Matrix capsules with EM routing
Abstract
A capsule is a group of neurons whose outputs represent different properties of the same entity. We describe a version of capsules in which each capsule has a logistic unit to represent the presence of an entity and a 4x4 pose matrix which could learn to represent the relationship between that entity and the viewer. A capsule in one layer votes for the pose matrices of many different capsules in the layer above by multiplying its own pose matrix by viewpoint-invariant transformation matrices that could learn to represent part-whole relationships. Each of these votes is weighted by an assignment coefficient. These coefficients are iteratively updated using the EM algorithm such that the output of each capsule is routed to a capsule in the layer above that receives a cluster of similar votes. The whole system is trained discriminatively by unrolling 3 iterations of EM between each pair of adjacent layers. On the smallNORB benchmark, capsules reduce the number of test errors by 45\% compared to the state-of-the-art. Capsules also show far more resistant to white box adversarial attack than our baseline convolutional neural network.
TL;DR
Capsule networks with learned pose matrices and EM routing improves state of the art classification on smallNORB, improves generalizability to new view points, and white box adversarial robustness.
Documentation
- Matrix capsules with EM routing
- https://openreview.net/forum?id=HJWLfGWRb
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99b7cb0c78706ad8e91c13a2242bb15b7de325ad.pdf