  Autoencoders represent an effective approach for computing the underlying
factors characterizing datasets of different types. The latent representation
of autoencoders have been studied in the context of enabling interpolation
between data points by decoding convex combinations of latent vectors. This
interpolation, however, often leads to artifacts or produces unrealistic
results during reconstruction. We argue that these incongruities are due to the
structure of the latent space and because such naively interpolated latent
vectors deviate from the data manifold. In this paper, we propose a
regularization technique that shapes the latent representation to follow a
manifold that is consistent with the training images and that drives the
manifold to be smooth and locally convex. This regularization not only enables
faithful interpolation between data points, as we show herein, but can also be
used as a general regularization technique to avoid overfitting or to produce
new samples for data augmentation.
