Title: Graphics Capsule: Learning hierarchical 3D representations from 2D images and its application on human faces. Abstract: The function of constructing the hierarchy of objects is important to the visual process of the human brain. Previous studies have successfully adopted capsule networks to decompose the digits and faces into parts in an unsupervised manner to investigate the similar perception mechanism of neural networks. However, their descriptions are restricted to the 2D space, limiting their capacities to imitate the intrinsic 3D perception ability of humans. In this paper, we propose an Inverse Graphics Capsule Network (IGC-Net) to learn the hierarchical 3D representations from large-scale unlabeled images. The core of IGC-Net is a new type of capsule, named graphics capsule, which represents 3D primitives with interpretable parameters in computer graphics (CG), including depth, albedo, and 3D pose. Specifically, IGC-Net first decomposes the objects into a set of semantic-consistent parts and then assembles them to the object-level descriptions to build the hierarchy. The learned graphics capsules reveal how the neural networks, oriented at visual perception, understand objects as a hierarchy of 3D models. Besides, the discovered parts can be deployed to the unsupervised face segmentation task to evaluate the semantic consistency of our method. Moreover, the part-level descriptions with explicit physical meanings give an insight into the face analysis that originally runs in a black box, such as the importance of shape and texture for face recognition. Experiments on CelebA, BP4D, and Multi-PIE validate the effectiveness of our method.