Capsule Pooling refers to the process of aggregating the outputs of capsules in a capsule network to produce a reduced but meaningful representation that takes into account both pose and activation information.
Formally, capsule pooling can be described as a function \( P: \{ \mathbf{v}_i \}_{i=1}^n \rightarrow \mathbf{v}_p \), where \( \mathbf{v}_i \in \mathbb{R}^d \) is the vector output of the i-th capsule and \( \mathbf{v}_p \) is the pooled capsule representation.
The aggregation can be done through weighted sums, e.g.:
\[ \mathbf{v}_p = \sum_{i=1}^n w_i \mathbf{v}_i, \quad ext{with} \quad w_i = rac{\exp(a_i)}{\sum_{j=1}^n \exp(a_j)} \]
where \( a_i \) are activation values or routing coefficients.
Capsule pooling differs from classical pooling methods by preserving pose information and considering the capsule structure, leading to improved model interpretability and performance.
Definition:
“Capsule pooling is an aggregation method in capsule networks that combines capsule outputs while preserving their pose and activation information to effectively represent spatial and hierarchical features.”
Source:
Hinton, G. E., Krizhevsky, A., & Wang, S. D. (2018). Matrix Capsules with EM Routing. Proceedings of the International Conference on Learning Representations (ICLR).