  Modern learning frameworks often train deep neural networks with massive
amounts of unlabeled data to learn representations by solving simple pretext
tasks, then use the representations as foundations for downstream tasks. These
networks are empirically designed; as such, they are usually not interpretable,
their representations are not structured, and their designs are potentially
redundant. White-box deep networks, in which each layer explicitly identifies
and transforms structures in the data, present a promising alternative.
However, existing white-box architectures have only been shown to work at scale
in supervised settings with labeled data, such as classification. In this work,
we provide the first instantiation of the white-box design paradigm that can be
applied to large-scale unsupervised representation learning. We do this by
exploiting a fundamental connection between diffusion, compression, and
(masked) completion, deriving a deep transformer-like masked autoencoder
architecture, called CRATE-MAE, in which the role of each layer is
mathematically fully interpretable: they transform the data distribution to and
from a structured representation. Extensive empirical evaluations confirm our
analytical insights. CRATE-MAE demonstrates highly promising performance on
large-scale imagery datasets while using only ~30% of the parameters compared
to the standard masked autoencoder with the same model configuration. The
representations learned by CRATE-MAE have explicit structure and also contain
semantic meaning. Code is available at https://github.com/Ma-Lab-Berkeley/CRATE .
