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Convolutional neural networks (CNNs) have become a key asset to most of fields in AI. Despite their successful performance, CNNs suffer from a major drawback. They fail to capture the hierarchy of spatial relation among different parts of an entity. As a remedy to this problem, the idea of capsules was proposed by Hinton. In this paper, we propose the SubSpace Capsule Network (SCN) that exploits the idea of capsule networks to model possible variations in the appearance or implicitly-defined properties of an entity through a group of capsule subspaces instead of simply grouping neurons to create capsules. A capsule is created by projecting an input feature vector from a lower layer onto the capsule subspace using a learnable transformation. This transformation finds the degree of alignment of the input with the properties modeled by the capsule subspace.We show that SCN is a general capsule network that can successfully be applied to both discriminative and generative models without incurring computational overhead compared to CNN during test time. Effectiveness of SCN is evaluated through a comprehensive set of experiments on supervised image classification, semi-supervised image classification and high-resolution image generation tasks using the generative adversarial network (GAN) framework. SCN significantly improves the performance of the baseline models in all 3 tasks. 

The classic Generative Adversarial Net (GAN) and its variants can be roughly categorized into two large families: the unregularized versus regularized GANs. By relaxing the non-parametric assumption on the discriminator in the classic GAN, the regularized GANs have better generalization ability to produce new samples drawn from the real distribution. Although the regularized GANs have shown compelling performances, there still exist some unaddressed problems. It is well known that the real data like natural images are not uniformly distributed over the whole data space. Instead, they are often restricted to a low-dimensional manifold of the ambient space. Such a manifold assumption suggests the distance over the manifold should be a better measure to characterize the distinct between real and fake samples. Thus, we define a pullback operator to map samples back to their data manifold, and a manifold margin is defined as the distance between the pullback representations to distinguish between real and fake samples and learn the optimal generators. We justify the proposed model from both theoretical and empirical perspectives, demonstrating it can produce high quality images as compared with the other state-of-the-art GAN models.