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MARGIN = 4
c_m_n = lambda m, n: math.factorial(n) / math.factorial(m) / math.factorial(n-m)
c_map = []
for i in range(MARGIN+1):
c_map.append(c_m_n(i, MARGIN))
def find_k_multi(cos_t):
cos_t = tf.cast(cos_t, dtype = tf.float64)
i = tf.constant(0, dtype = tf.float64)
def l_cond(i):
tf_pi = tf.constant(math.pi ,tf.float64)
left_range = tf.cast(tf.cos(tf_pi*(i+1)/MARGIN), dtype = tf.float64)
right_range = tf.cast(tf.cos(tf_pi*i/MARGIN), dtype = tf.float64)
logic = tf.logical_or(tf.greater(cos_t, right_range), tf.less(cos_t, left_range))
return logic
def l_body(i):
return tf.add(i, 1)
k = tf.while_loop(l_cond, l_body, [i])
k = tf.cast(k, dtype = tf.int32)
return k, k
def L_softmax(feature, labels, softmax_w, softmax_b , batch_size, labmda = 100):
f_feature = []
l_softmax_loss = []
c_v = []
o_v = []
for sample_index in range(batch_size):
sample_feature = tf.slice(feature, [sample_index, 0], [1, 512])
label = tf.squeeze(tf.slice(labels, [sample_index],[1]))
label = tf.cast(label, tf.int32)
w_label = tf.slice(softmax_w, [0, label], [512, 1])
b_label = tf.squeeze(tf.slice(softmax_b, [label], [1]))
wx = tf.squeeze(tf.matmul(sample_feature, w_label))
w_label_mod = tf.sqrt(2 * tf.nn.l2_loss(w_label))
b_label_mod = tf.sqrt(2 * tf.nn.l2_loss(tf.squeeze(b_label)))
sample_feature_mod = tf.sqrt(2 * tf.nn.l2_loss(tf.squeeze(sample_feature)))
cos_theta = wx/(w_label_mod * sample_feature_mod)
sin_theta_t = 1 - cos_theta * cos_theta
cos_m_theta = 0
flag = -1
for loop in range(int(MARGIN/2) + 1):
flag *= -1
cos_m_theta += flag * c_map[2 * loop] * tf.pow(cos_theta, MARGIN - 2 *loop) * tf.pow(sin_theta_t, loop)
k, log = find_k_multi(cos_theta)
phi_theta = tf.to_float(tf.pow(tf.constant(-1), k)) * cos_m_theta - 2 * tf.to_float(k)
label_value = (labmda * (w_label_mod * sample_feature_mod * cos_theta + b_label_mod) + \
(w_label_mod * sample_feature_mod * phi_theta + b_label_mod))/(1.0 + labmda)
other_value = tf.squeeze(tf.matmul(sample_feature, softmax_w) + softmax_b)
old_value = tf.slice(other_value, [label], [1])
to_substract_1 = tf.sparse_to_dense(label, other_value.get_shape(), old_value, default_value=0.)
to_substract_2 = tf.sparse_to_dense(label, other_value.get_shape(), label_value, default_value=0.)
l_feature = other_value - to_substract_1 + to_substract_2
f_feature.append(l_feature)
c_v.append(cos_theta)
o_v.append(k)
out_value = [c_v, o_v]
all_batch_feature = tf.stack(f_feature)
return all_batch_feature, out_value
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