Saturating sigmoid: 1.2 * sigmoid(x) - 0.1 cut to [0, 1].

def saturating_sigmoid(x):
  """Saturating sigmoid: 1.2 * sigmoid(x) - 0.1 cut to [0, 1]."""
  with tf.name_scope("saturating_sigmoid", values=[x]):
    y = tf.sigmoid(x)
    return tf.minimum(1.0, tf.maximum(0.0, 1.2 * y - 0.1))