# Neural Network Encapsulation

arXiv: https://arxiv.org/abs/1808.03749 · HTML: https://mlsanity.com/paper/1808.03749/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2018.

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

- [Found a Reason for me? Weakly-supervised Grounded Visual Question Answering using Capsules](https://mlsanity.com/paper/2105.04836/) (2021)
- [Spiking CapsNet: A Spiking Neural Network With A Biologically Plausible Routing Rule Between Capsules](https://mlsanity.com/paper/2111.07785/) (2021)
- [PICASO: Permutation-Invariant Cascaded Attentional Set Operator](https://mlsanity.com/paper/2107.08305/) (2021)
- [Capsule Networks Do Not Need to Model Everything](https://mlsanity.com/paper/2204.01298/) (2022)
- [β-CapsNet: Learning Disentangled Representation for CapsNet by Information Bottleneck](https://mlsanity.com/paper/2209.05239/) (2022)
- [RobCaps: Evaluating the Robustness of Capsule Networks against Affine Transformations and Adversarial Attacks](https://mlsanity.com/paper/2304.03973/) (2023)
- [How to Accelerate Capsule Convolutions in Capsule Networks](https://mlsanity.com/paper/2104.02621/) (2021)
- [Capsule networks with non-iterative cluster routing](https://mlsanity.com/paper/2109.09213/) (2021)
- [Capsule network with shortcut routing](https://mlsanity.com/paper/2307.10212/) (2023)

## Abstract (arXiv)

A capsule is a collection of neurons which represents different variants of a pattern in the network. The routing scheme ensures only certain capsules which resemble lower counterparts in the higher layer should be activated. However, the computational complexity becomes a bottleneck for scaling up to larger networks, as lower capsules need to correspond to each and every higher capsule. To resolve this limitation, we approximate the routing process with two branches: a master branch which collects primary information from its direct contact in the lower layer and an aide branch that replenishes master based on pattern variants encoded in other lower capsules. Compared with previous iterative and unsupervised routing scheme, these two branches are communicated in a fast, supervised and one-time pass fashion. The complexity and runtime of the model are therefore decreased by a large margin. Motivated by the routing to make higher capsule have agreement with lower capsule, we extend the mechanism as a compensation for the rapid loss of information in nearby layers. We devise a feedback agreement unit to send back higher capsules as feedback. It could be regarded as an additional regularization to the network. The feedback agreement is achieved by comparing the optimal transport divergence between two distributions (lower and higher capsules). Such an add-on witnesses a unanimous gain in both capsule and vanilla networks. Our proposed EncapNet performs favorably better against previous state-of-the-arts on CIFAR10/100, SVHN and a subset of ImageNet.