# Subspace Capsule Network

arXiv: https://arxiv.org/abs/2002.02924 · HTML: https://mlsanity.com/paper/2002.02924/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [Visual Dependency Transformers: Dependency Tree Emerges from Reversed Attention](https://mlsanity.com/paper/2304.03282/) (2023)
- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [Routing with Self-Attention for Multimodal Capsule Networks](https://mlsanity.com/paper/2112.00775/) (2021)
- [Spatiotemporal Capsule Neural Network for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2303.02880/) (2023)
- [DPR-CAE: Capsule Autoencoder with Dynamic Part Representation for Image Parsing](https://mlsanity.com/paper/2104.14735/) (2021)
- [Capsule Networks Do Not Need to Model Everything](https://mlsanity.com/paper/2204.01298/) (2022)
- [Hybrid Gromov-Wasserstein Embedding for Capsule Learning](https://mlsanity.com/paper/2209.00232/) (2022)
- [Brain tumor grade classification Using LSTM Neural Networks with Domain Pre-Transforms](https://mlsanity.com/paper/2106.10889/) (2021)
- [A Model-Agnostic Framework for Recommendation via Interest-aware Item Embeddings](https://mlsanity.com/paper/2308.09202/) (2023)

## Abstract (arXiv)

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.