How to Understand Masked Autoencoders

"Masked Autoencoders (MAE) Are Scalable Vision Learners" revolutionizes the self-supervised learning method in that it not only achieves the state-of-the-art for image pre-training, but is also a milestone that bridges the gap between visual and linguistic masked autoencoding (BERT-style) pre-trainings. However, to our knowledge, to date there are no theoretical perspectives to explain the powerful expressivity of MAE. In this paper, we, for the first time, propose a unified theoretical framework that provides a mathematical understanding for MAE. Specifically, we explain the patch-based attention approaches of MAE using an integral kernel under a non-overlapping domain decomposition setting. To help the research community to further comprehend the main reasons of the great success of MAE, based on our framework, we pose five questions and answer them with mathematical rigor using insights from operator theory.