Autoencoding slow representations for semi-supervised data-efficient regression

The slowness principle is a concept inspired by the visual cortex of the brain. It postu-lates that the underlying generative factors of a quickly varying sensory signal change on a different, slower time scale. By applying this principle to state-of-the-art unsupervised representation learning methods one can learn a latent embedding to perform supervised downstream regression tasks more data efficient. In this paper, we compare different approaches to unsupervised slow representation learning such as Lp norm based slowness regularization and the SlowVAE, and propose a new term based on Brownian motion used in our method, the S-VAE. We empirically evaluate these slowness regularization terms with respect to their downstream task performance and data efficiency in state estimation and behavioral cloning tasks. We find that slow representations show great performance improvements in settings where only sparse labeled training data is available. Furthermore, we present a theoretical and empirical comparison of the discussed slowness regulariza-tion terms. Finally, we discuss how the Frechet Inception Distance (FID), commonly used to determine the generative capabilities of GANs, can predict the performance of trained models in supervised downstream tasks.