  This paper demonstrates that a simple modification of the variational
autoencoder (VAE) formalism enables the method to identify and classify rotated
and distorted digits. In particular, the conventional objective (cost) function
employed during the training process of a VAE both quantifies the agreement
between the input and output data records and ensures that the latent space
representation of the input data record is statistically generated with an
appropriate mean and standard deviation. After training, simulated data
realizations are generated by decoding appropriate latent space points. Since,
however, standard VAE:s trained on randomly rotated MNIST digits cannot
reliably distinguish between different digit classes since the rotated input
data is effectively compared to a similarly rotated output data record. In
contrast, an alternative implementation in which the objective function
compares the output associated with each rotated digit to a corresponding fixed
unreferenced reference digit is shown here to discriminate accurately among the
rotated digits in latent space even when the dimension of the latent space is 2
or 3.
