2nd edition Chapter 12, VAE latent space sampler differences with 1st edition

[ghylander]

In the 2nd edition notebook of chapter 12 part 4, the latent space sampling layer is defined as the following class:

class Sampler(layers.Layer):
    def call(self, z_mean, z_log_var):
        batch_size = tf.shape(z_mean)[0]
        z_size = tf.shape(z_mean)[1]
        epsilon = tf.random.normal(shape=(batch_size, z_size))
        return z_mean + tf.exp(0.5 * z_log_var) * epsilon

In the 1st edition, it's defined as the following fucntion:

def sampling(args):
    z_mean, z_log_var = args
    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], 2),
                                          mean=0., stddev=1.)
    return z_mean + K.exp(z_log_var) * epsilon

Most changes come from following best practices and API changes, but I do have the folowing doubt: Why is z_log_var multiplied by 0.5 in the 2nd edition class? Is it because a difference between tf.exp() and tf.keras.backend.exp()? Is it becasue reducing it by half yields better results? Any other reason?