# in some cases especially in the early stages of training the sum may be almost zero
# and this results in NaN's. A workaround is to add a very small positive number ε to the sum.
a /= K.cast(K.sum(a, axis=1, keepdims=True) + K.epsilon(), K.floatx())
a = K.expand_dims(a)
c = K.sum(a * x, axis=1)
return c
def call(self, inputs, states):
prev_output = states[0]
h = K.dot(inputs, self.kernel)
output = h + K.dot(prev_output, self.recurrent_kernel)
return output, [output]
