Capsule Network Routing is a mechanism in capsule networks that controls the weighted forwarding of capsule outputs to the capsules of the next layer to enable hierarchical feature aggregation.
Formally, dynamic routing describes an iterative optimization of the routing coefficients \( c_{ij} \), which determine how strongly the output of capsule \( i \) is passed on to capsule \( j \).
The routing coefficients are iteratively adjusted based on the agreement between the prediction \( \hat{\mathbf{u}}_{j|i} = \mathbf{W}_{ij} \mathbf{u}_i \) and the output \( \mathbf{v}_j \) of the target capsule, typically using a softmax over the \( c_{ij} \) and a nonlinear squashing function for normalization.
This procedure enables hierarchical pooling of pose and activation information from parts to objects and is crucial for the ability of capsule networks to better capture spatial relationships than classical neural networks.
Definition:
“Capsule Network Routing is an iterative mechanism for weighted forwarding of capsule outputs between layers that enables hierarchical aggregation of neural features by adjusting the routing coefficients.”
Source:
Sabour, S., Frosst, N., & Hinton, G. E. (2017). Dynamic Routing Between Capsules. Advances in Neural Information Processing Systems (NeurIPS).