def _u_to_v(self, log_alpha, u, eps = 1e-8):
"""Convert u to tied randomness in v."""
u_prime = tf.nn.sigmoid(-log_alpha) # g(u') = 0
v_1 = (u - u_prime) / tf.clip_by_value(1 - u_prime, eps, 1)
v_1 = tf.clip_by_value(v_1, 0, 1)
v_1 = tf.stop_gradient(v_1)
v_1 = v_1*(1 - u_prime) + u_prime
v_0 = u / tf.clip_by_value(u_prime, eps, 1)
v_0 = tf.clip_by_value(v_0, 0, 1)
v_0 = tf.stop_gradient(v_0)
v_0 = v_0 * u_prime
v = tf.where(u > u_prime, v_1, v_0)
v = tf.check_numerics(v, 'v sampling is not numerically stable.')
v = v + tf.stop_gradient(-v + u) # v and u are the same up to numerical errors
return v
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